tree.h revision 277642
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 277642 2015-01-24 12:43:36Z kib $ */
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)						\
63struct 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)						\
75struct {								\
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)				\
120void name##_SPLAY(struct name *, struct type *);			\
121void name##_SPLAY_MINMAX(struct name *, int);				\
122struct type *name##_SPLAY_INSERT(struct name *, struct type *);		\
123struct type *name##_SPLAY_REMOVE(struct name *, struct type *);		\
124									\
125/* Finds the node with the same key as elm */				\
126static __inline struct type *						\
127name##_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									\
137static __inline struct type *						\
138name##_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									\
151static __inline struct type *						\
152name##_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)				\
162struct type *								\
163name##_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									\
186struct type *								\
187name##_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									\
207void									\
208name##_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 */									\
245void 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)						\
297struct 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)							\
311struct {								\
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	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#define RB_PROTOTYPE_INSERT_COLOR(name, type, attr)			\
396	attr void name##_RB_INSERT_COLOR(struct name *, struct type *)
397#define RB_PROTOTYPE_REMOVE_COLOR(name, type, attr)			\
398	attr void name##_RB_REMOVE_COLOR(struct name *, struct type *, struct type *)
399#define RB_PROTOTYPE_REMOVE(name, type, attr)				\
400	attr struct type *name##_RB_REMOVE(struct name *, struct type *)
401#define RB_PROTOTYPE_INSERT(name, type, attr)				\
402	attr struct type *name##_RB_INSERT(struct name *, struct type *)
403#define RB_PROTOTYPE_FIND(name, type, attr)				\
404	attr struct type *name##_RB_FIND(struct name *, struct type *)
405#define RB_PROTOTYPE_NFIND(name, type, attr)				\
406	attr struct type *name##_RB_NFIND(struct name *, struct type *)
407#define RB_PROTOTYPE_NEXT(name, type, attr)				\
408	attr struct type *name##_RB_NEXT(struct type *)
409#define RB_PROTOTYPE_PREV(name, type, attr)				\
410	attr struct type *name##_RB_PREV(struct type *)
411#define RB_PROTOTYPE_MINMAX(name, type, attr)				\
412	attr struct type *name##_RB_MINMAX(struct name *, int)
413
414/* Main rb operation.
415 * Moves node close to the key of elm to top
416 */
417#define	RB_GENERATE(name, type, field, cmp)				\
418	RB_GENERATE_INTERNAL(name, type, field, cmp,)
419#define	RB_GENERATE_STATIC(name, type, field, cmp)			\
420	RB_GENERATE_INTERNAL(name, type, field, cmp, __unused static)
421#define RB_GENERATE_INTERNAL(name, type, field, cmp, attr)		\
422	RB_GENERATE_INSERT_COLOR(name, type, field, attr)		\
423	RB_GENERATE_REMOVE_COLOR(name, type, field, attr)		\
424	RB_GENERATE_INSERT(name, type, field, cmp, attr)		\
425	RB_GENERATE_REMOVE(name, type, field, attr)			\
426	RB_GENERATE_FIND(name, type, field, cmp, attr)			\
