1// SPDX-License-Identifier: GPL-2.0+
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  linux/lib/rbtree.c
9*/
10
11#include <linux/rbtree_augmented.h>
12#ifndef __UBOOT__
13#include <linux/export.h>
14#else
15#include <ubi_uboot.h>
16#endif
17/*
18 * red-black trees properties:  http://en.wikipedia.org/wiki/Rbtree
19 *
20 *  1) A node is either red or black
21 *  2) The root is black
22 *  3) All leaves (NULL) are black
23 *  4) Both children of every red node are black
24 *  5) Every simple path from root to leaves contains the same number
25 *     of black nodes.
26 *
27 *  4 and 5 give the O(log n) guarantee, since 4 implies you cannot have two
28 *  consecutive red nodes in a path and every red node is therefore followed by
29 *  a black. So if B is the number of black nodes on every simple path (as per
30 *  5), then the longest possible path due to 4 is 2B.
31 *
32 *  We shall indicate color with case, where black nodes are uppercase and red
33 *  nodes will be lowercase. Unknown color nodes shall be drawn as red within
34 *  parentheses and have some accompanying text comment.
35 */
36
37static inline void rb_set_black(struct rb_node *rb)
38{
39	rb->__rb_parent_color |= RB_BLACK;
40}
41
42static inline struct rb_node *rb_red_parent(struct rb_node *red)
43{
44	return (struct rb_node *)red->__rb_parent_color;
45}
46
47/*
48 * Helper function for rotations:
49 * - old's parent and color get assigned to new
50 * - old gets assigned new as a parent and 'color' as a color.
51 */
52static inline void
53__rb_rotate_set_parents(struct rb_node *old, struct rb_node *new,
54			struct rb_root *root, int color)
55{
56	struct rb_node *parent = rb_parent(old);
57	new->__rb_parent_color = old->__rb_parent_color;
58	rb_set_parent_color(old, new, color);
59	__rb_change_child(old, new, parent, root);
60}
61
62static __always_inline void
63__rb_insert(struct rb_node *node, struct rb_root *root,
64	    void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
65{
66	struct rb_node *parent = rb_red_parent(node), *gparent, *tmp;
67
68	while (true) {
69		/*
70		 * Loop invariant: node is red
71		 *
72		 * If there is a black parent, we are done.
73		 * Otherwise, take some corrective action as we don't
74		 * want a red root or two consecutive red nodes.
75		 */
76		if (!parent) {
77			rb_set_parent_color(node, NULL, RB_BLACK);
78			break;
79		} else if (rb_is_black(parent))
80			break;
81
82		gparent = rb_red_parent(parent);
83
84		tmp = gparent->rb_right;
85		if (parent != tmp) {	/* parent == gparent->rb_left */
86			if (tmp && rb_is_red(tmp)) {
87				/*
88				 * Case 1 - color flips
89				 *
90				 *       G            g
91				 *      / \          / \
92				 *     p   u  -->   P   U
93				 *    /            /
94				 *   n            N
95				 *
96				 * However, since g's parent might be red, and
97				 * 4) does not allow this, we need to recurse
98				 * at g.
99				 */
100				rb_set_parent_color(tmp, gparent, RB_BLACK);
101				rb_set_parent_color(parent, gparent, RB_BLACK);
102				node = gparent;
103				parent = rb_parent(node);
104				rb_set_parent_color(node, parent, RB_RED);
105				continue;
106			}
107
108			tmp = parent->rb_right;
109			if (node == tmp) {
110				/*
111				 * Case 2 - left rotate at parent
112				 *
113				 *      G             G
114				 *     / \           / \
115				 *    p   U  -->    n   U
116				 *     \           /
117				 *      n         p
118				 *
119				 * This still leaves us in violation of 4), the
120				 * continuation into Case 3 will fix that.
