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1 // SPDX-License-Identifier: GPL-2.0+
2 /*
3   Red Black Trees
4   (C) 1999  Andrea Arcangeli <andrea@suse.de>
5   (C) 2002  David Woodhouse <dwmw2@infradead.org>
6   (C) 2012  Michel Lespinasse <walken@google.com>
7
8   linux/lib/rbtree.c
9 */
10
11 #include <linux/rbtree_augmented.h>
12 #ifndef __UBOOT__
13 #include <linux/export.h>
14 #else
15 #include <ubi_uboot.h>
16 #endif
17 /*
18  * red-black trees properties:  http://en.wikipedia.org/wiki/Rbtree
19  *
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
25  *     of black nodes.
26  *
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.
31  *
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.
35  */
36
37 static inline void rb_set_black(struct rb_node *rb)
38 {
39         rb->__rb_parent_color |= RB_BLACK;
40 }
41
42 static inline struct rb_node *rb_red_parent(struct rb_node *red)
43 {
44         return (struct rb_node *)red->__rb_parent_color;
45 }
46
47 /*
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.
51  */
52 static inline void
53 __rb_rotate_set_parents(struct rb_node *old, struct rb_node *new,
54                         struct rb_root *root, int color)
55 {
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);
60 }
61
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))
65 {
66         struct rb_node *parent = rb_red_parent(node), *gparent, *tmp;
67
68         while (true) {
69                 /*
70                  * Loop invariant: node is red
71                  *
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.
75                  */
76                 if (!parent) {
77                         rb_set_parent_color(node, NULL, RB_BLACK);
78                         break;
79                 } else if (rb_is_black(parent))
80                         break;
81
82                 gparent = rb_red_parent(parent);
83
84                 tmp = gparent->rb_right;
85                 if (parent != tmp) {    /* parent == gparent->rb_left */
86                         if (tmp && rb_is_red(tmp)) {
87                                 /*
88                                  * Case 1 - color flips
89                                  *
90                                  *       G            g
91                                  *      / \          / \
92                                  *     p   u  -->   P   U
93                                  *    /            /
94                                  *   n            N
95                                  *
96                                  * However, since g's parent might be red, and
97                                  * 4) does not allow this, we need to recurse
98                                  * at g.
99                                  */
100                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
101                                 rb_set_parent_color(parent, gparent, RB_BLACK);
102                                 node = gparent;
103                                 parent = rb_parent(node);
104                                 rb_set_parent_color(node, parent, RB_RED);
105                                 continue;
106                         }
107
108                         tmp = parent->rb_right;
109                         if (node == tmp) {
110                                 /*
111                                  * Case 2 - left rotate at parent
112                                  *
113                                  *      G             G
114                                  *     / \           / \
115                                  *    p   U  -->    n   U
116                                  *     \           /
117                                  *      n         p
118                                  *
119                                  * This still leaves us in violation of 4), the
120                                  * continuation into Case 3 will fix that.
121                                  */
122                                 parent->rb_right = tmp = node->rb_left;
123                                 node->rb_left = parent;
124                                 if (tmp)
125                                         rb_set_parent_color(tmp, parent,
126                                                             RB_BLACK);
127                                 rb_set_parent_color(parent, node, RB_RED);
128                                 augment_rotate(parent, node);
129                                 parent = node;
130                                 tmp = node->rb_right;
131                         }
132
133                         /*
134                          * Case 3 - right rotate at gparent
135                          *
136                          *        G           P
137                          *       / \         / \
138                          *      p   U  -->  n   g
139                          *     /                 \
140                          *    n                   U
141                          */
142                         gparent->rb_left = tmp;  /* == parent->rb_right */
143                         parent->rb_right = gparent;
144                         if (tmp)
145                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
146                         __rb_rotate_set_parents(gparent, parent, root, RB_RED);
147                         augment_rotate(gparent, parent);
148                         break;
149                 } else {
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);
155                                 node = gparent;
156                                 parent = rb_parent(node);
157                                 rb_set_parent_color(node, parent, RB_RED);
158                                 continue;
159                         }
160
161                         tmp = parent->rb_left;
162                         if (node == tmp) {
163                                 /* Case 2 - right rotate at parent */
164                                 parent->rb_left = tmp = node->rb_right;
165                                 node->rb_right = parent;
166                                 if (tmp)
167                                         rb_set_parent_color(tmp, parent,
168                                                             RB_BLACK);
169                                 rb_set_parent_color(parent, node, RB_RED);
170                                 augment_rotate(parent, node);
171                                 parent = node;
172                                 tmp = node->rb_left;
173                         }
174
175                         /* Case 3 - left rotate at gparent */
176                         gparent->rb_right = tmp;  /* == parent->rb_left */
177                         parent->rb_left = gparent;
178                         if (tmp)
179                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
180                         __rb_rotate_set_parents(gparent, parent, root, RB_RED);
181                         augment_rotate(gparent, parent);
182                         break;
183                 }
184         }
185 }
186
187 /*
188  * Inline version for rb_erase() use - we want to be able to inline
189  * and eliminate the dummy_rotate callback there
190  */
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))
194 {
195         struct rb_node *node = NULL, *sibling, *tmp1, *tmp2;
196
197         while (true) {
198                 /*
199                  * Loop invariants:
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.
