1 | /* $NetBSD: rb.c,v 1.13 2014/08/22 17:19:48 matt Exp $ */ |
2 | |
3 | /*- |
4 | * Copyright (c) 2001 The NetBSD Foundation, Inc. |
5 | * All rights reserved. |
6 | * |
7 | * This code is derived from software contributed to The NetBSD Foundation |
8 | * by Matt Thomas <matt@3am-software.com>. |
9 | * |
10 | * Redistribution and use in source and binary forms, with or without |
11 | * modification, are permitted provided that the following conditions |
12 | * are met: |
13 | * 1. Redistributions of source code must retain the above copyright |
14 | * notice, this list of conditions and the following disclaimer. |
15 | * 2. Redistributions in binary form must reproduce the above copyright |
16 | * notice, this list of conditions and the following disclaimer in the |
17 | * documentation and/or other materials provided with the distribution. |
18 | * |
19 | * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS |
20 | * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED |
21 | * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR |
22 | * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS |
23 | * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR |
24 | * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF |
25 | * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS |
26 | * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN |
27 | * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) |
28 | * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE |
29 | * POSSIBILITY OF SUCH DAMAGE. |
30 | */ |
31 | |
32 | #if !defined(_KERNEL) && !defined(_STANDALONE) |
33 | #include <sys/types.h> |
34 | #include <stddef.h> |
35 | #include <assert.h> |
36 | #include <stdbool.h> |
37 | #ifdef RBDEBUG |
38 | #define KASSERT(s) assert(s) |
39 | #else |
40 | #define KASSERT(s) do { } while (/*CONSTCOND*/ 0) |
41 | #endif |
42 | __RCSID("$NetBSD: rb.c,v 1.13 2014/08/22 17:19:48 matt Exp $" ); |
43 | #else |
44 | #include <lib/libkern/libkern.h> |
45 | __KERNEL_RCSID(0, "$NetBSD: rb.c,v 1.13 2014/08/22 17:19:48 matt Exp $" ); |
46 | #endif |
47 | |
48 | #ifdef _LIBC |
49 | __weak_alias(rb_tree_init, _rb_tree_init) |
50 | __weak_alias(rb_tree_find_node, _rb_tree_find_node) |
51 | __weak_alias(rb_tree_find_node_geq, _rb_tree_find_node_geq) |
52 | __weak_alias(rb_tree_find_node_leq, _rb_tree_find_node_leq) |
53 | __weak_alias(rb_tree_insert_node, _rb_tree_insert_node) |
54 | __weak_alias(rb_tree_remove_node, _rb_tree_remove_node) |
55 | __weak_alias(rb_tree_iterate, _rb_tree_iterate) |
56 | #ifdef RBDEBUG |
57 | __weak_alias(rb_tree_check, _rb_tree_check) |
58 | __weak_alias(rb_tree_depths, _rb_tree_depths) |
59 | #endif |
60 | |
61 | #include "namespace.h" |
62 | #endif |
63 | |
64 | #ifdef RBTEST |
65 | #include "rbtree.h" |
66 | #else |
67 | #include <sys/rbtree.h> |
68 | #endif |
69 | |
70 | static void rb_tree_insert_rebalance(struct rb_tree *, struct rb_node *); |
71 | static void rb_tree_removal_rebalance(struct rb_tree *, struct rb_node *, |
72 | unsigned int); |
73 | #ifdef RBDEBUG |
74 | static const struct rb_node *rb_tree_iterate_const(const struct rb_tree *, |
75 | const struct rb_node *, const unsigned int); |
76 | static bool rb_tree_check_node(const struct rb_tree *, const struct rb_node *, |
77 | const struct rb_node *, bool); |
78 | #else |
79 | #define rb_tree_check_node(a, b, c, d) true |
80 | #endif |
81 | |
82 | #define RB_NODETOITEM(rbto, rbn) \ |
83 | ((void *)((uintptr_t)(rbn) - (rbto)->rbto_node_offset)) |
84 | #define RB_ITEMTONODE(rbto, rbn) \ |
85 | ((rb_node_t *)((uintptr_t)(rbn) + (rbto)->rbto_node_offset)) |
86 | |
87 | #define RB_SENTINEL_NODE NULL |
88 | |
89 | void |
90 | rb_tree_init(struct rb_tree *rbt, const rb_tree_ops_t *ops) |
91 | { |
92 | |
93 | rbt->rbt_ops = ops; |
94 | rbt->rbt_root = RB_SENTINEL_NODE; |
95 | RB_TAILQ_INIT(&rbt->rbt_nodes); |
96 | #ifndef RBSMALL |
97 | rbt->rbt_minmax[RB_DIR_LEFT] = rbt->rbt_root; /* minimum node */ |
98 | rbt->rbt_minmax[RB_DIR_RIGHT] = rbt->rbt_root; /* maximum node */ |
99 | #endif |
100 | #ifdef RBSTATS |
101 | rbt->rbt_count = 0; |
102 | rbt->rbt_insertions = 0; |
103 | rbt->rbt_removals = 0; |
104 | rbt->rbt_insertion_rebalance_calls = 0; |
105 | rbt->rbt_insertion_rebalance_passes = 0; |
106 | rbt->rbt_removal_rebalance_calls = 0; |
107 | rbt->rbt_removal_rebalance_passes = 0; |
108 | #endif |
109 | } |
110 | |
111 | void * |
112 | rb_tree_find_node(struct rb_tree *rbt, const void *key) |
113 | { |
114 | const rb_tree_ops_t *rbto = rbt->rbt_ops; |
115 | rbto_compare_key_fn compare_key = rbto->rbto_compare_key; |
116 | struct rb_node *parent = rbt->rbt_root; |
117 | |
118 | while (!RB_SENTINEL_P(parent)) { |
119 | void *pobj = RB_NODETOITEM(rbto, parent); |
120 | const signed int diff = (*compare_key)(rbto->rbto_context, |
121 | pobj, key); |
122 | if (diff == 0) |
123 | return pobj; |
124 | parent = parent->rb_nodes[diff < 0]; |
125 | } |
126 | |
127 | return NULL; |
128 | } |
129 | |
130 | void * |
131 | rb_tree_find_node_geq(struct rb_tree *rbt, const void *key) |
132 | { |
133 | const rb_tree_ops_t *rbto = rbt->rbt_ops; |
134 | rbto_compare_key_fn compare_key = rbto->rbto_compare_key; |
135 | struct rb_node *parent = rbt->rbt_root, *last = NULL; |
136 | |
137 | while (!RB_SENTINEL_P(parent)) { |
138 | void *pobj = RB_NODETOITEM(rbto, parent); |
139 | const signed int diff = (*compare_key)(rbto->rbto_context, |
140 | pobj, key); |
141 | if (diff == 0) |
142 | return pobj; |
143 | if (diff > 0) |
144 | last = parent; |
145 | parent = parent->rb_nodes[diff < 0]; |
146 | } |
147 | |
148 | return last == NULL ? NULL : RB_NODETOITEM(rbto, last); |
149 | } |
150 | |
151 | void * |
152 | rb_tree_find_node_leq(struct rb_tree *rbt, const void *key) |
153 | { |
154 | const rb_tree_ops_t *rbto = rbt->rbt_ops; |
155 | rbto_compare_key_fn compare_key = rbto->rbto_compare_key; |
156 | struct rb_node *parent = rbt->rbt_root, *last = NULL; |
157 | |
158 | while (!RB_SENTINEL_P(parent)) { |
