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+
12 #include <linux/rbtree_augmented.h>
14 #include <linux/export.h>
16 #include <ubi_uboot.h>
19 * red-black trees properties: http://en.wikipedia.org/wiki/Rbtree
21 * 1) A node is either red or black
22 * 2) The root is black
23 * 3) All leaves (NULL) are black
24 * 4) Both children of every red node are black
25 * 5) Every simple path from root to leaves contains the same number
28 * 4 and 5 give the O(log n) guarantee, since 4 implies you cannot have two
29 * consecutive red nodes in a path and every red node is therefore followed by
30 * a black. So if B is the number of black nodes on every simple path (as per
31 * 5), then the longest possible path due to 4 is 2B.
33 * We shall indicate color with case, where black nodes are uppercase and red
34 * nodes will be lowercase. Unknown color nodes shall be drawn as red within
35 * parentheses and have some accompanying text comment.
38 static inline void rb_set_black(struct rb_node
*rb
)
40 rb
->__rb_parent_color
|= RB_BLACK
;
43 static inline struct rb_node
*rb_red_parent(struct rb_node
*red
)
45 return (struct rb_node
*)red
->__rb_parent_color
;
49 * Helper function for rotations:
50 * - old's parent and color get assigned to new
51 * - old gets assigned new as a parent and 'color' as a color.
54 __rb_rotate_set_parents(struct rb_node
*old
, struct rb_node
*new,
55 struct rb_root
*root
, int color
)
57 struct rb_node
*parent
= rb_parent(old
);
58 new->__rb_parent_color
= old
->__rb_parent_color
;
59 rb_set_parent_color(old
, new, color
);
60 __rb_change_child(old
, new, parent
, root
);
63 static __always_inline
void
64 __rb_insert(struct rb_node
*node
, struct rb_root
*root
,
65 void (*augment_rotate
)(struct rb_node
*old
, struct rb_node
*new))
67 struct rb_node
*parent
= rb_red_parent(node
), *gparent
, *tmp
;
71 * Loop invariant: node is red
73 * If there is a black parent, we are done.
74 * Otherwise, take some corrective action as we don't
75 * want a red root or two consecutive red nodes.
78 rb_set_parent_color(node
, NULL
, RB_BLACK
);
80 } else if (rb_is_black(parent
))
83 gparent
= rb_red_parent(parent
);
85 tmp
= gparent
->rb_right
;
86 if (parent
!= tmp
) { /* parent == gparent->rb_left */
87 if (tmp
&& rb_is_red(tmp
)) {
89 * Case 1 - color flips
97 * However, since g's parent might be red, and
98 * 4) does not allow this, we need to recurse
101 rb_set_parent_color(tmp
, gparent
, RB_BLACK
);
102 rb_set_parent_color(parent
, gparent
, RB_BLACK
);
104 parent
= rb_parent(node
);
105 rb_set_parent_color(node
, parent
, RB_RED
);
109 tmp
= parent
->rb_right
;
112 * Case 2 - left rotate at parent
120 * This still leaves us in violation of 4), the
121 * continuation into Case 3 will fix that.
123 parent
->rb_right
= tmp
= node
->rb_left
;
124 node
->rb_left
= parent
;
126 rb_set_parent_color(tmp
, parent
,
128 rb_set_parent_color(parent
, node
, RB_RED
);
129 augment_rotate(parent
, node
);
131 tmp
= node
->rb_right
;
135 * Case 3 - right rotate at gparent
143 gparent
->rb_left
= tmp
; /* == parent->rb_right */
144 parent
->rb_right
= gparent
;
146 rb_set_parent_color(tmp
, gparent
, RB_BLACK
);
147 __rb_rotate_set_parents(gparent
, parent
, root
, RB_RED
);
148 augment_rotate(gparent
, parent
);
151 tmp
= gparent
->rb_left
;
152 if (tmp
&& rb_is_red(tmp
)) {
153 /* Case 1 - color flips */
154 rb_set_parent_color(tmp
, gparent
, RB_BLACK
);
155 rb_set_parent_color(parent
, gparent
, RB_BLACK
);
157 parent
= rb_parent(node
);
158 rb_set_parent_color(node
, parent
, RB_RED
);
162 tmp
= parent
->rb_left
;
164 /* Case 2 - right rotate at parent */
165 parent
->rb_left
= tmp
= node
->rb_right
;
166 node
->rb_right
= parent
;
168 rb_set_parent_color(tmp
, parent
,
170 rb_set_parent_color(parent
, node
, RB_RED
);
171 augment_rotate(parent
, node
);
176 /* Case 3 - left rotate at gparent */
177 gparent
->rb_right
= tmp
; /* == parent->rb_left */
178 parent
->rb_left
= gparent
;
180 rb_set_parent_color(tmp
, gparent
, RB_BLACK
);
181 __rb_rotate_set_parents(gparent
, parent
, root
, RB_RED
);
182 augment_rotate(gparent
, parent
);
189 * Inline version for rb_erase() use - we want to be able to inline
190 * and eliminate the dummy_rotate callback there
192 static __always_inline
void
193 ____rb_erase_color(struct rb_node
*parent
, struct rb_root
*root
,
194 void (*augment_rotate
)(struct rb_node
*old
, struct rb_node
*new))
196 struct rb_node
*node
= NULL
, *sibling
, *tmp1
, *tmp2
;
201 * - node is black (or NULL on first iteration)
202 * - node is not the root (parent is not NULL)
203 * - All leaf paths going through parent and node have a
204 * black node count that is 1 lower than other leaf paths.
