xref: /freebsd/sys/sys/tree.h (revision 2f513db7)
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 /* $FreeBSD$ */
4 
5 /*-
6  * SPDX-License-Identifier: BSD-2-Clause-FreeBSD
7  *
8  * Copyright 2002 Niels Provos <provos@citi.umich.edu>
9  * All rights reserved.
10  *
11  * Redistribution and use in source and binary forms, with or without
12  * modification, are permitted provided that the following conditions
13  * are met:
14  * 1. Redistributions of source code must retain the above copyright
15  *    notice, this list of conditions and the following disclaimer.
16  * 2. Redistributions in binary form must reproduce the above copyright
17  *    notice, this list of conditions and the following disclaimer in the
18  *    documentation and/or other materials provided with the distribution.
19  *
20  * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
21  * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
22  * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
23  * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
24  * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
25  * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
26  * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
27  * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
28  * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
29  * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
30  */
31 
32 #ifndef	_SYS_TREE_H_
33 #define	_SYS_TREE_H_
34 
35 #include <sys/cdefs.h>
36 
37 /*
38  * This file defines data structures for different types of trees:
39  * splay trees and red-black trees.
40  *
41  * A splay tree is a self-organizing data structure.  Every operation
42  * on the tree causes a splay to happen.  The splay moves the requested
43  * node to the root of the tree and partly rebalances it.
44  *
45  * This has the benefit that request locality causes faster lookups as
46  * the requested nodes move to the top of the tree.  On the other hand,
47  * every lookup causes memory writes.
48  *
49  * The Balance Theorem bounds the total access time for m operations
50  * and n inserts on an initially empty tree as O((m + n)lg n).  The
51  * amortized cost for a sequence of m accesses to a splay tree is O(lg n);
52  *
53  * A red-black tree is a binary search tree with the node color as an
54  * extra attribute.  It fulfills a set of conditions:
55  *	- every search path from the root to a leaf consists of the
56  *	  same number of black nodes,
57  *	- each red node (except for the root) has a black parent,
58  *	- each leaf node is black.
59  *
60  * Every operation on a red-black tree is bounded as O(lg n).
61  * The maximum height of a red-black tree is 2lg (n+1).
62  */
63 
64 #define SPLAY_HEAD(name, type)						\
65 struct name {								\
66 	struct type *sph_root; /* root of the tree */			\
67 }
68 
69 #define SPLAY_INITIALIZER(root)						\
70 	{ NULL }
71 
72 #define SPLAY_INIT(root) do {						\
73 	(root)->sph_root = NULL;					\
74 } while (/*CONSTCOND*/ 0)
75 
76 #define SPLAY_ENTRY(type)						\
77 struct {								\
78 	struct type *spe_left; /* left element */			\
79 	struct type *spe_right; /* right element */			\
80 }
81 
82 #define SPLAY_LEFT(elm, field)		(elm)->field.spe_left
83 #define SPLAY_RIGHT(elm, field)		(elm)->field.spe_right
84 #define SPLAY_ROOT(head)		(head)->sph_root
85 #define SPLAY_EMPTY(head)		(SPLAY_ROOT(head) == NULL)
86 
87 /* SPLAY_ROTATE_{LEFT,RIGHT} expect that tmp hold SPLAY_{RIGHT,LEFT} */
88 #define SPLAY_ROTATE_RIGHT(head, tmp, field) do {			\
89 	SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(tmp, field);	\
90 	SPLAY_RIGHT(tmp, field) = (head)->sph_root;			\
91 	(head)->sph_root = tmp;						\
92 } while (/*CONSTCOND*/ 0)
93 
94 #define SPLAY_ROTATE_LEFT(head, tmp, field) do {			\
95 	SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(tmp, field);	\
96 	SPLAY_LEFT(tmp, field) = (head)->sph_root;			\
97 	(head)->sph_root = tmp;						\
98 } while (/*CONSTCOND*/ 0)
99 
100 #define SPLAY_LINKLEFT(head, tmp, field) do {				\
101 	SPLAY_LEFT(tmp, field) = (head)->sph_root;			\
102 	tmp = (head)->sph_root;						\
103 	(head)->sph_root = SPLAY_LEFT((head)->sph_root, field);		\
104 } while (/*CONSTCOND*/ 0)
105 
106 #define SPLAY_LINKRIGHT(head, tmp, field) do {				\
107 	SPLAY_RIGHT(tmp, field) = (head)->sph_root;			\
