1 /*	$NetBSD: tree.h,v 1.20 2013/09/14 13:20:45 joerg Exp $	*/
2 /*	$OpenBSD: tree.h,v 1.13 2011/07/09 00:19:45 pirofti Exp $	*/
3 /*
4  * Copyright 2002 Niels Provos <provos@citi.umich.edu>
5  * All rights reserved.
6  *
7  * Redistribution and use in source and binary forms, with or without
8  * modification, are permitted provided that the following conditions
9  * are met:
10  * 1. Redistributions of source code must retain the above copyright
11  *    notice, this list of conditions and the following disclaimer.
12  * 2. Redistributions in binary form must reproduce the above copyright
13  *    notice, this list of conditions and the following disclaimer in the
14  *    documentation and/or other materials provided with the distribution.
15  *
16  * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
17  * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
18  * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
19  * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
20  * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
21  * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
22  * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
23  * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
24  * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
25  * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
26  */
27 
28 #ifndef	_SYS_TREE_H_
29 #define	_SYS_TREE_H_
30 
31 /*
32  * This file defines data structures for different types of trees:
33  * splay trees and red-black trees.
34  *
35  * A splay tree is a self-organizing data structure.  Every operation
36  * on the tree causes a splay to happen.  The splay moves the requested
37  * node to the root of the tree and partly rebalances it.
38  *
39  * This has the benefit that request locality causes faster lookups as
40  * the requested nodes move to the top of the tree.  On the other hand,
41  * every lookup causes memory writes.
42  *
43  * The Balance Theorem bounds the total access time for m operations
44  * and n inserts on an initially empty tree as O((m + n)lg n).  The
45  * amortized cost for a sequence of m accesses to a splay tree is O(lg n);
46  *
47  * A red-black tree is a binary search tree with the node color as an
48  * extra attribute.  It fulfills a set of conditions:
49  *	- every search path from the root to a leaf consists of the
50  *	  same number of black nodes,
51  *	- each red node (except for the root) has a black parent,
52  *	- each leaf node is black.
53  *
54  * Every operation on a red-black tree is bounded as O(lg n).
55  * The maximum height of a red-black tree is 2lg (n+1).
56  */
57 
58 #define SPLAY_HEAD(name, type)						\
59 struct name {								\
60 	struct type *sph_root; /* root of the tree */			\
61 }
62 
63 #define SPLAY_INITIALIZER(root)						\
64 	{ NULL }
65 
66 #define SPLAY_INIT(root) do {						\
67 	(root)->sph_root = NULL;					\
68 } while (/*CONSTCOND*/ 0)
69 
70 #define SPLAY_ENTRY(type)						\
71 struct {								\
72 	struct type *spe_left; /* left element */			\
73 	struct type *spe_right; /* right element */			\
74 }
75 
76 #define SPLAY_LEFT(elm, field)		(elm)->field.spe_left
77 #define SPLAY_RIGHT(elm, field)		(elm)->field.spe_right
78 #define SPLAY_ROOT(head)		(head)->sph_root
79 #define SPLAY_EMPTY(head)		(SPLAY_ROOT(head) == NULL)
80 
81 /* SPLAY_ROTATE_{LEFT,RIGHT} expect that tmp hold SPLAY_{RIGHT,LEFT} */
82 #define SPLAY_ROTATE_RIGHT(head, tmp, field) do {			\
83 	SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(tmp, field);	\
84 	SPLAY_RIGHT(tmp, field) = (head)->sph_root;			\
85 	(head)->sph_root = tmp;						\
86 } while (/*CONSTCOND*/ 0)
87 
88 #define SPLAY_ROTATE_LEFT(head, tmp, field) do {			\
89 	SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(tmp, field);	\
90 	SPLAY_LEFT(tmp, field) = (head)->sph_root;			\
91 	(head)->sph_root = tmp;						\
