3 (C) 1999 Andrea Arcangeli <andrea@suse.de>
4 (C) 2002 David Woodhouse <dwmw2@infradead.org>
5 (C) 2012 Michel Lespinasse <walken@google.com>
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.
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.
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
24 #include <linux/rbtree_augmented.h>
25 #include <linux/export.h>
28 * red-black trees properties: http://en.wikipedia.org/wiki/Rbtree
30 * 1) A node is either red or black
31 * 2) The root is black
32 * 3) All leaves (NULL) are black
33 * 4) Both children of every red node are black
34 * 5) Every simple path from root to leaves contains the same number
37 * 4 and 5 give the O(log n) guarantee, since 4 implies you cannot have two
38 * consecutive red nodes in a path and every red node is therefore followed by
39 * a black. So if B is the number of black nodes on every simple path (as per
40 * 5), then the longest possible path due to 4 is 2B.
42 * We shall indicate color with case, where black nodes are uppercase and red
43 * nodes will be lowercase. Unknown color nodes shall be drawn as red within
44 * parentheses and have some accompanying text comment.
48 * Notes on lockless lookups:
50 * All stores to the tree structure (rb_left and rb_right) must be done using
51 * WRITE_ONCE(). And we must not inadvertently cause (temporary) loops in the
52 * tree structure as seen in program order.
54 * These two requirements will allow lockless iteration of the tree -- not
55 * correct iteration mind you, tree rotations are not atomic so a lookup might
56 * miss entire subtrees.
58 * But they do guarantee that any such traversal will only see valid elements
59 * and that it will indeed complete -- does not get stuck in a loop.
61 * It also guarantees that if the lookup returns an element it is the 'correct'
62 * one. But not returning an element does _NOT_ mean it's not present.
66 * Stores to __rb_parent_color are not important for simple lookups so those
67 * are left undone as of now. Nor did I check for loops involving parent
71 static inline void rb_set_black(struct rb_node *rb)
73 rb->__rb_parent_color |= RB_BLACK;
76 static inline struct rb_node *rb_red_parent(struct rb_node *red)
78 return (struct rb_node *)red->__rb_parent_color;
82 * Helper function for rotations:
83 * - old's parent and color get assigned to new
84 * - old gets assigned new as a parent and 'color' as a color.
87 __rb_rotate_set_parents(struct rb_node *old, struct rb_node *new,
88 struct rb_root *root, int color)
90 struct rb_node *parent = rb_parent(old);
91 new->__rb_parent_color = old->__rb_parent_color;
92 rb_set_parent_color(old, new, color);
93 __rb_change_child(old, new, parent, root);
96 static __always_inline void
97 __rb_insert(struct rb_node *node, struct rb_root *root,
98 bool newleft, struct rb_node **leftmost,
99 void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
101 struct rb_node *parent = rb_red_parent(node), *gparent, *tmp;
108 * Loop invariant: node is red
110 * If there is a black parent, we are done.
111 * Otherwise, take some corrective action as we don't
112 * want a red root or two consecutive red nodes.
115 rb_set_parent_color(node, NULL, RB_BLACK);
117 } else if (rb_is_black(parent))
120 gparent = rb_red_parent(parent);
122 tmp = gparent->rb_right;
123 if (parent != tmp) { /* parent == gparent->rb_left */
124 if (tmp && rb_is_red(tmp)) {
126 * Case 1 - color flips
134 * However, since g's parent might be red, and
135 * 4) does not allow this, we need to recurse
138 rb_set_parent_color(tmp, gparent, RB_BLACK);
139 rb_set_parent_color(parent, gparent, RB_BLACK);
141 parent = rb_parent(node);
142 rb_set_parent_color(node, parent, RB_RED);
146 tmp = parent->rb_right;
149 * Case 2 - left rotate at parent
157 * This still leaves us in violation of 4), the
158 * continuation into Case 3 will fix that.