108 	tmp = (head)->sph_root;						\
109 	(head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);	\
110 } while (/*CONSTCOND*/ 0)
111 
112 #define SPLAY_ASSEMBLE(head, node, left, right, field) do {		\
113 	SPLAY_RIGHT(left, field) = SPLAY_LEFT((head)->sph_root, field);	\
114 	SPLAY_LEFT(right, field) = SPLAY_RIGHT((head)->sph_root, field);\
115 	SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(node, field);	\
116 	SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(node, field);	\
117 } while (/*CONSTCOND*/ 0)
118 
119 /* Generates prototypes and inline functions */
120 
121 #define SPLAY_PROTOTYPE(name, type, field, cmp)				\
122 void name##_SPLAY(struct name *, struct type *);			\
123 void name##_SPLAY_MINMAX(struct name *, int);				\
124 struct type *name##_SPLAY_INSERT(struct name *, struct type *);		\
125 struct type *name##_SPLAY_REMOVE(struct name *, struct type *);		\
126 									\
127 /* Finds the node with the same key as elm */				\
128 static __unused __inline struct type *					\
129 name##_SPLAY_FIND(struct name *head, struct type *elm)			\
130 {									\
131 	if (SPLAY_EMPTY(head))						\
132 		return(NULL);						\
133 	name##_SPLAY(head, elm);					\
134 	if ((cmp)(elm, (head)->sph_root) == 0)				\
135 		return (head->sph_root);				\
136 	return (NULL);							\
137 }									\
138 									\
139 static __unused __inline struct type *					\
140 name##_SPLAY_NEXT(struct name *head, struct type *elm)			\
141 {									\
142 	name##_SPLAY(head, elm);					\
143 	if (SPLAY_RIGHT(elm, field) != NULL) {				\
144 		elm = SPLAY_RIGHT(elm, field);				\
145 		while (SPLAY_LEFT(elm, field) != NULL) {		\
146 			elm = SPLAY_LEFT(elm, field);			\
147 		}							\
148 	} else								\
149 		elm = NULL;						\
150 	return (elm);							\
151 }									\
152 									\
153 static __unused __inline struct type *					\
154 name##_SPLAY_MIN_MAX(struct name *head, int val)			\
155 {									\
156 	name##_SPLAY_MINMAX(head, val);					\
157         return (SPLAY_ROOT(head));					\
158 }
159 
160 /* Main splay operation.
161  * Moves node close to the key of elm to top
162  */
163 #define SPLAY_GENERATE(name, type, field, cmp)				\
164 struct type *								\
165 name##_SPLAY_INSERT(struct name *head, struct type *elm)		\
166 {									\
167     if (SPLAY_EMPTY(head)) {						\
168 	    SPLAY_LEFT(elm, field) = SPLAY_RIGHT(elm, field) = NULL;	\
169     } else {								\
170 	    int __comp;							\
171 	    name##_SPLAY(head, elm);					\
172 	    __comp = (cmp)(elm, (head)->sph_root);			\
173 	    if(__comp < 0) {						\
174 		    SPLAY_LEFT(elm, field) = SPLAY_LEFT((head)->sph_root, field);\
175 		    SPLAY_RIGHT(elm, field) = (head)->sph_root;		\
176 		    SPLAY_LEFT((head)->sph_root, field) = NULL;		\
177 	    } else if (__comp > 0) {					\
178 		    SPLAY_RIGHT(elm, field) = SPLAY_RIGHT((head)->sph_root, field);\
179 		    SPLAY_LEFT(elm, field) = (head)->sph_root;		\
180 		    SPLAY_RIGHT((head)->sph_root, field) = NULL;	\
181 	    } else							\
182 		    return ((head)->sph_root);				\
183     }									\
184     (head)->sph_root = (elm);						\
185     return (NULL);							\
186 }									\
187 									\
188 struct type *								\
189 name##_SPLAY_REMOVE(struct name *head, struct type *elm)		\
190 {									\
191 	struct type *__tmp;						\
192 	if (SPLAY_EMPTY(head))						\
193 		return (NULL);						\
194 	name##_SPLAY(head, elm);					\
195 	if ((cmp)(elm, (head)->sph_root) == 0) {			\
196 		if (SPLAY_LEFT((head)->sph_root, field) == NULL) {	\
197 			(head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);\
198 		} else {						\
199 			__tmp = SPLAY_RIGHT((head)->sph_root, field);	\
200 			(head)->sph_root = SPLAY_LEFT((head)->sph_root, field);\
201 			name##_SPLAY(head, elm);			\
202 			SPLAY_RIGHT((head)->sph_root, field) = __tmp;	\
203 		}							\
204 		return (elm);						\
205 	}								\
206 	return (NULL);							\
207 }									\
208 									\
209 void									\
210 name##_SPLAY(struct name *head, struct type *elm)			\
211 {									\
212 	struct type __node, *__left, *__right, *__tmp;			\
213 	int __comp;							\
214 \
215 	SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
216 	__left = __right = &__node;					\
217 \
218 	while ((__comp = (cmp)(elm, (head)->sph_root)) != 0) {		\
219 		if (__comp < 0) {					\
