xref: /freebsd/sys/sys/tree.h (revision 6419bb52)
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_ISRED(elm, field)		((elm) != NULL && RB_COLOR(elm, field) == RB_RED)
325 #define RB_ROOT(head)			(head)->rbh_root
326 #define RB_EMPTY(head)			(RB_ROOT(head) == NULL)
327 
328 #define RB_SET(elm, parent, field) do {					\
329 	RB_PARENT(elm, field) = parent;					\
330 	RB_LEFT(elm, field) = RB_RIGHT(elm, field) = NULL;		\
331 	RB_COLOR(elm, field) = RB_RED;					\
332 } while (/*CONSTCOND*/ 0)
333 
334 #define RB_SET_BLACKRED(black, red, field) do {				\
335 	RB_COLOR(black, field) = RB_BLACK;				\
336 	RB_COLOR(red, field) = RB_RED;					\
337 } while (/*CONSTCOND*/ 0)
338 
339 /*
340  * Something to be invoked in a loop at the root of every modified subtree,
341  * from the bottom up to the root, to update augmented node data.
342  */
343 #ifndef RB_AUGMENT
344 #define RB_AUGMENT(x)	break
345 #endif
346 
347 #define RB_ROTATE_LEFT(head, elm, tmp, field) do {			\
348 	(tmp) = RB_RIGHT(elm, field);					\
349 	if ((RB_RIGHT(elm, field) = RB_LEFT(tmp, field)) != NULL) {	\
350 		RB_PARENT(RB_LEFT(tmp, field), field) = (elm);		\
351 	}								\
352 	if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) {	\
353 		if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))	\
354 			RB_LEFT(RB_PARENT(elm, field), field) = (tmp);	\
355 		else							\
356 			RB_RIGHT(RB_PARENT(elm, field), field) = (tmp);	\
357 	} else								\
358 		(head)->rbh_root = (tmp);				\
359 	RB_LEFT(tmp, field) = (elm);					\
360 	RB_PARENT(elm, field) = (tmp);					\
361 	RB_AUGMENT(elm);						\
362 } while (/*CONSTCOND*/ 0)
363 
364 #define RB_ROTATE_RIGHT(head, elm, tmp, field) do {			\
365 	(tmp) = RB_LEFT(elm, field);					\
366 	if ((RB_LEFT(elm, field) = RB_RIGHT(tmp, field)) != NULL) {	\
367 		RB_PARENT(RB_RIGHT(tmp, field), field) = (elm);		\
368 	}								\
369 	if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) {	\
370 		if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))	\
371 			RB_LEFT(RB_PARENT(elm, field), field) = (tmp);	\
372 		else							\
373 			RB_RIGHT(RB_PARENT(elm, field), field) = (tmp);	\
374 	} else								\
375 		(head)->rbh_root = (tmp);				\
376 	RB_RIGHT(tmp, field) = (elm);					\
377 	RB_PARENT(elm, field) = (tmp);					\
378 	RB_AUGMENT(elm);						\
379 } while (/*CONSTCOND*/ 0)
380 
381 /* Generates prototypes and inline functions */
382 #define	RB_PROTOTYPE(name, type, field, cmp)				\
383 	RB_PROTOTYPE_INTERNAL(name, type, field, cmp,)
384 #define	RB_PROTOTYPE_STATIC(name, type, field, cmp)			\
385 	RB_PROTOTYPE_INTERNAL(name, type, field, cmp, __unused static)
386 #define RB_PROTOTYPE_INTERNAL(name, type, field, cmp, attr)		\
387 	RB_PROTOTYPE_INSERT_COLOR(name, type, attr);			\
388 	RB_PROTOTYPE_REMOVE_COLOR(name, type, attr);			\
389 	RB_PROTOTYPE_INSERT(name, type, attr);				\
390 	RB_PROTOTYPE_REMOVE(name, type, attr);				\
391 	RB_PROTOTYPE_FIND(name, type, attr);				\
392 	RB_PROTOTYPE_NFIND(name, type, attr);				\
393 	RB_PROTOTYPE_NEXT(name, type, attr);				\
394 	RB_PROTOTYPE_PREV(name, type, attr);				\
395 	RB_PROTOTYPE_MINMAX(name, type, attr);				\
396 	RB_PROTOTYPE_REINSERT(name, type, attr);
397 #define RB_PROTOTYPE_INSERT_COLOR(name, type, attr)			\
398 	attr void name##_RB_INSERT_COLOR(struct name *, struct type *)
