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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}
415
416/*
417 * Non-augmented rbtree manipulation functions.
418 *
419 * We use dummy augmented callbacks here, and have the compiler optimize them
420 * out of the rb_insert_color() and rb_erase() function definitions.
421 */
422
423static inline void dummy_propagate(struct rb_node *node, struct rb_node *stop) {}
424static inline void dummy_copy(struct rb_node *old, struct rb_node *new) {}
425static inline void dummy_rotate(struct rb_node *old, struct rb_node *new) {}
426
427static const struct rb_augment_callbacks dummy_callbacks = {
428 .propagate = dummy_propagate,
429 .copy = dummy_copy,
430 .rotate = dummy_rotate
431};
432
433void rb_insert_color(struct rb_node *node, struct rb_root *root)
434{
435 __rb_insert(node, root, dummy_rotate);
436}
437
438void rb_erase(struct rb_node *node, struct rb_root *root)
439{
440 struct rb_node *rebalance;
441 rebalance = __rb_erase_augmented(node, root, &dummy_callbacks);
442 if (rebalance)
443 ____rb_erase_color(rebalance, root, dummy_rotate);
444}
445
446/*
447 * Augmented rbtree manipulation functions.
448 *
449 * This instantiates the same __always_inline functions as in the non-augmented
450 * case, but this time with user-defined callbacks.
451 */
452
453void __rb_insert_augmented(struct rb_node *node, struct rb_root *root,
454 void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
455{
456 __rb_insert(node, root, augment_rotate);
457}
458
459/*
460 * This function returns the first node (in sort order) of the tree.
461 */
462struct rb_node *rb_first(const struct rb_root *root)
463{
464 struct rb_node *n;
465
466 n = root->rb_node;
467 if (!n)
468 return NULL;
469 while (n->rb_left)
470 n = n->rb_left;
471 return n;
472}
473
474struct rb_node *rb_last(const struct rb_root *root)
475{
476 struct rb_node *n;
477
478 n = root->rb_node;
479 if (!n)
480 return NULL;
481 while (n->rb_right)
482 n = n->rb_right;
483 return n;
484}
485
486struct rb_node *rb_next(const struct rb_node *node)
487{
488 struct rb_node *parent;
489
490 if (RB_EMPTY_NODE(node))
491 return NULL;
492
493 /*
494 * If we have a right-hand child, go down and then left as far
495 * as we can.
496 */
497 if (node->rb_right) {
498 node = node->rb_right;
499 while (node->rb_left)
500 node = node->rb_left;
501 return (struct rb_node *)node;
502 }
503
504 /*
505 * No right-hand children. Everything down and left is smaller than us,
506 * so any 'next' node must be in the general direction of our parent.
507 * Go up the tree; any time the ancestor is a right-hand child of its
508 * parent, keep going up. First time it's a left-hand child of its
509 * parent, said parent is our 'next' node.
510 */
511 while ((parent = rb_parent(node)) && node == parent->rb_right)
512 node = parent;
513
514 return parent;
515}
516
517struct rb_node *rb_prev(const struct rb_node *node)
518{
519 struct rb_node *parent;
520
521 if (RB_EMPTY_NODE(node))
522 return NULL;
523
524 /*
525 * If we have a left-hand child, go down and then right as far
526 * as we can.
527 */
528 if (node->rb_left) {
529 node = node->rb_left;
530 while (node->rb_right)
531 node = node->rb_right;
532 return (struct rb_node *)node;
533 }
534
535 /*
536 * No left-hand children. Go up till we find an ancestor which
537 * is a right-hand child of its parent.
