Import rbtrees from Linux
[akaros.git] / kern / 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_augmented.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 /*
48  * Notes on lockless lookups:
49  *
50  * All stores to the tree structure (rb_left and rb_right) must be done using
51  * WRITE_ONCE(). And we must not inadvertently cause (temporary) loops in the
52  * tree structure as seen in program order.
53  *
54  * These two requirements will allow lockless iteration of the tree -- not
55  * correct iteration mind you, tree rotations are not atomic so a lookup might
56  * miss entire subtrees.
57  *
58  * But they do guarantee that any such traversal will only see valid elements
59  * and that it will indeed complete -- does not get stuck in a loop.
60  *
61  * It also guarantees that if the lookup returns an element it is the 'correct'
62  * one. But not returning an element does _NOT_ mean it's not present.
63  *
64  * NOTE:
65  *
66  * Stores to __rb_parent_color are not important for simple lookups so those
67  * are left undone as of now. Nor did I check for loops involving parent
68  * pointers.
69  */
70
71 static inline void rb_set_black(struct rb_node *rb)
72 {
73         rb->__rb_parent_color |= RB_BLACK;
74 }
75
76 static inline struct rb_node *rb_red_parent(struct rb_node *red)
77 {
78         return (struct rb_node *)red->__rb_parent_color;
79 }
80
81 /*
82  * Helper function for rotations:
83  * - old's parent and color get assigned to new
84  * - old gets assigned new as a parent and 'color' as a color.
85  */
86 static inline void
87 __rb_rotate_set_parents(struct rb_node *old, struct rb_node *new,
88                         struct rb_root *root, int color)
89 {
90         struct rb_node *parent = rb_parent(old);
91         new->__rb_parent_color = old->__rb_parent_color;
92         rb_set_parent_color(old, new, color);
93         __rb_change_child(old, new, parent, root);
94 }
95
96 static __always_inline void
97 __rb_insert(struct rb_node *node, struct rb_root *root,
98             void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
99 {
100         struct rb_node *parent = rb_red_parent(node), *gparent, *tmp;
101
102         while (true) {
103                 /*
104                  * Loop invariant: node is red
105                  *
106                  * If there is a black parent, we are done.
107                  * Otherwise, take some corrective action as we don't
108                  * want a red root or two consecutive red nodes.
109                  */
110                 if (!parent) {
111                         rb_set_parent_color(node, NULL, RB_BLACK);
112                         break;
113                 } else if (rb_is_black(parent))
114                         break;
115
116                 gparent = rb_red_parent(parent);
117
118                 tmp = gparent->rb_right;
119                 if (parent != tmp) {    /* parent == gparent->rb_left */
120                         if (tmp && rb_is_red(tmp)) {
121                                 /*
122                                  * Case 1 - color flips
123                                  *
124                                  *       G            g
125                                  *      / \          / \
126                                  *     p   u  -->   P   U
127                                  *    /            /
128                                  *   n            n
129                                  *
130                                  * However, since g's parent might be red, and
131                                  * 4) does not allow this, we need to recurse
132                                  * at g.
133                                  */
134                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
135                                 rb_set_parent_color(parent, gparent, RB_BLACK);
136                                 node = gparent;
137                                 parent = rb_parent(node);
138                                 rb_set_parent_color(node, parent, RB_RED);
139                                 continue;
140                         }
141
142                         tmp = parent->rb_right;
143                         if (node == tmp) {
144                                 /*
145                                  * Case 2 - left rotate at parent
146                                  *
147                                  *      G             G
148                                  *     / \           / \
149                                  *    p   U  -->    n   U
150                                  *     \           /
151                                  *      n         p
152                                  *
153                                  * This still leaves us in violation of 4), the
154                                  * continuation into Case 3 will fix that.
