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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  
  6  This program is free software; you can redistribute it and/or modify
  7  it under the terms of the GNU General Public License as published by
  8  the Free Software Foundation; either version 2 of the License, or
  9  (at your option) any later version.
 10
 11  This program is distributed in the hope that it will be useful,
 12  but WITHOUT ANY WARRANTY; without even the implied warranty of
 13  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 14  GNU General Public License for more details.
 15
 16  You should have received a copy of the GNU General Public License
 17  along with this program; if not, write to the Free Software
 18  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 19
 20  linux/lib/rbtree.c
 21*/
 22
 23#include <linux/rbtree.h>
 24#include <linux/export.h>
 25
 26static void __rb_rotate_left(struct rb_node *node, struct rb_root *root)
 27{
 28	struct rb_node *right = node->rb_right;
 29	struct rb_node *parent = rb_parent(node);
 30
 31	if ((node->rb_right = right->rb_left))
 32		rb_set_parent(right->rb_left, node);
 33	right->rb_left = node;
 34
 35	rb_set_parent(right, parent);
 36
 37	if (parent)
 38	{
 39		if (node == parent->rb_left)
 40			parent->rb_left = right;
 41		else
 42			parent->rb_right = right;
 43	}
 44	else
 45		root->rb_node = right;
 46	rb_set_parent(node, right);
 47}
 48
 49static void __rb_rotate_right(struct rb_node *node, struct rb_root *root)
 50{
 51	struct rb_node *left = node->rb_left;
 52	struct rb_node *parent = rb_parent(node);
 53
 54	if ((node->rb_left = left->rb_right))
 55		rb_set_parent(left->rb_right, node);
 56	left->rb_right = node;
 57
 58	rb_set_parent(left, parent);
 59
 60	if (parent)
 61	{
 62		if (node == parent->rb_right)
 63			parent->rb_right = left;
 64		else
 65			parent->rb_left = left;
 66	}
 67	else
 68		root->rb_node = left;
 69	rb_set_parent(node, left);
 70}
 71
 72void rb_insert_color(struct rb_node *node, struct rb_root *root)
 73{
 74	struct rb_node *parent, *gparent;
 75
 76	while ((parent = rb_parent(node)) && rb_is_red(parent))
 77	{
 78		gparent = rb_parent(parent);
 79
 80		if (parent == gparent->rb_left)
 81		{
 82			{
 83				register struct rb_node *uncle = gparent->rb_right;
 84				if (uncle && rb_is_red(uncle))
 85				{
 86					rb_set_black(uncle);
 87					rb_set_black(parent);
 88					rb_set_red(gparent);
 89					node = gparent;
 90					continue;
 91				}
 92			}
 93
 94			if (parent->rb_right == node)
 95			{
 96				register struct rb_node *tmp;
 97				__rb_rotate_left(parent, root);
 98				tmp = parent;
 99				parent = node;
100				node = tmp;
101			}
102
103			rb_set_black(parent);
104			rb_set_red(gparent);
105			__rb_rotate_right(gparent, root);
106		} else {
107			{
108				register struct rb_node *uncle = gparent->rb_left;
109				if (uncle && rb_is_red(uncle))
110				{
111					rb_set_black(uncle);
112					rb_set_black(parent);
113					rb_set_red(gparent);
114					node = gparent;
115					continue;
116				}
117			}
118
119			if (parent->rb_left == node)
120			{
121				register struct rb_node *tmp;
122				__rb_rotate_right(parent, root);
123				tmp = parent;
124				parent = node;
125				node = tmp;
126			}
127
128			rb_set_black(parent);
129			rb_set_red(gparent);
130			__rb_rotate_left(gparent, root);
131		}
132	}
133
134	rb_set_black(root->rb_node);
135}
136EXPORT_SYMBOL(rb_insert_color);
137
138static void __rb_erase_color(struct rb_node *node, struct rb_node *parent,
139			     struct rb_root *root)
140{
141	struct rb_node *other;
142
143	while ((!node || rb_is_black(node)) && node != root->rb_node)
144	{
145		if (parent->rb_left == node)
146		{
147			other = parent->rb_right;
148			if (rb_is_red(other))
149			{
150				rb_set_black(other);
151				rb_set_red(parent);
152				__rb_rotate_left(parent, root);
153				other = parent->rb_right;
154			}
155			if ((!other->rb_left || rb_is_black(other->rb_left)) &&
156			    (!other->rb_right || rb_is_black(other->rb_right)))
157			{
158				rb_set_red(other);
159				node = parent;
160				parent = rb_parent(node);
161			}
162			else
163			{
164				if (!other->rb_right || rb_is_black(other->rb_right))
165				{
166					rb_set_black(other->rb_left);
167					rb_set_red(other);
168					__rb_rotate_right(other, root);