159 | void *pobj = RB_NODETOITEM(rbto, parent); |
160 | const signed int diff = (*compare_key)(rbto->rbto_context, |
161 | pobj, key); |
162 | if (diff == 0) |
163 | return pobj; |
164 | if (diff < 0) |
165 | last = parent; |
166 | parent = parent->rb_nodes[diff < 0]; |
167 | } |
168 | |
169 | return last == NULL ? NULL : RB_NODETOITEM(rbto, last); |
170 | } |
171 | |
172 | void * |
173 | rb_tree_insert_node(struct rb_tree *rbt, void *object) |
174 | { |
175 | const rb_tree_ops_t *rbto = rbt->rbt_ops; |
176 | rbto_compare_nodes_fn compare_nodes = rbto->rbto_compare_nodes; |
177 | struct rb_node *parent, *tmp, *self = RB_ITEMTONODE(rbto, object); |
178 | unsigned int position; |
179 | bool rebalance; |
180 | |
181 | RBSTAT_INC(rbt->rbt_insertions); |
182 | |
183 | tmp = rbt->rbt_root; |
184 | /* |
185 | * This is a hack. Because rbt->rbt_root is just a struct rb_node *, |
186 | * just like rb_node->rb_nodes[RB_DIR_LEFT], we can use this fact to |
187 | * avoid a lot of tests for root and know that even at root, |
188 | * updating RB_FATHER(rb_node)->rb_nodes[RB_POSITION(rb_node)] will |
189 | * update rbt->rbt_root. |
190 | */ |
191 | parent = (struct rb_node *)(void *)&rbt->rbt_root; |
192 | position = RB_DIR_LEFT; |
193 | |
194 | /* |
195 | * Find out where to place this new leaf. |
196 | */ |
197 | while (!RB_SENTINEL_P(tmp)) { |
198 | void *tobj = RB_NODETOITEM(rbto, tmp); |
199 | const signed int diff = (*compare_nodes)(rbto->rbto_context, |
200 | tobj, object); |
201 | if (__predict_false(diff == 0)) { |
202 | /* |
203 | * Node already exists; return it. |
204 | */ |
205 | return tobj; |
206 | } |
207 | parent = tmp; |
208 | position = (diff < 0); |
209 | tmp = parent->rb_nodes[position]; |
210 | } |
211 | |
212 | #ifdef RBDEBUG |
213 | { |
214 | struct rb_node *prev = NULL, *next = NULL; |
215 | |
216 | if (position == RB_DIR_RIGHT) |
217 | prev = parent; |
218 | else if (tmp != rbt->rbt_root) |
219 | next = parent; |
220 | |
221 | /* |
222 | * Verify our sequential position |
223 | */ |
224 | KASSERT(prev == NULL || !RB_SENTINEL_P(prev)); |
225 | KASSERT(next == NULL || !RB_SENTINEL_P(next)); |
226 | if (prev != NULL && next == NULL) |
227 | next = TAILQ_NEXT(prev, rb_link); |
228 | if (prev == NULL && next != NULL) |
229 | prev = TAILQ_PREV(next, rb_node_qh, rb_link); |
230 | KASSERT(prev == NULL || !RB_SENTINEL_P(prev)); |
231 | KASSERT(next == NULL || !RB_SENTINEL_P(next)); |
232 | KASSERT(prev == NULL || (*compare_nodes)(rbto->rbto_context, |
233 | RB_NODETOITEM(rbto, prev), RB_NODETOITEM(rbto, self)) < 0); |
234 | KASSERT(next == NULL || (*compare_nodes)(rbto->rbto_context, |
235 | RB_NODETOITEM(rbto, self), RB_NODETOITEM(rbto, next)) < 0); |
236 | } |
237 | #endif |
238 | |
239 | /* |
240 | * Initialize the node and insert as a leaf into the tree. |
241 | */ |
242 | RB_SET_FATHER(self, parent); |
243 | RB_SET_POSITION(self, position); |
244 | if (__predict_false(parent == (struct rb_node *)(void *)&rbt->rbt_root)) { |
245 | RB_MARK_BLACK(self); /* root is always black */ |
246 | #ifndef RBSMALL |
247 | rbt->rbt_minmax[RB_DIR_LEFT] = self; |
248 | rbt->rbt_minmax[RB_DIR_RIGHT] = self; |
249 | #endif |
250 | rebalance = false; |
251 | } else { |
252 | KASSERT(position == RB_DIR_LEFT || position == RB_DIR_RIGHT); |
253 | #ifndef RBSMALL |
254 | /* |
255 | * Keep track of the minimum and maximum nodes. If our |
256 | * parent is a minmax node and we on their min/max side, |
257 | * we must be the new min/max node. |
258 | */ |
259 | if (parent == rbt->rbt_minmax[position]) |
260 | rbt->rbt_minmax[position] = self; |
261 | #endif /* !RBSMALL */ |
262 | /* |
263 | * All new nodes are colored red. We only need to rebalance |
264 | * if our parent is also red. |
265 | */ |
266 | RB_MARK_RED(self); |
267 | rebalance = RB_RED_P(parent); |
268 | } |
269 | KASSERT(RB_SENTINEL_P(parent->rb_nodes[position])); |
270 | self->rb_left = parent->rb_nodes[position]; |
271 | self->rb_right = parent->rb_nodes[position]; |
272 | parent->rb_nodes[position] = self; |
273 | KASSERT(RB_CHILDLESS_P(self)); |
274 | |
275 | /* |
276 | * Insert the new node into a sorted list for easy sequential access |
277 | */ |
278 | RBSTAT_INC(rbt->rbt_count); |
279 | #ifdef RBDEBUG |
280 | if (RB_ROOT_P(rbt, self)) { |
281 | RB_TAILQ_INSERT_HEAD(&rbt->rbt_nodes, self, rb_link); |
282 | } else if (position == RB_DIR_LEFT) { |
283 | KASSERT((*compare_nodes)(rbto->rbto_context, |
284 | RB_NODETOITEM(rbto, self), |
285 | RB_NODETOITEM(rbto, RB_FATHER(self))) < 0); |
286 | RB_TAILQ_INSERT_BEFORE(RB_FATHER(self), self, rb_link); |
287 | } else { |
288 | KASSERT((*compare_nodes)(rbto->rbto_context, |
289 | RB_NODETOITEM(rbto, RB_FATHER(self)), |
290 | RB_NODETOITEM(rbto, self)) < 0); |
291 | RB_TAILQ_INSERT_AFTER(&rbt->rbt_nodes, RB_FATHER(self), |
292 | self, rb_link); |
293 | } |
294 | #endif |
295 | KASSERT(rb_tree_check_node(rbt, self, NULL, !rebalance)); |
296 | |
297 | /* |
298 | * Rebalance tree after insertion |
299 | */ |
300 | if (rebalance) { |
301 | rb_tree_insert_rebalance(rbt, self); |
302 | KASSERT(rb_tree_check_node(rbt, self, NULL, true)); |
303 | } |
304 | |
305 | /* Succesfully inserted, return our node pointer. */ |
306 | return object; |
307 | } |
308 | |
309 | /* |
310 | * Swap the location and colors of 'self' and its child @ which. The child |
311 | * can not be a sentinel node. This is our rotation function. However, |
312 | * since it preserves coloring, it great simplifies both insertion and |
313 | * removal since rotation almost always involves the exchanging of colors |
314 | * as a separate step. |
315 | */ |
316 | /*ARGSUSED*/ |
317 | static void |
318 | rb_tree_reparent_nodes(struct rb_tree *rbt, struct rb_node *old_father, |
319 | const unsigned int which) |
320 | { |
321 | const unsigned int other = which ^ RB_DIR_OTHER; |
322 | struct rb_node * const grandpa = RB_FATHER(old_father); |
323 | struct rb_node * const old_child = old_father->rb_nodes[which]; |
