938061ecbe61d08c09654d0ec9e6740630c6e68c
[sfrench/cifs-2.6.git] / lib / rbtree.c
1 /*
2   Red Black Trees
3   (C) 1999  Andrea Arcangeli <andrea@suse.de>
4   (C) 2002  David Woodhouse <dwmw2@infradead.org>
5   (C) 2012  Michel Lespinasse <walken@google.com>
6
7   This program is free software; you can redistribute it and/or modify
8   it under the terms of the GNU General Public License as published by
9   the Free Software Foundation; either version 2 of the License, or
10   (at your option) any later version.
11
12   This program is distributed in the hope that it will be useful,
13   but WITHOUT ANY WARRANTY; without even the implied warranty of
14   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
15   GNU General Public License for more details.
16
17   You should have received a copy of the GNU General Public License
18   along with this program; if not, write to the Free Software
19   Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
20
21   linux/lib/rbtree.c
22 */
23
24 #include <linux/rbtree.h>
25 #include <linux/export.h>
26
27 /*
28  * red-black trees properties:  http://en.wikipedia.org/wiki/Rbtree
29  *
30  *  1) A node is either red or black
31  *  2) The root is black
32  *  3) All leaves (NULL) are black
33  *  4) Both children of every red node are black
34  *  5) Every simple path from root to leaves contains the same number
35  *     of black nodes.
36  *
37  *  4 and 5 give the O(log n) guarantee, since 4 implies you cannot have two
38  *  consecutive red nodes in a path and every red node is therefore followed by
39  *  a black. So if B is the number of black nodes on every simple path (as per
40  *  5), then the longest possible path due to 4 is 2B.
41  *
42  *  We shall indicate color with case, where black nodes are uppercase and red
43  *  nodes will be lowercase. Unknown color nodes shall be drawn as red within
44  *  parentheses and have some accompanying text comment.
45  */
46
47 #define RB_RED          0
48 #define RB_BLACK        1
49
50 #define __rb_parent(pc)    ((struct rb_node *)(pc & ~3))
51
52 #define __rb_color(pc)     ((pc) & 1)
53 #define __rb_is_black(pc)  __rb_color(pc)
54 #define __rb_is_red(pc)    (!__rb_color(pc))
55 #define rb_color(rb)       __rb_color((rb)->__rb_parent_color)
56 #define rb_is_red(rb)      __rb_is_red((rb)->__rb_parent_color)
57 #define rb_is_black(rb)    __rb_is_black((rb)->__rb_parent_color)
58
59 static inline void rb_set_black(struct rb_node *rb)
60 {
61         rb->__rb_parent_color |= RB_BLACK;
62 }
63
64 static inline void rb_set_parent(struct rb_node *rb, struct rb_node *p)
65 {
66         rb->__rb_parent_color = rb_color(rb) | (unsigned long)p;
67 }
68
69 static inline void rb_set_parent_color(struct rb_node *rb,
70                                        struct rb_node *p, int color)
71 {
72         rb->__rb_parent_color = (unsigned long)p | color;
73 }
74
75 static inline struct rb_node *rb_red_parent(struct rb_node *red)
76 {
77         return (struct rb_node *)red->__rb_parent_color;
78 }
79
80 static inline void
81 __rb_change_child(struct rb_node *old, struct rb_node *new,
82                   struct rb_node *parent, struct rb_root *root)
83 {
84         if (parent) {
85                 if (parent->rb_left == old)
86                         parent->rb_left = new;
87                 else
88                         parent->rb_right = new;
89         } else
90                 root->rb_node = new;
91 }
92
93 /*
94  * Helper function for rotations:
95  * - old's parent and color get assigned to new
96  * - old gets assigned new as a parent and 'color' as a color.
97  */
98 static inline void
99 __rb_rotate_set_parents(struct rb_node *old, struct rb_node *new,
100                         struct rb_root *root, int color)
101 {
102         struct rb_node *parent = rb_parent(old);
103         new->__rb_parent_color = old->__rb_parent_color;
104         rb_set_parent_color(old, new, color);
105         __rb_change_child(old, new, parent, root);
106 }
107
108 void rb_insert_color(struct rb_node *node, struct rb_root *root)
109 {
110         struct rb_node *parent = rb_red_parent(node), *gparent, *tmp;
111
112         while (true) {
113                 /*
114                  * Loop invariant: node is red
115                  *
116                  * If there is a black parent, we are done.
117                  * Otherwise, take some corrective action as we don't
118                  * want a red root or two consecutive red nodes.
