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