324 | struct rb_node * const new_father = old_child; |
325 | struct rb_node * const new_child = old_father; |
326 | |
327 | KASSERT(which == RB_DIR_LEFT || which == RB_DIR_RIGHT); |
328 | |
329 | KASSERT(!RB_SENTINEL_P(old_child)); |
330 | KASSERT(RB_FATHER(old_child) == old_father); |
331 | |
332 | KASSERT(rb_tree_check_node(rbt, old_father, NULL, false)); |
333 | KASSERT(rb_tree_check_node(rbt, old_child, NULL, false)); |
334 | KASSERT(RB_ROOT_P(rbt, old_father) || |
335 | rb_tree_check_node(rbt, grandpa, NULL, false)); |
336 | |
337 | /* |
338 | * Exchange descendant linkages. |
339 | */ |
340 | grandpa->rb_nodes[RB_POSITION(old_father)] = new_father; |
341 | new_child->rb_nodes[which] = old_child->rb_nodes[other]; |
342 | new_father->rb_nodes[other] = new_child; |
343 | |
344 | /* |
345 | * Update ancestor linkages |
346 | */ |
347 | RB_SET_FATHER(new_father, grandpa); |
348 | RB_SET_FATHER(new_child, new_father); |
349 | |
350 | /* |
351 | * Exchange properties between new_father and new_child. The only |
352 | * change is that new_child's position is now on the other side. |
353 | */ |
354 | #if 0 |
355 | { |
356 | struct rb_node tmp; |
357 | tmp.rb_info = 0; |
358 | RB_COPY_PROPERTIES(&tmp, old_child); |
359 | RB_COPY_PROPERTIES(new_father, old_father); |
360 | RB_COPY_PROPERTIES(new_child, &tmp); |
361 | } |
362 | #else |
363 | RB_SWAP_PROPERTIES(new_father, new_child); |
364 | #endif |
365 | RB_SET_POSITION(new_child, other); |
366 | |
367 | /* |
368 | * Make sure to reparent the new child to ourself. |
369 | */ |
370 | if (!RB_SENTINEL_P(new_child->rb_nodes[which])) { |
371 | RB_SET_FATHER(new_child->rb_nodes[which], new_child); |
372 | RB_SET_POSITION(new_child->rb_nodes[which], which); |
373 | } |
374 | |
375 | KASSERT(rb_tree_check_node(rbt, new_father, NULL, false)); |
376 | KASSERT(rb_tree_check_node(rbt, new_child, NULL, false)); |
377 | KASSERT(RB_ROOT_P(rbt, new_father) || |
378 | rb_tree_check_node(rbt, grandpa, NULL, false)); |
379 | } |
380 | |
381 | static void |
382 | rb_tree_insert_rebalance(struct rb_tree *rbt, struct rb_node *self) |
383 | { |
384 | struct rb_node * father = RB_FATHER(self); |
385 | struct rb_node * grandpa = RB_FATHER(father); |
386 | struct rb_node * uncle; |
387 | unsigned int which; |
388 | unsigned int other; |
389 | |
390 | KASSERT(!RB_ROOT_P(rbt, self)); |
391 | KASSERT(RB_RED_P(self)); |
392 | KASSERT(RB_RED_P(father)); |
393 | RBSTAT_INC(rbt->rbt_insertion_rebalance_calls); |
394 | |
395 | for (;;) { |
396 | KASSERT(!RB_SENTINEL_P(self)); |
397 | |
398 | KASSERT(RB_RED_P(self)); |
399 | KASSERT(RB_RED_P(father)); |
400 | /* |
401 | * We are red and our parent is red, therefore we must have a |
402 | * grandfather and he must be black. |
403 | */ |
404 | grandpa = RB_FATHER(father); |
405 | KASSERT(RB_BLACK_P(grandpa)); |
406 | KASSERT(RB_DIR_RIGHT == 1 && RB_DIR_LEFT == 0); |
407 | which = (father == grandpa->rb_right); |
408 | other = which ^ RB_DIR_OTHER; |
409 | uncle = grandpa->rb_nodes[other]; |
410 | |
411 | if (RB_BLACK_P(uncle)) |
412 | break; |
413 | |
414 | RBSTAT_INC(rbt->rbt_insertion_rebalance_passes); |
415 | /* |
416 | * Case 1: our uncle is red |
417 | * Simply invert the colors of our parent and |
418 | * uncle and make our grandparent red. And |
419 | * then solve the problem up at his level. |
420 | */ |
421 | RB_MARK_BLACK(uncle); |
422 | RB_MARK_BLACK(father); |
423 | if (__predict_false(RB_ROOT_P(rbt, grandpa))) { |
424 | /* |
425 | * If our grandpa is root, don't bother |
426 | * setting him to red, just return. |
427 | */ |
428 | KASSERT(RB_BLACK_P(grandpa)); |
429 | return; |
430 | } |
431 | RB_MARK_RED(grandpa); |
432 | self = grandpa; |
433 | father = RB_FATHER(self); |
434 | KASSERT(RB_RED_P(self)); |
435 | if (RB_BLACK_P(father)) { |
436 | /* |
437 | * If our greatgrandpa is black, we're done. |
438 | */ |
439 | KASSERT(RB_BLACK_P(rbt->rbt_root)); |
440 | return; |
441 | } |
442 | } |
443 | |
444 | KASSERT(!RB_ROOT_P(rbt, self)); |
445 | KASSERT(RB_RED_P(self)); |
446 | KASSERT(RB_RED_P(father)); |
447 | KASSERT(RB_BLACK_P(uncle)); |
448 | KASSERT(RB_BLACK_P(grandpa)); |
449 | /* |
450 | * Case 2&3: our uncle is black. |
451 | */ |
452 | if (self == father->rb_nodes[other]) { |
453 | /* |
454 | * Case 2: we are on the same side as our uncle |
455 | * Swap ourselves with our parent so this case |
456 | * becomes case 3. Basically our parent becomes our |
457 | * child. |
458 | */ |
459 | rb_tree_reparent_nodes(rbt, father, other); |
460 | KASSERT(RB_FATHER(father) == self); |
461 | KASSERT(self->rb_nodes[which] == father); |
462 | KASSERT(RB_FATHER(self) == grandpa); |
463 | self = father; |
464 | father = RB_FATHER(self); |
465 | } |
466 | KASSERT(RB_RED_P(self) && RB_RED_P(father)); |
467 | KASSERT(grandpa->rb_nodes[which] == father); |
468 | /* |
469 | * Case 3: we are opposite a child of a black uncle. |
470 | * Swap our parent and grandparent. Since our grandfather |
471 | * is black, our father will become black and our new sibling |
472 | * (former grandparent) will become red. |
473 | */ |
474 | rb_tree_reparent_nodes(rbt, grandpa, which); |
475 | KASSERT(RB_FATHER(self) == father); |
476 | KASSERT(RB_FATHER(self)->rb_nodes[RB_POSITION(self) ^ RB_DIR_OTHER] == grandpa); |
477 | KASSERT(RB_RED_P(self)); |
478 | KASSERT(RB_BLACK_P(father)); |
479 | KASSERT(RB_RED_P(grandpa)); |
480 | |
481 | /* |
482 | * Final step: Set the root to black. |
483 | */ |
484 | RB_MARK_BLACK(rbt->rbt_root); |
485 | } |
486 | |
487 | static void |
488 | rb_tree_prune_node(struct rb_tree *rbt, struct rb_node *self, bool rebalance) |
489 | { |
490 | const unsigned int which = RB_POSITION(self); |
491 | struct rb_node *father = RB_FATHER(self); |
492 | #ifndef RBSMALL |
493 | const bool was_root = RB_ROOT_P(rbt, self); |
494 | #endif |
495 | |
496 | KASSERT(rebalance || (RB_ROOT_P(rbt, self) || RB_RED_P(self))); |
497 | KASSERT(!rebalance || RB_BLACK_P(self)); |
498 | KASSERT(RB_CHILDLESS_P(self)); |