155                                  */
156                                 tmp = node->rb_left;
157                                 WRITE_ONCE(parent->rb_right, tmp);
158                                 WRITE_ONCE(node->rb_left, parent);
159                                 if (tmp)
160                                         rb_set_parent_color(tmp, parent,
161                                                             RB_BLACK);
162                                 rb_set_parent_color(parent, node, RB_RED);
163                                 augment_rotate(parent, node);
164                                 parent = node;
165                                 tmp = node->rb_right;
166                         }
167
168                         /*
169                          * Case 3 - right rotate at gparent
170                          *
171                          *        G           P
172                          *       / \         / \
173                          *      p   U  -->  n   g
174                          *     /                 \
175                          *    n                   U
176                          */
177                         WRITE_ONCE(gparent->rb_left, tmp); /* == parent->rb_right */
178                         WRITE_ONCE(parent->rb_right, gparent);
179                         if (tmp)
180                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
181                         __rb_rotate_set_parents(gparent, parent, root, RB_RED);
182                         augment_rotate(gparent, parent);
183                         break;
184                 } else {
185                         tmp = gparent->rb_left;
186                         if (tmp && rb_is_red(tmp)) {
187                                 /* Case 1 - color flips */
188                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
189                                 rb_set_parent_color(parent, gparent, RB_BLACK);
190                                 node = gparent;
191                                 parent = rb_parent(node);
192                                 rb_set_parent_color(node, parent, RB_RED);
193                                 continue;
194                         }
195
196                         tmp = parent->rb_left;
197                         if (node == tmp) {
198                                 /* Case 2 - right rotate at parent */
199                                 tmp = node->rb_right;
200                                 WRITE_ONCE(parent->rb_left, tmp);
201                                 WRITE_ONCE(node->rb_right, parent);
202                                 if (tmp)
203                                         rb_set_parent_color(tmp, parent,
204                                                             RB_BLACK);
205                                 rb_set_parent_color(parent, node, RB_RED);
206                                 augment_rotate(parent, node);
207                                 parent = node;
208                                 tmp = node->rb_left;
209                         }
210
211                         /* Case 3 - left rotate at gparent */
212                         WRITE_ONCE(gparent->rb_right, tmp); /* == parent->rb_left */
213                         WRITE_ONCE(parent->rb_left, gparent);
214                         if (tmp)
215                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
216                         __rb_rotate_set_parents(gparent, parent, root, RB_RED);
217                         augment_rotate(gparent, parent);
218                         break;
219                 }
220         }
221 }
222
223 /*
224  * Inline version for rb_erase() use - we want to be able to inline
225  * and eliminate the dummy_rotate callback there
226  */
227 static __always_inline void
228 ____rb_erase_color(struct rb_node *parent, struct rb_root *root,
229         void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
230 {
231         struct rb_node *node = NULL, *sibling, *tmp1, *tmp2;
232
233         while (true) {
234                 /*
235                  * Loop invariants:
236                  * - node is black (or NULL on first iteration)
237                  * - node is not the root (parent is not NULL)
238                  * - All leaf paths going through parent and node have a
239                  *   black node count that is 1 lower than other leaf paths.
240                  */
241                 sibling = parent->rb_right;
242                 if (node != sibling) {  /* node == parent->rb_left */
243                         if (rb_is_red(sibling)) {
244                                 /*
245                                  * Case 1 - left rotate at parent
246                                  *
247                                  *     P               S
248                                  *    / \             / \
249                                  *   N   s    -->    p   Sr
250                                  *      / \         / \
251                                  *     Sl  Sr      N   Sl
252                                  */
253                                 tmp1 = sibling->rb_left;
254                                 WRITE_ONCE(parent->rb_right, tmp1);
255                                 WRITE_ONCE(sibling->rb_left, parent);
256                                 rb_set_parent_color(tmp1, parent, RB_BLACK);
257                                 __rb_rotate_set_parents(parent, sibling, root,
258                                                         RB_RED);
259                                 augment_rotate(parent, sibling);
260                                 sibling = tmp1;
261                         }
262                         tmp1 = sibling->rb_right;
263                         if (!tmp1 || rb_is_black(tmp1)) {
264                                 tmp2 = sibling->rb_left;
265                                 if (!tmp2 || rb_is_black(tmp2)) {
266                                         /*
267                                          * Case 2 - sibling color flip
268                                          * (p could be either color here)
269                                          *
270                                          *    (p)           (p)
271                                          *    / \           / \
272                                          *   N   S    -->  N   s
273                                          *      / \           / \
274                                          *     Sl  Sr        Sl  Sr
275                                          *
276                                          * This leaves us violating 5) which
277                                          * can be fixed by flipping p to black
278                                          * if it was red, or by recursing at p.
