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Linux/tools/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:  http://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             bool newleft, struct rb_node **leftmost,
 87             void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
 88 {
 89         struct rb_node *parent = rb_red_parent(node), *gparent, *tmp;
 90 
 91         if (newleft)
 92                 *leftmost = node;
 93 
 94         while (true) {
 95                 /*
 96                  * Loop invariant: node is red.
 97                  */
 98                 if (unlikely(!parent)) {
 99                         /*
100                          * The inserted node is root. Either this is the
101                          * first node, or we recursed at Case 1 below and
102                          * are no longer violating 4).
103                          */
104                         rb_set_parent_color(node, NULL, RB_BLACK);
105                         break;
106                 }
107 
108                 /*
109                  * If there is a black parent, we are done.
110                  * Otherwise, take some corrective action as,
111                  * per 4), we don't want a red root or two
112                  * consecutive red nodes.
113                  */
114                 if(rb_is_black(parent))
115                         break;
116 
117                 gparent = rb_red_parent(parent);
118 
119                 tmp = gparent->rb_right;
120                 if (parent != tmp) {    /* parent == gparent->rb_left */
121                         if (tmp && rb_is_red(tmp)) {
122                                 /*
123                                  * Case 1 - node's uncle is red (color flips).
124                                  *
125                                  *       G            g
126                                  *      / \          / \
127                                  *     p   u  -->   P   U
128                                  *    /            /
129                                  *   n            n
130                                  *
131                                  * However, since g's parent might be red, and
132                                  * 4) does not allow this, we need to recurse
133                                  * at g.
134                                  */
135                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
136                                 rb_set_parent_color(parent, gparent, RB_BLACK);
137                                 node = gparent;
138                                 parent = rb_parent(node);
139                                 rb_set_parent_color(node, parent, RB_RED);
140                                 continue;
141                         }
142 
143                         tmp = parent->rb_right;
144                         if (node == tmp) {
145                                 /*
146                                  * Case 2 - node's uncle is black and node is
147                                  * the parent's right child (left rotate at parent).
148                                  *
149                                  *      G             G
150                                  *     / \           / \
151                                  *    p   U  -->    n   U
152                                  *     \           /
153                                  *      n         p
154                                  *
155                                  * This still leaves us in violation of 4), the
156                                  * continuation into Case 3 will fix that.
157                                  */
158                                 tmp = node->rb_left;
159                                 WRITE_ONCE(parent->rb_right, tmp);
160                                 WRITE_ONCE(node->rb_left, parent);
161                                 if (tmp)
162                                         rb_set_parent_color(tmp, parent,
163                                                             RB_BLACK);
164                                 rb_set_parent_color(parent, node, RB_RED);
165                                 augment_rotate(parent, node);
166                                 parent = node;
167                                 tmp = node->rb_right;
168                         }
169 
170                         /*
171                          * Case 3 - node's uncle is black and node is
172                          * the parent's left child (right rotate at gparent).
173                          *
174                          *        G           P
175                          *       / \         / \
176                          *      p   U  -->  n   g
177                          *     /                 \
178                          *    n                   U
179                          */
180                         WRITE_ONCE(gparent->rb_left, tmp); /* == parent->rb_right */
181                         WRITE_ONCE(parent->rb_right, gparent);
182                         if (tmp)
183                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
184                         __rb_rotate_set_parents(gparent, parent, root, RB_RED);
185                         augment_rotate(gparent, parent);
186                         break;
187                 } else {
188                         tmp = gparent->rb_left;
189                         if (tmp && rb_is_red(tmp)) {
190                                 /* Case 1 - color flips */
191                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
192                                 rb_set_parent_color(parent, gparent, RB_BLACK);
193                                 node = gparent;
194                                 parent = rb_parent(node);
195                                 rb_set_parent_color(node, parent, RB_RED);
196                                 continue;
197                         }
198 
199                         tmp = parent->rb_left;
200                         if (node == tmp) {
201                                 /* Case 2 - right rotate at parent */
202                                 tmp = node->rb_right;
203                                 WRITE_ONCE(parent->rb_left, tmp);
204                                 WRITE_ONCE(node->rb_right, parent);
205                                 if (tmp)
206                                         rb_set_parent_color(tmp, parent,
207                                                             RB_BLACK);
208                                 rb_set_parent_color(parent, node, RB_RED);
209                                 augment_rotate(parent, node);
210                                 parent = node;
211                                 tmp = node->rb_left;
212                         }
213 
214                         /* Case 3 - left rotate at gparent */
215                         WRITE_ONCE(gparent->rb_right, tmp); /* == parent->rb_left */
216                         WRITE_ONCE(parent->rb_left, gparent);
217                         if (tmp)
218                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
219                         __rb_rotate_set_parents(gparent, parent, root, RB_RED);
220                         augment_rotate(gparent, parent);
221                         break;
222                 }
223         }
224 }
225 
226 /*
227  * Inline version for rb_erase() use - we want to be able to inline
228  * and eliminate the dummy_rotate callback there
229  */
230 static __always_inline void
231 ____rb_erase_color(struct rb_node *parent, struct rb_root *root,
232         void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
233 {
234         struct rb_node *node = NULL, *sibling, *tmp1, *tmp2;
235 
236         while (true) {
237                 /*
238                  * Loop invariants:
239                  * - node is black (or NULL on first iteration)
240                  * - node is not the root (parent is not NULL)
241                  * - All leaf paths going through parent and node have a
242                  *   black node count that is 1 lower than other leaf paths.