499 | KASSERT(rb_tree_check_node(rbt, self, NULL, false)); |
500 | |
501 | /* |
502 | * Since we are childless, we know that self->rb_left is pointing |
503 | * to the sentinel node. |
504 | */ |
505 | father->rb_nodes[which] = self->rb_left; |
506 | |
507 | /* |
508 | * Remove ourselves from the node list, decrement the count, |
509 | * and update min/max. |
510 | */ |
511 | RB_TAILQ_REMOVE(&rbt->rbt_nodes, self, rb_link); |
512 | RBSTAT_DEC(rbt->rbt_count); |
513 | #ifndef RBSMALL |
514 | if (__predict_false(rbt->rbt_minmax[RB_POSITION(self)] == self)) { |
515 | rbt->rbt_minmax[RB_POSITION(self)] = father; |
516 | /* |
517 | * When removing the root, rbt->rbt_minmax[RB_DIR_LEFT] is |
518 | * updated automatically, but we also need to update |
519 | * rbt->rbt_minmax[RB_DIR_RIGHT]; |
520 | */ |
521 | if (__predict_false(was_root)) { |
522 | rbt->rbt_minmax[RB_DIR_RIGHT] = father; |
523 | } |
524 | } |
525 | RB_SET_FATHER(self, NULL); |
526 | #endif |
527 | |
528 | /* |
529 | * Rebalance if requested. |
530 | */ |
531 | if (rebalance) |
532 | rb_tree_removal_rebalance(rbt, father, which); |
533 | KASSERT(was_root || rb_tree_check_node(rbt, father, NULL, true)); |
534 | } |
535 | |
536 | /* |
537 | * When deleting an interior node |
538 | */ |
539 | static void |
540 | rb_tree_swap_prune_and_rebalance(struct rb_tree *rbt, struct rb_node *self, |
541 | struct rb_node *standin) |
542 | { |
543 | const unsigned int standin_which = RB_POSITION(standin); |
544 | unsigned int standin_other = standin_which ^ RB_DIR_OTHER; |
545 | struct rb_node *standin_son; |
546 | struct rb_node *standin_father = RB_FATHER(standin); |
547 | bool rebalance = RB_BLACK_P(standin); |
548 | |
549 | if (standin_father == self) { |
550 | /* |
551 | * As a child of self, any childen would be opposite of |
552 | * our parent. |
553 | */ |
554 | KASSERT(RB_SENTINEL_P(standin->rb_nodes[standin_other])); |
555 | standin_son = standin->rb_nodes[standin_which]; |
556 | } else { |
557 | /* |
558 | * Since we aren't a child of self, any childen would be |
559 | * on the same side as our parent. |
560 | */ |
561 | KASSERT(RB_SENTINEL_P(standin->rb_nodes[standin_which])); |
562 | standin_son = standin->rb_nodes[standin_other]; |
563 | } |
564 | |
565 | /* |
566 | * the node we are removing must have two children. |
567 | */ |
568 | KASSERT(RB_TWOCHILDREN_P(self)); |
569 | /* |
570 | * If standin has a child, it must be red. |
571 | */ |
572 | KASSERT(RB_SENTINEL_P(standin_son) || RB_RED_P(standin_son)); |
573 | |
574 | /* |
575 | * Verify things are sane. |
576 | */ |
577 | KASSERT(rb_tree_check_node(rbt, self, NULL, false)); |
578 | KASSERT(rb_tree_check_node(rbt, standin, NULL, false)); |
579 | |
580 | if (__predict_false(RB_RED_P(standin_son))) { |
581 | /* |
582 | * We know we have a red child so if we flip it to black |
583 | * we don't have to rebalance. |
584 | */ |
585 | KASSERT(rb_tree_check_node(rbt, standin_son, NULL, true)); |
586 | RB_MARK_BLACK(standin_son); |
587 | rebalance = false; |
588 | |
589 | if (standin_father == self) { |
590 | KASSERT(RB_POSITION(standin_son) == standin_which); |
591 | } else { |
592 | KASSERT(RB_POSITION(standin_son) == standin_other); |
593 | /* |
594 | * Change the son's parentage to point to his grandpa. |
595 | */ |
596 | RB_SET_FATHER(standin_son, standin_father); |
597 | RB_SET_POSITION(standin_son, standin_which); |
598 | } |
599 | } |
600 | |
601 | if (standin_father == self) { |
602 | /* |
603 | * If we are about to delete the standin's father, then when |
604 | * we call rebalance, we need to use ourselves as our father. |
605 | * Otherwise remember our original father. Also, sincef we are |
606 | * our standin's father we only need to reparent the standin's |
607 | * brother. |
608 | * |
609 | * | R --> S | |
610 | * | Q S --> Q T | |
611 | * | t --> | |
612 | */ |
613 | KASSERT(RB_SENTINEL_P(standin->rb_nodes[standin_other])); |
614 | KASSERT(!RB_SENTINEL_P(self->rb_nodes[standin_other])); |
615 | KASSERT(self->rb_nodes[standin_which] == standin); |
616 | /* |
617 | * Have our son/standin adopt his brother as his new son. |
618 | */ |
619 | standin_father = standin; |
620 | } else { |
621 | /* |
622 | * | R --> S . | |
623 | * | / \ | T --> / \ | / | |
624 | * | ..... | S --> ..... | T | |
625 | * |
626 | * Sever standin's connection to his father. |
627 | */ |
628 | standin_father->rb_nodes[standin_which] = standin_son; |
629 | /* |
630 | * Adopt the far son. |
631 | */ |
632 | standin->rb_nodes[standin_other] = self->rb_nodes[standin_other]; |
633 | RB_SET_FATHER(standin->rb_nodes[standin_other], standin); |
634 | KASSERT(RB_POSITION(self->rb_nodes[standin_other]) == standin_other); |
635 | /* |
636 | * Use standin_other because we need to preserve standin_which |
637 | * for the removal_rebalance. |
638 | */ |
639 | standin_other = standin_which; |
640 | } |
641 | |
642 | /* |
643 | * Move the only remaining son to our standin. If our standin is our |
644 | * son, this will be the only son needed to be moved. |
645 | */ |
646 | KASSERT(standin->rb_nodes[standin_other] != self->rb_nodes[standin_other]); |
647 | standin->rb_nodes[standin_other] = self->rb_nodes[standin_other]; |
648 | RB_SET_FATHER(standin->rb_nodes[standin_other], standin); |
649 | |
650 | /* |
651 | * Now copy the result of self to standin and then replace |
652 | * self with standin in the tree. |
653 | */ |
654 | RB_COPY_PROPERTIES(standin, self); |
655 | RB_SET_FATHER(standin, RB_FATHER(self)); |
656 | RB_FATHER(standin)->rb_nodes[RB_POSITION(standin)] = standin; |
657 | |
658 | /* |
659 | * Remove ourselves from the node list, decrement the count, |
660 | * and update min/max. |
661 | */ |
662 | RB_TAILQ_REMOVE(&rbt->rbt_nodes, self, rb_link); |
663 | RBSTAT_DEC(rbt->rbt_count); |
664 | #ifndef RBSMALL |
665 | if (__predict_false(rbt->rbt_minmax[RB_POSITION(self)] == self)) |
666 | rbt->rbt_minmax[RB_POSITION(self)] = RB_FATHER(self); |
667 | RB_SET_FATHER(self, NULL); |
