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Linux/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                                  * Note: p might be red, and then both
306                                  * p and sl are red after rotation(which
307                                  * breaks property 4). This is fixed in
308                                  * Case 4 (in __rb_rotate_set_parents()
309                                  *         which set sl the color of p
310                                  *         and set p RB_BLACK)
311                                  *
312                                  *   (p)            (sl)
313                                  *   / \            /  \
314                                  *  N   sl   -->   P    S
315                                  *       \        /      \
316                                  *        S      N        Sr
317                                  *         \
318                                  *          Sr
319                                  */
320                                 tmp1 = tmp2->rb_right;
321                                 WRITE_ONCE(sibling->rb_left, tmp1);
322                                 WRITE_ONCE(tmp2->rb_right, sibling);
323                                 WRITE_ONCE(parent->rb_right, tmp2);
324                                 if (tmp1)
325                                         rb_set_parent_color(tmp1, sibling,
326                                                             RB_BLACK);
327                                 augment_rotate(sibling, tmp2);
328                                 tmp1 = sibling;
329                                 sibling = tmp2;
330                         }
331                         /*
332                          * Case 4 - left rotate at parent + color flips
333                          * (p and sl could be either color here.
334                          *  After rotation, p becomes black, s acquires
335                          *  p's color, and sl keeps its color)
336                          *
337                          *      (p)             (s)
338                          *      / \             / \
339                          *     N   S     -->   P   Sr
340                          *        / \         / \
341                          *      (sl) sr      N  (sl)
342                          */
343                         tmp2 = sibling->rb_left;
344                         WRITE_ONCE(parent->rb_right, tmp2);
345                         WRITE_ONCE(sibling->rb_left, parent);
346                         rb_set_parent_color(tmp1, sibling, RB_BLACK);
347                         if (tmp2)
348                                 rb_set_parent(tmp2, parent);
349                         __rb_rotate_set_parents(parent, sibling, root,
350                                                 RB_BLACK);
351                         augment_rotate(parent, sibling);
352                         break;
353                 } else {
354                         sibling = parent->rb_left;
355                         if (rb_is_red(sibling)) {
356                                 /* Case 1 - right rotate at parent */
357                                 tmp1 = sibling->rb_right;
358                                 WRITE_ONCE(parent->rb_left, tmp1);
359                                 WRITE_ONCE(sibling->rb_right, parent);
360                                 rb_set_parent_color(tmp1, parent, RB_BLACK);
361                                 __rb_rotate_set_parents(parent, sibling, root,
362                                                         RB_RED);
363                                 augment_rotate(parent, sibling);
364                                 sibling = tmp1;
365                         }
366                         tmp1 = sibling->rb_left;
367                         if (!tmp1 || rb_is_black(tmp1)) {
368                                 tmp2 = sibling->rb_right;
369                                 if (!tmp2 || rb_is_black(tmp2)) {
370                                         /* Case 2 - sibling color flip */
371                                         rb_set_parent_color(sibling, parent,
372                                                             RB_RED);
373                                         if (rb_is_red(parent))
374                                                 rb_set_black(parent);
375                                         else {
376                                                 node = parent;
377                                                 parent = rb_parent(node);
378                                                 if (parent)
379                                                         continue;
380                                         }
381                                         break;
382                                 }
383                                 /* Case 3 - left rotate at sibling */
384                                 tmp1 = tmp2->rb_left;
385                                 WRITE_ONCE(sibling->rb_right, tmp1);
386                                 WRITE_ONCE(tmp2->rb_left, sibling);
387                                 WRITE_ONCE(parent->rb_left, tmp2);
388                                 if (tmp1)
389                                         rb_set_parent_color(tmp1, sibling,
390                                                             RB_BLACK);
391                                 augment_rotate(sibling, tmp2);
392                                 tmp1 = sibling;
393                                 sibling = tmp2;
394                         }
395                         /* Case 4 - right rotate at parent + color flips */
396                         tmp2 = sibling->rb_right;
397                         WRITE_ONCE(parent->rb_left, tmp2);
398                         WRITE_ONCE(sibling->rb_right, parent);
399                         rb_set_parent_color(tmp1, sibling, RB_BLACK);
400                         if (tmp2)
401                                 rb_set_parent(tmp2, parent);
402                         __rb_rotate_set_parents(parent, sibling, root,
403                                                 RB_BLACK);
404                         augment_rotate(parent, sibling);
405                         break;
406                 }
407         }
408 }
409 
410 /* Non-inline version for rb_erase_augmented() use */
411 void __rb_erase_color(struct rb_node *parent, struct rb_root *root,
412         void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
413 {
414         ____rb_erase_color(parent, root, augment_rotate);
415 }
416 EXPORT_SYMBOL(__rb_erase_color);
417 
418 /*
419  * Non-augmented rbtree manipulation functions.