427	RB_GENERATE_NFIND(name, type, field, cmp, attr)			\
428	RB_GENERATE_NEXT(name, type, field, attr)			\
429	RB_GENERATE_PREV(name, type, field, attr)			\
430	RB_GENERATE_MINMAX(name, type, field, attr)
431
432#define RB_GENERATE_INSERT_COLOR(name, type, field, attr)		\
433attr void								\
434name##_RB_INSERT_COLOR(struct name *head, struct type *elm)		\
435{									\
436	struct type *parent, *gparent, *tmp;				\
437	while ((parent = RB_PARENT(elm, field)) != NULL &&		\
438	    RB_COLOR(parent, field) == RB_RED) {			\
439		gparent = RB_PARENT(parent, field);			\
440		if (parent == RB_LEFT(gparent, field)) {		\
441			tmp = RB_RIGHT(gparent, field);			\
442			if (tmp && RB_COLOR(tmp, field) == RB_RED) {	\
443				RB_COLOR(tmp, field) = RB_BLACK;	\
444				RB_SET_BLACKRED(parent, gparent, field);\
445				elm = gparent;				\
446				continue;				\
447			}						\
448			if (RB_RIGHT(parent, field) == elm) {		\
449				RB_ROTATE_LEFT(head, parent, tmp, field);\
450				tmp = parent;				\
451				parent = elm;				\
452				elm = tmp;				\
453			}						\
454			RB_SET_BLACKRED(parent, gparent, field);	\
455			RB_ROTATE_RIGHT(head, gparent, tmp, field);	\
456		} else {						\
457			tmp = RB_LEFT(gparent, field);			\
458			if (tmp && RB_COLOR(tmp, field) == RB_RED) {	\
459				RB_COLOR(tmp, field) = RB_BLACK;	\
460				RB_SET_BLACKRED(parent, gparent, field);\
461				elm = gparent;				\
462				continue;				\
463			}						\
464			if (RB_LEFT(parent, field) == elm) {		\
465				RB_ROTATE_RIGHT(head, parent, tmp, field);\
466				tmp = parent;				\
467				parent = elm;				\
468				elm = tmp;				\
469			}						\
470			RB_SET_BLACKRED(parent, gparent, field);	\
471			RB_ROTATE_LEFT(head, gparent, tmp, field);	\
472		}							\
473	}								\
474	RB_COLOR(head->rbh_root, field) = RB_BLACK;			\
475}
476
477#define RB_GENERATE_REMOVE_COLOR(name, type, field, attr)		\
478attr void								\
479name##_RB_REMOVE_COLOR(struct name *head, struct type *parent, struct type *elm) \
480{									\
481	struct type *tmp;						\
482	while ((elm == NULL || RB_COLOR(elm, field) == RB_BLACK) &&	\
483	    elm != RB_ROOT(head)) {					\
484		if (RB_LEFT(parent, field) == elm) {			\
485			tmp = RB_RIGHT(parent, field);			\
486			if (RB_COLOR(tmp, field) == RB_RED) {		\
487				RB_SET_BLACKRED(tmp, parent, field);	\
488				RB_ROTATE_LEFT(head, parent, tmp, field);\
489				tmp = RB_RIGHT(parent, field);		\
490			}						\
491			if ((RB_LEFT(tmp, field) == NULL ||		\
492			    RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
493			    (RB_RIGHT(tmp, field) == NULL ||		\
494			    RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
495				RB_COLOR(tmp, field) = RB_RED;		\
496				elm = parent;				\
497				parent = RB_PARENT(elm, field);		\
498			} else {					\
499				if (RB_RIGHT(tmp, field) == NULL ||	\
500				    RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK) {\
501					struct type *oleft;		\
502					if ((oleft = RB_LEFT(tmp, field)) \
503					    != NULL)			\
504						RB_COLOR(oleft, field) = RB_BLACK;\
505					RB_COLOR(tmp, field) = RB_RED;	\
506					RB_ROTATE_RIGHT(head, tmp, oleft, field);\
507					tmp = RB_RIGHT(parent, field);	\
508				}					\
509				RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