119                  */
120                 if (!parent) {
121                         rb_set_parent_color(node, NULL, RB_BLACK);
122                         break;
123                 } else if (rb_is_black(parent))
124                         break;
125
126                 gparent = rb_red_parent(parent);
127
128                 tmp = gparent->rb_right;
129                 if (parent != tmp) {    /* parent == gparent->rb_left */
130                         if (tmp && rb_is_red(tmp)) {
131                                 /*
132                                  * Case 1 - color flips
133                                  *
134                                  *       G            g
135                                  *      / \          / \
136                                  *     p   u  -->   P   U
137                                  *    /            /
138                                  *   n            N
139                                  *
140                                  * However, since g's parent might be red, and
141                                  * 4) does not allow this, we need to recurse
142                                  * at g.
143                                  */
144                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
145                                 rb_set_parent_color(parent, gparent, RB_BLACK);
146                                 node = gparent;
147                                 parent = rb_parent(node);
148                                 rb_set_parent_color(node, parent, RB_RED);
149                                 continue;
150                         }
151
152                         tmp = parent->rb_right;
153                         if (node == tmp) {
154                                 /*
155                                  * Case 2 - left rotate at parent
156                                  *
157                                  *      G             G
158                                  *     / \           / \
159                                  *    p   U  -->    n   U
160                                  *     \           /
161                                  *      n         p
162                                  *
163                                  * This still leaves us in violation of 4), the
164                                  * continuation into Case 3 will fix that.
165                                  */
166                                 parent->rb_right = tmp = node->rb_left;
167                                 node->rb_left = parent;
168                                 if (tmp)
169                                         rb_set_parent_color(tmp, parent,
170                                                             RB_BLACK);
171                                 rb_set_parent_color(parent, node, RB_RED);
172                                 parent = node;
173                                 tmp = node->rb_right;
174                         }
175
176                         /*
177                          * Case 3 - right rotate at gparent
178                          *
179                          *        G           P
180                          *       / \         / \
181                          *      p   U  -->  n   g
182                          *     /                 \
183                          *    n                   U
184                          */
185                         gparent->rb_left = tmp;  /* == parent->rb_right */
186                         parent->rb_right = gparent;
187                         if (tmp)
188                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
189                         __rb_rotate_set_parents(gparent, parent, root, RB_RED);
190                         break;
191                 } else {
192                         tmp = gparent->rb_left;
193                         if (tmp && rb_is_red(tmp)) {
194                                 /* Case 1 - color flips */
195                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
196                                 rb_set_parent_color(parent, gparent, RB_BLACK);
197                                 node = gparent;
198                                 parent = rb_parent(node);
199                                 rb_set_parent_color(node, parent, RB_RED);
200                                 continue;
201                         }
202
203                         tmp = parent->rb_left;
204                         if (node == tmp) {
205                                 /* Case 2 - right rotate at parent */
206                                 parent->rb_left = tmp = node->rb_right;
207                                 node->rb_right = parent;
208                                 if (tmp)
209                                         rb_set_parent_color(tmp, parent,
210                                                             RB_BLACK);
211                                 rb_set_parent_color(parent, node, RB_RED);
212                                 parent = node;
213                                 tmp = node->rb_left;
214                         }
215
216                         /* Case 3 - left rotate at gparent */
217                         gparent->rb_right = tmp;  /* == parent->rb_left */
218                         parent->rb_left = gparent;
219                         if (tmp)
220                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
221                         __rb_rotate_set_parents(gparent, parent, root, RB_RED);
222                         break;
223                 }
224         }
225 }
226 EXPORT_SYMBOL(rb_insert_color);
227
228 static void __rb_erase_color(struct rb_node *parent, struct rb_root *root)
229 {
230         struct rb_node *node = NULL, *sibling, *tmp1, *tmp2;
231
232         while (true) {
233                 /*
234                  * Loop invariants:
235                  * - node is black (or NULL on first iteration)
236                  * - node is not the root (parent is not NULL)
237                  * - All leaf paths going through parent and node have a
238                  *   black node count that is 1 lower than other leaf paths.
