idr: fix top layer handling
[linux-3.10.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_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 static inline void rb_set_black(struct rb_node *rb)
48 {
49         rb->__rb_parent_color |= RB_BLACK;
50 }
51
52 static inline struct rb_node *rb_red_parent(struct rb_node *red)
53 {
54         return (struct rb_node *)red->__rb_parent_color;
55 }
56
57 /*
58  * Helper function for rotations:
59  * - old's parent and color get assigned to new
60  * - old gets assigned new as a parent and 'color' as a color.
61  */
62 static inline void
63 __rb_rotate_set_parents(struct rb_node *old, struct rb_node *new,
64                         struct rb_root *root, int color)
65 {
66         struct rb_node *parent = rb_parent(old);
67         new->__rb_parent_color = old->__rb_parent_color;
68         rb_set_parent_color(old, new, color);
69         __rb_change_child(old, new, parent, root);
70 }
71
72 static __always_inline void
73 __rb_insert(struct rb_node *node, struct rb_root *root,
74             void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
75 {
76         struct rb_node *parent = rb_red_parent(node), *gparent, *tmp;
77
78         while (true) {
79                 /*
80                  * Loop invariant: node is red
81                  *
82                  * If there is a black parent, we are done.
83                  * Otherwise, take some corrective action as we don't
84                  * want a red root or two consecutive red nodes.
85                  */
86                 if (!parent) {
87                         rb_set_parent_color(node, NULL, RB_BLACK);
88                         break;
89                 } else if (rb_is_black(parent))
90                         break;
91
92                 gparent = rb_red_parent(parent);
93
94                 tmp = gparent->rb_right;
95                 if (parent != tmp) {    /* parent == gparent->rb_left */
96                         if (tmp && rb_is_red(tmp)) {
97                                 /*
98                                  * Case 1 - color flips
99                                  *
100                                  *       G            g
101                                  *      / \          / \
102                                  *     p   u  -->   P   U
103                                  *    /            /
104                                  *   n            N
105                                  *
106                                  * However, since g's parent might be red, and
107                                  * 4) does not allow this, we need to recurse
108                                  * at g.
109                                  */
110                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
111                                 rb_set_parent_color(parent, gparent, RB_BLACK);
112                                 node = gparent;
113                                 parent = rb_parent(node);
114                                 rb_set_parent_color(node, parent, RB_RED);
115                                 continue;
116                         }
117
118                         tmp = parent->rb_right;
119                         if (node == tmp) {
120                                 /*
121                                  * Case 2 - left rotate at parent
122                                  *
123                                  *      G             G
124                                  *     / \           / \
125                                  *    p   U  -->    n   U
126                                  *     \           /
127                                  *      n         p
128                                  *
129                                  * This still leaves us in violation of 4), the
130                                  * continuation into Case 3 will fix that.
131                                  */
132                                 parent->rb_right = tmp = node->rb_left;
133                                 node->rb_left = parent;
134                                 if (tmp)
135                                         rb_set_parent_color(tmp, parent,
136                                                             RB_BLACK);
137                                 rb_set_parent_color(parent, node, RB_RED);
138                                 augment_rotate(parent, node);
139                                 parent = node;
140                                 tmp = node->rb_right;
141                         }
142
143                         /*
144                          * Case 3 - right rotate at gparent
145                          *
146                          *        G           P
147                          *       / \         / \
148                          *      p   U  -->  n   g
149                          *     /                 \
150                          *    n                   U
151                          */
152                         gparent->rb_left = tmp;  /* == parent->rb_right */
153                         parent->rb_right = gparent;
154                         if (tmp)
155                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
156                         __rb_rotate_set_parents(gparent, parent, root, RB_RED);
157                         augment_rotate(gparent, parent);
158                         break;
159                 } else {
160                         tmp = gparent->rb_left;
161                         if (tmp && rb_is_red(tmp)) {
162                                 /* Case 1 - color flips */
163                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
164                                 rb_set_parent_color(parent, gparent, RB_BLACK);
165                                 node = gparent;
166                                 parent = rb_parent(node);
167                                 rb_set_parent_color(node, parent, RB_RED);
168                                 continue;
169                         }
170
171                         tmp = parent->rb_left;
172                         if (node == tmp) {
173                                 /* Case 2 - right rotate at parent */
174                                 parent->rb_left = tmp = node->rb_right;
175                                 node->rb_right = parent;
176                                 if (tmp)