420  *
421  * We use dummy augmented callbacks here, and have the compiler optimize them
422  * out of the rb_insert_color() and rb_erase() function definitions.
423  */
424 
425 static inline void dummy_propagate(struct rb_node *node, struct rb_node *stop) {}
426 static inline void dummy_copy(struct rb_node *old, struct rb_node *new) {}
427 static inline void dummy_rotate(struct rb_node *old, struct rb_node *new) {}
428 
429 static const struct rb_augment_callbacks dummy_callbacks = {
430         dummy_propagate, dummy_copy, dummy_rotate
431 };
432 
433 void rb_insert_color(struct rb_node *node, struct rb_root *root)
434 {
435         __rb_insert(node, root, dummy_rotate);
436 }
437 EXPORT_SYMBOL(rb_insert_color);
438 
439 void rb_erase(struct rb_node *node, struct rb_root *root)
440 {
441         struct rb_node *rebalance;
442         rebalance = __rb_erase_augmented(node, root, &dummy_callbacks);
443         if (rebalance)
444                 ____rb_erase_color(rebalance, root, dummy_rotate);
445 }
446 EXPORT_SYMBOL(rb_erase);
447 
448 /*
449  * Augmented rbtree manipulation functions.
450  *
451  * This instantiates the same __always_inline functions as in the non-augmented
452  * case, but this time with user-defined callbacks.
453  */
454 
455 void __rb_insert_augmented(struct rb_node *node, struct rb_root *root,
456         void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
457 {
458         __rb_insert(node, root, augment_rotate);
459 }
460 EXPORT_SYMBOL(__rb_insert_augmented);
461 
462 /*
463  * This function returns the first node (in sort order) of the tree.
464  */
465 struct rb_node *rb_first(const struct rb_root *root)
466 {
467         struct rb_node  *n;
468 
469         n = root->rb_node;
470         if (!n)
471                 return NULL;
472         while (n->rb_left)
473                 n = n->rb_left;
474         return n;
475 }
476 EXPORT_SYMBOL(rb_first);
477 
478 struct rb_node *rb_last(const struct rb_root *root)
479 {
480         struct rb_node  *n;
481 
482         n = root->rb_node;
483         if (!n)
484                 return NULL;
485         while (n->rb_right)
486                 n = n->rb_right;
487         return n;
488 }
489 EXPORT_SYMBOL(rb_last);
490 
491 struct rb_node *rb_next(const struct rb_node *node)
492 {
493         struct rb_node *parent;
494 
495         if (RB_EMPTY_NODE(node))
496                 return NULL;
497 
498         /*
499          * If we have a right-hand child, go down and then left as far
500          * as we can.
501          */
502         if (node->rb_right) {
503                 node = node->rb_right; 
504                 while (node->rb_left)
505                         node=node->rb_left;
506                 return (struct rb_node *)node;
507         }
508 
509         /*
510          * No right-hand children. Everything down and left is smaller than us,
511          * so any 'next' node must be in the general direction of our parent.
