rbtree: faster augmented rbtree manipulation
[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 static __always_inline void
109 __rb_insert(struct rb_node *node, struct rb_root *root,
110             void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
111 {
112         struct rb_node *parent = rb_red_parent(node), *gparent, *tmp;
113
114         while (true) {
115                 /*
116                  * Loop invariant: node is red
117                  *
118                  * If there is a black parent, we are done.
119                  * Otherwise, take some corrective action as we don't
120                  * want a red root or two consecutive red nodes.
121                  */
122                 if (!parent) {
123                         rb_set_parent_color(node, NULL, RB_BLACK);
124                         break;
125                 } else if (rb_is_black(parent))
126                         break;
127
128                 gparent = rb_red_parent(parent);
129
130                 tmp = gparent->rb_right;
131                 if (parent != tmp) {    /* parent == gparent->rb_left */
132                         if (tmp && rb_is_red(tmp)) {
133                                 /*
134                                  * Case 1 - color flips
135                                  *
136                                  *       G            g
137                                  *      / \          / \
138                                  *     p   u  -->   P   U
139                                  *    /            /
140                                  *   n            N
141                                  *
142                                  * However, since g's parent might be red, and
143                                  * 4) does not allow this, we need to recurse
144                                  * at g.
145                                  */
146                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
147                                 rb_set_parent_color(parent, gparent, RB_BLACK);
148                                 node = gparent;
149                                 parent = rb_parent(node);
150                                 rb_set_parent_color(node, parent, RB_RED);
151                                 continue;
152                         }
153
154                         tmp = parent->rb_right;
155                         if (node == tmp) {
156                                 /*
157                                  * Case 2 - left rotate at parent
158                                  *
159                                  *      G             G
160                                  *     / \           / \
161                                  *    p   U  -->    n   U
162                                  *     \           /
163                                  *      n         p
164                                  *
165                                  * This still leaves us in violation of 4), the
166                                  * continuation into Case 3 will fix that.
167                                  */
168                                 parent->rb_right = tmp = node->rb_left;
169                                 node->rb_left = parent;
170                                 if (tmp)
171                                         rb_set_parent_color(tmp, parent,
172                                                             RB_BLACK);
173                                 rb_set_parent_color(parent, node, RB_RED);
174                                 augment_rotate(parent, node);
175                                 parent = node;
176                                 tmp = node->rb_right;
177                         }
178
179                         /*
180                          * Case 3 - right rotate at gparent
181                          *
182                          *        G           P
183                          *       / \         / \
184                          *      p   U  -->  n   g
185                          *     /                 \
186                          *    n                   U
187                          */
188                         gparent->rb_left = tmp;  /* == parent->rb_right */
189                         parent->rb_right = gparent;
190                         if (tmp)
191                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
192                         __rb_rotate_set_parents(gparent, parent, root, RB_RED);
193                         augment_rotate(gparent, parent);
194                         break;
195                 } else {
196                         tmp = gparent->rb_left;
197                         if (tmp && rb_is_red(tmp)) {
198                                 /* Case 1 - color flips */
199                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
200                                 rb_set_parent_color(parent, gparent, RB_BLACK);
201                                 node = gparent;
202                                 parent = rb_parent(node);
203                                 rb_set_parent_color(node, parent, RB_RED);
204                                 continue;
205                         }
206
207                         tmp = parent->rb_left;
208                         if (node == tmp) {
209                                 /* Case 2 - right rotate at parent */
210                                 parent->rb_left = tmp = node->rb_right;
211                                 node->rb_right = parent;
212                                 if (tmp)
213                                         rb_set_parent_color(tmp, parent,
214                                                             RB_BLACK);
215                                 rb_set_parent_color(parent, node, RB_RED);
216                                 augment_rotate(parent, node);
217                                 parent = node;
218                                 tmp = node->rb_left;
219                         }
220
221                         /* Case 3 - left rotate at gparent */
222                         gparent->rb_right = tmp;  /* == parent->rb_left */
223                         parent->rb_left = gparent;
224                         if (tmp)
225                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
226                         __rb_rotate_set_parents(gparent, parent, root, RB_RED);
227                         augment_rotate(gparent, parent);
228                         break;
229                 }
230         }
231 }
232
233 static __always_inline void
234 __rb_erase_color(struct rb_node *parent, struct rb_root *root,
235                  const struct rb_augment_callbacks *augment)
236 {
237         struct rb_node *node = NULL, *sibling, *tmp1, *tmp2;
238
239         while (true) {
240                 /*
241                  * Loop invariants:
242                  * - node is black (or NULL on first iteration)
243                  * - node is not the root (parent is not NULL)
244                  * - All leaf paths going through parent and node have a
245                  *   black node count that is 1 lower than other leaf paths.