177                                         rb_set_parent_color(tmp, parent,
178                                                             RB_BLACK);
179                                 rb_set_parent_color(parent, node, RB_RED);
180                                 augment_rotate(parent, node);
181                                 parent = node;
182                                 tmp = node->rb_left;
183                         }
184
185                         /* Case 3 - left rotate at gparent */
186                         gparent->rb_right = tmp;  /* == parent->rb_left */
187                         parent->rb_left = gparent;
188                         if (tmp)
189                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
190                         __rb_rotate_set_parents(gparent, parent, root, RB_RED);
191                         augment_rotate(gparent, parent);
192                         break;
193                 }
194         }
195 }
196
197 /*
198  * Inline version for rb_erase() use - we want to be able to inline
199  * and eliminate the dummy_rotate callback there
200  */
201 static __always_inline void
202 ____rb_erase_color(struct rb_node *parent, struct rb_root *root,
203         void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
204 {
205         struct rb_node *node = NULL, *sibling, *tmp1, *tmp2;
206
207         while (true) {
208                 /*
209                  * Loop invariants:
210                  * - node is black (or NULL on first iteration)
211                  * - node is not the root (parent is not NULL)
212                  * - All leaf paths going through parent and node have a
213                  *   black node count that is 1 lower than other leaf paths.
214                  */
215                 sibling = parent->rb_right;
216                 if (node != sibling) {  /* node == parent->rb_left */
217                         if (rb_is_red(sibling)) {
218                                 /*
219                                  * Case 1 - left rotate at parent
220                                  *
221                                  *     P               S
222                                  *    / \             / \
223                                  *   N   s    -->    p   Sr
224                                  *      / \         / \
225                                  *     Sl  Sr      N   Sl
226                                  */
227                                 parent->rb_right = tmp1 = sibling->rb_left;
228                                 sibling->rb_left = parent;
229                                 rb_set_parent_color(tmp1, parent, RB_BLACK);
230                                 __rb_rotate_set_parents(parent, sibling, root,
231                                                         RB_RED);
232                                 augment_rotate(parent, sibling);
233                                 sibling = tmp1;
234                         }
235                         tmp1 = sibling->rb_right;
236                         if (!tmp1 || rb_is_black(tmp1)) {
237                                 tmp2 = sibling->rb_left;
238                                 if (!tmp2 || rb_is_black(tmp2)) {
239                                         /*
240                                          * Case 2 - sibling color flip
241                                          * (p could be either color here)
242                                          *
243                                          *    (p)           (p)
244                                          *    / \           / \
245                                          *   N   S    -->  N   s
246                                          *      / \           / \
247                                          *     Sl  Sr        Sl  Sr
248                                          *
249                                          * This leaves us violating 5) which
250                                          * can be fixed by flipping p to black
251                                          * if it was red, or by recursing at p.
252                                          * p is red when coming from Case 1.
253                                          */
254                                         rb_set_parent_color(sibling, parent,
255                                                             RB_RED);
256                                         if (rb_is_red(parent))
257                                                 rb_set_black(parent);
258                                         else {
259                                                 node = parent;
260                                                 parent = rb_parent(node);
261                                                 if (parent)
262                                                         continue;
263                                         }
264                                         break;
265                                 }
266                                 /*
267                                  * Case 3 - right rotate at sibling
268                                  * (p could be either color here)
269                                  *
270                                  *   (p)           (p)
271                                  *   / \           / \
272                                  *  N   S    -->  N   Sl
273                                  *     / \             \
274                                  *    sl  Sr            s
275                                  *                       \
276                                  *                        Sr
277                                  */
278                                 sibling->rb_left = tmp1 = tmp2->rb_right;
279                                 tmp2->rb_right = sibling;
280                                 parent->rb_right = tmp2;
281                                 if (tmp1)
282                                         rb_set_parent_color(tmp1, sibling,
283                                                             RB_BLACK);
284                                 augment_rotate(sibling, tmp2);
285                                 tmp1 = sibling;
286                                 sibling = tmp2;
287                         }
288                         /*
289                          * Case 4 - left rotate at parent + color flips
290                          * (p and sl could be either color here.
