xref: /dragonfly/sys/libprop/prop_rb.c (revision 0db87cb7)
1 /*	$NetBSD: prop_rb.c,v 1.9 2008/06/17 21:29:47 thorpej 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 #include <libprop/proplib.h>
33 
34 #include "prop_object_impl.h"
35 #include "prop_rb_impl.h"
36 
37 #undef KASSERT
38 #ifdef RBDEBUG
39 #define	KASSERT(x)	_PROP_ASSERT(x)
40 #else
41 #define	KASSERT(x)	/* nothing */
42 #endif
43 
44 #ifndef __predict_false
45 #define	__predict_false(x)	(x)
46 #endif
47 
48 static void rb_tree_insert_rebalance(struct rb_tree *, struct rb_node *);
49 static void rb_tree_removal_rebalance(struct rb_tree *, struct rb_node *,
50 	unsigned int);
51 #ifdef RBDEBUG
52 static const struct rb_node *rb_tree_iterate_const(const struct rb_tree *,
53 	const struct rb_node *, const unsigned int);
54 static bool rb_tree_check_node(const struct rb_tree *, const struct rb_node *,
55 	const struct rb_node *, bool);
56 #else
57 #define	rb_tree_check_node(a, b, c, d)	true
58 #endif
59 
60 #ifdef RBDEBUG
61 #define	RBT_COUNT_INCR(rbt)	(rbt)->rbt_count++
62 #define	RBT_COUNT_DECR(rbt)	(rbt)->rbt_count--
63 #else
64 #define	RBT_COUNT_INCR(rbt)	/* nothing */
65 #define	RBT_COUNT_DECR(rbt)	/* nothing */
66 #endif
67 
68 #define	RBUNCONST(a)	((void *)(unsigned long)(const void *)(a))
69 
70 #define	RB_NODETOITEM(rbto, rbn)	\
71     ((void *)((uintptr_t)(rbn) - (rbto)->rbto_node_offset))
72 #define	RB_ITEMTONODE(rbto, rbn)	\
73     ((rb_node_t *)((uintptr_t)(rbn) + (rbto)->rbto_node_offset))
74 
75 #define	RB_SENTINEL_NODE	NULL
76 
77 void
78 _prop_rb_tree_init(struct rb_tree *rbt, const rb_tree_ops_t *ops)
79 {
80 	RB_TAILQ_INIT(&rbt->rbt_nodes);
81 #ifdef RBDEBUG
82 	rbt->rbt_count = 0;
83 #endif
84 	rbt->rbt_ops = ops;
85 	rbt->rbt_root = RB_SENTINEL_NODE;
86 }
87 
88 
89 void *
90 _prop_rb_tree_find(struct rb_tree *rbt, const void *key)
91 {
92 	const rb_tree_ops_t *rbto = rbt->rbt_ops;
93 	rbto_compare_key_fn compare_key = rbto->rbto_compare_key;
94 	struct rb_node *parent = rbt->rbt_root;
95 
96 	while (!RB_SENTINEL_P(parent)) {
97 		void *pobj = RB_NODETOITEM(rbto, parent);
98 		const signed int diff = (*compare_key)(rbto->rbto_context,
99 		    pobj, key);
100 		if (diff == 0)
101 			return pobj;
102 		parent = parent->rb_nodes[diff < 0];
103 	}
104 
105 	return NULL;
106 }
107 
108 void *
109 _prop_rb_tree_insert_node(struct rb_tree *rbt, void *object)
110 {
111 	const rb_tree_ops_t *rbto = rbt->rbt_ops;
112 	rbto_compare_nodes_fn compare_nodes = rbto->rbto_compare_nodes;
113 	struct rb_node *parent, *tmp, *self = RB_ITEMTONODE(rbto, object);
114 	unsigned int position;
115 	bool rebalance;
116 
117 	RBSTAT_INC(rbt->rbt_insertions);
118 
119 	tmp = rbt->rbt_root;
120 	/*
121 	 * This is a hack.  Because rbt->rbt_root is just a struct rb_node *,
122 	 * just like rb_node->rb_nodes[RB_DIR_LEFT], we can use this fact to
123 	 * avoid a lot of tests for root and know that even at root,
124 	 * updating RB_FATHER(rb_node)->rb_nodes[RB_POSITION(rb_node)] will
125 	 * update rbt->rbt_root.
126 	 */
127 	parent = (struct rb_node *)(void *)&rbt->rbt_root;
128 	position = RB_DIR_LEFT;
129 
130 	/*
131 	 * Find out where to place this new leaf.
132 	 */
133 	while (!RB_SENTINEL_P(tmp)) {
134 		void *tobj = RB_NODETOITEM(rbto, tmp);
135 		const signed int diff = (*compare_nodes)(rbto->rbto_context,
136 		    tobj, object);
137 		if (__predict_false(diff == 0)) {
138 			/*
139 			 * Node already exists; return it.
140 			 */
141 			return tobj;
142 		}
143 		parent = tmp;
144 		position = (diff < 0);
145 		tmp = parent->rb_nodes[position];
146 	}
147 
148 #ifdef RBDEBUG
149 	{
150 		struct rb_node *prev = NULL, *next = NULL;
151 
152 		if (position == RB_DIR_RIGHT)
153 			prev = parent;
154 		else if (tmp != rbt->rbt_root)
155 			next = parent;
156 
157 		/*
158 		 * Verify our sequential position
159 		 */
160 		KASSERT(prev == NULL || !RB_SENTINEL_P(prev));
161 		KASSERT(next == NULL || !RB_SENTINEL_P(next));
162 		if (prev != NULL && next == NULL)
163 			next = TAILQ_NEXT(prev, rb_link);
164 		if (prev == NULL && next != NULL)
165 			prev = TAILQ_PREV(next, rb_node_qh, rb_link);
166 		KASSERT(prev == NULL || !RB_SENTINEL_P(prev));
167 		KASSERT(next == NULL || !RB_SENTINEL_P(next));
168 		KASSERT(prev == NULL || (*compare_nodes)(rbto->rbto_context,
169 		    RB_NODETOITEM(rbto, prev), RB_NODETOITEM(rbto, self)) < 0);
170 		KASSERT(next == NULL || (*compare_nodes)(rbto->rbto_context,
171 		    RB_NODETOITEM(rbto, self), RB_NODETOITEM(rbto, next)) < 0);
172 	}
173 #endif
174 
175 	/*
176 	 * Initialize the node and insert as a leaf into the tree.
177 	 */
178 	RB_SET_FATHER(self, parent);
179 	RB_SET_POSITION(self, position);
180 	if (__predict_false(parent == (struct rb_node *)(void *)&rbt->rbt_root)) {
181 		RB_MARK_BLACK(self);		/* root is always black */
182 #ifndef RBSMALL
183 		rbt->rbt_minmax[RB_DIR_LEFT] = self;
184 		rbt->rbt_minmax[RB_DIR_RIGHT] = self;
185 #endif
186 		rebalance = false;
187 	} else {
188 		KASSERT(position == RB_DIR_LEFT || position == RB_DIR_RIGHT);
189 #ifndef RBSMALL
190 		/*
191 		 * Keep track of the minimum and maximum nodes.  If our
192 		 * parent is a minmax node and we on their min/max side,
193 		 * we must be the new min/max node.