243                  */
244                 sibling = parent->rb_right;
245                 if (node != sibling) {  /* node == parent->rb_left */
246                         if (rb_is_red(sibling)) {
247                                 /*
248                                  * Case 1 - left rotate at parent
249                                  *
250                                  *     P               S
251                                  *    / \             / \
252                                  *   N   s    -->    p   Sr
253                                  *      / \         / \
254                                  *     Sl  Sr      N   Sl
255                                  */
256                                 tmp1 = sibling->rb_left;
257                                 WRITE_ONCE(parent->rb_right, tmp1);
258                                 WRITE_ONCE(sibling->rb_left, parent);
259                                 rb_set_parent_color(tmp1, parent, RB_BLACK);
260                                 __rb_rotate_set_parents(parent, sibling, root,
261                                                         RB_RED);
262                                 augment_rotate(parent, sibling);
263                                 sibling = tmp1;
264                         }
265                         tmp1 = sibling->rb_right;
266                         if (!tmp1 || rb_is_black(tmp1)) {
267                                 tmp2 = sibling->rb_left;
268                                 if (!tmp2 || rb_is_black(tmp2)) {
269                                         /*
270                                          * Case 2 - sibling color flip
271                                          * (p could be either color here)
272                                          *
273                                          *    (p)           (p)
274                                          *    / \           / \
275                                          *   N   S    -->  N   s
276                                          *      / \           / \
277                                          *     Sl  Sr        Sl  Sr
278                                          *
279                                          * This leaves us violating 5) which
280                                          * can be fixed by flipping p to black
281                                          * if it was red, or by recursing at p.
282                                          * p is red when coming from Case 1.
283                                          */
284                                         rb_set_parent_color(sibling, parent,
285                                                             RB_RED);
286                                         if (rb_is_red(parent))
287                                                 rb_set_black(parent);
288                                         else {
289                                                 node = parent;
290                                                 parent = rb_parent(node);
291                                                 if (parent)
292                                                         continue;
293                                         }
294                                         break;
295                                 }
296                                 /*
297                                  * Case 3 - right rotate at sibling
298                                  * (p could be either color here)
299                                  *
300                                  *   (p)           (p)
301                                  *   / \           / \
302                                  *  N   S    -->  N   sl
303                                  *     / \             \
304                                  *    sl  Sr            S
305                                  *                       \
306                                  *                        Sr
307                                  *
308                                  * Note: p might be red, and then both
309                                  * p and sl are red after rotation(which
310                                  * breaks property 4). This is fixed in
311                                  * Case 4 (in __rb_rotate_set_parents()
312                                  *         which set sl the color of p
313                                  *         and set p RB_BLACK)
314                                  *
315                                  *   (p)            (sl)
316                                  *   / \            /  \
317                                  *  N   sl   -->   P    S
318                                  *       \        /      \
319                                  *        S      N        Sr
320                                  *         \
321                                  *          Sr
322                                  */
323                                 tmp1 = tmp2->rb_right;
324                                 WRITE_ONCE(sibling->rb_left, tmp1);
325                                 WRITE_ONCE(tmp2->rb_right, sibling);
326                                 WRITE_ONCE(parent->rb_right, tmp2);
327                                 if (tmp1)
328                                         rb_set_parent_color(tmp1, sibling,
329                                                             RB_BLACK);
330                                 augment_rotate(sibling, tmp2);
331                                 tmp1 = sibling;
332                                 sibling = tmp2;
333                         }
334                         /*
335                          * Case 4 - left rotate at parent + color flips
336                          * (p and sl could be either color here.