239                  */
240                 sibling = parent->rb_right;
241                 if (node != sibling) {  /* node == parent->rb_left */
242                         if (rb_is_red(sibling)) {
243                                 /*
244                                  * Case 1 - left rotate at parent
245                                  *
246                                  *     P               S
247                                  *    / \             / \
248                                  *   N   s    -->    p   Sr
249                                  *      / \         / \
250                                  *     Sl  Sr      N   Sl
251                                  */
252                                 parent->rb_right = tmp1 = sibling->rb_left;
253                                 sibling->rb_left = parent;
254                                 rb_set_parent_color(tmp1, parent, RB_BLACK);
255                                 __rb_rotate_set_parents(parent, sibling, root,
256                                                         RB_RED);
257                                 sibling = tmp1;
258                         }
259                         tmp1 = sibling->rb_right;
260                         if (!tmp1 || rb_is_black(tmp1)) {
261                                 tmp2 = sibling->rb_left;
262                                 if (!tmp2 || rb_is_black(tmp2)) {
263                                         /*
264                                          * Case 2 - sibling color flip
265                                          * (p could be either color here)
266                                          *
267                                          *    (p)           (p)
268                                          *    / \           / \
269                                          *   N   S    -->  N   s
270                                          *      / \           / \
271                                          *     Sl  Sr        Sl  Sr
272                                          *
273                                          * This leaves us violating 5) which
274                                          * can be fixed by flipping p to black
275                                          * if it was red, or by recursing at p.
276                                          * p is red when coming from Case 1.
277                                          */
278                                         rb_set_parent_color(sibling, parent,
279                                                             RB_RED);
280                                         if (rb_is_red(parent))
281                                                 rb_set_black(parent);
282                                         else {
283                                                 node = parent;
284                                                 parent = rb_parent(node);
285                                                 if (parent)
286                                                         continue;
287                                         }
288                                         break;
289                                 }
290                                 /*
291                                  * Case 3 - right rotate at sibling
292                                  * (p could be either color here)
293                                  *
294                                  *   (p)           (p)
295                                  *   / \           / \
296                                  *  N   S    -->  N   Sl
297                                  *     / \             \
298                                  *    sl  Sr            s
299                                  *                       \
300                                  *                        Sr
301                                  */
302                                 sibling->rb_left = tmp1 = tmp2->rb_right;
303                                 tmp2->rb_right = sibling;
304                                 parent->rb_right = tmp2;
305                                 if (tmp1)
306                                         rb_set_parent_color(tmp1, sibling,
307                                                             RB_BLACK);
308                                 tmp1 = sibling;
309                                 sibling = tmp2;
310                         }
311                         /*
312                          * Case 4 - left rotate at parent + color flips
313                          * (p and sl could be either color here.
314                          *  After rotation, p becomes black, s acquires
315                          *  p's color, and sl keeps its color)
316                          *
317                          *      (p)             (s)
318                          *      / \             / \
319                          *     N   S     -->   P   Sr
320                          *        / \         / \
321                          *      (sl) sr      N  (sl)
322                          */
323                         parent->rb_right = tmp2 = sibling->rb_left;
324                         sibling->rb_left = parent;
325                         rb_set_parent_color(tmp1, sibling, RB_BLACK);
326                         if (tmp2)
327                                 rb_set_parent(tmp2, parent);
328                         __rb_rotate_set_parents(parent, sibling, root,
329                                                 RB_BLACK);
330                         break;
331                 } else {
332                         sibling = parent->rb_left;
333                         if (rb_is_red(sibling)) {
334                                 /* Case 1 - right rotate at parent */
335                                 parent->rb_left = tmp1 = sibling->rb_right;
336                                 sibling->rb_right = parent;
337                                 rb_set_parent_color(tmp1, parent, RB_BLACK);
338                                 __rb_rotate_set_parents(parent, sibling, root,
339                                                         RB_RED);
340                                 sibling = tmp1;
341                         }
342                         tmp1 = sibling->rb_left;
343                         if (!tmp1 || rb_is_black(tmp1)) {
344                                 tmp2 = sibling->rb_right;
345                                 if (!tmp2 || rb_is_black(tmp2)) {
346                                         /* Case 2 - sibling color flip */
347                                         rb_set_parent_color(sibling, parent,
348                                                             RB_RED);
349                                         if (rb_is_red(parent))
350                                                 rb_set_black(parent);
351                                         else {
352                                                 node = parent;
353                                                 parent = rb_parent(node);
354                                                 if (parent)
355                                                         continue;
356                                         }
357                                         break;
358                                 }
359                                 /* Case 3 - right rotate at sibling */
360                                 sibling->rb_right = tmp1 = tmp2->rb_left;
361                                 tmp2->rb_left = sibling;
362                                 parent->rb_left = tmp2;
363                                 if (tmp1)
364                                         rb_set_parent_color(tmp1, sibling,
365                                                             RB_BLACK);
366                                 tmp1 = sibling;
367                                 sibling = tmp2;
368                         }
369                         /* Case 4 - left rotate at parent + color flips */
370                         parent->rb_left = tmp2 = sibling->rb_right;
371                         sibling->rb_right = parent;
372                         rb_set_parent_color(tmp1, sibling, RB_BLACK);
373                         if (tmp2)
374                                 rb_set_parent(tmp2, parent);
375                         __rb_rotate_set_parents(parent, sibling, root,
376                                                 RB_BLACK);
377                         break;
378                 }
379         }
380 }
381
382 void rb_erase(struct rb_node *node, struct rb_root *root)
383 {
384         struct rb_node *child = node->rb_right, *tmp = node->rb_left;
385         struct rb_node *parent, *rebalance;
386         unsigned long pc;
387
388         if (!tmp) {
389                 /*
390                  * Case 1: node to erase has no more than 1 child (easy!)
