xref: /illumos-gate/usr/src/contrib/bhyve/sys/tree.h (revision d0b3c59b)
1 /*	$NetBSD: tree.h,v 1.8 2004/03/28 19:38:30 provos Exp $	*/
2 /*	$OpenBSD: tree.h,v 1.7 2002/10/17 21:51:54 art Exp $	*/
3 /* $FreeBSD: head/sys/sys/tree.h 189204 2009-03-01 04:57:23Z bms $ */
4 
5 /*-
6  * Copyright 2002 Niels Provos <provos@citi.umich.edu>
7  * All rights reserved.
8  *
9  * Redistribution and use in source and binary forms, with or without
10  * modification, are permitted provided that the following conditions
11  * are met:
12  * 1. Redistributions of source code must retain the above copyright
13  *    notice, this list of conditions and the following disclaimer.
14  * 2. Redistributions in binary form must reproduce the above copyright
15  *    notice, this list of conditions and the following disclaimer in the
16  *    documentation and/or other materials provided with the distribution.
17  *
18  * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
19  * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
20  * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
21  * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
22  * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
23  * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
24  * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
25  * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
26  * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
27  * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
28  */
29 
30 #ifndef	_SYS_TREE_H_
31 #define	_SYS_TREE_H_
32 
33 #include <sys/cdefs.h>
34 
35 /*
36  * This file defines data structures for different types of trees:
37  * splay trees and red-black trees.
38  *
39  * A splay tree is a self-organizing data structure.  Every operation
40  * on the tree causes a splay to happen.  The splay moves the requested
41  * node to the root of the tree and partly rebalances it.
42  *
43  * This has the benefit that request locality causes faster lookups as
44  * the requested nodes move to the top of the tree.  On the other hand,
45  * every lookup causes memory writes.
46  *
47  * The Balance Theorem bounds the total access time for m operations
48  * and n inserts on an initially empty tree as O((m + n)lg n).  The
49  * amortized cost for a sequence of m accesses to a splay tree is O(lg n);
50  *
51  * A red-black tree is a binary search tree with the node color as an
52  * extra attribute.  It fulfills a set of conditions:
53  *	- every search path from the root to a leaf consists of the
54  *	  same number of black nodes,
55  *	- each red node (except for the root) has a black parent,
56  *	- each leaf node is black.
57  *
58  * Every operation on a red-black tree is bounded as O(lg n).
59  * The maximum height of a red-black tree is 2lg (n+1).
60  */
61 
62 #define SPLAY_HEAD(name, type)						\
63 struct name {								\
64 	struct type *sph_root; /* root of the tree */			\
65 }
66 
67 #define SPLAY_INITIALIZER(root)						\
68 	{ NULL }
69 
70 #define SPLAY_INIT(root) do {						\
71 	(root)->sph_root = NULL;					\
72 } while (/*CONSTCOND*/ 0)
73 
74 #define SPLAY_ENTRY(type)						\
75 struct {								\
76 	struct type *spe_left; /* left element */			\
77 	struct type *spe_right; /* right element */			\
78 }
79 
80 #define SPLAY_LEFT(elm, field)		(elm)->field.spe_left
81 #define SPLAY_RIGHT(elm, field)		(elm)->field.spe_right
82 #define SPLAY_ROOT(head)		(head)->sph_root
83 #define SPLAY_EMPTY(head)		(SPLAY_ROOT(head) == NULL)
84 
85 /* SPLAY_ROTATE_{LEFT,RIGHT} expect that tmp hold SPLAY_{RIGHT,LEFT} */
86 #define SPLAY_ROTATE_RIGHT(head, tmp, field) do {			\
87 	SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(tmp, field);	\
88 	SPLAY_RIGHT(tmp, field) = (head)->sph_root;			\
89 	(head)->sph_root = tmp;						\
90 } while (/*CONSTCOND*/ 0)
91 
92 #define SPLAY_ROTATE_LEFT(head, tmp, field) do {			\