337                          *  After rotation, p becomes black, s acquires
338                          *  p's color, and sl keeps its color)
339                          *
340                          *      (p)             (s)
341                          *      / \             / \
342                          *     N   S     -->   P   Sr
343                          *        / \         / \
344                          *      (sl) sr      N  (sl)
345                          */
346                         tmp2 = sibling->rb_left;
347                         WRITE_ONCE(parent->rb_right, tmp2);
348                         WRITE_ONCE(sibling->rb_left, parent);
349                         rb_set_parent_color(tmp1, sibling, RB_BLACK);
350                         if (tmp2)
351                                 rb_set_parent(tmp2, parent);
352                         __rb_rotate_set_parents(parent, sibling, root,
353                                                 RB_BLACK);
354                         augment_rotate(parent, sibling);
355                         break;
356                 } else {
357                         sibling = parent->rb_left;
358                         if (rb_is_red(sibling)) {
359                                 /* Case 1 - right rotate at parent */
360                                 tmp1 = sibling->rb_right;
361                                 WRITE_ONCE(parent->rb_left, tmp1);
362                                 WRITE_ONCE(sibling->rb_right, parent);
363                                 rb_set_parent_color(tmp1, parent, RB_BLACK);
364                                 __rb_rotate_set_parents(parent, sibling, root,
365                                                         RB_RED);
366                                 augment_rotate(parent, sibling);
367                                 sibling = tmp1;
368                         }
369                         tmp1 = sibling->rb_left;
370                         if (!tmp1 || rb_is_black(tmp1)) {
371                                 tmp2 = sibling->rb_right;
372                                 if (!tmp2 || rb_is_black(tmp2)) {
373                                         /* Case 2 - sibling color flip */
374                                         rb_set_parent_color(sibling, parent,
375                                                             RB_RED);
376                                         if (rb_is_red(parent))
377                                                 rb_set_black(parent);
378                                         else {
379                                                 node = parent;
380                                                 parent = rb_parent(node);
381                                                 if (parent)
382                                                         continue;
383                                         }
384                                         break;
385                                 }
386                                 /* Case 3 - left rotate at sibling */
387                                 tmp1 = tmp2->rb_left;
388                                 WRITE_ONCE(sibling->rb_right, tmp1);
389                                 WRITE_ONCE(tmp2->rb_left, sibling);
390                                 WRITE_ONCE(parent->rb_left, tmp2);
391                                 if (tmp1)
392                                         rb_set_parent_color(tmp1, sibling,
393                                                             RB_BLACK);
394                                 augment_rotate(sibling, tmp2);
395                                 tmp1 = sibling;
396                                 sibling = tmp2;
397                         }
398                         /* Case 4 - right rotate at parent + color flips */
399                         tmp2 = sibling->rb_right;
400                         WRITE_ONCE(parent->rb_left, tmp2);
401                         WRITE_ONCE(sibling->rb_right, parent);
402                         rb_set_parent_color(tmp1, sibling, RB_BLACK);
403                         if (tmp2)
404                                 rb_set_parent(tmp2, parent);
405                         __rb_rotate_set_parents(parent, sibling, root,
406                                                 RB_BLACK);
407                         augment_rotate(parent, sibling);
408                         break;
409                 }
410         }
411 }
412 
413 /* Non-inline version for rb_erase_augmented() use */
414 void __rb_erase_color(struct rb_node *parent, struct rb_root *root,
415         void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
416 {
417         ____rb_erase_color(parent, root, augment_rotate);
418 }
419 
420 /*
421  * Non-augmented rbtree manipulation functions.
422  *
423  * We use dummy augmented callbacks here, and have the compiler optimize them
424  * out of the rb_insert_color() and rb_erase() function definitions.
