1 /*-
2  * Copyright (c) 2001 The NetBSD Foundation, Inc.
3  * All rights reserved.
4  *
5  * This code is derived from software contributed to The NetBSD Foundation
6  * by Matt Thomas <matt@3am-software.com>.
7  *
8  * Redistribution and use in source and binary forms, with or without
9  * modification, are permitted provided that the following conditions
10  * are met:
11  * 1. Redistributions of source code must retain the above copyright
12  *    notice, this list of conditions and the following disclaimer.
13  * 2. Redistributions in binary form must reproduce the above copyright
14  *    notice, this list of conditions and the following disclaimer in the
15  *    documentation and/or other materials provided with the distribution.
16  *
17  * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS
18  * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
19  * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
20  * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS
21  * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
22  * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
23  * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
24  * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
25  * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
26  * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
27  * POSSIBILITY OF SUCH DAMAGE.
28  *
29  * Based on: NetBSD: rb.c,v 1.6 2010/04/30 13:58:09 joerg Exp
30  */
31 
32 #include "archive_platform.h"
33 
34 #include <stddef.h>
35 
36 #include "archive_rb.h"
37 
38 /* Keep in sync with archive_rb.h */
39 #define	RB_DIR_LEFT		0
40 #define	RB_DIR_RIGHT		1
41 #define	RB_DIR_OTHER		1
42 #define	rb_left			rb_nodes[RB_DIR_LEFT]
43 #define	rb_right		rb_nodes[RB_DIR_RIGHT]
44 
45 #define	RB_FLAG_POSITION	0x2
46 #define	RB_FLAG_RED		0x1
47 #define	RB_FLAG_MASK		(RB_FLAG_POSITION|RB_FLAG_RED)
48 #define	RB_FATHER(rb) \
49     ((struct archive_rb_node *)((rb)->rb_info & ~RB_FLAG_MASK))
50 #define	RB_SET_FATHER(rb, father) \
51     ((void)((rb)->rb_info = (uintptr_t)(father)|((rb)->rb_info & RB_FLAG_MASK)))
52 
53 #define	RB_SENTINEL_P(rb)	((rb) == NULL)
54 #define	RB_LEFT_SENTINEL_P(rb)	RB_SENTINEL_P((rb)->rb_left)
55 #define	RB_RIGHT_SENTINEL_P(rb)	RB_SENTINEL_P((rb)->rb_right)
56 #define	RB_FATHER_SENTINEL_P(rb) RB_SENTINEL_P(RB_FATHER((rb)))
57 #define	RB_CHILDLESS_P(rb) \
58     (RB_SENTINEL_P(rb) || (RB_LEFT_SENTINEL_P(rb) && RB_RIGHT_SENTINEL_P(rb)))
59 #define	RB_TWOCHILDREN_P(rb) \
60     (!RB_SENTINEL_P(rb) && !RB_LEFT_SENTINEL_P(rb) && !RB_RIGHT_SENTINEL_P(rb))
61 
62 #define	RB_POSITION(rb)	\
63     (((rb)->rb_info & RB_FLAG_POSITION) ? RB_DIR_RIGHT : RB_DIR_LEFT)
64 #define	RB_RIGHT_P(rb)		(RB_POSITION(rb) == RB_DIR_RIGHT)
65 #define	RB_LEFT_P(rb)		(RB_POSITION(rb) == RB_DIR_LEFT)
66 #define	RB_RED_P(rb) 		(!RB_SENTINEL_P(rb) && ((rb)->rb_info & RB_FLAG_RED) != 0)
67 #define	RB_BLACK_P(rb) 		(RB_SENTINEL_P(rb) || ((rb)->rb_info & RB_FLAG_RED) == 0)
68 #define	RB_MARK_RED(rb) 	((void)((rb)->rb_info |= RB_FLAG_RED))
69 #define	RB_MARK_BLACK(rb) 	((void)((rb)->rb_info &= ~RB_FLAG_RED))
70 #define	RB_INVERT_COLOR(rb) 	((void)((rb)->rb_info ^= RB_FLAG_RED))
71 #define	RB_ROOT_P(rbt, rb)	((rbt)->rbt_root == (rb))
72 #define	RB_SET_POSITION(rb, position) \
