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 * SPDX-License-Identifier: GPL-2.0+
13 #include <linux/rbtree_augmented.h>
15 #include <linux/export.h>
17 #include <ubi_uboot.h>
20 * red-black trees properties: http://en.wikipedia.org/wiki/Rbtree
22 * 1) A node is either red or black
23 * 2) The root is black
24 * 3) All leaves (NULL) are black
25 * 4) Both children of every red node are black
26 * 5) Every simple path from root to leaves contains the same number
29 * 4 and 5 give the O(log n) guarantee, since 4 implies you cannot have two
30 * consecutive red nodes in a path and every red node is therefore followed by
31 * a black. So if B is the number of black nodes on every simple path (as per
32 * 5), then the longest possible path due to 4 is 2B.
34 * We shall indicate color with case, where black nodes are uppercase and red
35 * nodes will be lowercase. Unknown color nodes shall be drawn as red within
36 * parentheses and have some accompanying text comment.
39 static inline void rb_set_black(struct rb_node
*rb
)
41 rb
->__rb_parent_color
|= RB_BLACK
;
44 static inline struct rb_node
*rb_red_parent(struct rb_node
*red
)
46 return (struct rb_node
*)red
->__rb_parent_color
;
50 * Helper function for rotations:
51 * - old's parent and color get assigned to new
52 * - old gets assigned new as a parent and 'color' as a color.
55 __rb_rotate_set_parents(struct rb_node
*old
, struct rb_node
*new,
56 struct rb_root
*root
, int color
)
58 struct rb_node
*parent
= rb_parent(old
);
59 new->__rb_parent_color
= old
->__rb_parent_color
;
60 rb_set_parent_color(old
, new, color
);
61 __rb_change_child(old
, new, parent
, root
);
64 static __always_inline
void
65 __rb_insert(struct rb_node
*node
, struct rb_root
*root
,
66 void (*augment_rotate
)(struct rb_node
*old
, struct rb_node
*new))
68 struct rb_node
*parent
= rb_red_parent(node
), *gparent
, *tmp
;
72 * Loop invariant: node is red
74 * If there is a black parent, we are done.
75 * Otherwise, take some corrective action as we don't
76 * want a red root or two consecutive red nodes.
79 rb_set_parent_color(node
, NULL
, RB_BLACK
);
81 } else if (rb_is_black(parent
))
84 gparent
= rb_red_parent(parent
);
86 tmp
= gparent
->rb_right
;
87 if (parent
!= tmp
) { /* parent == gparent->rb_left */
88 if (tmp
&& rb_is_red(tmp
)) {
90 * Case 1 - color flips
98 * However, since g's parent might be red, and
99 * 4) does not allow this, we need to recurse
102 rb_set_parent_color(tmp
, gparent
, RB_BLACK
);
103 rb_set_parent_color(parent
, gparent
, RB_BLACK
);
105 parent
= rb_parent(node
);
106 rb_set_parent_color(node
, parent
, RB_RED
);
110 tmp
= parent
->rb_right
;
113 * Case 2 - left rotate at parent
121 * This still leaves us in violation of 4), the
122 * continuation into Case 3 will fix that.
124 parent
->rb_right
= tmp
= node
->rb_left
;
125 node
->rb_left
= parent
;
127 rb_set_parent_color(tmp
, parent
,
129 rb_set_parent_color(parent
, node
, RB_RED
);
130 augment_rotate(parent
, node
);
132 tmp
= node
->rb_right
;
136 * Case 3 - right rotate at gparent
144 gparent
->rb_left
= tmp
; /* == parent->rb_right */
145 parent
->rb_right
= gparent
;
147 rb_set_parent_color(tmp
, gparent
, RB_BLACK
);
148 __rb_rotate_set_parents(gparent
, parent
, root
, RB_RED
);
149 augment_rotate(gparent
, parent
);
152 tmp
= gparent
->rb_left
;
153 if (tmp
&& rb_is_red(tmp
)) {
154 /* Case 1 - color flips */
155 rb_set_parent_color(tmp
, gparent
, RB_BLACK
);
156 rb_set_parent_color(parent
, gparent
, RB_BLACK
);
158 parent
= rb_parent(node
);
159 rb_set_parent_color(node
, parent
, RB_RED
);
163 tmp
= parent
->rb_left
;
165 /* Case 2 - right rotate at parent */
166 parent
->rb_left
= tmp
= node
->rb_right
;
167 node
->rb_right
= parent
;
169 rb_set_parent_color(tmp
, parent
,
171 rb_set_parent_color(parent
, node
, RB_RED
);
172 augment_rotate(parent
, node
);
177 /* Case 3 - left rotate at gparent */
178 gparent
->rb_right
= tmp
; /* == parent->rb_left */
179 parent
->rb_left
= gparent
;
181 rb_set_parent_color(tmp
, gparent
, RB_BLACK
);
182 __rb_rotate_set_parents(gparent
, parent
, root
, RB_RED
);
183 augment_rotate(gparent
, parent
);
190 * Inline version for rb_erase() use - we want to be able to inline
191 * and eliminate the dummy_rotate callback there
193 static __always_inline
void
194 ____rb_erase_color(struct rb_node
*parent
, struct rb_root
*root
,
195 void (*augment_rotate
)(struct rb_node
*old
, struct rb_node
*new))
197 struct rb_node
*node
= NULL
, *sibling
, *tmp1
, *tmp2
;
202 * - node is black (or NULL on first iteration)
203 * - node is not the root (parent is not NULL)
204 * - All leaf paths going through parent and node have a
205 * black node count that is 1 lower than other leaf paths.
