Lines Matching +full:root +full:- +full:node
1 // SPDX-License-Identifier: GPL-2.0-or-later
16 * red-black trees properties: https://en.wikipedia.org/wiki/Rbtree
18 * 1) A node is either red or black
19 * 2) The root is black
21 * 4) Both children of every red node are black
22 * 5) Every simple path from root to leaves contains the same number
26 * consecutive red nodes in a path and every red node is therefore followed by
42 * These two requirements will allow lockless iteration of the tree -- not
47 * and that it will indeed complete -- does not get stuck in a loop.
61 rb->__rb_parent_color += RB_BLACK; in rb_set_black()
66 return (struct rb_node *)red->__rb_parent_color; in rb_red_parent()
71 * - old's parent and color get assigned to new
72 * - old gets assigned new as a parent and 'color' as a color.
76 struct rb_root *root, int color) in __rb_rotate_set_parents() argument
79 new->__rb_parent_color = old->__rb_parent_color; in __rb_rotate_set_parents()
81 __rb_change_child(old, new, parent, root); in __rb_rotate_set_parents()
85 __rb_insert(struct rb_node *node, struct rb_root *root, in __rb_insert() argument
88 struct rb_node *parent = rb_red_parent(node), *gparent, *tmp; in __rb_insert()
92 * Loop invariant: node is red. in __rb_insert()
96 * The inserted node is root. Either this is the in __rb_insert()
97 * first node, or we recursed at Case 1 below and in __rb_insert()
100 rb_set_parent_color(node, NULL, RB_BLACK); in __rb_insert()
107 * per 4), we don't want a red root or two in __rb_insert()
115 tmp = gparent->rb_right; in __rb_insert()
116 if (parent != tmp) { /* parent == gparent->rb_left */ in __rb_insert()
119 * Case 1 - node's uncle is red (color flips). in __rb_insert()
123 * p u --> P U in __rb_insert()
133 node = gparent; in __rb_insert()
134 parent = rb_parent(node); in __rb_insert()
135 rb_set_parent_color(node, parent, RB_RED); in __rb_insert()
139 tmp = parent->rb_right; in __rb_insert()
140 if (node == tmp) { in __rb_insert()
142 * Case 2 - node's uncle is black and node is in __rb_insert()
147 * p U --> n U in __rb_insert()
154 tmp = node->rb_left; in __rb_insert()
155 WRITE_ONCE(parent->rb_right, tmp); in __rb_insert()
156 WRITE_ONCE(node->rb_left, parent); in __rb_insert()
160 rb_set_parent_color(parent, node, RB_RED); in __rb_insert()
161 augment_rotate(parent, node); in __rb_insert()
162 parent = node; in __rb_insert()
163 tmp = node->rb_right; in __rb_insert()
167 * Case 3 - node's uncle is black and node is in __rb_insert()
172 * p U --> n g in __rb_insert()
176 WRITE_ONCE(gparent->rb_left, tmp); /* == parent->rb_right */ in __rb_insert()
177 WRITE_ONCE(parent->rb_right, gparent); in __rb_insert()
180 __rb_rotate_set_parents(gparent, parent, root, RB_RED); in __rb_insert()
184 tmp = gparent->rb_left; in __rb_insert()
186 /* Case 1 - color flips */ in __rb_insert()
189 node = gparent; in __rb_insert()
190 parent = rb_parent(node); in __rb_insert()
191 rb_set_parent_color(node, parent, RB_RED); in __rb_insert()
195 tmp = parent->rb_left; in __rb_insert()
196 if (node == tmp) { in __rb_insert()
197 /* Case 2 - right rotate at parent */ in __rb_insert()
198 tmp = node->rb_right; in __rb_insert()
199 WRITE_ONCE(parent->rb_left, tmp); in __rb_insert()
200 WRITE_ONCE(node->rb_right, parent); in __rb_insert()
204 rb_set_parent_color(parent, node, RB_RED); in __rb_insert()
205 augment_rotate(parent, node); in __rb_insert()
206 parent = node; in __rb_insert()
207 tmp = node->rb_left; in __rb_insert()
210 /* Case 3 - left rotate at gparent */ in __rb_insert()
211 WRITE_ONCE(gparent->rb_right, tmp); /* == parent->rb_left */ in __rb_insert()
212 WRITE_ONCE(parent->rb_left, gparent); in __rb_insert()
215 __rb_rotate_set_parents(gparent, parent, root, RB_RED); in __rb_insert()
223 * Inline version for rb_erase() use - we want to be able to inline
227 ____rb_erase_color(struct rb_node *parent, struct rb_root *root, in ____rb_erase_color() argument
230 struct rb_node *node = NULL, *sibling, *tmp1, *tmp2; in ____rb_erase_color() local
235 * - node is black (or NULL on first iteration) in ____rb_erase_color()