93 	SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(tmp, field);	\
94 	SPLAY_LEFT(tmp, field) = (head)->sph_root;			\
95 	(head)->sph_root = tmp;						\
96 } while (/*CONSTCOND*/ 0)
97 
98 #define SPLAY_LINKLEFT(head, tmp, field) do {				\
99 	SPLAY_LEFT(tmp, field) = (head)->sph_root;			\
100 	tmp = (head)->sph_root;						\
101 	(head)->sph_root = SPLAY_LEFT((head)->sph_root, field);		\
102 } while (/*CONSTCOND*/ 0)
103 
104 #define SPLAY_LINKRIGHT(head, tmp, field) do {				\
105 	SPLAY_RIGHT(tmp, field) = (head)->sph_root;			\
106 	tmp = (head)->sph_root;						\
107 	(head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);	\
108 } while (/*CONSTCOND*/ 0)
109 
110 #define SPLAY_ASSEMBLE(head, node, left, right, field) do {		\
111 	SPLAY_RIGHT(left, field) = SPLAY_LEFT((head)->sph_root, field);	\
112 	SPLAY_LEFT(right, field) = SPLAY_RIGHT((head)->sph_root, field);\
113 	SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(node, field);	\
114 	SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(node, field);	\
115 } while (/*CONSTCOND*/ 0)
116 
117 /* Generates prototypes and inline functions */
118 
119 #define SPLAY_PROTOTYPE(name, type, field, cmp)				\
120 void name##_SPLAY(struct name *, struct type *);			\
121 void name##_SPLAY_MINMAX(struct name *, int);				\
122 struct type *name##_SPLAY_INSERT(struct name *, struct type *);		\
123 struct type *name##_SPLAY_REMOVE(struct name *, struct type *);		\
124 									\
125 /* Finds the node with the same key as elm */				\
126 static __inline struct type *						\
127 name##_SPLAY_FIND(struct name *head, struct type *elm)			\
128 {									\
129 	if (SPLAY_EMPTY(head))						\
130 		return(NULL);						\
131 	name##_SPLAY(head, elm);					\
132 	if ((cmp)(elm, (head)->sph_root) == 0)				\
133 		return (head->sph_root);				\
134 	return (NULL);							\
135 }									\
136 									\
137 static __inline struct type *						\
138 name##_SPLAY_NEXT(struct name *head, struct type *elm)			\
139 {									\
140 	name##_SPLAY(head, elm);					\
141 	if (SPLAY_RIGHT(elm, field) != NULL) {				\
142 		elm = SPLAY_RIGHT(elm, field);				\
143 		while (SPLAY_LEFT(elm, field) != NULL) {		\
144 			elm = SPLAY_LEFT(elm, field);			\
145 		}							\
146 	} else								\
147 		elm = NULL;						\
148 	return (elm);							\
149 }									\
150 									\
151 static __inline struct type *						\
152 name##_SPLAY_MIN_MAX(struct name *head, int val)			\
153 {									\
154 	name##_SPLAY_MINMAX(head, val);					\
155         return (SPLAY_ROOT(head));					\
156 }
157 
158 /* Main splay operation.
159  * Moves node close to the key of elm to top
160  */
161 #define SPLAY_GENERATE(name, type, field, cmp)				\
162 struct type *								\
163 name##_SPLAY_INSERT(struct name *head, struct type *elm)		\
164 {									\
165     if (SPLAY_EMPTY(head)) {						\
166 	    SPLAY_LEFT(elm, field) = SPLAY_RIGHT(elm, field) = NULL;	\
167     } else {								\
168 	    int __comp;							\
169 	    name##_SPLAY(head, elm);					\
170 	    __comp = (cmp)(elm, (head)->sph_root);			\
171 	    if(__comp < 0) {						\
172 		    SPLAY_LEFT(elm, field) = SPLAY_LEFT((head)->sph_root, field);\
173 		    SPLAY_RIGHT(elm, field) = (head)->sph_root;		\
174 		    SPLAY_LEFT((head)->sph_root, field) = NULL;		\
175 	    } else if (__comp > 0) {					\
176 		    SPLAY_RIGHT(elm, field) = SPLAY_RIGHT((head)->sph_root, field);\
177 		    SPLAY_LEFT(elm, field) = (head)->sph_root;		\
178 		    SPLAY_RIGHT((head)->sph_root, field) = NULL;	\
179 	    } else							\
180 		    return ((head)->sph_root);				\
181     }									\
182     (head)->sph_root = (elm);						\
183     return (NULL);							\
184 }									\
185 									\
186 struct type *								\
187 name##_SPLAY_REMOVE(struct name *head, struct type *elm)		\
188 {									\
189 	struct type *__tmp;						\
190 	if (SPLAY_EMPTY(head))						\
191 		return (NULL);						\
192 	name##_SPLAY(head, elm);					\