291                          *  After rotation, p becomes black, s acquires
292                          *  p's color, and sl keeps its color)
293                          *
294                          *      (p)             (s)
295                          *      / \             / \
296                          *     N   S     -->   P   Sr
297                          *        / \         / \
298                          *      (sl) sr      N  (sl)
299                          */
300                         parent->rb_right = tmp2 = sibling->rb_left;
301                         sibling->rb_left = parent;
302                         rb_set_parent_color(tmp1, sibling, RB_BLACK);
303                         if (tmp2)
304                                 rb_set_parent(tmp2, parent);
305                         __rb_rotate_set_parents(parent, sibling, root,
306                                                 RB_BLACK);
307                         augment_rotate(parent, sibling);
308                         break;
309                 } else {
310                         sibling = parent->rb_left;
311                         if (rb_is_red(sibling)) {
312                                 /* Case 1 - right rotate at parent */
313                                 parent->rb_left = tmp1 = sibling->rb_right;
314                                 sibling->rb_right = parent;
315                                 rb_set_parent_color(tmp1, parent, RB_BLACK);
316                                 __rb_rotate_set_parents(parent, sibling, root,
317                                                         RB_RED);
318                                 augment_rotate(parent, sibling);
319                                 sibling = tmp1;
320                         }
321                         tmp1 = sibling->rb_left;
322                         if (!tmp1 || rb_is_black(tmp1)) {
323                                 tmp2 = sibling->rb_right;
324                                 if (!tmp2 || rb_is_black(tmp2)) {
325                                         /* Case 2 - sibling color flip */
326                                         rb_set_parent_color(sibling, parent,
327                                                             RB_RED);
328                                         if (rb_is_red(parent))
329                                                 rb_set_black(parent);
330                                         else {
331                                                 node = parent;
332                                                 parent = rb_parent(node);
333                                                 if (parent)
334                                                         continue;
335                                         }
336                                         break;
337                                 }
338                                 /* Case 3 - right rotate at sibling */
339                                 sibling->rb_right = tmp1 = tmp2->rb_left;
340                                 tmp2->rb_left = sibling;
341                                 parent->rb_left = tmp2;
342                                 if (tmp1)
343                                         rb_set_parent_color(tmp1, sibling,
344                                                             RB_BLACK);
345                                 augment_rotate(sibling, tmp2);
346                                 tmp1 = sibling;
347                                 sibling = tmp2;
348                         }
349                         /* Case 4 - left rotate at parent + color flips */
350                         parent->rb_left = tmp2 = sibling->rb_right;
351                         sibling->rb_right = parent;
352                         rb_set_parent_color(tmp1, sibling, RB_BLACK);
353                         if (tmp2)
354                                 rb_set_parent(tmp2, parent);
355                         __rb_rotate_set_parents(parent, sibling, root,
356                                                 RB_BLACK);
357                         augment_rotate(parent, sibling);
358                         break;
359                 }
360         }
361 }
362
363 /* Non-inline version for rb_erase_augmented() use */
364 void __rb_erase_color(struct rb_node *parent, struct rb_root *root,
365         void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
366 {
367         ____rb_erase_color(parent, root, augment_rotate);
368 }
369 EXPORT_SYMBOL(__rb_erase_color);
370
371 /*
372  * Non-augmented rbtree manipulation functions.
373  *
374  * We use dummy augmented callbacks here, and have the compiler optimize them
375  * out of the rb_insert_color() and rb_erase() function definitions.