246                  */
247                 sibling = parent->rb_right;
248                 if (node != sibling) {  /* node == parent->rb_left */
249                         if (rb_is_red(sibling)) {
250                                 /*
251                                  * Case 1 - left rotate at parent
252                                  *
253                                  *     P               S
254                                  *    / \             / \
255                                  *   N   s    -->    p   Sr
256                                  *      / \         / \
257                                  *     Sl  Sr      N   Sl
258                                  */
259                                 parent->rb_right = tmp1 = sibling->rb_left;
260                                 sibling->rb_left = parent;
261                                 rb_set_parent_color(tmp1, parent, RB_BLACK);
262                                 __rb_rotate_set_parents(parent, sibling, root,
263                                                         RB_RED);
264                                 augment->rotate(parent, sibling);
265                                 sibling = tmp1;
266                         }
267                         tmp1 = sibling->rb_right;
268                         if (!tmp1 || rb_is_black(tmp1)) {
269                                 tmp2 = sibling->rb_left;
270                                 if (!tmp2 || rb_is_black(tmp2)) {
271                                         /*
272                                          * Case 2 - sibling color flip
273                                          * (p could be either color here)
274                                          *
275                                          *    (p)           (p)
276                                          *    / \           / \
277                                          *   N   S    -->  N   s
278                                          *      / \           / \
279                                          *     Sl  Sr        Sl  Sr
280                                          *
281                                          * This leaves us violating 5) which
282                                          * can be fixed by flipping p to black
283                                          * if it was red, or by recursing at p.
284                                          * p is red when coming from Case 1.
285                                          */
286                                         rb_set_parent_color(sibling, parent,
287                                                             RB_RED);
288                                         if (rb_is_red(parent))
289                                                 rb_set_black(parent);
290                                         else {
291                                                 node = parent;
292                                                 parent = rb_parent(node);
293                                                 if (parent)
294                                                         continue;
295                                         }
296                                         break;
297                                 }
298                                 /*
299                                  * Case 3 - right rotate at sibling
300                                  * (p could be either color here)
301                                  *
302                                  *   (p)           (p)
303                                  *   / \           / \
304                                  *  N   S    -->  N   Sl
305                                  *     / \             \
306                                  *    sl  Sr            s
307                                  *                       \
308                                  *                        Sr
309                                  */
310                                 sibling->rb_left = tmp1 = tmp2->rb_right;
311                                 tmp2->rb_right = sibling;
312                                 parent->rb_right = tmp2;
313                                 if (tmp1)
314                                         rb_set_parent_color(tmp1, sibling,
315                                                             RB_BLACK);
316                                 augment->rotate(sibling, tmp2);
317                                 tmp1 = sibling;
318                                 sibling = tmp2;
319                         }
320                         /*
321                          * Case 4 - left rotate at parent + color flips
322                          * (p and sl could be either color here.
