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TOMOYO Linux Cross Reference
Linux/lib/rbtree.c

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  1 // SPDX-License-Identifier: GPL-2.0-or-later
  2 /*
  3   Red Black Trees
  4   (C) 1999  Andrea Arcangeli <andrea@suse.de>
  5   (C) 2002  David Woodhouse <dwmw2@infradead.org>
  6   (C) 2012  Michel Lespinasse <walken@google.com>
  7 
  8 
  9   linux/lib/rbtree.c
 10 */
 11 
 12 #include <linux/rbtree_augmented.h>
 13 #include <linux/export.h>
 14 
 15 /*
 16  * red-black trees properties:  https://en.wikipedia.org/wiki/Rbtree
 17  *
 18  *  1) A node is either red or black
 19  *  2) The root is black
 20  *  3) All leaves (NULL) are black
 21  *  4) Both children of every red node are black
 22  *  5) Every simple path from root to leaves contains the same number
 23  *     of black nodes.
 24  *
 25  *  4 and 5 give the O(log n) guarantee, since 4 implies you cannot have two
 26  *  consecutive red nodes in a path and every red node is therefore followed by
 27  *  a black. So if B is the number of black nodes on every simple path (as per
 28  *  5), then the longest possible path due to 4 is 2B.
 29  *
 30  *  We shall indicate color with case, where black nodes are uppercase and red
 31  *  nodes will be lowercase. Unknown color nodes shall be drawn as red within
 32  *  parentheses and have some accompanying text comment.
 33  */
 34 
 35 /*
 36  * Notes on lockless lookups:
 37  *
 38  * All stores to the tree structure (rb_left and rb_right) must be done using
 39  * WRITE_ONCE(). And we must not inadvertently cause (temporary) loops in the
 40  * tree structure as seen in program order.
 41  *
 42  * These two requirements will allow lockless iteration of the tree -- not
 43  * correct iteration mind you, tree rotations are not atomic so a lookup might
 44  * miss entire subtrees.
 45  *
 46  * But they do guarantee that any such traversal will only see valid elements
 47  * and that it will indeed complete -- does not get stuck in a loop.
 48  *
 49  * It also guarantees that if the lookup returns an element it is the 'correct'
 50  * one. But not returning an element does _NOT_ mean it's not present.
 51  *
 52  * NOTE:
 53  *
 54  * Stores to __rb_parent_color are not important for simple lookups so those
 55  * are left undone as of now. Nor did I check for loops involving parent
 56  * pointers.
 57  */
 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 struct rb_node *rb_red_parent(struct rb_node *red)
 65 {
 66         return (struct rb_node *)red->__rb_parent_color;
 67 }
 68 
 69 /*
 70  * Helper function for rotations:
 71  * - old's parent and color get assigned to new
 72  * - old gets assigned new as a parent and 'color' as a color.
 73  */
 74 static inline void
 75 __rb_rotate_set_parents(struct rb_node *old, struct rb_node *new,
 76                         struct rb_root *root, int color)
 77 {
 78         struct rb_node *parent = rb_parent(old);
 79         new->__rb_parent_color = old->__rb_parent_color;
 80         rb_set_parent_color(old, new, color);
 81         __rb_change_child(old, new, parent, root);
 82 }
 83 
 84 static __always_inline void
 85 __rb_insert(struct rb_node *node, struct rb_root *root,
 86             void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
 87 {
 88         struct rb_node *parent = rb_red_parent(node), *gparent, *tmp;
 89 
 90         while (true) {
 91                 /*
 92                  * Loop invariant: node is red.
 93                  */
 94                 if (unlikely(!parent)) {
 95                         /*
 96                          * The inserted node is root. Either this is the
 97                          * first node, or we recursed at Case 1 below and
 98                          * are no longer violating 4).
 99                          */
100                         rb_set_parent_color(node, NULL, RB_BLACK);
101                         break;
102                 }
103 
104                 /*
105                  * If there is a black parent, we are done.
106                  * Otherwise, take some corrective action as,
107                  * per 4), we don't want a red root or two
108                  * consecutive red nodes.
109                  */
110                 if(rb_is_black(parent))
111                         break;
112 
113                 gparent = rb_red_parent(parent);
114 
115                 tmp = gparent->rb_right;
116                 if (parent != tmp) {    /* parent == gparent->rb_left */
117                         if (tmp && rb_is_red(tmp)) {
118                                 /*
119                                  * Case 1 - node's uncle is red (color flips).