425  */
426 
427 static inline void dummy_propagate(struct rb_node *node, struct rb_node *stop) {}
428 static inline void dummy_copy(struct rb_node *old, struct rb_node *new) {}
429 static inline void dummy_rotate(struct rb_node *old, struct rb_node *new) {}
430 
431 static const struct rb_augment_callbacks dummy_callbacks = {
432         .propagate = dummy_propagate,
433         .copy = dummy_copy,
434         .rotate = dummy_rotate
435 };
436 
437 void rb_insert_color(struct rb_node *node, struct rb_root *root)
438 {
439         __rb_insert(node, root, false, NULL, dummy_rotate);
440 }
441 
442 void rb_erase(struct rb_node *node, struct rb_root *root)
443 {
444         struct rb_node *rebalance;
445         rebalance = __rb_erase_augmented(node, root,
446                                          NULL, &dummy_callbacks);
447         if (rebalance)
448                 ____rb_erase_color(rebalance, root, dummy_rotate);
449 }
450 
451 void rb_insert_color_cached(struct rb_node *node,
452                             struct rb_root_cached *root, bool leftmost)
453 {
454         __rb_insert(node, &root->rb_root, leftmost,
455                     &root->rb_leftmost, dummy_rotate);
456 }
457 
458 void rb_erase_cached(struct rb_node *node, struct rb_root_cached *root)
459 {
460         struct rb_node *rebalance;
461         rebalance = __rb_erase_augmented(node, &root->rb_root,
462                                          &root->rb_leftmost, &dummy_callbacks);
463         if (rebalance)
464                 ____rb_erase_color(rebalance, &root->rb_root, dummy_rotate);
465 }
466 
467 /*
468  * Augmented rbtree manipulation functions.
469  *
470  * This instantiates the same __always_inline functions as in the non-augmented
471  * case, but this time with user-defined callbacks.
472  */
473 
474 void __rb_insert_augmented(struct rb_node *node, struct rb_root *root,
475                            bool newleft, struct rb_node **leftmost,
476         void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
477 {
478         __rb_insert(node, root, newleft, leftmost, augment_rotate);
479 }
480 
481 /*
482  * This function returns the first node (in sort order) of the tree.
483  */
484 struct rb_node *rb_first(const struct rb_root *root)
485 {
486         struct rb_node  *n;
487 
488         n = root->rb_node;
489         if (!n)
490                 return NULL;
491         while (n->rb_left)
492                 n = n->rb_left;
493         return n;
494 }
495 
496 struct rb_node *rb_last(const struct rb_root *root)
497 {
498         struct rb_node  *n;
499 
500         n = root->rb_node;
501         if (!n)
502                 return NULL;
503         while (n->rb_right)
504                 n = n->rb_right;
505         return n;
506 }
507 
508 struct rb_node *rb_next(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 right-hand child, go down and then left as far
517          * as we can.
518          */
519         if (node->rb_right) {
520                 node = node->rb_right;
521                 while (node->rb_left)
522                         node=node->rb_left;
523                 return (struct rb_node *)node;
524         }
525 
526         /*
527          * No right-hand children. Everything down and left is smaller than us,
528          * so any 'next' node must be in the general direction of our parent.
529          * Go up the tree; any time the ancestor is a right-hand child of its
530          * parent, keep going up. First time it's a left-hand child of its
531          * parent, said parent is our 'next' node.
532          */
533         while ((parent = rb_parent(node)) && node == parent->rb_right)
534                 node = parent;
535 
536         return parent;
537 }
538 
539 struct rb_node *rb_prev(const struct rb_node *node)
540 {
541         struct rb_node *parent;
542 
543         if (RB_EMPTY_NODE(node))
544                 return NULL;
545 
546         /*
547          * If we have a left-hand child, go down and then right as far
548          * as we can.
549          */
550         if (node->rb_left) {
551                 node = node->rb_left;
552                 while (node->rb_right)
553                         node=node->rb_right;
554                 return (struct rb_node *)node;
555         }
556 
557         /*
558          * No left-hand children. Go up till we find an ancestor which
559          * is a right-hand child of its parent.
560          */
561         while ((parent = rb_parent(node)) && node == parent->rb_left)
562                 node = parent;
563 
564         return parent;
565 }
566 
567 void rb_replace_node(struct rb_node *victim, struct rb_node *new,
568                      struct rb_root *root)
569 {
570         struct rb_node *parent = rb_parent(victim);
571 
572         /* Copy the pointers/colour from the victim to the replacement */
573         *new = *victim;
574 
575         /* Set the surrounding nodes to point to the replacement */
576         if (victim->rb_left)
577                 rb_set_parent(victim->rb_left, new);
578         if (victim->rb_right)
579                 rb_set_parent(victim->rb_right, new);
580         __rb_change_child(victim, new, parent, root);
581 }
582 
583 void rb_replace_node_cached(struct rb_node *victim, struct rb_node *new,
584                             struct rb_root_cached *root)
585 {
586         rb_replace_node(victim, new, &root->rb_root);
587 
588         if (root->rb_leftmost == victim)
589                 root->rb_leftmost = new;
590 }
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 
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 

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