323                          *  After rotation, p becomes black, s acquires
324                          *  p's color, and sl keeps its color)
325                          *
326                          *      (p)             (s)
327                          *      / \             / \
328                          *     N   S     -->   P   Sr
329                          *        / \         / \
330                          *      (sl) sr      N  (sl)
331                          */
332                         parent->rb_right = tmp2 = sibling->rb_left;
333                         sibling->rb_left = parent;
334                         rb_set_parent_color(tmp1, sibling, RB_BLACK);
335                         if (tmp2)
336                                 rb_set_parent(tmp2, parent);
337                         __rb_rotate_set_parents(parent, sibling, root,
338                                                 RB_BLACK);
339                         augment->rotate(parent, sibling);
340                         break;
341                 } else {
342                         sibling = parent->rb_left;
343                         if (rb_is_red(sibling)) {
344                                 /* Case 1 - right rotate at parent */
345                                 parent->rb_left = tmp1 = sibling->rb_right;
346                                 sibling->rb_right = parent;
347                                 rb_set_parent_color(tmp1, parent, RB_BLACK);
348                                 __rb_rotate_set_parents(parent, sibling, root,
349                                                         RB_RED);
350                                 augment->rotate(parent, sibling);
351                                 sibling = tmp1;
352                         }
353                         tmp1 = sibling->rb_left;
354                         if (!tmp1 || rb_is_black(tmp1)) {
355                                 tmp2 = sibling->rb_right;
356                                 if (!tmp2 || rb_is_black(tmp2)) {
357                                         /* Case 2 - sibling color flip */
358                                         rb_set_parent_color(sibling, parent,
359                                                             RB_RED);
360                                         if (rb_is_red(parent))
361                                                 rb_set_black(parent);
362                                         else {
363                                                 node = parent;
364                                                 parent = rb_parent(node);
365                                                 if (parent)
366                                                         continue;
367                                         }
368                                         break;
369                                 }
370                                 /* Case 3 - right rotate at sibling */
371                                 sibling->rb_right = tmp1 = tmp2->rb_left;
372                                 tmp2->rb_left = sibling;
373                                 parent->rb_left = tmp2;
374                                 if (tmp1)
375                                         rb_set_parent_color(tmp1, sibling,
376                                                             RB_BLACK);
377                                 augment->rotate(sibling, tmp2);
378                                 tmp1 = sibling;
379                                 sibling = tmp2;
380                         }
381                         /* Case 4 - left rotate at parent + color flips */
382                         parent->rb_left = tmp2 = sibling->rb_right;
383                         sibling->rb_right = parent;
384                         rb_set_parent_color(tmp1, sibling, RB_BLACK);
385                         if (tmp2)
386                                 rb_set_parent(tmp2, parent);
387                         __rb_rotate_set_parents(parent, sibling, root,
388                                                 RB_BLACK);
389                         augment->rotate(parent, sibling);
390                         break;
391                 }
392         }
393 }
394
395 static __always_inline void
396 __rb_erase(struct rb_node *node, struct rb_root *root,
397            const struct rb_augment_callbacks *augment)
398 {
399         struct rb_node *child = node->rb_right, *tmp = node->rb_left;
400         struct rb_node *parent, *rebalance;
401         unsigned long pc;
402
403         if (!tmp) {
404                 /*
405                  * Case 1: node to erase has no more than 1 child (easy!)
406                  *
407                  * Note that if there is one child it must be red due to 5)
408                  * and node must be black due to 4). We adjust colors locally
409                  * so as to bypass __rb_erase_color() later on.
410                  */
411                 pc = node->__rb_parent_color;
412                 parent = __rb_parent(pc);
413                 __rb_change_child(node, child, parent, root);
414                 if (child) {
415                         child->__rb_parent_color = pc;
416                         rebalance = NULL;
417                 } else
418                         rebalance = __rb_is_black(pc) ? parent : NULL;
419                 tmp = parent;
420         } else if (!child) {
421                 /* Still case 1, but this time the child is node->rb_left */
422                 tmp->__rb_parent_color = pc = node->__rb_parent_color;
423                 parent = __rb_parent(pc);
424                 __rb_change_child(node, tmp, parent, root);
425                 rebalance = NULL;
426                 tmp = parent;
427         } else {
428                 struct rb_node *successor = child, *child2;
429                 tmp = child->rb_left;
430                 if (!tmp) {
431                         /*
432                          * Case 2: node's successor is its right child
433                          *
434                          *    (n)          (s)
435                          *    / \          / \
436                          *  (x) (s)  ->  (x) (c)