73     ((void)((position) ? ((rb)->rb_info |= RB_FLAG_POSITION) : \
74     ((rb)->rb_info &= ~RB_FLAG_POSITION)))
75 #define	RB_ZERO_PROPERTIES(rb)	((void)((rb)->rb_info &= ~RB_FLAG_MASK))
76 #define	RB_COPY_PROPERTIES(dst, src) \
77     ((void)((dst)->rb_info ^= ((dst)->rb_info ^ (src)->rb_info) & RB_FLAG_MASK))
78 #define RB_SWAP_PROPERTIES(a, b) do { \
79     uintptr_t xorinfo = ((a)->rb_info ^ (b)->rb_info) & RB_FLAG_MASK; \
80     (a)->rb_info ^= xorinfo; \
81     (b)->rb_info ^= xorinfo; \
82   } while (/*CONSTCOND*/ 0)
83 
84 static void __archive_rb_tree_insert_rebalance(struct archive_rb_tree *,
85     struct archive_rb_node *);
86 static void __archive_rb_tree_removal_rebalance(struct archive_rb_tree *,
87     struct archive_rb_node *, unsigned int);
88 
89 #define	RB_SENTINEL_NODE	NULL
90 
91 #define T	1
92 #define	F	0
93 
94 void
95 __archive_rb_tree_init(struct archive_rb_tree *rbt,
96     const struct archive_rb_tree_ops *ops)
97 {
98 	rbt->rbt_ops = ops;
99 	*((struct archive_rb_node **)&rbt->rbt_root) = RB_SENTINEL_NODE;
100 }
101 
102 struct archive_rb_node *
103 __archive_rb_tree_find_node(struct archive_rb_tree *rbt, const void *key)
104 {
105 	archive_rbto_compare_key_fn compare_key = rbt->rbt_ops->rbto_compare_key;
106 	struct archive_rb_node *parent = rbt->rbt_root;
107 
108 	while (!RB_SENTINEL_P(parent)) {
109 		const signed int diff = (*compare_key)(parent, key);
110 		if (diff == 0)
111 			return parent;
112 		parent = parent->rb_nodes[diff > 0];
113 	}
114 
115 	return NULL;
116 }
117 
118 struct archive_rb_node *
119 __archive_rb_tree_find_node_geq(struct archive_rb_tree *rbt, const void *key)
120 {
121 	archive_rbto_compare_key_fn compare_key = rbt->rbt_ops->rbto_compare_key;
122 	struct archive_rb_node *parent = rbt->rbt_root;
123 	struct archive_rb_node *last = NULL;
124 
125 	while (!RB_SENTINEL_P(parent)) {
126 		const signed int diff = (*compare_key)(parent, key);
127 		if (diff == 0)
128 			return parent;
129 		if (diff < 0)
130 			last = parent;
131 		parent = parent->rb_nodes[diff > 0];
132 	}
133 
134 	return last;
135 }
136 
137 struct archive_rb_node *
138 __archive_rb_tree_find_node_leq(struct archive_rb_tree *rbt, const void *key)
139 {
140 	archive_rbto_compare_key_fn compare_key = rbt->rbt_ops->rbto_compare_key;
141 	struct archive_rb_node *parent = rbt->rbt_root;
142 	struct archive_rb_node *last = NULL;
143 
144 	while (!RB_SENTINEL_P(parent)) {
145 		const signed int diff = (*compare_key)(parent, key);
146 		if (diff == 0)
147 			return parent;
148 		if (diff > 0)
149 			last = parent;
150 		parent = parent->rb_nodes[diff > 0];
151 	}
152 
153 	return last;
154 }
155 
156 int
157 __archive_rb_tree_insert_node(struct archive_rb_tree *rbt,
158     struct archive_rb_node *self)
159 {
160 	archive_rbto_compare_nodes_fn compare_nodes = rbt->rbt_ops->rbto_compare_nodes;
161 	struct archive_rb_node *parent, *tmp;
162 	unsigned int position;
163 	int rebalance;
164 
165 	tmp = rbt->rbt_root;
166 	/*
167 	 * This is a hack.  Because rbt->rbt_root is just a
168 	 * struct archive_rb_node *, just like rb_node->rb_nodes[RB_DIR_LEFT],
169 	 * we can use this fact to avoid a lot of tests for root and know
170 	 * that even at root, updating
171 	 * RB_FATHER(rb_node)->rb_nodes[RB_POSITION(rb_node)] will
172 	 * update rbt->rbt_root.
