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: src/sys/sys/tree.h,v 1.7 2007/12/28 07:03:26 jasone Exp $ */
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/*
34 * This file defines data structures for different types of trees:
35 * splay trees and red-black trees.
36 *
37 * A splay tree is a self-organizing data structure.  Every operation
38 * on the tree causes a splay to happen.  The splay moves the requested
39 * node to the root of the tree and partly rebalances it.
40 *
41 * This has the benefit that request locality causes faster lookups as
42 * the requested nodes move to the top of the tree.  On the other hand,
43 * every lookup causes memory writes.
44 *
45 * The Balance Theorem bounds the total access time for m operations
46 * and n inserts on an initially empty tree as O((m + n)lg n).  The
47 * amortized cost for a sequence of m accesses to a splay tree is O(lg n);
48 *
49 * A red-black tree is a binary search tree with the node color as an
50 * extra attribute.  It fulfills a set of conditions:
51 *	- every search path from the root to a leaf consists of the
52 *	  same number of black nodes,
53 *	- each red node (except for the root) has a black parent,
54 *	- each leaf node is black.
55 *
56 * Every operation on a red-black tree is bounded as O(lg n).
57 * The maximum height of a red-black tree is 2lg (n+1).
58 */
59
60#define SPLAY_HEAD(name, type)						\
61struct name {								\
62	struct type *sph_root; /* root of the tree */			\
63}
64
65#define SPLAY_INITIALIZER(root)						\
66	{ NULL }
67
68#define SPLAY_INIT(root) do {						\
69	(root)->sph_root = NULL;					\
70} while (/*CONSTCOND*/ 0)
71
72#define SPLAY_ENTRY(type)						\
73struct {								\
74	struct type *spe_left; /* left element */			\
75	struct type *spe_right; /* right element */			\
76}
77
78#define SPLAY_LEFT(elm, field)		(elm)->field.spe_left
79#define SPLAY_RIGHT(elm, field)		(elm)->field.spe_right
80#define SPLAY_ROOT(head)		(head)->sph_root
81#define SPLAY_EMPTY(head)		(SPLAY_ROOT(head) == NULL)
82
83/* SPLAY_ROTATE_{LEFT,RIGHT} expect that tmp hold SPLAY_{RIGHT,LEFT} */
84#define SPLAY_ROTATE_RIGHT(head, tmp, field) do {			\
85	SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(tmp, field);	\
86	SPLAY_RIGHT(tmp, field) = (head)->sph_root;			\
87	(head)->sph_root = tmp;						\
88} while (/*CONSTCOND*/ 0)
89
90#define SPLAY_ROTATE_LEFT(head, tmp, field) do {			\
91	SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(tmp, field);	\
92	SPLAY_LEFT(tmp, field) = (head)->sph_root;			\
93	(head)->sph_root = tmp;						\
94} while (/*CONSTCOND*/ 0)
95
96#define SPLAY_LINKLEFT(head, tmp, field) do {				\
97	SPLAY_LEFT(tmp, field) = (head)->sph_root;			\
98	tmp = (head)->sph_root;						\
99	(head)->sph_root = SPLAY_LEFT((head)->sph_root, field);		\
100} while (/*CONSTCOND*/ 0)
101
102#define SPLAY_LINKRIGHT(head, tmp, field) do {				\
103	SPLAY_RIGHT(tmp, field) = (head)->sph_root;			\
104	tmp = (head)->sph_root;						\
105	(head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);	\
106} while (/*CONSTCOND*/ 0)
107
108#define SPLAY_ASSEMBLE(head, node, left, right, field) do {		\
109	SPLAY_RIGHT(left, field) = SPLAY_LEFT((head)->sph_root, field);	\
110	SPLAY_LEFT(right, field) = SPLAY_RIGHT((head)->sph_root, field);\
111	SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(node, field);	\
112	SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(node, field);	\