399 #define RB_PROTOTYPE_REMOVE_COLOR(name, type, attr)			\
400 	attr void name##_RB_REMOVE_COLOR(struct name *, struct type *)
401 #define RB_PROTOTYPE_REMOVE(name, type, attr)				\
402 	attr struct type *name##_RB_REMOVE(struct name *, struct type *)
403 #define RB_PROTOTYPE_INSERT(name, type, attr)				\
404 	attr struct type *name##_RB_INSERT(struct name *, struct type *)
405 #define RB_PROTOTYPE_FIND(name, type, attr)				\
406 	attr struct type *name##_RB_FIND(struct name *, struct type *)
407 #define RB_PROTOTYPE_NFIND(name, type, attr)				\
408 	attr struct type *name##_RB_NFIND(struct name *, struct type *)
409 #define RB_PROTOTYPE_NEXT(name, type, attr)				\
410 	attr struct type *name##_RB_NEXT(struct type *)
411 #define RB_PROTOTYPE_PREV(name, type, attr)				\
412 	attr struct type *name##_RB_PREV(struct type *)
413 #define RB_PROTOTYPE_MINMAX(name, type, attr)				\
414 	attr struct type *name##_RB_MINMAX(struct name *, int)
415 #define RB_PROTOTYPE_REINSERT(name, type, attr)			\
416 	attr struct type *name##_RB_REINSERT(struct name *, struct type *)
417 
418 /* Main rb operation.
419  * Moves node close to the key of elm to top
420  */
421 #define	RB_GENERATE(name, type, field, cmp)				\
422 	RB_GENERATE_INTERNAL(name, type, field, cmp,)
423 #define	RB_GENERATE_STATIC(name, type, field, cmp)			\
424 	RB_GENERATE_INTERNAL(name, type, field, cmp, __unused static)
425 #define RB_GENERATE_INTERNAL(name, type, field, cmp, attr)		\
426 	RB_GENERATE_INSERT_COLOR(name, type, field, attr)		\
427 	RB_GENERATE_REMOVE_COLOR(name, type, field, attr)		\
428 	RB_GENERATE_INSERT(name, type, field, cmp, attr)		\
429 	RB_GENERATE_REMOVE(name, type, field, attr)			\
430 	RB_GENERATE_FIND(name, type, field, cmp, attr)			\
431 	RB_GENERATE_NFIND(name, type, field, cmp, attr)			\
432 	RB_GENERATE_NEXT(name, type, field, attr)			\
433 	RB_GENERATE_PREV(name, type, field, attr)			\
434 	RB_GENERATE_MINMAX(name, type, field, attr)			\
435 	RB_GENERATE_REINSERT(name, type, field, cmp, attr)
436 
437 
438 #define RB_GENERATE_INSERT_COLOR(name, type, field, attr)		\
439 attr void								\
440 name##_RB_INSERT_COLOR(struct name *head, struct type *elm)		\
441 {									\
442 	struct type *parent, *gparent, *tmp;				\
443 	while (RB_ISRED((parent = RB_PARENT(elm, field)), field)) {	\
444 		gparent = RB_PARENT(parent, field);			\
445 		if (parent == RB_LEFT(gparent, field)) {		\
446 			tmp = RB_RIGHT(gparent, field);			\
447 			if (RB_ISRED(tmp, field)) {			\
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 (RB_ISRED(tmp, field)) {			\
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)		\
485 {									\
486 	struct type *elm, *tmp;						\
487 	elm = NULL;							\
488 	do {								\
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_ISRED(RB_LEFT(tmp, field), field)) {	\
497 				struct type *oleft;			\
498 				oleft = RB_LEFT(tmp, field);		\
499 				RB_COLOR(oleft, field) = RB_BLACK;	\
500 				RB_COLOR(tmp, field) = RB_RED;		\
501 				RB_ROTATE_RIGHT(head, tmp, oleft, field); \
502 				tmp = RB_RIGHT(parent, field);		\
503 			} else if (!RB_ISRED(RB_RIGHT(tmp, field), field)) { \
504 				RB_COLOR(tmp, field) = RB_RED;		\
505 				elm = parent;				\
506 				parent = RB_PARENT(elm, field);		\
507 				continue;				\
508 			}						\
509 			if (RB_ISRED(RB_RIGHT(tmp, field), field))	\