121				 */
122				parent->rb_right = tmp = node->rb_left;
123				node->rb_left = parent;
124				if (tmp)
125					rb_set_parent_color(tmp, parent,
126							    RB_BLACK);
127				rb_set_parent_color(parent, node, RB_RED);
128				augment_rotate(parent, node);
129				parent = node;
130				tmp = node->rb_right;
131			}
132
133			/*
134			 * Case 3 - right rotate at gparent
135			 *
136			 *        G           P
137			 *       / \         / \
138			 *      p   U  -->  n   g
139			 *     /                 \
140			 *    n                   U
141			 */
142			gparent->rb_left = tmp;  /* == parent->rb_right */
143			parent->rb_right = gparent;
144			if (tmp)
145				rb_set_parent_color(tmp, gparent, RB_BLACK);
146			__rb_rotate_set_parents(gparent, parent, root, RB_RED);
147			augment_rotate(gparent, parent);
148			break;
149		} else {
150			tmp = gparent->rb_left;
151			if (tmp && rb_is_red(tmp)) {
152				/* Case 1 - color flips */
153				rb_set_parent_color(tmp, gparent, RB_BLACK);
154				rb_set_parent_color(parent, gparent, RB_BLACK);
155				node = gparent;
156				parent = rb_parent(node);
157				rb_set_parent_color(node, parent, RB_RED);
158				continue;
159			}
160
161			tmp = parent->rb_left;
162			if (node == tmp) {
163				/* Case 2 - right rotate at parent */
164				parent->rb_left = tmp = node->rb_right;
165				node->rb_right = parent;
166				if (tmp)
167					rb_set_parent_color(tmp, parent,
168							    RB_BLACK);
169				rb_set_parent_color(parent, node, RB_RED);
170				augment_rotate(parent, node);
171				parent = node;
172				tmp = node->rb_left;
173			}
174
175			/* Case 3 - left rotate at gparent */
176			gparent->rb_right = tmp;  /* == parent->rb_left */
177			parent->rb_left = gparent;
178			if (tmp)
179				rb_set_parent_color(tmp, gparent, RB_BLACK);
180			__rb_rotate_set_parents(gparent, parent, root, RB_RED);
181			augment_rotate(gparent, parent);
182			break;
183		}
184	}
185}
186
187/*
188 * Inline version for rb_erase() use - we want to be able to inline
189 * and eliminate the dummy_rotate callback there
190 */
191static __always_inline void
192____rb_erase_color(struct rb_node *parent, struct rb_root *root,
193	void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
194{
195	struct rb_node *node = NULL, *sibling, *tmp1, *tmp2;
196
197	while (true) {
198		/*
199		 * Loop invariants:
200		 * - node is black (or NULL on first iteration)
201		 * - node is not the root (parent is not NULL)
202		 * - All leaf paths going through parent and node have a
203		 *   black node count that is 1 lower than other leaf paths.
204		 */
205		sibling = parent->rb_right;
206		if (node != sibling) {	/* node == parent->rb_left */
207			if (rb_is_red(sibling)) {
208				/*
209				 * Case 1 - left rotate at parent
210				 *
211				 *     P               S
212				 *    / \             / \
213				 *   N   s    -->    p   Sr
214				 *      / \         / \
215				 *     Sl  Sr      N   Sl
216				 */
217				parent->rb_right = tmp1 = sibling->rb_left;
218				sibling->rb_left = parent;
219				rb_set_parent_color(tmp1, parent, RB_BLACK);
220				__rb_rotate_set_parents(parent, sibling, root,
221							RB_RED);
222				augment_rotate(parent, sibling);
223				sibling = tmp1;
224			}
225			tmp1 = sibling->rb_right;
226			if (!tmp1 || rb_is_black(tmp1)) {
227				tmp2 = sibling->rb_left;
228				if (!tmp2 || rb_is_black(tmp2)) {
229					/*
230					 * Case 2 - sibling color flip
231					 * (p could be either color here)
232					 *
233					 *    (p)           (p)
234					 *    / \           / \
235					 *   N   S    -->  N   s
236					 *      / \           / \
237					 *     Sl  Sr        Sl  Sr
238					 *
239					 * This leaves us violating 5) which
240					 * can be fixed by flipping p to black
241					 * if it was red, or by recursing at p.
242					 * p is red when coming from Case 1.
243					 */
244					rb_set_parent_color(sibling, parent,
245							    RB_RED);
246					if (rb_is_red(parent))
247						rb_set_black(parent);
248					else {
249						node = parent;
250						parent = rb_parent(node);
251						if (parent)
252							continue;
253					}
254					break;
255				}
256				/*
257				 * Case 3 - right rotate at sibling
258				 * (p could be either color here)
259				 *
260				 *   (p)           (p)
261				 *   / \           / \
262				 *  N   S    -->  N   Sl
263				 *     / \             \
264				 *    sl  Sr            s
265				 *                       \
266				 *                        Sr
267				 */
268				sibling->rb_left = tmp1 = tmp2->rb_right;
269				tmp2->rb_right = sibling;
270				parent->rb_right = tmp2;
271				if (tmp1)
272					rb_set_parent_color(tmp1, sibling,
273							    RB_BLACK);
274				augment_rotate(sibling, tmp2);
275				tmp1 = sibling;
276				sibling = tmp2;
277			}
278			/*
279			 * Case 4 - left rotate at parent + color flips
280			 * (p and sl could be either color here.