92 } while (/*CONSTCOND*/ 0)
93 
94 #define SPLAY_LINKLEFT(head, tmp, field) do {				\
95 	SPLAY_LEFT(tmp, field) = (head)->sph_root;			\
96 	tmp = (head)->sph_root;						\
97 	(head)->sph_root = SPLAY_LEFT((head)->sph_root, field);		\
98 } while (/*CONSTCOND*/ 0)
99 
100 #define SPLAY_LINKRIGHT(head, tmp, field) do {				\
101 	SPLAY_RIGHT(tmp, field) = (head)->sph_root;			\
102 	tmp = (head)->sph_root;						\
103 	(head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);	\
104 } while (/*CONSTCOND*/ 0)
105 
106 #define SPLAY_ASSEMBLE(head, node, left, right, field) do {		\
107 	SPLAY_RIGHT(left, field) = SPLAY_LEFT((head)->sph_root, field);	\
108 	SPLAY_LEFT(right, field) = SPLAY_RIGHT((head)->sph_root, field);\
109 	SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(node, field);	\
110 	SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(node, field);	\
111 } while (/*CONSTCOND*/ 0)
112 
113 /* Generates prototypes and inline functions */
114 
115 #define SPLAY_PROTOTYPE(name, type, field, cmp)				\
116 void name##_SPLAY(struct name *, struct type *);			\
117 void name##_SPLAY_MINMAX(struct name *, int);				\
118 struct type *name##_SPLAY_INSERT(struct name *, struct type *);		\
119 struct type *name##_SPLAY_REMOVE(struct name *, struct type *);		\
120 									\
121 /* Finds the node with the same key as elm */				\
122 static __inline struct type *						\
123 name##_SPLAY_FIND(struct name *head, struct type *elm)			\
124 {									\
125 	if (SPLAY_EMPTY(head))						\
126 		return(NULL);						\
127 	name##_SPLAY(head, elm);					\
128 	if ((cmp)(elm, (head)->sph_root) == 0)				\
129 		return (head->sph_root);				\
130 	return (NULL);							\
131 }									\
132 									\
133 static __inline __unused struct type *					\
134 name##_SPLAY_NEXT(struct name *head, struct type *elm)			\
135 {									\
136 	name##_SPLAY(head, elm);					\
137 	if (SPLAY_RIGHT(elm, field) != NULL) {				\
138 		elm = SPLAY_RIGHT(elm, field);				\
139 		while (SPLAY_LEFT(elm, field) != NULL) {		\
140 			elm = SPLAY_LEFT(elm, field);			\
141 		}							\
142 	} else								\
143 		elm = NULL;						\
144 	return (elm);							\
145 }									\
146 									\
147 static __unused __inline struct type *					\
148 name##_SPLAY_MIN_MAX(struct name *head, int val)			\
149 {									\
150 	name##_SPLAY_MINMAX(head, val);					\
151         return (SPLAY_ROOT(head));					\
152 }
153 
154 /* Main splay operation.
155  * Moves node close to the key of elm to top
156  */
157 #define SPLAY_GENERATE(name, type, field, cmp)				\
158 struct type *								\
159 name##_SPLAY_INSERT(struct name *head, struct type *elm)		\
160 {									\
161     if (SPLAY_EMPTY(head)) {						\
162 	    SPLAY_LEFT(elm, field) = SPLAY_RIGHT(elm, field) = NULL;	\
163     } else {								\
164 	    int __comp;							\
165 	    name##_SPLAY(head, elm);					\
166 	    __comp = (cmp)(elm, (head)->sph_root);			\
167 	    if(__comp < 0) {						\
168 		    SPLAY_LEFT(elm, field) = SPLAY_LEFT((head)->sph_root, field);\
169 		    SPLAY_RIGHT(elm, field) = (head)->sph_root;		\
170 		    SPLAY_LEFT((head)->sph_root, field) = NULL;		\
171 	    } else if (__comp > 0) {					\
172 		    SPLAY_RIGHT(elm, field) = SPLAY_RIGHT((head)->sph_root, field);\
173 		    SPLAY_LEFT(elm, field) = (head)->sph_root;		\
174 		    SPLAY_RIGHT((head)->sph_root, field) = NULL;	\
175 	    } else							\
176 		    return ((head)->sph_root);				\
177     }									\
178     (head)->sph_root = (elm);						\
179     return (NULL);							\
180 }									\
181 									\
182 struct type *								\
183 name##_SPLAY_REMOVE(struct name *head, struct type *elm)		\
184 {									\
185 	struct type *__tmp;						\
186 	if (SPLAY_EMPTY(head))						\
187 		return (NULL);						\
188 	name##_SPLAY(head, elm);					\
189 	if ((cmp)(elm, (head)->sph_root) == 0) {			\
190 		if (SPLAY_LEFT((head)->sph_root, field) == NULL) {	\