220 			__tmp = SPLAY_LEFT((head)->sph_root, field);	\
221 			if (__tmp == NULL)				\
222 				break;					\
223 			if ((cmp)(elm, __tmp) < 0){			\
224 				SPLAY_ROTATE_RIGHT(head, __tmp, field);	\
225 				if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
226 					break;				\
227 			}						\
228 			SPLAY_LINKLEFT(head, __right, field);		\
229 		} else if (__comp > 0) {				\
230 			__tmp = SPLAY_RIGHT((head)->sph_root, field);	\
231 			if (__tmp == NULL)				\
232 				break;					\
233 			if ((cmp)(elm, __tmp) > 0){			\
234 				SPLAY_ROTATE_LEFT(head, __tmp, field);	\
235 				if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
236 					break;				\
237 			}						\
238 			SPLAY_LINKRIGHT(head, __left, field);		\
239 		}							\
240 	}								\
241 	SPLAY_ASSEMBLE(head, &__node, __left, __right, field);		\
242 }									\
243 									\
244 /* Splay with either the minimum or the maximum element			\
245  * Used to find minimum or maximum element in tree.			\
246  */									\
247 void name##_SPLAY_MINMAX(struct name *head, int __comp) \
248 {									\
249 	struct type __node, *__left, *__right, *__tmp;			\
250 \
251 	SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
252 	__left = __right = &__node;					\
253 \
254 	while (1) {							\
255 		if (__comp < 0) {					\
256 			__tmp = SPLAY_LEFT((head)->sph_root, field);	\
257 			if (__tmp == NULL)				\
258 				break;					\
259 			if (__comp < 0){				\
260 				SPLAY_ROTATE_RIGHT(head, __tmp, field);	\
261 				if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
262 					break;				\
263 			}						\
264 			SPLAY_LINKLEFT(head, __right, field);		\
265 		} else if (__comp > 0) {				\
266 			__tmp = SPLAY_RIGHT((head)->sph_root, field);	\
267 			if (__tmp == NULL)				\
268 				break;					\
269 			if (__comp > 0) {				\
270 				SPLAY_ROTATE_LEFT(head, __tmp, field);	\
271 				if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
272 					break;				\
273 			}						\
274 			SPLAY_LINKRIGHT(head, __left, field);		\
275 		}							\
276 	}								\
277 	SPLAY_ASSEMBLE(head, &__node, __left, __right, field);		\
278 }
279 
280 #define SPLAY_NEGINF	-1
281 #define SPLAY_INF	1
282 
283 #define SPLAY_INSERT(name, x, y)	name##_SPLAY_INSERT(x, y)
284 #define SPLAY_REMOVE(name, x, y)	name##_SPLAY_REMOVE(x, y)
285 #define SPLAY_FIND(name, x, y)		name##_SPLAY_FIND(x, y)
286 #define SPLAY_NEXT(name, x, y)		name##_SPLAY_NEXT(x, y)
287 #define SPLAY_MIN(name, x)		(SPLAY_EMPTY(x) ? NULL	\
288 					: name##_SPLAY_MIN_MAX(x, SPLAY_NEGINF))
289 #define SPLAY_MAX(name, x)		(SPLAY_EMPTY(x) ? NULL	\
290 					: name##_SPLAY_MIN_MAX(x, SPLAY_INF))
291 
292 #define SPLAY_FOREACH(x, name, head)					\
293 	for ((x) = SPLAY_MIN(name, head);				\
294 	     (x) != NULL;						\
295 	     (x) = SPLAY_NEXT(name, head, x))
296 
297 /* Macros that define a red-black tree */
298 #define RB_HEAD(name, type)						\
299 struct name {								\
300 	struct type *rbh_root; /* root of the tree */			\
301 }
302 
303 #define RB_INITIALIZER(root)						\
304 	{ NULL }
305 
306 #define RB_INIT(root) do {						\
307 	(root)->rbh_root = NULL;					\
308 } while (/*CONSTCOND*/ 0)
309 
310 #define RB_BLACK	0
311 #define RB_RED		1
312 #define RB_ENTRY(type)							\
313 struct {								\
314 	struct type *rbe_left;		/* left element */		\
315 	struct type *rbe_right;		/* right element */		\
316 	struct type *rbe_parent;	/* parent element */		\
317 	int rbe_color;			/* node color */		\
318 }
319 
320 #define RB_LEFT(elm, field)		(elm)->field.rbe_left
321 #define RB_RIGHT(elm, field)		(elm)->field.rbe_right
322 #define RB_PARENT(elm, field)		(elm)->field.rbe_parent
323 #define RB_COLOR(elm, field)		(elm)->field.rbe_color
324 #define RB_ROOT(head)			(head)->rbh_root
325 #define RB_EMPTY(head)			(RB_ROOT(head) == NULL)
326 
327 #define RB_SET(elm, parent, field) do {					\
328 	RB_PARENT(elm, field) = parent;					\
329 	RB_LEFT(elm, field) = RB_RIGHT(elm, field) = NULL;		\
330 	RB_COLOR(elm, field) = RB_RED;					\
331 } while (/*CONSTCOND*/ 0)
332 
333 #define RB_SET_BLACKRED(black, red, field) do {				\
334 	RB_COLOR(black, field) = RB_BLACK;				\
335 	RB_COLOR(red, field) = RB_RED;					\
336 } while (/*CONSTCOND*/ 0)
337 
338 /*
339  * Something to be invoked in a loop at the root of every modified subtree,
340  * from the bottom up to the root, to update augmented node data.