194 		 */
195 		if (parent == rbt->rbt_minmax[position])
196 			rbt->rbt_minmax[position] = self;
197 #endif /* !RBSMALL */
198 		/*
199 		 * All new nodes are colored red.  We only need to rebalance
200 		 * if our parent is also red.
201 		 */
202 		RB_MARK_RED(self);
203 		rebalance = RB_RED_P(parent);
204 	}
205 	KASSERT(RB_SENTINEL_P(parent->rb_nodes[position]));
206 	self->rb_left = parent->rb_nodes[position];
207 	self->rb_right = parent->rb_nodes[position];
208 	parent->rb_nodes[position] = self;
209 	KASSERT(RB_CHILDLESS_P(self));
210 
211 	/*
212 	 * Insert the new node into a sorted list for easy sequential access
213 	 */
214 	RBSTAT_INC(rbt->rbt_count);
215 #ifdef RBDEBUG
216 	if (RB_ROOT_P(rbt, self)) {
217 		RB_TAILQ_INSERT_HEAD(&rbt->rbt_nodes, self, rb_link);
218 	} else if (position == RB_DIR_LEFT) {
219 		KASSERT((*compare_nodes)(rbto->rbto_context,
220 		    RB_NODETOITEM(rbto, self),
221 		    RB_NODETOITEM(rbto, RB_FATHER(self))) < 0);
222 		RB_TAILQ_INSERT_BEFORE(RB_FATHER(self), self, rb_link);
223 	} else {
224 		KASSERT((*compare_nodes)(rbto->rbto_context,
225 		    RB_NODETOITEM(rbto, RB_FATHER(self)),
226 		    RB_NODETOITEM(rbto, self)) < 0);
227 		RB_TAILQ_INSERT_AFTER(&rbt->rbt_nodes, RB_FATHER(self),
228 		    self, rb_link);
229 	}
230 #endif
231 	KASSERT(rb_tree_check_node(rbt, self, NULL, !rebalance));
232 
233 	/*
234 	 * Rebalance tree after insertion
235 	 */
236 	if (rebalance) {
237 		rb_tree_insert_rebalance(rbt, self);
238 		KASSERT(rb_tree_check_node(rbt, self, NULL, true));
239 	}
240 
241 	/* Succesfully inserted, return our node pointer. */
242 	return object;
243 }
244 
245 /*
246  * Swap the location and colors of 'self' and its child @ which.  The child
247  * can not be a sentinel node.  This is our rotation function.  However,
248  * since it preserves coloring, it great simplifies both insertion and
249  * removal since rotation almost always involves the exchanging of colors
250  * as a separate step.
251  */
252 /*ARGSUSED*/
253 static void
254 rb_tree_reparent_nodes(struct rb_tree *rbt, struct rb_node *old_father,
255 	const unsigned int which)
256 {
257 	const unsigned int other = which ^ RB_DIR_OTHER;
258 	struct rb_node * const grandpa = RB_FATHER(old_father);
259 	struct rb_node * const old_child = old_father->rb_nodes[which];
260 	struct rb_node * const new_father = old_child;
261 	struct rb_node * const new_child = old_father;
262 
263 	KASSERT(which == RB_DIR_LEFT || which == RB_DIR_RIGHT);
264 
265 	KASSERT(!RB_SENTINEL_P(old_child));
266 	KASSERT(RB_FATHER(old_child) == old_father);
267 
268 	KASSERT(rb_tree_check_node(rbt, old_father, NULL, false));
269 	KASSERT(rb_tree_check_node(rbt, old_child, NULL, false));
270 	KASSERT(RB_ROOT_P(rbt, old_father) ||
271 	    rb_tree_check_node(rbt, grandpa, NULL, false));
272 
273 	/*
274 	 * Exchange descendant linkages.
275 	 */
276 	grandpa->rb_nodes[RB_POSITION(old_father)] = new_father;
277 	new_child->rb_nodes[which] = old_child->rb_nodes[other];
278 	new_father->rb_nodes[other] = new_child;
279 
280 	/*
281 	 * Update ancestor linkages
282 	 */
283 	RB_SET_FATHER(new_father, grandpa);
284 	RB_SET_FATHER(new_child, new_father);
285 
286 	/*
287 	 * Exchange properties between new_father and new_child.  The only
288 	 * change is that new_child's position is now on the other side.
289 	 */
290 #if 0
291 	{
292 		struct rb_node tmp;
293 		tmp.rb_info = 0;
294 		RB_COPY_PROPERTIES(&tmp, old_child);
295 		RB_COPY_PROPERTIES(new_father, old_father);
296 		RB_COPY_PROPERTIES(new_child, &tmp);
297 	}
298 #else
299 	RB_SWAP_PROPERTIES(new_father, new_child);
300 #endif
301 	RB_SET_POSITION(new_child, other);
302 
303 	/*
304 	 * Make sure to reparent the new child to ourself.
305 	 */
306 	if (!RB_SENTINEL_P(new_child->rb_nodes[which])) {
307 		RB_SET_FATHER(new_child->rb_nodes[which], new_child);
308 		RB_SET_POSITION(new_child->rb_nodes[which], which);
309 	}
310 
311 	KASSERT(rb_tree_check_node(rbt, new_father, NULL, false));
312 	KASSERT(rb_tree_check_node(rbt, new_child, NULL, false));
313 	KASSERT(RB_ROOT_P(rbt, new_father) ||
314 	    rb_tree_check_node(rbt, grandpa, NULL, false));
315 }
316 
317 static void
318 rb_tree_insert_rebalance(struct rb_tree *rbt, struct rb_node *self)
319 {
320 	struct rb_node * father = RB_FATHER(self);
321 	struct rb_node * grandpa = RB_FATHER(father);
322 	struct rb_node * uncle;
323 	unsigned int which;
324 	unsigned int other;
325 
326 	KASSERT(!RB_ROOT_P(rbt, self));
327 	KASSERT(RB_RED_P(self));
328 	KASSERT(RB_RED_P(father));
329 	RBSTAT_INC(rbt->rbt_insertion_rebalance_calls);
330 
331 	for (;;) {
332 		KASSERT(!RB_SENTINEL_P(self));
333 
334 		KASSERT(RB_RED_P(self));
335 		KASSERT(RB_RED_P(father));
336 		/*
337 		 * We are red and our parent is red, therefore we must have a
338 		 * grandfather and he must be black.
