1 // SPDX-License-Identifier: GPL-2.0+
4 (C) 1999 Andrea Arcangeli <andrea@suse.de>
5 (C) 2002 David Woodhouse <dwmw2@infradead.org>
6 (C) 2012 Michel Lespinasse <walken@google.com>
11 #include <linux/rbtree_augmented.h>
13 #include <linux/export.h>
15 #include <ubi_uboot.h>
18 * red-black trees properties: http://en.wikipedia.org/wiki/Rbtree
20 * 1) A node is either red or black
21 * 2) The root is black
22 * 3) All leaves (NULL) are black
23 * 4) Both children of every red node are black
24 * 5) Every simple path from root to leaves contains the same number
27 * 4 and 5 give the O(log n) guarantee, since 4 implies you cannot have two
28 * consecutive red nodes in a path and every red node is therefore followed by
29 * a black. So if B is the number of black nodes on every simple path (as per
30 * 5), then the longest possible path due to 4 is 2B.
32 * We shall indicate color with case, where black nodes are uppercase and red
33 * nodes will be lowercase. Unknown color nodes shall be drawn as red within
34 * parentheses and have some accompanying text comment.
37 static inline void rb_set_black(struct rb_node
*rb
)
39 rb
->__rb_parent_color
|= RB_BLACK
;
42 static inline struct rb_node
*rb_red_parent(struct rb_node
*red
)
44 return (struct rb_node
*)red
->__rb_parent_color
;
48 * Helper function for rotations:
49 * - old's parent and color get assigned to new
50 * - old gets assigned new as a parent and 'color' as a color.
53 __rb_rotate_set_parents(struct rb_node
*old
, struct rb_node
*new,
54 struct rb_root
*root
, int color
)
56 struct rb_node
*parent
= rb_parent(old
);
57 new->__rb_parent_color
= old
->__rb_parent_color
;
58 rb_set_parent_color(old
, new, color
);
59 __rb_change_child(old
, new, parent
, root
);
62 static __always_inline
void
63 __rb_insert(struct rb_node
*node
, struct rb_root
*root
,
64 void (*augment_rotate
)(struct rb_node
*old
, struct rb_node
*new))
66 struct rb_node
*parent
= rb_red_parent(node
), *gparent
, *tmp
;
70 * Loop invariant: node is red
72 * If there is a black parent, we are done.
73 * Otherwise, take some corrective action as we don't
74 * want a red root or two consecutive red nodes.
77 rb_set_parent_color(node
, NULL
, RB_BLACK
);
79 } else if (rb_is_black(parent
))
82 gparent
= rb_red_parent(parent
);
84 tmp
= gparent
->rb_right
;
85 if (parent
!= tmp
) { /* parent == gparent->rb_left */
86 if (tmp
&& rb_is_red(tmp
)) {
88 * Case 1 - color flips
96 * However, since g's parent might be red, and
97 * 4) does not allow this, we need to recurse
100 rb_set_parent_color(tmp
, gparent
, RB_BLACK
);
101 rb_set_parent_color(parent
, gparent
, RB_BLACK
);
103 parent
= rb_parent(node
);
104 rb_set_parent_color(node
, parent
, RB_RED
);
108 tmp
= parent
->rb_right
;
111 * Case 2 - left rotate at parent
119 * This still leaves us in violation of 4), the
120 * continuation into Case 3 will fix that.
122 parent
->rb_right
= tmp
= node
->rb_left
;
123 node
->rb_left
= parent
;
125 rb_set_parent_color(tmp
, parent
,
127 rb_set_parent_color(parent
, node
, RB_RED
);
128 augment_rotate(parent
, node
);
130 tmp
= node
->rb_right
;
134 * Case 3 - right rotate at gparent
142 gparent
->rb_left
= tmp
; /* == parent->rb_right */
143 parent
->rb_right
= gparent
;
145 rb_set_parent_color(tmp
, gparent
, RB_BLACK
);
146 __rb_rotate_set_parents(gparent
, parent
, root
, RB_RED
);
147 augment_rotate(gparent
, parent
);
150 tmp
= gparent
->rb_left
;
151 if (tmp
&& rb_is_red(tmp
)) {
152 /* Case 1 - color flips */
153 rb_set_parent_color(tmp
, gparent
, RB_BLACK
);
154 rb_set_parent_color(parent
, gparent
, RB_BLACK
);
156 parent
= rb_parent(node
);
157 rb_set_parent_color(node
, parent
, RB_RED
);
161 tmp
= parent
->rb_left
;
163 /* Case 2 - right rotate at parent */
164 parent
->rb_left
= tmp
= node
->rb_right
;
165 node
->rb_right
= parent
;
167 rb_set_parent_color(tmp
, parent
,
169 rb_set_parent_color(parent
, node
, RB_RED
);
170 augment_rotate(parent
, node
);
175 /* Case 3 - left rotate at gparent */
176 gparent
->rb_right
= tmp
; /* == parent->rb_left */
177 parent
->rb_left
= 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
);
188 * Inline version for rb_erase() use - we want to be able to inline
189 * and eliminate the dummy_rotate callback there
191 static __always_inline
void
192 ____rb_erase_color(struct rb_node
*parent
, struct rb_root
*root
,
193 void (*augment_rotate
)(struct rb_node
*old
, struct rb_node
*new))
195 struct rb_node
*node
= NULL
, *sibling
, *tmp1
, *tmp2
;
200 * - node is black (or NULL on first iteration)
201 * - node is not the root (parent is not NULL)
202 * - All leaf paths going through parent and node have a
203 * black node count that is 1 lower than other leaf paths.