538 */
539 while ((parent = rb_parent(node)) && node == parent->rb_left)
540 node = parent;
541
542 return parent;
543}
544
545void rb_replace_node(struct rb_node *victim, struct rb_node *new,
546 struct rb_root *root)
547{
548 struct rb_node *parent = rb_parent(victim);
549
550 /* Copy the pointers/colour from the victim to the replacement */
551 *new = *victim;
552
553 /* Set the surrounding nodes to point to the replacement */
554 if (victim->rb_left)
555 rb_set_parent(victim->rb_left, new);
556 if (victim->rb_right)
557 rb_set_parent(victim->rb_right, new);
558 __rb_change_child(victim, new, parent, root);
559}
560
561static struct rb_node *rb_left_deepest_node(const struct rb_node *node)
562{
563 for (;;) {
564 if (node->rb_left)
565 node = node->rb_left;
566 else if (node->rb_right)
567 node = node->rb_right;
568 else
569 return (struct rb_node *)node;
570 }
571}
572
573struct rb_node *rb_next_postorder(const struct rb_node *node)
574{
575 const struct rb_node *parent;
576 if (!node)
577 return NULL;
578 parent = rb_parent(node);
579
580 /* If we're sitting on node, we've already seen our children */
581 if (parent && node == parent->rb_left && parent->rb_right) {
582 /* If we are the parent's left node, go to the parent's right
583 * node then all the way down to the left */
584 return rb_left_deepest_node(parent->rb_right);
585 } else
586 /* Otherwise we are the parent's right node, and the parent
587 * should be next */
588 return (struct rb_node *)parent;
589}
590
591struct rb_node *rb_first_postorder(const struct rb_root *root)
592{
593 if (!root->rb_node)
594 return NULL;
595
596 return rb_left_deepest_node(root->rb_node);
597}
1/*
2 Red Black Trees
3 (C) 1999 Andrea Arcangeli <andrea@suse.de>
4 (C) 2002 David Woodhouse <dwmw2@infradead.org>
5 (C) 2012 Michel Lespinasse <walken@google.com>
6
7 This program is free software; you can redistribute it and/or modify
8 it under the terms of the GNU General Public License as published by
9 the Free Software Foundation; either version 2 of the License, or
10 (at your option) any later version.
11
12 This program is distributed in the hope that it will be useful,
13 but WITHOUT ANY WARRANTY; without even the implied warranty of
14 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
15 GNU General Public License for more details.
16
17 You should have received a copy of the GNU General Public License
18 along with this program; if not, write to the Free Software
19 Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
20
21 linux/lib/rbtree.c
22*/
23
24#include <linux/rbtree_augmented.h>
25
26/*
27 * red-black trees properties: http://en.wikipedia.org/wiki/Rbtree
28 *
29 * 1) A node is either red or black
30 * 2) The root is black
31 * 3) All leaves (NULL) are black
32 * 4) Both children of every red node are black
33 * 5) Every simple path from root to leaves contains the same number
34 * of black nodes.
35 *
36 * 4 and 5 give the O(log n) guarantee, since 4 implies you cannot have two
37 * consecutive red nodes in a path and every red node is therefore followed by
38 * a black. So if B is the number of black nodes on every simple path (as per
39 * 5), then the longest possible path due to 4 is 2B.
40 *
41 * We shall indicate color with case, where black nodes are uppercase and red
42 * nodes will be lowercase. Unknown color nodes shall be drawn as red within
43 * parentheses and have some accompanying text comment.
44 */
45
46static inline void rb_set_black(struct rb_node *rb)
47{
48 rb->__rb_parent_color |= RB_BLACK;
49}
50
51static inline struct rb_node *rb_red_parent(struct rb_node *red)
52{
53 return (struct rb_node *)red->__rb_parent_color;
54}
55
56/*
57 * Helper function for rotations:
58 * - old's parent and color get assigned to new
59 * - old gets assigned new as a parent and 'color' as a color.
60 */
61static inline void
62__rb_rotate_set_parents(struct rb_node *old, struct rb_node *new,
63 struct rb_root *root, int color)
64{
65 struct rb_node *parent = rb_parent(old);
66 new->__rb_parent_color = old->__rb_parent_color;
67 rb_set_parent_color(old, new, color);
68 __rb_change_child(old, new, parent, root);
69}
70
71static __always_inline void
72__rb_insert(struct rb_node *node, struct rb_root *root,
73 void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
74{
75 struct rb_node *parent = rb_red_parent(node), *gparent, *tmp;
76
77 while (true) {
78 /*
79 * Loop invariant: node is red
80 *
81 * If there is a black parent, we are done.
82 * Otherwise, take some corrective action as we don't
83 * want a red root or two consecutive red nodes.
84 */
85 if (!parent) {
86 rb_set_parent_color(node, NULL, RB_BLACK);
87 break;
88 } else if (rb_is_black(parent))
89 break;
90
91 gparent = rb_red_parent(parent);
92
93 tmp = gparent->rb_right;
94 if (parent != tmp) { /* parent == gparent->rb_left */
95 if (tmp && rb_is_red(tmp)) {
96 /*
97 * Case 1 - color flips
98 *
99 * G g
100 * / \ / \
101 * p u --> P U
102 * / /
103 * n n
104 *
105 * However, since g's parent might be red, and
106 * 4) does not allow this, we need to recurse
107 * at g.