173 	 */
174 	parent = (struct archive_rb_node *)(void *)&rbt->rbt_root;
175 	position = RB_DIR_LEFT;
176 
177 	/*
178 	 * Find out where to place this new leaf.
179 	 */
180 	while (!RB_SENTINEL_P(tmp)) {
181 		const signed int diff = (*compare_nodes)(tmp, self);
182 		if (diff == 0) {
183 			/*
184 			 * Node already exists; don't insert.
185 			 */
186 			return F;
187 		}
188 		parent = tmp;
189 		position = (diff > 0);
190 		tmp = parent->rb_nodes[position];
191 	}
192 
193 	/*
194 	 * Initialize the node and insert as a leaf into the tree.
195 	 */
196 	RB_SET_FATHER(self, parent);
197 	RB_SET_POSITION(self, position);
198 	if (parent == (struct archive_rb_node *)(void *)&rbt->rbt_root) {
199 		RB_MARK_BLACK(self);		/* root is always black */
200 		rebalance = F;
201 	} else {
202 		/*
203 		 * All new nodes are colored red.  We only need to rebalance
204 		 * if our parent is also red.
205 		 */
206 		RB_MARK_RED(self);
207 		rebalance = RB_RED_P(parent);
208 	}
209 	self->rb_left = parent->rb_nodes[position];
210 	self->rb_right = parent->rb_nodes[position];
211 	parent->rb_nodes[position] = self;
212 
213 	/*
214 	 * Rebalance tree after insertion
215 	 */
216 	if (rebalance)
217 		__archive_rb_tree_insert_rebalance(rbt, self);
218 
219 	return T;
220 }
221 
222 /*
223  * Swap the location and colors of 'self' and its child @ which.  The child
224  * can not be a sentinel node.  This is our rotation function.  However,
225  * since it preserves coloring, it great simplifies both insertion and
226  * removal since rotation almost always involves the exchanging of colors
227  * as a separate step.
228  */
229 /*ARGSUSED*/
230 static void
231 __archive_rb_tree_reparent_nodes(
232     struct archive_rb_node *old_father, const unsigned int which)
233 {
234 	const unsigned int other = which ^ RB_DIR_OTHER;
235 	struct archive_rb_node * const grandpa = RB_FATHER(old_father);
236 	struct archive_rb_node * const old_child = old_father->rb_nodes[which];
237 	struct archive_rb_node * const new_father = old_child;
238 	struct archive_rb_node * const new_child = old_father;
239 
240 	if (new_father == NULL)
241 		return;
242 	/*
243 	 * Exchange descendant linkages.
244 	 */
245 	grandpa->rb_nodes[RB_POSITION(old_father)] = new_father;
246 	new_child->rb_nodes[which] = old_child->rb_nodes[other];
247 	new_father->rb_nodes[other] = new_child;
248 
249 	/*
250 	 * Update ancestor linkages
251 	 */
252 	RB_SET_FATHER(new_father, grandpa);
253 	RB_SET_FATHER(new_child, new_father);
254 
255 	/*
256 	 * Exchange properties between new_father and new_child.  The only
257 	 * change is that new_child's position is now on the other side.
258 	 */
259 	RB_SWAP_PROPERTIES(new_father, new_child);
260 	RB_SET_POSITION(new_child, other);
261 
262 	/*
263 	 * Make sure to reparent the new child to ourself.