279                                          * p is red when coming from Case 1.
280                                          */
281                                         rb_set_parent_color(sibling, parent,
282                                                             RB_RED);
283                                         if (rb_is_red(parent))
284                                                 rb_set_black(parent);
285                                         else {
286                                                 node = parent;
287                                                 parent = rb_parent(node);
288                                                 if (parent)
289                                                         continue;
290                                         }
291                                         break;
292                                 }
293                                 /*
294                                  * Case 3 - right rotate at sibling
295                                  * (p could be either color here)
296                                  *
297                                  *   (p)           (p)
298                                  *   / \           / \
299                                  *  N   S    -->  N   Sl
300                                  *     / \             \
301                                  *    sl  Sr            s
302                                  *                       \
303                                  *                        Sr
304                                  */
305                                 tmp1 = tmp2->rb_right;
306                                 WRITE_ONCE(sibling->rb_left, tmp1);
307                                 WRITE_ONCE(tmp2->rb_right, sibling);
308                                 WRITE_ONCE(parent->rb_right, tmp2);
309                                 if (tmp1)
310                                         rb_set_parent_color(tmp1, sibling,
311                                                             RB_BLACK);
312                                 augment_rotate(sibling, tmp2);
313                                 tmp1 = sibling;
314                                 sibling = tmp2;
315                         }
316                         /*
317                          * Case 4 - left rotate at parent + color flips
318                          * (p and sl could be either color here.
319                          *  After rotation, p becomes black, s acquires
320                          *  p's color, and sl keeps its color)
321                          *
322                          *      (p)             (s)
323                          *      / \             / \
324                          *     N   S     -->   P   Sr
325                          *        / \         / \
326                          *      (sl) sr      N  (sl)
327                          */
328                         tmp2 = sibling->rb_left;
329                         WRITE_ONCE(parent->rb_right, tmp2);
330                         WRITE_ONCE(sibling->rb_left, parent);
331                         rb_set_parent_color(tmp1, sibling, RB_BLACK);
332                         if (tmp2)
333                                 rb_set_parent(tmp2, parent);
334                         __rb_rotate_set_parents(parent, sibling, root,
335                                                 RB_BLACK);
336                         augment_rotate(parent, sibling);
337                         break;
338                 } else {
339                         sibling = parent->rb_left;
340                         if (rb_is_red(sibling)) {
341                                 /* Case 1 - right rotate at parent */
342                                 tmp1 = sibling->rb_right;
343                                 WRITE_ONCE(parent->rb_left, tmp1);
344                                 WRITE_ONCE(sibling->rb_right, parent);
345                                 rb_set_parent_color(tmp1, parent, RB_BLACK);
346                                 __rb_rotate_set_parents(parent, sibling, root,
347                                                         RB_RED);
348                                 augment_rotate(parent, sibling);
349                                 sibling = tmp1;
350                         }
351                         tmp1 = sibling->rb_left;
352                         if (!tmp1 || rb_is_black(tmp1)) {
353                                 tmp2 = sibling->rb_right;
354                                 if (!tmp2 || rb_is_black(tmp2)) {
355                                         /* Case 2 - sibling color flip */
356                                         rb_set_parent_color(sibling, parent,
357                                                             RB_RED);
358                                         if (rb_is_red(parent))
359                                                 rb_set_black(parent);
360                                         else {
361                                                 node = parent;
362                                                 parent = rb_parent(node);
363                                                 if (parent)
364                                                         continue;
365                                         }
366                                         break;
367                                 }
368                                 /* Case 3 - right rotate at sibling */
369                                 tmp1 = tmp2->rb_left;
370                                 WRITE_ONCE(sibling->rb_right, tmp1);
371                                 WRITE_ONCE(tmp2->rb_left, sibling);
372                                 WRITE_ONCE(parent->rb_left, tmp2);
373                                 if (tmp1)
374                                         rb_set_parent_color(tmp1, sibling,
375                                                             RB_BLACK);
376                                 augment_rotate(sibling, tmp2);
377                                 tmp1 = sibling;
378                                 sibling = tmp2;
379                         }
380                         /* Case 4 - left rotate at parent + color flips */
381                         tmp2 = sibling->rb_right;
382                         WRITE_ONCE(parent->rb_left, tmp2);
383                         WRITE_ONCE(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 /* Non-inline version for rb_erase_augmented() use */
396 void __rb_erase_color(struct rb_node *parent, struct rb_root *root,
397         void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
398 {
399         ____rb_erase_color(parent, root, augment_rotate);
400 }
401 EXPORT_SYMBOL(__rb_erase_color);
402
403 /*
404  * Non-augmented rbtree manipulation functions.