113} while (/*CONSTCOND*/ 0)
114
115/* Generates prototypes and inline functions */
116
117#define SPLAY_PROTOTYPE(name, type, field, cmp)				\
118void name##_SPLAY(struct name *, struct type *);			\
119void name##_SPLAY_MINMAX(struct name *, int);				\
120struct type *name##_SPLAY_INSERT(struct name *, struct type *);		\
121struct type *name##_SPLAY_REMOVE(struct name *, struct type *);		\
122									\
123/* Finds the node with the same key as elm */				\
124static __inline struct type *						\
125name##_SPLAY_FIND(struct name *head, struct type *elm)			\
126{									\
127	if (SPLAY_EMPTY(head))						\
128		return(NULL);						\
129	name##_SPLAY(head, elm);					\
130	if ((cmp)(elm, (head)->sph_root) == 0)				\
131		return (head->sph_root);				\
132	return (NULL);							\
133}									\
134									\
135static __inline struct type *						\
136name##_SPLAY_NEXT(struct name *head, struct type *elm)			\
137{									\
138	name##_SPLAY(head, elm);					\
139	if (SPLAY_RIGHT(elm, field) != NULL) {				\
140		elm = SPLAY_RIGHT(elm, field);				\
141		while (SPLAY_LEFT(elm, field) != NULL) {		\
142			elm = SPLAY_LEFT(elm, field);			\
143		}							\
144	} else								\
145		elm = NULL;						\
146	return (elm);							\
147}									\
148									\
149static __inline struct type *						\
150name##_SPLAY_MIN_MAX(struct name *head, int val)			\
151{									\
152	name##_SPLAY_MINMAX(head, val);					\
153        return (SPLAY_ROOT(head));					\
154}
155
156/* Main splay operation.
157 * Moves node close to the key of elm to top
158 */
159#define SPLAY_GENERATE(name, type, field, cmp)				\
160struct type *								\
161name##_SPLAY_INSERT(struct name *head, struct type *elm)		\
162{									\
163    if (SPLAY_EMPTY(head)) {						\
164	    SPLAY_LEFT(elm, field) = SPLAY_RIGHT(elm, field) = NULL;	\
165    } else {								\
166	    int __comp;							\
167	    name##_SPLAY(head, elm);					\
168	    __comp = (cmp)(elm, (head)->sph_root);			\
169	    if(__comp < 0) {						\
170		    SPLAY_LEFT(elm, field) = SPLAY_LEFT((head)->sph_root, field);\
171		    SPLAY_RIGHT(elm, field) = (head)->sph_root;		\
172		    SPLAY_LEFT((head)->sph_root, field) = NULL;		\
173	    } else if (__comp > 0) {					\
174		    SPLAY_RIGHT(elm, field) = SPLAY_RIGHT((head)->sph_root, field);\
175		    SPLAY_LEFT(elm, field) = (head)->sph_root;		\
176		    SPLAY_RIGHT((head)->sph_root, field) = NULL;	\
177	    } else							\
178		    return ((head)->sph_root);				\
179    }									\
180    (head)->sph_root = (elm);						\
181    return (NULL);							\
182}									\
183									\
184struct type *								\
185name##_SPLAY_REMOVE(struct name *head, struct type *elm)		\
186{									\
187	struct type *__tmp;						\
188	if (SPLAY_EMPTY(head))						\
189		return (NULL);						\
190	name##_SPLAY(head, elm);					\
191	if ((cmp)(elm, (head)->sph_root) == 0) {			\
192		if (SPLAY_LEFT((head)->sph_root, field) == NULL) {	\
193			(head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);\
194		} else {						\
195			__tmp = SPLAY_RIGHT((head)->sph_root, field);	\
196			(head)->sph_root = SPLAY_LEFT((head)->sph_root, field);\
197			name##_SPLAY(head, elm);			\
198			SPLAY_RIGHT((head)->sph_root, field) = __tmp;	\
199		}							\
200		return (elm);						\
201	}								\
202	return (NULL);							\
203}									\
204									\
205void									\
206name##_SPLAY(struct name *head, struct type *elm)			\