510				RB_COLOR(parent, field) = RB_BLACK;	\
511				if (RB_RIGHT(tmp, field))		\
512					RB_COLOR(RB_RIGHT(tmp, field), field) = RB_BLACK;\
513				RB_ROTATE_LEFT(head, parent, tmp, field);\
514				elm = RB_ROOT(head);			\
515				break;					\
516			}						\
517		} else {						\
518			tmp = RB_LEFT(parent, field);			\
519			if (RB_COLOR(tmp, field) == RB_RED) {		\
520				RB_SET_BLACKRED(tmp, parent, field);	\
521				RB_ROTATE_RIGHT(head, parent, tmp, field);\
522				tmp = RB_LEFT(parent, field);		\
523			}						\
524			if ((RB_LEFT(tmp, field) == NULL ||		\
525			    RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
526			    (RB_RIGHT(tmp, field) == NULL ||		\
527			    RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
528				RB_COLOR(tmp, field) = RB_RED;		\
529				elm = parent;				\
530				parent = RB_PARENT(elm, field);		\
531			} else {					\
532				if (RB_LEFT(tmp, field) == NULL ||	\
533				    RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) {\
534					struct type *oright;		\
535					if ((oright = RB_RIGHT(tmp, field)) \
536					    != NULL)			\
537						RB_COLOR(oright, field) = RB_BLACK;\
538					RB_COLOR(tmp, field) = RB_RED;	\
539					RB_ROTATE_LEFT(head, tmp, oright, field);\
540					tmp = RB_LEFT(parent, field);	\
541				}					\
542				RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
543				RB_COLOR(parent, field) = RB_BLACK;	\
544				if (RB_LEFT(tmp, field))		\
545					RB_COLOR(RB_LEFT(tmp, field), field) = RB_BLACK;\
546				RB_ROTATE_RIGHT(head, parent, tmp, field);\
547				elm = RB_ROOT(head);			\
548				break;					\
549			}						\
550		}							\
551	}								\
552	if (elm)							\
553		RB_COLOR(elm, field) = RB_BLACK;			\
554}
555
556#define RB_GENERATE_REMOVE(name, type, field, attr)			\
557attr struct type *							\
558name##_RB_REMOVE(struct name *head, struct type *elm)			\
559{									\
560	struct type *child, *parent, *old = elm;			\
561	int color;							\
562	if (RB_LEFT(elm, field) == NULL)				\
563		child = RB_RIGHT(elm, field);				\
564	else if (RB_RIGHT(elm, field) == NULL)				\
565		child = RB_LEFT(elm, field);				\
566	else {								\
567		struct type *left;					\
568		elm = RB_RIGHT(elm, field);				\
569		while ((left = RB_LEFT(elm, field)) != NULL)		\
570			elm = left;					\
571		child = RB_RIGHT(elm, field);				\
572		parent = RB_PARENT(elm, field);				\
573		color = RB_COLOR(elm, field);				\
574		if (child)						\
575			RB_PARENT(child, field) = parent;		\
576		if (parent) {						\
577			if (RB_LEFT(parent, field) == elm)		\
578				RB_LEFT(parent, field) = child;		\
579			else						\
580				RB_RIGHT(parent, field) = child;	\
581			RB_AUGMENT(parent);				\
582		} else							\
583			RB_ROOT(head) = child;				\
584		if (RB_PARENT(elm, field) == old)			\
585			parent = elm;					\
586		(elm)->field = (old)->field;				\
587		if (RB_PARENT(old, field)) {				\
588			if (RB_LEFT(RB_PARENT(old, field), field) == old)\
589				RB_LEFT(RB_PARENT(old, field), field) = elm;\
590			else						\
591				RB_RIGHT(RB_PARENT(old, field), field) = elm;\
592			RB_AUGMENT(RB_PARENT(old, field));		\
593		} else							\
594			RB_ROOT(head) = elm;				\
595		RB_PARENT(RB_LEFT(old, field), field) = elm;		\
596		if (RB_RIGHT(old, field))				\