193 	if ((cmp)(elm, (head)->sph_root) == 0) {			\
194 		if (SPLAY_LEFT((head)->sph_root, field) == NULL) {	\
195 			(head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);\
196 		} else {						\
197 			__tmp = SPLAY_RIGHT((head)->sph_root, field);	\
198 			(head)->sph_root = SPLAY_LEFT((head)->sph_root, field);\
199 			name##_SPLAY(head, elm);			\
200 			SPLAY_RIGHT((head)->sph_root, field) = __tmp;	\
201 		}							\
202 		return (elm);						\
203 	}								\
204 	return (NULL);							\
205 }									\
206 									\
207 void									\
208 name##_SPLAY(struct name *head, struct type *elm)			\
209 {									\
210 	struct type __node, *__left, *__right, *__tmp;			\
211 	int __comp;							\
212 \
213 	SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
214 	__left = __right = &__node;					\
215 \
216 	while ((__comp = (cmp)(elm, (head)->sph_root)) != 0) {		\
217 		if (__comp < 0) {					\
218 			__tmp = SPLAY_LEFT((head)->sph_root, field);	\
219 			if (__tmp == NULL)				\
220 				break;					\
221 			if ((cmp)(elm, __tmp) < 0){			\
222 				SPLAY_ROTATE_RIGHT(head, __tmp, field);	\
223 				if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
224 					break;				\
225 			}						\
226 			SPLAY_LINKLEFT(head, __right, field);		\
227 		} else if (__comp > 0) {				\
228 			__tmp = SPLAY_RIGHT((head)->sph_root, field);	\
229 			if (__tmp == NULL)				\
230 				break;					\
231 			if ((cmp)(elm, __tmp) > 0){			\
232 				SPLAY_ROTATE_LEFT(head, __tmp, field);	\
233 				if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
234 					break;				\
235 			}						\
236 			SPLAY_LINKRIGHT(head, __left, field);		\
237 		}							\
238 	}								\
239 	SPLAY_ASSEMBLE(head, &__node, __left, __right, field);		\
240 }									\
241 									\
242 /* Splay with either the minimum or the maximum element			\
243  * Used to find minimum or maximum element in tree.			\
244  */									\
245 void name##_SPLAY_MINMAX(struct name *head, int __comp) \
246 {									\
247 	struct type __node, *__left, *__right, *__tmp;			\
248 \
249 	SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
250 	__left = __right = &__node;					\
251 \
252 	while (1) {							\
253 		if (__comp < 0) {					\
254 			__tmp = SPLAY_LEFT((head)->sph_root, field);	\
255 			if (__tmp == NULL)				\
256 				break;					\
257 			if (__comp < 0){				\
258 				SPLAY_ROTATE_RIGHT(head, __tmp, field);	\
259 				if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
260 					break;				\
261 			}						\
262 			SPLAY_LINKLEFT(head, __right, field);		\
263 		} else if (__comp > 0) {				\
264 			__tmp = SPLAY_RIGHT((head)->sph_root, field);	\
265 			if (__tmp == NULL)				\
266 				break;					\
267 			if (__comp > 0) {				\
268 				SPLAY_ROTATE_LEFT(head, __tmp, field);	\
269 				if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
270 					break;				\
271 			}						\
272 			SPLAY_LINKRIGHT(head, __left, field);		\
273 		}							\
274 	}								\
275 	SPLAY_ASSEMBLE(head, &__node, __left, __right, field);		\
276 }
277 
278 #define SPLAY_NEGINF	-1
279 #define SPLAY_INF	1
280 
281 #define SPLAY_INSERT(name, x, y)	name##_SPLAY_INSERT(x, y)
282 #define SPLAY_REMOVE(name, x, y)	name##_SPLAY_REMOVE(x, y)
283 #define SPLAY_FIND(name, x, y)		name##_SPLAY_FIND(x, y)
284 #define SPLAY_NEXT(name, x, y)		name##_SPLAY_NEXT(x, y)
285 #define SPLAY_MIN(name, x)		(SPLAY_EMPTY(x) ? NULL	\
286 					: name##_SPLAY_MIN_MAX(x, SPLAY_NEGINF))
287 #define SPLAY_MAX(name, x)		(SPLAY_EMPTY(x) ? NULL	\
288 					: name##_SPLAY_MIN_MAX(x, SPLAY_INF))
289 
290 #define SPLAY_FOREACH(x, name, head)					\
291 	for ((x) = SPLAY_MIN(name, head);				\
292 	     (x) != NULL;						\
293 	     (x) = SPLAY_NEXT(name, head, x))
294 
295 /* Macros that define a red-black tree */
296 #define RB_HEAD(name, type)						\
297 struct name {								\
298 	struct type *rbh_root; /* root of the tree */			\
299 }
300 
301 #define RB_INITIALIZER(root)						\
302 	{ NULL }