376  */
377
378 static inline void dummy_propagate(struct rb_node *node, struct rb_node *stop) {}
379 static inline void dummy_copy(struct rb_node *old, struct rb_node *new) {}
380 static inline void dummy_rotate(struct rb_node *old, struct rb_node *new) {}
381
382 static const struct rb_augment_callbacks dummy_callbacks = {
383         dummy_propagate, dummy_copy, dummy_rotate
384 };
385
386 void rb_insert_color(struct rb_node *node, struct rb_root *root)
387 {
388         __rb_insert(node, root, dummy_rotate);
389 }
390 EXPORT_SYMBOL(rb_insert_color);
391
392 void rb_erase(struct rb_node *node, struct rb_root *root)
393 {
394         struct rb_node *rebalance;
395         rebalance = __rb_erase_augmented(node, root, &dummy_callbacks);
396         if (rebalance)
397                 ____rb_erase_color(rebalance, root, dummy_rotate);
398 }
399 EXPORT_SYMBOL(rb_erase);
400
401 /*
402  * Augmented rbtree manipulation functions.
403  *
404  * This instantiates the same __always_inline functions as in the non-augmented
405  * case, but this time with user-defined callbacks.
406  */
407
408 void __rb_insert_augmented(struct rb_node *node, struct rb_root *root,
409         void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
410 {
411         __rb_insert(node, root, augment_rotate);
412 }
413 EXPORT_SYMBOL(__rb_insert_augmented);
414
415 /*
416  * This function returns the first node (in sort order) of the tree.
417  */
418 struct rb_node *rb_first(const struct rb_root *root)
419 {
420         struct rb_node  *n;
421
422         n = root->rb_node;
423         if (!n)
424                 return NULL;
425         while (n->rb_left)
426                 n = n->rb_left;
427         return n;
428 }
429 EXPORT_SYMBOL(rb_first);
430
431 struct rb_node *rb_last(const struct rb_root *root)
432 {
433         struct rb_node  *n;
434
435         n = root->rb_node;
436         if (!n)
437                 return NULL;
438         while (n->rb_right)
439                 n = n->rb_right;
440         return n;
441 }
442 EXPORT_SYMBOL(rb_last);
443
444 struct rb_node *rb_next(const struct rb_node *node)
445 {
446         struct rb_node *parent;
447
448         if (RB_EMPTY_NODE(node))
449                 return NULL;
450
451         /*
452          * If we have a right-hand child, go down and then left as far
453          * as we can.
454          */
455         if (node->rb_right) {
456                 node = node->rb_right; 
457                 while (node->rb_left)
458                         node=node->rb_left;
459                 return (struct rb_node *)node;
460         }
461
462         /*
463          * No right-hand children. Everything down and left is smaller than us,
464          * so any 'next' node must be in the general direction of our parent.
465          * Go up the tree; any time the ancestor is a right-hand child of its
466          * parent, keep going up. First time it's a left-hand child of its
467          * parent, said parent is our 'next' node.
468          */
469         while ((parent = rb_parent(node)) && node == parent->rb_right)
470                 node = parent;
471
472         return parent;
473 }
474 EXPORT_SYMBOL(rb_next);
475
476 struct rb_node *rb_prev(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 left-hand child, go down and then right as far
485          * as we can.
486          */
487         if (node->rb_left) {
488                 node = node->rb_left; 
489                 while (node->rb_right)
490                         node=node->rb_right;
491                 return (struct rb_node *)node;
492         }
493
494         /*
495          * No left-hand children. Go up till we find an ancestor which
496          * is a right-hand child of its parent.
497          */
498         while ((parent = rb_parent(node)) && node == parent->rb_left)
499                 node = parent;
500
501         return parent;
502 }
503 EXPORT_SYMBOL(rb_prev);
504
505 void rb_replace_node(struct rb_node *victim, struct rb_node *new,
506                      struct rb_root *root)
507 {
508         struct rb_node *parent = rb_parent(victim);
509
510         /* Set the surrounding nodes to point to the replacement */
511         __rb_change_child(victim, new, parent, root);
512         if (victim->rb_left)
513                 rb_set_parent(victim->rb_left, new);
514         if (victim->rb_right)
515                 rb_set_parent(victim->rb_right, new);
516
517         /* Copy the pointers/colour from the victim to the replacement */
518         *new = *victim;
519 }
520 EXPORT_SYMBOL(rb_replace_node);