207{									\
208	struct type __node, *__left, *__right, *__tmp;			\
209	int __comp;							\
210\
211	SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
212	__left = __right = &__node;					\
213\
214	while ((__comp = (cmp)(elm, (head)->sph_root)) != 0) {		\
215		if (__comp < 0) {					\
216			__tmp = SPLAY_LEFT((head)->sph_root, field);	\
217			if (__tmp == NULL)				\
218				break;					\
219			if ((cmp)(elm, __tmp) < 0){			\
220				SPLAY_ROTATE_RIGHT(head, __tmp, field);	\
221				if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
222					break;				\
223			}						\
224			SPLAY_LINKLEFT(head, __right, field);		\
225		} else if (__comp > 0) {				\
226			__tmp = SPLAY_RIGHT((head)->sph_root, field);	\
227			if (__tmp == NULL)				\
228				break;					\
229			if ((cmp)(elm, __tmp) > 0){			\
230				SPLAY_ROTATE_LEFT(head, __tmp, field);	\
231				if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
232					break;				\
233			}						\
234			SPLAY_LINKRIGHT(head, __left, field);		\
235		}							\
236	}								\
237	SPLAY_ASSEMBLE(head, &__node, __left, __right, field);		\
238}									\
239									\
240/* Splay with either the minimum or the maximum element			\
241 * Used to find minimum or maximum element in tree.			\
242 */									\
243void name##_SPLAY_MINMAX(struct name *head, int __comp) \
244{									\
245	struct type __node, *__left, *__right, *__tmp;			\
246\
247	SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
248	__left = __right = &__node;					\
249\
250	while (1) {							\
251		if (__comp < 0) {					\
252			__tmp = SPLAY_LEFT((head)->sph_root, field);	\
253			if (__tmp == NULL)				\
254				break;					\
255			if (__comp < 0){				\
256				SPLAY_ROTATE_RIGHT(head, __tmp, field);	\
257				if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
258					break;				\
259			}						\
260			SPLAY_LINKLEFT(head, __right, field);		\
261		} else if (__comp > 0) {				\
262			__tmp = SPLAY_RIGHT((head)->sph_root, field);	\
263			if (__tmp == NULL)				\
264				break;					\
265			if (__comp > 0) {				\
266				SPLAY_ROTATE_LEFT(head, __tmp, field);	\
267				if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
268					break;				\
269			}						\
270			SPLAY_LINKRIGHT(head, __left, field);		\
271		}							\
272	}								\
273	SPLAY_ASSEMBLE(head, &__node, __left, __right, field);		\
274}
275
276#define SPLAY_NEGINF	-1
277#define SPLAY_INF	1
278
279#define SPLAY_INSERT(name, x, y)	name##_SPLAY_INSERT(x, y)
280#define SPLAY_REMOVE(name, x, y)	name##_SPLAY_REMOVE(x, y)
281#define SPLAY_FIND(name, x, y)		name##_SPLAY_FIND(x, y)
282#define SPLAY_NEXT(name, x, y)		name##_SPLAY_NEXT(x, y)
283#define SPLAY_MIN(name, x)		(SPLAY_EMPTY(x) ? NULL	\
284					: name##_SPLAY_MIN_MAX(x, SPLAY_NEGINF))
285#define SPLAY_MAX(name, x)		(SPLAY_EMPTY(x) ? NULL	\
286					: name##_SPLAY_MIN_MAX(x, SPLAY_INF))
287
288#define SPLAY_FOREACH(x, name, head)					\
289	for ((x) = SPLAY_MIN(name, head);				\
290	     (x) != NULL;						\
291	     (x) = SPLAY_NEXT(name, head, x))
292
293/* Macros that define a red-black tree */
294#define RB_HEAD(name, type)						\
295struct name {								\
296	struct type *rbh_root; /* root of the tree */			\
297}
298
299#define RB_INITIALIZER(root)						\
300	{ NULL }
301
302#define RB_INIT(root) do {						\
303	(root)->rbh_root = NULL;					\
304} while (/*CONSTCOND*/ 0)
305
306/*
307 * Undef for Linux
308 */