303 
304 #define RB_INIT(root) do {						\
305 	(root)->rbh_root = NULL;					\
306 } while (/*CONSTCOND*/ 0)
307 
308 #define RB_BLACK	0
309 #define RB_RED		1
310 #define RB_ENTRY(type)							\
311 struct {								\
312 	struct type *rbe_left;		/* left element */		\
313 	struct type *rbe_right;		/* right element */		\
314 	struct type *rbe_parent;	/* parent element */		\
315 	int rbe_color;			/* node color */		\
316 }
317 
318 #define RB_LEFT(elm, field)		(elm)->field.rbe_left
319 #define RB_RIGHT(elm, field)		(elm)->field.rbe_right
320 #define RB_PARENT(elm, field)		(elm)->field.rbe_parent
321 #define RB_COLOR(elm, field)		(elm)->field.rbe_color
322 #define RB_ROOT(head)			(head)->rbh_root
323 #define RB_EMPTY(head)			(RB_ROOT(head) == NULL)
324 
325 #define RB_SET(elm, parent, field) do {					\
326 	RB_PARENT(elm, field) = parent;					\
327 	RB_LEFT(elm, field) = RB_RIGHT(elm, field) = NULL;		\
328 	RB_COLOR(elm, field) = RB_RED;					\
329 } while (/*CONSTCOND*/ 0)
330 
331 #define RB_SET_BLACKRED(black, red, field) do {				\
332 	RB_COLOR(black, field) = RB_BLACK;				\
333 	RB_COLOR(red, field) = RB_RED;					\
334 } while (/*CONSTCOND*/ 0)
335 
336 #ifndef RB_AUGMENT
337 #define RB_AUGMENT(x)	do {} while (0)
338 #endif
339 
340 #define RB_ROTATE_LEFT(head, elm, tmp, field) do {			\
341 	(tmp) = RB_RIGHT(elm, field);					\
342 	if ((RB_RIGHT(elm, field) = RB_LEFT(tmp, field)) != NULL) {	\
343 		RB_PARENT(RB_LEFT(tmp, field), field) = (elm);		\
344 	}								\
345 	RB_AUGMENT(elm);						\
346 	if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) {	\
347 		if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))	\
348 			RB_LEFT(RB_PARENT(elm, field), field) = (tmp);	\
349 		else							\
350 			RB_RIGHT(RB_PARENT(elm, field), field) = (tmp);	\
351 	} else								\
352 		(head)->rbh_root = (tmp);				\
353 	RB_LEFT(tmp, field) = (elm);					\
354 	RB_PARENT(elm, field) = (tmp);					\
355 	RB_AUGMENT(tmp);						\
356 	if ((RB_PARENT(tmp, field)))					\
357 		RB_AUGMENT(RB_PARENT(tmp, field));			\
358 } while (/*CONSTCOND*/ 0)
359 
360 #define RB_ROTATE_RIGHT(head, elm, tmp, field) do {			\
361 	(tmp) = RB_LEFT(elm, field);					\
362 	if ((RB_LEFT(elm, field) = RB_RIGHT(tmp, field)) != NULL) {	\
363 		RB_PARENT(RB_RIGHT(tmp, field), field) = (elm);		\
364 	}								\
365 	RB_AUGMENT(elm);						\
366 	if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) {	\
367 		if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))	\
368 			RB_LEFT(RB_PARENT(elm, field), field) = (tmp);	\
369 		else							\
370 			RB_RIGHT(RB_PARENT(elm, field), field) = (tmp);	\
371 	} else								\
372 		(head)->rbh_root = (tmp);				\
373 	RB_RIGHT(tmp, field) = (elm);					\
374 	RB_PARENT(elm, field) = (tmp);					\
375 	RB_AUGMENT(tmp);						\
376 	if ((RB_PARENT(tmp, field)))					\
377 		RB_AUGMENT(RB_PARENT(tmp, field));			\
378 } while (/*CONSTCOND*/ 0)
379 
380 /* Generates prototypes and inline functions */
381 #define	RB_PROTOTYPE(name, type, field, cmp)				\
382 	RB_PROTOTYPE_INTERNAL(name, type, field, cmp,)
383 #define	RB_PROTOTYPE_STATIC(name, type, field, cmp)			\
384 	RB_PROTOTYPE_INTERNAL(name, type, field, cmp, __unused static)
385 #define RB_PROTOTYPE_INTERNAL(name, type, field, cmp, attr)		\
386 attr void name##_RB_INSERT_COLOR(struct name *, struct type *);		\
387 attr void name##_RB_REMOVE_COLOR(struct name *, struct type *, struct type *);\
388 attr struct type *name##_RB_REMOVE(struct name *, struct type *);	\
389 attr struct type *name##_RB_INSERT(struct name *, struct type *);	\
390 attr struct type *name##_RB_FIND(struct name *, struct type *);		\
391 attr struct type *name##_RB_NFIND(struct name *, struct type *);	\
392 attr struct type *name##_RB_NEXT(struct type *);			\
393 attr struct type *name##_RB_PREV(struct type *);			\
394 attr struct type *name##_RB_MINMAX(struct name *, int);			\
395 									\
396 
397 /* Main rb operation.