204                  */
205                 sibling = parent->rb_right;
206                 if (node != sibling) {  /* node == parent->rb_left */
207                         if (rb_is_red(sibling)) {
208                                 /*
209                                  * Case 1 - left rotate at parent
210                                  *
211                                  *     P               S
212                                  *    / \             / \
213                                  *   N   s    -->    p   Sr
214                                  *      / \         / \
215                                  *     Sl  Sr      N   Sl
216                                  */
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,
221                                                         RB_RED);
222                                 augment_rotate(parent, sibling);
223                                 sibling = tmp1;
224                         }
225                         tmp1 = sibling->rb_right;
226                         if (!tmp1 || rb_is_black(tmp1)) {
227                                 tmp2 = sibling->rb_left;
228                                 if (!tmp2 || rb_is_black(tmp2)) {
229                                         /*
230                                          * Case 2 - sibling color flip
231                                          * (p could be either color here)
232                                          *
233                                          *    (p)           (p)
234                                          *    / \           / \
235                                          *   N   S    -->  N   s
236                                          *      / \           / \
237                                          *     Sl  Sr        Sl  Sr
238                                          *
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.
243                                          */
244                                         rb_set_parent_color(sibling, parent,
245                                                             RB_RED);
246                                         if (rb_is_red(parent))
247                                                 rb_set_black(parent);
248                                         else {
249                                                 node = parent;
250                                                 parent = rb_parent(node);
251                                                 if (parent)
252                                                         continue;
253                                         }
254                                         break;
255                                 }
256                                 /*
257                                  * Case 3 - right rotate at sibling
258                                  * (p could be either color here)
259                                  *
260                                  *   (p)           (p)
261                                  *   / \           / \
262                                  *  N   S    -->  N   Sl
263                                  *     / \             \
264                                  *    sl  Sr            s
265                                  *                       \
266                                  *                        Sr
267                                  */
268                                 sibling->rb_left = tmp1 = tmp2->rb_right;
269                                 tmp2->rb_right = sibling;
270                                 parent->rb_right = tmp2;
271                                 if (tmp1)
272                                         rb_set_parent_color(tmp1, sibling,
273                                                             RB_BLACK);
274                                 augment_rotate(sibling, tmp2);
275                                 tmp1 = sibling;
276                                 sibling = tmp2;
277                         }
278                         /*
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)
283                          *
284                          *      (p)             (s)
285                          *      / \             / \
286                          *     N   S     -->   P   Sr
287                          *        / \         / \
288                          *      (sl) sr      N  (sl)
289                          */
290                         parent->rb_right = tmp2 = sibling->rb_left;
291                         sibling->rb_left = parent;
292                         rb_set_parent_color(tmp1, sibling, RB_BLACK);
293                         if (tmp2)
294                                 rb_set_parent(tmp2, parent);
295                         __rb_rotate_set_parents(parent, sibling, root,
296                                                 RB_BLACK);
297                         augment_rotate(parent, sibling);
298                         break;
299                 } else {
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,
307                                                         RB_RED);
308                                 augment_rotate(parent, sibling);
309                                 sibling = tmp1;
310                         }
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,
317                                                             RB_RED);
318                                         if (rb_is_red(parent))
319                                                 rb_set_black(parent);
320                                         else {
321                                                 node = parent;
322                                                 parent = rb_parent(node);
323                                                 if (parent)
324                                                         continue;
325                                         }
326                                         break;
327                                 }
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;
332                                 if (tmp1)
333                                         rb_set_parent_color(tmp1, sibling,
334                                                             RB_BLACK);
335                                 augment_rotate(sibling, tmp2);
336                                 tmp1 = sibling;
337                                 sibling = tmp2;
338                         }
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);
343                         if (tmp2)
344                                 rb_set_parent(tmp2, parent);
345                         __rb_rotate_set_parents(parent, sibling, root,
346                                                 RB_BLACK);
347                         augment_rotate(parent, sibling);
348                         break;
349                 }
350         }
351 }
352
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))
356 {
357         ____rb_erase_color(parent, root, augment_rotate);
358 }
359 EXPORT_SYMBOL(__rb_erase_color);
360
361 /*
362  * Non-augmented rbtree manipulation functions.
363  *
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.
