1 // SPDX-License-Identifier: GPL-2.0-or-later
4 (C) 1999 Andrea Arcangeli <andrea@suse.de>
5 (C) 2002 David Woodhouse <dwmw2@infradead.org>
6 (C) 2012 Michel Lespinasse <walken@google.com>
12 #include <linux/rbtree_augmented.h>
13 #include <linux/export.h>
16 * red-black trees properties: http://en.wikipedia.org/wiki/Rbtree
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
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.
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.
36 * Notes on lockless lookups:
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.
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.
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.
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.
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
59 static inline void rb_set_black(struct rb_node *rb)
61 rb->__rb_parent_color |= RB_BLACK;
64 static inline struct rb_node *rb_red_parent(struct rb_node *red)
66 return (struct rb_node *)red->__rb_parent_color;
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.
75 __rb_rotate_set_parents(struct rb_node *old, struct rb_node *new,
76 struct rb_root *root, int color)
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);
84 static __always_inline void
85 __rb_insert(struct rb_node *node, struct rb_root *root,
86 bool newleft, struct rb_node **leftmost,
87 void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
89 struct rb_node *parent = rb_red_parent(node), *gparent, *tmp;
96 * Loop invariant: node is red.
98 if (unlikely(!parent)) {
100 * The inserted node is root. Either this is the
101 * first node, or we recursed at Case 1 below and
102 * are no longer violating 4).
104 rb_set_parent_color(node, NULL, RB_BLACK);
109 * If there is a black parent, we are done.
110 * Otherwise, take some corrective action as,
111 * per 4), we don't want a red root or two
112 * consecutive red nodes.
114 if(rb_is_black(parent))
117 gparent = rb_red_parent(parent);
119 tmp = gparent->rb_right;
120 if (parent != tmp) { /* parent == gparent->rb_left */
121 if (tmp && rb_is_red(tmp)) {
123 * Case 1 - node's uncle is red (color flips).
131 * However, since g's parent might be red, and
132 * 4) does not allow this, we need to recurse
135 rb_set_parent_color(tmp, gparent, RB_BLACK);
136 rb_set_parent_color(parent, gparent, RB_BLACK);
138 parent = rb_parent(node);
139 rb_set_parent_color(node, parent, RB_RED);
143 tmp = parent->rb_right;
146 * Case 2 - node's uncle is black and node is
147 * the parent's right child (left rotate at parent).
155 * This still leaves us in violation of 4), the
156 * continuation into Case 3 will fix that.
159 WRITE_ONCE(parent->rb_right, tmp);
160 WRITE_ONCE(node->rb_left, parent);
162 rb_set_parent_color(tmp, parent,
164 rb_set_parent_color(parent, node, RB_RED);
165 augment_rotate(parent, node);
167 tmp = node->rb_right;
171 * Case 3 - node's uncle is black and node is
172 * the parent's left child (right rotate at gparent).
180 WRITE_ONCE(gparent->rb_left, tmp); /* == parent->rb_right */
181 WRITE_ONCE(parent->rb_right, gparent);
183 rb_set_parent_color(tmp, gparent, RB_BLACK);
184 __rb_rotate_set_parents(gparent, parent, root, RB_RED);
185 augment_rotate(gparent, parent);
188 tmp = gparent->rb_left;
189 if (tmp && rb_is_red(tmp)) {
190 /* Case 1 - color flips */
191 rb_set_parent_color(tmp, gparent, RB_BLACK);
192 rb_set_parent_color(parent, gparent, RB_BLACK);
194 parent = rb_parent(node);
195 rb_set_parent_color(node, parent, RB_RED);
199 tmp = parent->rb_left;
201 /* Case 2 - right rotate at parent */
202 tmp = node->rb_right;
203 WRITE_ONCE(parent->rb_left, tmp);
204 WRITE_ONCE(node->rb_right, parent);
206 rb_set_parent_color(tmp, parent,
208 rb_set_parent_color(parent, node, RB_RED);
209 augment_rotate(parent, node);
214 /* Case 3 - left rotate at gparent */
215 WRITE_ONCE(gparent->rb_right, tmp); /* == parent->rb_left */
216 WRITE_ONCE(parent->rb_left, gparent);
218 rb_set_parent_color(tmp, gparent, RB_BLACK);
219 __rb_rotate_set_parents(gparent, parent, root, RB_RED);
220 augment_rotate(gparent, parent);
227 * Inline version for rb_erase() use - we want to be able to inline
228 * and eliminate the dummy_rotate callback there
230 static __always_inline void
231 ____rb_erase_color(struct rb_node *parent, struct rb_root *root,
232 void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
234 struct rb_node *node = NULL, *sibling, *tmp1, *tmp2;
239 * - node is black (or NULL on first iteration)
240 * - node is not the root (parent is not NULL)
241 * - All leaf paths going through parent and node have a
242 * black node count that is 1 lower than other leaf paths.