169					other = parent->rb_right;
170				}
171				rb_set_color(other, rb_color(parent));
172				rb_set_black(parent);
173				rb_set_black(other->rb_right);
174				__rb_rotate_left(parent, root);
175				node = root->rb_node;
176				break;
177			}
178		}
179		else
180		{
181			other = parent->rb_left;
182			if (rb_is_red(other))
183			{
184				rb_set_black(other);
185				rb_set_red(parent);
186				__rb_rotate_right(parent, root);
187				other = parent->rb_left;
188			}
189			if ((!other->rb_left || rb_is_black(other->rb_left)) &&
190			    (!other->rb_right || rb_is_black(other->rb_right)))
191			{
192				rb_set_red(other);
193				node = parent;
194				parent = rb_parent(node);
195			}
196			else
197			{
198				if (!other->rb_left || rb_is_black(other->rb_left))
199				{
200					rb_set_black(other->rb_right);
201					rb_set_red(other);
202					__rb_rotate_left(other, root);
203					other = parent->rb_left;
204				}
205				rb_set_color(other, rb_color(parent));
206				rb_set_black(parent);
207				rb_set_black(other->rb_left);
208				__rb_rotate_right(parent, root);
209				node = root->rb_node;
210				break;
211			}
212		}
213	}
214	if (node)
215		rb_set_black(node);
216}
217
218void rb_erase(struct rb_node *node, struct rb_root *root)
219{
220	struct rb_node *child, *parent;
221	int color;
222
223	if (!node->rb_left)
224		child = node->rb_right;
225	else if (!node->rb_right)
226		child = node->rb_left;
227	else
228	{
229		struct rb_node *old = node, *left;
230
231		node = node->rb_right;
232		while ((left = node->rb_left) != NULL)
233			node = left;
234
235		if (rb_parent(old)) {
236			if (rb_parent(old)->rb_left == old)
237				rb_parent(old)->rb_left = node;
238			else
239				rb_parent(old)->rb_right = node;
240		} else
241			root->rb_node = node;
242
243		child = node->rb_right;
244		parent = rb_parent(node);
245		color = rb_color(node);
246
247		if (parent == old) {
248			parent = node;
249		} else {
250			if (child)
251				rb_set_parent(child, parent);
252			parent->rb_left = child;
253
254			node->rb_right = old->rb_right;
255			rb_set_parent(old->rb_right, node);
256		}
257
258		node->rb_parent_color = old->rb_parent_color;
259		node->rb_left = old->rb_left;
260		rb_set_parent(old->rb_left, node);
261
262		goto color;
263	}
264
265	parent = rb_parent(node);
266	color = rb_color(node);
267
268	if (child)
269		rb_set_parent(child, parent);
270	if (parent)
271	{
272		if (parent->rb_left == node)
273			parent->rb_left = child;
274		else
275			parent->rb_right = child;
276	}
277	else
278		root->rb_node = child;
279
280 color:
281	if (color == RB_BLACK)
282		__rb_erase_color(child, parent, root);
283}
284EXPORT_SYMBOL(rb_erase);
285
286static void rb_augment_path(struct rb_node *node, rb_augment_f func, void *data)
287{
288	struct rb_node *parent;
289
290up:
291	func(node, data);
292	parent = rb_parent(node);
293	if (!parent)
294		return;
295
296	if (node == parent->rb_left && parent->rb_right)
297		func(parent->rb_right, data);
298	else if (parent->rb_left)
299		func(parent->rb_left, data);
300
301	node = parent;
302	goto up;
303}
304
305/*
306 * after inserting @node into the tree, update the tree to account for
307 * both the new entry and any damage done by rebalance
308 */
309void rb_augment_insert(struct rb_node *node, rb_augment_f func, void *data)
310{
311	if (node->rb_left)
312		node = node->rb_left;
313	else if (node->rb_right)
314		node = node->rb_right;
315
316	rb_augment_path(node, func, data);
317}
318EXPORT_SYMBOL(rb_augment_insert);
319
320/*
321 * before removing the node, find the deepest node on the rebalance path
322 * that will still be there after @node gets removed
323 */
324struct rb_node *rb_augment_erase_begin(struct rb_node *node)
325{
326	struct rb_node *deepest;
327
328	if (!node->rb_right && !node->rb_left)
329		deepest = rb_parent(node);
330	else if (!node->rb_right)
331		deepest = node->rb_left;
332	else if (!node->rb_left)
333		deepest = node->rb_right;
334	else {
335		deepest = rb_next(node);
336		if (deepest->rb_right)
337			deepest = deepest->rb_right;
338		else if (rb_parent(deepest) != node)
339			deepest = rb_parent(deepest);
340	}
341
342	return deepest;
343}
344EXPORT_SYMBOL(rb_augment_erase_begin);
345
346/*
347 * after removal, update the tree to account for the removed entry
348 * and any rebalance damage.
