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 (unlikely(!parent)) {
112 * The inserted node is root. Either this is the
113 * first node, or we recursed at Case 1 below and
114 * are no longer violating 4).
116 rb_set_parent_color(node, NULL, RB_BLACK);
121 * If there is a black parent, we are done.
122 * Otherwise, take some corrective action as,
123 * per 4), we don't want a red root or two
124 * consecutive red nodes.
126 if(rb_is_black(parent))
129 gparent = rb_red_parent(parent);
131 tmp = gparent->rb_right;
132 if (parent != tmp) { /* parent == gparent->rb_left */
133 if (tmp && rb_is_red(tmp)) {
135 * Case 1 - node's uncle is red (color flips).
143 * However, since g's parent might be red, and
144 * 4) does not allow this, we need to recurse
147 rb_set_parent_color(tmp, gparent, RB_BLACK);
148 rb_set_parent_color(parent, gparent, RB_BLACK);
150 parent = rb_parent(node);
151 rb_set_parent_color(node, parent, RB_RED);
155 tmp = parent->rb_right;
158 * Case 2 - node's uncle is black and node is
159 * the parent's right child (left rotate at parent).
167 * This still leaves us in violation of 4), the
168 * continuation into Case 3 will fix that.
171 WRITE_ONCE(parent->rb_right, tmp);
172 WRITE_ONCE(node->rb_left, parent);
174 rb_set_parent_color(tmp, parent,
176 rb_set_parent_color(parent, node, RB_RED);
177 augment_rotate(parent, node);
179 tmp = node->rb_right;
183 * Case 3 - node's uncle is black and node is
184 * the parent's left child (right rotate at gparent).
192 WRITE_ONCE(gparent->rb_left, tmp); /* == parent->rb_right */
193 WRITE_ONCE(parent->rb_right, gparent);
195 rb_set_parent_color(tmp, gparent, RB_BLACK);
196 __rb_rotate_set_parents(gparent, parent, root, RB_RED);
197 augment_rotate(gparent, parent);
200 tmp = gparent->rb_left;
201 if (tmp && rb_is_red(tmp)) {
202 /* Case 1 - color flips */
203 rb_set_parent_color(tmp, gparent, RB_BLACK);
204 rb_set_parent_color(parent, gparent, RB_BLACK);
206 parent = rb_parent(node);
207 rb_set_parent_color(node, parent, RB_RED);
211 tmp = parent->rb_left;
213 /* Case 2 - right rotate at parent */
214 tmp = node->rb_right;
215 WRITE_ONCE(parent->rb_left, tmp);
216 WRITE_ONCE(node->rb_right, parent);
218 rb_set_parent_color(tmp, parent,
220 rb_set_parent_color(parent, node, RB_RED);
221 augment_rotate(parent, node);
226 /* Case 3 - left rotate at gparent */
227 WRITE_ONCE(gparent->rb_right, tmp); /* == parent->rb_left */
228 WRITE_ONCE(parent->rb_left, gparent);
230 rb_set_parent_color(tmp, gparent, RB_BLACK);
231 __rb_rotate_set_parents(gparent, parent, root, RB_RED);
232 augment_rotate(gparent, parent);
239 * Inline version for rb_erase() use - we want to be able to inline
240 * and eliminate the dummy_rotate callback there
242 static __always_inline void
243 ____rb_erase_color(struct rb_node *parent, struct rb_root *root,
244 void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
246 struct rb_node *node = NULL, *sibling, *tmp1, *tmp2;
251 * - node is black (or NULL on first iteration)
252 * - node is not the root (parent is not NULL)
253 * - All leaf paths going through parent and node have a
254 * black node count that is 1 lower than other leaf paths.
256 sibling = parent->rb_right;
257 if (node != sibling) { /* node == parent->rb_left */
258 if (rb_is_red(sibling)) {
260 * Case 1 - left rotate at parent
268 tmp1 = sibling->rb_left;
269 WRITE_ONCE(parent->rb_right, tmp1);
270 WRITE_ONCE(sibling->rb_left, parent);
271 rb_set_parent_color(tmp1, parent, RB_BLACK);
272 __rb_rotate_set_parents(parent, sibling, root,
274 augment_rotate(parent, sibling);
277 tmp1 = sibling->rb_right;
278 if (!tmp1 || rb_is_black(tmp1)) {
279 tmp2 = sibling->rb_left;
280 if (!tmp2 || rb_is_black(tmp2)) {
282 * Case 2 - sibling color flip
283 * (p could be either color here)
291 * This leaves us violating 5) which
292 * can be fixed by flipping p to black
293 * if it was red, or by recursing at p.
294 * p is red when coming from Case 1.