668 | #endif |
669 | |
670 | KASSERT(rb_tree_check_node(rbt, standin, NULL, false)); |
671 | KASSERT(RB_FATHER_SENTINEL_P(standin) |
672 | || rb_tree_check_node(rbt, standin_father, NULL, false)); |
673 | KASSERT(RB_LEFT_SENTINEL_P(standin) |
674 | || rb_tree_check_node(rbt, standin->rb_left, NULL, false)); |
675 | KASSERT(RB_RIGHT_SENTINEL_P(standin) |
676 | || rb_tree_check_node(rbt, standin->rb_right, NULL, false)); |
677 | |
678 | if (!rebalance) |
679 | return; |
680 | |
681 | rb_tree_removal_rebalance(rbt, standin_father, standin_which); |
682 | KASSERT(rb_tree_check_node(rbt, standin, NULL, true)); |
683 | } |
684 | |
685 | /* |
686 | * We could do this by doing |
687 | * rb_tree_node_swap(rbt, self, which); |
688 | * rb_tree_prune_node(rbt, self, false); |
689 | * |
690 | * But it's more efficient to just evalate and recolor the child. |
691 | */ |
692 | static void |
693 | rb_tree_prune_blackred_branch(struct rb_tree *rbt, struct rb_node *self, |
694 | unsigned int which) |
695 | { |
696 | struct rb_node *father = RB_FATHER(self); |
697 | struct rb_node *son = self->rb_nodes[which]; |
698 | #ifndef RBSMALL |
699 | const bool was_root = RB_ROOT_P(rbt, self); |
700 | #endif |
701 | |
702 | KASSERT(which == RB_DIR_LEFT || which == RB_DIR_RIGHT); |
703 | KASSERT(RB_BLACK_P(self) && RB_RED_P(son)); |
704 | KASSERT(!RB_TWOCHILDREN_P(son)); |
705 | KASSERT(RB_CHILDLESS_P(son)); |
706 | KASSERT(rb_tree_check_node(rbt, self, NULL, false)); |
707 | KASSERT(rb_tree_check_node(rbt, son, NULL, false)); |
708 | |
709 | /* |
710 | * Remove ourselves from the tree and give our former child our |
711 | * properties (position, color, root). |
712 | */ |
713 | RB_COPY_PROPERTIES(son, self); |
714 | father->rb_nodes[RB_POSITION(son)] = son; |
715 | RB_SET_FATHER(son, father); |
716 | |
717 | /* |
718 | * Remove ourselves from the node list, decrement the count, |
719 | * and update minmax. |
720 | */ |
721 | RB_TAILQ_REMOVE(&rbt->rbt_nodes, self, rb_link); |
722 | RBSTAT_DEC(rbt->rbt_count); |
723 | #ifndef RBSMALL |
724 | if (__predict_false(was_root)) { |
725 | KASSERT(rbt->rbt_minmax[which] == son); |
726 | rbt->rbt_minmax[which ^ RB_DIR_OTHER] = son; |
727 | } else if (rbt->rbt_minmax[RB_POSITION(self)] == self) { |
728 | rbt->rbt_minmax[RB_POSITION(self)] = son; |
729 | } |
730 | RB_SET_FATHER(self, NULL); |
731 | #endif |
732 | |
733 | KASSERT(was_root || rb_tree_check_node(rbt, father, NULL, true)); |
734 | KASSERT(rb_tree_check_node(rbt, son, NULL, true)); |
735 | } |
736 | |
737 | void |
738 | rb_tree_remove_node(struct rb_tree *rbt, void *object) |
739 | { |
740 | const rb_tree_ops_t *rbto = rbt->rbt_ops; |
741 | struct rb_node *standin, *self = RB_ITEMTONODE(rbto, object); |
742 | unsigned int which; |
743 | |
744 | KASSERT(!RB_SENTINEL_P(self)); |
745 | RBSTAT_INC(rbt->rbt_removals); |
746 | |
747 | /* |
748 | * In the following diagrams, we (the node to be removed) are S. Red |
749 | * nodes are lowercase. T could be either red or black. |
750 | * |
751 | * Remember the major axiom of the red-black tree: the number of |
752 | * black nodes from the root to each leaf is constant across all |
753 | * leaves, only the number of red nodes varies. |
754 | * |
755 | * Thus removing a red leaf doesn't require any other changes to a |
756 | * red-black tree. So if we must remove a node, attempt to rearrange |
757 | * the tree so we can remove a red node. |
758 | * |
759 | * The simpliest case is a childless red node or a childless root node: |
760 | * |
761 | * | T --> T | or | R --> * | |
762 | * | s --> * | |
763 | */ |
764 | if (RB_CHILDLESS_P(self)) { |
765 | const bool rebalance = RB_BLACK_P(self) && !RB_ROOT_P(rbt, self); |
766 | rb_tree_prune_node(rbt, self, rebalance); |
767 | return; |
768 | } |
769 | KASSERT(!RB_CHILDLESS_P(self)); |
770 | if (!RB_TWOCHILDREN_P(self)) { |
771 | /* |
772 | * The next simpliest case is the node we are deleting is |
773 | * black and has one red child. |
774 | * |
775 | * | T --> T --> T | |
776 | * | S --> R --> R | |
777 | * | r --> s --> * | |
778 | */ |
779 | which = RB_LEFT_SENTINEL_P(self) ? RB_DIR_RIGHT : RB_DIR_LEFT; |
780 | KASSERT(RB_BLACK_P(self)); |
781 | KASSERT(RB_RED_P(self->rb_nodes[which])); |
782 | KASSERT(RB_CHILDLESS_P(self->rb_nodes[which])); |
783 | rb_tree_prune_blackred_branch(rbt, self, which); |
784 | return; |
785 | } |
786 | KASSERT(RB_TWOCHILDREN_P(self)); |
787 | |
788 | /* |
789 | * We invert these because we prefer to remove from the inside of |
790 | * the tree. |
791 | */ |
792 | which = RB_POSITION(self) ^ RB_DIR_OTHER; |
793 | |
794 | /* |
795 | * Let's find the node closes to us opposite of our parent |
796 | * Now swap it with ourself, "prune" it, and rebalance, if needed. |
797 | */ |
798 | standin = RB_ITEMTONODE(rbto, rb_tree_iterate(rbt, object, which)); |
799 | rb_tree_swap_prune_and_rebalance(rbt, self, standin); |
800 | } |
801 | |
802 | static void |
803 | rb_tree_removal_rebalance(struct rb_tree *rbt, struct rb_node *parent, |
804 | unsigned int which) |
805 | { |
806 | KASSERT(!RB_SENTINEL_P(parent)); |
807 | KASSERT(RB_SENTINEL_P(parent->rb_nodes[which])); |
808 | KASSERT(which == RB_DIR_LEFT || which == RB_DIR_RIGHT); |
809 | RBSTAT_INC(rbt->rbt_removal_rebalance_calls); |
810 | |
811 | while (RB_BLACK_P(parent->rb_nodes[which])) { |
812 | unsigned int other = which ^ RB_DIR_OTHER; |
813 | struct rb_node *brother = parent->rb_nodes[other]; |
814 | |
815 | RBSTAT_INC(rbt->rbt_removal_rebalance_passes); |
816 | |
817 | KASSERT(!RB_SENTINEL_P(brother)); |
818 | /* |
819 | * For cases 1, 2a, and 2b, our brother's children must |
820 | * be black and our father must be black |
821 | */ |
822 | if (RB_BLACK_P(parent) |
823 | && RB_BLACK_P(brother->rb_left) |
824 | && RB_BLACK_P(brother->rb_right)) { |
825 | if (RB_RED_P(brother)) { |
826 | /* |
827 | * Case 1: Our brother is red, swap its |
828 | * position (and colors) with our parent. |
829 | * This should now be case 2b (unless C or E |