309#undef	RB_BLACK
310#undef	RB_RED
311#undef	RB_ROOT
312
313#define RB_BLACK	0
314#define RB_RED		1
315#define RB_ENTRY(type)							\
316struct {								\
317	struct type *rbe_left;		/* left element */		\
318	struct type *rbe_right;		/* right element */		\
319	struct type *rbe_parent;	/* parent element */		\
320	int rbe_color;			/* node color */		\
321}
322
323#define RB_LEFT(elm, field)		(elm)->field.rbe_left
324#define RB_RIGHT(elm, field)		(elm)->field.rbe_right
325#define RB_PARENT(elm, field)		(elm)->field.rbe_parent
326#define RB_COLOR(elm, field)		(elm)->field.rbe_color
327#define RB_ROOT(head)			(head)->rbh_root
328#define RB_EMPTY(head)			(RB_ROOT(head) == NULL)
329
330#define RB_SET(elm, parent, field) do {					\
331	RB_PARENT(elm, field) = parent;					\
332	RB_LEFT(elm, field) = RB_RIGHT(elm, field) = NULL;		\
333	RB_COLOR(elm, field) = RB_RED;					\
334} while (/*CONSTCOND*/ 0)
335
336#define RB_SET_BLACKRED(black, red, field) do {				\
337	RB_COLOR(black, field) = RB_BLACK;				\
338	RB_COLOR(red, field) = RB_RED;					\
339} while (/*CONSTCOND*/ 0)
340
341#ifndef RB_AUGMENT
342#define RB_AUGMENT(x)	do {} while (0)
343#endif
344
345#define RB_ROTATE_LEFT(head, elm, tmp, field) do {			\
346	(tmp) = RB_RIGHT(elm, field);					\
347	if ((RB_RIGHT(elm, field) = RB_LEFT(tmp, field)) != NULL) {	\
348		RB_PARENT(RB_LEFT(tmp, field), field) = (elm);		\
349	}								\
350	RB_AUGMENT(elm);						\
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(tmp);						\
361	if ((RB_PARENT(tmp, field)))					\
362		RB_AUGMENT(RB_PARENT(tmp, field));			\
363} while (/*CONSTCOND*/ 0)
364
365#define RB_ROTATE_RIGHT(head, elm, tmp, field) do {			\
366	(tmp) = RB_LEFT(elm, field);					\
367	if ((RB_LEFT(elm, field) = RB_RIGHT(tmp, field)) != NULL) {	\
368		RB_PARENT(RB_RIGHT(tmp, field), field) = (elm);		\
369	}								\
370	RB_AUGMENT(elm);						\
371	if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) {	\
372		if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))	\
373			RB_LEFT(RB_PARENT(elm, field), field) = (tmp);	\
374		else							\
375			RB_RIGHT(RB_PARENT(elm, field), field) = (tmp);	\
376	} else								\
377		(head)->rbh_root = (tmp);				\
378	RB_RIGHT(tmp, field) = (elm);					\
379	RB_PARENT(elm, field) = (tmp);					\
380	RB_AUGMENT(tmp);						\
381	if ((RB_PARENT(tmp, field)))					\
382		RB_AUGMENT(RB_PARENT(tmp, field));			\
383} while (/*CONSTCOND*/ 0)
384
385/* Generates prototypes and inline functions */
386#define	RB_PROTOTYPE(name, type, field, cmp)				\
387	RB_PROTOTYPE_INTERNAL(name, type, field, cmp,)
388#define	RB_PROTOTYPE_STATIC(name, type, field, cmp)			\
389	RB_PROTOTYPE_INTERNAL(name, type, field, cmp, __unused static)
390#define RB_PROTOTYPE_INTERNAL(name, type, field, cmp, attr)		\
391attr void name##_RB_INSERT_COLOR(struct name *, struct type *);		\
392attr void name##_RB_REMOVE_COLOR(struct name *, struct type *, struct type *);\
393attr struct type *name##_RB_REMOVE(struct name *, struct type *);	\
394attr struct type *name##_RB_INSERT(struct name *, struct type *);	\
395attr struct type *name##_RB_FIND(struct name *, struct type *);		\
396attr struct type *name##_RB_NFIND(struct name *, struct type *);	\
397attr struct type *name##_RB_NEXT(struct type *);			\
398attr struct type *name##_RB_PREV(struct type *);			\
399attr struct type *name##_RB_MINMAX(struct name *, int);			\
400									\
401
402/* Main rb operation.