120                                  *
121                                  *       G            g
122                                  *      / \          / \
123                                  *     p   u  -->   P   U
124                                  *    /            /
125                                  *   n            n
126                                  *
127                                  * However, since g's parent might be red, and
128                                  * 4) does not allow this, we need to recurse
129                                  * at g.
130                                  */
131                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
132                                 rb_set_parent_color(parent, gparent, RB_BLACK);
133                                 node = gparent;
134                                 parent = rb_parent(node);
135                                 rb_set_parent_color(node, parent, RB_RED);
136                                 continue;
137                         }
138 
139                         tmp = parent->rb_right;
140                         if (node == tmp) {
141                                 /*
142                                  * Case 2 - node's uncle is black and node is
143                                  * the parent's right child (left rotate at parent).
144                                  *
145                                  *      G             G
146                                  *     / \           / \
147                                  *    p   U  -->    n   U
148                                  *     \           /
149                                  *      n         p
150                                  *
151                                  * This still leaves us in violation of 4), the
152                                  * continuation into Case 3 will fix that.
153                                  */
154                                 tmp = node->rb_left;
155                                 WRITE_ONCE(parent->rb_right, tmp);
156                                 WRITE_ONCE(node->rb_left, parent);
157                                 if (tmp)
158                                         rb_set_parent_color(tmp, parent,
159                                                             RB_BLACK);
160                                 rb_set_parent_color(parent, node, RB_RED);
161                                 augment_rotate(parent, node);
162                                 parent = node;
163                                 tmp = node->rb_right;
164                         }
165 
166                         /*
167                          * Case 3 - node's uncle is black and node is
168                          * the parent's left child (right rotate at gparent).
169                          *
170                          *        G           P
171                          *       / \         / \
172                          *      p   U  -->  n   g
173                          *     /                 \
174                          *    n                   U
175                          */
176                         WRITE_ONCE(gparent->rb_left, tmp); /* == parent->rb_right */
177                         WRITE_ONCE(parent->rb_right, gparent);
178                         if (tmp)
179                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
180                         __rb_rotate_set_parents(gparent, parent, root, RB_RED);
181                         augment_rotate(gparent, parent);
182                         break;
183                 } else {
184                         tmp = gparent->rb_left;
185                         if (tmp && rb_is_red(tmp)) {
186                                 /* Case 1 - color flips */
187                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
188                                 rb_set_parent_color(parent, gparent, RB_BLACK);
189                                 node = gparent;
190                                 parent = rb_parent(node);
191                                 rb_set_parent_color(node, parent, RB_RED);
192                                 continue;
193                         }
194 
195                         tmp = parent->rb_left;
196                         if (node == tmp) {
197                                 /* Case 2 - right rotate at parent */
198                                 tmp = node->rb_right;
199                                 WRITE_ONCE(parent->rb_left, tmp);
200                                 WRITE_ONCE(node->rb_right, parent);
201                                 if (tmp)
202                                         rb_set_parent_color(tmp, parent,
203                                                             RB_BLACK);
204                                 rb_set_parent_color(parent, node, RB_RED);
205                                 augment_rotate(parent, node);
206                                 parent = node;
207                                 tmp = node->rb_left;
208                         }
209 
210                         /* Case 3 - left rotate at gparent */
211                         WRITE_ONCE(gparent->rb_right, tmp); /* == parent->rb_left */
212                         WRITE_ONCE(parent->rb_left, gparent);
213                         if (tmp)
214                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
215                         __rb_rotate_set_parents(gparent, parent, root, RB_RED);
216                         augment_rotate(gparent, parent);
217                         break;
218                 }
219         }
220 }
221 
222 /*
223  * Inline version for rb_erase() use - we want to be able to inline
224  * and eliminate the dummy_rotate callback there
225  */
226 static __always_inline void
227 ____rb_erase_color(struct rb_node *parent, struct rb_root *root,
228         void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
229 {
230         struct rb_node *node = NULL, *sibling, *tmp1, *tmp2;
231 
232         while (true) {
233                 /*
234                  * Loop invariants:
235                  * - node is black (or NULL on first iteration)
236                  * - node is not the root (parent is not NULL)
237                  * - All leaf paths going through parent and node have a
238                  *   black node count that is 1 lower than other leaf paths.