341  */
342 #ifndef RB_AUGMENT
343 #define RB_AUGMENT(x)	break
344 #endif
345 
346 #define RB_ROTATE_LEFT(head, elm, tmp, field) do {			\
347 	(tmp) = RB_RIGHT(elm, field);					\
348 	if ((RB_RIGHT(elm, field) = RB_LEFT(tmp, field)) != NULL) {	\
349 		RB_PARENT(RB_LEFT(tmp, field), field) = (elm);		\
350 	}								\
351 	if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) {	\
352 		if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))	\
353 			RB_LEFT(RB_PARENT(elm, field), field) = (tmp);	\
354 		else							\
355 			RB_RIGHT(RB_PARENT(elm, field), field) = (tmp);	\
356 	} else								\
357 		(head)->rbh_root = (tmp);				\
358 	RB_LEFT(tmp, field) = (elm);					\
359 	RB_PARENT(elm, field) = (tmp);					\
360 	RB_AUGMENT(elm);						\
361 } while (/*CONSTCOND*/ 0)
362 
363 #define RB_ROTATE_RIGHT(head, elm, tmp, field) do {			\
364 	(tmp) = RB_LEFT(elm, field);					\
365 	if ((RB_LEFT(elm, field) = RB_RIGHT(tmp, field)) != NULL) {	\
366 		RB_PARENT(RB_RIGHT(tmp, field), field) = (elm);		\
367 	}								\
368 	if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) {	\
369 		if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))	\
370 			RB_LEFT(RB_PARENT(elm, field), field) = (tmp);	\
371 		else							\
372 			RB_RIGHT(RB_PARENT(elm, field), field) = (tmp);	\
373 	} else								\
374 		(head)->rbh_root = (tmp);				\
375 	RB_RIGHT(tmp, field) = (elm);					\
376 	RB_PARENT(elm, field) = (tmp);					\
377 	RB_AUGMENT(elm);						\
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 	RB_PROTOTYPE_INSERT_COLOR(name, type, attr);			\
387 	RB_PROTOTYPE_REMOVE_COLOR(name, type, attr);			\
388 	RB_PROTOTYPE_INSERT(name, type, attr);				\
389 	RB_PROTOTYPE_REMOVE(name, type, attr);				\
390 	RB_PROTOTYPE_FIND(name, type, attr);				\
391 	RB_PROTOTYPE_NFIND(name, type, attr);				\
392 	RB_PROTOTYPE_NEXT(name, type, attr);				\
393 	RB_PROTOTYPE_PREV(name, type, attr);				\
394 	RB_PROTOTYPE_MINMAX(name, type, attr);				\
395 	RB_PROTOTYPE_REINSERT(name, type, attr);
396 #define RB_PROTOTYPE_INSERT_COLOR(name, type, attr)			\
397 	attr void name##_RB_INSERT_COLOR(struct name *, struct type *)
398 #define RB_PROTOTYPE_REMOVE_COLOR(name, type, attr)			\
399 	attr void name##_RB_REMOVE_COLOR(struct name *, struct type *, struct type *)
400 #define RB_PROTOTYPE_REMOVE(name, type, attr)				\
401 	attr struct type *name##_RB_REMOVE(struct name *, struct type *)
402 #define RB_PROTOTYPE_INSERT(name, type, attr)				\
403 	attr struct type *name##_RB_INSERT(struct name *, struct type *)
404 #define RB_PROTOTYPE_FIND(name, type, attr)				\
405 	attr struct type *name##_RB_FIND(struct name *, struct type *)
406 #define RB_PROTOTYPE_NFIND(name, type, attr)				\
407 	attr struct type *name##_RB_NFIND(struct name *, struct type *)
408 #define RB_PROTOTYPE_NEXT(name, type, attr)				\
409 	attr struct type *name##_RB_NEXT(struct type *)
410 #define RB_PROTOTYPE_PREV(name, type, attr)				\
411 	attr struct type *name##_RB_PREV(struct type *)
412 #define RB_PROTOTYPE_MINMAX(name, type, attr)				\
413 	attr struct type *name##_RB_MINMAX(struct name *, int)
414 #define RB_PROTOTYPE_REINSERT(name, type, attr)			\
415 	attr struct type *name##_RB_REINSERT(struct name *, struct type *)
416 
417 /* Main rb operation.