349 */
350void rb_augment_erase_end(struct rb_node *node, rb_augment_f func, void *data)
351{
352	if (node)
353		rb_augment_path(node, func, data);
354}
355EXPORT_SYMBOL(rb_augment_erase_end);
356
357/*
358 * This function returns the first node (in sort order) of the tree.
359 */
360struct rb_node *rb_first(const struct rb_root *root)
361{
362	struct rb_node	*n;
363
364	n = root->rb_node;
365	if (!n)
366		return NULL;
367	while (n->rb_left)
368		n = n->rb_left;
369	return n;
370}
371EXPORT_SYMBOL(rb_first);
372
373struct rb_node *rb_last(const struct rb_root *root)
374{
375	struct rb_node	*n;
376
377	n = root->rb_node;
378	if (!n)
379		return NULL;
380	while (n->rb_right)
381		n = n->rb_right;
382	return n;
383}
384EXPORT_SYMBOL(rb_last);
385
386struct rb_node *rb_next(const struct rb_node *node)
387{
388	struct rb_node *parent;
389
390	if (rb_parent(node) == node)
391		return NULL;
392
393	/* If we have a right-hand child, go down and then left as far
394	   as we can. */
395	if (node->rb_right) {
396		node = node->rb_right; 
397		while (node->rb_left)
398			node=node->rb_left;
399		return (struct rb_node *)node;
400	}
401
402	/* No right-hand children.  Everything down and left is
403	   smaller than us, so any 'next' node must be in the general
404	   direction of our parent. Go up the tree; any time the
405	   ancestor is a right-hand child of its parent, keep going
406	   up. First time it's a left-hand child of its parent, said
407	   parent is our 'next' node. */
408	while ((parent = rb_parent(node)) && node == parent->rb_right)
409		node = parent;
410
411	return parent;
412}
413EXPORT_SYMBOL(rb_next);
414
415struct rb_node *rb_prev(const struct rb_node *node)
416{
417	struct rb_node *parent;
418
419	if (rb_parent(node) == node)
420		return NULL;
421
422	/* If we have a left-hand child, go down and then right as far
423	   as we can. */
424	if (node->rb_left) {
425		node = node->rb_left; 
426		while (node->rb_right)
427			node=node->rb_right;
428		return (struct rb_node *)node;
429	}
430
431	/* No left-hand children. Go up till we find an ancestor which
432	   is a right-hand child of its parent */
433	while ((parent = rb_parent(node)) && node == parent->rb_left)
434		node = parent;
435
436	return parent;
437}
438EXPORT_SYMBOL(rb_prev);
439
440void rb_replace_node(struct rb_node *victim, struct rb_node *new,
441		     struct rb_root *root)
442{
443	struct rb_node *parent = rb_parent(victim);
444
445	/* Set the surrounding nodes to point to the replacement */
446	if (parent) {
447		if (victim == parent->rb_left)
448			parent->rb_left = new;
449		else
450			parent->rb_right = new;
451	} else {
452		root->rb_node = new;
453	}
454	if (victim->rb_left)
455		rb_set_parent(victim->rb_left, new);
456	if (victim->rb_right)
457		rb_set_parent(victim->rb_right, new);
458
459	/* Copy the pointers/colour from the victim to the replacement */
460	*new = *victim;
461}
462EXPORT_SYMBOL(rb_replace_node);
  1// SPDX-License-Identifier: GPL-2.0-or-later
  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
  9  linux/lib/rbtree.c
 10*/
 11
 12#include <linux/rbtree_augmented.h>
 13#include <linux/export.h>
 14
 15/*
 16 * red-black trees properties:  https://en.wikipedia.org/wiki/Rbtree
 17 *
 18 *  1) A node is either red or black
 19 *  2) The root is black
 20 *  3) All leaves (NULL) are black
 21 *  4) Both children of every red node are black
 22 *  5) Every simple path from root to leaves contains the same number
 23 *     of black nodes.