597			RB_PARENT(RB_RIGHT(old, field), field) = elm;	\
598		if (parent) {						\
599			left = parent;					\
600			do {						\
601				RB_AUGMENT(left);			\
602			} while ((left = RB_PARENT(left, field)) != NULL); \
603		}							\
604		goto color;						\
605	}								\
606	parent = RB_PARENT(elm, field);					\
607	color = RB_COLOR(elm, field);					\
608	if (child)							\
609		RB_PARENT(child, field) = parent;			\
610	if (parent) {							\
611		if (RB_LEFT(parent, field) == elm)			\
612			RB_LEFT(parent, field) = child;			\
613		else							\
614			RB_RIGHT(parent, field) = child;		\
615		RB_AUGMENT(parent);					\
616	} else								\
617		RB_ROOT(head) = child;					\
618color:									\
619	if (color == RB_BLACK)						\
620		name##_RB_REMOVE_COLOR(head, parent, child);		\
621	return (old);							\
622}									\
623
624#define RB_GENERATE_INSERT(name, type, field, cmp, attr)		\
625/* Inserts a node into the RB tree */					\
626attr struct type *							\
627name##_RB_INSERT(struct name *head, struct type *elm)			\
628{									\
629	struct type *tmp;						\
630	struct type *parent = NULL;					\
631	int comp = 0;							\
632	tmp = RB_ROOT(head);						\
633	while (tmp) {							\
634		parent = tmp;						\
635		comp = (cmp)(elm, parent);				\
636		if (comp < 0)						\
637			tmp = RB_LEFT(tmp, field);			\
638		else if (comp > 0)					\
639			tmp = RB_RIGHT(tmp, field);			\
640		else							\
641			return (tmp);					\
642	}								\
643	RB_SET(elm, parent, field);					\
644	if (parent != NULL) {						\
645		if (comp < 0)						\
646			RB_LEFT(parent, field) = elm;			\
647		else							\
648			RB_RIGHT(parent, field) = elm;			\
649		RB_AUGMENT(parent);					\
650	} else								\
651		RB_ROOT(head) = elm;					\
652	name##_RB_INSERT_COLOR(head, elm);				\
653	return (NULL);							\
654}
655
656#define RB_GENERATE_FIND(name, type, field, cmp, attr)			\
657/* Finds the node with the same key as elm */				\
658attr struct type *							\
659name##_RB_FIND(struct name *head, struct type *elm)			\
660{									\
661	struct type *tmp = RB_ROOT(head);				\
662	int comp;							\
663	while (tmp) {							\
664		comp = cmp(elm, tmp);					\
665		if (comp < 0)						\
666			tmp = RB_LEFT(tmp, field);			\
667		else if (comp > 0)					\
668			tmp = RB_RIGHT(tmp, field);			\
669		else							\
670			return (tmp);					\
671	}								\
672	return (NULL);							\
673}
674
675#define RB_GENERATE_NFIND(name, type, field, cmp, attr)			\
676/* Finds the first node greater than or equal to the search key */	\
677attr struct type *							\
678name##_RB_NFIND(struct name *head, struct type *elm)			\
679{									\
680	struct type *tmp = RB_ROOT(head);				\
681	struct type *res = NULL;					\
682	int comp;							\
683	while (tmp) {							\
684		comp = cmp(elm, tmp);					\
685		if (comp < 0) {						\
686			res = tmp;					\
687			tmp = RB_LEFT(tmp, field);			\
688		}							\
689		else if (comp > 0)					\
690			tmp = RB_RIGHT(tmp, field);			\
691		else							\
692			return (tmp);					\
693	}								\
694	return (res);							\
695}
696
697#define RB_GENERATE_NEXT(name, type, field, attr)			\
698/* ARGSUSED */								\
699attr struct type *							\
700name##_RB_NEXT(struct type *elm)					\
701{									\
702	if (RB_RIGHT(elm, field)) {					\
703		elm = RB_RIGHT(elm, field);				\