418  * Moves node close to the key of elm to top
419  */
420 #define	RB_GENERATE(name, type, field, cmp)				\
421 	RB_GENERATE_INTERNAL(name, type, field, cmp,)
422 #define	RB_GENERATE_STATIC(name, type, field, cmp)			\
423 	RB_GENERATE_INTERNAL(name, type, field, cmp, __unused static)
424 #define RB_GENERATE_INTERNAL(name, type, field, cmp, attr)		\
425 	RB_GENERATE_INSERT_COLOR(name, type, field, attr)		\
426 	RB_GENERATE_REMOVE_COLOR(name, type, field, attr)		\
427 	RB_GENERATE_INSERT(name, type, field, cmp, attr)		\
428 	RB_GENERATE_REMOVE(name, type, field, attr)			\
429 	RB_GENERATE_FIND(name, type, field, cmp, attr)			\
430 	RB_GENERATE_NFIND(name, type, field, cmp, attr)			\
431 	RB_GENERATE_NEXT(name, type, field, attr)			\
432 	RB_GENERATE_PREV(name, type, field, attr)			\
433 	RB_GENERATE_MINMAX(name, type, field, attr)			\
434 	RB_GENERATE_REINSERT(name, type, field, cmp, attr)
435 
436 
437 #define RB_GENERATE_INSERT_COLOR(name, type, field, attr)		\
438 attr void								\
439 name##_RB_INSERT_COLOR(struct name *head, struct type *elm)		\
440 {									\
441 	struct type *parent, *gparent, *tmp;				\
442 	while ((parent = RB_PARENT(elm, field)) != NULL &&		\
443 	    RB_COLOR(parent, field) == RB_RED) {			\
444 		gparent = RB_PARENT(parent, field);			\
445 		if (parent == RB_LEFT(gparent, field)) {		\
446 			tmp = RB_RIGHT(gparent, field);			\
447 			if (tmp && RB_COLOR(tmp, field) == RB_RED) {	\
448 				RB_COLOR(tmp, field) = RB_BLACK;	\
449 				RB_SET_BLACKRED(parent, gparent, field);\
450 				elm = gparent;				\
451 				continue;				\
452 			}						\
453 			if (RB_RIGHT(parent, field) == elm) {		\
454 				RB_ROTATE_LEFT(head, parent, tmp, field);\
455 				tmp = parent;				\
456 				parent = elm;				\
457 				elm = tmp;				\
458 			}						\
459 			RB_SET_BLACKRED(parent, gparent, field);	\
460 			RB_ROTATE_RIGHT(head, gparent, tmp, field);	\
461 		} else {						\
462 			tmp = RB_LEFT(gparent, field);			\
463 			if (tmp && RB_COLOR(tmp, field) == RB_RED) {	\
464 				RB_COLOR(tmp, field) = RB_BLACK;	\
465 				RB_SET_BLACKRED(parent, gparent, field);\
466 				elm = gparent;				\
467 				continue;				\
468 			}						\
469 			if (RB_LEFT(parent, field) == elm) {		\
470 				RB_ROTATE_RIGHT(head, parent, tmp, field);\
471 				tmp = parent;				\
472 				parent = elm;				\
473 				elm = tmp;				\
474 			}						\
475 			RB_SET_BLACKRED(parent, gparent, field);	\
476 			RB_ROTATE_LEFT(head, gparent, tmp, field);	\
477 		}							\
478 	}								\
479 	RB_COLOR(head->rbh_root, field) = RB_BLACK;			\
480 }
481 
482 #define RB_GENERATE_REMOVE_COLOR(name, type, field, attr)		\
483 attr void								\
484 name##_RB_REMOVE_COLOR(struct name *head, struct type *parent, struct type *elm) \
485 {									\
486 	struct type *tmp;						\
487 	while ((elm == NULL || RB_COLOR(elm, field) == RB_BLACK) &&	\
488 	    elm != RB_ROOT(head)) {					\
489 		if (RB_LEFT(parent, field) == elm) {			\
490 			tmp = RB_RIGHT(parent, field);			\
491 			if (RB_COLOR(tmp, field) == RB_RED) {		\
492 				RB_SET_BLACKRED(tmp, parent, field);	\
493 				RB_ROTATE_LEFT(head, parent, tmp, field);\
494 				tmp = RB_RIGHT(parent, field);		\
495 			}						\
496 			if ((RB_LEFT(tmp, field) == NULL ||		\
497 			    RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
498 			    (RB_RIGHT(tmp, field) == NULL ||		\
499 			    RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
500 				RB_COLOR(tmp, field) = RB_RED;		\
501 				elm = parent;				\
502 				parent = RB_PARENT(elm, field);		\
503 			} else {					\
