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