437                          *        \
438                          *        (c)
439                          */
440                         parent = successor;
441                         child2 = successor->rb_right;
442                         augment->copy(node, successor);
443                 } else {
444                         /*
445                          * Case 3: node's successor is leftmost under
446                          * node's right child subtree
447                          *
448                          *    (n)          (s)
449                          *    / \          / \
450                          *  (x) (y)  ->  (x) (y)
451                          *      /            /
452                          *    (p)          (p)
453                          *    /            /
454                          *  (s)          (c)
455                          *    \
456                          *    (c)
457                          */
458                         do {
459                                 parent = successor;
460                                 successor = tmp;
461                                 tmp = tmp->rb_left;
462                         } while (tmp);
463                         parent->rb_left = child2 = successor->rb_right;
464                         successor->rb_right = child;
465                         rb_set_parent(child, successor);
466                         augment->copy(node, successor);
467                         augment->propagate(parent, successor);
468                 }
469
470                 successor->rb_left = tmp = node->rb_left;
471                 rb_set_parent(tmp, successor);
472
473                 pc = node->__rb_parent_color;
474                 tmp = __rb_parent(pc);
475                 __rb_change_child(node, successor, tmp, root);
476                 if (child2) {
477                         successor->__rb_parent_color = pc;
478                         rb_set_parent_color(child2, parent, RB_BLACK);
479                         rebalance = NULL;
480                 } else {
481                         unsigned long pc2 = successor->__rb_parent_color;
482                         successor->__rb_parent_color = pc;
483                         rebalance = __rb_is_black(pc2) ? parent : NULL;
484                 }
485                 tmp = successor;
486         }
487
488         augment->propagate(tmp, NULL);
489         if (rebalance)
490                 __rb_erase_color(rebalance, root, augment);
491 }
492
493 /*
494  * Non-augmented rbtree manipulation functions.
495  *
496  * We use dummy augmented callbacks here, and have the compiler optimize them
497  * out of the rb_insert_color() and rb_erase() function definitions.
498  */
499
500 static inline void dummy_propagate(struct rb_node *node, struct rb_node *stop) {}
501 static inline void dummy_copy(struct rb_node *old, struct rb_node *new) {}
502 static inline void dummy_rotate(struct rb_node *old, struct rb_node *new) {}
503
504 static const struct rb_augment_callbacks dummy_callbacks = {
505         dummy_propagate, dummy_copy, dummy_rotate
506 };
507
508 void rb_insert_color(struct rb_node *node, struct rb_root *root)
509 {
510         __rb_insert(node, root, dummy_rotate);
511 }
512 EXPORT_SYMBOL(rb_insert_color);
513
514 void rb_erase(struct rb_node *node, struct rb_root *root)
515 {
516         __rb_erase(node, root, &dummy_callbacks);
517 }
518 EXPORT_SYMBOL(rb_erase);
519
520 /*
521  * Augmented rbtree manipulation functions.
522  *
523  * This instantiates the same __always_inline functions as in the non-augmented
524  * case, but this time with user-defined callbacks.
525  */
526
527 void __rb_insert_augmented(struct rb_node *node, struct rb_root *root,
528         void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
529 {
530         __rb_insert(node, root, augment_rotate);
531 }
532 EXPORT_SYMBOL(__rb_insert_augmented);
533
534 void rb_erase_augmented(struct rb_node *node, struct rb_root *root,
535                         const struct rb_augment_callbacks *augment)
536 {
537         __rb_erase(node, root, augment);
538 }
539 EXPORT_SYMBOL(rb_erase_augmented);
540
541 static void rb_augment_path(struct rb_node *node, rb_augment_f func, void *data)
542 {
543         struct rb_node *parent;
544
545 up:
546         func(node, data);
547         parent = rb_parent(node);
548         if (!parent)
549                 return;
550
551         if (node == parent->rb_left && parent->rb_right)
552                 func(parent->rb_right, data);
553         else if (parent->rb_left)
554                 func(parent->rb_left, data);
555
556         node = parent;
557         goto up;
558 }
559
560 /*
561  * after inserting @node into the tree, update the tree to account for
562  * both the new entry and any damage done by rebalance
563  */
564 void rb_augment_insert(struct rb_node *node, rb_augment_f func, void *data)
565 {
566         if (node->rb_left)
567                 node = node->rb_left;
568         else if (node->rb_right)
569                 node = node->rb_right;
570
571         rb_augment_path(node, func, data);
572 }
573 EXPORT_SYMBOL(rb_augment_insert);
574
575 /*
576  * before removing the node, find the deepest node on the rebalance path
577  * that will still be there after @node gets removed
578  */
579 struct rb_node *rb_augment_erase_begin(struct rb_node *node)
580 {
581         struct rb_node *deepest;
582
583         if (!node->rb_right && !node->rb_left)
584                 deepest = rb_parent(node);
585         else if (!node->rb_right)
586                 deepest = node->rb_left;
587         else if (!node->rb_left)
588                 deepest = node->rb_right;
589         else {
590                 deepest = rb_next(node);
591                 if (deepest->rb_right)
592                         deepest = deepest->rb_right;
593                 else if (rb_parent(deepest) != node)
594                         deepest = rb_parent(deepest);
595         }
596
597         return deepest;
598 }
599 EXPORT_SYMBOL(rb_augment_erase_begin);
600
601 /*
602  * after removal, update the tree to account for the removed entry
603  * and any rebalance damage.