339 		 */
340 		grandpa = RB_FATHER(father);
341 		KASSERT(RB_BLACK_P(grandpa));
342 		KASSERT(RB_DIR_RIGHT == 1 && RB_DIR_LEFT == 0);
343 		which = (father == grandpa->rb_right);
344 		other = which ^ RB_DIR_OTHER;
345 		uncle = grandpa->rb_nodes[other];
346 
347 		if (RB_BLACK_P(uncle))
348 			break;
349 
350 		RBSTAT_INC(rbt->rbt_insertion_rebalance_passes);
351 		/*
352 		 * Case 1: our uncle is red
353 		 *   Simply invert the colors of our parent and
354 		 *   uncle and make our grandparent red.  And
355 		 *   then solve the problem up at his level.
356 		 */
357 		RB_MARK_BLACK(uncle);
358 		RB_MARK_BLACK(father);
359 		if (__predict_false(RB_ROOT_P(rbt, grandpa))) {
360 			/*
361 			 * If our grandpa is root, don't bother
362 			 * setting him to red, just return.
363 			 */
364 			KASSERT(RB_BLACK_P(grandpa));
365 			return;
366 		}
367 		RB_MARK_RED(grandpa);
368 		self = grandpa;
369 		father = RB_FATHER(self);
370 		KASSERT(RB_RED_P(self));
371 		if (RB_BLACK_P(father)) {
372 			/*
373 			 * If our greatgrandpa is black, we're done.
374 			 */
375 			KASSERT(RB_BLACK_P(rbt->rbt_root));
376 			return;
377 		}
378 	}
379 
380 	KASSERT(!RB_ROOT_P(rbt, self));
381 	KASSERT(RB_RED_P(self));
382 	KASSERT(RB_RED_P(father));
383 	KASSERT(RB_BLACK_P(uncle));
384 	KASSERT(RB_BLACK_P(grandpa));
385 	/*
386 	 * Case 2&3: our uncle is black.
387 	 */
388 	if (self == father->rb_nodes[other]) {
389 		/*
390 		 * Case 2: we are on the same side as our uncle
391 		 *   Swap ourselves with our parent so this case
392 		 *   becomes case 3.  Basically our parent becomes our
393 		 *   child.
394 		 */
395 		rb_tree_reparent_nodes(rbt, father, other);
396 		KASSERT(RB_FATHER(father) == self);
397 		KASSERT(self->rb_nodes[which] == father);
398 		KASSERT(RB_FATHER(self) == grandpa);
399 		self = father;
400 		father = RB_FATHER(self);
401 	}
402 	KASSERT(RB_RED_P(self) && RB_RED_P(father));
403 	KASSERT(grandpa->rb_nodes[which] == father);
404 	/*
405 	 * Case 3: we are opposite a child of a black uncle.
406 	 *   Swap our parent and grandparent.  Since our grandfather
407 	 *   is black, our father will become black and our new sibling
408 	 *   (former grandparent) will become red.
409 	 */
410 	rb_tree_reparent_nodes(rbt, grandpa, which);
411 	KASSERT(RB_FATHER(self) == father);
412 	KASSERT(RB_FATHER(self)->rb_nodes[RB_POSITION(self) ^ RB_DIR_OTHER] == grandpa);
413 	KASSERT(RB_RED_P(self));
414 	KASSERT(RB_BLACK_P(father));
415 	KASSERT(RB_RED_P(grandpa));
416 
417 	/*
418 	 * Final step: Set the root to black.
419 	 */
420 	RB_MARK_BLACK(rbt->rbt_root);
421 }
422 
423 static void
424 rb_tree_prune_node(struct rb_tree *rbt, struct rb_node *self, bool rebalance)
425 {
426 	const unsigned int which = RB_POSITION(self);
427 	struct rb_node *father = RB_FATHER(self);
428 #ifndef RBSMALL
429 	const bool was_root = RB_ROOT_P(rbt, self);
430 #endif
431 
432 	KASSERT(rebalance || (RB_ROOT_P(rbt, self) || RB_RED_P(self)));
433 	KASSERT(!rebalance || RB_BLACK_P(self));
434 	KASSERT(RB_CHILDLESS_P(self));
435 	KASSERT(rb_tree_check_node(rbt, self, NULL, false));
436 
437 	/*
438 	 * Since we are childless, we know that self->rb_left is pointing
439 	 * to the sentinel node.
440 	 */
441 	father->rb_nodes[which] = self->rb_left;
442 
443 	/*
444 	 * Remove ourselves from the node list, decrement the count,
445 	 * and update min/max.
446 	 */
447 	RB_TAILQ_REMOVE(&rbt->rbt_nodes, self, rb_link);
448 	RBSTAT_DEC(rbt->rbt_count);
449 #ifndef RBSMALL
450 	if (__predict_false(rbt->rbt_minmax[RB_POSITION(self)] == self)) {
451 		rbt->rbt_minmax[RB_POSITION(self)] = father;
452 		/*
453 		 * When removing the root, rbt->rbt_minmax[RB_DIR_LEFT] is
454 		 * updated automatically, but we also need to update
455 		 * rbt->rbt_minmax[RB_DIR_RIGHT];
456 		 */
457 		if (__predict_false(was_root)) {
458 			rbt->rbt_minmax[RB_DIR_RIGHT] = father;
459 		}
460 	}
461 	RB_SET_FATHER(self, NULL);
462 #endif
463 
464 	/*
465 	 * Rebalance if requested.
466 	 */
467 	if (rebalance)
468 		rb_tree_removal_rebalance(rbt, father, which);
469 	KASSERT(was_root || rb_tree_check_node(rbt, father, NULL, true));
470 }
471 
472 /*
473  * When deleting an interior node
474  */
475 static void
476 rb_tree_swap_prune_and_rebalance(struct rb_tree *rbt, struct rb_node *self,
477 	struct rb_node *standin)
478 {
479 	const unsigned int standin_which = RB_POSITION(standin);
480 	unsigned int standin_other = standin_which ^ RB_DIR_OTHER;
481 	struct rb_node *standin_son;
482 	struct rb_node *standin_father = RB_FATHER(standin);
483 	bool rebalance = RB_BLACK_P(standin);
484 
485 	if (standin_father == self) {
486 		/*
487 		 * As a child of self, any childen would be opposite of
488 		 * our parent.
489 		 */
490 		KASSERT(RB_SENTINEL_P(standin->rb_nodes[standin_other]));
491 		standin_son = standin->rb_nodes[standin_which];
492 	} else {
493 		/*
494 		 * Since we aren't a child of self, any childen would be
495 		 * on the same side as our parent.
496 		 */
497 		KASSERT(RB_SENTINEL_P(standin->rb_nodes[standin_which]));
498 		standin_son = standin->rb_nodes[standin_other];
499 	}
500 
501 	/*
502 	 * the node we are removing must have two children.
503 	 */
504 	KASSERT(RB_TWOCHILDREN_P(self));
505 	/*
506 	 * If standin has a child, it must be red.
507 	 */
508 	KASSERT(RB_SENTINEL_P(standin_son) || RB_RED_P(standin_son));
509 
510 	/*
511 	 * Verify things are sane.