191 			(head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);\
192 		} else {						\
193 			__tmp = SPLAY_RIGHT((head)->sph_root, field);	\
194 			(head)->sph_root = SPLAY_LEFT((head)->sph_root, field);\
195 			name##_SPLAY(head, elm);			\
196 			SPLAY_RIGHT((head)->sph_root, field) = __tmp;	\
197 		}							\
198 		return (elm);						\
199 	}								\
200 	return (NULL);							\
201 }									\
202 									\
203 void									\
204 name##_SPLAY(struct name *head, struct type *elm)			\
205 {									\
206 	struct type __node, *__left, *__right, *__tmp;			\
207 	int __comp;							\
208 \
209 	SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
210 	__left = __right = &__node;					\
211 \
212 	while ((__comp = (cmp)(elm, (head)->sph_root)) != 0) {		\
213 		if (__comp < 0) {					\
214 			__tmp = SPLAY_LEFT((head)->sph_root, field);	\
215 			if (__tmp == NULL)				\
216 				break;					\
217 			if ((cmp)(elm, __tmp) < 0){			\
218 				SPLAY_ROTATE_RIGHT(head, __tmp, field);	\
219 				if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
220 					break;				\
221 			}						\
222 			SPLAY_LINKLEFT(head, __right, field);		\
223 		} else if (__comp > 0) {				\
224 			__tmp = SPLAY_RIGHT((head)->sph_root, field);	\
225 			if (__tmp == NULL)				\
226 				break;					\
227 			if ((cmp)(elm, __tmp) > 0){			\
228 				SPLAY_ROTATE_LEFT(head, __tmp, field);	\
229 				if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
230 					break;				\
231 			}						\
232 			SPLAY_LINKRIGHT(head, __left, field);		\
233 		}							\
234 	}								\
235 	SPLAY_ASSEMBLE(head, &__node, __left, __right, field);		\
236 }									\
237 									\
238 /* Splay with either the minimum or the maximum element			\
239  * Used to find minimum or maximum element in tree.			\
240  */									\
241 void name##_SPLAY_MINMAX(struct name *head, int __comp) \
242 {									\
243 	struct type __node, *__left, *__right, *__tmp;			\
244 \
245 	SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
246 	__left = __right = &__node;					\
247 \
248 	while (1) {							\
249 		if (__comp < 0) {					\
250 			__tmp = SPLAY_LEFT((head)->sph_root, field);	\
251 			if (__tmp == NULL)				\
252 				break;					\
253 			if (__comp < 0){				\
254 				SPLAY_ROTATE_RIGHT(head, __tmp, field);	\
255 				if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
256 					break;				\
257 			}						\
258 			SPLAY_LINKLEFT(head, __right, field);		\
259 		} else if (__comp > 0) {				\
260 			__tmp = SPLAY_RIGHT((head)->sph_root, field);	\
261 			if (__tmp == NULL)				\
262 				break;					\
263 			if (__comp > 0) {				\
264 				SPLAY_ROTATE_LEFT(head, __tmp, field);	\
265 				if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
266 					break;				\
267 			}						\
268 			SPLAY_LINKRIGHT(head, __left, field);		\
269 		}							\
270 	}								\
271 	SPLAY_ASSEMBLE(head, &__node, __left, __right, field);		\
272 }
273 
274 #define SPLAY_NEGINF	-1
275 #define SPLAY_INF	1
276 
277 #define SPLAY_INSERT(name, x, y)	name##_SPLAY_INSERT(x, y)
278 #define SPLAY_REMOVE(name, x, y)	name##_SPLAY_REMOVE(x, y)
279 #define SPLAY_FIND(name, x, y)		name##_SPLAY_FIND(x, y)
280 #define SPLAY_NEXT(name, x, y)		name##_SPLAY_NEXT(x, y)
281 #define SPLAY_MIN(name, x)		(SPLAY_EMPTY(x) ? NULL	\
282 					: name##_SPLAY_MIN_MAX(x, SPLAY_NEGINF))
283 #define SPLAY_MAX(name, x)		(SPLAY_EMPTY(x) ? NULL	\
284 					: name##_SPLAY_MIN_MAX(x, SPLAY_INF))
285 
286 #define SPLAY_FOREACH(x, name, head)					\
287 	for ((x) = SPLAY_MIN(name, head);				\
288 	     (x) != NULL;						\
289 	     (x) = SPLAY_NEXT(name, head, x))
290 
291 /* Macros that define a red-black tree */
292 #define RB_HEAD(name, type)						\
293 struct name {								\
294 	struct type *rbh_root; /* root of the tree */			\
295 }
296 
297 #define RB_INITIALIZER(root)						\
298 	{ NULL }
299 
300 #define RB_INIT(root) do {						\