264 	 */
265 	if (!RB_SENTINEL_P(new_child->rb_nodes[which])) {
266 		RB_SET_FATHER(new_child->rb_nodes[which], new_child);
267 		RB_SET_POSITION(new_child->rb_nodes[which], which);
268 	}
269 
270 }
271 
272 static void
273 __archive_rb_tree_insert_rebalance(struct archive_rb_tree *rbt,
274     struct archive_rb_node *self)
275 {
276 	struct archive_rb_node * father = RB_FATHER(self);
277 	struct archive_rb_node * grandpa;
278 	struct archive_rb_node * uncle;
279 	unsigned int which;
280 	unsigned int other;
281 
282 	for (;;) {
283 		/*
284 		 * We are red and our parent is red, therefore we must have a
285 		 * grandfather and he must be black.
286 		 */
287 		grandpa = RB_FATHER(father);
288 		which = (father == grandpa->rb_right);
289 		other = which ^ RB_DIR_OTHER;
290 		uncle = grandpa->rb_nodes[other];
291 
292 		if (RB_BLACK_P(uncle))
293 			break;
294 
295 		/*
296 		 * Case 1: our uncle is red
297 		 *   Simply invert the colors of our parent and
298 		 *   uncle and make our grandparent red.  And
299 		 *   then solve the problem up at his level.
300 		 */
301 		RB_MARK_BLACK(uncle);
302 		RB_MARK_BLACK(father);
303 		if (RB_ROOT_P(rbt, grandpa)) {
304 			/*
305 			 * If our grandpa is root, don't bother
306 			 * setting him to red, just return.
307 			 */
308 			return;
309 		}
310 		RB_MARK_RED(grandpa);
311 		self = grandpa;
312 		father = RB_FATHER(self);
313 		if (RB_BLACK_P(father)) {
314 			/*
315 			 * If our great-grandpa is black, we're done.
316 			 */
317 			return;
318 		}
319 	}
320 
321 	/*
322 	 * Case 2&3: our uncle is black.
323 	 */
324 	if (self == father->rb_nodes[other]) {
325 		/*
326 		 * Case 2: we are on the same side as our uncle
327 		 *   Swap ourselves with our parent so this case
328 		 *   becomes case 3.  Basically our parent becomes our
329 		 *   child.
330 		 */
331 		__archive_rb_tree_reparent_nodes(father, other);
332 	}
333 	/*
334 	 * Case 3: we are opposite a child of a black uncle.
335 	 *   Swap our parent and grandparent.  Since our grandfather
336 	 *   is black, our father will become black and our new sibling
337 	 *   (former grandparent) will become red.
338 	 */
339 	__archive_rb_tree_reparent_nodes(grandpa, which);
340 
341 	/*
342 	 * Final step: Set the root to black.
343 	 */
344 	RB_MARK_BLACK(rbt->rbt_root);
345 }
346 
347 static void
348 __archive_rb_tree_prune_node(struct archive_rb_tree *rbt,
349     struct archive_rb_node *self, int rebalance)
350 {
351 	const unsigned int which = RB_POSITION(self);
352 	struct archive_rb_node *father = RB_FATHER(self);
353 
354 	/*
355 	 * Since we are childless, we know that self->rb_left is pointing
356 	 * to the sentinel node.
357 	 */
358 	father->rb_nodes[which] = self->rb_left;
359 
360 	/*
361 	 * Rebalance if requested.
362 	 */
363 	if (rebalance)
364 		__archive_rb_tree_removal_rebalance(rbt, father, which);
365 }
366 
367 /*
368  * When deleting an interior node
369  */
370 static void
371 __archive_rb_tree_swap_prune_and_rebalance(struct archive_rb_tree *rbt,
372     struct archive_rb_node *self, struct archive_rb_node *standin)
373 {
374 	const unsigned int standin_which = RB_POSITION(standin);
375 	unsigned int standin_other = standin_which ^ RB_DIR_OTHER;
376 	struct archive_rb_node *standin_son;
377 	struct archive_rb_node *standin_father = RB_FATHER(standin);
378 	int rebalance = RB_BLACK_P(standin);
379 
380 	if (standin_father == self) {
381 		/*
382 		 * As a child of self, any children would be opposite of
383 		 * our parent.
384 		 */
385 		standin_son = standin->rb_nodes[standin_which];
386 	} else {
387 		/*
388 		 * Since we aren't a child of self, any children would be
389 		 * on the same side as our parent.