512 	 */
513 	KASSERT(rb_tree_check_node(rbt, self, NULL, false));
514 	KASSERT(rb_tree_check_node(rbt, standin, NULL, false));
515 
516 	if (__predict_false(RB_RED_P(standin_son))) {
517 		/*
518 		 * We know we have a red child so if we flip it to black
519 		 * we don't have to rebalance.
520 		 */
521 		KASSERT(rb_tree_check_node(rbt, standin_son, NULL, true));
522 		RB_MARK_BLACK(standin_son);
523 		rebalance = false;
524 
525 		if (standin_father == self) {
526 			KASSERT(RB_POSITION(standin_son) == standin_which);
527 		} else {
528 			KASSERT(RB_POSITION(standin_son) == standin_other);
529 			/*
530 			 * Change the son's parentage to point to his grandpa.
531 			 */
532 			RB_SET_FATHER(standin_son, standin_father);
533 			RB_SET_POSITION(standin_son, standin_which);
534 		}
535 	}
536 
537 	if (standin_father == self) {
538 		/*
539 		 * If we are about to delete the standin's father, then when
540 		 * we call rebalance, we need to use ourselves as our father.
541 		 * Otherwise remember our original father.  Also, sincef we are
542 		 * our standin's father we only need to reparent the standin's
543 		 * brother.
544 		 *
545 		 * |    R      -->     S    |
546 		 * |  Q   S    -->   Q   T  |
547 		 * |        t  -->          |
548 		 */
549 		KASSERT(RB_SENTINEL_P(standin->rb_nodes[standin_other]));
550 		KASSERT(!RB_SENTINEL_P(self->rb_nodes[standin_other]));
551 		KASSERT(self->rb_nodes[standin_which] == standin);
552 		/*
553 		 * Have our son/standin adopt his brother as his new son.
554 		 */
555 		standin_father = standin;
556 	} else {
557 		/*
558 		 * |    R          -->    S       .  |
559 		 * |   / \  |   T  -->   / \  |  /   |
560 		 * |  ..... | S    -->  ..... | T    |
561 		 *
562 		 * Sever standin's connection to his father.
563 		 */
564 		standin_father->rb_nodes[standin_which] = standin_son;
565 		/*
566 		 * Adopt the far son.
567 		 */
568 		standin->rb_nodes[standin_other] = self->rb_nodes[standin_other];
569 		RB_SET_FATHER(standin->rb_nodes[standin_other], standin);
570 		KASSERT(RB_POSITION(self->rb_nodes[standin_other]) == standin_other);
571 		/*
572 		 * Use standin_other because we need to preserve standin_which
573 		 * for the removal_rebalance.
574 		 */
575 		standin_other = standin_which;
576 	}
577 
578 	/*
579 	 * Move the only remaining son to our standin.  If our standin is our
580 	 * son, this will be the only son needed to be moved.
581 	 */
582 	KASSERT(standin->rb_nodes[standin_other] != self->rb_nodes[standin_other]);
583 	standin->rb_nodes[standin_other] = self->rb_nodes[standin_other];
584 	RB_SET_FATHER(standin->rb_nodes[standin_other], standin);
585 
586 	/*
587 	 * Now copy the result of self to standin and then replace
588 	 * self with standin in the tree.
589 	 */
590 	RB_COPY_PROPERTIES(standin, self);
591 	RB_SET_FATHER(standin, RB_FATHER(self));
592 	RB_FATHER(standin)->rb_nodes[RB_POSITION(standin)] = standin;
593 
594 	/*
595 	 * Remove ourselves from the node list, decrement the count,
596 	 * and update min/max.
597 	 */
598 	RB_TAILQ_REMOVE(&rbt->rbt_nodes, self, rb_link);
599 	RBSTAT_DEC(rbt->rbt_count);
600 #ifndef RBSMALL
601 	if (__predict_false(rbt->rbt_minmax[RB_POSITION(self)] == self))
602 		rbt->rbt_minmax[RB_POSITION(self)] = RB_FATHER(self);
603 	RB_SET_FATHER(self, NULL);
604 #endif
605 
606 	KASSERT(rb_tree_check_node(rbt, standin, NULL, false));
607 	KASSERT(RB_FATHER_SENTINEL_P(standin)
608 		|| rb_tree_check_node(rbt, standin_father, NULL, false));
609 	KASSERT(RB_LEFT_SENTINEL_P(standin)
610 		|| rb_tree_check_node(rbt, standin->rb_left, NULL, false));
611 	KASSERT(RB_RIGHT_SENTINEL_P(standin)
612 		|| rb_tree_check_node(rbt, standin->rb_right, NULL, false));
613 
614 	if (!rebalance)
615 		return;
616 
617 	rb_tree_removal_rebalance(rbt, standin_father, standin_which);
618 	KASSERT(rb_tree_check_node(rbt, standin, NULL, true));
619 }
620 
621 /*
622  * We could do this by doing
623  *	rb_tree_node_swap(rbt, self, which);
624  *	rb_tree_prune_node(rbt, self, false);
625  *
626  * But it's more efficient to just evalate and recolor the child.
627  */
628 static void
629 rb_tree_prune_blackred_branch(struct rb_tree *rbt, struct rb_node *self,
630 	unsigned int which)
631 {
632 	struct rb_node *father = RB_FATHER(self);
633 	struct rb_node *son = self->rb_nodes[which];
634 #ifndef RBSMALL
635 	const bool was_root = RB_ROOT_P(rbt, self);
636 #endif
637 
638 	KASSERT(which == RB_DIR_LEFT || which == RB_DIR_RIGHT);
639 	KASSERT(RB_BLACK_P(self) && RB_RED_P(son));
640 	KASSERT(!RB_TWOCHILDREN_P(son));
641 	KASSERT(RB_CHILDLESS_P(son));
642 	KASSERT(rb_tree_check_node(rbt, self, NULL, false));
643 	KASSERT(rb_tree_check_node(rbt, son, NULL, false));
644 
645 	/*
646 	 * Remove ourselves from the tree and give our former child our
647 	 * properties (position, color, root).
648 	 */
649 	RB_COPY_PROPERTIES(son, self);
650 	father->rb_nodes[RB_POSITION(son)] = son;
651 	RB_SET_FATHER(son, father);
652 
653 	/*
654 	 * Remove ourselves from the node list, decrement the count,
655 	 * and update minmax.