403 * Moves node close to the key of elm to top
404 */
405#define	RB_GENERATE(name, type, field, cmp)				\
406	RB_GENERATE_INTERNAL(name, type, field, cmp,)
407#define	RB_GENERATE_STATIC(name, type, field, cmp)			\
408	RB_GENERATE_INTERNAL(name, type, field, cmp, __unused static)
409#define RB_GENERATE_INTERNAL(name, type, field, cmp, attr)		\
410attr void								\
411name##_RB_INSERT_COLOR(struct name *head, struct type *elm)		\
412{									\
413	struct type *parent, *gparent, *tmp;				\
414	while ((parent = RB_PARENT(elm, field)) != NULL &&		\
415	    RB_COLOR(parent, field) == RB_RED) {			\
416		gparent = RB_PARENT(parent, field);			\
417		if (parent == RB_LEFT(gparent, field)) {		\
418			tmp = RB_RIGHT(gparent, field);			\
419			if (tmp && RB_COLOR(tmp, field) == RB_RED) {	\
420				RB_COLOR(tmp, field) = RB_BLACK;	\
421				RB_SET_BLACKRED(parent, gparent, field);\
422				elm = gparent;				\
423				continue;				\
424			}						\
425			if (RB_RIGHT(parent, field) == elm) {		\
426				RB_ROTATE_LEFT(head, parent, tmp, field);\
427				tmp = parent;				\
428				parent = elm;				\
429				elm = tmp;				\
430			}						\
431			RB_SET_BLACKRED(parent, gparent, field);	\
432			RB_ROTATE_RIGHT(head, gparent, tmp, field);	\
433		} else {						\
434			tmp = RB_LEFT(gparent, field);			\
435			if (tmp && RB_COLOR(tmp, field) == RB_RED) {	\
436				RB_COLOR(tmp, field) = RB_BLACK;	\
437				RB_SET_BLACKRED(parent, gparent, field);\
438				elm = gparent;				\
439				continue;				\
440			}						\
441			if (RB_LEFT(parent, field) == elm) {		\
442				RB_ROTATE_RIGHT(head, parent, tmp, field);\
443				tmp = parent;				\
444				parent = elm;				\
445				elm = tmp;				\
446			}						\
447			RB_SET_BLACKRED(parent, gparent, field);	\
448			RB_ROTATE_LEFT(head, gparent, tmp, field);	\
449		}							\
450	}								\
451	RB_COLOR(head->rbh_root, field) = RB_BLACK;			\
452}									\
453									\
454attr void								\
455name##_RB_REMOVE_COLOR(struct name *head, struct type *parent, struct type *elm) \
456{									\
457	struct type *tmp;						\
458	while ((elm == NULL || RB_COLOR(elm, field) == RB_BLACK) &&	\
459	    elm != RB_ROOT(head)) {					\
460		if (RB_LEFT(parent, field) == elm) {			\
461			tmp = RB_RIGHT(parent, field);			\
462			if (RB_COLOR(tmp, field) == RB_RED) {		\
463				RB_SET_BLACKRED(tmp, parent, field);	\
464				RB_ROTATE_LEFT(head, parent, tmp, field);\
465				tmp = RB_RIGHT(parent, field);		\
466			}						\
467			if ((RB_LEFT(tmp, field) == NULL ||		\
468			    RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
469			    (RB_RIGHT(tmp, field) == NULL ||		\
470			    RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
471				RB_COLOR(tmp, field) = RB_RED;		\
472				elm = parent;				\
473				parent = RB_PARENT(elm, field);		\
474			} else {					\
475				if (RB_RIGHT(tmp, field) == NULL ||	\
476				    RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK) {\
477					struct type *oleft;		\
478					if ((oleft = RB_LEFT(tmp, field)) \
479					    != NULL)			\
