tree.h revision 154227
1218155Slstewart/*	$NetBSD: tree.h,v 1.8 2004/03/28 19:38:30 provos Exp $	*/
2218155Slstewart/*	$OpenBSD: tree.h,v 1.7 2002/10/17 21:51:54 art Exp $	*/
3218155Slstewart/* $FreeBSD: head/sys/sys/tree.h 154227 2006-01-11 15:48:36Z jasone $ */
4218155Slstewart
5218155Slstewart/*-
6218155Slstewart * Copyright 2002 Niels Provos <provos@citi.umich.edu>
7218155Slstewart * All rights reserved.
8218155Slstewart *
9218155Slstewart * 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#define RB_BLACK	0
307#define RB_RED		1
308#define RB_ENTRY(type)							\
309struct {								\
310	struct type *rbe_left;		/* left element */		\
311	struct type *rbe_right;		/* right element */		\
312	struct type *rbe_parent;	/* parent element */		\
313	int rbe_color;			/* node color */		\
314}
315
316#define RB_LEFT(elm, field)		(elm)->field.rbe_left
317#define RB_RIGHT(elm, field)		(elm)->field.rbe_right
318#define RB_PARENT(elm, field)		(elm)->field.rbe_parent
319#define RB_COLOR(elm, field)		(elm)->field.rbe_color
320#define RB_ROOT(head)			(head)->rbh_root
321#define RB_EMPTY(head)			(RB_ROOT(head) == NULL)
322
323#define RB_SET(elm, parent, field) do {					\
324	RB_PARENT(elm, field) = parent;					\
325	RB_LEFT(elm, field) = RB_RIGHT(elm, field) = NULL;		\
326	RB_COLOR(elm, field) = RB_RED;					\
327} while (/*CONSTCOND*/ 0)
328
329#define RB_SET_BLACKRED(black, red, field) do {				\
330	RB_COLOR(black, field) = RB_BLACK;				\
331	RB_COLOR(red, field) = RB_RED;					\
332} while (/*CONSTCOND*/ 0)
333
334#ifndef RB_AUGMENT
335#define RB_AUGMENT(x)	do {} while (0)
336#endif
337
338#define RB_ROTATE_LEFT(head, elm, tmp, field) do {			\
339	(tmp) = RB_RIGHT(elm, field);					\
340	if ((RB_RIGHT(elm, field) = RB_LEFT(tmp, field)) != NULL) {	\
341		RB_PARENT(RB_LEFT(tmp, field), field) = (elm);		\
342	}								\
343	RB_AUGMENT(elm);						\
344	if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) {	\
345		if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))	\
346			RB_LEFT(RB_PARENT(elm, field), field) = (tmp);	\
347		else							\
348			RB_RIGHT(RB_PARENT(elm, field), field) = (tmp);	\
349	} else								\
350		(head)->rbh_root = (tmp);				\
351	RB_LEFT(tmp, field) = (elm);					\
352	RB_PARENT(elm, field) = (tmp);					\
353	RB_AUGMENT(tmp);						\
354	if ((RB_PARENT(tmp, field)))					\
355		RB_AUGMENT(RB_PARENT(tmp, field));			\
356} while (/*CONSTCOND*/ 0)
357
358#define RB_ROTATE_RIGHT(head, elm, tmp, field) do {			\
359	(tmp) = RB_LEFT(elm, field);					\
360	if ((RB_LEFT(elm, field) = RB_RIGHT(tmp, field)) != NULL) {	\
361		RB_PARENT(RB_RIGHT(tmp, field), field) = (elm);		\
362	}								\
363	RB_AUGMENT(elm);						\
364	if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) {	\
365		if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))	\
366			RB_LEFT(RB_PARENT(elm, field), field) = (tmp);	\
367		else							\
368			RB_RIGHT(RB_PARENT(elm, field), field) = (tmp);	\
369	} else								\
370		(head)->rbh_root = (tmp);				\
371	RB_RIGHT(tmp, field) = (elm);					\
372	RB_PARENT(elm, field) = (tmp);					\
373	RB_AUGMENT(tmp);						\
374	if ((RB_PARENT(tmp, field)))					\
375		RB_AUGMENT(RB_PARENT(tmp, field));			\
376} while (/*CONSTCOND*/ 0)
377
378/* Generates prototypes and inline functions */
379#define RB_PROTOTYPE(name, type, field, cmp)				\
380void name##_RB_INSERT_COLOR(struct name *, struct type *);	\
381void name##_RB_REMOVE_COLOR(struct name *, struct type *, struct type *);\
382struct type *name##_RB_REMOVE(struct name *, struct type *);		\
383struct type *name##_RB_INSERT(struct name *, struct type *);		\
384struct type *name##_RB_FIND(struct name *, struct type *);		\
385struct type *name##_RB_NFIND(struct name *, struct type *);		\
386struct type *name##_RB_NEXT(struct type *);				\
387struct type *name##_RB_MINMAX(struct name *, int);			\
388									\
389
390/* Main rb operation.