830 | * has a red child which is case 3; thus no |
831 | * explicit branch to case 2b). |
832 | * |
833 | * B -> D |
834 | * A d -> b E |
835 | * C E -> A C |
836 | */ |
837 | KASSERT(RB_BLACK_P(parent)); |
838 | rb_tree_reparent_nodes(rbt, parent, other); |
839 | brother = parent->rb_nodes[other]; |
840 | KASSERT(!RB_SENTINEL_P(brother)); |
841 | KASSERT(RB_RED_P(parent)); |
842 | KASSERT(RB_BLACK_P(brother)); |
843 | KASSERT(rb_tree_check_node(rbt, brother, NULL, false)); |
844 | KASSERT(rb_tree_check_node(rbt, parent, NULL, false)); |
845 | } else { |
846 | /* |
847 | * Both our parent and brother are black. |
848 | * Change our brother to red, advance up rank |
849 | * and go through the loop again. |
850 | * |
851 | * B -> *B |
852 | * *A D -> A d |
853 | * C E -> C E |
854 | */ |
855 | RB_MARK_RED(brother); |
856 | KASSERT(RB_BLACK_P(brother->rb_left)); |
857 | KASSERT(RB_BLACK_P(brother->rb_right)); |
858 | if (RB_ROOT_P(rbt, parent)) |
859 | return; /* root == parent == black */ |
860 | KASSERT(rb_tree_check_node(rbt, brother, NULL, false)); |
861 | KASSERT(rb_tree_check_node(rbt, parent, NULL, false)); |
862 | which = RB_POSITION(parent); |
863 | parent = RB_FATHER(parent); |
864 | continue; |
865 | } |
866 | } |
867 | /* |
868 | * Avoid an else here so that case 2a above can hit either |
869 | * case 2b, 3, or 4. |
870 | */ |
871 | if (RB_RED_P(parent) |
872 | && RB_BLACK_P(brother) |
873 | && RB_BLACK_P(brother->rb_left) |
874 | && RB_BLACK_P(brother->rb_right)) { |
875 | KASSERT(RB_RED_P(parent)); |
876 | KASSERT(RB_BLACK_P(brother)); |
877 | KASSERT(RB_BLACK_P(brother->rb_left)); |
878 | KASSERT(RB_BLACK_P(brother->rb_right)); |
879 | /* |
880 | * We are black, our father is red, our brother and |
881 | * both nephews are black. Simply invert/exchange the |
882 | * colors of our father and brother (to black and red |
883 | * respectively). |
884 | * |
885 | * | f --> F | |
886 | * | * B --> * b | |
887 | * | N N --> N N | |
888 | */ |
889 | RB_MARK_BLACK(parent); |
890 | RB_MARK_RED(brother); |
891 | KASSERT(rb_tree_check_node(rbt, brother, NULL, true)); |
892 | break; /* We're done! */ |
893 | } else { |
894 | /* |
895 | * Our brother must be black and have at least one |
896 | * red child (it may have two). |
897 | */ |
898 | KASSERT(RB_BLACK_P(brother)); |
899 | KASSERT(RB_RED_P(brother->rb_nodes[which]) || |
900 | RB_RED_P(brother->rb_nodes[other])); |
901 | if (RB_BLACK_P(brother->rb_nodes[other])) { |
902 | /* |
903 | * Case 3: our brother is black, our near |
904 | * nephew is red, and our far nephew is black. |
905 | * Swap our brother with our near nephew. |
906 | * This result in a tree that matches case 4. |
907 | * (Our father could be red or black). |
908 | * |
909 | * | F --> F | |
910 | * | x B --> x B | |
911 | * | n --> n | |
912 | */ |
913 | KASSERT(RB_RED_P(brother->rb_nodes[which])); |
914 | rb_tree_reparent_nodes(rbt, brother, which); |
915 | KASSERT(RB_FATHER(brother) == parent->rb_nodes[other]); |
916 | brother = parent->rb_nodes[other]; |
917 | KASSERT(RB_RED_P(brother->rb_nodes[other])); |
918 | } |
919 | /* |
920 | * Case 4: our brother is black and our far nephew |
921 | * is red. Swap our father and brother locations and |
922 | * change our far nephew to black. (these can be |
923 | * done in either order so we change the color first). |
924 | * The result is a valid red-black tree and is a |
925 | * terminal case. (again we don't care about the |
926 | * father's color) |
927 | * |
928 | * If the father is red, we will get a red-black-black |
929 | * tree: |
930 | * | f -> f --> b | |
931 | * | B -> B --> F N | |
932 | * | n -> N --> | |
933 | * |
934 | * If the father is black, we will get an all black |
935 | * tree: |
936 | * | F -> F --> B | |
937 | * | B -> B --> F N | |
938 | * | n -> N --> | |
939 | * |
940 | * If we had two red nephews, then after the swap, |
941 | * our former father would have a red grandson. |
942 | */ |
943 | KASSERT(RB_BLACK_P(brother)); |
944 | KASSERT(RB_RED_P(brother->rb_nodes[other])); |
945 | RB_MARK_BLACK(brother->rb_nodes[other]); |
946 | rb_tree_reparent_nodes(rbt, parent, other); |
947 | break; /* We're done! */ |
948 | } |
949 | } |
950 | KASSERT(rb_tree_check_node(rbt, parent, NULL, true)); |
951 | } |
952 | |
953 | void * |
954 | rb_tree_iterate(struct rb_tree *rbt, void *object, const unsigned int direction) |
955 | { |
956 | const rb_tree_ops_t *rbto = rbt->rbt_ops; |
957 | const unsigned int other = direction ^ RB_DIR_OTHER; |
958 | struct rb_node *self; |
959 | |
960 | KASSERT(direction == RB_DIR_LEFT || direction == RB_DIR_RIGHT); |
961 | |
962 | if (object == NULL) { |
963 | #ifndef RBSMALL |
964 | if (RB_SENTINEL_P(rbt->rbt_root)) |
965 | return NULL; |
966 | return RB_NODETOITEM(rbto, rbt->rbt_minmax[direction]); |
967 | #else |
968 | self = rbt->rbt_root; |
969 | if (RB_SENTINEL_P(self)) |
970 | return NULL; |
971 | while (!RB_SENTINEL_P(self->rb_nodes[direction])) |
972 | self = self->rb_nodes[direction]; |
973 | return RB_NODETOITEM(rbto, self); |
974 | #endif /* !RBSMALL */ |
975 | } |
976 | self = RB_ITEMTONODE(rbto, object); |
977 | KASSERT(!RB_SENTINEL_P(self)); |
978 | /* |
979 | * We can't go any further in this direction. We proceed up in the |
980 | * opposite direction until our parent is in direction we want to go. |
981 | */ |
982 | if (RB_SENTINEL_P(self->rb_nodes[direction])) { |
983 | while (!RB_ROOT_P(rbt, self)) { |
984 | if (other == RB_POSITION(self)) |
985 | return RB_NODETOITEM(rbto, RB_FATHER(self)); |
986 | self = RB_FATHER(self); |
987 | } |
988 | return NULL; |
989 | } |
990 | |
991 | /* |
992 | * Advance down one in current direction and go down as far as possible |
993 | * in the opposite direction. |
994 | */ |
995 | self = self->rb_nodes[direction]; |
996 | KASSERT(!RB_SENTINEL_P(self)); |
997 | while (!RB_SENTINEL_P(self->rb_nodes[other])) |
998 | self = self->rb_nodes[other]; |
999 | return RB_NODETOITEM(rbto, self); |
1000 | } |