161 WRITE_ONCE(parent->rb_right, tmp);
162 WRITE_ONCE(node->rb_left, parent);
164 rb_set_parent_color(tmp, parent,
166 rb_set_parent_color(parent, node, RB_RED);
167 augment_rotate(parent, node);
169 tmp = node->rb_right;
173 * Case 3 - right rotate at gparent
181 WRITE_ONCE(gparent->rb_left, tmp); /* == parent->rb_right */
182 WRITE_ONCE(parent->rb_right, gparent);
184 rb_set_parent_color(tmp, gparent, RB_BLACK);
185 __rb_rotate_set_parents(gparent, parent, root, RB_RED);
186 augment_rotate(gparent, parent);
189 tmp = gparent->rb_left;
190 if (tmp && rb_is_red(tmp)) {
191 /* Case 1 - color flips */
192 rb_set_parent_color(tmp, gparent, RB_BLACK);
193 rb_set_parent_color(parent, gparent, RB_BLACK);
195 parent = rb_parent(node);
196 rb_set_parent_color(node, parent, RB_RED);
200 tmp = parent->rb_left;
202 /* Case 2 - right rotate at parent */
203 tmp = node->rb_right;
204 WRITE_ONCE(parent->rb_left, tmp);
205 WRITE_ONCE(node->rb_right, parent);
207 rb_set_parent_color(tmp, parent,
209 rb_set_parent_color(parent, node, RB_RED);
210 augment_rotate(parent, node);
215 /* Case 3 - left rotate at gparent */
216 WRITE_ONCE(gparent->rb_right, tmp); /* == parent->rb_left */
217 WRITE_ONCE(parent->rb_left, gparent);
219 rb_set_parent_color(tmp, gparent, RB_BLACK);
220 __rb_rotate_set_parents(gparent, parent, root, RB_RED);
221 augment_rotate(gparent, parent);
228 * Inline version for rb_erase() use - we want to be able to inline
229 * and eliminate the dummy_rotate callback there
231 static __always_inline void
232 ____rb_erase_color(struct rb_node *parent, struct rb_root *root,
233 void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
235 struct rb_node *node = NULL, *sibling, *tmp1, *tmp2;
240 * - node is black (or NULL on first iteration)
241 * - node is not the root (parent is not NULL)
242 * - All leaf paths going through parent and node have a
243 * black node count that is 1 lower than other leaf paths.
245 sibling = parent->rb_right;
246 if (node != sibling) { /* node == parent->rb_left */
247 if (rb_is_red(sibling)) {
249 * Case 1 - left rotate at parent
257 tmp1 = sibling->rb_left;
258 WRITE_ONCE(parent->rb_right, tmp1);
259 WRITE_ONCE(sibling->rb_left, parent);
260 rb_set_parent_color(tmp1, parent, RB_BLACK);
261 __rb_rotate_set_parents(parent, sibling, root,
263 augment_rotate(parent, sibling);
266 tmp1 = sibling->rb_right;
267 if (!tmp1 || rb_is_black(tmp1)) {
268 tmp2 = sibling->rb_left;
269 if (!tmp2 || rb_is_black(tmp2)) {
271 * Case 2 - sibling color flip
272 * (p could be either color here)
280 * This leaves us violating 5) which
281 * can be fixed by flipping p to black
282 * if it was red, or by recursing at p.
283 * p is red when coming from Case 1.
285 rb_set_parent_color(sibling, parent,
287 if (rb_is_red(parent))
288 rb_set_black(parent);
291 parent = rb_parent(node);
298 * Case 3 - right rotate at sibling
299 * (p could be either color here)
309 tmp1 = tmp2->rb_right;
310 WRITE_ONCE(sibling->rb_left, tmp1);
311 WRITE_ONCE(tmp2->rb_right, sibling);
312 WRITE_ONCE(parent->rb_right, tmp2);
314 rb_set_parent_color(tmp1, sibling,
316 augment_rotate(sibling, tmp2);
321 * Case 4 - left rotate at parent + color flips
322 * (p and sl could be either color here.