206 sibling
= parent
->rb_right
;
207 if (node
!= sibling
) { /* node == parent->rb_left */
208 if (rb_is_red(sibling
)) {
210 * Case 1 - left rotate at parent
218 parent
->rb_right
= tmp1
= sibling
->rb_left
;
219 sibling
->rb_left
= parent
;
220 rb_set_parent_color(tmp1
, parent
, RB_BLACK
);
221 __rb_rotate_set_parents(parent
, sibling
, root
,
223 augment_rotate(parent
, sibling
);
226 tmp1
= sibling
->rb_right
;
227 if (!tmp1
|| rb_is_black(tmp1
)) {
228 tmp2
= sibling
->rb_left
;
229 if (!tmp2
|| rb_is_black(tmp2
)) {
231 * Case 2 - sibling color flip
232 * (p could be either color here)
240 * This leaves us violating 5) which
241 * can be fixed by flipping p to black
242 * if it was red, or by recursing at p.
243 * p is red when coming from Case 1.
245 rb_set_parent_color(sibling
, parent
,
247 if (rb_is_red(parent
))
248 rb_set_black(parent
);
251 parent
= rb_parent(node
);
258 * Case 3 - right rotate at sibling
259 * (p could be either color here)
269 sibling
->rb_left
= tmp1
= tmp2
->rb_right
;
270 tmp2
->rb_right
= sibling
;
271 parent
->rb_right
= tmp2
;
273 rb_set_parent_color(tmp1
, sibling
,
275 augment_rotate(sibling
, tmp2
);
280 * Case 4 - left rotate at parent + color flips
281 * (p and sl could be either color here.
282 * After rotation, p becomes black, s acquires
283 * p's color, and sl keeps its color)
291 parent
->rb_right
= tmp2
= sibling
->rb_left
;
292 sibling
->rb_left
= parent
;
293 rb_set_parent_color(tmp1
, sibling
, RB_BLACK
);
295 rb_set_parent(tmp2
, parent
);
296 __rb_rotate_set_parents(parent
, sibling
, root
,
298 augment_rotate(parent
, sibling
);
301 sibling
= parent
->rb_left
;
302 if (rb_is_red(sibling
)) {
303 /* Case 1 - right rotate at parent */
304 parent
->rb_left
= tmp1
= sibling
->rb_right
;
305 sibling
->rb_right
= parent
;
306 rb_set_parent_color(tmp1
, parent
, RB_BLACK
);
307 __rb_rotate_set_parents(parent
, sibling
, root
,
309 augment_rotate(parent
, sibling
);
312 tmp1
= sibling
->rb_left
;
313 if (!tmp1
|| rb_is_black(tmp1
)) {
314 tmp2
= sibling
->rb_right
;
315 if (!tmp2
|| rb_is_black(tmp2
)) {
316 /* Case 2 - sibling color flip */
317 rb_set_parent_color(sibling
, parent
,
319 if (rb_is_red(parent
))
320 rb_set_black(parent
);
323 parent
= rb_parent(node
);
329 /* Case 3 - right rotate at sibling */
330 sibling
->rb_right
= tmp1
= tmp2
->rb_left
;
331 tmp2
->rb_left
= sibling
;
332 parent
->rb_left
= tmp2
;
334 rb_set_parent_color(tmp1
, sibling
,
336 augment_rotate(sibling
, tmp2
);
340 /* Case 4 - left rotate at parent + color flips */
341 parent
->rb_left
= tmp2
= sibling
->rb_right
;
342 sibling
->rb_right
= parent
;
343 rb_set_parent_color(tmp1
, sibling
, RB_BLACK
);
345 rb_set_parent(tmp2
, parent
);
346 __rb_rotate_set_parents(parent
, sibling
, root
,
348 augment_rotate(parent
, sibling
);
354 /* Non-inline version for rb_erase_augmented() use */
355 void __rb_erase_color(struct rb_node
*parent
, struct rb_root
*root
,
356 void (*augment_rotate
)(struct rb_node
*old
, struct rb_node
*new))
358 ____rb_erase_color(parent
, root
, augment_rotate
);
360 EXPORT_SYMBOL(__rb_erase_color
);
363 * Non-augmented rbtree manipulation functions.