205 sibling
= parent
->rb_right
;
206 if (node
!= sibling
) { /* node == parent->rb_left */
207 if (rb_is_red(sibling
)) {
209 * Case 1 - left rotate at parent
217 parent
->rb_right
= tmp1
= sibling
->rb_left
;
218 sibling
->rb_left
= parent
;
219 rb_set_parent_color(tmp1
, parent
, RB_BLACK
);
220 __rb_rotate_set_parents(parent
, sibling
, root
,
222 augment_rotate(parent
, sibling
);
225 tmp1
= sibling
->rb_right
;
226 if (!tmp1
|| rb_is_black(tmp1
)) {
227 tmp2
= sibling
->rb_left
;
228 if (!tmp2
|| rb_is_black(tmp2
)) {
230 * Case 2 - sibling color flip
231 * (p could be either color here)
239 * This leaves us violating 5) which
240 * can be fixed by flipping p to black
241 * if it was red, or by recursing at p.
242 * p is red when coming from Case 1.
244 rb_set_parent_color(sibling
, parent
,
246 if (rb_is_red(parent
))
247 rb_set_black(parent
);
250 parent
= rb_parent(node
);
257 * Case 3 - right rotate at sibling
258 * (p could be either color here)
268 sibling
->rb_left
= tmp1
= tmp2
->rb_right
;
269 tmp2
->rb_right
= sibling
;
270 parent
->rb_right
= tmp2
;
272 rb_set_parent_color(tmp1
, sibling
,
274 augment_rotate(sibling
, tmp2
);
279 * Case 4 - left rotate at parent + color flips
280 * (p and sl could be either color here.
281 * After rotation, p becomes black, s acquires
282 * p's color, and sl keeps its color)
290 parent
->rb_right
= tmp2
= sibling
->rb_left
;
291 sibling
->rb_left
= parent
;
292 rb_set_parent_color(tmp1
, sibling
, RB_BLACK
);
294 rb_set_parent(tmp2
, parent
);
295 __rb_rotate_set_parents(parent
, sibling
, root
,
297 augment_rotate(parent
, sibling
);
300 sibling
= parent
->rb_left
;
301 if (rb_is_red(sibling
)) {
302 /* Case 1 - right rotate at parent */
303 parent
->rb_left
= tmp1
= sibling
->rb_right
;
304 sibling
->rb_right
= parent
;
305 rb_set_parent_color(tmp1
, parent
, RB_BLACK
);
306 __rb_rotate_set_parents(parent
, sibling
, root
,
308 augment_rotate(parent
, sibling
);
311 tmp1
= sibling
->rb_left
;
312 if (!tmp1
|| rb_is_black(tmp1
)) {
313 tmp2
= sibling
->rb_right
;
314 if (!tmp2
|| rb_is_black(tmp2
)) {
315 /* Case 2 - sibling color flip */
316 rb_set_parent_color(sibling
, parent
,
318 if (rb_is_red(parent
))
319 rb_set_black(parent
);
322 parent
= rb_parent(node
);
328 /* Case 3 - right rotate at sibling */
329 sibling
->rb_right
= tmp1
= tmp2
->rb_left
;
330 tmp2
->rb_left
= sibling
;
331 parent
->rb_left
= tmp2
;
333 rb_set_parent_color(tmp1
, sibling
,
335 augment_rotate(sibling
, tmp2
);
339 /* Case 4 - left rotate at parent + color flips */
340 parent
->rb_left
= tmp2
= sibling
->rb_right
;
341 sibling
->rb_right
= parent
;
342 rb_set_parent_color(tmp1
, sibling
, RB_BLACK
);
344 rb_set_parent(tmp2
, parent
);
345 __rb_rotate_set_parents(parent
, sibling
, root
,
347 augment_rotate(parent
, sibling
);
353 /* Non-inline version for rb_erase_augmented() use */
354 void __rb_erase_color(struct rb_node
*parent
, struct rb_root
*root
,
355 void (*augment_rotate
)(struct rb_node
*old
, struct rb_node
*new))
357 ____rb_erase_color(parent
, root
, augment_rotate
);
359 EXPORT_SYMBOL(__rb_erase_color
);
362 * Non-augmented rbtree manipulation functions.