366  */
367
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) {}
371
372 static const struct rb_augment_callbacks dummy_callbacks = {
373         dummy_propagate, dummy_copy, dummy_rotate
374 };
375
376 void rb_insert_color(struct rb_node *node, struct rb_root *root)
377 {
378         __rb_insert(node, root, dummy_rotate);
379 }
380 EXPORT_SYMBOL(rb_insert_color);
381
382 void rb_erase(struct rb_node *node, struct rb_root *root)
383 {
384         struct rb_node *rebalance;
385         rebalance = __rb_erase_augmented(node, root, &dummy_callbacks);
386         if (rebalance)
387                 ____rb_erase_color(rebalance, root, dummy_rotate);
388 }
389 EXPORT_SYMBOL(rb_erase);
390
391 /*
392  * Augmented rbtree manipulation functions.
393  *
394  * This instantiates the same __always_inline functions as in the non-augmented
395  * case, but this time with user-defined callbacks.
396  */
397
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))
400 {
401         __rb_insert(node, root, augment_rotate);
402 }
403 EXPORT_SYMBOL(__rb_insert_augmented);
404
405 /*
406  * This function returns the first node (in sort order) of the tree.
407  */
408 struct rb_node *rb_first(const struct rb_root *root)
409 {
410         struct rb_node  *n;
411
412         n = root->rb_node;
413         if (!n)
414                 return NULL;
415         while (n->rb_left)
416                 n = n->rb_left;
417         return n;
418 }
419 EXPORT_SYMBOL(rb_first);
420
421 struct rb_node *rb_last(const struct rb_root *root)
422 {
423         struct rb_node  *n;
424
425         n = root->rb_node;
426         if (!n)
427                 return NULL;
428         while (n->rb_right)
429                 n = n->rb_right;
430         return n;
431 }
432 EXPORT_SYMBOL(rb_last);
433
434 struct rb_node *rb_next(const struct rb_node *node)
435 {
436         struct rb_node *parent;
437
438         if (RB_EMPTY_NODE(node))
439                 return NULL;
440
441         /*
442          * If we have a right-hand child, go down and then left as far
443          * as we can.
444          */
445         if (node->rb_right) {
446                 node = node->rb_right; 
447                 while (node->rb_left)
448                         node=node->rb_left;
449                 return (struct rb_node *)node;
450         }
451
452         /*
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.
458          */
459         while ((parent = rb_parent(node)) && node == parent->rb_right)
460                 node = parent;
461
462         return parent;
463 }
464 EXPORT_SYMBOL(rb_next);
465
466 struct rb_node *rb_prev(const struct rb_node *node)
467 {
468         struct rb_node *parent;
469
470         if (RB_EMPTY_NODE(node))
471                 return NULL;
472
473         /*
474          * If we have a left-hand child, go down and then right as far
475          * as we can.
476          */
477         if (node->rb_left) {
478                 node = node->rb_left; 
479                 while (node->rb_right)
480                         node=node->rb_right;
481                 return (struct rb_node *)node;
482         }
483
484         /*
485          * No left-hand children. Go up till we find an ancestor which
486          * is a right-hand child of its parent.
487          */
488         while ((parent = rb_parent(node)) && node == parent->rb_left)
489                 node = parent;
490
491         return parent;
492 }
493 EXPORT_SYMBOL(rb_prev);
494
495 void rb_replace_node(struct rb_node *victim, struct rb_node *new,
496                      struct rb_root *root)
497 {
498         struct rb_node *parent = rb_parent(victim);
499
500         /* Set the surrounding nodes to point to the replacement */
501         __rb_change_child(victim, new, parent, root);
502         if (victim->rb_left)
503                 rb_set_parent(victim->rb_left, new);
504         if (victim->rb_right)
505                 rb_set_parent(victim->rb_right, new);
506
507         /* Copy the pointers/colour from the victim to the replacement */
508         *new = *victim;
509 }
510 EXPORT_SYMBOL(rb_replace_node);
511
512 static struct rb_node *rb_left_deepest_node(const struct rb_node *node)
513 {
514         for (;;) {
515                 if (node->rb_left)
516                         node = node->rb_left;
517                 else if (node->rb_right)
518                         node = node->rb_right;
519                 else
520                         return (struct rb_node *)node;
521         }
522 }
523
524 struct rb_node *rb_next_postorder(const struct rb_node *node)
525 {
526         const struct rb_node *parent;
527         if (!node)
528                 return NULL;
529         parent = rb_parent(node);
530
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);
536         } else
537                 /* Otherwise we are the parent's right node, and the parent
538                  * should be next */
539                 return (struct rb_node *)parent;
540 }
541 EXPORT_SYMBOL(rb_next_postorder);
542
543 struct rb_node *rb_first_postorder(const struct rb_root *root)
544 {
545         if (!root->rb_node)
546                 return NULL;
547
548         return rb_left_deepest_node(root->rb_node);
549 }
550 EXPORT_SYMBOL(rb_first_postorder);