656 	 */
657 	RB_TAILQ_REMOVE(&rbt->rbt_nodes, self, rb_link);
658 	RBSTAT_DEC(rbt->rbt_count);
659 #ifndef RBSMALL
660 	if (__predict_false(was_root)) {
661 		KASSERT(rbt->rbt_minmax[which] == son);
662 		rbt->rbt_minmax[which ^ RB_DIR_OTHER] = son;
663 	} else if (rbt->rbt_minmax[RB_POSITION(self)] == self) {
664 		rbt->rbt_minmax[RB_POSITION(self)] = son;
665 	}
666 	RB_SET_FATHER(self, NULL);
667 #endif
668 
669 	KASSERT(was_root || rb_tree_check_node(rbt, father, NULL, true));
670 	KASSERT(rb_tree_check_node(rbt, son, NULL, true));
671 }
672 
673 void
674 _prop_rb_tree_remove_node(struct rb_tree *rbt, void *object)
675 {
676 	const rb_tree_ops_t *rbto = rbt->rbt_ops;
677 	struct rb_node *standin, *self = RB_ITEMTONODE(rbto, object);
678 	unsigned int which;
679 
680 	KASSERT(!RB_SENTINEL_P(self));
681 	RBSTAT_INC(rbt->rbt_removals);
682 
683 	/*
684 	 * In the following diagrams, we (the node to be removed) are S.  Red
685 	 * nodes are lowercase.  T could be either red or black.
686 	 *
687 	 * Remember the major axiom of the red-black tree: the number of
688 	 * black nodes from the root to each leaf is constant across all
689 	 * leaves, only the number of red nodes varies.
690 	 *
691 	 * Thus removing a red leaf doesn't require any other changes to a
692 	 * red-black tree.  So if we must remove a node, attempt to rearrange
693 	 * the tree so we can remove a red node.
694 	 *
695 	 * The simpliest case is a childless red node or a childless root node:
696 	 *
697 	 * |    T  -->    T  |    or    |  R  -->  *  |
698 	 * |  s    -->  *    |
699 	 */
700 	if (RB_CHILDLESS_P(self)) {
701 		const bool rebalance = RB_BLACK_P(self) && !RB_ROOT_P(rbt, self);
702 		rb_tree_prune_node(rbt, self, rebalance);
703 		return;
704 	}
705 	KASSERT(!RB_CHILDLESS_P(self));
706 	if (!RB_TWOCHILDREN_P(self)) {
707 		/*
708 		 * The next simpliest case is the node we are deleting is
709 		 * black and has one red child.
710 		 *
711 		 * |      T  -->      T  -->      T  |
712 		 * |    S    -->  R      -->  R      |
713 		 * |  r      -->    s    -->    *    |
714 		 */
715 		which = RB_LEFT_SENTINEL_P(self) ? RB_DIR_RIGHT : RB_DIR_LEFT;
716 		KASSERT(RB_BLACK_P(self));
717 		KASSERT(RB_RED_P(self->rb_nodes[which]));
718 		KASSERT(RB_CHILDLESS_P(self->rb_nodes[which]));
719 		rb_tree_prune_blackred_branch(rbt, self, which);
720 		return;
721 	}
722 	KASSERT(RB_TWOCHILDREN_P(self));
723 
724 	/*
725 	 * We invert these because we prefer to remove from the inside of
726 	 * the tree.
727 	 */
728 	which = RB_POSITION(self) ^ RB_DIR_OTHER;
729 
730 	/*
731 	 * Let's find the node closes to us opposite of our parent
732 	 * Now swap it with ourself, "prune" it, and rebalance, if needed.
733 	 */
734 	standin = RB_ITEMTONODE(rbto, _prop_rb_tree_iterate(rbt, object, which));
735 	rb_tree_swap_prune_and_rebalance(rbt, self, standin);
736 }
737 
738 static void
739 rb_tree_removal_rebalance(struct rb_tree *rbt, struct rb_node *parent,
740 	unsigned int which)
741 {
742 	KASSERT(!RB_SENTINEL_P(parent));
743 	KASSERT(RB_SENTINEL_P(parent->rb_nodes[which]));
744 	KASSERT(which == RB_DIR_LEFT || which == RB_DIR_RIGHT);
745 	RBSTAT_INC(rbt->rbt_removal_rebalance_calls);
746 
747 	while (RB_BLACK_P(parent->rb_nodes[which])) {
748 		unsigned int other = which ^ RB_DIR_OTHER;
749 		struct rb_node *brother = parent->rb_nodes[other];
750 
751 		RBSTAT_INC(rbt->rbt_removal_rebalance_passes);
752 
753 		KASSERT(!RB_SENTINEL_P(brother));
754 		/*
755 		 * For cases 1, 2a, and 2b, our brother's children must
756 		 * be black and our father must be black
757 		 */
758 		if (RB_BLACK_P(parent)
759 		    && RB_BLACK_P(brother->rb_left)
760 		    && RB_BLACK_P(brother->rb_right)) {
761 			if (RB_RED_P(brother)) {
762 				/*
763 				 * Case 1: Our brother is red, swap its
764 				 * position (and colors) with our parent.
765 				 * This should now be case 2b (unless C or E
766 				 * has a red child which is case 3; thus no
767 				 * explicit branch to case 2b).
768 				 *
769 				 *    B         ->        D
770 				 *  A     d     ->    b     E
771 				 *      C   E   ->  A   C
772 				 */
773 				KASSERT(RB_BLACK_P(parent));
774 				rb_tree_reparent_nodes(rbt, parent, other);
775 				brother = parent->rb_nodes[other];
776 				KASSERT(!RB_SENTINEL_P(brother));
777 				KASSERT(RB_RED_P(parent));
778 				KASSERT(RB_BLACK_P(brother));
779 				KASSERT(rb_tree_check_node(rbt, brother, NULL, false));
780 				KASSERT(rb_tree_check_node(rbt, parent, NULL, false));
781 			} else {
782 				/*
783 				 * Both our parent and brother are black.
784 				 * Change our brother to red, advance up rank
785 				 * and go through the loop again.
786 				 *
787 				 *    B         ->   *B
788 				 * *A     D     ->  A     d
789 				 *      C   E   ->      C   E
790 				 */
791 				RB_MARK_RED(brother);
792 				KASSERT(RB_BLACK_P(brother->rb_left));
793 				KASSERT(RB_BLACK_P(brother->rb_right));
794 				if (RB_ROOT_P(rbt, parent))
795 					return;	/* root == parent == black */
796 				KASSERT(rb_tree_check_node(rbt, brother, NULL, false));
797 				KASSERT(rb_tree_check_node(rbt, parent, NULL, false));
798 				which = RB_POSITION(parent);
799 				parent = RB_FATHER(parent);
800 				continue;
801 			}
802 		}
803 		/*
804 		 * Avoid an else here so that case 2a above can hit either
805 		 * case 2b, 3, or 4.
806 		 */
807 		if (RB_RED_P(parent)
808 		    && RB_BLACK_P(brother)
809 		    && RB_BLACK_P(brother->rb_left)
810 		    && RB_BLACK_P(brother->rb_right)) {
811 			KASSERT(RB_RED_P(parent));
812 			KASSERT(RB_BLACK_P(brother));
813 			KASSERT(RB_BLACK_P(brother->rb_left));
814 			KASSERT(RB_BLACK_P(brother->rb_right));
815 			/*
816 			 * We are black, our father is red, our brother and
817 			 * both nephews are black.  Simply invert/exchange the
818 			 * colors of our father and brother (to black and red
819 			 * respectively).