1001 | |
1002 | #ifdef RBDEBUG |
1003 | static const struct rb_node * |
1004 | rb_tree_iterate_const(const struct rb_tree *rbt, const struct rb_node *self, |
1005 | const unsigned int direction) |
1006 | { |
1007 | const unsigned int other = direction ^ RB_DIR_OTHER; |
1008 | KASSERT(direction == RB_DIR_LEFT || direction == RB_DIR_RIGHT); |
1009 | |
1010 | if (self == NULL) { |
1011 | #ifndef RBSMALL |
1012 | if (RB_SENTINEL_P(rbt->rbt_root)) |
1013 | return NULL; |
1014 | return rbt->rbt_minmax[direction]; |
1015 | #else |
1016 | self = rbt->rbt_root; |
1017 | if (RB_SENTINEL_P(self)) |
1018 | return NULL; |
1019 | while (!RB_SENTINEL_P(self->rb_nodes[direction])) |
1020 | self = self->rb_nodes[direction]; |
1021 | return self; |
1022 | #endif /* !RBSMALL */ |
1023 | } |
1024 | KASSERT(!RB_SENTINEL_P(self)); |
1025 | /* |
1026 | * We can't go any further in this direction. We proceed up in the |
1027 | * opposite direction until our parent is in direction we want to go. |
1028 | */ |
1029 | if (RB_SENTINEL_P(self->rb_nodes[direction])) { |
1030 | while (!RB_ROOT_P(rbt, self)) { |
1031 | if (other == RB_POSITION(self)) |
1032 | return RB_FATHER(self); |
1033 | self = RB_FATHER(self); |
1034 | } |
1035 | return NULL; |
1036 | } |
1037 | |
1038 | /* |
1039 | * Advance down one in current direction and go down as far as possible |
1040 | * in the opposite direction. |
1041 | */ |
1042 | self = self->rb_nodes[direction]; |
1043 | KASSERT(!RB_SENTINEL_P(self)); |
1044 | while (!RB_SENTINEL_P(self->rb_nodes[other])) |
1045 | self = self->rb_nodes[other]; |
1046 | return self; |
1047 | } |
1048 | |
1049 | static unsigned int |
1050 | rb_tree_count_black(const struct rb_node *self) |
1051 | { |
1052 | unsigned int left, right; |
1053 | |
1054 | if (RB_SENTINEL_P(self)) |
1055 | return 0; |
1056 | |
1057 | left = rb_tree_count_black(self->rb_left); |
1058 | right = rb_tree_count_black(self->rb_right); |
1059 | |
1060 | KASSERT(left == right); |
1061 | |
1062 | return left + RB_BLACK_P(self); |
1063 | } |
1064 | |
1065 | static bool |
1066 | rb_tree_check_node(const struct rb_tree *rbt, const struct rb_node *self, |
1067 | const struct rb_node *prev, bool red_check) |
1068 | { |
1069 | const rb_tree_ops_t *rbto = rbt->rbt_ops; |
1070 | rbto_compare_nodes_fn compare_nodes = rbto->rbto_compare_nodes; |
1071 | |
1072 | KASSERT(!RB_SENTINEL_P(self)); |
1073 | KASSERT(prev == NULL || (*compare_nodes)(rbto->rbto_context, |
1074 | RB_NODETOITEM(rbto, prev), RB_NODETOITEM(rbto, self)) < 0); |
1075 | |
1076 | /* |
1077 | * Verify our relationship to our parent. |
1078 | */ |
1079 | if (RB_ROOT_P(rbt, self)) { |
1080 | KASSERT(self == rbt->rbt_root); |
1081 | KASSERT(RB_POSITION(self) == RB_DIR_LEFT); |
1082 | KASSERT(RB_FATHER(self)->rb_nodes[RB_DIR_LEFT] == self); |
1083 | KASSERT(RB_FATHER(self) == (const struct rb_node *) &rbt->rbt_root); |
1084 | } else { |
1085 | int diff = (*compare_nodes)(rbto->rbto_context, |
1086 | RB_NODETOITEM(rbto, self), |
1087 | RB_NODETOITEM(rbto, RB_FATHER(self))); |
1088 | |
1089 | KASSERT(self != rbt->rbt_root); |
1090 | KASSERT(!RB_FATHER_SENTINEL_P(self)); |
1091 | if (RB_POSITION(self) == RB_DIR_LEFT) { |
1092 | KASSERT(diff < 0); |
1093 | KASSERT(RB_FATHER(self)->rb_nodes[RB_DIR_LEFT] == self); |
1094 | } else { |
1095 | KASSERT(diff > 0); |
1096 | KASSERT(RB_FATHER(self)->rb_nodes[RB_DIR_RIGHT] == self); |
1097 | } |
1098 | } |
1099 | |
1100 | /* |
1101 | * Verify our position in the linked list against the tree itself. |
1102 | */ |
1103 | { |
1104 | const struct rb_node *prev0 = rb_tree_iterate_const(rbt, self, RB_DIR_LEFT); |
1105 | const struct rb_node *next0 = rb_tree_iterate_const(rbt, self, RB_DIR_RIGHT); |
1106 | KASSERT(prev0 == TAILQ_PREV(self, rb_node_qh, rb_link)); |
1107 | KASSERT(next0 == TAILQ_NEXT(self, rb_link)); |
1108 | #ifndef RBSMALL |
1109 | KASSERT(prev0 != NULL || self == rbt->rbt_minmax[RB_DIR_LEFT]); |
1110 | KASSERT(next0 != NULL || self == rbt->rbt_minmax[RB_DIR_RIGHT]); |
1111 | #endif |
1112 | } |
1113 | |
1114 | /* |
1115 | * The root must be black. |
1116 | * There can never be two adjacent red nodes. |
1117 | */ |
1118 | if (red_check) { |
1119 | KASSERT(!RB_ROOT_P(rbt, self) || RB_BLACK_P(self)); |
1120 | (void) rb_tree_count_black(self); |
1121 | if (RB_RED_P(self)) { |
1122 | const struct rb_node *brother; |
1123 | KASSERT(!RB_ROOT_P(rbt, self)); |
1124 | brother = RB_FATHER(self)->rb_nodes[RB_POSITION(self) ^ RB_DIR_OTHER]; |
1125 | KASSERT(RB_BLACK_P(RB_FATHER(self))); |
1126 | /* |
1127 | * I'm red and have no children, then I must either |
1128 | * have no brother or my brother also be red and |
1129 | * also have no children. (black count == 0) |
1130 | */ |
1131 | KASSERT(!RB_CHILDLESS_P(self) |
1132 | || RB_SENTINEL_P(brother) |
1133 | || RB_RED_P(brother) |
1134 | || RB_CHILDLESS_P(brother)); |
1135 | /* |
1136 | * If I'm not childless, I must have two children |
1137 | * and they must be both be black. |
1138 | */ |
1139 | KASSERT(RB_CHILDLESS_P(self) |
1140 | || (RB_TWOCHILDREN_P(self) |
1141 | && RB_BLACK_P(self->rb_left) |
1142 | && RB_BLACK_P(self->rb_right))); |
1143 | /* |
1144 | * If I'm not childless, thus I have black children, |
1145 | * then my brother must either be black or have two |
1146 | * black children. |
1147 | */ |
1148 | KASSERT(RB_CHILDLESS_P(self) |
1149 | || RB_BLACK_P(brother) |
1150 | || (RB_TWOCHILDREN_P(brother) |
1151 | && RB_BLACK_P(brother->rb_left) |
1152 | && RB_BLACK_P(brother->rb_right))); |
1153 | } else { |
1154 | /* |
1155 | * If I'm black and have one child, that child must |
1156 | * be red and childless. |
1157 | */ |
1158 | KASSERT(RB_CHILDLESS_P(self) |
1159 | || RB_TWOCHILDREN_P(self) |
1160 | || (!RB_LEFT_SENTINEL_P(self) |
1161 | && RB_RIGHT_SENTINEL_P(self) |
1162 | && RB_RED_P(self->rb_left) |
1163 | && RB_CHILDLESS_P(self->rb_left)) |
1164 | || (!RB_RIGHT_SENTINEL_P(self) |
1165 | && RB_LEFT_SENTINEL_P(self) |
1166 | && RB_RED_P(self->rb_right) |