390 		 */
391 		standin_son = standin->rb_nodes[standin_other];
392 	}
393 
394 	if (RB_RED_P(standin_son)) {
395 		/*
396 		 * We know we have a red child so if we flip it to black
397 		 * we don't have to rebalance.
398 		 */
399 		RB_MARK_BLACK(standin_son);
400 		rebalance = F;
401 
402 		if (standin_father != self) {
403 			/*
404 			 * Change the son's parentage to point to his grandpa.
405 			 */
406 			RB_SET_FATHER(standin_son, standin_father);
407 			RB_SET_POSITION(standin_son, standin_which);
408 		}
409 	}
410 
411 	if (standin_father == self) {
412 		/*
413 		 * If we are about to delete the standin's father, then when
414 		 * we call rebalance, we need to use ourselves as our father.
415 		 * Otherwise remember our original father.  Also, since we are
416 		 * our standin's father we only need to reparent the standin's
417 		 * brother.
418 		 *
419 		 * |    R      -->     S    |
420 		 * |  Q   S    -->   Q   T  |
421 		 * |        t  -->          |
422 		 *
423 		 * Have our son/standin adopt his brother as his new son.
424 		 */
425 		standin_father = standin;
426 	} else {
427 		/*
428 		 * |    R          -->    S       .  |
429 		 * |   / \  |   T  -->   / \  |  /   |
430 		 * |  ..... | S    -->  ..... | T    |
431 		 *
432 		 * Sever standin's connection to his father.
433 		 */
434 		standin_father->rb_nodes[standin_which] = standin_son;
435 		/*
436 		 * Adopt the far son.
437 		 */
438 		standin->rb_nodes[standin_other] = self->rb_nodes[standin_other];
439 		RB_SET_FATHER(standin->rb_nodes[standin_other], standin);
440 		/*
441 		 * Use standin_other because we need to preserve standin_which
442 		 * for the removal_rebalance.
443 		 */
444 		standin_other = standin_which;
445 	}
446 
447 	/*
448 	 * Move the only remaining son to our standin.  If our standin is our
449 	 * son, this will be the only son needed to be moved.
450 	 */
451 	standin->rb_nodes[standin_other] = self->rb_nodes[standin_other];
452 	RB_SET_FATHER(standin->rb_nodes[standin_other], standin);
453 
454 	/*
455 	 * Now copy the result of self to standin and then replace
456 	 * self with standin in the tree.
457 	 */
458 	RB_COPY_PROPERTIES(standin, self);
459 	RB_SET_FATHER(standin, RB_FATHER(self));
460 	RB_FATHER(standin)->rb_nodes[RB_POSITION(standin)] = standin;
461 
462 	if (rebalance)
463 		__archive_rb_tree_removal_rebalance(rbt, standin_father, standin_which);
464 }
465 
466 /*
467  * We could do this by doing
468  *	__archive_rb_tree_node_swap(rbt, self, which);
469  *	__archive_rb_tree_prune_node(rbt, self, F);
470  *
471  * But it's more efficient to just evaluate and recolor the child.
472  */
473 static void
474 __archive_rb_tree_prune_blackred_branch(
475     struct archive_rb_node *self, unsigned int which)
476 {
477 	struct archive_rb_node *father = RB_FATHER(self);
478 	struct archive_rb_node *son = self->rb_nodes[which];
479 
480 	/*
481 	 * Remove ourselves from the tree and give our former child our
482 	 * properties (position, color, root).
483 	 */
484 	RB_COPY_PROPERTIES(son, self);
485 	father->rb_nodes[RB_POSITION(son)] = son;
486 	RB_SET_FATHER(son, father);
487 }
488 /*
489  *
490  */
491 void
492 __archive_rb_tree_remove_node(struct archive_rb_tree *rbt,
493     struct archive_rb_node *self)
494 {
495 	struct archive_rb_node *standin;
496 	unsigned int which;
497 
498 	/*
499 	 * In the following diagrams, we (the node to be removed) are S.  Red
500 	 * nodes are lowercase.  T could be either red or black.