244 sibling = parent->rb_right;
245 if (node != sibling) { /* node == parent->rb_left */
246 if (rb_is_red(sibling)) {
248 * Case 1 - left rotate at parent
256 tmp1 = sibling->rb_left;
257 WRITE_ONCE(parent->rb_right, tmp1);
258 WRITE_ONCE(sibling->rb_left, parent);
259 rb_set_parent_color(tmp1, parent, RB_BLACK);
260 __rb_rotate_set_parents(parent, sibling, root,
262 augment_rotate(parent, sibling);
265 tmp1 = sibling->rb_right;
266 if (!tmp1 || rb_is_black(tmp1)) {
267 tmp2 = sibling->rb_left;
268 if (!tmp2 || rb_is_black(tmp2)) {
270 * Case 2 - sibling color flip
271 * (p could be either color here)
279 * This leaves us violating 5) which
280 * can be fixed by flipping p to black
281 * if it was red, or by recursing at p.
282 * p is red when coming from Case 1.
284 rb_set_parent_color(sibling, parent,
286 if (rb_is_red(parent))
287 rb_set_black(parent);
290 parent = rb_parent(node);
297 * Case 3 - right rotate at sibling
298 * (p could be either color here)
308 * Note: p might be red, and then both
309 * p and sl are red after rotation(which
310 * breaks property 4). This is fixed in
311 * Case 4 (in __rb_rotate_set_parents()
312 * which set sl the color of p
313 * and set p RB_BLACK)
323 tmp1 = tmp2->rb_right;
324 WRITE_ONCE(sibling->rb_left, tmp1);
325 WRITE_ONCE(tmp2->rb_right, sibling);
326 WRITE_ONCE(parent->rb_right, tmp2);
328 rb_set_parent_color(tmp1, sibling,
330 augment_rotate(sibling, tmp2);
335 * Case 4 - left rotate at parent + color flips
336 * (p and sl could be either color here.
337 * After rotation, p becomes black, s acquires
338 * p's color, and sl keeps its color)
346 tmp2 = sibling->rb_left;
347 WRITE_ONCE(parent->rb_right, tmp2);
348 WRITE_ONCE(sibling->rb_left, parent);
349 rb_set_parent_color(tmp1, sibling, RB_BLACK);
351 rb_set_parent(tmp2, parent);
352 __rb_rotate_set_parents(parent, sibling, root,
354 augment_rotate(parent, sibling);
357 sibling = parent->rb_left;
358 if (rb_is_red(sibling)) {
359 /* Case 1 - right rotate at parent */
360 tmp1 = sibling->rb_right;
361 WRITE_ONCE(parent->rb_left, tmp1);
362 WRITE_ONCE(sibling->rb_right, parent);
363 rb_set_parent_color(tmp1, parent, RB_BLACK);
364 __rb_rotate_set_parents(parent, sibling, root,
366 augment_rotate(parent, sibling);
369 tmp1 = sibling->rb_left;
370 if (!tmp1 || rb_is_black(tmp1)) {
371 tmp2 = sibling->rb_right;
372 if (!tmp2 || rb_is_black(tmp2)) {
373 /* Case 2 - sibling color flip */
374 rb_set_parent_color(sibling, parent,
376 if (rb_is_red(parent))
377 rb_set_black(parent);
380 parent = rb_parent(node);
386 /* Case 3 - left rotate at sibling */
387 tmp1 = tmp2->rb_left;
388 WRITE_ONCE(sibling->rb_right, tmp1);
389 WRITE_ONCE(tmp2->rb_left, sibling);
390 WRITE_ONCE(parent->rb_left, tmp2);
392 rb_set_parent_color(tmp1, sibling,
394 augment_rotate(sibling, tmp2);
398 /* Case 4 - right rotate at parent + color flips */
399 tmp2 = sibling->rb_right;
400 WRITE_ONCE(parent->rb_left, tmp2);
401 WRITE_ONCE(sibling->rb_right, parent);
402 rb_set_parent_color(tmp1, sibling, RB_BLACK);
404 rb_set_parent(tmp2, parent);
405 __rb_rotate_set_parents(parent, sibling, root,
407 augment_rotate(parent, sibling);
413 /* Non-inline version for rb_erase_augmented() use */
414 void __rb_erase_color(struct rb_node *parent, struct rb_root *root,
415 void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
417 ____rb_erase_color(parent, root, augment_rotate);
421 * Non-augmented rbtree manipulation functions.