236 * - node is not the root (parent is not NULL) in ____rb_erase_color()
237 * - All leaf paths going through parent and node have a in ____rb_erase_color()
238 * black node count that is 1 lower than other leaf paths. in ____rb_erase_color()
240 sibling = parent->rb_right; in ____rb_erase_color()
241 if (node != sibling) { /* node == parent->rb_left */ in ____rb_erase_color()
244 * Case 1 - left rotate at parent in ____rb_erase_color()
248 * N s --> p Sr in ____rb_erase_color()
252 tmp1 = sibling->rb_left; in ____rb_erase_color()
253 WRITE_ONCE(parent->rb_right, tmp1); in ____rb_erase_color()
254 WRITE_ONCE(sibling->rb_left, parent); in ____rb_erase_color()
256 __rb_rotate_set_parents(parent, sibling, root, in ____rb_erase_color()
261 tmp1 = sibling->rb_right; in ____rb_erase_color()
263 tmp2 = sibling->rb_left; in ____rb_erase_color()
266 * Case 2 - sibling color flip in ____rb_erase_color()
271 * N S --> N s in ____rb_erase_color()
285 node = parent; in ____rb_erase_color()
286 parent = rb_parent(node); in ____rb_erase_color()
293 * Case 3 - right rotate at sibling in ____rb_erase_color()
298 * N S --> N sl in ____rb_erase_color()
313 * N sl --> P S in ____rb_erase_color()
319 tmp1 = tmp2->rb_right; in ____rb_erase_color()
320 WRITE_ONCE(sibling->rb_left, tmp1); in ____rb_erase_color()
321 WRITE_ONCE(tmp2->rb_right, sibling); in ____rb_erase_color()
322 WRITE_ONCE(parent->rb_right, tmp2); in ____rb_erase_color()
331 * Case 4 - left rotate at parent + color flips in ____rb_erase_color()
338 * N S --> P Sr in ____rb_erase_color()
342 tmp2 = sibling->rb_left; in ____rb_erase_color()
343 WRITE_ONCE(parent->rb_right, tmp2); in ____rb_erase_color()
344 WRITE_ONCE(sibling->rb_left, parent); in ____rb_erase_color()
348 __rb_rotate_set_parents(parent, sibling, root, in ____rb_erase_color()
353 sibling = parent->rb_left; in ____rb_erase_color()
355 /* Case 1 - right rotate at parent */ in ____rb_erase_color()
356 tmp1 = sibling->rb_right; in ____rb_erase_color()
357 WRITE_ONCE(parent->rb_left, tmp1); in ____rb_erase_color()
358 WRITE_ONCE(sibling->rb_right, parent); in ____rb_erase_color()
360 __rb_rotate_set_parents(parent, sibling, root, in ____rb_erase_color()
365 tmp1 = sibling->rb_left; in ____rb_erase_color()
367 tmp2 = sibling->rb_right; in ____rb_erase_color()
369 /* Case 2 - sibling color flip */ in ____rb_erase_color()
375 node = parent; in ____rb_erase_color()
376 parent = rb_parent(node); in ____rb_erase_color()
382 /* Case 3 - left rotate at sibling */ in ____rb_erase_color()
383 tmp1 = tmp2->rb_left; in ____rb_erase_color()
384 WRITE_ONCE(sibling->rb_right, tmp1); in ____rb_erase_color()
385 WRITE_ONCE(tmp2->rb_left, sibling); in ____rb_erase_color()
386 WRITE_ONCE(parent->rb_left, tmp2); in ____rb_erase_color()
394 /* Case 4 - right rotate at parent + color flips */ in ____rb_erase_color()
395 tmp2 = sibling->rb_right; in ____rb_erase_color()
396 WRITE_ONCE(parent->rb_left, tmp2); in ____rb_erase_color()
397 WRITE_ONCE(sibling->rb_right, parent); in ____rb_erase_color()
401 __rb_rotate_set_parents(parent, sibling, root, in ____rb_erase_color()
409 /* Non-inline version for rb_erase_augmented() use */
410 void __rb_erase_color(struct rb_node *parent, struct rb_root *root, in __rb_erase_color() argument
413 ____rb_erase_color(parent, root, augment_rotate); in __rb_erase_color()
418 * Non-augmented rbtree manipulation functions.
424 static inline void dummy_propagate(struct rb_node *node, struct rb_node *stop) {} in dummy_propagate() argument
434 void rb_insert_color(struct rb_node *node, struct rb_root *root) in rb_insert_color() argument
436 __rb_insert(node, root, dummy_rotate); in rb_insert_color()
440 void rb_erase(struct rb_node *node, struct rb_root *root) in rb_erase() argument
443 rebalance = __rb_erase_augmented(node, root, &dummy_callbacks); in rb_erase()
445 ____rb_erase_color(rebalance, root, dummy_rotate); in rb_erase()
452 * This instantiates the same __always_inline functions as in the non-augmented
453 * case, but this time with user-defined callbacks.