281			 *  After rotation, p becomes black, s acquires
282			 *  p's color, and sl keeps its color)
283			 *
284			 *      (p)             (s)
285			 *      / \             / \
286			 *     N   S     -->   P   Sr
287			 *        / \         / \
288			 *      (sl) sr      N  (sl)
289			 */
290			parent->rb_right = tmp2 = sibling->rb_left;
291			sibling->rb_left = parent;
292			rb_set_parent_color(tmp1, sibling, RB_BLACK);
293			if (tmp2)
294				rb_set_parent(tmp2, parent);
295			__rb_rotate_set_parents(parent, sibling, root,
296						RB_BLACK);
297			augment_rotate(parent, sibling);
298			break;
299		} else {
300			sibling = parent->rb_left;
301			if (rb_is_red(sibling)) {
302				/* Case 1 - right rotate at parent */
303				parent->rb_left = tmp1 = sibling->rb_right;
304				sibling->rb_right = parent;
305				rb_set_parent_color(tmp1, parent, RB_BLACK);
306				__rb_rotate_set_parents(parent, sibling, root,
307							RB_RED);
308				augment_rotate(parent, sibling);
309				sibling = tmp1;
310			}
311			tmp1 = sibling->rb_left;
312			if (!tmp1 || rb_is_black(tmp1)) {
313				tmp2 = sibling->rb_right;
314				if (!tmp2 || rb_is_black(tmp2)) {
315					/* Case 2 - sibling color flip */
316					rb_set_parent_color(sibling, parent,
317							    RB_RED);
318					if (rb_is_red(parent))
319						rb_set_black(parent);
320					else {
321						node = parent;
322						parent = rb_parent(node);
323						if (parent)
324							continue;
325					}
326					break;
327				}
328				/* Case 3 - right rotate at sibling */
329				sibling->rb_right = tmp1 = tmp2->rb_left;
330				tmp2->rb_left = sibling;
331				parent->rb_left = tmp2;
332				if (tmp1)
333					rb_set_parent_color(tmp1, sibling,
334							    RB_BLACK);
335				augment_rotate(sibling, tmp2);
336				tmp1 = sibling;
337				sibling = tmp2;
338			}
339			/* Case 4 - left rotate at parent + color flips */
340			parent->rb_left = tmp2 = sibling->rb_right;
341			sibling->rb_right = parent;
342			rb_set_parent_color(tmp1, sibling, RB_BLACK);
343			if (tmp2)
344				rb_set_parent(tmp2, parent);
345			__rb_rotate_set_parents(parent, sibling, root,
346						RB_BLACK);
347			augment_rotate(parent, sibling);
348			break;
349		}
350	}
351}
352
353/* Non-inline version for rb_erase_augmented() use */
354void __rb_erase_color(struct rb_node *parent, struct rb_root *root,
355	void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
356{
357	____rb_erase_color(parent, root, augment_rotate);
358}
359EXPORT_SYMBOL(__rb_erase_color);
360
361/*
362 * Non-augmented rbtree manipulation functions.
363 *
364 * We use dummy augmented callbacks here, and have the compiler optimize them
365 * out of the rb_insert_color() and rb_erase() function definitions.
366 */
367
368static inline void dummy_propagate(struct rb_node *node, struct rb_node *stop) {}
369static inline void dummy_copy(struct rb_node *old, struct rb_node *new) {}
370static inline void dummy_rotate(struct rb_node *old, struct rb_node *new) {}
371
372static const struct rb_augment_callbacks dummy_callbacks = {
373	dummy_propagate, dummy_copy, dummy_rotate
374};
375
376void rb_insert_color(struct rb_node *node, struct rb_root *root)
377{
378	__rb_insert(node, root, dummy_rotate);
379}
380EXPORT_SYMBOL(rb_insert_color);
381
382void rb_erase(struct rb_node *node, struct rb_root *root)
383{
384	struct rb_node *rebalance;
385	rebalance = __rb_erase_augmented(node, root, &dummy_callbacks);
386	if (rebalance)
387		____rb_erase_color(rebalance, root, dummy_rotate);
388}
389EXPORT_SYMBOL(rb_erase);
390
391/*
392 * Augmented rbtree manipulation functions.
393 *
394 * This instantiates the same __always_inline functions as in the non-augmented
395 * case, but this time with user-defined callbacks.