423 * We use dummy augmented callbacks here, and have the compiler optimize them
424 * out of the rb_insert_color() and rb_erase() function definitions.
427 static inline void dummy_propagate(struct rb_node *node, struct rb_node *stop) {}
428 static inline void dummy_copy(struct rb_node *old, struct rb_node *new) {}
429 static inline void dummy_rotate(struct rb_node *old, struct rb_node *new) {}
431 static const struct rb_augment_callbacks dummy_callbacks = {
432 .propagate = dummy_propagate,
434 .rotate = dummy_rotate
437 void rb_insert_color(struct rb_node *node, struct rb_root *root)
439 __rb_insert(node, root, false, NULL, dummy_rotate);
442 void rb_erase(struct rb_node *node, struct rb_root *root)
444 struct rb_node *rebalance;
445 rebalance = __rb_erase_augmented(node, root,
446 NULL, &dummy_callbacks);
448 ____rb_erase_color(rebalance, root, dummy_rotate);
451 void rb_insert_color_cached(struct rb_node *node,
452 struct rb_root_cached *root, bool leftmost)
454 __rb_insert(node, &root->rb_root, leftmost,
455 &root->rb_leftmost, dummy_rotate);
458 void rb_erase_cached(struct rb_node *node, struct rb_root_cached *root)
460 struct rb_node *rebalance;
461 rebalance = __rb_erase_augmented(node, &root->rb_root,
462 &root->rb_leftmost, &dummy_callbacks);
464 ____rb_erase_color(rebalance, &root->rb_root, dummy_rotate);
468 * Augmented rbtree manipulation functions.
470 * This instantiates the same __always_inline functions as in the non-augmented
471 * case, but this time with user-defined callbacks.
474 void __rb_insert_augmented(struct rb_node *node, struct rb_root *root,
475 bool newleft, struct rb_node **leftmost,
476 void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
478 __rb_insert(node, root, newleft, leftmost, augment_rotate);
482 * This function returns the first node (in sort order) of the tree.
484 struct rb_node *rb_first(const struct rb_root *root)
496 struct rb_node *rb_last(const struct rb_root *root)
508 struct rb_node *rb_next(const struct rb_node *node)
510 struct rb_node *parent;
512 if (RB_EMPTY_NODE(node))
516 * If we have a right-hand child, go down and then left as far
519 if (node->rb_right) {
520 node = node->rb_right;
521 while (node->rb_left)
523 return (struct rb_node *)node;
527 * No right-hand children. Everything down and left is smaller than us,
528 * so any 'next' node must be in the general direction of our parent.
529 * Go up the tree; any time the ancestor is a right-hand child of its
530 * parent, keep going up. First time it's a left-hand child of its
531 * parent, said parent is our 'next' node.
533 while ((parent = rb_parent(node)) && node == parent->rb_right)
539 struct rb_node *rb_prev(const struct rb_node *node)
541 struct rb_node *parent;
543 if (RB_EMPTY_NODE(node))
547 * If we have a left-hand child, go down and then right as far
551 node = node->rb_left;
552 while (node->rb_right)
554 return (struct rb_node *)node;
558 * No left-hand children. Go up till we find an ancestor which
559 * is a right-hand child of its parent.
561 while ((parent = rb_parent(node)) && node == parent->rb_left)
567 void rb_replace_node(struct rb_node *victim, struct rb_node *new,
568 struct rb_root *root)
570 struct rb_node *parent = rb_parent(victim);
572 /* Copy the pointers/colour from the victim to the replacement */
575 /* Set the surrounding nodes to point to the replacement */
577 rb_set_parent(victim->rb_left, new);
578 if (victim->rb_right)
579 rb_set_parent(victim->rb_right, new);
580 __rb_change_child(victim, new, parent, root);
583 void rb_replace_node_cached(struct rb_node *victim, struct rb_node *new,
584 struct rb_root_cached *root)
586 rb_replace_node(victim, new, &root->rb_root);
588 if (root->rb_leftmost == victim)
589 root->rb_leftmost = new;
592 static struct rb_node *rb_left_deepest_node(const struct rb_node *node)
596 node = node->rb_left;
597 else if (node->rb_right)
598 node = node->rb_right;
600 return (struct rb_node *)node;
604 struct rb_node *rb_next_postorder(const struct rb_node *node)
606 const struct rb_node *parent;
609 parent = rb_parent(node);
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);
617 /* Otherwise we are the parent's right node, and the parent
619 return (struct rb_node *)parent;
622 struct rb_node *rb_first_postorder(const struct rb_root *root)
627 return rb_left_deepest_node(root->rb_node);