 24 *
 25 *  4 and 5 give the O(log n) guarantee, since 4 implies you cannot have two
 26 *  consecutive red nodes in a path and every red node is therefore followed by
 27 *  a black. So if B is the number of black nodes on every simple path (as per
 28 *  5), then the longest possible path due to 4 is 2B.
 29 *
 30 *  We shall indicate color with case, where black nodes are uppercase and red
 31 *  nodes will be lowercase. Unknown color nodes shall be drawn as red within
 32 *  parentheses and have some accompanying text comment.
 33 */
 34
 35/*
 36 * Notes on lockless lookups:
 37 *
 38 * All stores to the tree structure (rb_left and rb_right) must be done using
 39 * WRITE_ONCE(). And we must not inadvertently cause (temporary) loops in the
 40 * tree structure as seen in program order.
 41 *
 42 * These two requirements will allow lockless iteration of the tree -- not
 43 * correct iteration mind you, tree rotations are not atomic so a lookup might
 44 * miss entire subtrees.
 45 *
 46 * But they do guarantee that any such traversal will only see valid elements
 47 * and that it will indeed complete -- does not get stuck in a loop.
 48 *
 49 * It also guarantees that if the lookup returns an element it is the 'correct'
 50 * one. But not returning an element does _NOT_ mean it's not present.
 51 *
 52 * NOTE:
 53 *
 54 * Stores to __rb_parent_color are not important for simple lookups so those
 55 * are left undone as of now. Nor did I check for loops involving parent
 56 * pointers.
 57 */
 58
 59static inline void rb_set_black(struct rb_node *rb)
 60{
 61	rb->__rb_parent_color |= RB_BLACK;
 62}
 63
 64static inline struct rb_node *rb_red_parent(struct rb_node *red)
 65{
 66	return (struct rb_node *)red->__rb_parent_color;
 67}
 68
 69/*
 70 * Helper function for rotations:
 71 * - old's parent and color get assigned to new
 72 * - old gets assigned new as a parent and 'color' as a color.
 73 */
 74static inline void
 75__rb_rotate_set_parents(struct rb_node *old, struct rb_node *new,
 76			struct rb_root *root, int color)
 77{
 78	struct rb_node *parent = rb_parent(old);
 79	new->__rb_parent_color = old->__rb_parent_color;
 80	rb_set_parent_color(old, new, color);
 81	__rb_change_child(old, new, parent, root);
 82}
 83
 84static __always_inline void
 85__rb_insert(struct rb_node *node, struct rb_root *root,
 86	    void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
 87{
 88	struct rb_node *parent = rb_red_parent(node), *gparent, *tmp;
 89
 90	while (true) {
 91		/*
 92		 * Loop invariant: node is red.
 93		 */
 94		if (unlikely(!parent)) {
 95			/*
 96			 * The inserted node is root. Either this is the
 97			 * first node, or we recursed at Case 1 below and
 98			 * are no longer violating 4).
 99			 */
100			rb_set_parent_color(node, NULL, RB_BLACK);
101			break;
102		}
103
104		/*
105		 * If there is a black parent, we are done.
106		 * Otherwise, take some corrective action as,
107		 * per 4), we don't want a red root or two
108		 * consecutive red nodes.
109		 */
110		if(rb_is_black(parent))
111			break;
112
113		gparent = rb_red_parent(parent);
114
115		tmp = gparent->rb_right;
116		if (parent != tmp) {	/* parent == gparent->rb_left */
117			if (tmp && rb_is_red(tmp)) {
118				/*
119				 * Case 1 - node's uncle is red (color flips).