504 				if (RB_RIGHT(tmp, field) == NULL ||	\
505 				    RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK) {\
506 					struct type *oleft;		\
507 					if ((oleft = RB_LEFT(tmp, field)) \
508 					    != NULL)			\
509 						RB_COLOR(oleft, field) = RB_BLACK;\
510 					RB_COLOR(tmp, field) = RB_RED;	\
511 					RB_ROTATE_RIGHT(head, tmp, oleft, field);\
512 					tmp = RB_RIGHT(parent, field);	\
513 				}					\
514 				RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
515 				RB_COLOR(parent, field) = RB_BLACK;	\
516 				if (RB_RIGHT(tmp, field))		\
517 					RB_COLOR(RB_RIGHT(tmp, field), field) = RB_BLACK;\
518 				RB_ROTATE_LEFT(head, parent, tmp, field);\
519 				elm = RB_ROOT(head);			\
520 				break;					\
521 			}						\
522 		} else {						\
523 			tmp = RB_LEFT(parent, field);			\
524 			if (RB_COLOR(tmp, field) == RB_RED) {		\
525 				RB_SET_BLACKRED(tmp, parent, field);	\
526 				RB_ROTATE_RIGHT(head, parent, tmp, field);\
527 				tmp = RB_LEFT(parent, field);		\
528 			}						\
529 			if ((RB_LEFT(tmp, field) == NULL ||		\
530 			    RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
531 			    (RB_RIGHT(tmp, field) == NULL ||		\
532 			    RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
533 				RB_COLOR(tmp, field) = RB_RED;		\
534 				elm = parent;				\
535 				parent = RB_PARENT(elm, field);		\
536 			} else {					\
537 				if (RB_LEFT(tmp, field) == NULL ||	\
538 				    RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) {\
539 					struct type *oright;		\
540 					if ((oright = RB_RIGHT(tmp, field)) \
541 					    != NULL)			\
542 						RB_COLOR(oright, field) = RB_BLACK;\
543 					RB_COLOR(tmp, field) = RB_RED;	\
544 					RB_ROTATE_LEFT(head, tmp, oright, field);\
545 					tmp = RB_LEFT(parent, field);	\
546 				}					\
547 				RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
548 				RB_COLOR(parent, field) = RB_BLACK;	\
549 				if (RB_LEFT(tmp, field))		\
550 					RB_COLOR(RB_LEFT(tmp, field), field) = RB_BLACK;\
551 				RB_ROTATE_RIGHT(head, parent, tmp, field);\
552 				elm = RB_ROOT(head);			\
553 				break;					\
554 			}						\
555 		}							\
556 	}								\
557 	if (elm)							\
558 		RB_COLOR(elm, field) = RB_BLACK;			\
559 }
560 
561 #define RB_GENERATE_REMOVE(name, type, field, attr)			\
562 attr struct type *							\
563 name##_RB_REMOVE(struct name *head, struct type *elm)			\
564 {									\
565 	struct type *child, *parent, *old = elm;			\
566 	int color;							\
567 	if (RB_LEFT(elm, field) == NULL)				\
568 		child = RB_RIGHT(elm, field);				\
569 	else if (RB_RIGHT(elm, field) == NULL)				\
570 		child = RB_LEFT(elm, field);				\
571 	else {								\
572 		elm = RB_RIGHT(old, field);				\
573 		if ((child = RB_LEFT(elm, field)) == NULL) {		\
574 			child = RB_RIGHT(elm, field);			\
575 			RB_RIGHT(old, field) = child;			\
576 			RB_PARENT(elm, field) = elm;			\
577 		} else {						\
578 			do						\
579 				elm = child;				\
580 			while ((child = RB_LEFT(elm, field)) != NULL);	\
581 			child = RB_RIGHT(elm, field);			\
582 			RB_PARENT(RB_RIGHT(old, field), field) = elm;	\
583 		}							\
584 		RB_PARENT(RB_LEFT(old, field), field) = elm;		\
585 		parent = RB_PARENT(old, field);				\
586 		if (parent != NULL) {					\
587 			if (RB_LEFT(parent, field) == old)		\
588 				RB_LEFT(parent, field) = elm;		\
589 			else						\
590 				RB_RIGHT(parent, field) = elm;		\
591 		} else							\
592 			RB_ROOT(head) = elm;				\
593 	}								\
594 	parent = RB_PARENT(elm, field);					\
595 	color = RB_COLOR(elm, field);					\
596 	if (child != NULL)						\