480						RB_COLOR(oleft, field) = RB_BLACK;\
481					RB_COLOR(tmp, field) = RB_RED;	\
482					RB_ROTATE_RIGHT(head, tmp, oleft, field);\
483					tmp = RB_RIGHT(parent, field);	\
484				}					\
485				RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
486				RB_COLOR(parent, field) = RB_BLACK;	\
487				if (RB_RIGHT(tmp, field))		\
488					RB_COLOR(RB_RIGHT(tmp, field), field) = RB_BLACK;\
489				RB_ROTATE_LEFT(head, parent, tmp, field);\
490				elm = RB_ROOT(head);			\
491				break;					\
492			}						\
493		} else {						\
494			tmp = RB_LEFT(parent, field);			\
495			if (RB_COLOR(tmp, field) == RB_RED) {		\
496				RB_SET_BLACKRED(tmp, parent, field);	\
497				RB_ROTATE_RIGHT(head, parent, tmp, field);\
498				tmp = RB_LEFT(parent, field);		\
499			}						\
500			if ((RB_LEFT(tmp, field) == NULL ||		\
501			    RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
502			    (RB_RIGHT(tmp, field) == NULL ||		\
503			    RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
504				RB_COLOR(tmp, field) = RB_RED;		\
505				elm = parent;				\
506				parent = RB_PARENT(elm, field);		\
507			} else {					\
508				if (RB_LEFT(tmp, field) == NULL ||	\
509				    RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) {\
510					struct type *oright;		\
511					if ((oright = RB_RIGHT(tmp, field)) \
512					    != NULL)			\
513						RB_COLOR(oright, field) = RB_BLACK;\
514					RB_COLOR(tmp, field) = RB_RED;	\
515					RB_ROTATE_LEFT(head, tmp, oright, field);\
516					tmp = RB_LEFT(parent, field);	\
517				}					\
518				RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
519				RB_COLOR(parent, field) = RB_BLACK;	\
520				if (RB_LEFT(tmp, field))		\
521					RB_COLOR(RB_LEFT(tmp, field), field) = RB_BLACK;\
522				RB_ROTATE_RIGHT(head, parent, tmp, field);\
523				elm = RB_ROOT(head);			\
524				break;					\
525			}						\
526		}							\
527	}								\
528	if (elm)							\
529		RB_COLOR(elm, field) = RB_BLACK;			\
530}									\
531									\
532attr struct type *							\
533name##_RB_REMOVE(struct name *head, struct type *elm)			\
534{									\
535	struct type *child, *parent, *old = elm;			\
536	int color;							\
537	if (RB_LEFT(elm, field) == NULL)				\
538		child = RB_RIGHT(elm, field);				\
539	else if (RB_RIGHT(elm, field) == NULL)				\
540		child = RB_LEFT(elm, field);				\
541	else {								\
542		struct type *left;					\
543		elm = RB_RIGHT(elm, field);				\
544		while ((left = RB_LEFT(elm, field)) != NULL)		\
545			elm = left;					\
546		child = RB_RIGHT(elm, field);				\
547		parent = RB_PARENT(elm, field);				\
548		color = RB_COLOR(elm, field);				\
549		if (child)						\
550			RB_PARENT(child, field) = parent;		\
551		if (parent) {						\
552			if (RB_LEFT(parent, field) == elm)		\
553				RB_LEFT(parent, field) = child;		\
554			else						\
555				RB_RIGHT(parent, field) = child;	\
556			RB_AUGMENT(parent);				\
557		} else							\
558			RB_ROOT(head) = child;				\
559		if (RB_PARENT(elm, field) == old)			\
560			parent = elm;					\