1167 | && RB_CHILDLESS_P(self->rb_right))); |
1168 | |
1169 | /* |
1170 | * If I'm a childless black node and my parent is |
1171 | * black, my 2nd closet relative away from my parent |
1172 | * is either red or has a red parent or red children. |
1173 | */ |
1174 | if (!RB_ROOT_P(rbt, self) |
1175 | && RB_CHILDLESS_P(self) |
1176 | && RB_BLACK_P(RB_FATHER(self))) { |
1177 | const unsigned int which = RB_POSITION(self); |
1178 | const unsigned int other = which ^ RB_DIR_OTHER; |
1179 | const struct rb_node *relative0, *relative; |
1180 | |
1181 | relative0 = rb_tree_iterate_const(rbt, |
1182 | self, other); |
1183 | KASSERT(relative0 != NULL); |
1184 | relative = rb_tree_iterate_const(rbt, |
1185 | relative0, other); |
1186 | KASSERT(relative != NULL); |
1187 | KASSERT(RB_SENTINEL_P(relative->rb_nodes[which])); |
1188 | #if 0 |
1189 | KASSERT(RB_RED_P(relative) |
1190 | || RB_RED_P(relative->rb_left) |
1191 | || RB_RED_P(relative->rb_right) |
1192 | || RB_RED_P(RB_FATHER(relative))); |
1193 | #endif |
1194 | } |
1195 | } |
1196 | /* |
1197 | * A grandparent's children must be real nodes and not |
1198 | * sentinels. First check out grandparent. |
1199 | */ |
1200 | KASSERT(RB_ROOT_P(rbt, self) |
1201 | || RB_ROOT_P(rbt, RB_FATHER(self)) |
1202 | || RB_TWOCHILDREN_P(RB_FATHER(RB_FATHER(self)))); |
1203 | /* |
1204 | * If we are have grandchildren on our left, then |
1205 | * we must have a child on our right. |
1206 | */ |
1207 | KASSERT(RB_LEFT_SENTINEL_P(self) |
1208 | || RB_CHILDLESS_P(self->rb_left) |
1209 | || !RB_RIGHT_SENTINEL_P(self)); |
1210 | /* |
1211 | * If we are have grandchildren on our right, then |
1212 | * we must have a child on our left. |
1213 | */ |
1214 | KASSERT(RB_RIGHT_SENTINEL_P(self) |
1215 | || RB_CHILDLESS_P(self->rb_right) |
1216 | || !RB_LEFT_SENTINEL_P(self)); |
1217 | |
1218 | /* |
1219 | * If we have a child on the left and it doesn't have two |
1220 | * children make sure we don't have great-great-grandchildren on |
1221 | * the right. |
1222 | */ |
1223 | KASSERT(RB_TWOCHILDREN_P(self->rb_left) |
1224 | || RB_CHILDLESS_P(self->rb_right) |
1225 | || RB_CHILDLESS_P(self->rb_right->rb_left) |
1226 | || RB_CHILDLESS_P(self->rb_right->rb_left->rb_left) |
1227 | || RB_CHILDLESS_P(self->rb_right->rb_left->rb_right) |
1228 | || RB_CHILDLESS_P(self->rb_right->rb_right) |
1229 | || RB_CHILDLESS_P(self->rb_right->rb_right->rb_left) |
1230 | || RB_CHILDLESS_P(self->rb_right->rb_right->rb_right)); |
1231 | |
1232 | /* |
1233 | * If we have a child on the right and it doesn't have two |
1234 | * children make sure we don't have great-great-grandchildren on |
1235 | * the left. |
1236 | */ |
1237 | KASSERT(RB_TWOCHILDREN_P(self->rb_right) |
1238 | || RB_CHILDLESS_P(self->rb_left) |
1239 | || RB_CHILDLESS_P(self->rb_left->rb_left) |
1240 | || RB_CHILDLESS_P(self->rb_left->rb_left->rb_left) |
1241 | || RB_CHILDLESS_P(self->rb_left->rb_left->rb_right) |
1242 | || RB_CHILDLESS_P(self->rb_left->rb_right) |
1243 | || RB_CHILDLESS_P(self->rb_left->rb_right->rb_left) |
1244 | || RB_CHILDLESS_P(self->rb_left->rb_right->rb_right)); |
1245 | |
1246 | /* |
1247 | * If we are fully interior node, then our predecessors and |
1248 | * successors must have no children in our direction. |
1249 | */ |
1250 | if (RB_TWOCHILDREN_P(self)) { |
1251 | const struct rb_node *prev0; |
1252 | const struct rb_node *next0; |
1253 | |
1254 | prev0 = rb_tree_iterate_const(rbt, self, RB_DIR_LEFT); |
1255 | KASSERT(prev0 != NULL); |
1256 | KASSERT(RB_RIGHT_SENTINEL_P(prev0)); |
1257 | |
1258 | next0 = rb_tree_iterate_const(rbt, self, RB_DIR_RIGHT); |
1259 | KASSERT(next0 != NULL); |
1260 | KASSERT(RB_LEFT_SENTINEL_P(next0)); |
1261 | } |
1262 | } |
1263 | |
1264 | return true; |
1265 | } |
1266 | |
1267 | void |
1268 | rb_tree_check(const struct rb_tree *rbt, bool red_check) |
1269 | { |
1270 | const struct rb_node *self; |
1271 | const struct rb_node *prev; |
1272 | #ifdef RBSTATS |
1273 | unsigned int count = 0; |
1274 | #endif |
1275 | |
1276 | KASSERT(rbt->rbt_root != NULL); |
1277 | KASSERT(RB_LEFT_P(rbt->rbt_root)); |
1278 | |
1279 | #if defined(RBSTATS) && !defined(RBSMALL) |
1280 | KASSERT(rbt->rbt_count > 1 |
1281 | || rbt->rbt_minmax[RB_DIR_LEFT] == rbt->rbt_minmax[RB_DIR_RIGHT]); |
1282 | #endif |
1283 | |
1284 | prev = NULL; |
1285 | TAILQ_FOREACH(self, &rbt->rbt_nodes, rb_link) { |
1286 | rb_tree_check_node(rbt, self, prev, false); |
1287 | #ifdef RBSTATS |
1288 | count++; |
1289 | #endif |
1290 | } |
1291 | #ifdef RBSTATS |
1292 | KASSERT(rbt->rbt_count == count); |
1293 | #endif |
1294 | if (red_check) { |
1295 | KASSERT(RB_BLACK_P(rbt->rbt_root)); |
1296 | KASSERT(RB_SENTINEL_P(rbt->rbt_root) |
1297 | || rb_tree_count_black(rbt->rbt_root)); |
1298 | |
1299 | /* |
1300 | * The root must be black. |
1301 | * There can never be two adjacent red nodes. |
1302 | */ |
1303 | TAILQ_FOREACH(self, &rbt->rbt_nodes, rb_link) { |
1304 | rb_tree_check_node(rbt, self, NULL, true); |
1305 | } |
1306 | } |
1307 | } |
1308 | #endif /* RBDEBUG */ |
1309 | |
1310 | #ifdef RBSTATS |
1311 | static void |
1312 | rb_tree_mark_depth(const struct rb_tree *rbt, const struct rb_node *self, |
1313 | size_t *depths, size_t depth) |
1314 | { |
1315 | if (RB_SENTINEL_P(self)) |
1316 | return; |
1317 | |
1318 | if (RB_TWOCHILDREN_P(self)) { |
1319 | rb_tree_mark_depth(rbt, self->rb_left, depths, depth + 1); |
1320 | rb_tree_mark_depth(rbt, self->rb_right, depths, depth + 1); |
1321 | return; |
1322 | } |
1323 | depths[depth]++; |
1324 | if (!RB_LEFT_SENTINEL_P(self)) { |
1325 | rb_tree_mark_depth(rbt, self->rb_left, depths, depth + 1); |
1326 | } |
1327 | if (!RB_RIGHT_SENTINEL_P(self)) { |
1328 | rb_tree_mark_depth(rbt, self->rb_right, depths, depth + 1); |
1329 | } |
1330 | } |
1331 | |
1332 | void |
1333 | rb_tree_depths(const struct rb_tree *rbt, size_t *depths) |
1334 | { |
1335 | rb_tree_mark_depth(rbt, rbt->rbt_root, depths, 1); |
1336 | } |
1337 | #endif /* RBSTATS */ |
1338 | |