510 				RB_COLOR(RB_RIGHT(tmp, field), field) = RB_BLACK; \
511 			RB_COLOR(tmp, field) = RB_COLOR(parent, field);	\
512 			RB_COLOR(parent, field) = RB_BLACK;		\
513 			RB_ROTATE_LEFT(head, parent, tmp, field);	\
514 			elm = RB_ROOT(head);				\
515 			break;						\
516 		} else {						\
517 			tmp = RB_LEFT(parent, field);			\
518 			if (RB_COLOR(tmp, field) == RB_RED) {		\
519 				RB_SET_BLACKRED(tmp, parent, field);	\
520 				RB_ROTATE_RIGHT(head, parent, tmp, field);\
521 				tmp = RB_LEFT(parent, field);		\
522 			}						\
523 			if (RB_ISRED(RB_RIGHT(tmp, field), field)) {	\
524 				struct type *oright;			\
525 				oright = RB_RIGHT(tmp, field);		\
526 				RB_COLOR(oright, field) = RB_BLACK;	\
527 				RB_COLOR(tmp, field) = RB_RED;		\
528 				RB_ROTATE_LEFT(head, tmp, oright, field); \
529 				tmp = RB_LEFT(parent, field);		\
530 			} else if (!RB_ISRED(RB_LEFT(tmp, field), field)) { \
531 				RB_COLOR(tmp, field) = RB_RED;		\
532 				elm = parent;				\
533 				parent = RB_PARENT(elm, field);		\
534 				continue;				\
535 			}						\
536 			if (RB_ISRED(RB_LEFT(tmp, field), field))	\
537 				RB_COLOR(RB_LEFT(tmp, field), field) = RB_BLACK; \
538 			RB_COLOR(tmp, field) = RB_COLOR(parent, field);	\
539 			RB_COLOR(parent, field) = RB_BLACK;		\
540 			RB_ROTATE_RIGHT(head, parent, tmp, field);	\
541 			elm = RB_ROOT(head);				\
542 			break;						\
543 		}							\
544 	} while (!RB_ISRED(elm, field) && parent != NULL);		\
545 	RB_COLOR(elm, field) = RB_BLACK;				\
546 }
547 
548 #define RB_GENERATE_REMOVE(name, type, field, attr)			\
549 attr struct type *							\
550 name##_RB_REMOVE(struct name *head, struct type *elm)			\
551 {									\
552 	struct type *child, *old, *parent, *parent_old, *right;		\
553 	int color;							\
554 									\
555 	old = elm;							\
556 	parent_old = parent = RB_PARENT(elm, field);			\
557 	right = RB_RIGHT(elm, field);					\
558 	color = RB_COLOR(elm, field);					\
559 	if (RB_LEFT(elm, field) == NULL)				\
560 		elm = child = right;					\
561 	else if (right == NULL)						\
562 		elm = child = RB_LEFT(elm, field);			\
563 	else {								\
564 		if ((child = RB_LEFT(right, field)) == NULL) {		\
565 			child = RB_RIGHT(right, field);			\
566 			RB_RIGHT(old, field) = child;			\
567 			parent = elm = right;				\
568 		} else {						\
569 			do						\
570 				elm = child;				\
571 			while ((child = RB_LEFT(elm, field)) != NULL);	\
572 			child = RB_RIGHT(elm, field);			\
573 			parent = RB_PARENT(elm, field);			\
574 			RB_LEFT(parent, field) = child;			\
575 			RB_PARENT(RB_RIGHT(old, field), field) = elm;	\
576 		}							\
577 		RB_PARENT(RB_LEFT(old, field), field) = elm;		\
578 		color = RB_COLOR(elm, field);				\
579 		elm->field = old->field;				\
580 	}								\
581 	if (parent_old == NULL)						\
582 		RB_ROOT(head) = elm;					\
583 	else if (RB_LEFT(parent_old, field) == old)			\
584 		RB_LEFT(parent_old, field) = elm;			\
585 	else								\
586 		RB_RIGHT(parent_old, field) = elm;			\
587 	if (child != NULL) {						\
588 		RB_PARENT(child, field) = parent;			\
589 		RB_COLOR(child, field) = RB_BLACK;			\
590 	} else if (color != RB_RED && parent != NULL)			\
591 		name##_RB_REMOVE_COLOR(head, parent);			\
592 	while (parent != NULL) {					\
593 		RB_AUGMENT(parent);					\
594 		parent = RB_PARENT(parent, field);			\
595 	}								\