391 * Moves node close to the key of elm to top
392 */
393#define RB_GENERATE(name, type, field, cmp)				\
394void									\
395name##_RB_INSERT_COLOR(struct name *head, struct type *elm)		\
396{									\
397	struct type *parent, *gparent, *tmp;				\
398	while ((parent = RB_PARENT(elm, field)) != NULL &&		\
399	    RB_COLOR(parent, field) == RB_RED) {			\
400		gparent = RB_PARENT(parent, field);			\
401		if (parent == RB_LEFT(gparent, field)) {		\
402			tmp = RB_RIGHT(gparent, field);			\
403			if (tmp && RB_COLOR(tmp, field) == RB_RED) {	\
404				RB_COLOR(tmp, field) = RB_BLACK;	\
405				RB_SET_BLACKRED(parent, gparent, field);\
406				elm = gparent;				\
407				continue;				\
408			}						\
409			if (RB_RIGHT(parent, field) == elm) {		\
410				RB_ROTATE_LEFT(head, parent, tmp, field);\
411				tmp = parent;				\
412				parent = elm;				\
413				elm = tmp;				\
414			}						\
415			RB_SET_BLACKRED(parent, gparent, field);	\
416			RB_ROTATE_RIGHT(head, gparent, tmp, field);	\
417		} else {						\
418			tmp = RB_LEFT(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_LEFT(parent, field) == elm) {		\
426				RB_ROTATE_RIGHT(head, parent, tmp, field);\
427				tmp = parent;				\
428				parent = elm;				\
429				elm = tmp;				\
430			}						\
431			RB_SET_BLACKRED(parent, gparent, field);	\
432			RB_ROTATE_LEFT(head, gparent, tmp, field);	\
433		}							\
434	}								\
435	RB_COLOR(head->rbh_root, field) = RB_BLACK;			\
436}									\
437									\
438void									\
439name##_RB_REMOVE_COLOR(struct name *head, struct type *parent, struct type *elm) \
440{									\
441	struct type *tmp;						\
442	while ((elm == NULL || RB_COLOR(elm, field) == RB_BLACK) &&	\
443	    elm != RB_ROOT(head)) {					\
444		if (RB_LEFT(parent, field) == elm) {			\
445			tmp = RB_RIGHT(parent, field);			\
446			if (RB_COLOR(tmp, field) == RB_RED) {		\
447				RB_SET_BLACKRED(tmp, parent, field);	\
448				RB_ROTATE_LEFT(head, parent, tmp, field);\
449				tmp = RB_RIGHT(parent, field);		\
450			}						\
451			if ((RB_LEFT(tmp, field) == NULL ||		\
452			    RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
453			    (RB_RIGHT(tmp, field) == NULL ||		\
454			    RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
455				RB_COLOR(tmp, field) = RB_RED;		\
456				elm = parent;				\
457				parent = RB_PARENT(elm, field);		\
458			} else {					\
459				if (RB_RIGHT(tmp, field) == NULL ||	\
460				    RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK) {\
461					struct type *oleft;		\
462					if ((oleft = RB_LEFT(tmp, field)) \
463					    != NULL)			\
464						RB_COLOR(oleft, field) = RB_BLACK;\
465					RB_COLOR(tmp, field) = RB_RED;	\
466					RB_ROTATE_RIGHT(head, tmp, oleft, field);\
467					tmp = RB_RIGHT(parent, field);	\
468				}					\
469				RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
470				RB_COLOR(parent, field) = RB_BLACK;	\
471				if (RB_RIGHT(tmp, field))		\
472					RB_COLOR(RB_RIGHT(tmp, field), field) = RB_BLACK;\
473				RB_ROTATE_LEFT(head, parent, tmp, field);\
474				elm = RB_ROOT(head);			\
475				break;					\
476			}						\
477		} else {						\
478			tmp = RB_LEFT(parent, field);			\
479			if (RB_COLOR(tmp, field) == RB_RED) {		\
480				RB_SET_BLACKRED(tmp, parent, field);	\
481				RB_ROTATE_RIGHT(head, parent, tmp, field);\
482				tmp = RB_LEFT(parent, field);		\
483			}						\
484			if ((RB_LEFT(tmp, field) == NULL ||		\
485			    RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
486			    (RB_RIGHT(tmp, field) == NULL ||		\
487			    RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
488				RB_COLOR(tmp, field) = RB_RED;		\
489				elm = parent;				\