512          * Go up the tree; any time the ancestor is a right-hand child of its
513          * parent, keep going up. First time it's a left-hand child of its
514          * parent, said parent is our 'next' node.
515          */
516         while ((parent = rb_parent(node)) && node == parent->rb_right)
517                 node = parent;
518 
519         return parent;
520 }
521 EXPORT_SYMBOL(rb_next);
522 
523 struct rb_node *rb_prev(const struct rb_node *node)
524 {
525         struct rb_node *parent;
526 
527         if (RB_EMPTY_NODE(node))
528                 return NULL;
529 
530         /*
531          * If we have a left-hand child, go down and then right as far
532          * as we can.
533          */
534         if (node->rb_left) {
535                 node = node->rb_left; 
536                 while (node->rb_right)
537                         node=node->rb_right;
538                 return (struct rb_node *)node;
539         }
540 
541         /*
542          * No left-hand children. Go up till we find an ancestor which
543          * is a right-hand child of its parent.
544          */
545         while ((parent = rb_parent(node)) && node == parent->rb_left)
546                 node = parent;
547 
548         return parent;
549 }
550 EXPORT_SYMBOL(rb_prev);
551 
552 void rb_replace_node(struct rb_node *victim, struct rb_node *new,
553                      struct rb_root *root)
554 {
555         struct rb_node *parent = rb_parent(victim);
556 
557         /* Copy the pointers/colour from the victim to the replacement */
558         *new = *victim;
559 
560         /* Set the surrounding nodes to point to the replacement */
561         if (victim->rb_left)
562                 rb_set_parent(victim->rb_left, new);
563         if (victim->rb_right)
564                 rb_set_parent(victim->rb_right, new);
565         __rb_change_child(victim, new, parent, root);
566 }
567 EXPORT_SYMBOL(rb_replace_node);
568 
569 void rb_replace_node_rcu(struct rb_node *victim, struct rb_node *new,
570                          struct rb_root *root)
571 {
572         struct rb_node *parent = rb_parent(victim);
573 
574         /* Copy the pointers/colour from the victim to the replacement */
575         *new = *victim;
576 
577         /* Set the surrounding nodes to point to the replacement */
578         if (victim->rb_left)
579                 rb_set_parent(victim->rb_left, new);
580         if (victim->rb_right)
581                 rb_set_parent(victim->rb_right, new);
582 
583         /* Set the parent's pointer to the new node last after an RCU barrier
584          * so that the pointers onwards are seen to be set correctly when doing
585          * an RCU walk over the tree.
586          */
587         __rb_change_child_rcu(victim, new, parent, root);
588 }
589 EXPORT_SYMBOL(rb_replace_node_rcu);
590 
591 static struct rb_node *rb_left_deepest_node(const struct rb_node *node)
592 {
593         for (;;) {
594                 if (node->rb_left)
595                         node = node->rb_left;
596                 else if (node->rb_right)
597                         node = node->rb_right;
598                 else
599                         return (struct rb_node *)node;
600         }
601 }
602 
603 struct rb_node *rb_next_postorder(const struct rb_node *node)
604 {
605         const struct rb_node *parent;
606         if (!node)
607                 return NULL;
608         parent = rb_parent(node);
609 
610         /* If we're sitting on node, we've already seen our children */
611         if (parent && node == parent->rb_left && parent->rb_right) {
612                 /* If we are the parent's left node, go to the parent's right
613                  * node then all the way down to the left */
614                 return rb_left_deepest_node(parent->rb_right);
615         } else
616                 /* Otherwise we are the parent's right node, and the parent
617                  * should be next */
618                 return (struct rb_node *)parent;
619 }
620 EXPORT_SYMBOL(rb_next_postorder);
621 
622 struct rb_node *rb_first_postorder(const struct rb_root *root)
623 {
624         if (!root->rb_node)
625                 return NULL;
626 
627         return rb_left_deepest_node(root->rb_node);
628 }
629 EXPORT_SYMBOL(rb_first_postorder);
630 

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