597 		RB_PARENT(child, field) = parent;			\
598 	if (parent != NULL) {						\
599 		if (RB_LEFT(parent, field) == elm)			\
600 			RB_LEFT(parent, field) = child;			\
601 		else							\
602 			RB_RIGHT(parent, field) = child;		\
603 	} else								\
604 		RB_ROOT(head) = child;					\
605 	if (elm != old)							\
606 		(elm)->field = (old)->field;				\
607 	if (color == RB_BLACK)						\
608 		name##_RB_REMOVE_COLOR(head, parent, child);		\
609 	while (parent != NULL) {					\
610 		RB_AUGMENT(parent);					\
611 		parent = RB_PARENT(parent, field);			\
612 	}								\
613 	return (old);							\
614 }
615 
616 #define RB_GENERATE_INSERT(name, type, field, cmp, attr)		\
617 /* Inserts a node into the RB tree */					\
618 attr struct type *							\
619 name##_RB_INSERT(struct name *head, struct type *elm)			\
620 {									\
621 	struct type *tmp;						\
622 	struct type *parent = NULL;					\
623 	int comp = 0;							\
624 	tmp = RB_ROOT(head);						\
625 	while (tmp) {							\
626 		parent = tmp;						\
627 		comp = (cmp)(elm, parent);				\
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 	RB_SET(elm, parent, field);					\
636 	if (parent != NULL) {						\
637 		if (comp < 0)						\
638 			RB_LEFT(parent, field) = elm;			\
639 		else							\
640 			RB_RIGHT(parent, field) = elm;			\
641 	} else								\
642 		RB_ROOT(head) = elm;					\
643 	name##_RB_INSERT_COLOR(head, elm);				\
644 	while (elm != NULL) {						\
645 		RB_AUGMENT(elm);					\
646 		elm = RB_PARENT(elm, field);				\
647 	}								\
648 	return (NULL);							\
649 }
650 
651 #define RB_GENERATE_FIND(name, type, field, cmp, attr)			\
652 /* Finds the node with the same key as elm */				\
653 attr struct type *							\
654 name##_RB_FIND(struct name *head, struct type *elm)			\
655 {									\
656 	struct type *tmp = RB_ROOT(head);				\
657 	int comp;							\
658 	while (tmp) {							\
659 		comp = cmp(elm, tmp);					\
660 		if (comp < 0)						\
661 			tmp = RB_LEFT(tmp, field);			\
662 		else if (comp > 0)					\
663 			tmp = RB_RIGHT(tmp, field);			\
664 		else							\
665 			return (tmp);					\
666 	}								\
667 	return (NULL);							\
668 }
669 
670 #define RB_GENERATE_NFIND(name, type, field, cmp, attr)			\
671 /* Finds the first node greater than or equal to the search key */	\
672 attr struct type *							\
673 name##_RB_NFIND(struct name *head, struct type *elm)			\
674 {									\
675 	struct type *tmp = RB_ROOT(head);				\
676 	struct type *res = NULL;					\
677 	int comp;							\
678 	while (tmp) {							\
679 		comp = cmp(elm, tmp);					\
680 		if (comp < 0) {						\
681 			res = tmp;					\
682 			tmp = RB_LEFT(tmp, field);			\
683 		}							\
684 		else if (comp > 0)					\
685 			tmp = RB_RIGHT(tmp, field);			\
686 		else							\
687 			return (tmp);					\
688 	}								\
689 	return (res);							\
690 }
691 
692 #define RB_GENERATE_NEXT(name, type, field, attr)			\
693 /* ARGSUSED */								\
694 attr struct type *							\
695 name##_RB_NEXT(struct type *elm)					\
696 {									\
697 	if (RB_RIGHT(elm, field)) {					\
698 		elm = RB_RIGHT(elm, field);				\
699 		while (RB_LEFT(elm, field))				\
700 			elm = RB_LEFT(elm, field);			\
701 	} else {							\
702 		if (RB_PARENT(elm, field) &&				\
703 		    (elm == RB_LEFT(RB_PARENT(elm, field), field)))	\
704 			elm = RB_PARENT(elm, field);			\
705 		else {							\
706 			while (RB_PARENT(elm, field) &&			\
707 			    (elm == RB_RIGHT(RB_PARENT(elm, field), field)))\
708 				elm = RB_PARENT(elm, field);		\
709 			elm = RB_PARENT(elm, field);			\
710 		}							\