604  */
605 void rb_augment_erase_end(struct rb_node *node, rb_augment_f func, void *data)
606 {
607         if (node)
608                 rb_augment_path(node, func, data);
609 }
610 EXPORT_SYMBOL(rb_augment_erase_end);
611
612 /*
613  * This function returns the first node (in sort order) of the tree.
614  */
615 struct rb_node *rb_first(const struct rb_root *root)
616 {
617         struct rb_node  *n;
618
619         n = root->rb_node;
620         if (!n)
621                 return NULL;
622         while (n->rb_left)
623                 n = n->rb_left;
624         return n;
625 }
626 EXPORT_SYMBOL(rb_first);
627
628 struct rb_node *rb_last(const struct rb_root *root)
629 {
630         struct rb_node  *n;
631
632         n = root->rb_node;
633         if (!n)
634                 return NULL;
635         while (n->rb_right)
636                 n = n->rb_right;
637         return n;
638 }
639 EXPORT_SYMBOL(rb_last);
640
641 struct rb_node *rb_next(const struct rb_node *node)
642 {
643         struct rb_node *parent;
644
645         if (RB_EMPTY_NODE(node))
646                 return NULL;
647
648         /*
649          * If we have a right-hand child, go down and then left as far
650          * as we can.
651          */
652         if (node->rb_right) {
653                 node = node->rb_right; 
654                 while (node->rb_left)
655                         node=node->rb_left;
656                 return (struct rb_node *)node;
657         }
658
659         /*
660          * No right-hand children. Everything down and left is smaller than us,
661          * so any 'next' node must be in the general direction of our parent.
662          * Go up the tree; any time the ancestor is a right-hand child of its
663          * parent, keep going up. First time it's a left-hand child of its
664          * parent, said parent is our 'next' node.
665          */
666         while ((parent = rb_parent(node)) && node == parent->rb_right)
667                 node = parent;
668
669         return parent;
670 }
671 EXPORT_SYMBOL(rb_next);
672
673 struct rb_node *rb_prev(const struct rb_node *node)
674 {
675         struct rb_node *parent;
676
677         if (RB_EMPTY_NODE(node))
678                 return NULL;
679
680         /*
681          * If we have a left-hand child, go down and then right as far
682          * as we can.
683          */
684         if (node->rb_left) {
685                 node = node->rb_left; 
686                 while (node->rb_right)
687                         node=node->rb_right;
688                 return (struct rb_node *)node;
689         }
690
691         /*
692          * No left-hand children. Go up till we find an ancestor which
693          * is a right-hand child of its parent.
694          */
695         while ((parent = rb_parent(node)) && node == parent->rb_left)
696                 node = parent;
697
698         return parent;
699 }
700 EXPORT_SYMBOL(rb_prev);
701
702 void rb_replace_node(struct rb_node *victim, struct rb_node *new,
703                      struct rb_root *root)
704 {
705         struct rb_node *parent = rb_parent(victim);
706
707         /* Set the surrounding nodes to point to the replacement */
708         __rb_change_child(victim, new, parent, root);
709         if (victim->rb_left)
710                 rb_set_parent(victim->rb_left, new);
711         if (victim->rb_right)
712                 rb_set_parent(victim->rb_right, new);
713
714         /* Copy the pointers/colour from the victim to the replacement */
715         *new = *victim;
716 }
717 EXPORT_SYMBOL(rb_replace_node);