398  * Moves node close to the key of elm to top
399  */
400 #define	RB_GENERATE(name, type, field, cmp)				\
401 	RB_GENERATE_INTERNAL(name, type, field, cmp,)
402 #define	RB_GENERATE_STATIC(name, type, field, cmp)			\
403 	RB_GENERATE_INTERNAL(name, type, field, cmp, __unused static)
404 #define RB_GENERATE_INTERNAL(name, type, field, cmp, attr)		\
405 attr void								\
406 name##_RB_INSERT_COLOR(struct name *head, struct type *elm)		\
407 {									\
408 	struct type *parent, *gparent, *tmp;				\
409 	while ((parent = RB_PARENT(elm, field)) != NULL &&		\
410 	    RB_COLOR(parent, field) == RB_RED) {			\
411 		gparent = RB_PARENT(parent, field);			\
412 		if (parent == RB_LEFT(gparent, field)) {		\
413 			tmp = RB_RIGHT(gparent, field);			\
414 			if (tmp && RB_COLOR(tmp, field) == RB_RED) {	\
415 				RB_COLOR(tmp, field) = RB_BLACK;	\
416 				RB_SET_BLACKRED(parent, gparent, field);\
417 				elm = gparent;				\
418 				continue;				\
419 			}						\
420 			if (RB_RIGHT(parent, field) == elm) {		\
421 				RB_ROTATE_LEFT(head, parent, tmp, field);\
422 				tmp = parent;				\
423 				parent = elm;				\
424 				elm = tmp;				\
425 			}						\
426 			RB_SET_BLACKRED(parent, gparent, field);	\
427 			RB_ROTATE_RIGHT(head, gparent, tmp, field);	\
428 		} else {						\
429 			tmp = RB_LEFT(gparent, field);			\
430 			if (tmp && RB_COLOR(tmp, field) == RB_RED) {	\
431 				RB_COLOR(tmp, field) = RB_BLACK;	\
432 				RB_SET_BLACKRED(parent, gparent, field);\
433 				elm = gparent;				\
434 				continue;				\
435 			}						\
436 			if (RB_LEFT(parent, field) == elm) {		\
437 				RB_ROTATE_RIGHT(head, parent, tmp, field);\
438 				tmp = parent;				\
439 				parent = elm;				\
440 				elm = tmp;				\
441 			}						\
442 			RB_SET_BLACKRED(parent, gparent, field);	\
443 			RB_ROTATE_LEFT(head, gparent, tmp, field);	\
444 		}							\
445 	}								\
446 	RB_COLOR(head->rbh_root, field) = RB_BLACK;			\
447 }									\
448 									\
449 attr void								\
450 name##_RB_REMOVE_COLOR(struct name *head, struct type *parent, struct type *elm) \
451 {									\
452 	struct type *tmp;						\
453 	while ((elm == NULL || RB_COLOR(elm, field) == RB_BLACK) &&	\
454 	    elm != RB_ROOT(head)) {					\
455 		if (RB_LEFT(parent, field) == elm) {			\
456 			tmp = RB_RIGHT(parent, field);			\
457 			if (RB_COLOR(tmp, field) == RB_RED) {		\
458 				RB_SET_BLACKRED(tmp, parent, field);	\
459 				RB_ROTATE_LEFT(head, parent, tmp, field);\
460 				tmp = RB_RIGHT(parent, field);		\
461 			}						\
462 			if ((RB_LEFT(tmp, field) == NULL ||		\
463 			    RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
464 			    (RB_RIGHT(tmp, field) == NULL ||		\
465 			    RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
466 				RB_COLOR(tmp, field) = RB_RED;		\
467 				elm = parent;				\
468 				parent = RB_PARENT(elm, field);		\
469 			} else {					\
470 				if (RB_RIGHT(tmp, field) == NULL ||	\
471 				    RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK) {\
472 					struct type *oleft;		\
473 					if ((oleft = RB_LEFT(tmp, field)) \
474 					    != NULL)			\
475 						RB_COLOR(oleft, field) = RB_BLACK;\
476 					RB_COLOR(tmp, field) = RB_RED;	\
477 					RB_ROTATE_RIGHT(head, tmp, oleft, field);\
478 					tmp = RB_RIGHT(parent, field);	\