108 */
109 rb_set_parent_color(tmp, gparent, RB_BLACK);
110 rb_set_parent_color(parent, gparent, RB_BLACK);
111 node = gparent;
112 parent = rb_parent(node);
113 rb_set_parent_color(node, parent, RB_RED);
114 continue;
115 }
116
117 tmp = parent->rb_right;
118 if (node == tmp) {
119 /*
120 * Case 2 - left rotate at parent
121 *
122 * G G
123 * / \ / \
124 * p U --> n U
125 * \ /
126 * n p
127 *
128 * This still leaves us in violation of 4), the
129 * continuation into Case 3 will fix that.
130 */
131 parent->rb_right = tmp = node->rb_left;
132 node->rb_left = parent;
133 if (tmp)
134 rb_set_parent_color(tmp, parent,
135 RB_BLACK);
136 rb_set_parent_color(parent, node, RB_RED);
137 augment_rotate(parent, node);
138 parent = node;
139 tmp = node->rb_right;
140 }
141
142 /*
143 * Case 3 - right rotate at gparent
144 *
145 * G P
146 * / \ / \
147 * p U --> n g
148 * / \
149 * n U
150 */
151 gparent->rb_left = tmp; /* == parent->rb_right */
152 parent->rb_right = gparent;
153 if (tmp)
154 rb_set_parent_color(tmp, gparent, RB_BLACK);
155 __rb_rotate_set_parents(gparent, parent, root, RB_RED);
156 augment_rotate(gparent, parent);
157 break;
158 } else {
159 tmp = gparent->rb_left;
160 if (tmp && rb_is_red(tmp)) {
161 /* Case 1 - color flips */
162 rb_set_parent_color(tmp, gparent, RB_BLACK);
163 rb_set_parent_color(parent, gparent, RB_BLACK);
164 node = gparent;
165 parent = rb_parent(node);
166 rb_set_parent_color(node, parent, RB_RED);
167 continue;
168 }
169
170 tmp = parent->rb_left;
171 if (node == tmp) {
172 /* Case 2 - right rotate at parent */
173 parent->rb_left = tmp = node->rb_right;
174 node->rb_right = parent;
175 if (tmp)
176 rb_set_parent_color(tmp, parent,
177 RB_BLACK);
178 rb_set_parent_color(parent, node, RB_RED);
179 augment_rotate(parent, node);
180 parent = node;
181 tmp = node->rb_left;
182 }
183
184 /* Case 3 - left rotate at gparent */
185 gparent->rb_right = tmp; /* == parent->rb_left */
186 parent->rb_left = gparent;
187 if (tmp)
188 rb_set_parent_color(tmp, gparent, RB_BLACK);
189 __rb_rotate_set_parents(gparent, parent, root, RB_RED);
190 augment_rotate(gparent, parent);
191 break;
192 }
193 }
194}
195
196/*
197 * Inline version for rb_erase() use - we want to be able to inline
198 * and eliminate the dummy_rotate callback there
199 */
200static __always_inline void
201____rb_erase_color(struct rb_node *parent, struct rb_root *root,
202 void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
203{
204 struct rb_node *node = NULL, *sibling, *tmp1, *tmp2;
205
206 while (true) {
207 /*
208 * Loop invariants:
209 * - node is black (or NULL on first iteration)
210 * - node is not the root (parent is not NULL)
211 * - All leaf paths going through parent and node have a
212 * black node count that is 1 lower than other leaf paths.
213 */
214 sibling = parent->rb_right;
215 if (node != sibling) { /* node == parent->rb_left */
216 if (rb_is_red(sibling)) {
217 /*
218 * Case 1 - left rotate at parent
219 *
220 * P S
221 * / \ / \
222 * N s --> p Sr
223 * / \ / \
224 * Sl Sr N Sl
225 */
226 parent->rb_right = tmp1 = sibling->rb_left;
227 sibling->rb_left = parent;
228 rb_set_parent_color(tmp1, parent, RB_BLACK);
229 __rb_rotate_set_parents(parent, sibling, root,
230 RB_RED);
231 augment_rotate(parent, sibling);
232 sibling = tmp1;
233 }
234 tmp1 = sibling->rb_right;
235 if (!tmp1 || rb_is_black(tmp1)) {
236 tmp2 = sibling->rb_left;
237 if (!tmp2 || rb_is_black(tmp2)) {
238 /*
239 * Case 2 - sibling color flip
240 * (p could be either color here)
241 *
242 * (p) (p)
243 * / \ / \
244 * N S --> N s
245 * / \ / \
246 * Sl Sr Sl Sr
247 *
248 * This leaves us violating 5) which
249 * can be fixed by flipping p to black
250 * if it was red, or by recursing at p.