365 * We use dummy augmented callbacks here, and have the compiler optimize them
366 * out of the rb_insert_color() and rb_erase() function definitions.
369 static inline void dummy_propagate(struct rb_node
*node
, struct rb_node
*stop
) {}
370 static inline void dummy_copy(struct rb_node
*old
, struct rb_node
*new) {}
371 static inline void dummy_rotate(struct rb_node
*old
, struct rb_node
*new) {}
373 static const struct rb_augment_callbacks dummy_callbacks
= {
374 dummy_propagate
, dummy_copy
, dummy_rotate
377 void rb_insert_color(struct rb_node
*node
, struct rb_root
*root
)
379 __rb_insert(node
, root
, dummy_rotate
);
381 EXPORT_SYMBOL(rb_insert_color
);
383 void rb_erase(struct rb_node
*node
, struct rb_root
*root
)
385 struct rb_node
*rebalance
;
386 rebalance
= __rb_erase_augmented(node
, root
, &dummy_callbacks
);
388 ____rb_erase_color(rebalance
, root
, dummy_rotate
);
390 EXPORT_SYMBOL(rb_erase
);
393 * Augmented rbtree manipulation functions.
395 * This instantiates the same __always_inline functions as in the non-augmented
396 * case, but this time with user-defined callbacks.
399 void __rb_insert_augmented(struct rb_node
*node
, struct rb_root
*root
,
400 void (*augment_rotate
)(struct rb_node
*old
, struct rb_node
*new))
402 __rb_insert(node
, root
, augment_rotate
);
404 EXPORT_SYMBOL(__rb_insert_augmented
);
407 * This function returns the first node (in sort order) of the tree.
409 struct rb_node
*rb_first(const struct rb_root
*root
)
420 EXPORT_SYMBOL(rb_first
);
422 struct rb_node
*rb_last(const struct rb_root
*root
)
433 EXPORT_SYMBOL(rb_last
);
435 struct rb_node
*rb_next(const struct rb_node
*node
)
437 struct rb_node
*parent
;
439 if (RB_EMPTY_NODE(node
))
443 * If we have a right-hand child, go down and then left as far
446 if (node
->rb_right
) {
447 node
= node
->rb_right
;
448 while (node
->rb_left
)
450 return (struct rb_node
*)node
;
454 * No right-hand children. Everything down and left is smaller than us,
455 * so any 'next' node must be in the general direction of our parent.
456 * Go up the tree; any time the ancestor is a right-hand child of its
457 * parent, keep going up. First time it's a left-hand child of its
458 * parent, said parent is our 'next' node.
460 while ((parent
= rb_parent(node
)) && node
== parent
->rb_right
)
465 EXPORT_SYMBOL(rb_next
);
467 struct rb_node
*rb_prev(const struct rb_node
*node
)
469 struct rb_node
*parent
;
471 if (RB_EMPTY_NODE(node
))
475 * If we have a left-hand child, go down and then right as far
479 node
= node
->rb_left
;
480 while (node
->rb_right
)
482 return (struct rb_node
*)node
;
486 * No left-hand children. Go up till we find an ancestor which
487 * is a right-hand child of its parent.
489 while ((parent
= rb_parent(node
)) && node
== parent
->rb_left
)
494 EXPORT_SYMBOL(rb_prev
);
496 void rb_replace_node(struct rb_node
*victim
, struct rb_node
*new,
497 struct rb_root
*root
)
499 struct rb_node
*parent
= rb_parent(victim
);
501 /* Set the surrounding nodes to point to the replacement */
502 __rb_change_child(victim
, new, parent
, root
);
504 rb_set_parent(victim
->rb_left
, new);
505 if (victim
->rb_right
)
506 rb_set_parent(victim
->rb_right
, new);
508 /* Copy the pointers/colour from the victim to the replacement */
511 EXPORT_SYMBOL(rb_replace_node
);
513 static struct rb_node
*rb_left_deepest_node(const struct rb_node
*node
)
517 node
= node
->rb_left
;
518 else if (node
->rb_right
)
519 node
= node
->rb_right
;
521 return (struct rb_node
*)node
;
525 struct rb_node
*rb_next_postorder(const struct rb_node
*node
)
527 const struct rb_node
*parent
;
530 parent
= rb_parent(node
);
532 /* If we're sitting on node, we've already seen our children */
533 if (parent
&& node
== parent
->rb_left
&& parent
->rb_right
) {
534 /* If we are the parent's left node, go to the parent's right
535 * node then all the way down to the left */
536 return rb_left_deepest_node(parent
->rb_right
);
538 /* Otherwise we are the parent's right node, and the parent
540 return (struct rb_node
*)parent
;
542 EXPORT_SYMBOL(rb_next_postorder
);
544 struct rb_node
*rb_first_postorder(const struct rb_root
*root
)
549 return rb_left_deepest_node(root
->rb_node
);
551 EXPORT_SYMBOL(rb_first_postorder
);