479 				}					\
480 				RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
481 				RB_COLOR(parent, field) = RB_BLACK;	\
482 				if (RB_RIGHT(tmp, field))		\
483 					RB_COLOR(RB_RIGHT(tmp, field), field) = RB_BLACK;\
484 				RB_ROTATE_LEFT(head, parent, tmp, field);\
485 				elm = RB_ROOT(head);			\
486 				break;					\
487 			}						\
488 		} else {						\
489 			tmp = RB_LEFT(parent, field);			\
490 			if (RB_COLOR(tmp, field) == RB_RED) {		\
491 				RB_SET_BLACKRED(tmp, parent, field);	\
492 				RB_ROTATE_RIGHT(head, parent, tmp, field);\
493 				tmp = RB_LEFT(parent, field);		\
494 			}						\
495 			if ((RB_LEFT(tmp, field) == NULL ||		\
496 			    RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
497 			    (RB_RIGHT(tmp, field) == NULL ||		\
498 			    RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
499 				RB_COLOR(tmp, field) = RB_RED;		\
500 				elm = parent;				\
501 				parent = RB_PARENT(elm, field);		\
502 			} else {					\
503 				if (RB_LEFT(tmp, field) == NULL ||	\
504 				    RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) {\
505 					struct type *oright;		\
506 					if ((oright = RB_RIGHT(tmp, field)) \
507 					    != NULL)			\
508 						RB_COLOR(oright, field) = RB_BLACK;\
509 					RB_COLOR(tmp, field) = RB_RED;	\
510 					RB_ROTATE_LEFT(head, tmp, oright, field);\
511 					tmp = RB_LEFT(parent, field);	\
512 				}					\
513 				RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
514 				RB_COLOR(parent, field) = RB_BLACK;	\
515 				if (RB_LEFT(tmp, field))		\
516 					RB_COLOR(RB_LEFT(tmp, field), field) = RB_BLACK;\
517 				RB_ROTATE_RIGHT(head, parent, tmp, field);\
518 				elm = RB_ROOT(head);			\
519 				break;					\
520 			}						\
521 		}							\
522 	}								\
523 	if (elm)							\
524 		RB_COLOR(elm, field) = RB_BLACK;			\
525 }									\
526 									\
527 attr struct type *							\
528 name##_RB_REMOVE(struct name *head, struct type *elm)			\
529 {									\
530 	struct type *child, *parent, *old = elm;			\
531 	int color;							\
532 	if (RB_LEFT(elm, field) == NULL)				\
533 		child = RB_RIGHT(elm, field);				\
534 	else if (RB_RIGHT(elm, field) == NULL)				\
535 		child = RB_LEFT(elm, field);				\
536 	else {								\
537 		struct type *left;					\
538 		elm = RB_RIGHT(elm, field);				\
539 		while ((left = RB_LEFT(elm, field)) != NULL)		\
540 			elm = left;					\
541 		child = RB_RIGHT(elm, field);				\
542 		parent = RB_PARENT(elm, field);				\
543 		color = RB_COLOR(elm, field);				\
544 		if (child)						\
545 			RB_PARENT(child, field) = parent;		\
546 		if (parent) {						\
547 			if (RB_LEFT(parent, field) == elm)		\
548 				RB_LEFT(parent, field) = child;		\
549 			else						\
550 				RB_RIGHT(parent, field) = child;	\
551 			RB_AUGMENT(parent);				\
552 		} else							\
553 			RB_ROOT(head) = child;				\
554 		if (RB_PARENT(elm, field) == old)			\
555 			parent = elm;					\
556 		(elm)->field = (old)->field;				\
557 		if (RB_PARENT(old, field)) {				\
558 			if (RB_LEFT(RB_PARENT(old, field), field) == old)\
559 				RB_LEFT(RB_PARENT(old, field), field) = elm;\
560 			else						\
561 				RB_RIGHT(RB_PARENT(old, field), field) = elm;\
562 			RB_AUGMENT(RB_PARENT(old, field));		\
563 		} else							\
564 			RB_ROOT(head) = elm;				\