120				 *
121				 *       G            g
122				 *      / \          / \
123				 *     p   u  -->   P   U
124				 *    /            /
125				 *   n            n
126				 *
127				 * However, since g's parent might be red, and
128				 * 4) does not allow this, we need to recurse
129				 * at g.
130				 */
131				rb_set_parent_color(tmp, gparent, RB_BLACK);
132				rb_set_parent_color(parent, gparent, RB_BLACK);
133				node = gparent;
134				parent = rb_parent(node);
135				rb_set_parent_color(node, parent, RB_RED);
136				continue;
137			}
138
139			tmp = parent->rb_right;
140			if (node == tmp) {
141				/*
142				 * Case 2 - node's uncle is black and node is
143				 * the parent's right child (left rotate at parent).
144				 *
145				 *      G             G
146				 *     / \           / \
147				 *    p   U  -->    n   U
148				 *     \           /
149				 *      n         p
150				 *
151				 * This still leaves us in violation of 4), the
152				 * continuation into Case 3 will fix that.
153				 */
154				tmp = node->rb_left;
155				WRITE_ONCE(parent->rb_right, tmp);
156				WRITE_ONCE(node->rb_left, parent);
157				if (tmp)
158					rb_set_parent_color(tmp, parent,
159							    RB_BLACK);
160				rb_set_parent_color(parent, node, RB_RED);
161				augment_rotate(parent, node);
162				parent = node;
163				tmp = node->rb_right;
164			}
165
166			/*
167			 * Case 3 - node's uncle is black and node is
168			 * the parent's left child (right rotate at gparent).
169			 *
170			 *        G           P
171			 *       / \         / \
172			 *      p   U  -->  n   g
173			 *     /                 \
174			 *    n                   U
175			 */
176			WRITE_ONCE(gparent->rb_left, tmp); /* == parent->rb_right */
177			WRITE_ONCE(parent->rb_right, 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		} else {
184			tmp = gparent->rb_left;
185			if (tmp && rb_is_red(tmp)) {
186				/* Case 1 - color flips */
187				rb_set_parent_color(tmp, gparent, RB_BLACK);
188				rb_set_parent_color(parent, gparent, RB_BLACK);
189				node = gparent;
190				parent = rb_parent(node);
191				rb_set_parent_color(node, parent, RB_RED);
192				continue;
193			}
194
195			tmp = parent->rb_left;
196			if (node == tmp) {
197				/* Case 2 - right rotate at parent */
198				tmp = node->rb_right;
199				WRITE_ONCE(parent->rb_left, tmp);
200				WRITE_ONCE(node->rb_right, parent);
201				if (tmp)
202					rb_set_parent_color(tmp, parent,
203							    RB_BLACK);
204				rb_set_parent_color(parent, node, RB_RED);
205				augment_rotate(parent, node);
206				parent = node;
207				tmp = node->rb_left;
208			}
209
210			/* Case 3 - left rotate at gparent */
211			WRITE_ONCE(gparent->rb_right, tmp); /* == parent->rb_left */
212			WRITE_ONCE(parent->rb_left, gparent);
213			if (tmp)
214				rb_set_parent_color(tmp, gparent, RB_BLACK);
215			__rb_rotate_set_parents(gparent, parent, root, RB_RED);
216			augment_rotate(gparent, parent);
217			break;
218		}
219	}
220}
221
222/*
223 * Inline version for rb_erase() use - we want to be able to inline
224 * and eliminate the dummy_rotate callback there
225 */
226static __always_inline void
227____rb_erase_color(struct rb_node *parent, struct rb_root *root,
228	void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
229{
230	struct rb_node *node = NULL, *sibling, *tmp1, *tmp2;
231
232	while (true) {
233		/*
234		 * Loop invariants:
235		 * - node is black (or NULL on first iteration)
236		 * - node is not the root (parent is not NULL)
237		 * - All leaf paths going through parent and node have a
238		 *   black node count that is 1 lower than other leaf paths.