704		while (RB_LEFT(elm, field))				\
705			elm = RB_LEFT(elm, field);			\
706	} else {							\
707		if (RB_PARENT(elm, field) &&				\
708		    (elm == RB_LEFT(RB_PARENT(elm, field), field)))	\
709			elm = RB_PARENT(elm, field);			\
710		else {							\
711			while (RB_PARENT(elm, field) &&			\
712			    (elm == RB_RIGHT(RB_PARENT(elm, field), field)))\
713				elm = RB_PARENT(elm, field);		\
714			elm = RB_PARENT(elm, field);			\
715		}							\
716	}								\
717	return (elm);							\
718}
719
720#define RB_GENERATE_PREV(name, type, field, attr)			\
721/* ARGSUSED */								\
722attr struct type *							\
723name##_RB_PREV(struct type *elm)					\
724{									\
725	if (RB_LEFT(elm, field)) {					\
726		elm = RB_LEFT(elm, field);				\
727		while (RB_RIGHT(elm, field))				\
728			elm = RB_RIGHT(elm, field);			\
729	} else {							\
730		if (RB_PARENT(elm, field) &&				\
731		    (elm == RB_RIGHT(RB_PARENT(elm, field), field)))	\
732			elm = RB_PARENT(elm, field);			\
733		else {							\
734			while (RB_PARENT(elm, field) &&			\
735			    (elm == RB_LEFT(RB_PARENT(elm, field), field)))\
736				elm = RB_PARENT(elm, field);		\
737			elm = RB_PARENT(elm, field);			\
738		}							\
739	}								\
740	return (elm);							\
741}
742
743#define RB_GENERATE_MINMAX(name, type, field, attr)			\
744attr struct type *							\
745name##_RB_MINMAX(struct name *head, int val)				\
746{									\
747	struct type *tmp = RB_ROOT(head);				\
748	struct type *parent = NULL;					\
749	while (tmp) {							\
750		parent = tmp;						\
751		if (val < 0)						\
752			tmp = RB_LEFT(tmp, field);			\
753		else							\
754			tmp = RB_RIGHT(tmp, field);			\
755	}								\
756	return (parent);						\
757}
758
759#define RB_NEGINF	-1
760#define RB_INF	1
761
762#define RB_INSERT(name, x, y)	name##_RB_INSERT(x, y)
763#define RB_REMOVE(name, x, y)	name##_RB_REMOVE(x, y)
764#define RB_FIND(name, x, y)	name##_RB_FIND(x, y)
765#define RB_NFIND(name, x, y)	name##_RB_NFIND(x, y)
766#define RB_NEXT(name, x, y)	name##_RB_NEXT(y)
767#define RB_PREV(name, x, y)	name##_RB_PREV(y)
768#define RB_MIN(name, x)		name##_RB_MINMAX(x, RB_NEGINF)
769#define RB_MAX(name, x)		name##_RB_MINMAX(x, RB_INF)
770
771#define RB_FOREACH(x, name, head)					\
772	for ((x) = RB_MIN(name, head);					\
773	     (x) != NULL;						\
774	     (x) = name##_RB_NEXT(x))
775
776#define RB_FOREACH_FROM(x, name, y)					\
777	for ((x) = (y);							\
778	    ((x) != NULL) && ((y) = name##_RB_NEXT(x), (x) != NULL);	\
779	     (x) = (y))
780
781#define RB_FOREACH_SAFE(x, name, head, y)				\
782	for ((x) = RB_MIN(name, head);					\
783	    ((x) != NULL) && ((y) = name##_RB_NEXT(x), (x) != NULL);	\
784	     (x) = (y))
785
786#define RB_FOREACH_REVERSE(x, name, head)				\
787	for ((x) = RB_MAX(name, head);					\
788	     (x) != NULL;						\
789	     (x) = name##_RB_PREV(x))
790
791#define RB_FOREACH_REVERSE_FROM(x, name, y)				\
792	for ((x) = (y);							\
793	    ((x) != NULL) && ((y) = name##_RB_PREV(x), (x) != NULL);	\
794	     (x) = (y))
795
796#define RB_FOREACH_REVERSE_SAFE(x, name, head, y)			\
797	for ((x) = RB_MAX(name, head);					\
798	    ((x) != NULL) && ((y) = name##_RB_PREV(x), (x) != NULL);	\
799	     (x) = (y))
800
801#endif	/* _SYS_TREE_H_ */
802