565 		RB_PARENT(RB_LEFT(old, field), field) = elm;		\
566 		if (RB_RIGHT(old, field))				\
567 			RB_PARENT(RB_RIGHT(old, field), field) = elm;	\
568 		if (parent) {						\
569 			left = parent;					\
570 			do {						\
571 				RB_AUGMENT(left);			\
572 			} while ((left = RB_PARENT(left, field)) != NULL); \
573 		}							\
574 		goto color;						\
575 	}								\
576 	parent = RB_PARENT(elm, field);					\
577 	color = RB_COLOR(elm, field);					\
578 	if (child)							\
579 		RB_PARENT(child, field) = parent;			\
580 	if (parent) {							\
581 		if (RB_LEFT(parent, field) == elm)			\
582 			RB_LEFT(parent, field) = child;			\
583 		else							\
584 			RB_RIGHT(parent, field) = child;		\
585 		RB_AUGMENT(parent);					\
586 	} else								\
587 		RB_ROOT(head) = child;					\
588 color:									\
589 	if (color == RB_BLACK)						\
590 		name##_RB_REMOVE_COLOR(head, parent, child);		\
591 	return (old);							\
592 }									\
593 									\
594 /* Inserts a node into the RB tree */					\
595 attr struct type *							\
596 name##_RB_INSERT(struct name *head, struct type *elm)			\
597 {									\
598 	struct type *tmp;						\
599 	struct type *parent = NULL;					\
600 	int comp = 0;							\
601 	tmp = RB_ROOT(head);						\
602 	while (tmp) {							\
603 		parent = tmp;						\
604 		comp = (cmp)(elm, parent);				\
605 		if (comp < 0)						\
606 			tmp = RB_LEFT(tmp, field);			\
607 		else if (comp > 0)					\
608 			tmp = RB_RIGHT(tmp, field);			\
609 		else							\
610 			return (tmp);					\
611 	}								\
612 	RB_SET(elm, parent, field);					\
613 	if (parent != NULL) {						\
614 		if (comp < 0)						\
615 			RB_LEFT(parent, field) = elm;			\
616 		else							\
617 			RB_RIGHT(parent, field) = elm;			\
618 		RB_AUGMENT(parent);					\
619 	} else								\
620 		RB_ROOT(head) = elm;					\
621 	name##_RB_INSERT_COLOR(head, elm);				\
622 	return (NULL);							\
623 }									\
624 									\
625 /* Finds the node with the same key as elm */				\
626 attr struct type *							\
627 name##_RB_FIND(struct name *head, struct type *elm)			\
628 {									\
629 	struct type *tmp = RB_ROOT(head);				\
630 	int comp;							\
631 	while (tmp) {							\
632 		comp = cmp(elm, tmp);					\
633 		if (comp < 0)						\
634 			tmp = RB_LEFT(tmp, field);			\
635 		else if (comp > 0)					\
636 			tmp = RB_RIGHT(tmp, field);			\
637 		else							\
638 			return (tmp);					\
639 	}								\
640 	return (NULL);							\
641 }									\
642 									\
643 /* Finds the first node greater than or equal to the search key */	\
644 attr struct type *							\
645 name##_RB_NFIND(struct name *head, struct type *elm)			\
646 {									\
647 	struct type *tmp = RB_ROOT(head);				\
648 	struct type *res = NULL;					\
649 	int comp;							\
650 	while (tmp) {							\
651 		comp = cmp(elm, tmp);					\
652 		if (comp < 0) {						\
653 			res = tmp;					\
654 			tmp = RB_LEFT(tmp, field);			\
655 		}							\
656 		else if (comp > 0)					\
657 			tmp = RB_RIGHT(tmp, field);			\
658 		else							\
659 			return (tmp);					\
660 	}								\
661 	return (res);							\
662 }									\
663 									\
664 /* ARGSUSED */								\
665 attr struct type *							\
666 name##_RB_NEXT(struct type *elm)					\
667 {									\
668 	if (RB_RIGHT(elm, field)) {					\
669 		elm = RB_RIGHT(elm, field);				\