391                  *
392                  * Note that if there is one child it must be red due to 5)
393                  * and node must be black due to 4). We adjust colors locally
394                  * so as to bypass __rb_erase_color() later on.
395                  */
396                 pc = node->__rb_parent_color;
397                 parent = __rb_parent(pc);
398                 __rb_change_child(node, child, parent, root);
399                 if (child) {
400                         child->__rb_parent_color = pc;
401                         rebalance = NULL;
402                 } else
403                         rebalance = __rb_is_black(pc) ? parent : NULL;
404         } else if (!child) {
405                 /* Still case 1, but this time the child is node->rb_left */
406                 tmp->__rb_parent_color = pc = node->__rb_parent_color;
407                 parent = __rb_parent(pc);
408                 __rb_change_child(node, tmp, parent, root);
409                 rebalance = NULL;
410         } else {
411                 struct rb_node *successor = child, *child2;
412                 tmp = child->rb_left;
413                 if (!tmp) {
414                         /*
415                          * Case 2: node's successor is its right child
416                          *
417                          *    (n)          (s)
418                          *    / \          / \
419                          *  (x) (s)  ->  (x) (c)
420                          *        \
421                          *        (c)
422                          */
423                         parent = child;
424                         child2 = child->rb_right;
425                 } else {
426                         /*
427                          * Case 3: node's successor is leftmost under
428                          * node's right child subtree
429                          *
430                          *    (n)          (s)
431                          *    / \          / \
432                          *  (x) (y)  ->  (x) (y)
433                          *      /            /
434                          *    (p)          (p)
435                          *    /            /
436                          *  (s)          (c)
437                          *    \
438                          *    (c)
439                          */
440                         do {
441                                 parent = successor;
442                                 successor = tmp;
443                                 tmp = tmp->rb_left;
444                         } while (tmp);
445                         parent->rb_left = child2 = successor->rb_right;
446                         successor->rb_right = child;
447                         rb_set_parent(child, successor);
448                 }
449
450                 successor->rb_left = tmp = node->rb_left;
451                 rb_set_parent(tmp, successor);
452
453                 pc = node->__rb_parent_color;
454                 tmp = __rb_parent(pc);
455                 __rb_change_child(node, successor, tmp, root);
456                 if (child2) {
457                         successor->__rb_parent_color = pc;
458                         rb_set_parent_color(child2, parent, RB_BLACK);
459                         rebalance = NULL;
460                 } else {
461                         unsigned long pc2 = successor->__rb_parent_color;
462                         successor->__rb_parent_color = pc;
463                         rebalance = __rb_is_black(pc2) ? parent : NULL;
464                 }
465         }
466
467         if (rebalance)
468                 __rb_erase_color(rebalance, root);
469 }
470 EXPORT_SYMBOL(rb_erase);
471
472 static void rb_augment_path(struct rb_node *node, rb_augment_f func, void *data)
473 {
474         struct rb_node *parent;
475
476 up:
477         func(node, data);
478         parent = rb_parent(node);
479         if (!parent)
480                 return;
481
482         if (node == parent->rb_left && parent->rb_right)
483                 func(parent->rb_right, data);
484         else if (parent->rb_left)
485                 func(parent->rb_left, data);
486
487         node = parent;
488         goto up;
489 }
490
491 /*
492  * after inserting @node into the tree, update the tree to account for
493  * both the new entry and any damage done by rebalance
494  */
495 void rb_augment_insert(struct rb_node *node, rb_augment_f func, void *data)
496 {
497         if (node->rb_left)
498                 node = node->rb_left;
499         else if (node->rb_right)
500                 node = node->rb_right;
501
502         rb_augment_path(node, func, data);
503 }
504 EXPORT_SYMBOL(rb_augment_insert);
505
506 /*
507  * before removing the node, find the deepest node on the rebalance path
508  * that will still be there after @node gets removed
509  */
510 struct rb_node *rb_augment_erase_begin(struct rb_node *node)
511 {
512         struct rb_node *deepest;
513
514         if (!node->rb_right && !node->rb_left)
515                 deepest = rb_parent(node);
516         else if (!node->rb_right)
517                 deepest = node->rb_left;
518         else if (!node->rb_left)
519                 deepest = node->rb_right;
520         else {
521                 deepest = rb_next(node);
522                 if (deepest->rb_right)
523                         deepest = deepest->rb_right;
524                 else if (rb_parent(deepest) != node)
525                         deepest = rb_parent(deepest);
526         }
527
528         return deepest;
529 }
530 EXPORT_SYMBOL(rb_augment_erase_begin);
531
532 /*
533  * after removal, update the tree to account for the removed entry
534  * and any rebalance damage.