301 	(root)->rbh_root = NULL;					\
302 } while (/*CONSTCOND*/ 0)
303 
304 #define RB_BLACK	0
305 #define RB_RED		1
306 #define RB_ENTRY(type)							\
307 struct {								\
308 	struct type *rbe_left;		/* left element */		\
309 	struct type *rbe_right;		/* right element */		\
310 	struct type *rbe_parent;	/* parent element */		\
311 	int rbe_color;			/* node color */		\
312 }
313 
314 #define RB_LEFT(elm, field)		(elm)->field.rbe_left
315 #define RB_RIGHT(elm, field)		(elm)->field.rbe_right
316 #define RB_PARENT(elm, field)		(elm)->field.rbe_parent
317 #define RB_COLOR(elm, field)		(elm)->field.rbe_color
318 #define RB_ROOT(head)			(head)->rbh_root
319 #define RB_EMPTY(head)			(RB_ROOT(head) == NULL)
320 
321 #define RB_SET(elm, parent, field) do {					\
322 	RB_PARENT(elm, field) = parent;					\
323 	RB_LEFT(elm, field) = RB_RIGHT(elm, field) = NULL;		\
324 	RB_COLOR(elm, field) = RB_RED;					\
325 } while (/*CONSTCOND*/ 0)
326 
327 #define RB_SET_BLACKRED(black, red, field) do {				\
328 	RB_COLOR(black, field) = RB_BLACK;				\
329 	RB_COLOR(red, field) = RB_RED;					\
330 } while (/*CONSTCOND*/ 0)
331 
332 #ifndef RB_AUGMENT
333 #define RB_AUGMENT(x)	do {} while (/*CONSTCOND*/ 0)
334 #endif
335 
336 #define RB_ROTATE_LEFT(head, elm, tmp, field) do {			\
337 	(tmp) = RB_RIGHT(elm, field);					\
338 	if ((RB_RIGHT(elm, field) = RB_LEFT(tmp, field)) != NULL) {	\
339 		RB_PARENT(RB_LEFT(tmp, field), field) = (elm);		\
340 	}								\
341 	RB_AUGMENT(elm);						\
342 	if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) {	\
343 		if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))	\
344 			RB_LEFT(RB_PARENT(elm, field), field) = (tmp);	\
345 		else							\
346 			RB_RIGHT(RB_PARENT(elm, field), field) = (tmp);	\
347 	} else								\
348 		(head)->rbh_root = (tmp);				\
349 	RB_LEFT(tmp, field) = (elm);					\
350 	RB_PARENT(elm, field) = (tmp);					\
351 	RB_AUGMENT(tmp);						\
352 	if ((RB_PARENT(tmp, field)))					\
353 		RB_AUGMENT(RB_PARENT(tmp, field));			\
354 } while (/*CONSTCOND*/ 0)
355 
356 #define RB_ROTATE_RIGHT(head, elm, tmp, field) do {			\
357 	(tmp) = RB_LEFT(elm, field);					\
358 	if ((RB_LEFT(elm, field) = RB_RIGHT(tmp, field)) != NULL) {	\
359 		RB_PARENT(RB_RIGHT(tmp, field), field) = (elm);		\
360 	}								\
361 	RB_AUGMENT(elm);						\
362 	if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) {	\
363 		if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))	\
364 			RB_LEFT(RB_PARENT(elm, field), field) = (tmp);	\
365 		else							\
366 			RB_RIGHT(RB_PARENT(elm, field), field) = (tmp);	\
367 	} else								\
368 		(head)->rbh_root = (tmp);				\
369 	RB_RIGHT(tmp, field) = (elm);					\
370 	RB_PARENT(elm, field) = (tmp);					\
371 	RB_AUGMENT(tmp);						\
372 	if ((RB_PARENT(tmp, field)))					\
373 		RB_AUGMENT(RB_PARENT(tmp, field));			\
374 } while (/*CONSTCOND*/ 0)
375 
376 /* Generates prototypes and inline functions */
377 #define RB_PROTOTYPE(name, type, field, cmp)				\
378 	RB_PROTOTYPE_INTERNAL(name, type, field, cmp,)
379 #define	RB_PROTOTYPE_STATIC(name, type, field, cmp)			\
380 	RB_PROTOTYPE_INTERNAL(name, type, field, cmp, __unused static)
381 #define RB_PROTOTYPE_INTERNAL(name, type, field, cmp, attr)		\
382 attr void name##_RB_INSERT_COLOR(struct name *, struct type *);		\
383 attr void name##_RB_REMOVE_COLOR(struct name *, struct type *, struct type *);\
384 attr struct type *name##_RB_REMOVE(struct name *, struct type *);	\
385 attr struct type *name##_RB_INSERT(struct name *, struct type *);	\
386 attr struct type *name##_RB_FIND(struct name *, struct type *);		\
387 attr struct type *name##_RB_NFIND(struct name *, struct type *);	\
388 attr struct type *name##_RB_NEXT(struct type *);			\
389 attr struct type *name##_RB_PREV(struct type *);			\
390 attr struct type *name##_RB_MINMAX(struct name *, int);			\
391 									\
392 
393 /* Main rb operation.