296 rb_set_parent_color(sibling, parent,
298 if (rb_is_red(parent))
299 rb_set_black(parent);
302 parent = rb_parent(node);
309 * Case 3 - right rotate at sibling
310 * (p could be either color here)
320 * Note: p might be red, and then both
321 * p and sl are red after rotation(which
322 * breaks property 4). This is fixed in
323 * Case 4 (in __rb_rotate_set_parents()
324 * which set sl the color of p
325 * and set p RB_BLACK)
335 tmp1 = tmp2->rb_right;
336 WRITE_ONCE(sibling->rb_left, tmp1);
337 WRITE_ONCE(tmp2->rb_right, sibling);
338 WRITE_ONCE(parent->rb_right, tmp2);
340 rb_set_parent_color(tmp1, sibling,
342 augment_rotate(sibling, tmp2);
347 * Case 4 - left rotate at parent + color flips
348 * (p and sl could be either color here.
349 * After rotation, p becomes black, s acquires
350 * p's color, and sl keeps its color)
358 tmp2 = sibling->rb_left;
359 WRITE_ONCE(parent->rb_right, tmp2);
360 WRITE_ONCE(sibling->rb_left, parent);
361 rb_set_parent_color(tmp1, sibling, RB_BLACK);
363 rb_set_parent(tmp2, parent);
364 __rb_rotate_set_parents(parent, sibling, root,
366 augment_rotate(parent, sibling);
369 sibling = parent->rb_left;
370 if (rb_is_red(sibling)) {
371 /* Case 1 - right rotate at parent */
372 tmp1 = sibling->rb_right;
373 WRITE_ONCE(parent->rb_left, tmp1);
374 WRITE_ONCE(sibling->rb_right, parent);
375 rb_set_parent_color(tmp1, parent, RB_BLACK);
376 __rb_rotate_set_parents(parent, sibling, root,
378 augment_rotate(parent, sibling);
381 tmp1 = sibling->rb_left;
382 if (!tmp1 || rb_is_black(tmp1)) {
383 tmp2 = sibling->rb_right;
384 if (!tmp2 || rb_is_black(tmp2)) {
385 /* Case 2 - sibling color flip */
386 rb_set_parent_color(sibling, parent,
388 if (rb_is_red(parent))
389 rb_set_black(parent);
392 parent = rb_parent(node);
398 /* Case 3 - left rotate at sibling */
399 tmp1 = tmp2->rb_left;
400 WRITE_ONCE(sibling->rb_right, tmp1);
401 WRITE_ONCE(tmp2->rb_left, sibling);
402 WRITE_ONCE(parent->rb_left, tmp2);
404 rb_set_parent_color(tmp1, sibling,
406 augment_rotate(sibling, tmp2);
410 /* Case 4 - right rotate at parent + color flips */
411 tmp2 = sibling->rb_right;
412 WRITE_ONCE(parent->rb_left, tmp2);
413 WRITE_ONCE(sibling->rb_right, parent);
414 rb_set_parent_color(tmp1, sibling, RB_BLACK);
416 rb_set_parent(tmp2, parent);
417 __rb_rotate_set_parents(parent, sibling, root,
419 augment_rotate(parent, sibling);
425 /* Non-inline version for rb_erase_augmented() use */
426 void __rb_erase_color(struct rb_node *parent, struct rb_root *root,
427 void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
429 ____rb_erase_color(parent, root, augment_rotate);
431 EXPORT_SYMBOL(__rb_erase_color);
434 * Non-augmented rbtree manipulation functions.
436 * We use dummy augmented callbacks here, and have the compiler optimize them
437 * out of the rb_insert_color() and rb_erase() function definitions.
440 static inline void dummy_propagate(struct rb_node *node, struct rb_node *stop) {}
441 static inline void dummy_copy(struct rb_node *old, struct rb_node *new) {}
442 static inline void dummy_rotate(struct rb_node *old, struct rb_node *new) {}
444 static const struct rb_augment_callbacks dummy_callbacks = {
445 .propagate = dummy_propagate,
447 .rotate = dummy_rotate
450 void rb_insert_color(struct rb_node *node, struct rb_root *root)
452 __rb_insert(node, root, false, NULL, dummy_rotate);
454 EXPORT_SYMBOL(rb_insert_color);
456 void rb_erase(struct rb_node *node, struct rb_root *root)
458 struct rb_node *rebalance;
459 rebalance = __rb_erase_augmented(node, root,
460 NULL, &dummy_callbacks);
462 ____rb_erase_color(rebalance, root, dummy_rotate);
464 EXPORT_SYMBOL(rb_erase);
466 void rb_insert_color_cached(struct rb_node *node,
467 struct rb_root_cached *root, bool leftmost)
469 __rb_insert(node, &root->rb_root, leftmost,
470 &root->rb_leftmost, dummy_rotate);
472 EXPORT_SYMBOL(rb_insert_color_cached);
474 void rb_erase_cached(struct rb_node *node, struct rb_root_cached *root)
476 struct rb_node *rebalance;
477 rebalance = __rb_erase_augmented(node, &root->rb_root,
478 &root->rb_leftmost, &dummy_callbacks);
480 ____rb_erase_color(rebalance, &root->rb_root, dummy_rotate);
482 EXPORT_SYMBOL(rb_erase_cached);
485 * Augmented rbtree manipulation functions.