239                  */
240                 sibling = parent->rb_right;
241                 if (node != sibling) {  /* node == parent->rb_left */
242                         if (rb_is_red(sibling)) {
243                                 /*
244                                  * Case 1 - left rotate at parent
245                                  *
246                                  *     P               S
247                                  *    / \             / \
248                                  *   N   s    -->    p   Sr
249                                  *      / \         / \
250                                  *     Sl  Sr      N   Sl
251                                  */
252                                 tmp1 = sibling->rb_left;
253                                 WRITE_ONCE(parent->rb_right, tmp1);
254                                 WRITE_ONCE(sibling->rb_left, parent);
255                                 rb_set_parent_color(tmp1, parent, RB_BLACK);
256                                 __rb_rotate_set_parents(parent, sibling, root,
257                                                         RB_RED);
258                                 augment_rotate(parent, sibling);
259                                 sibling = tmp1;
260                         }
261                         tmp1 = sibling->rb_right;
262                         if (!tmp1 || rb_is_black(tmp1)) {
263                                 tmp2 = sibling->rb_left;
264                                 if (!tmp2 || rb_is_black(tmp2)) {
265                                         /*
266                                          * Case 2 - sibling color flip
267                                          * (p could be either color here)
268                                          *
269                                          *    (p)           (p)
270                                          *    / \           / \
271                                          *   N   S    -->  N   s
272                                          *      / \           / \
273                                          *     Sl  Sr        Sl  Sr
274                                          *
275                                          * This leaves us violating 5) which
276                                          * can be fixed by flipping p to black
277                                          * if it was red, or by recursing at p.
278                                          * p is red when coming from Case 1.
279                                          */
280                                         rb_set_parent_color(sibling, parent,
281                                                             RB_RED);
282                                         if (rb_is_red(parent))
283                                                 rb_set_black(parent);
284                                         else {
285                                                 node = parent;
286                                                 parent = rb_parent(node);
287                                                 if (parent)
288                                                         continue;
289                                         }
290                                         break;
291                                 }
292                                 /*
293                                  * Case 3 - right rotate at sibling
294                                  * (p could be either color here)
295                                  *
296                                  *   (p)           (p)
297                                  *   / \           / \
298                                  *  N   S    -->  N   sl
299                                  *     / \             \
300                                  *    sl  Sr            S
301                                  *                       \
302                                  *                        Sr
303                                  *
304                                  * Note: p might be red, and then both
305                                  * p and sl are red after rotation(which
306                                  * breaks property 4). This is fixed in
307                                  * Case 4 (in __rb_rotate_set_parents()
308                                  *         which set sl the color of p
309                                  *         and set p RB_BLACK)
310                                  *
311                                  *   (p)            (sl)
312                                  *   / \            /  \
313                                  *  N   sl   -->   P    S
314                                  *       \        /      \
315                                  *        S      N        Sr
316                                  *         \
317                                  *          Sr
318                                  */
319                                 tmp1 = tmp2->rb_right;
320                                 WRITE_ONCE(sibling->rb_left, tmp1);
321                                 WRITE_ONCE(tmp2->rb_right, sibling);
322                                 WRITE_ONCE(parent->rb_right, tmp2);
323                                 if (tmp1)
324                                         rb_set_parent_color(tmp1, sibling,
325                                                             RB_BLACK);
326                                 augment_rotate(sibling, tmp2);
327                                 tmp1 = sibling;
328                                 sibling = tmp2;
329                         }
330                         /*
331                          * Case 4 - left rotate at parent + color flips
332                          * (p and sl could be either color here.
333                          *  After rotation, p becomes black, s acquires
334                          *  p's color, and sl keeps its color)
335                          *
336                          *      (p)             (s)
337                          *      / \             / \
338                          *     N   S     -->   P   Sr
339                          *        / \         / \
340                          *      (sl) sr      N  (sl)
341                          */
342                         tmp2 = sibling->rb_left;
343                         WRITE_ONCE(parent->rb_right, tmp2);
344                         WRITE_ONCE(sibling->rb_left, parent);
345                         rb_set_parent_color(tmp1, sibling, RB_BLACK);
346                         if (tmp2)