394  * Moves node close to the key of elm to top
395  */
396 #define	RB_GENERATE(name, type, field, cmp)				\
397 	RB_GENERATE_INTERNAL(name, type, field, cmp,)
398 #define	RB_GENERATE_STATIC(name, type, field, cmp)			\
399 	RB_GENERATE_INTERNAL(name, type, field, cmp, __unused static)
400 #define RB_GENERATE_INTERNAL(name, type, field, cmp, attr)		\
401 attr void								\
402 name##_RB_INSERT_COLOR(struct name *head, struct type *elm)		\
403 {									\
404 	struct type *parent, *gparent, *tmp;				\
405 	while ((parent = RB_PARENT(elm, field)) != NULL &&		\
406 	    RB_COLOR(parent, field) == RB_RED) {			\
407 		gparent = RB_PARENT(parent, field);			\
408 		if (parent == RB_LEFT(gparent, field)) {		\
409 			tmp = RB_RIGHT(gparent, field);			\
410 			if (tmp && RB_COLOR(tmp, field) == RB_RED) {	\
411 				RB_COLOR(tmp, field) = RB_BLACK;	\
412 				RB_SET_BLACKRED(parent, gparent, field);\
413 				elm = gparent;				\
414 				continue;				\
415 			}						\
416 			if (RB_RIGHT(parent, field) == elm) {		\
417 				RB_ROTATE_LEFT(head, parent, tmp, field);\
418 				tmp = parent;				\
419 				parent = elm;				\
420 				elm = tmp;				\
421 			}						\
422 			RB_SET_BLACKRED(parent, gparent, field);	\
423 			RB_ROTATE_RIGHT(head, gparent, tmp, field);	\
424 		} else {						\
425 			tmp = RB_LEFT(gparent, field);			\
426 			if (tmp && RB_COLOR(tmp, field) == RB_RED) {	\
427 				RB_COLOR(tmp, field) = RB_BLACK;	\
428 				RB_SET_BLACKRED(parent, gparent, field);\
429 				elm = gparent;				\
430 				continue;				\
431 			}						\
432 			if (RB_LEFT(parent, field) == elm) {		\
433 				RB_ROTATE_RIGHT(head, parent, tmp, field);\
434 				tmp = parent;				\
435 				parent = elm;				\
436 				elm = tmp;				\
437 			}						\
438 			RB_SET_BLACKRED(parent, gparent, field);	\
439 			RB_ROTATE_LEFT(head, gparent, tmp, field);	\
440 		}							\
441 	}								\
442 	RB_COLOR(head->rbh_root, field) = RB_BLACK;			\
443 }									\
444 									\
445 attr void								\
446 name##_RB_REMOVE_COLOR(struct name *head, struct type *parent, struct type *elm) \
447 {									\
448 	struct type *tmp;						\
449 	while ((elm == NULL || RB_COLOR(elm, field) == RB_BLACK) &&	\
450 	    elm != RB_ROOT(head)) {					\
451 		if (RB_LEFT(parent, field) == elm) {			\
452 			tmp = RB_RIGHT(parent, field);			\
453 			if (RB_COLOR(tmp, field) == RB_RED) {		\
454 				RB_SET_BLACKRED(tmp, parent, field);	\
455 				RB_ROTATE_LEFT(head, parent, tmp, field);\
456 				tmp = RB_RIGHT(parent, field);		\
457 			}						\
458 			if ((RB_LEFT(tmp, field) == NULL ||		\
459 			    RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
460 			    (RB_RIGHT(tmp, field) == NULL ||		\
461 			    RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
462 				RB_COLOR(tmp, field) = RB_RED;		\
463 				elm = parent;				\
464 				parent = RB_PARENT(elm, field);		\
465 			} else {					\
466 				if (RB_RIGHT(tmp, field) == NULL ||	\
467 				    RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK) {\
468 					struct type *oleft;		\
469 					if ((oleft = RB_LEFT(tmp, field)) \
470 					    != NULL)			\
471 						RB_COLOR(oleft, field) = RB_BLACK;\
472 					RB_COLOR(tmp, field) = RB_RED;	\
473 					RB_ROTATE_RIGHT(head, tmp, oleft, field);\
474 					tmp = RB_RIGHT(parent, field);	\