487 * This instantiates the same __always_inline functions as in the non-augmented
488 * case, but this time with user-defined callbacks.
491 void __rb_insert_augmented(struct rb_node *node, struct rb_root *root,
492 bool newleft, struct rb_node **leftmost,
493 void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
495 __rb_insert(node, root, newleft, leftmost, augment_rotate);
497 EXPORT_SYMBOL(__rb_insert_augmented);
500 * This function returns the first node (in sort order) of the tree.
502 struct rb_node *rb_first(const struct rb_root *root)
513 EXPORT_SYMBOL(rb_first);
515 struct rb_node *rb_last(const struct rb_root *root)
526 EXPORT_SYMBOL(rb_last);
528 struct rb_node *rb_next(const struct rb_node *node)
530 struct rb_node *parent;
532 if (RB_EMPTY_NODE(node))
536 * If we have a right-hand child, go down and then left as far
539 if (node->rb_right) {
540 node = node->rb_right;
541 while (node->rb_left)
543 return (struct rb_node *)node;
547 * No right-hand children. Everything down and left is smaller than us,
548 * so any 'next' node must be in the general direction of our parent.
549 * Go up the tree; any time the ancestor is a right-hand child of its
550 * parent, keep going up. First time it's a left-hand child of its
551 * parent, said parent is our 'next' node.
553 while ((parent = rb_parent(node)) && node == parent->rb_right)
558 EXPORT_SYMBOL(rb_next);
560 struct rb_node *rb_prev(const struct rb_node *node)
562 struct rb_node *parent;
564 if (RB_EMPTY_NODE(node))
568 * If we have a left-hand child, go down and then right as far
572 node = node->rb_left;
573 while (node->rb_right)
575 return (struct rb_node *)node;
579 * No left-hand children. Go up till we find an ancestor which
580 * is a right-hand child of its parent.
582 while ((parent = rb_parent(node)) && node == parent->rb_left)
587 EXPORT_SYMBOL(rb_prev);
589 void rb_replace_node(struct rb_node *victim, struct rb_node *new,
590 struct rb_root *root)
592 struct rb_node *parent = rb_parent(victim);
594 /* Copy the pointers/colour from the victim to the replacement */
597 /* Set the surrounding nodes to point to the replacement */
599 rb_set_parent(victim->rb_left, new);
600 if (victim->rb_right)
601 rb_set_parent(victim->rb_right, new);
602 __rb_change_child(victim, new, parent, root);
604 EXPORT_SYMBOL(rb_replace_node);
606 void rb_replace_node_rcu(struct rb_node *victim, struct rb_node *new,
607 struct rb_root *root)
609 struct rb_node *parent = rb_parent(victim);
611 /* Copy the pointers/colour from the victim to the replacement */
614 /* Set the surrounding nodes to point to the replacement */
616 rb_set_parent(victim->rb_left, new);
617 if (victim->rb_right)
618 rb_set_parent(victim->rb_right, new);
620 /* Set the parent's pointer to the new node last after an RCU barrier
621 * so that the pointers onwards are seen to be set correctly when doing
622 * an RCU walk over the tree.
624 __rb_change_child_rcu(victim, new, parent, root);
626 EXPORT_SYMBOL(rb_replace_node_rcu);
628 static struct rb_node *rb_left_deepest_node(const struct rb_node *node)
632 node = node->rb_left;
633 else if (node->rb_right)
634 node = node->rb_right;
636 return (struct rb_node *)node;
640 struct rb_node *rb_next_postorder(const struct rb_node *node)
642 const struct rb_node *parent;
645 parent = rb_parent(node);
647 /* If we're sitting on node, we've already seen our children */
648 if (parent && node == parent->rb_left && parent->rb_right) {
649 /* If we are the parent's left node, go to the parent's right
650 * node then all the way down to the left */
651 return rb_left_deepest_node(parent->rb_right);
653 /* Otherwise we are the parent's right node, and the parent
655 return (struct rb_node *)parent;
657 EXPORT_SYMBOL(rb_next_postorder);
659 struct rb_node *rb_first_postorder(const struct rb_root *root)
664 return rb_left_deepest_node(root->rb_node);
666 EXPORT_SYMBOL(rb_first_postorder);