207 sibling
= parent
->rb_right
;
208 if (node
!= sibling
) { /* node == parent->rb_left */
209 if (rb_is_red(sibling
)) {
211 * Case 1 - left rotate at parent
219 parent
->rb_right
= tmp1
= sibling
->rb_left
;
220 sibling
->rb_left
= parent
;
221 rb_set_parent_color(tmp1
, parent
, RB_BLACK
);
222 __rb_rotate_set_parents(parent
, sibling
, root
,
224 augment_rotate(parent
, sibling
);
227 tmp1
= sibling
->rb_right
;
228 if (!tmp1
|| rb_is_black(tmp1
)) {
229 tmp2
= sibling
->rb_left
;
230 if (!tmp2
|| rb_is_black(tmp2
)) {
232 * Case 2 - sibling color flip
233 * (p could be either color here)
241 * This leaves us violating 5) which
242 * can be fixed by flipping p to black
243 * if it was red, or by recursing at p.
244 * p is red when coming from Case 1.
246 rb_set_parent_color(sibling
, parent
,
248 if (rb_is_red(parent
))
249 rb_set_black(parent
);
252 parent
= rb_parent(node
);
259 * Case 3 - right rotate at sibling
260 * (p could be either color here)
270 sibling
->rb_left
= tmp1
= tmp2
->rb_right
;
271 tmp2
->rb_right
= sibling
;
272 parent
->rb_right
= tmp2
;
274 rb_set_parent_color(tmp1
, sibling
,
276 augment_rotate(sibling
, tmp2
);
281 * Case 4 - left rotate at parent + color flips
282 * (p and sl could be either color here.
283 * After rotation, p becomes black, s acquires
284 * p's color, and sl keeps its color)
292 parent
->rb_right
= tmp2
= sibling
->rb_left
;
293 sibling
->rb_left
= parent
;
294 rb_set_parent_color(tmp1
, sibling
, RB_BLACK
);
296 rb_set_parent(tmp2
, parent
);
297 __rb_rotate_set_parents(parent
, sibling
, root
,
299 augment_rotate(parent
, sibling
);
302 sibling
= parent
->rb_left
;
303 if (rb_is_red(sibling
)) {
304 /* Case 1 - right rotate at parent */
305 parent
->rb_left
= tmp1
= sibling
->rb_right
;
306 sibling
->rb_right
= parent
;
307 rb_set_parent_color(tmp1
, parent
, RB_BLACK
);
308 __rb_rotate_set_parents(parent
, sibling
, root
,
310 augment_rotate(parent
, sibling
);
313 tmp1
= sibling
->rb_left
;
314 if (!tmp1
|| rb_is_black(tmp1
)) {
315 tmp2
= sibling
->rb_right
;
316 if (!tmp2
|| rb_is_black(tmp2
)) {
317 /* Case 2 - sibling color flip */
318 rb_set_parent_color(sibling
, parent
,
320 if (rb_is_red(parent
))
321 rb_set_black(parent
);
324 parent
= rb_parent(node
);
330 /* Case 3 - right rotate at sibling */
331 sibling
->rb_right
= tmp1
= tmp2
->rb_left
;
332 tmp2
->rb_left
= sibling
;
333 parent
->rb_left
= tmp2
;
335 rb_set_parent_color(tmp1
, sibling
,
337 augment_rotate(sibling
, tmp2
);
341 /* Case 4 - left rotate at parent + color flips */
342 parent
->rb_left
= tmp2
= sibling
->rb_right
;
343 sibling
->rb_right
= parent
;
344 rb_set_parent_color(tmp1
, sibling
, RB_BLACK
);
346 rb_set_parent(tmp2
, parent
);
347 __rb_rotate_set_parents(parent
, sibling
, root
,
349 augment_rotate(parent
, sibling
);
355 /* Non-inline version for rb_erase_augmented() use */
356 void __rb_erase_color(struct rb_node
*parent
, struct rb_root
*root
,
357 void (*augment_rotate
)(struct rb_node
*old
, struct rb_node
*new))
359 ____rb_erase_color(parent
, root
, augment_rotate
);
361 EXPORT_SYMBOL(__rb_erase_color
);
364 * Non-augmented rbtree manipulation functions.