596 	return (old);							\
597 }
598 
599 #define RB_GENERATE_INSERT(name, type, field, cmp, attr)		\
600 /* Inserts a node into the RB tree */					\
601 attr struct type *							\
602 name##_RB_INSERT(struct name *head, struct type *elm)			\
603 {									\
604 	struct type *tmp;						\
605 	struct type *parent = NULL;					\
606 	int comp = 0;							\
607 	tmp = RB_ROOT(head);						\
608 	while (tmp) {							\
609 		parent = tmp;						\
610 		comp = (cmp)(elm, parent);				\
611 		if (comp < 0)						\
612 			tmp = RB_LEFT(tmp, field);			\
613 		else if (comp > 0)					\
614 			tmp = RB_RIGHT(tmp, field);			\
615 		else							\
616 			return (tmp);					\
617 	}								\
618 	RB_SET(elm, parent, field);					\
619 	if (parent != NULL) {						\
620 		if (comp < 0)						\
621 			RB_LEFT(parent, field) = elm;			\
622 		else							\
623 			RB_RIGHT(parent, field) = elm;			\
624 	} else								\
625 		RB_ROOT(head) = elm;					\
626 	name##_RB_INSERT_COLOR(head, elm);				\
627 	while (elm != NULL) {						\
628 		RB_AUGMENT(elm);					\
629 		elm = RB_PARENT(elm, field);				\
630 	}								\
631 	return (NULL);							\
632 }
633 
634 #define RB_GENERATE_FIND(name, type, field, cmp, attr)			\
635 /* Finds the node with the same key as elm */				\
636 attr struct type *							\
637 name##_RB_FIND(struct name *head, struct type *elm)			\
638 {									\
639 	struct type *tmp = RB_ROOT(head);				\
640 	int comp;							\
641 	while (tmp) {							\
642 		comp = cmp(elm, tmp);					\
643 		if (comp < 0)						\
644 			tmp = RB_LEFT(tmp, field);			\
645 		else if (comp > 0)					\
646 			tmp = RB_RIGHT(tmp, field);			\
647 		else							\
648 			return (tmp);					\
649 	}								\
650 	return (NULL);							\
651 }
652 
653 #define RB_GENERATE_NFIND(name, type, field, cmp, attr)			\
654 /* Finds the first node greater than or equal to the search key */	\
655 attr struct type *							\
656 name##_RB_NFIND(struct name *head, struct type *elm)			\
657 {									\
658 	struct type *tmp = RB_ROOT(head);				\
659 	struct type *res = NULL;					\
660 	int comp;							\
661 	while (tmp) {							\
662 		comp = cmp(elm, tmp);					\
663 		if (comp < 0) {						\
664 			res = tmp;					\
665 			tmp = RB_LEFT(tmp, field);			\
666 		}							\
667 		else if (comp > 0)					\
668 			tmp = RB_RIGHT(tmp, field);			\
669 		else							\
670 			return (tmp);					\
671 	}								\
672 	return (res);							\
673 }
674 
675 #define RB_GENERATE_NEXT(name, type, field, attr)			\
676 /* ARGSUSED */								\
677 attr struct type *							\
678 name##_RB_NEXT(struct type *elm)					\
679 {									\
680 	if (RB_RIGHT(elm, field)) {					\
681 		elm = RB_RIGHT(elm, field);				\
682 		while (RB_LEFT(elm, field))				\
683 			elm = RB_LEFT(elm, field);			\
684 	} else {							\
685 		if (RB_PARENT(elm, field) &&				\
686 		    (elm == RB_LEFT(RB_PARENT(elm, field), field)))	\
687 			elm = RB_PARENT(elm, field);			\
688 		else {							\
689 			while (RB_PARENT(elm, field) &&			\
690 			    (elm == RB_RIGHT(RB_PARENT(elm, field), field)))\
691 				elm = RB_PARENT(elm, field);		\
692 			elm = RB_PARENT(elm, field);			\
693 		}							\
694 	}								\
695 	return (elm);							\
696 }
697 
698 #define RB_GENERATE_PREV(name, type, field, attr)			\
699 /* ARGSUSED */								\
700 attr struct type *							\
701 name##_RB_PREV(struct type *elm)					\