239		 */
240		sibling = parent->rb_right;
241		if (node != sibling) {	/* node == parent->rb_left */
242			if (rb_is_red(sibling)) {
243				/*
244				 * Case 1 - left rotate at parent
245				 *
246				 *     P               S
247				 *    / \             / \
248				 *   N   s    -->    p   Sr
249				 *      / \         / \
250				 *     Sl  Sr      N   Sl
251				 */
252				tmp1 = sibling->rb_left;
253				WRITE_ONCE(parent->rb_right, tmp1);
254				WRITE_ONCE(sibling->rb_left, parent);
255				rb_set_parent_color(tmp1, parent, RB_BLACK);
256				__rb_rotate_set_parents(parent, sibling, root,
257							RB_RED);
258				augment_rotate(parent, sibling);
259				sibling = tmp1;
260			}
261			tmp1 = sibling->rb_right;
262			if (!tmp1 || rb_is_black(tmp1)) {
263				tmp2 = sibling->rb_left;
264				if (!tmp2 || rb_is_black(tmp2)) {
265					/*
266					 * Case 2 - sibling color flip
267					 * (p could be either color here)
268					 *
269					 *    (p)           (p)
270					 *    / \           / \
271					 *   N   S    -->  N   s
272					 *      / \           / \
273					 *     Sl  Sr        Sl  Sr
274					 *
275					 * This leaves us violating 5) which
276					 * can be fixed by flipping p to black
277					 * if it was red, or by recursing at p.
278					 * p is red when coming from Case 1.
279					 */
280					rb_set_parent_color(sibling, parent,
281							    RB_RED);
282					if (rb_is_red(parent))
283						rb_set_black(parent);
284					else {
285						node = parent;
286						parent = rb_parent(node);
287						if (parent)
288							continue;
289					}
290					break;
291				}
292				/*
293				 * Case 3 - right rotate at sibling
294				 * (p could be either color here)
295				 *
296				 *   (p)           (p)
297				 *   / \           / \
298				 *  N   S    -->  N   sl
299				 *     / \             \
300				 *    sl  Sr            S
301				 *                       \
302				 *                        Sr
303				 *
304				 * Note: p might be red, and then both
305				 * p and sl are red after rotation(which
306				 * breaks property 4). This is fixed in
307				 * Case 4 (in __rb_rotate_set_parents()
308				 *         which set sl the color of p
309				 *         and set p RB_BLACK)
310				 *
311				 *   (p)            (sl)
312				 *   / \            /  \
313				 *  N   sl   -->   P    S
314				 *       \        /      \
315				 *        S      N        Sr
316				 *         \
317				 *          Sr
318				 */
319				tmp1 = tmp2->rb_right;
320				WRITE_ONCE(sibling->rb_left, tmp1);
321				WRITE_ONCE(tmp2->rb_right, sibling);
322				WRITE_ONCE(parent->rb_right, tmp2);
323				if (tmp1)
324					rb_set_parent_color(tmp1, sibling,
325							    RB_BLACK);
326				augment_rotate(sibling, tmp2);
327				tmp1 = sibling;
328				sibling = tmp2;
329			}
330			/*
331			 * Case 4 - left rotate at parent + color flips
332			 * (p and sl could be either color here.
333			 *  After rotation, p becomes black, s acquires
334			 *  p's color, and sl keeps its color)
335			 *
336			 *      (p)             (s)
337			 *      / \             / \
338			 *     N   S     -->   P   Sr
339			 *        / \         / \
340			 *      (sl) sr      N  (sl)
341			 */
342			tmp2 = sibling->rb_left;
343			WRITE_ONCE(parent->rb_right, tmp2);
344			WRITE_ONCE(sibling->rb_left, parent);
345			rb_set_parent_color(tmp1, sibling, RB_BLACK);
346			if (tmp2)
347				rb_set_parent(tmp2, parent);
348			__rb_rotate_set_parents(parent, sibling, root,
349						RB_BLACK);
350			augment_rotate(parent, sibling);
351			break;
352		} else {
353			sibling = parent->rb_left;
354			if (rb_is_red(sibling)) {
355				/* Case 1 - right rotate at parent */
356				tmp1 = sibling->rb_right;
357				WRITE_ONCE(parent->rb_left, tmp1);
358				WRITE_ONCE(sibling->rb_right, parent);
359				rb_set_parent_color(tmp1, parent, RB_BLACK);
360				__rb_rotate_set_parents(parent, sibling, root,
361							RB_RED);
362				augment_rotate(parent, sibling);