711 	}								\
712 	return (elm);							\
713 }
714 
715 #define RB_GENERATE_PREV(name, type, field, attr)			\
716 /* ARGSUSED */								\
717 attr struct type *							\
718 name##_RB_PREV(struct type *elm)					\
719 {									\
720 	if (RB_LEFT(elm, field)) {					\
721 		elm = RB_LEFT(elm, field);				\
722 		while (RB_RIGHT(elm, field))				\
723 			elm = RB_RIGHT(elm, field);			\
724 	} else {							\
725 		if (RB_PARENT(elm, field) &&				\
726 		    (elm == RB_RIGHT(RB_PARENT(elm, field), field)))	\
727 			elm = RB_PARENT(elm, field);			\
728 		else {							\
729 			while (RB_PARENT(elm, field) &&			\
730 			    (elm == RB_LEFT(RB_PARENT(elm, field), field)))\
731 				elm = RB_PARENT(elm, field);		\
732 			elm = RB_PARENT(elm, field);			\
733 		}							\
734 	}								\
735 	return (elm);							\
736 }
737 
738 #define RB_GENERATE_MINMAX(name, type, field, attr)			\
739 attr struct type *							\
740 name##_RB_MINMAX(struct name *head, int val)				\
741 {									\
742 	struct type *tmp = RB_ROOT(head);				\
743 	struct type *parent = NULL;					\
744 	while (tmp) {							\
745 		parent = tmp;						\
746 		if (val < 0)						\
747 			tmp = RB_LEFT(tmp, field);			\
748 		else							\
749 			tmp = RB_RIGHT(tmp, field);			\
750 	}								\
751 	return (parent);						\
752 }
753 
754 #define	RB_GENERATE_REINSERT(name, type, field, cmp, attr)		\
755 attr struct type *							\
756 name##_RB_REINSERT(struct name *head, struct type *elm)			\
757 {									\
758 	struct type *cmpelm;						\
759 	if (((cmpelm = RB_PREV(name, head, elm)) != NULL &&		\
760 	    cmp(cmpelm, elm) >= 0) ||					\
761 	    ((cmpelm = RB_NEXT(name, head, elm)) != NULL &&		\
762 	    cmp(elm, cmpelm) >= 0)) {					\
763 		/* XXXLAS: Remove/insert is heavy handed. */		\
764 		RB_REMOVE(name, head, elm);				\
765 		return (RB_INSERT(name, head, elm));			\
766 	}								\
767 	return (NULL);							\
768 }									\
769 
770 #define RB_NEGINF	-1
771 #define RB_INF	1
772 
773 #define RB_INSERT(name, x, y)	name##_RB_INSERT(x, y)
774 #define RB_REMOVE(name, x, y)	name##_RB_REMOVE(x, y)
775 #define RB_FIND(name, x, y)	name##_RB_FIND(x, y)
776 #define RB_NFIND(name, x, y)	name##_RB_NFIND(x, y)
777 #define RB_NEXT(name, x, y)	name##_RB_NEXT(y)
778 #define RB_PREV(name, x, y)	name##_RB_PREV(y)
779 #define RB_MIN(name, x)		name##_RB_MINMAX(x, RB_NEGINF)
780 #define RB_MAX(name, x)		name##_RB_MINMAX(x, RB_INF)
781 #define RB_REINSERT(name, x, y)	name##_RB_REINSERT(x, y)
782 
783 #define RB_FOREACH(x, name, head)					\
784 	for ((x) = RB_MIN(name, head);					\
785 	     (x) != NULL;						\
786 	     (x) = name##_RB_NEXT(x))
787 
788 #define RB_FOREACH_FROM(x, name, y)					\
789 	for ((x) = (y);							\
790 	    ((x) != NULL) && ((y) = name##_RB_NEXT(x), (x) != NULL);	\
791 	     (x) = (y))
792 
793 #define RB_FOREACH_SAFE(x, name, head, y)				\
794 	for ((x) = RB_MIN(name, head);					\
795 	    ((x) != NULL) && ((y) = name##_RB_NEXT(x), (x) != NULL);	\
796 	     (x) = (y))
797 
798 #define RB_FOREACH_REVERSE(x, name, head)				\
799 	for ((x) = RB_MAX(name, head);					\
800 	     (x) != NULL;						\
801 	     (x) = name##_RB_PREV(x))
802 
803 #define RB_FOREACH_REVERSE_FROM(x, name, y)				\
804 	for ((x) = (y);							\
805 	    ((x) != NULL) && ((y) = name##_RB_PREV(x), (x) != NULL);	\
806 	     (x) = (y))
807 
808 #define RB_FOREACH_REVERSE_SAFE(x, name, head, y)			\
809 	for ((x) = RB_MAX(name, head);					\
810 	    ((x) != NULL) && ((y) = name##_RB_PREV(x), (x) != NULL);	\
811 	     (x) = (y))
812 
813 #endif	/* _SYS_TREE_H_ */
814