347                                 rb_set_parent(tmp2, parent);
348                         __rb_rotate_set_parents(parent, sibling, root,
349                                                 RB_BLACK);
350                         augment_rotate(parent, sibling);
351                         break;
352                 } else {
353                         sibling = parent->rb_left;
354                         if (rb_is_red(sibling)) {
355                                 /* Case 1 - right rotate at parent */
356                                 tmp1 = sibling->rb_right;
357                                 WRITE_ONCE(parent->rb_left, tmp1);
358                                 WRITE_ONCE(sibling->rb_right, parent);
359                                 rb_set_parent_color(tmp1, parent, RB_BLACK);
360                                 __rb_rotate_set_parents(parent, sibling, root,
361                                                         RB_RED);
362                                 augment_rotate(parent, sibling);
363                                 sibling = tmp1;
364                         }
365                         tmp1 = sibling->rb_left;
366                         if (!tmp1 || rb_is_black(tmp1)) {
367                                 tmp2 = sibling->rb_right;
368                                 if (!tmp2 || rb_is_black(tmp2)) {
369                                         /* Case 2 - sibling color flip */
370                                         rb_set_parent_color(sibling, parent,
371                                                             RB_RED);
372                                         if (rb_is_red(parent))
373                                                 rb_set_black(parent);
374                                         else {
375                                                 node = parent;
376                                                 parent = rb_parent(node);
377                                                 if (parent)
378                                                         continue;
379                                         }
380                                         break;
381                                 }
382                                 /* Case 3 - left rotate at sibling */
383                                 tmp1 = tmp2->rb_left;
384                                 WRITE_ONCE(sibling->rb_right, tmp1);
385                                 WRITE_ONCE(tmp2->rb_left, sibling);
386                                 WRITE_ONCE(parent->rb_left, tmp2);
387                                 if (tmp1)
388                                         rb_set_parent_color(tmp1, sibling,
389                                                             RB_BLACK);
390                                 augment_rotate(sibling, tmp2);
391                                 tmp1 = sibling;
392                                 sibling = tmp2;
393                         }
394                         /* Case 4 - right rotate at parent + color flips */
395                         tmp2 = sibling->rb_right;
396                         WRITE_ONCE(parent->rb_left, tmp2);
397                         WRITE_ONCE(sibling->rb_right, parent);
398                         rb_set_parent_color(tmp1, sibling, RB_BLACK);
399                         if (tmp2)
400                                 rb_set_parent(tmp2, parent);
401                         __rb_rotate_set_parents(parent, sibling, root,
402                                                 RB_BLACK);
403                         augment_rotate(parent, sibling);
404                         break;
405                 }
406         }
407 }
408 
409 /* Non-inline version for rb_erase_augmented() use */
410 void __rb_erase_color(struct rb_node *parent, struct rb_root *root,
411         void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
412 {
413         ____rb_erase_color(parent, root, augment_rotate);
414 }
415 EXPORT_SYMBOL(__rb_erase_color);
416 
417 /*
418  * Non-augmented rbtree manipulation functions.
419  *
420  * We use dummy augmented callbacks here, and have the compiler optimize them
421  * out of the rb_insert_color() and rb_erase() function definitions.
422  */
423 
424 static inline void dummy_propagate(struct rb_node *node, struct rb_node *stop) {}
425 static inline void dummy_copy(struct rb_node *old, struct rb_node *new) {}
426 static inline void dummy_rotate(struct rb_node *old, struct rb_node *new) {}
427 
428 static const struct rb_augment_callbacks dummy_callbacks = {
429         .propagate = dummy_propagate,
430         .copy = dummy_copy,
431         .rotate = dummy_rotate
432 };
433 
434 void rb_insert_color(struct rb_node *node, struct rb_root *root)
435 {
436         __rb_insert(node, root, dummy_rotate);
437 }
438 EXPORT_SYMBOL(rb_insert_color);
439 
440 void rb_erase(struct rb_node *node, struct rb_root *root)
441 {
442         struct rb_node *rebalance;
443         rebalance = __rb_erase_augmented(node, root, &dummy_callbacks);
444         if (rebalance)
445                 ____rb_erase_color(rebalance, root, dummy_rotate);
446 }
447 EXPORT_SYMBOL(rb_erase);
448 
449 /*
450  * Augmented rbtree manipulation functions.
451  *
452  * This instantiates the same __always_inline functions as in the non-augmented
453  * case, but this time with user-defined callbacks.
454  */
455 
456 void __rb_insert_augmented(struct rb_node *node, struct rb_root *root,
457         void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
458 {
459         __rb_insert(node, root, augment_rotate);
460 }
461 EXPORT_SYMBOL(__rb_insert_augmented);
462 
463 /*
464  * This function returns the first node (in sort order) of the tree.
465  */
466 struct rb_node *rb_first(const struct rb_root *root)
467 {
468         struct rb_node  *n;
469 
470         n = root->rb_node;
471         if (!n)
472                 return NULL;
473         while (n->rb_left)
474                 n = n->rb_left;
475         return n;
476 }
477 EXPORT_SYMBOL(rb_first);
478 
479 struct rb_node *rb_last(const struct rb_root *root)
480 {
481         struct rb_node  *n;
482 
483         n = root->rb_node;
484         if (!n)
485                 return NULL;
486         while (n->rb_right)
487                 n = n->rb_right;
488         return n;
489 }
490 EXPORT_SYMBOL(rb_last);
491 
492 struct rb_node *rb_next(const struct rb_node *node)
493 {
494         struct rb_node *parent;
495 
496         if (RB_EMPTY_NODE(node))
497                 return NULL;
498 
499         /*
500          * If we have a right-hand child, go down and then left as far
501          * as we can.