251 * p is red when coming from Case 1.
252 */
253 rb_set_parent_color(sibling, parent,
254 RB_RED);
255 if (rb_is_red(parent))
256 rb_set_black(parent);
257 else {
258 node = parent;
259 parent = rb_parent(node);
260 if (parent)
261 continue;
262 }
263 break;
264 }
265 /*
266 * Case 3 - right rotate at sibling
267 * (p could be either color here)
268 *
269 * (p) (p)
270 * / \ / \
271 * N S --> N Sl
272 * / \ \
273 * sl Sr s
274 * \
275 * Sr
276 */
277 sibling->rb_left = tmp1 = tmp2->rb_right;
278 tmp2->rb_right = sibling;
279 parent->rb_right = tmp2;
280 if (tmp1)
281 rb_set_parent_color(tmp1, sibling,
282 RB_BLACK);
283 augment_rotate(sibling, tmp2);
284 tmp1 = sibling;
285 sibling = tmp2;
286 }
287 /*
288 * Case 4 - left rotate at parent + color flips
289 * (p and sl could be either color here.
290 * After rotation, p becomes black, s acquires
291 * p's color, and sl keeps its color)
292 *
293 * (p) (s)
294 * / \ / \
295 * N S --> P Sr
296 * / \ / \
297 * (sl) sr N (sl)
298 */
299 parent->rb_right = tmp2 = sibling->rb_left;
300 sibling->rb_left = parent;
301 rb_set_parent_color(tmp1, sibling, RB_BLACK);
302 if (tmp2)
303 rb_set_parent(tmp2, parent);
304 __rb_rotate_set_parents(parent, sibling, root,
305 RB_BLACK);
306 augment_rotate(parent, sibling);
307 break;
308 } else {
309 sibling = parent->rb_left;
310 if (rb_is_red(sibling)) {
311 /* Case 1 - right rotate at parent */
312 parent->rb_left = tmp1 = sibling->rb_right;
313 sibling->rb_right = parent;
314 rb_set_parent_color(tmp1, parent, RB_BLACK);
315 __rb_rotate_set_parents(parent, sibling, root,
316 RB_RED);
317 augment_rotate(parent, sibling);
318 sibling = tmp1;
319 }
320 tmp1 = sibling->rb_left;
321 if (!tmp1 || rb_is_black(tmp1)) {
322 tmp2 = sibling->rb_right;
323 if (!tmp2 || rb_is_black(tmp2)) {
324 /* Case 2 - sibling color flip */
325 rb_set_parent_color(sibling, parent,
326 RB_RED);
327 if (rb_is_red(parent))
328 rb_set_black(parent);
329 else {
330 node = parent;
331 parent = rb_parent(node);
332 if (parent)
333 continue;
334 }
335 break;
336 }
337 /* Case 3 - right rotate at sibling */
338 sibling->rb_right = tmp1 = tmp2->rb_left;
339 tmp2->rb_left = sibling;
340 parent->rb_left = tmp2;
341 if (tmp1)
342 rb_set_parent_color(tmp1, sibling,
343 RB_BLACK);
344 augment_rotate(sibling, tmp2);
345 tmp1 = sibling;
346 sibling = tmp2;
347 }
348 /* Case 4 - left rotate at parent + color flips */
349 parent->rb_left = tmp2 = sibling->rb_right;
350 sibling->rb_right = parent;
351 rb_set_parent_color(tmp1, sibling, RB_BLACK);
352 if (tmp2)
353 rb_set_parent(tmp2, parent);
354 __rb_rotate_set_parents(parent, sibling, root,
355 RB_BLACK);
356 augment_rotate(parent, sibling);
357 break;
358 }
359 }
360}
361
362/* Non-inline version for rb_erase_augmented() use */
363void __rb_erase_color(struct rb_node *parent, struct rb_root *root,
364 void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
365{
366 ____rb_erase_color(parent, root, augment_rotate);
367}
368
369/*
370 * Non-augmented rbtree manipulation functions.