405  *
406  * We use dummy augmented callbacks here, and have the compiler optimize them
407  * out of the rb_insert_color() and rb_erase() function definitions.
408  */
409
410 static inline void dummy_propagate(struct rb_node *node, struct rb_node *stop) {}
411 static inline void dummy_copy(struct rb_node *old, struct rb_node *new) {}
412 static inline void dummy_rotate(struct rb_node *old, struct rb_node *new) {}
413
414 static const struct rb_augment_callbacks dummy_callbacks = {
415         dummy_propagate, dummy_copy, dummy_rotate
416 };
417
418 void rb_insert_color(struct rb_node *node, struct rb_root *root)
419 {
420         __rb_insert(node, root, dummy_rotate);
421 }
422 EXPORT_SYMBOL(rb_insert_color);
423
424 void rb_erase(struct rb_node *node, struct rb_root *root)
425 {
426         struct rb_node *rebalance;
427         rebalance = __rb_erase_augmented(node, root, &dummy_callbacks);
428         if (rebalance)
429                 ____rb_erase_color(rebalance, root, dummy_rotate);
430 }
431 EXPORT_SYMBOL(rb_erase);
432
433 /*
434  * Augmented rbtree manipulation functions.
435  *
436  * This instantiates the same __always_inline functions as in the non-augmented
437  * case, but this time with user-defined callbacks.
438  */
439
440 void __rb_insert_augmented(struct rb_node *node, struct rb_root *root,
441         void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
442 {
443         __rb_insert(node, root, augment_rotate);
444 }
445 EXPORT_SYMBOL(__rb_insert_augmented);
446
447 /*
448  * This function returns the first node (in sort order) of the tree.
449  */
450 struct rb_node *rb_first(const struct rb_root *root)
451 {
452         struct rb_node  *n;
453
454         n = root->rb_node;
455         if (!n)
456                 return NULL;
457         while (n->rb_left)
458                 n = n->rb_left;
459         return n;
460 }
461 EXPORT_SYMBOL(rb_first);
462
463 struct rb_node *rb_last(const struct rb_root *root)
464 {
465         struct rb_node  *n;
466
467         n = root->rb_node;
468         if (!n)
469                 return NULL;
470         while (n->rb_right)
471                 n = n->rb_right;
472         return n;
473 }
474 EXPORT_SYMBOL(rb_last);
475
476 struct rb_node *rb_next(const struct rb_node *node)
477 {
478         struct rb_node *parent;
479
480         if (RB_EMPTY_NODE(node))
481                 return NULL;
482
483         /*
484          * If we have a right-hand child, go down and then left as far
485          * as we can.
486          */
487         if (node->rb_right) {
488                 node = node->rb_right; 
489                 while (node->rb_left)
490                         node=node->rb_left;
491                 return (struct rb_node *)node;
492         }
493
494         /*
495          * No right-hand children. Everything down and left is smaller than us,
496          * so any 'next' node must be in the general direction of our parent.