561		(elm)->field = (old)->field;				\
562		if (RB_PARENT(old, field)) {				\
563			if (RB_LEFT(RB_PARENT(old, field), field) == old)\
564				RB_LEFT(RB_PARENT(old, field), field) = elm;\
565			else						\
566				RB_RIGHT(RB_PARENT(old, field), field) = elm;\
567			RB_AUGMENT(RB_PARENT(old, field));		\
568		} else							\
569			RB_ROOT(head) = elm;				\
570		RB_PARENT(RB_LEFT(old, field), field) = elm;		\
571		if (RB_RIGHT(old, field))				\
572			RB_PARENT(RB_RIGHT(old, field), field) = elm;	\
573		if (parent) {						\
574			left = parent;					\
575			do {						\
576				RB_AUGMENT(left);			\
577			} while ((left = RB_PARENT(left, field)) != NULL); \
578		}							\
579		goto color;						\
580	}								\
581	parent = RB_PARENT(elm, field);					\
582	color = RB_COLOR(elm, field);					\
583	if (child)							\
584		RB_PARENT(child, field) = parent;			\
585	if (parent) {							\
586		if (RB_LEFT(parent, field) == elm)			\
587			RB_LEFT(parent, field) = child;			\
588		else							\
589			RB_RIGHT(parent, field) = child;		\
590		RB_AUGMENT(parent);					\
591	} else								\
592		RB_ROOT(head) = child;					\
593color:									\
594	if (color == RB_BLACK)						\
595		name##_RB_REMOVE_COLOR(head, parent, child);		\
596	return (old);							\
597}									\
598									\
599/* Inserts a node into the RB tree */					\
600attr struct type *							\
601name##_RB_INSERT(struct name *head, struct type *elm)			\
602{									\
603	struct type *tmp;						\
604	struct type *parent = NULL;					\
605	int comp = 0;							\
606	tmp = RB_ROOT(head);						\
607	while (tmp) {							\
608		parent = tmp;						\
609		comp = (cmp)(elm, parent);				\
610		if (comp < 0)						\
611			tmp = RB_LEFT(tmp, field);			\
612		else if (comp > 0)					\
613			tmp = RB_RIGHT(tmp, field);			\
614		else							\
615			return (tmp);					\
616	}								\
617	RB_SET(elm, parent, field);					\
618	if (parent != NULL) {						\
619		if (comp < 0)						\
620			RB_LEFT(parent, field) = elm;			\
621		else							\
622			RB_RIGHT(parent, field) = elm;			\
623		RB_AUGMENT(parent);					\
624	} else								\
625		RB_ROOT(head) = elm;					\
626	name##_RB_INSERT_COLOR(head, elm);				\
627	return (NULL);							\
628}									\
629									\
630/* Finds the node with the same key as elm */				\
631attr struct type *							\
632name##_RB_FIND(struct name *head, struct type *elm)			\
633{									\
634	struct type *tmp = RB_ROOT(head);				\
635	int comp;							\
636	while (tmp) {							\
637		comp = cmp(elm, tmp);					\
638		if (comp < 0)						\
639			tmp = RB_LEFT(tmp, field);			\
640		else if (comp > 0)					\
641			tmp = RB_RIGHT(tmp, field);			\
642		else							\
643			return (tmp);					\
644	}								\
645	return (NULL);							\
646}									\
647									\
648/* Finds the first node greater than or equal to the search key */	\
649attr struct type *							\
650name##_RB_NFIND(struct name *head, struct type *elm)			\
651{									\
652	struct type *tmp = RB_ROOT(head);				\
653	struct type *res = NULL;					\