323 * After rotation, p becomes black, s acquires
324 * p's color, and sl keeps its color)
332 tmp2 = sibling->rb_left;
333 WRITE_ONCE(parent->rb_right, tmp2);
334 WRITE_ONCE(sibling->rb_left, parent);
335 rb_set_parent_color(tmp1, sibling, RB_BLACK);
337 rb_set_parent(tmp2, parent);
338 __rb_rotate_set_parents(parent, sibling, root,
340 augment_rotate(parent, sibling);
343 sibling = parent->rb_left;
344 if (rb_is_red(sibling)) {
345 /* Case 1 - right rotate at parent */
346 tmp1 = sibling->rb_right;
347 WRITE_ONCE(parent->rb_left, tmp1);
348 WRITE_ONCE(sibling->rb_right, parent);
349 rb_set_parent_color(tmp1, parent, RB_BLACK);
350 __rb_rotate_set_parents(parent, sibling, root,
352 augment_rotate(parent, sibling);
355 tmp1 = sibling->rb_left;
356 if (!tmp1 || rb_is_black(tmp1)) {
357 tmp2 = sibling->rb_right;
358 if (!tmp2 || rb_is_black(tmp2)) {
359 /* Case 2 - sibling color flip */
360 rb_set_parent_color(sibling, parent,
362 if (rb_is_red(parent))
363 rb_set_black(parent);
366 parent = rb_parent(node);
372 /* Case 3 - right rotate at sibling */
373 tmp1 = tmp2->rb_left;
374 WRITE_ONCE(sibling->rb_right, tmp1);
375 WRITE_ONCE(tmp2->rb_left, sibling);
376 WRITE_ONCE(parent->rb_left, tmp2);
378 rb_set_parent_color(tmp1, sibling,
380 augment_rotate(sibling, tmp2);
384 /* Case 4 - left rotate at parent + color flips */
385 tmp2 = sibling->rb_right;
386 WRITE_ONCE(parent->rb_left, tmp2);
387 WRITE_ONCE(sibling->rb_right, parent);
388 rb_set_parent_color(tmp1, sibling, RB_BLACK);
390 rb_set_parent(tmp2, parent);
391 __rb_rotate_set_parents(parent, sibling, root,
393 augment_rotate(parent, sibling);
399 /* Non-inline version for rb_erase_augmented() use */
400 void __rb_erase_color(struct rb_node *parent, struct rb_root *root,
401 void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
403 ____rb_erase_color(parent, root, augment_rotate);
405 EXPORT_SYMBOL(__rb_erase_color);
408 * Non-augmented rbtree manipulation functions.
410 * We use dummy augmented callbacks here, and have the compiler optimize them
411 * out of the rb_insert_color() and rb_erase() function definitions.
414 static inline void dummy_propagate(struct rb_node *node, struct rb_node *stop) {}
415 static inline void dummy_copy(struct rb_node *old, struct rb_node *new) {}
416 static inline void dummy_rotate(struct rb_node *old, struct rb_node *new) {}
418 static const struct rb_augment_callbacks dummy_callbacks = {
419 dummy_propagate, dummy_copy, dummy_rotate
422 void rb_insert_color(struct rb_node *node, struct rb_root *root)
424 __rb_insert(node, root, false, NULL, dummy_rotate);
426 EXPORT_SYMBOL(rb_insert_color);
428 void rb_erase(struct rb_node *node, struct rb_root *root)
430 struct rb_node *rebalance;
431 rebalance = __rb_erase_augmented(node, root,
432 NULL, &dummy_callbacks);
434 ____rb_erase_color(rebalance, root, dummy_rotate);
436 EXPORT_SYMBOL(rb_erase);
438 void rb_insert_color_cached(struct rb_node *node,
439 struct rb_root_cached *root, bool leftmost)
441 __rb_insert(node, &root->rb_root, leftmost,
442 &root->rb_leftmost, dummy_rotate);
444 EXPORT_SYMBOL(rb_insert_color_cached);
446 void rb_erase_cached(struct rb_node *node, struct rb_root_cached *root)
448 struct rb_node *rebalance;
449 rebalance = __rb_erase_augmented(node, &root->rb_root,
450 &root->rb_leftmost, &dummy_callbacks);
452 ____rb_erase_color(rebalance, &root->rb_root, dummy_rotate);
454 EXPORT_SYMBOL(rb_erase_cached);
457 * Augmented rbtree manipulation functions.
459 * This instantiates the same __always_inline functions as in the non-augmented
460 * case, but this time with user-defined callbacks.