820 			 *
821 			 *	|    f        -->    F        |
822 			 *	|  *     B    -->  *     b    |
823 			 *	|      N   N  -->      N   N  |
824 			 */
825 			RB_MARK_BLACK(parent);
826 			RB_MARK_RED(brother);
827 			KASSERT(rb_tree_check_node(rbt, brother, NULL, true));
828 			break;		/* We're done! */
829 		} else {
830 			/*
831 			 * Our brother must be black and have at least one
832 			 * red child (it may have two).
833 			 */
834 			KASSERT(RB_BLACK_P(brother));
835 			KASSERT(RB_RED_P(brother->rb_nodes[which]) ||
836 				RB_RED_P(brother->rb_nodes[other]));
837 			if (RB_BLACK_P(brother->rb_nodes[other])) {
838 				/*
839 				 * Case 3: our brother is black, our near
840 				 * nephew is red, and our far nephew is black.
841 				 * Swap our brother with our near nephew.
842 				 * This result in a tree that matches case 4.
843 				 * (Our father could be red or black).
844 				 *
845 				 *	|    F      -->    F      |
846 				 *	|  x     B  -->  x   B    |
847 				 *	|      n    -->        n  |
848 				 */
849 				KASSERT(RB_RED_P(brother->rb_nodes[which]));
850 				rb_tree_reparent_nodes(rbt, brother, which);
851 				KASSERT(RB_FATHER(brother) == parent->rb_nodes[other]);
852 				brother = parent->rb_nodes[other];
853 				KASSERT(RB_RED_P(brother->rb_nodes[other]));
854 			}
855 			/*
856 			 * Case 4: our brother is black and our far nephew
857 			 * is red.  Swap our father and brother locations and
858 			 * change our far nephew to black.  (these can be
859 			 * done in either order so we change the color first).
860 			 * The result is a valid red-black tree and is a
861 			 * terminal case.  (again we don't care about the
862 			 * father's color)
863 			 *
864 			 * If the father is red, we will get a red-black-black
865 			 * tree:
866 			 *	|  f      ->  f      -->    b    |
867 			 *	|    B    ->    B    -->  F   N  |
868 			 *	|      n  ->      N  -->         |
869 			 *
870 			 * If the father is black, we will get an all black
871 			 * tree:
872 			 *	|  F      ->  F      -->    B    |
873 			 *	|    B    ->    B    -->  F   N  |
874 			 *	|      n  ->      N  -->         |
875 			 *
876 			 * If we had two red nephews, then after the swap,
877 			 * our former father would have a red grandson.
878 			 */
879 			KASSERT(RB_BLACK_P(brother));
880 			KASSERT(RB_RED_P(brother->rb_nodes[other]));
881 			RB_MARK_BLACK(brother->rb_nodes[other]);
882 			rb_tree_reparent_nodes(rbt, parent, other);
883 			break;		/* We're done! */
884 		}
885 	}
886 	KASSERT(rb_tree_check_node(rbt, parent, NULL, true));
887 }
888 
889 void *
890 _prop_rb_tree_iterate(struct rb_tree *rbt, void *object, const unsigned int direction)
891 {
892 	const rb_tree_ops_t *rbto = rbt->rbt_ops;
893 	const unsigned int other = direction ^ RB_DIR_OTHER;
894 	struct rb_node *self;
895 
896 	KASSERT(direction == RB_DIR_LEFT || direction == RB_DIR_RIGHT);
897 
898 	if (object == NULL) {
899 #ifndef RBSMALL
900 		if (RB_SENTINEL_P(rbt->rbt_root))
901 			return NULL;
902 		return RB_NODETOITEM(rbto, rbt->rbt_minmax[direction]);
903 #else
904 		self = rbt->rbt_root;
905 		if (RB_SENTINEL_P(self))
906 			return NULL;
907 		while (!RB_SENTINEL_P(self->rb_nodes[direction]))
908 			self = self->rb_nodes[direction];
909 		return RB_NODETOITEM(rbto, self);
910 #endif /* !RBSMALL */
911 	}
912 	self = RB_ITEMTONODE(rbto, object);
913 	KASSERT(!RB_SENTINEL_P(self));
914 	/*
915 	 * We can't go any further in this direction.  We proceed up in the
916 	 * opposite direction until our parent is in direction we want to go.
917 	 */
918 	if (RB_SENTINEL_P(self->rb_nodes[direction])) {
919 		while (!RB_ROOT_P(rbt, self)) {
920 			if (other == RB_POSITION(self))
921 				return RB_NODETOITEM(rbto, RB_FATHER(self));
922 			self = RB_FATHER(self);
923 		}
924 		return NULL;
925 	}
926 
927 	/*
928 	 * Advance down one in current direction and go down as far as possible
929 	 * in the opposite direction.
930 	 */
931 	self = self->rb_nodes[direction];
932 	KASSERT(!RB_SENTINEL_P(self));
933 	while (!RB_SENTINEL_P(self->rb_nodes[other]))
934 		self = self->rb_nodes[other];
935 	return RB_NODETOITEM(rbto, self);
936 }
937 
938 #ifdef RBDEBUG
939 static const struct rb_node *
940 rb_tree_iterate_const(const struct rb_tree *rbt, const struct rb_node *self,
941 	const unsigned int direction)
942 {
943 	const unsigned int other = direction ^ RB_DIR_OTHER;
944 	KASSERT(direction == RB_DIR_LEFT || direction == RB_DIR_RIGHT);
945 
946 	if (self == NULL) {
947 #ifndef RBSMALL
948 		if (RB_SENTINEL_P(rbt->rbt_root))
949 			return NULL;
950 		return rbt->rbt_minmax[direction];
951 #else
952 		self = rbt->rbt_root;
953 		if (RB_SENTINEL_P(self))
954 			return NULL;
955 		while (!RB_SENTINEL_P(self->rb_nodes[direction]))
956 			self = self->rb_nodes[direction];
957 		return self;
958 #endif /* !RBSMALL */
959 	}
960 	KASSERT(!RB_SENTINEL_P(self));
961 	/*
962 	 * We can't go any further in this direction.  We proceed up in the
963 	 * opposite direction until our parent is in direction we want to go.
964 	 */
965 	if (RB_SENTINEL_P(self->rb_nodes[direction])) {
966 		while (!RB_ROOT_P(rbt, self)) {
967 			if (other == RB_POSITION(self))
968 				return RB_FATHER(self);
969 			self = RB_FATHER(self);
970 		}
971 		return NULL;
972 	}
973 
974 	/*
975 	 * Advance down one in current direction and go down as far as possible
976 	 * in the opposite direction.
