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 void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
88 struct rb_node *parent = rb_red_parent(node), *gparent, *tmp;
92 * Loop invariant: node is red.
94 if (unlikely(!parent)) {
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).
100 rb_set_parent_color(node, NULL, RB_BLACK);
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.
110 if(rb_is_black(parent))
113 gparent = rb_red_parent(parent);
115 tmp = gparent->rb_right;
116 if (parent != tmp) { /* parent == gparent->rb_left */
117 if (tmp && rb_is_red(tmp)) {
119 * Case 1 - node's uncle is red (color flips).
127 * However, since g's parent might be red, and
128 * 4) does not allow this, we need to recurse
131 rb_set_parent_color(tmp, gparent, RB_BLACK);
132 rb_set_parent_color(parent, gparent, RB_BLACK);
134 parent = rb_parent(node);
135 rb_set_parent_color(node, parent, RB_RED);
139 tmp = parent->rb_right;
142 * Case 2 - node's uncle is black and node is
143 * the parent's right child (left rotate at parent).
151 * This still leaves us in violation of 4), the
152 * continuation into Case 3 will fix that.
155 WRITE_ONCE(parent->rb_right, tmp);
156 WRITE_ONCE(node->rb_left, parent);
158 rb_set_parent_color(tmp, parent,
160 rb_set_parent_color(parent, node, RB_RED);
161 augment_rotate(parent, node);
163 tmp = node->rb_right;
167 * Case 3 - node's uncle is black and node is
168 * the parent's left child (right rotate at gparent).
176 WRITE_ONCE(gparent->rb_left, tmp); /* == parent->rb_right */
177 WRITE_ONCE(parent->rb_right, gparent);
179 rb_set_parent_color(tmp, gparent, RB_BLACK);
180 __rb_rotate_set_parents(gparent, parent, root, RB_RED);
181 augment_rotate(gparent, parent);
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);
190 parent = rb_parent(node);
191 rb_set_parent_color(node, parent, RB_RED);
195 tmp = parent->rb_left;
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);
202 rb_set_parent_color(tmp, parent,
204 rb_set_parent_color(parent, node, RB_RED);
205 augment_rotate(parent, node);
210 /* Case 3 - left rotate at gparent */
211 WRITE_ONCE(gparent->rb_right, tmp); /* == parent->rb_left */
212 WRITE_ONCE(parent->rb_left, gparent);
214 rb_set_parent_color(tmp, gparent, RB_BLACK);
215 __rb_rotate_set_parents(gparent, parent, root, RB_RED);
216 augment_rotate(gparent, parent);
223 * Inline version for rb_erase() use - we want to be able to inline
224 * and eliminate the dummy_rotate callback there
226 static __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))
230 struct rb_node *node = NULL, *sibling, *tmp1, *tmp2;
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.
240 sibling = parent->rb_right;
241 if (node != sibling) { /* node == parent->rb_left */
242 if (rb_is_red(sibling)) {
244 * Case 1 - left rotate at parent
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,
258 augment_rotate(parent, sibling);
261 tmp1 = sibling->rb_right;
262 if (!tmp1 || rb_is_black(tmp1)) {
263 tmp2 = sibling->rb_left;
264 if (!tmp2 || rb_is_black(tmp2)) {
266 * Case 2 - sibling color flip
267 * (p could be either color here)
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.
280 rb_set_parent_color(sibling, parent,
282 if (rb_is_red(parent))
283 rb_set_black(parent);
286 parent = rb_parent(node);
293 * Case 3 - right rotate at sibling
294 * (p could be either color here)
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)
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);
324 rb_set_parent_color(tmp1, sibling,
326 augment_rotate(sibling, tmp2);
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)
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);
347 rb_set_parent(tmp2, parent);
348 __rb_rotate_set_parents(parent, sibling, root,
350 augment_rotate(parent, sibling);
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,
362 augment_rotate(parent, sibling);
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,
372 if (rb_is_red(parent))
373 rb_set_black(parent);
376 parent = rb_parent(node);
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);
388 rb_set_parent_color(tmp1, sibling,
390 augment_rotate(sibling, tmp2);
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);
400 rb_set_parent(tmp2, parent);
401 __rb_rotate_set_parents(parent, sibling, root,
403 augment_rotate(parent, sibling);
409 /* Non-inline version for rb_erase_augmented() use */
410 void __rb_erase_color(struct rb_node *parent, struct rb_root *root,
411 void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
413 ____rb_erase_color(parent, root, augment_rotate);
417 * Non-augmented rbtree manipulation functions.
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.
423 static inline void dummy_propagate(struct rb_node *node, struct rb_node *stop) {}
424 static inline void dummy_copy(struct rb_node *old, struct rb_node *new) {}
425 static inline void dummy_rotate(struct rb_node *old, struct rb_node *new) {}
427 static const struct rb_augment_callbacks dummy_callbacks = {
428 .propagate = dummy_propagate,
430 .rotate = dummy_rotate
433 void rb_insert_color(struct rb_node *node, struct rb_root *root)
435 __rb_insert(node, root, dummy_rotate);
438 void rb_erase(struct rb_node *node, struct rb_root *root)
440 struct rb_node *rebalance;
441 rebalance = __rb_erase_augmented(node, root, &dummy_callbacks);
443 ____rb_erase_color(rebalance, root, dummy_rotate);
447 * Augmented rbtree manipulation functions.
449 * This instantiates the same __always_inline functions as in the non-augmented
450 * case, but this time with user-defined callbacks.
453 void __rb_insert_augmented(struct rb_node *node, struct rb_root *root,
454 void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
456 __rb_insert(node, root, augment_rotate);
460 * This function returns the first node (in sort order) of the tree.
462 struct rb_node *rb_first(const struct rb_root *root)
474 struct rb_node *rb_last(const struct rb_root *root)
486 struct rb_node *rb_next(const struct rb_node *node)
488 struct rb_node *parent;
490 if (RB_EMPTY_NODE(node))
494 * If we have a right-hand child, go down and then left as far
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;
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.
511 while ((parent = rb_parent(node)) && node == parent->rb_right)
517 struct rb_node *rb_prev(const struct rb_node *node)
519 struct rb_node *parent;
521 if (RB_EMPTY_NODE(node))
525 * If we have a left-hand child, go down and then right as far
529 node = node->rb_left;
530 while (node->rb_right)
531 node = node->rb_right;
532 return (struct rb_node *)node;
536 * No left-hand children. Go up till we find an ancestor which
537 * is a right-hand child of its parent.
539 while ((parent = rb_parent(node)) && node == parent->rb_left)
545 void rb_replace_node(struct rb_node *victim, struct rb_node *new,
546 struct rb_root *root)
548 struct rb_node *parent = rb_parent(victim);
550 /* Copy the pointers/colour from the victim to the replacement */
553 /* Set the surrounding nodes to point to the replacement */
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);
561 static struct rb_node *rb_left_deepest_node(const struct rb_node *node)
565 node = node->rb_left;
566 else if (node->rb_right)
567 node = node->rb_right;
569 return (struct rb_node *)node;
573 struct rb_node *rb_next_postorder(const struct rb_node *node)
575 const struct rb_node *parent;
578 parent = rb_parent(node);
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);
586 /* Otherwise we are the parent's right node, and the parent
588 return (struct rb_node *)parent;
591 struct rb_node *rb_first_postorder(const struct rb_root *root)
596 return rb_left_deepest_node(root->rb_node);