463 void __rb_insert_augmented(struct rb_node *node, struct rb_root *root,
464 bool newleft, struct rb_node **leftmost,
465 void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
467 __rb_insert(node, root, newleft, leftmost, augment_rotate);
469 EXPORT_SYMBOL(__rb_insert_augmented);
472 * This function returns the first node (in sort order) of the tree.
474 struct rb_node *rb_first(const struct rb_root *root)
485 EXPORT_SYMBOL(rb_first);
487 struct rb_node *rb_last(const struct rb_root *root)
498 EXPORT_SYMBOL(rb_last);
500 struct rb_node *rb_next(const struct rb_node *node)
502 struct rb_node *parent;
504 if (RB_EMPTY_NODE(node))
508 * If we have a right-hand child, go down and then left as far
511 if (node->rb_right) {
512 node = node->rb_right;
513 while (node->rb_left)
515 return (struct rb_node *)node;
519 * No right-hand children. Everything down and left is smaller than us,
520 * so any 'next' node must be in the general direction of our parent.
521 * Go up the tree; any time the ancestor is a right-hand child of its
522 * parent, keep going up. First time it's a left-hand child of its
523 * parent, said parent is our 'next' node.
525 while ((parent = rb_parent(node)) && node == parent->rb_right)
530 EXPORT_SYMBOL(rb_next);
532 struct rb_node *rb_prev(const struct rb_node *node)
534 struct rb_node *parent;
536 if (RB_EMPTY_NODE(node))
540 * If we have a left-hand child, go down and then right as far
544 node = node->rb_left;
545 while (node->rb_right)
547 return (struct rb_node *)node;
551 * No left-hand children. Go up till we find an ancestor which
552 * is a right-hand child of its parent.
554 while ((parent = rb_parent(node)) && node == parent->rb_left)
559 EXPORT_SYMBOL(rb_prev);
561 void rb_replace_node(struct rb_node *victim, struct rb_node *new,
562 struct rb_root *root)
564 struct rb_node *parent = rb_parent(victim);
566 /* Copy the pointers/colour from the victim to the replacement */
569 /* Set the surrounding nodes to point to the replacement */
571 rb_set_parent(victim->rb_left, new);
572 if (victim->rb_right)
573 rb_set_parent(victim->rb_right, new);
574 __rb_change_child(victim, new, parent, root);
576 EXPORT_SYMBOL(rb_replace_node);
578 void rb_replace_node_rcu(struct rb_node *victim, struct rb_node *new,
579 struct rb_root *root)
581 struct rb_node *parent = rb_parent(victim);
583 /* Copy the pointers/colour from the victim to the replacement */
586 /* Set the surrounding nodes to point to the replacement */
588 rb_set_parent(victim->rb_left, new);
589 if (victim->rb_right)
590 rb_set_parent(victim->rb_right, new);
592 /* Set the parent's pointer to the new node last after an RCU barrier
593 * so that the pointers onwards are seen to be set correctly when doing
594 * an RCU walk over the tree.
596 __rb_change_child_rcu(victim, new, parent, root);
598 EXPORT_SYMBOL(rb_replace_node_rcu);
600 static struct rb_node *rb_left_deepest_node(const struct rb_node *node)
604 node = node->rb_left;
605 else if (node->rb_right)
606 node = node->rb_right;
608 return (struct rb_node *)node;
612 struct rb_node *rb_next_postorder(const struct rb_node *node)
614 const struct rb_node *parent;
617 parent = rb_parent(node);
619 /* If we're sitting on node, we've already seen our children */
620 if (parent && node == parent->rb_left && parent->rb_right) {
621 /* If we are the parent's left node, go to the parent's right
622 * node then all the way down to the left */
623 return rb_left_deepest_node(parent->rb_right);
625 /* Otherwise we are the parent's right node, and the parent
627 return (struct rb_node *)parent;
629 EXPORT_SYMBOL(rb_next_postorder);
631 struct rb_node *rb_first_postorder(const struct rb_root *root)
636 return rb_left_deepest_node(root->rb_node);
638 EXPORT_SYMBOL(rb_first_postorder);