977 	 */
978 	self = self->rb_nodes[direction];
979 	KASSERT(!RB_SENTINEL_P(self));
980 	while (!RB_SENTINEL_P(self->rb_nodes[other]))
981 		self = self->rb_nodes[other];
982 	return self;
983 }
984 
985 static unsigned int
986 rb_tree_count_black(const struct rb_node *self)
987 {
988 	unsigned int left, right;
989 
990 	if (RB_SENTINEL_P(self))
991 		return 0;
992 
993 	left = rb_tree_count_black(self->rb_left);
994 	right = rb_tree_count_black(self->rb_right);
995 
996 	KASSERT(left == right);
997 
998 	return left + RB_BLACK_P(self);
999 }
1000 
1001 static bool
1002 rb_tree_check_node(const struct rb_tree *rbt, const struct rb_node *self,
1003 	const struct rb_node *prev, bool red_check)
1004 {
1005 	const rb_tree_ops_t *rbto = rbt->rbt_ops;
1006 	rbto_compare_nodes_fn compare_nodes = rbto->rbto_compare_nodes;
1007 
1008 	KASSERT(!RB_SENTINEL_P(self));
1009 	KASSERT(prev == NULL || (*compare_nodes)(rbto->rbto_context,
1010 	    RB_NODETOITEM(rbto, prev), RB_NODETOITEM(rbto, self)) < 0);
1011 
1012 	/*
1013 	 * Verify our relationship to our parent.
1014 	 */
1015 	if (RB_ROOT_P(rbt, self)) {
1016 		KASSERT(self == rbt->rbt_root);
1017 		KASSERT(RB_POSITION(self) == RB_DIR_LEFT);
1018 		KASSERT(RB_FATHER(self)->rb_nodes[RB_DIR_LEFT] == self);
1019 		KASSERT(RB_FATHER(self) == (const struct rb_node *) &rbt->rbt_root);
1020 	} else {
1021 		int diff = (*compare_nodes)(rbto->rbto_context,
1022 		    RB_NODETOITEM(rbto, self),
1023 		    RB_NODETOITEM(rbto, RB_FATHER(self)));
1024 
1025 		KASSERT(self != rbt->rbt_root);
1026 		KASSERT(!RB_FATHER_SENTINEL_P(self));
1027 		if (RB_POSITION(self) == RB_DIR_LEFT) {
1028 			KASSERT(diff < 0);
1029 			KASSERT(RB_FATHER(self)->rb_nodes[RB_DIR_LEFT] == self);
1030 		} else {
1031 			KASSERT(diff > 0);
1032 			KASSERT(RB_FATHER(self)->rb_nodes[RB_DIR_RIGHT] == self);
1033 		}
1034 	}
1035 
1036 	/*
1037 	 * Verify our position in the linked list against the tree itself.
1038 	 */
1039 	{
1040 		const struct rb_node *prev0 = rb_tree_iterate_const(rbt, self, RB_DIR_LEFT);
1041 		const struct rb_node *next0 = rb_tree_iterate_const(rbt, self, RB_DIR_RIGHT);
1042 		KASSERT(prev0 == TAILQ_PREV(self, rb_node_qh, rb_link));
1043 		KASSERT(next0 == TAILQ_NEXT(self, rb_link));
1044 #ifndef RBSMALL
1045 		KASSERT(prev0 != NULL || self == rbt->rbt_minmax[RB_DIR_LEFT]);
1046 		KASSERT(next0 != NULL || self == rbt->rbt_minmax[RB_DIR_RIGHT]);
1047 #endif
1048 	}
1049 
1050 	/*
1051 	 * The root must be black.
1052 	 * There can never be two adjacent red nodes.
1053 	 */
1054 	if (red_check) {
1055 		KASSERT(!RB_ROOT_P(rbt, self) || RB_BLACK_P(self));
1056 		(void) rb_tree_count_black(self);
1057 		if (RB_RED_P(self)) {
1058 			const struct rb_node *brother;
1059 			KASSERT(!RB_ROOT_P(rbt, self));
1060 			brother = RB_FATHER(self)->rb_nodes[RB_POSITION(self) ^ RB_DIR_OTHER];
1061 			KASSERT(RB_BLACK_P(RB_FATHER(self)));
1062 			/*
1063 			 * I'm red and have no children, then I must either
1064 			 * have no brother or my brother also be red and
1065 			 * also have no children.  (black count == 0)
1066 			 */
1067 			KASSERT(!RB_CHILDLESS_P(self)
1068 				|| RB_SENTINEL_P(brother)
1069 				|| RB_RED_P(brother)
1070 				|| RB_CHILDLESS_P(brother));
1071 			/*
1072 			 * If I'm not childless, I must have two children
1073 			 * and they must be both be black.
1074 			 */
1075 			KASSERT(RB_CHILDLESS_P(self)
1076 				|| (RB_TWOCHILDREN_P(self)
1077 				    && RB_BLACK_P(self->rb_left)
1078 				    && RB_BLACK_P(self->rb_right)));
1079 			/*
1080 			 * If I'm not childless, thus I have black children,
1081 			 * then my brother must either be black or have two
1082 			 * black children.
1083 			 */
1084 			KASSERT(RB_CHILDLESS_P(self)
1085 				|| RB_BLACK_P(brother)
1086 				|| (RB_TWOCHILDREN_P(brother)
1087 				    && RB_BLACK_P(brother->rb_left)
1088 				    && RB_BLACK_P(brother->rb_right)));
1089 		} else {
1090 			/*
1091 			 * If I'm black and have one child, that child must
1092 			 * be red and childless.
1093 			 */
1094 			KASSERT(RB_CHILDLESS_P(self)
1095 				|| RB_TWOCHILDREN_P(self)
1096 				|| (!RB_LEFT_SENTINEL_P(self)
1097 				    && RB_RIGHT_SENTINEL_P(self)
1098 				    && RB_RED_P(self->rb_left)
1099 				    && RB_CHILDLESS_P(self->rb_left))
1100 				|| (!RB_RIGHT_SENTINEL_P(self)
1101 				    && RB_LEFT_SENTINEL_P(self)
1102 				    && RB_RED_P(self->rb_right)
1103 				    && RB_CHILDLESS_P(self->rb_right)));
1104 
1105 			/*
1106 			 * If I'm a childless black node and my parent is
1107 			 * black, my 2nd closet relative away from my parent
1108 			 * is either red or has a red parent or red children.
1109 			 */
1110 			if (!RB_ROOT_P(rbt, self)
1111 			    && RB_CHILDLESS_P(self)
1112 			    && RB_BLACK_P(RB_FATHER(self))) {
1113 				const unsigned int which = RB_POSITION(self);
1114 				const unsigned int other = which ^ RB_DIR_OTHER;
1115 				const struct rb_node *relative0, *relative;
1116 
1117 				relative0 = rb_tree_iterate_const(rbt,
1118 				    self, other);
1119 				KASSERT(relative0 != NULL);
1120 				relative = rb_tree_iterate_const(rbt,
1121 				    relative0, other);
1122 				KASSERT(relative != NULL);
1123 				KASSERT(RB_SENTINEL_P(relative->rb_nodes[which]));
1124 #if 0
1125 				KASSERT(RB_RED_P(relative)
1126 					|| RB_RED_P(relative->rb_left)
1127 					|| RB_RED_P(relative->rb_right)
1128 					|| RB_RED_P(RB_FATHER(relative)));
1129 #endif
1130 			}
1131 		}
1132 		/*
1133 		 * A grandparent's children must be real nodes and not
1134 		 * sentinels.  First check out grandparent.