702 {									\
703 	if (RB_LEFT(elm, field)) {					\
704 		elm = RB_LEFT(elm, field);				\
705 		while (RB_RIGHT(elm, field))				\
706 			elm = RB_RIGHT(elm, field);			\
707 	} else {							\
708 		if (RB_PARENT(elm, field) &&				\
709 		    (elm == RB_RIGHT(RB_PARENT(elm, field), field)))	\
710 			elm = RB_PARENT(elm, field);			\
711 		else {							\
712 			while (RB_PARENT(elm, field) &&			\
713 			    (elm == RB_LEFT(RB_PARENT(elm, field), field)))\
714 				elm = RB_PARENT(elm, field);		\
715 			elm = RB_PARENT(elm, field);			\
716 		}							\
717 	}								\
718 	return (elm);							\
719 }
720 
721 #define RB_GENERATE_MINMAX(name, type, field, attr)			\
722 attr struct type *							\
723 name##_RB_MINMAX(struct name *head, int val)				\
724 {									\
725 	struct type *tmp = RB_ROOT(head);				\
726 	struct type *parent = NULL;					\
727 	while (tmp) {							\
728 		parent = tmp;						\
729 		if (val < 0)						\
730 			tmp = RB_LEFT(tmp, field);			\
731 		else							\
732 			tmp = RB_RIGHT(tmp, field);			\
733 	}								\
734 	return (parent);						\
735 }
736 
737 #define	RB_GENERATE_REINSERT(name, type, field, cmp, attr)		\
738 attr struct type *							\
739 name##_RB_REINSERT(struct name *head, struct type *elm)			\
740 {									\
741 	struct type *cmpelm;						\
742 	if (((cmpelm = RB_PREV(name, head, elm)) != NULL &&		\
743 	    cmp(cmpelm, elm) >= 0) ||					\
744 	    ((cmpelm = RB_NEXT(name, head, elm)) != NULL &&		\
745 	    cmp(elm, cmpelm) >= 0)) {					\
746 		/* XXXLAS: Remove/insert is heavy handed. */		\
747 		RB_REMOVE(name, head, elm);				\
748 		return (RB_INSERT(name, head, elm));			\
749 	}								\
750 	return (NULL);							\
751 }									\
752 
753 #define RB_NEGINF	-1
754 #define RB_INF	1
755 
756 #define RB_INSERT(name, x, y)	name##_RB_INSERT(x, y)
757 #define RB_REMOVE(name, x, y)	name##_RB_REMOVE(x, y)
758 #define RB_FIND(name, x, y)	name##_RB_FIND(x, y)
759 #define RB_NFIND(name, x, y)	name##_RB_NFIND(x, y)
760 #define RB_NEXT(name, x, y)	name##_RB_NEXT(y)
761 #define RB_PREV(name, x, y)	name##_RB_PREV(y)
762 #define RB_MIN(name, x)		name##_RB_MINMAX(x, RB_NEGINF)
763 #define RB_MAX(name, x)		name##_RB_MINMAX(x, RB_INF)
764 #define RB_REINSERT(name, x, y)	name##_RB_REINSERT(x, y)
765 
766 #define RB_FOREACH(x, name, head)					\
767 	for ((x) = RB_MIN(name, head);					\
768 	     (x) != NULL;						\
769 	     (x) = name##_RB_NEXT(x))
770 
771 #define RB_FOREACH_FROM(x, name, y)					\
772 	for ((x) = (y);							\
773 	    ((x) != NULL) && ((y) = name##_RB_NEXT(x), (x) != NULL);	\
774 	     (x) = (y))
775 
776 #define RB_FOREACH_SAFE(x, name, head, y)				\
777 	for ((x) = RB_MIN(name, head);					\
778 	    ((x) != NULL) && ((y) = name##_RB_NEXT(x), (x) != NULL);	\
779 	     (x) = (y))
780 
781 #define RB_FOREACH_REVERSE(x, name, head)				\
782 	for ((x) = RB_MAX(name, head);					\
783 	     (x) != NULL;						\
784 	     (x) = name##_RB_PREV(x))
785 
786 #define RB_FOREACH_REVERSE_FROM(x, name, y)				\
787 	for ((x) = (y);							\
788 	    ((x) != NULL) && ((y) = name##_RB_PREV(x), (x) != NULL);	\
789 	     (x) = (y))
790 
791 #define RB_FOREACH_REVERSE_SAFE(x, name, head, y)			\
792 	for ((x) = RB_MAX(name, head);					\
793 	    ((x) != NULL) && ((y) = name##_RB_PREV(x), (x) != NULL);	\
794 	     (x) = (y))
795 
796 #endif	/* _SYS_TREE_H_ */
797