366 * We use dummy augmented callbacks here, and have the compiler optimize them
367 * out of the rb_insert_color() and rb_erase() function definitions.
370 static inline void dummy_propagate(struct rb_node
*node
, struct rb_node
*stop
) {}
371 static inline void dummy_copy(struct rb_node
*old
, struct rb_node
*new) {}
372 static inline void dummy_rotate(struct rb_node
*old
, struct rb_node
*new) {}
374 static const struct rb_augment_callbacks dummy_callbacks
= {
375 dummy_propagate
, dummy_copy
, dummy_rotate
378 void rb_insert_color(struct rb_node
*node
, struct rb_root
*root
)
380 __rb_insert(node
, root
, dummy_rotate
);
382 EXPORT_SYMBOL(rb_insert_color
);
384 void rb_erase(struct rb_node
*node
, struct rb_root
*root
)
386 struct rb_node
*rebalance
;
387 rebalance
= __rb_erase_augmented(node
, root
, &dummy_callbacks
);
389 ____rb_erase_color(rebalance
, root
, dummy_rotate
);
391 EXPORT_SYMBOL(rb_erase
);
394 * Augmented rbtree manipulation functions.
396 * This instantiates the same __always_inline functions as in the non-augmented
397 * case, but this time with user-defined callbacks.
400 void __rb_insert_augmented(struct rb_node
*node
, struct rb_root
*root
,
401 void (*augment_rotate
)(struct rb_node
*old
, struct rb_node
*new))
403 __rb_insert(node
, root
, augment_rotate
);
405 EXPORT_SYMBOL(__rb_insert_augmented
);
408 * This function returns the first node (in sort order) of the tree.
410 struct rb_node
*rb_first(const struct rb_root
*root
)
421 EXPORT_SYMBOL(rb_first
);
423 struct rb_node
*rb_last(const struct rb_root
*root
)
434 EXPORT_SYMBOL(rb_last
);
436 struct rb_node
*rb_next(const struct rb_node
*node
)
438 struct rb_node
*parent
;
440 if (RB_EMPTY_NODE(node
))
444 * If we have a right-hand child, go down and then left as far
447 if (node
->rb_right
) {
448 node
= node
->rb_right
;
449 while (node
->rb_left
)
451 return (struct rb_node
*)node
;
455 * No right-hand children. Everything down and left is smaller than us,
456 * so any 'next' node must be in the general direction of our parent.
457 * Go up the tree; any time the ancestor is a right-hand child of its
458 * parent, keep going up. First time it's a left-hand child of its
459 * parent, said parent is our 'next' node.
461 while ((parent
= rb_parent(node
)) && node
== parent
->rb_right
)
466 EXPORT_SYMBOL(rb_next
);
468 struct rb_node
*rb_prev(const struct rb_node
*node
)
470 struct rb_node
*parent
;
472 if (RB_EMPTY_NODE(node
))
476 * If we have a left-hand child, go down and then right as far
480 node
= node
->rb_left
;
481 while (node
->rb_right
)
483 return (struct rb_node
*)node
;
487 * No left-hand children. Go up till we find an ancestor which
488 * is a right-hand child of its parent.
490 while ((parent
= rb_parent(node
)) && node
== parent
->rb_left
)
495 EXPORT_SYMBOL(rb_prev
);
497 void rb_replace_node(struct rb_node
*victim
, struct rb_node
*new,
498 struct rb_root
*root
)
500 struct rb_node
*parent
= rb_parent(victim
);
502 /* Set the surrounding nodes to point to the replacement */
503 __rb_change_child(victim
, new, parent
, root
);
505 rb_set_parent(victim
->rb_left
, new);
506 if (victim
->rb_right
)
507 rb_set_parent(victim
->rb_right
, new);
509 /* Copy the pointers/colour from the victim to the replacement */
512 EXPORT_SYMBOL(rb_replace_node
);
514 static struct rb_node
*rb_left_deepest_node(const struct rb_node
*node
)
518 node
= node
->rb_left
;
519 else if (node
->rb_right
)
520 node
= node
->rb_right
;
522 return (struct rb_node
*)node
;
526 struct rb_node
*rb_next_postorder(const struct rb_node
*node
)
528 const struct rb_node
*parent
;
531 parent
= rb_parent(node
);
533 /* If we're sitting on node, we've already seen our children */
534 if (parent
&& node
== parent
->rb_left
&& parent
->rb_right
) {
535 /* If we are the parent's left node, go to the parent's right
536 * node then all the way down to the left */
537 return rb_left_deepest_node(parent
->rb_right
);
539 /* Otherwise we are the parent's right node, and the parent
541 return (struct rb_node
*)parent
;
543 EXPORT_SYMBOL(rb_next_postorder
);
545 struct rb_node
*rb_first_postorder(const struct rb_root
*root
)
550 return rb_left_deepest_node(root
->rb_node
);
552 EXPORT_SYMBOL(rb_first_postorder
);