475 				}					\
476 				RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
477 				RB_COLOR(parent, field) = RB_BLACK;	\
478 				if (RB_RIGHT(tmp, field))		\
479 					RB_COLOR(RB_RIGHT(tmp, field), field) = RB_BLACK;\
480 				RB_ROTATE_LEFT(head, parent, tmp, field);\
481 				elm = RB_ROOT(head);			\
482 				break;					\
483 			}						\
484 		} else {						\
485 			tmp = RB_LEFT(parent, field);			\
486 			if (RB_COLOR(tmp, field) == RB_RED) {		\
487 				RB_SET_BLACKRED(tmp, parent, field);	\
488 				RB_ROTATE_RIGHT(head, parent, tmp, field);\
489 				tmp = RB_LEFT(parent, field);		\
490 			}						\
491 			if ((RB_LEFT(tmp, field) == NULL ||		\
492 			    RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
493 			    (RB_RIGHT(tmp, field) == NULL ||		\
494 			    RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
495 				RB_COLOR(tmp, field) = RB_RED;		\
496 				elm = parent;				\
497 				parent = RB_PARENT(elm, field);		\
498 			} else {					\
499 				if (RB_LEFT(tmp, field) == NULL ||	\
500 				    RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) {\
501 					struct type *oright;		\
502 					if ((oright = RB_RIGHT(tmp, field)) \
503 					    != NULL)			\
504 						RB_COLOR(oright, field) = RB_BLACK;\
505 					RB_COLOR(tmp, field) = RB_RED;	\
506 					RB_ROTATE_LEFT(head, tmp, oright, field);\
507 					tmp = RB_LEFT(parent, field);	\
508 				}					\
509 				RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
510 				RB_COLOR(parent, field) = RB_BLACK;	\
511 				if (RB_LEFT(tmp, field))		\
512 					RB_COLOR(RB_LEFT(tmp, field), field) = RB_BLACK;\
513 				RB_ROTATE_RIGHT(head, parent, tmp, field);\
514 				elm = RB_ROOT(head);			\
515 				break;					\
516 			}						\
517 		}							\
518 	}								\
519 	if (elm)							\
520 		RB_COLOR(elm, field) = RB_BLACK;			\
521 }									\
522 									\
523 attr struct type *							\
524 name##_RB_REMOVE(struct name *head, struct type *elm)			\
525 {									\
526 	struct type *child, *parent, *old = elm;			\
527 	int color;							\
528 	if (RB_LEFT(elm, field) == NULL)				\
529 		child = RB_RIGHT(elm, field);				\
530 	else if (RB_RIGHT(elm, field) == NULL)				\
531 		child = RB_LEFT(elm, field);				\
532 	else {								\
533 		struct type *left;					\
534 		elm = RB_RIGHT(elm, field);				\
535 		while ((left = RB_LEFT(elm, field)) != NULL)		\
536 			elm = left;					\
537 		child = RB_RIGHT(elm, field);				\
538 		parent = RB_PARENT(elm, field);				\
539 		color = RB_COLOR(elm, field);				\
540 		if (child)						\
541 			RB_PARENT(child, field) = parent;		\
542 		if (parent) {						\
543 			if (RB_LEFT(parent, field) == elm)		\
544 				RB_LEFT(parent, field) = child;		\
545 			else						\
546 				RB_RIGHT(parent, field) = child;	\
547 			RB_AUGMENT(parent);				\
548 		} else							\
549 			RB_ROOT(head) = child;				\
550 		if (RB_PARENT(elm, field) == old)			\
551 			parent = elm;					\
552 		(elm)->field = (old)->field;				\
553 		if (RB_PARENT(old, field)) {				\
554 			if (RB_LEFT(RB_PARENT(old, field), field) == old)\
555 				RB_LEFT(RB_PARENT(old, field), field) = elm;\
556 			else						\
557 				RB_RIGHT(RB_PARENT(old, field), field) = elm;\
558 			RB_AUGMENT(RB_PARENT(old, field));		\
559 		} else							\
560 			RB_ROOT(head) = elm;				\