490				parent = RB_PARENT(elm, field);		\
491			} else {					\
492				if (RB_LEFT(tmp, field) == NULL ||	\
493				    RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) {\
494					struct type *oright;		\
495					if ((oright = RB_RIGHT(tmp, field)) \
496					    != NULL)			\
497						RB_COLOR(oright, field) = RB_BLACK;\
498					RB_COLOR(tmp, field) = RB_RED;	\
499					RB_ROTATE_LEFT(head, tmp, oright, field);\
500					tmp = RB_LEFT(parent, field);	\
501				}					\
502				RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
503				RB_COLOR(parent, field) = RB_BLACK;	\
504				if (RB_LEFT(tmp, field))		\
505					RB_COLOR(RB_LEFT(tmp, field), field) = RB_BLACK;\
506				RB_ROTATE_RIGHT(head, parent, tmp, field);\
507				elm = RB_ROOT(head);			\
508				break;					\
509			}						\
510		}							\
511	}								\
512	if (elm)							\
513		RB_COLOR(elm, field) = RB_BLACK;			\
514}									\
515									\
516struct type *								\
517name##_RB_REMOVE(struct name *head, struct type *elm)			\
518{									\
519	struct type *child, *parent, *old = elm;			\
520	int color;							\
521	if (RB_LEFT(elm, field) == NULL)				\
522		child = RB_RIGHT(elm, field);				\
523	else if (RB_RIGHT(elm, field) == NULL)				\
524		child = RB_LEFT(elm, field);				\
525	else {								\
526		struct type *left;					\
527		elm = RB_RIGHT(elm, field);				\
528		while ((left = RB_LEFT(elm, field)) != NULL)		\
529			elm = left;					\
530		child = RB_RIGHT(elm, field);				\
531		parent = RB_PARENT(elm, field);				\
532		color = RB_COLOR(elm, field);				\
533		if (child)						\
534			RB_PARENT(child, field) = parent;		\
535		if (parent) {						\
536			if (RB_LEFT(parent, field) == elm)		\
537				RB_LEFT(parent, field) = child;		\
538			else						\
539				RB_RIGHT(parent, field) = child;	\
540			RB_AUGMENT(parent);				\
541		} else							\
542			RB_ROOT(head) = child;				\
543		if (RB_PARENT(elm, field) == old)			\
544			parent = elm;					\
545		(elm)->field = (old)->field;				\
546		if (RB_PARENT(old, field)) {				\
547			if (RB_LEFT(RB_PARENT(old, field), field) == old)\
548				RB_LEFT(RB_PARENT(old, field), field) = elm;\
549			else						\
550				RB_RIGHT(RB_PARENT(old, field), field) = elm;\
551			RB_AUGMENT(RB_PARENT(old, field));		\
552		} else							\
553			RB_ROOT(head) = elm;				\
554		RB_PARENT(RB_LEFT(old, field), field) = elm;		\
555		if (RB_RIGHT(old, field))				\
556			RB_PARENT(RB_RIGHT(old, field), field) = elm;	\
557		if (parent) {						\
558			left = parent;					\
559			do {						\
560				RB_AUGMENT(left);			\
561			} while ((left = RB_PARENT(left, field)) != NULL); \
562		}							\
563		goto color;						\
564	}								\
565	parent = RB_PARENT(elm, field);					\
566	color = RB_COLOR(elm, field);					\
567	if (child)							\
568		RB_PARENT(child, field) = parent;			\
569	if (parent) {							\
570		if (RB_LEFT(parent, field) == elm)			\
571			RB_LEFT(parent, field) = child;			\
572		else							\
573			RB_RIGHT(parent, field) = child;		\
574		RB_AUGMENT(parent);					\
575	} else								\
576		RB_ROOT(head) = child;					\
577color:									\
578	if (color == RB_BLACK)						\
579		name##_RB_REMOVE_COLOR(head, parent, child);		\
580	return (old);							\
581}									\
582									\
583/* Inserts a node into the RB tree */					\
584struct type *								\
585name##_RB_INSERT(struct name *head, struct type *elm)			\
586{									\
587	struct type *tmp;						\
588	struct type *parent = NULL;					\
589	int comp = 0;							\
590	tmp = RB_ROOT(head);						\
591	while (tmp) {							\
592		parent = tmp;						\
593		comp = (cmp)(elm, parent);				\
594		if (comp < 0)						\
595			tmp = RB_LEFT(tmp, field);			\