502          */
503         if (node->rb_right) {
504                 node = node->rb_right;
505                 while (node->rb_left)
506                         node = node->rb_left;
507                 return (struct rb_node *)node;
508         }
509 
510         /*
511          * No right-hand children. Everything down and left is smaller than us,
512          * so any 'next' node must be in the general direction of our parent.
513          * Go up the tree; any time the ancestor is a right-hand child of its
514          * parent, keep going up. First time it's a left-hand child of its
515          * parent, said parent is our 'next' node.
516          */
517         while ((parent = rb_parent(node)) && node == parent->rb_right)
518                 node = parent;
519 
520         return parent;
521 }
522 EXPORT_SYMBOL(rb_next);
523 
524 struct rb_node *rb_prev(const struct rb_node *node)
525 {
526         struct rb_node *parent;
527 
528         if (RB_EMPTY_NODE(node))
529                 return NULL;
530 
531         /*
532          * If we have a left-hand child, go down and then right as far
533          * as we can.
534          */
535         if (node->rb_left) {
536                 node = node->rb_left;
537                 while (node->rb_right)
538                         node = node->rb_right;
539                 return (struct rb_node *)node;
540         }
541 
542         /*
543          * No left-hand children. Go up till we find an ancestor which
544          * is a right-hand child of its parent.
545          */
546         while ((parent = rb_parent(node)) && node == parent->rb_left)
547                 node = parent;
548 
549         return parent;
550 }
551 EXPORT_SYMBOL(rb_prev);
552 
553 void rb_replace_node(struct rb_node *victim, struct rb_node *new,
554                      struct rb_root *root)
555 {
556         struct rb_node *parent = rb_parent(victim);
557 
558         /* Copy the pointers/colour from the victim to the replacement */
559         *new = *victim;
560 
561         /* Set the surrounding nodes to point to the replacement */
562         if (victim->rb_left)
563                 rb_set_parent(victim->rb_left, new);
564         if (victim->rb_right)
565                 rb_set_parent(victim->rb_right, new);
566         __rb_change_child(victim, new, parent, root);
567 }
568 EXPORT_SYMBOL(rb_replace_node);
569 
570 void rb_replace_node_rcu(struct rb_node *victim, struct rb_node *new,
571                          struct rb_root *root)
572 {
573         struct rb_node *parent = rb_parent(victim);
574 
575         /* Copy the pointers/colour from the victim to the replacement */
576         *new = *victim;
577 
578         /* Set the surrounding nodes to point to the replacement */
579         if (victim->rb_left)
580                 rb_set_parent(victim->rb_left, new);
581         if (victim->rb_right)
582                 rb_set_parent(victim->rb_right, new);
583 
584         /* Set the parent's pointer to the new node last after an RCU barrier
585          * so that the pointers onwards are seen to be set correctly when doing
586          * an RCU walk over the tree.
587          */
588         __rb_change_child_rcu(victim, new, parent, root);
589 }
590 EXPORT_SYMBOL(rb_replace_node_rcu);
591 
592 static struct rb_node *rb_left_deepest_node(const struct rb_node *node)
593 {
594         for (;;) {
595                 if (node->rb_left)
596                         node = node->rb_left;
597                 else if (node->rb_right)
598                         node = node->rb_right;
599                 else
600                         return (struct rb_node *)node;
601         }
602 }
603 
604 struct rb_node *rb_next_postorder(const struct rb_node *node)
605 {
606         const struct rb_node *parent;
607         if (!node)
608                 return NULL;
609         parent = rb_parent(node);
610 
611         /* If we're sitting on node, we've already seen our children */
612         if (parent && node == parent->rb_left && parent->rb_right) {
613                 /* If we are the parent's left node, go to the parent's right
614                  * node then all the way down to the left */
615                 return rb_left_deepest_node(parent->rb_right);
616         } else
617                 /* Otherwise we are the parent's right node, and the parent
618                  * should be next */
619                 return (struct rb_node *)parent;
620 }
621 EXPORT_SYMBOL(rb_next_postorder);
622 
623 struct rb_node *rb_first_postorder(const struct rb_root *root)
624 {
625         if (!root->rb_node)
626                 return NULL;
627 
628         return rb_left_deepest_node(root->rb_node);
629 }
630 EXPORT_SYMBOL(rb_first_postorder);
631 

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