561 		RB_PARENT(RB_LEFT(old, field), field) = elm;		\
562 		if (RB_RIGHT(old, field))				\
563 			RB_PARENT(RB_RIGHT(old, field), field) = elm;	\
564 		if (parent) {						\
565 			left = parent;					\
566 			do {						\
567 				RB_AUGMENT(left);			\
568 			} while ((left = RB_PARENT(left, field)) != NULL); \
569 		}							\
570 		goto color;						\
571 	}								\
572 	parent = RB_PARENT(elm, field);					\
573 	color = RB_COLOR(elm, field);					\
574 	if (child)							\
575 		RB_PARENT(child, field) = parent;			\
576 	if (parent) {							\
577 		if (RB_LEFT(parent, field) == elm)			\
578 			RB_LEFT(parent, field) = child;			\
579 		else							\
580 			RB_RIGHT(parent, field) = child;		\
581 		RB_AUGMENT(parent);					\
582 	} else								\
583 		RB_ROOT(head) = child;					\
584 color:									\
585 	if (color == RB_BLACK)						\
586 		name##_RB_REMOVE_COLOR(head, parent, child);		\
587 	return (old);							\
588 }									\
589 									\
590 /* Inserts a node into the RB tree */					\
591 attr struct type *							\
592 name##_RB_INSERT(struct name *head, struct type *elm)			\
593 {									\
594 	struct type *tmp;						\
595 	struct type *parent = NULL;					\
596 	int comp = 0;							\
597 	tmp = RB_ROOT(head);						\
598 	while (tmp) {							\
599 		parent = tmp;						\
600 		comp = (cmp)(elm, parent);				\
601 		if (comp < 0)						\
602 			tmp = RB_LEFT(tmp, field);			\
603 		else if (comp > 0)					\
604 			tmp = RB_RIGHT(tmp, field);			\
605 		else							\
606 			return (tmp);					\
607 	}								\
608 	RB_SET(elm, parent, field);					\
609 	if (parent != NULL) {						\
610 		if (comp < 0)						\
611 			RB_LEFT(parent, field) = elm;			\
612 		else							\
613 			RB_RIGHT(parent, field) = elm;			\
614 		RB_AUGMENT(parent);					\
615 	} else								\
616 		RB_ROOT(head) = elm;					\
617 	name##_RB_INSERT_COLOR(head, elm);				\
618 	return (NULL);							\
619 }									\
620 									\
621 /* Finds the node with the same key as elm */				\
622 attr struct type *							\
623 name##_RB_FIND(struct name *head, struct type *elm)			\
624 {									\
625 	struct type *tmp = RB_ROOT(head);				\
626 	int comp;							\
627 	while (tmp) {							\
628 		comp = cmp(elm, tmp);					\
629 		if (comp < 0)						\
630 			tmp = RB_LEFT(tmp, field);			\
631 		else if (comp > 0)					\
632 			tmp = RB_RIGHT(tmp, field);			\
633 		else							\
634 			return (tmp);					\
635 	}								\
636 	return (NULL);							\
637 }									\
638 									\
639 /* Finds the first node greater than or equal to the search key */	\
640 attr struct type *							\
641 name##_RB_NFIND(struct name *head, struct type *elm)			\
642 {									\
643 	struct type *tmp = RB_ROOT(head);				\
644 	struct type *res = NULL;					\
645 	int comp;							\
646 	while (tmp) {							\
647 		comp = cmp(elm, tmp);					\
648 		if (comp < 0) {						\
649 			res = tmp;					\
650 			tmp = RB_LEFT(tmp, field);			\
651 		}							\
652 		else if (comp > 0)					\
653 			tmp = RB_RIGHT(tmp, field);			\
654 		else							\
655 			return (tmp);					\
656 	}								\
657 	return (res);							\
658 }									\
659 									\
660 /* ARGSUSED */								\
661 attr struct type *							\
662 name##_RB_NEXT(struct type *elm)					\
663 {									\
664 	if (RB_RIGHT(elm, field)) {					\
665 		elm = RB_RIGHT(elm, field);				\