501 	 *
502 	 * Remember the major axiom of the red-black tree: the number of
503 	 * black nodes from the root to each leaf is constant across all
504 	 * leaves, only the number of red nodes varies.
505 	 *
506 	 * Thus removing a red leaf doesn't require any other changes to a
507 	 * red-black tree.  So if we must remove a node, attempt to rearrange
508 	 * the tree so we can remove a red node.
509 	 *
510 	 * The simplest case is a childless red node or a childless root node:
511 	 *
512 	 * |    T  -->    T  |    or    |  R  -->  *  |
513 	 * |  s    -->  *    |
514 	 */
515 	if (RB_CHILDLESS_P(self)) {
516 		const int rebalance = RB_BLACK_P(self) && !RB_ROOT_P(rbt, self);
517 		__archive_rb_tree_prune_node(rbt, self, rebalance);
518 		return;
519 	}
520 	if (!RB_TWOCHILDREN_P(self)) {
521 		/*
522 		 * The next simplest case is the node we are deleting is
523 		 * black and has one red child.
524 		 *
525 		 * |      T  -->      T  -->      T  |
526 		 * |    S    -->  R      -->  R      |
527 		 * |  r      -->    s    -->    *    |
528 		 */
529 		which = RB_LEFT_SENTINEL_P(self) ? RB_DIR_RIGHT : RB_DIR_LEFT;
530 		__archive_rb_tree_prune_blackred_branch(self, which);
531 		return;
532 	}
533 
534 	/*
535 	 * We invert these because we prefer to remove from the inside of
536 	 * the tree.
537 	 */
538 	which = RB_POSITION(self) ^ RB_DIR_OTHER;
539 
540 	/*
541 	 * Let's find the node closes to us opposite of our parent
542 	 * Now swap it with ourself, "prune" it, and rebalance, if needed.
543 	 */
544 	standin = __archive_rb_tree_iterate(rbt, self, which);
545 	__archive_rb_tree_swap_prune_and_rebalance(rbt, self, standin);
546 }
547 
548 static void
549 __archive_rb_tree_removal_rebalance(struct archive_rb_tree *rbt,
550     struct archive_rb_node *parent, unsigned int which)
551 {
552 
553 	while (RB_BLACK_P(parent->rb_nodes[which])) {
554 		unsigned int other = which ^ RB_DIR_OTHER;
555 		struct archive_rb_node *brother = parent->rb_nodes[other];
556 
557 		if (brother == NULL)
558 			return;/* The tree may be broken. */
559 		/*
560 		 * For cases 1, 2a, and 2b, our brother's children must
561 		 * be black and our father must be black
562 		 */
563 		if (RB_BLACK_P(parent)
564 		    && RB_BLACK_P(brother->rb_left)
565 		    && RB_BLACK_P(brother->rb_right)) {
566 			if (RB_RED_P(brother)) {
567 				/*
568 				 * Case 1: Our brother is red, swap its
569 				 * position (and colors) with our parent.
570 				 * This should now be case 2b (unless C or E
571 				 * has a red child which is case 3; thus no
572 				 * explicit branch to case 2b).
573 				 *
574 				 *    B         ->        D
575 				 *  A     d     ->    b     E
576 				 *      C   E   ->  A   C
577 				 */
578 				__archive_rb_tree_reparent_nodes(parent, other);
579 				brother = parent->rb_nodes[other];
580 				if (brother == NULL)
581 					return;/* The tree may be broken. */
582 			} else {
583 				/*
584 				 * Both our parent and brother are black.
585 				 * Change our brother to red, advance up rank
586 				 * and go through the loop again.
587 				 *
588 				 *    B         ->   *B
589 				 * *A     D     ->  A     d
590 				 *      C   E   ->      C   E
591 				 */
592 				RB_MARK_RED(brother);
593 				if (RB_ROOT_P(rbt, parent))
594 					return;	/* root == parent == black */
595 				which = RB_POSITION(parent);
596 				parent = RB_FATHER(parent);
597 				continue;
598 			}
599 		}
600 		/*
601 		 * Avoid an else here so that case 2a above can hit either
602 		 * case 2b, 3, or 4.