363				sibling = tmp1;
364			}
365			tmp1 = sibling->rb_left;
366			if (!tmp1 || rb_is_black(tmp1)) {
367				tmp2 = sibling->rb_right;
368				if (!tmp2 || rb_is_black(tmp2)) {
369					/* Case 2 - sibling color flip */
370					rb_set_parent_color(sibling, parent,
371							    RB_RED);
372					if (rb_is_red(parent))
373						rb_set_black(parent);
374					else {
375						node = parent;
376						parent = rb_parent(node);
377						if (parent)
378							continue;
379					}
380					break;
381				}
382				/* Case 3 - left rotate at sibling */
383				tmp1 = tmp2->rb_left;
384				WRITE_ONCE(sibling->rb_right, tmp1);
385				WRITE_ONCE(tmp2->rb_left, sibling);
386				WRITE_ONCE(parent->rb_left, tmp2);
387				if (tmp1)
388					rb_set_parent_color(tmp1, sibling,
389							    RB_BLACK);
390				augment_rotate(sibling, tmp2);
391				tmp1 = sibling;
392				sibling = tmp2;
393			}
394			/* Case 4 - right rotate at parent + color flips */
395			tmp2 = sibling->rb_right;
396			WRITE_ONCE(parent->rb_left, tmp2);
397			WRITE_ONCE(sibling->rb_right, parent);
398			rb_set_parent_color(tmp1, sibling, RB_BLACK);
399			if (tmp2)
400				rb_set_parent(tmp2, parent);
401			__rb_rotate_set_parents(parent, sibling, root,
402						RB_BLACK);
403			augment_rotate(parent, sibling);
404			break;
405		}
406	}
407}
408
409/* Non-inline version for rb_erase_augmented() use */
410void __rb_erase_color(struct rb_node *parent, struct rb_root *root,
411	void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
412{
413	____rb_erase_color(parent, root, augment_rotate);
414}
415EXPORT_SYMBOL(__rb_erase_color);
416
417/*
418 * Non-augmented rbtree manipulation functions.
419 *
420 * We use dummy augmented callbacks here, and have the compiler optimize them
421 * out of the rb_insert_color() and rb_erase() function definitions.
422 */
423
424static inline void dummy_propagate(struct rb_node *node, struct rb_node *stop) {}
425static inline void dummy_copy(struct rb_node *old, struct rb_node *new) {}
426static inline void dummy_rotate(struct rb_node *old, struct rb_node *new) {}
427
428static const struct rb_augment_callbacks dummy_callbacks = {
429	.propagate = dummy_propagate,
430	.copy = dummy_copy,
431	.rotate = dummy_rotate
432};
433
434void rb_insert_color(struct rb_node *node, struct rb_root *root)
435{
436	__rb_insert(node, root, dummy_rotate);
437}
438EXPORT_SYMBOL(rb_insert_color);
439
440void rb_erase(struct rb_node *node, struct rb_root *root)
441{
442	struct rb_node *rebalance;
443	rebalance = __rb_erase_augmented(node, root, &dummy_callbacks);
444	if (rebalance)
445		____rb_erase_color(rebalance, root, dummy_rotate);
446}
447EXPORT_SYMBOL(rb_erase);
448
449/*
450 * Augmented rbtree manipulation functions.
451 *
452 * This instantiates the same __always_inline functions as in the non-augmented
453 * case, but this time with user-defined callbacks.
454 */
455
456void __rb_insert_augmented(struct rb_node *node, struct rb_root *root,
457	void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
458{
459	__rb_insert(node, root, augment_rotate);
460}
461EXPORT_SYMBOL(__rb_insert_augmented);
462
463/*
464 * This function returns the first node (in sort order) of the tree.
465 */
466struct rb_node *rb_first(const struct rb_root *root)
467{
468	struct rb_node	*n;
469
470	n = root->rb_node;
471	if (!n)
472		return NULL;
473	while (n->rb_left)
474		n = n->rb_left;
475	return n;
476}
477EXPORT_SYMBOL(rb_first);
478
479struct rb_node *rb_last(const struct rb_root *root)
480{
481	struct rb_node	*n;
482
483	n = root->rb_node;
484	if (!n)
485		return NULL;
486	while (n->rb_right)
487		n = n->rb_right;
488	return n;
489}
490EXPORT_SYMBOL(rb_last);
491
492struct rb_node *rb_next(const struct rb_node *node)
493{
494	struct rb_node *parent;
495
496	if (RB_EMPTY_NODE(node))
497		return NULL;
498
499	/*
500	 * If we have a right-hand child, go down and then left as far
501	 * as we can.