456 void __rb_insert_augmented(struct rb_node *node, struct rb_root *root, in __rb_insert_augmented() argument
459 __rb_insert(node, root, augment_rotate); in __rb_insert_augmented()
464 * This function returns the first node (in sort order) of the tree.
466 struct rb_node *rb_first(const struct rb_root *root) in rb_first() argument
470 n = root->rb_node; in rb_first()
473 while (n->rb_left) in rb_first()
474 n = n->rb_left; in rb_first()
479 struct rb_node *rb_last(const struct rb_root *root) in rb_last() argument
483 n = root->rb_node; in rb_last()
486 while (n->rb_right) in rb_last()
487 n = n->rb_right; in rb_last()
492 struct rb_node *rb_next(const struct rb_node *node) in rb_next() argument
496 if (RB_EMPTY_NODE(node)) in rb_next()
500 * If we have a right-hand child, go down and then left as far in rb_next()
503 if (node->rb_right) { in rb_next()
504 node = node->rb_right; in rb_next()
505 while (node->rb_left) in rb_next()
506 node = node->rb_left; in rb_next()
507 return (struct rb_node *)node; in rb_next()
511 * No right-hand children. Everything down and left is smaller than us, in rb_next()
512 * so any 'next' node must be in the general direction of our parent. in rb_next()
513 * Go up the tree; any time the ancestor is a right-hand child of its in rb_next()
514 * parent, keep going up. First time it's a left-hand child of its in rb_next()
515 * parent, said parent is our 'next' node. in rb_next()
517 while ((parent = rb_parent(node)) && node == parent->rb_right) in rb_next()
518 node = parent; in rb_next()
524 struct rb_node *rb_prev(const struct rb_node *node) in rb_prev() argument
528 if (RB_EMPTY_NODE(node)) in rb_prev()
532 * If we have a left-hand child, go down and then right as far in rb_prev()
535 if (node->rb_left) { in rb_prev()
536 node = node->rb_left; in rb_prev()
537 while (node->rb_right) in rb_prev()
538 node = node->rb_right; in rb_prev()
539 return (struct rb_node *)node; in rb_prev()
543 * No left-hand children. Go up till we find an ancestor which in rb_prev()
544 * is a right-hand child of its parent. in rb_prev()
546 while ((parent = rb_parent(node)) && node == parent->rb_left) in rb_prev()
547 node = parent; in rb_prev()
554 struct rb_root *root) in rb_replace_node() argument
562 if (victim->rb_left) in rb_replace_node()
563 rb_set_parent(victim->rb_left, new); in rb_replace_node()
564 if (victim->rb_right) in rb_replace_node()
565 rb_set_parent(victim->rb_right, new); in rb_replace_node()
566 __rb_change_child(victim, new, parent, root); in rb_replace_node()
571 struct rb_root *root) in rb_replace_node_rcu() argument
579 if (victim->rb_left) in rb_replace_node_rcu()
580 rb_set_parent(victim->rb_left, new); in rb_replace_node_rcu()
581 if (victim->rb_right) in rb_replace_node_rcu()
582 rb_set_parent(victim->rb_right, new); in rb_replace_node_rcu()
584 /* Set the parent's pointer to the new node last after an RCU barrier in rb_replace_node_rcu()
588 __rb_change_child_rcu(victim, new, parent, root); in rb_replace_node_rcu()
592 static struct rb_node *rb_left_deepest_node(const struct rb_node *node) in rb_left_deepest_node() argument
595 if (node->rb_left) in rb_left_deepest_node()
596 node = node->rb_left; in rb_left_deepest_node()
597 else if (node->rb_right) in rb_left_deepest_node()
598 node = node->rb_right; in rb_left_deepest_node()
600 return (struct rb_node *)node; in rb_left_deepest_node()
604 struct rb_node *rb_next_postorder(const struct rb_node *node) in rb_next_postorder() argument
607 if (!node) in rb_next_postorder()
609 parent = rb_parent(node); in rb_next_postorder()
611 /* If we're sitting on node, we've already seen our children */ in rb_next_postorder()
612 if (parent && node == parent->rb_left && parent->rb_right) { in rb_next_postorder()
613 /* If we are the parent's left node, go to the parent's right in rb_next_postorder()
614 * node then all the way down to the left */ in rb_next_postorder()
615 return rb_left_deepest_node(parent->rb_right); in rb_next_postorder()
617 /* Otherwise we are the parent's right node, and the parent in rb_next_postorder()
623 struct rb_node *rb_first_postorder(const struct rb_root *root) in rb_first_postorder() argument
625 if (!root->rb_node) in rb_first_postorder()
628 return rb_left_deepest_node(root->rb_node); in rb_first_postorder()