666 		while (RB_LEFT(elm, field))				\
667 			elm = RB_LEFT(elm, field);			\
668 	} else {							\
669 		if (RB_PARENT(elm, field) &&				\
670 		    (elm == RB_LEFT(RB_PARENT(elm, field), field)))	\
671 			elm = RB_PARENT(elm, field);			\
672 		else {							\
673 			while (RB_PARENT(elm, field) &&			\
674 			    (elm == RB_RIGHT(RB_PARENT(elm, field), field)))\
675 				elm = RB_PARENT(elm, field);		\
676 			elm = RB_PARENT(elm, field);			\
677 		}							\
678 	}								\
679 	return (elm);							\
680 }									\
681 									\
682 /* ARGSUSED */								\
683 attr struct type *							\
684 name##_RB_PREV(struct type *elm)					\
685 {									\
686 	if (RB_LEFT(elm, field)) {					\
687 		elm = RB_LEFT(elm, field);				\
688 		while (RB_RIGHT(elm, field))				\
689 			elm = RB_RIGHT(elm, field);			\
690 	} else {							\
691 		if (RB_PARENT(elm, field) &&				\
692 		    (elm == RB_RIGHT(RB_PARENT(elm, field), field)))	\
693 			elm = RB_PARENT(elm, field);			\
694 		else {							\
695 			while (RB_PARENT(elm, field) &&			\
696 			    (elm == RB_LEFT(RB_PARENT(elm, field), field)))\
697 				elm = RB_PARENT(elm, field);		\
698 			elm = RB_PARENT(elm, field);			\
699 		}							\
700 	}								\
701 	return (elm);							\
702 }									\
703 									\
704 attr struct type *							\
705 name##_RB_MINMAX(struct name *head, int val)				\
706 {									\
707 	struct type *tmp = RB_ROOT(head);				\
708 	struct type *parent = NULL;					\
709 	while (tmp) {							\
710 		parent = tmp;						\
711 		if (val < 0)						\
712 			tmp = RB_LEFT(tmp, field);			\
713 		else							\
714 			tmp = RB_RIGHT(tmp, field);			\
715 	}								\
716 	return (parent);						\
717 }
718 
719 #define RB_NEGINF	-1
720 #define RB_INF	1
721 
722 #define RB_INSERT(name, x, y)	name##_RB_INSERT(x, y)
723 #define RB_REMOVE(name, x, y)	name##_RB_REMOVE(x, y)
724 #define RB_FIND(name, x, y)	name##_RB_FIND(x, y)
725 #define RB_NFIND(name, x, y)	name##_RB_NFIND(x, y)
726 #define RB_NEXT(name, x, y)	name##_RB_NEXT(y)
727 #define RB_PREV(name, x, y)	name##_RB_PREV(y)
728 #define RB_MIN(name, x)		name##_RB_MINMAX(x, RB_NEGINF)
729 #define RB_MAX(name, x)		name##_RB_MINMAX(x, RB_INF)
730 
731 #define RB_FOREACH(x, name, head)					\
732 	for ((x) = RB_MIN(name, head);					\
733 	     (x) != NULL;						\
734 	     (x) = name##_RB_NEXT(x))
735 
736 #define RB_FOREACH_FROM(x, name, y)					\
737 	for ((x) = (y);							\
738 	    ((x) != NULL) && ((y) = name##_RB_NEXT(x), (x) != NULL);	\
739 	     (x) = (y))
740 
741 #define RB_FOREACH_SAFE(x, name, head, y)				\
742 	for ((x) = RB_MIN(name, head);					\
743 	    ((x) != NULL) && ((y) = name##_RB_NEXT(x), (x) != NULL);	\
744 	     (x) = (y))
745 
746 #define RB_FOREACH_REVERSE(x, name, head)				\
747 	for ((x) = RB_MAX(name, head);					\
748 	     (x) != NULL;						\
749 	     (x) = name##_RB_PREV(x))
750 
751 #define RB_FOREACH_REVERSE_FROM(x, name, y)				\
752 	for ((x) = (y);							\
753 	    ((x) != NULL) && ((y) = name##_RB_PREV(x), (x) != NULL);	\
754 	     (x) = (y))
755 
756 #define RB_FOREACH_REVERSE_SAFE(x, name, head, y)			\
757 	for ((x) = RB_MAX(name, head);					\
758 	    ((x) != NULL) && ((y) = name##_RB_PREV(x), (x) != NULL);	\
759 	     (x) = (y))
760 
761 #endif	/* _SYS_TREE_H_ */
762