371 *
372 * We use dummy augmented callbacks here, and have the compiler optimize them
373 * out of the rb_insert_color() and rb_erase() function definitions.
374 */
375
376static inline void dummy_propagate(struct rb_node *node, struct rb_node *stop) {}
377static inline void dummy_copy(struct rb_node *old, struct rb_node *new) {}
378static inline void dummy_rotate(struct rb_node *old, struct rb_node *new) {}
379
380static const struct rb_augment_callbacks dummy_callbacks = {
381 dummy_propagate, dummy_copy, dummy_rotate
382};
383
384void rb_insert_color(struct rb_node *node, struct rb_root *root)
385{
386 __rb_insert(node, root, dummy_rotate);
387}
388
389void rb_erase(struct rb_node *node, struct rb_root *root)
390{
391 struct rb_node *rebalance;
392 rebalance = __rb_erase_augmented(node, root, &dummy_callbacks);
393 if (rebalance)
394 ____rb_erase_color(rebalance, root, dummy_rotate);
395}
396
397/*
398 * Augmented rbtree manipulation functions.
399 *
400 * This instantiates the same __always_inline functions as in the non-augmented
401 * case, but this time with user-defined callbacks.
402 */
403
404void __rb_insert_augmented(struct rb_node *node, struct rb_root *root,
405 void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
406{
407 __rb_insert(node, root, augment_rotate);
408}
409
410/*
411 * This function returns the first node (in sort order) of the tree.
412 */
413struct rb_node *rb_first(const struct rb_root *root)
414{
415 struct rb_node *n;
416
417 n = root->rb_node;
418 if (!n)
419 return NULL;
420 while (n->rb_left)
421 n = n->rb_left;
422 return n;
423}
424
425struct rb_node *rb_last(const struct rb_root *root)
426{
427 struct rb_node *n;
428
429 n = root->rb_node;
430 if (!n)
431 return NULL;
432 while (n->rb_right)
433 n = n->rb_right;
434 return n;
435}
436
437struct rb_node *rb_next(const struct rb_node *node)
438{
439 struct rb_node *parent;
440
441 if (RB_EMPTY_NODE(node))
442 return NULL;
443
444 /*
445 * If we have a right-hand child, go down and then left as far
446 * as we can.
447 */
448 if (node->rb_right) {
449 node = node->rb_right;
450 while (node->rb_left)
451 node=node->rb_left;
452 return (struct rb_node *)node;
453 }
454
455 /*
456 * No right-hand children. Everything down and left is smaller than us,
457 * so any 'next' node must be in the general direction of our parent.
458 * Go up the tree; any time the ancestor is a right-hand child of its
459 * parent, keep going up. First time it's a left-hand child of its
460 * parent, said parent is our 'next' node.
461 */
462 while ((parent = rb_parent(node)) && node == parent->rb_right)
463 node = parent;
464
465 return parent;
466}
467
468struct rb_node *rb_prev(const struct rb_node *node)
469{
470 struct rb_node *parent;
471
472 if (RB_EMPTY_NODE(node))
473 return NULL;
474
475 /*
476 * If we have a left-hand child, go down and then right as far
477 * as we can.
478 */
479 if (node->rb_left) {
480 node = node->rb_left;
481 while (node->rb_right)
482 node=node->rb_right;
483 return (struct rb_node *)node;
484 }
485
486 /*
487 * No left-hand children. Go up till we find an ancestor which
488 * is a right-hand child of its parent.
489 */
490 while ((parent = rb_parent(node)) && node == parent->rb_left)
491 node = parent;
492
493 return parent;
494}
495
496void rb_replace_node(struct rb_node *victim, struct rb_node *new,
497 struct rb_root *root)
498{
499 struct rb_node *parent = rb_parent(victim);
500
501 /* Set the surrounding nodes to point to the replacement */
502 __rb_change_child(victim, new, parent, root);
503 if (victim->rb_left)
504 rb_set_parent(victim->rb_left, new);
505 if (victim->rb_right)
506 rb_set_parent(victim->rb_right, new);
507
508 /* Copy the pointers/colour from the victim to the replacement */
509 *new = *victim;
510}
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}
541
542struct rb_node *rb_first_postorder(const struct rb_root *root)
543{
544 if (!root->rb_node)
545 return NULL;
546
547 return rb_left_deepest_node(root->rb_node);
548}