396 */
397
398void __rb_insert_augmented(struct rb_node *node, struct rb_root *root,
399	void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
400{
401	__rb_insert(node, root, augment_rotate);
402}
403EXPORT_SYMBOL(__rb_insert_augmented);
404
405/*
406 * This function returns the first node (in sort order) of the tree.
407 */
408struct rb_node *rb_first(const struct rb_root *root)
409{
410	struct rb_node	*n;
411
412	n = root->rb_node;
413	if (!n)
414		return NULL;
415	while (n->rb_left)
416		n = n->rb_left;
417	return n;
418}
419EXPORT_SYMBOL(rb_first);
420
421struct rb_node *rb_last(const struct rb_root *root)
422{
423	struct rb_node	*n;
424
425	n = root->rb_node;
426	if (!n)
427		return NULL;
428	while (n->rb_right)
429		n = n->rb_right;
430	return n;
431}
432EXPORT_SYMBOL(rb_last);
433
434struct rb_node *rb_next(const struct rb_node *node)
435{
436	struct rb_node *parent;
437
438	if (RB_EMPTY_NODE(node))
439		return NULL;
440
441	/*
442	 * If we have a right-hand child, go down and then left as far
443	 * as we can.
444	 */
445	if (node->rb_right) {
446		node = node->rb_right;
447		while (node->rb_left)
448			node=node->rb_left;
449		return (struct rb_node *)node;
450	}
451
452	/*
453	 * No right-hand children. Everything down and left is smaller than us,
454	 * so any 'next' node must be in the general direction of our parent.
455	 * Go up the tree; any time the ancestor is a right-hand child of its
456	 * parent, keep going up. First time it's a left-hand child of its
457	 * parent, said parent is our 'next' node.
458	 */
459	while ((parent = rb_parent(node)) && node == parent->rb_right)
460		node = parent;
461
462	return parent;
463}
464EXPORT_SYMBOL(rb_next);
465
466struct rb_node *rb_prev(const struct rb_node *node)
467{
468	struct rb_node *parent;
469
470	if (RB_EMPTY_NODE(node))
471		return NULL;
472
473	/*
474	 * If we have a left-hand child, go down and then right as far
475	 * as we can.
476	 */
477	if (node->rb_left) {
478		node = node->rb_left;
479		while (node->rb_right)
480			node=node->rb_right;
481		return (struct rb_node *)node;
482	}
483
484	/*
485	 * No left-hand children. Go up till we find an ancestor which
486	 * is a right-hand child of its parent.
487	 */
488	while ((parent = rb_parent(node)) && node == parent->rb_left)
489		node = parent;
490
491	return parent;
492}
493EXPORT_SYMBOL(rb_prev);
494
495void rb_replace_node(struct rb_node *victim, struct rb_node *new,
496		     struct rb_root *root)
497{
498	struct rb_node *parent = rb_parent(victim);
499
500	/* Set the surrounding nodes to point to the replacement */
501	__rb_change_child(victim, new, parent, root);
502	if (victim->rb_left)
503		rb_set_parent(victim->rb_left, new);
504	if (victim->rb_right)
505		rb_set_parent(victim->rb_right, new);
506
507	/* Copy the pointers/colour from the victim to the replacement */
508	*new = *victim;
509}
510EXPORT_SYMBOL(rb_replace_node);
511
512static struct rb_node *rb_left_deepest_node(const struct rb_node *node)
513{
514	for (;;) {
515		if (node->rb_left)
516			node = node->rb_left;
517		else if (node->rb_right)
518			node = node->rb_right;
519		else
520			return (struct rb_node *)node;
521	}
522}
523
524struct rb_node *rb_next_postorder(const struct rb_node *node)
525{
526	const struct rb_node *parent;
527	if (!node)
528		return NULL;
529	parent = rb_parent(node);
530
531	/* If we're sitting on node, we've already seen our children */
532	if (parent && node == parent->rb_left && parent->rb_right) {
533		/* If we are the parent's left node, go to the parent's right
534		 * node then all the way down to the left */
535		return rb_left_deepest_node(parent->rb_right);
536	} else
537		/* Otherwise we are the parent's right node, and the parent
538		 * should be next */
539		return (struct rb_node *)parent;
540}
541EXPORT_SYMBOL(rb_next_postorder);
542
543struct rb_node *rb_first_postorder(const struct rb_root *root)
544{
545	if (!root->rb_node)
546		return NULL;
547
548	return rb_left_deepest_node(root->rb_node);
549}
550EXPORT_SYMBOL(rb_first_postorder);
551