497          * Go up the tree; any time the ancestor is a right-hand child of its
498          * parent, keep going up. First time it's a left-hand child of its
499          * parent, said parent is our 'next' node.
500          */
501         while ((parent = rb_parent(node)) && node == parent->rb_right)
502                 node = parent;
503
504         return parent;
505 }
506 EXPORT_SYMBOL(rb_next);
507
508 struct rb_node *rb_prev(const struct rb_node *node)
509 {
510         struct rb_node *parent;
511
512         if (RB_EMPTY_NODE(node))
513                 return NULL;
514
515         /*
516          * If we have a left-hand child, go down and then right as far
517          * as we can.
518          */
519         if (node->rb_left) {
520                 node = node->rb_left; 
521                 while (node->rb_right)
522                         node=node->rb_right;
523                 return (struct rb_node *)node;
524         }
525
526         /*
527          * No left-hand children. Go up till we find an ancestor which
528          * is a right-hand child of its parent.
529          */
530         while ((parent = rb_parent(node)) && node == parent->rb_left)
531                 node = parent;
532
533         return parent;
534 }
535 EXPORT_SYMBOL(rb_prev);
536
537 void rb_replace_node(struct rb_node *victim, struct rb_node *new,
538                      struct rb_root *root)
539 {
540         struct rb_node *parent = rb_parent(victim);
541
542         /* Copy the pointers/colour from the victim to the replacement */
543         *new = *victim;
544
545         /* Set the surrounding nodes to point to the replacement */
546         if (victim->rb_left)
547                 rb_set_parent(victim->rb_left, new);
548         if (victim->rb_right)
549                 rb_set_parent(victim->rb_right, new);
550         __rb_change_child(victim, new, parent, root);
551 }
552 EXPORT_SYMBOL(rb_replace_node);
553
554 void rb_replace_node_rcu(struct rb_node *victim, struct rb_node *new,
555                          struct rb_root *root)
556 {
557         struct rb_node *parent = rb_parent(victim);
558
559         /* Copy the pointers/colour from the victim to the replacement */
560         *new = *victim;
561
562         /* Set the surrounding nodes to point to the replacement */
563         if (victim->rb_left)
564                 rb_set_parent(victim->rb_left, new);
565         if (victim->rb_right)
566                 rb_set_parent(victim->rb_right, new);
567
568         /* Set the parent's pointer to the new node last after an RCU barrier
569          * so that the pointers onwards are seen to be set correctly when doing
570          * an RCU walk over the tree.
571          */
572         __rb_change_child_rcu(victim, new, parent, root);
573 }
574 EXPORT_SYMBOL(rb_replace_node_rcu);
575
576 static struct rb_node *rb_left_deepest_node(const struct rb_node *node)
577 {
578         for (;;) {
579                 if (node->rb_left)
580                         node = node->rb_left;
581                 else if (node->rb_right)
582                         node = node->rb_right;
583                 else
584                         return (struct rb_node *)node;
585         }
586 }
587
588 struct rb_node *rb_next_postorder(const struct rb_node *node)
589 {
590         const struct rb_node *parent;
591         if (!node)
592                 return NULL;
593         parent = rb_parent(node);
594
595         /* If we're sitting on node, we've already seen our children */
596         if (parent && node == parent->rb_left && parent->rb_right) {
597                 /* If we are the parent's left node, go to the parent's right
598                  * node then all the way down to the left */
599                 return rb_left_deepest_node(parent->rb_right);
600         } else
601                 /* Otherwise we are the parent's right node, and the parent
602                  * should be next */
603                 return (struct rb_node *)parent;
604 }
605 EXPORT_SYMBOL(rb_next_postorder);
606
607 struct rb_node *rb_first_postorder(const struct rb_root *root)
608 {
609         if (!root->rb_node)
610                 return NULL;
611
612         return rb_left_deepest_node(root->rb_node);
613 }
614 EXPORT_SYMBOL(rb_first_postorder);