502	 */
503	if (node->rb_right) {
504		node = node->rb_right;
505		while (node->rb_left)
506			node = node->rb_left;
507		return (struct rb_node *)node;
508	}
509
510	/*
511	 * No right-hand children. Everything down and left is smaller than us,
512	 * so any 'next' node must be in the general direction of our parent.
513	 * Go up the tree; any time the ancestor is a right-hand child of its
514	 * parent, keep going up. First time it's a left-hand child of its
515	 * parent, said parent is our 'next' node.
516	 */
517	while ((parent = rb_parent(node)) && node == parent->rb_right)
518		node = parent;
519
520	return parent;
521}
522EXPORT_SYMBOL(rb_next);
523
524struct rb_node *rb_prev(const struct rb_node *node)
525{
526	struct rb_node *parent;
527
528	if (RB_EMPTY_NODE(node))
529		return NULL;
530
531	/*
532	 * If we have a left-hand child, go down and then right as far
533	 * as we can.
534	 */
535	if (node->rb_left) {
536		node = node->rb_left;
537		while (node->rb_right)
538			node = node->rb_right;
539		return (struct rb_node *)node;
540	}
541
542	/*
543	 * No left-hand children. Go up till we find an ancestor which
544	 * is a right-hand child of its parent.
545	 */
546	while ((parent = rb_parent(node)) && node == parent->rb_left)
547		node = parent;
548
549	return parent;
550}
551EXPORT_SYMBOL(rb_prev);
552
553void rb_replace_node(struct rb_node *victim, struct rb_node *new,
554		     struct rb_root *root)
555{
556	struct rb_node *parent = rb_parent(victim);
557
558	/* Copy the pointers/colour from the victim to the replacement */
559	*new = *victim;
560
561	/* Set the surrounding nodes to point to the replacement */
562	if (victim->rb_left)
563		rb_set_parent(victim->rb_left, new);
564	if (victim->rb_right)
565		rb_set_parent(victim->rb_right, new);
566	__rb_change_child(victim, new, parent, root);
567}
568EXPORT_SYMBOL(rb_replace_node);
569
570void rb_replace_node_rcu(struct rb_node *victim, struct rb_node *new,
571			 struct rb_root *root)
572{
573	struct rb_node *parent = rb_parent(victim);
574
575	/* Copy the pointers/colour from the victim to the replacement */
576	*new = *victim;
577
578	/* Set the surrounding nodes to point to the replacement */
579	if (victim->rb_left)
580		rb_set_parent(victim->rb_left, new);
581	if (victim->rb_right)
582		rb_set_parent(victim->rb_right, new);
583
584	/* Set the parent's pointer to the new node last after an RCU barrier
585	 * so that the pointers onwards are seen to be set correctly when doing
586	 * an RCU walk over the tree.
587	 */
588	__rb_change_child_rcu(victim, new, parent, root);
589}
590EXPORT_SYMBOL(rb_replace_node_rcu);
591
592static struct rb_node *rb_left_deepest_node(const struct rb_node *node)
593{
594	for (;;) {
595		if (node->rb_left)
596			node = node->rb_left;
597		else if (node->rb_right)
598			node = node->rb_right;
599		else
600			return (struct rb_node *)node;
601	}
602}
603
604struct rb_node *rb_next_postorder(const struct rb_node *node)
605{
606	const struct rb_node *parent;
607	if (!node)
608		return NULL;
609	parent = rb_parent(node);
610
611	/* If we're sitting on node, we've already seen our children */
612	if (parent && node == parent->rb_left && parent->rb_right) {
613		/* If we are the parent's left node, go to the parent's right
614		 * node then all the way down to the left */
615		return rb_left_deepest_node(parent->rb_right);
616	} else
617		/* Otherwise we are the parent's right node, and the parent
618		 * should be next */
619		return (struct rb_node *)parent;
620}
621EXPORT_SYMBOL(rb_next_postorder);
622
623struct rb_node *rb_first_postorder(const struct rb_root *root)
624{
625	if (!root->rb_node)
626		return NULL;
627
628	return rb_left_deepest_node(root->rb_node);
629}
630EXPORT_SYMBOL(rb_first_postorder);