596		else if (comp > 0)					\
597			tmp = RB_RIGHT(tmp, field);			\
598		else							\
599			return (tmp);					\
600	}								\
601	RB_SET(elm, parent, field);					\
602	if (parent != NULL) {						\
603		if (comp < 0)						\
604			RB_LEFT(parent, field) = elm;			\
605		else							\
606			RB_RIGHT(parent, field) = elm;			\
607		RB_AUGMENT(parent);					\
608	} else								\
609		RB_ROOT(head) = elm;					\
610	name##_RB_INSERT_COLOR(head, elm);				\
611	return (NULL);							\
612}									\
613									\
614/* Finds the node with the same key as elm */				\
615struct type *								\
616name##_RB_FIND(struct name *head, struct type *elm)			\
617{									\
618	struct type *tmp = RB_ROOT(head);				\
619	int comp;							\
620	while (tmp) {							\
621		comp = cmp(elm, tmp);					\
622		if (comp < 0)						\
623			tmp = RB_LEFT(tmp, field);			\
624		else if (comp > 0)					\
625			tmp = RB_RIGHT(tmp, field);			\
626		else							\
627			return (tmp);					\
628	}								\
629	return (NULL);							\
630}									\
631									\
632/* Finds the first node greater than or equal to the search key */	\
633struct type *								\
634name##_RB_NFIND(struct name *head, struct type *elm)			\
635{									\
636	struct type *ret = RB_ROOT(head);				\
637	struct type *tmp;						\
638	int comp;							\
639	while (ret && (comp = cmp(elm, ret)) != 0) {			\
640		if (comp < 0) {						\
641			if ((tmp = RB_LEFT(ret, field)) == NULL)	\
642				break;					\
643			ret = tmp;					\
644		} else {						\
645			if ((tmp = RB_RIGHT(ret, field)) == NULL) {	\
646				tmp = ret;				\
647				ret = RB_PARENT(ret, field);		\
648				while (ret && tmp == RB_RIGHT(ret,	\
649				    field)) {				\
650					tmp = ret;			\
651					ret = RB_PARENT(ret, field);	\
652				}					\
653				break;					\
654			}						\
655			ret = tmp;					\
656		}							\
657	}								\
658	return (ret);							\
659}									\
660									\
661/* ARGSUSED */								\
662struct type *								\
663name##_RB_NEXT(struct type *elm)					\
664{									\
665	if (RB_RIGHT(elm, field)) {					\
666		elm = RB_RIGHT(elm, field);				\
667		while (RB_LEFT(elm, field))				\
668			elm = RB_LEFT(elm, field);			\
669	} else {							\
670		if (RB_PARENT(elm, field) &&				\
671		    (elm == RB_LEFT(RB_PARENT(elm, field), field)))	\
672			elm = RB_PARENT(elm, field);			\
673		else {							\
674			while (RB_PARENT(elm, field) &&			\
675			    (elm == RB_RIGHT(RB_PARENT(elm, field), field)))\
676				elm = RB_PARENT(elm, field);		\
677			elm = RB_PARENT(elm, field);			\
678		}							\
679	}								\
680	return (elm);							\
681}									\
682									\
683struct type *								\
684name##_RB_MINMAX(struct name *head, int val)				\
685{									\
686	struct type *tmp = RB_ROOT(head);				\
687	struct type *parent = NULL;					\
688	while (tmp) {							\
689		parent = tmp;						\
690		if (val < 0)						\
691			tmp = RB_LEFT(tmp, field);			\
692		else							\
693			tmp = RB_RIGHT(tmp, field);			\
694	}								\
695	return (parent);						\
696}
697
698#define RB_NEGINF	-1
699#define RB_INF	1
700
701#define RB_INSERT(name, x, y)	name##_RB_INSERT(x, y)
702#define RB_REMOVE(name, x, y)	name##_RB_REMOVE(x, y)
703#define RB_FIND(name, x, y)	name##_RB_FIND(x, y)
704#define RB_NFIND(name, x, y)	name##_RB_NFIND(x, y)
705#define RB_NEXT(name, x, y)	name##_RB_NEXT(y)
706#define RB_MIN(name, x)		name##_RB_MINMAX(x, RB_NEGINF)
707#define RB_MAX(name, x)		name##_RB_MINMAX(x, RB_INF)
708
709#define RB_FOREACH(x, name, head)					\
710	for ((x) = RB_MIN(name, head);					\
711	     (x) != NULL;						\
712	     (x) = name##_RB_NEXT(x))
713
714#endif	/* _SYS_TREE_H_ */
715