535  */
536 void rb_augment_erase_end(struct rb_node *node, rb_augment_f func, void *data)
537 {
538         if (node)
539                 rb_augment_path(node, func, data);
540 }
541 EXPORT_SYMBOL(rb_augment_erase_end);
542
543 /*
544  * This function returns the first node (in sort order) of the tree.
545  */
546 struct rb_node *rb_first(const struct rb_root *root)
547 {
548         struct rb_node  *n;
549
550         n = root->rb_node;
551         if (!n)
552                 return NULL;
553         while (n->rb_left)
554                 n = n->rb_left;
555         return n;
556 }
557 EXPORT_SYMBOL(rb_first);
558
559 struct rb_node *rb_last(const struct rb_root *root)
560 {
561         struct rb_node  *n;
562
563         n = root->rb_node;
564         if (!n)
565                 return NULL;
566         while (n->rb_right)
567                 n = n->rb_right;
568         return n;
569 }
570 EXPORT_SYMBOL(rb_last);
571
572 struct rb_node *rb_next(const struct rb_node *node)
573 {
574         struct rb_node *parent;
575
576         if (RB_EMPTY_NODE(node))
577                 return NULL;
578
579         /*
580          * If we have a right-hand child, go down and then left as far
581          * as we can.
582          */
583         if (node->rb_right) {
584                 node = node->rb_right; 
585                 while (node->rb_left)
586                         node=node->rb_left;
587                 return (struct rb_node *)node;
588         }
589
590         /*
591          * No right-hand children. Everything down and left is smaller than us,
592          * so any 'next' node must be in the general direction of our parent.
593          * Go up the tree; any time the ancestor is a right-hand child of its
594          * parent, keep going up. First time it's a left-hand child of its
595          * parent, said parent is our 'next' node.
596          */
597         while ((parent = rb_parent(node)) && node == parent->rb_right)
598                 node = parent;
599
600         return parent;
601 }
602 EXPORT_SYMBOL(rb_next);
603
604 struct rb_node *rb_prev(const struct rb_node *node)
605 {
606         struct rb_node *parent;
607
608         if (RB_EMPTY_NODE(node))
609                 return NULL;
610
611         /*
612          * If we have a left-hand child, go down and then right as far
613          * as we can.
614          */
615         if (node->rb_left) {
616                 node = node->rb_left; 
617                 while (node->rb_right)
618                         node=node->rb_right;
619                 return (struct rb_node *)node;
620         }
621
622         /*
623          * No left-hand children. Go up till we find an ancestor which
624          * is a right-hand child of its parent.
625          */
626         while ((parent = rb_parent(node)) && node == parent->rb_left)
627                 node = parent;
628
629         return parent;
630 }
631 EXPORT_SYMBOL(rb_prev);
632
633 void rb_replace_node(struct rb_node *victim, struct rb_node *new,
634                      struct rb_root *root)
635 {
636         struct rb_node *parent = rb_parent(victim);
637
638         /* Set the surrounding nodes to point to the replacement */
639         __rb_change_child(victim, new, parent, root);
640         if (victim->rb_left)
641                 rb_set_parent(victim->rb_left, new);
642         if (victim->rb_right)
643                 rb_set_parent(victim->rb_right, new);
644
645         /* Copy the pointers/colour from the victim to the replacement */
646         *new = *victim;
647 }
648 EXPORT_SYMBOL(rb_replace_node);