603 		 */
604 		if (RB_RED_P(parent)
605 		    && RB_BLACK_P(brother)
606 		    && RB_BLACK_P(brother->rb_left)
607 		    && RB_BLACK_P(brother->rb_right)) {
608 			/*
609 			 * We are black, our father is red, our brother and
610 			 * both nephews are black.  Simply invert/exchange the
611 			 * colors of our father and brother (to black and red
612 			 * respectively).
613 			 *
614 			 *	|    f        -->    F        |
615 			 *	|  *     B    -->  *     b    |
616 			 *	|      N   N  -->      N   N  |
617 			 */
618 			RB_MARK_BLACK(parent);
619 			RB_MARK_RED(brother);
620 			break;		/* We're done! */
621 		} else {
622 			/*
623 			 * Our brother must be black and have at least one
624 			 * red child (it may have two).
625 			 */
626 			if (RB_BLACK_P(brother->rb_nodes[other])) {
627 				/*
628 				 * Case 3: our brother is black, our near
629 				 * nephew is red, and our far nephew is black.
630 				 * Swap our brother with our near nephew.
631 				 * This result in a tree that matches case 4.
632 				 * (Our father could be red or black).
633 				 *
634 				 *	|    F      -->    F      |
635 				 *	|  x     B  -->  x   B    |
636 				 *	|      n    -->        n  |
637 				 */
638 				__archive_rb_tree_reparent_nodes(brother, which);
639 				brother = parent->rb_nodes[other];
640 			}
641 			/*
642 			 * Case 4: our brother is black and our far nephew
643 			 * is red.  Swap our father and brother locations and
644 			 * change our far nephew to black.  (these can be
645 			 * done in either order so we change the color first).
646 			 * The result is a valid red-black tree and is a
647 			 * terminal case.  (again we don't care about the
648 			 * father's color)
649 			 *
650 			 * If the father is red, we will get a red-black-black
651 			 * tree:
652 			 *	|  f      ->  f      -->    b    |
653 			 *	|    B    ->    B    -->  F   N  |
654 			 *	|      n  ->      N  -->         |
655 			 *
656 			 * If the father is black, we will get an all black
657 			 * tree:
658 			 *	|  F      ->  F      -->    B    |
659 			 *	|    B    ->    B    -->  F   N  |
660 			 *	|      n  ->      N  -->         |
661 			 *
662 			 * If we had two red nephews, then after the swap,
663 			 * our former father would have a red grandson.
664 			 */
665 			if (brother->rb_nodes[other] == NULL)
666 				return;/* The tree may be broken. */
667 			RB_MARK_BLACK(brother->rb_nodes[other]);
668 			__archive_rb_tree_reparent_nodes(parent, other);
669 			break;		/* We're done! */
670 		}
671 	}
672 }
673 
674 struct archive_rb_node *
675 __archive_rb_tree_iterate(struct archive_rb_tree *rbt,
676     struct archive_rb_node *self, const unsigned int direction)
677 {
678 	const unsigned int other = direction ^ RB_DIR_OTHER;
679 
680 	if (self == NULL) {
681 		self = rbt->rbt_root;
682 		if (RB_SENTINEL_P(self))
683 			return NULL;
684 		while (!RB_SENTINEL_P(self->rb_nodes[direction]))
685 			self = self->rb_nodes[direction];
686 		return self;
687 	}
688 	/*
689 	 * We can't go any further in this direction.  We proceed up in the
690 	 * opposite direction until our parent is in direction we want to go.
691 	 */
692 	if (RB_SENTINEL_P(self->rb_nodes[direction])) {
693 		while (!RB_ROOT_P(rbt, self)) {
694 			if (other == (unsigned int)RB_POSITION(self))
695 				return RB_FATHER(self);
696 			self = RB_FATHER(self);
697 		}
698 		return NULL;
699 	}
700 
701 	/*
702 	 * Advance down one in current direction and go down as far as possible
703 	 * in the opposite direction.
704 	 */
705 	self = self->rb_nodes[direction];
706 	while (!RB_SENTINEL_P(self->rb_nodes[other]))
707 		self = self->rb_nodes[other];
708 	return self;
709 }
710