1135 		 */
1136 		KASSERT(RB_ROOT_P(rbt, self)
1137 			|| RB_ROOT_P(rbt, RB_FATHER(self))
1138 			|| RB_TWOCHILDREN_P(RB_FATHER(RB_FATHER(self))));
1139 		/*
1140 		 * If we are have grandchildren on our left, then
1141 		 * we must have a child on our right.
1142 		 */
1143 		KASSERT(RB_LEFT_SENTINEL_P(self)
1144 			|| RB_CHILDLESS_P(self->rb_left)
1145 			|| !RB_RIGHT_SENTINEL_P(self));
1146 		/*
1147 		 * If we are have grandchildren on our right, then
1148 		 * we must have a child on our left.
1149 		 */
1150 		KASSERT(RB_RIGHT_SENTINEL_P(self)
1151 			|| RB_CHILDLESS_P(self->rb_right)
1152 			|| !RB_LEFT_SENTINEL_P(self));
1153 
1154 		/*
1155 		 * If we have a child on the left and it doesn't have two
1156 		 * children make sure we don't have great-great-grandchildren on
1157 		 * the right.
1158 		 */
1159 		KASSERT(RB_TWOCHILDREN_P(self->rb_left)
1160 			|| RB_CHILDLESS_P(self->rb_right)
1161 			|| RB_CHILDLESS_P(self->rb_right->rb_left)
1162 			|| RB_CHILDLESS_P(self->rb_right->rb_left->rb_left)
1163 			|| RB_CHILDLESS_P(self->rb_right->rb_left->rb_right)
1164 			|| RB_CHILDLESS_P(self->rb_right->rb_right)
1165 			|| RB_CHILDLESS_P(self->rb_right->rb_right->rb_left)
1166 			|| RB_CHILDLESS_P(self->rb_right->rb_right->rb_right));
1167 
1168 		/*
1169 		 * If we have a child on the right and it doesn't have two
1170 		 * children make sure we don't have great-great-grandchildren on
1171 		 * the left.
1172 		 */
1173 		KASSERT(RB_TWOCHILDREN_P(self->rb_right)
1174 			|| RB_CHILDLESS_P(self->rb_left)
1175 			|| RB_CHILDLESS_P(self->rb_left->rb_left)
1176 			|| RB_CHILDLESS_P(self->rb_left->rb_left->rb_left)
1177 			|| RB_CHILDLESS_P(self->rb_left->rb_left->rb_right)
1178 			|| RB_CHILDLESS_P(self->rb_left->rb_right)
1179 			|| RB_CHILDLESS_P(self->rb_left->rb_right->rb_left)
1180 			|| RB_CHILDLESS_P(self->rb_left->rb_right->rb_right));
1181 
1182 		/*
1183 		 * If we are fully interior node, then our predecessors and
1184 		 * successors must have no children in our direction.
1185 		 */
1186 		if (RB_TWOCHILDREN_P(self)) {
1187 			const struct rb_node *prev0;
1188 			const struct rb_node *next0;
1189 
1190 			prev0 = rb_tree_iterate_const(rbt, self, RB_DIR_LEFT);
1191 			KASSERT(prev0 != NULL);
1192 			KASSERT(RB_RIGHT_SENTINEL_P(prev0));
1193 
1194 			next0 = rb_tree_iterate_const(rbt, self, RB_DIR_RIGHT);
1195 			KASSERT(next0 != NULL);
1196 			KASSERT(RB_LEFT_SENTINEL_P(next0));
1197 		}
1198 	}
1199 
1200 	return true;
1201 }
1202 
1203 void
1204 rb_tree_check(const struct rb_tree *rbt, bool red_check)
1205 {
1206 	const struct rb_node *self;
1207 	const struct rb_node *prev;
1208 #ifdef RBSTATS
1209 	unsigned int count = 0;
1210 #endif
1211 
1212 	KASSERT(rbt->rbt_root != NULL);
1213 	KASSERT(RB_LEFT_P(rbt->rbt_root));
1214 
1215 #if defined(RBSTATS) && !defined(RBSMALL)
1216 	KASSERT(rbt->rbt_count > 1
1217 	    || rbt->rbt_minmax[RB_DIR_LEFT] == rbt->rbt_minmax[RB_DIR_RIGHT]);
1218 #endif
1219 
1220 	prev = NULL;
1221 	TAILQ_FOREACH(self, &rbt->rbt_nodes, rb_link) {
1222 		rb_tree_check_node(rbt, self, prev, false);
1223 #ifdef RBSTATS
1224 		count++;
1225 #endif
1226 	}
1227 #ifdef RBSTATS
1228 	KASSERT(rbt->rbt_count == count);
1229 #endif
1230 	if (red_check) {
1231 		KASSERT(RB_BLACK_P(rbt->rbt_root));
1232 		KASSERT(RB_SENTINEL_P(rbt->rbt_root)
1233 			|| rb_tree_count_black(rbt->rbt_root));
1234 
1235 		/*
1236 		 * The root must be black.
1237 		 * There can never be two adjacent red nodes.
1238 		 */
1239 		TAILQ_FOREACH(self, &rbt->rbt_nodes, rb_link) {
1240 			rb_tree_check_node(rbt, self, NULL, true);
1241 		}
1242 	}
1243 }
1244 #endif /* RBDEBUG */
1245 
1246 #ifdef RBSTATS
1247 static void
1248 rb_tree_mark_depth(const struct rb_tree *rbt, const struct rb_node *self,
1249 	size_t *depths, size_t depth)
1250 {
1251 	if (RB_SENTINEL_P(self))
1252 		return;
1253 
1254 	if (RB_TWOCHILDREN_P(self)) {
1255 		rb_tree_mark_depth(rbt, self->rb_left, depths, depth + 1);
1256 		rb_tree_mark_depth(rbt, self->rb_right, depths, depth + 1);
1257 		return;
1258 	}
1259 	depths[depth]++;
1260 	if (!RB_LEFT_SENTINEL_P(self)) {
1261 		rb_tree_mark_depth(rbt, self->rb_left, depths, depth + 1);
1262 	}
1263 	if (!RB_RIGHT_SENTINEL_P(self)) {
1264 		rb_tree_mark_depth(rbt, self->rb_right, depths, depth + 1);
1265 	}
1266 }
1267 
1268 void
1269 rb_tree_depths(const struct rb_tree *rbt, size_t *depths)
1270 {
1271 	rb_tree_mark_depth(rbt, rbt->rbt_root, depths, 1);
1272 }
1273 #endif /* RBSTATS */
1274