670 		while (RB_LEFT(elm, field))				\
671 			elm = RB_LEFT(elm, field);			\
672 	} else {							\
673 		if (RB_PARENT(elm, field) &&				\
674 		    (elm == RB_LEFT(RB_PARENT(elm, field), field)))	\
675 			elm = RB_PARENT(elm, field);			\
676 		else {							\
677 			while (RB_PARENT(elm, field) &&			\
678 			    (elm == RB_RIGHT(RB_PARENT(elm, field), field)))\
679 				elm = RB_PARENT(elm, field);		\
680 			elm = RB_PARENT(elm, field);			\
681 		}							\
682 	}								\
683 	return (elm);							\
684 }									\
685 									\
686 /* ARGSUSED */								\
687 attr struct type *							\
688 name##_RB_PREV(struct type *elm)					\
689 {									\
690 	if (RB_LEFT(elm, field)) {					\
691 		elm = RB_LEFT(elm, field);				\
692 		while (RB_RIGHT(elm, field))				\
693 			elm = RB_RIGHT(elm, field);			\
694 	} else {							\
695 		if (RB_PARENT(elm, field) &&				\
696 		    (elm == RB_RIGHT(RB_PARENT(elm, field), field)))	\
697 			elm = RB_PARENT(elm, field);			\
698 		else {							\
699 			while (RB_PARENT(elm, field) &&			\
700 			    (elm == RB_LEFT(RB_PARENT(elm, field), field)))\
701 				elm = RB_PARENT(elm, field);		\
702 			elm = RB_PARENT(elm, field);			\
703 		}							\
704 	}								\
705 	return (elm);							\
706 }									\
707 									\
708 attr struct type *							\
709 name##_RB_MINMAX(struct name *head, int val)				\
710 {									\
711 	struct type *tmp = RB_ROOT(head);				\
712 	struct type *parent = NULL;					\
713 	while (tmp) {							\
714 		parent = tmp;						\
715 		if (val < 0)						\
716 			tmp = RB_LEFT(tmp, field);			\
717 		else							\
718 			tmp = RB_RIGHT(tmp, field);			\
719 	}								\
720 	return (parent);						\
721 }
722 
723 #define RB_NEGINF	-1
724 #define RB_INF	1
725 
726 #define RB_INSERT(name, x, y)	name##_RB_INSERT(x, y)
727 #define RB_REMOVE(name, x, y)	name##_RB_REMOVE(x, y)
728 #define RB_FIND(name, x, y)	name##_RB_FIND(x, y)
729 #define RB_NFIND(name, x, y)	name##_RB_NFIND(x, y)
730 #define RB_NEXT(name, x, y)	name##_RB_NEXT(y)
731 #define RB_PREV(name, x, y)	name##_RB_PREV(y)
732 #define RB_MIN(name, x)		name##_RB_MINMAX(x, RB_NEGINF)
733 #define RB_MAX(name, x)		name##_RB_MINMAX(x, RB_INF)
734 
735 #define RB_FOREACH(x, name, head)					\
736 	for ((x) = RB_MIN(name, head);					\
737 	     (x) != NULL;						\
738 	     (x) = name##_RB_NEXT(x))
739 
740 #define RB_FOREACH_FROM(x, name, y)					\
741 	for ((x) = (y);							\
742 	    ((x) != NULL) && ((y) = name##_RB_NEXT(x), (x) != NULL);	\
743 	     (x) = (y))
744 
745 #define RB_FOREACH_SAFE(x, name, head, y)				\
746 	for ((x) = RB_MIN(name, head);					\
747 	    ((x) != NULL) && ((y) = name##_RB_NEXT(x), (x) != NULL);	\
748 	     (x) = (y))
749 
750 #define RB_FOREACH_REVERSE(x, name, head)				\
751 	for ((x) = RB_MAX(name, head);					\
752 	     (x) != NULL;						\
753 	     (x) = name##_RB_PREV(x))
754 
755 #define RB_FOREACH_REVERSE_FROM(x, name, y)				\
756 	for ((x) = (y);							\
757 	    ((x) != NULL) && ((y) = name##_RB_PREV(x), (x) != NULL);	\
758 	     (x) = (y))
759 
760 #define RB_FOREACH_REVERSE_SAFE(x, name, head, y)			\
761 	for ((x) = RB_MAX(name, head);					\
762 	    ((x) != NULL) && ((y) = name##_RB_PREV(x), (x) != NULL);	\
763 	     (x) = (y))
764 
765 #endif	/* _SYS_TREE_H_ */
766