654	int comp;							\
655	while (tmp) {							\
656		comp = cmp(elm, tmp);					\
657		if (comp < 0) {						\
658			res = tmp;					\
659			tmp = RB_LEFT(tmp, field);			\
660		}							\
661		else if (comp > 0)					\
662			tmp = RB_RIGHT(tmp, field);			\
663		else							\
664			return (tmp);					\
665	}								\
666	return (res);							\
667}									\
668									\
669/* ARGSUSED */								\
670attr struct type *							\
671name##_RB_NEXT(struct type *elm)					\
672{									\
673	if (RB_RIGHT(elm, field)) {					\
674		elm = RB_RIGHT(elm, field);				\
675		while (RB_LEFT(elm, field))				\
676			elm = RB_LEFT(elm, field);			\
677	} else {							\
678		if (RB_PARENT(elm, field) &&				\
679		    (elm == RB_LEFT(RB_PARENT(elm, field), field)))	\
680			elm = RB_PARENT(elm, field);			\
681		else {							\
682			while (RB_PARENT(elm, field) &&			\
683			    (elm == RB_RIGHT(RB_PARENT(elm, field), field)))\
684				elm = RB_PARENT(elm, field);		\
685			elm = RB_PARENT(elm, field);			\
686		}							\
687	}								\
688	return (elm);							\
689}									\
690									\
691/* ARGSUSED */								\
692attr struct type *							\
693name##_RB_PREV(struct type *elm)					\
694{									\
695	if (RB_LEFT(elm, field)) {					\
696		elm = RB_LEFT(elm, field);				\
697		while (RB_RIGHT(elm, field))				\
698			elm = RB_RIGHT(elm, field);			\
699	} else {							\
700		if (RB_PARENT(elm, field) &&				\
701		    (elm == RB_RIGHT(RB_PARENT(elm, field), field)))	\
702			elm = RB_PARENT(elm, field);			\
703		else {							\
704			while (RB_PARENT(elm, field) &&			\
705			    (elm == RB_LEFT(RB_PARENT(elm, field), field)))\
706				elm = RB_PARENT(elm, field);		\
707			elm = RB_PARENT(elm, field);			\
708		}							\
709	}								\
710	return (elm);							\
711}									\
712									\
713attr struct type *							\
714name##_RB_MINMAX(struct name *head, int val)				\
715{									\
716	struct type *tmp = RB_ROOT(head);				\
717	struct type *parent = NULL;					\
718	while (tmp) {							\
719		parent = tmp;						\
720		if (val < 0)						\
721			tmp = RB_LEFT(tmp, field);			\
722		else							\
723			tmp = RB_RIGHT(tmp, field);			\
724	}								\
725	return (parent);						\
726}
727
728#define RB_NEGINF	-1
729#define RB_INF	1
730
731#define RB_INSERT(name, x, y)	name##_RB_INSERT(x, y)
732#define RB_REMOVE(name, x, y)	name##_RB_REMOVE(x, y)
733#define RB_FIND(name, x, y)	name##_RB_FIND(x, y)
734#define RB_NFIND(name, x, y)	name##_RB_NFIND(x, y)
735#define RB_NEXT(name, x, y)	name##_RB_NEXT(y)
736#define RB_PREV(name, x, y)	name##_RB_PREV(y)
737#define RB_MIN(name, x)		name##_RB_MINMAX(x, RB_NEGINF)
738#define RB_MAX(name, x)		name##_RB_MINMAX(x, RB_INF)
739
740#define RB_FOREACH(x, name, head)					\
741	for ((x) = RB_MIN(name, head);					\
742	     (x) != NULL;						\
743	     (x) = name##_RB_NEXT(x))
744
745#define RB_FOREACH_REVERSE(x, name, head)				\
746	for ((x) = RB_MAX(name, head);					\
747	     (x) != NULL;						\
748	     (x) = name##_RB_PREV(x))
749
750#endif	/* _SYS_TREE_H_ */
751