364 * We use dummy augmented callbacks here, and have the compiler optimize them
365 * out of the rb_insert_color() and rb_erase() function definitions.
368 static inline void dummy_propagate(struct rb_node
*node
, struct rb_node
*stop
) {}
369 static inline void dummy_copy(struct rb_node
*old
, struct rb_node
*new) {}
370 static inline void dummy_rotate(struct rb_node
*old
, struct rb_node
*new) {}
372 static const struct rb_augment_callbacks dummy_callbacks
= {
373 dummy_propagate
, dummy_copy
, dummy_rotate
376 void rb_insert_color(struct rb_node
*node
, struct rb_root
*root
)
378 __rb_insert(node
, root
, dummy_rotate
);
380 EXPORT_SYMBOL(rb_insert_color
);
382 void rb_erase(struct rb_node
*node
, struct rb_root
*root
)
384 struct rb_node
*rebalance
;
385 rebalance
= __rb_erase_augmented(node
, root
, &dummy_callbacks
);
387 ____rb_erase_color(rebalance
, root
, dummy_rotate
);
389 EXPORT_SYMBOL(rb_erase
);
392 * Augmented rbtree manipulation functions.
394 * This instantiates the same __always_inline functions as in the non-augmented
395 * case, but this time with user-defined callbacks.
398 void __rb_insert_augmented(struct rb_node
*node
, struct rb_root
*root
,
399 void (*augment_rotate
)(struct rb_node
*old
, struct rb_node
*new))
401 __rb_insert(node
, root
, augment_rotate
);
403 EXPORT_SYMBOL(__rb_insert_augmented
);
406 * This function returns the first node (in sort order) of the tree.
408 struct rb_node
*rb_first(const struct rb_root
*root
)
419 EXPORT_SYMBOL(rb_first
);
421 struct rb_node
*rb_last(const struct rb_root
*root
)
432 EXPORT_SYMBOL(rb_last
);
434 struct rb_node
*rb_next(const struct rb_node
*node
)
436 struct rb_node
*parent
;
438 if (RB_EMPTY_NODE(node
))
442 * If we have a right-hand child, go down and then left as far
445 if (node
->rb_right
) {
446 node
= node
->rb_right
;
447 while (node
->rb_left
)
449 return (struct rb_node
*)node
;
453 * No right-hand children. Everything down and left is smaller than us,
454 * so any 'next' node must be in the general direction of our parent.
455 * Go up the tree; any time the ancestor is a right-hand child of its
456 * parent, keep going up. First time it's a left-hand child of its
457 * parent, said parent is our 'next' node.
459 while ((parent
= rb_parent(node
)) && node
== parent
->rb_right
)
464 EXPORT_SYMBOL(rb_next
);
466 struct rb_node
*rb_prev(const struct rb_node
*node
)
468 struct rb_node
*parent
;
470 if (RB_EMPTY_NODE(node
))
474 * If we have a left-hand child, go down and then right as far
478 node
= node
->rb_left
;
479 while (node
->rb_right
)
481 return (struct rb_node
*)node
;
485 * No left-hand children. Go up till we find an ancestor which
486 * is a right-hand child of its parent.
488 while ((parent
= rb_parent(node
)) && node
== parent
->rb_left
)
493 EXPORT_SYMBOL(rb_prev
);
495 void rb_replace_node(struct rb_node
*victim
, struct rb_node
*new,
496 struct rb_root
*root
)
498 struct rb_node
*parent
= rb_parent(victim
);
500 /* Set the surrounding nodes to point to the replacement */
501 __rb_change_child(victim
, new, parent
, root
);
503 rb_set_parent(victim
->rb_left
, new);
504 if (victim
->rb_right
)
505 rb_set_parent(victim
->rb_right
, new);
507 /* Copy the pointers/colour from the victim to the replacement */
510 EXPORT_SYMBOL(rb_replace_node
);
512 static struct rb_node
*rb_left_deepest_node(const struct rb_node
*node
)
516 node
= node
->rb_left
;
517 else if (node
->rb_right
)
518 node
= node
->rb_right
;
520 return (struct rb_node
*)node
;
524 struct rb_node
*rb_next_postorder(const struct rb_node
*node
)
526 const struct rb_node
*parent
;
529 parent
= rb_parent(node
);
531 /* If we're sitting on node, we've already seen our children */
532 if (parent
&& node
== parent
->rb_left
&& parent
->rb_right
) {
533 /* If we are the parent's left node, go to the parent's right
534 * node then all the way down to the left */
535 return rb_left_deepest_node(parent
->rb_right
);
537 /* Otherwise we are the parent's right node, and the parent
539 return (struct rb_node
*)parent
;
541 EXPORT_SYMBOL(rb_next_postorder
);
543 struct rb_node
*rb_first_postorder(const struct rb_root
*root
)
548 return rb_left_deepest_node(root
->rb_node
);
550 EXPORT_SYMBOL(rb_first_postorder
);