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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);