/*	$NetBSD: tree.h,v 1.20 2013/09/14 13:20:45 joerg Exp $	*/

/*	$OpenBSD: tree.h,v 1.13 2011/07/09 00:19:45 pirofti Exp $	*/

/*

 * Copyright 2002 Niels Provos <provos@citi.umich.edu>

 * All rights reserved.

 *

 * Redistribution and use in source and binary forms, with or without

 * modification, are permitted provided that the following conditions

 * are met:

 * 1. Redistributions of source code must retain the above copyright

 *    notice, this list of conditions and the following disclaimer.

 * 2. Redistributions in binary form must reproduce the above copyright

 *    notice, this list of conditions and the following disclaimer in the

 *    documentation and/or other materials provided with the distribution.

 *

 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR

 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES

 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.

 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,

 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT

 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,

 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY

 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT

 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF

 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

 */

#ifndef	_SYS_TREE_H_

#define	_SYS_TREE_H_

/*

 * This file defines data structures for different types of trees:

 * splay trees and red-black trees.

 *

 * A splay tree is a self-organizing data structure.  Every operation

 * on the tree causes a splay to happen.  The splay moves the requested

 * node to the root of the tree and partly rebalances it.

 *

 * This has the benefit that request locality causes faster lookups as

 * the requested nodes move to the top of the tree.  On the other hand,

 * every lookup causes memory writes.

 *

 * The Balance Theorem bounds the total access time for m operations

 * and n inserts on an initially empty tree as O((m + n)lg n).  The

 * amortized cost for a sequence of m accesses to a splay tree is O(lg n);

 *

 * A red-black tree is a binary search tree with the node color as an

 * extra attribute.  It fulfills a set of conditions:

 *	- every search path from the root to a leaf consists of the

 *	  same number of black nodes,

 *	- each red node (except for the root) has a black parent,

 *	- each leaf node is black.

 *

 * Every operation on a red-black tree is bounded as O(lg n).

 * The maximum height of a red-black tree is 2lg (n+1).

 */

#define SPLAY_HEAD(name, type)						\

struct name {								\

	struct type *sph_root; /* root of the tree */			\

}

#define SPLAY_INITIALIZER(root)						\

	{ NULL }

#define SPLAY_INIT(root) do {						\

	(root)->sph_root = NULL;					\

} while (/*CONSTCOND*/ 0)

#define SPLAY_ENTRY(type)						\

struct {								\

	struct type *spe_left; /* left element */			\

	struct type *spe_right; /* right element */			\

}

#define SPLAY_LEFT(elm, field)		(elm)->field.spe_left

#define SPLAY_RIGHT(elm, field)		(elm)->field.spe_right

#define SPLAY_ROOT(head)		(head)->sph_root

#define SPLAY_EMPTY(head)		(SPLAY_ROOT(head) == NULL)

/* SPLAY_ROTATE_{LEFT,RIGHT} expect that tmp hold SPLAY_{RIGHT,LEFT} */

#define SPLAY_ROTATE_RIGHT(head, tmp, field) do {			\

	SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(tmp, field);	\

	SPLAY_RIGHT(tmp, field) = (head)->sph_root;			\

	(head)->sph_root = tmp;						\

} while (/*CONSTCOND*/ 0)

#define SPLAY_ROTATE_LEFT(head, tmp, field) do {			\

	SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(tmp, field);	\

	SPLAY_LEFT(tmp, field) = (head)->sph_root;			\

	(head)->sph_root = tmp;						\

} while (/*CONSTCOND*/ 0)

#define SPLAY_LINKLEFT(head, tmp, field) do {				\

	SPLAY_LEFT(tmp, field) = (head)->sph_root;			\

	tmp = (head)->sph_root;						\

	(head)->sph_root = SPLAY_LEFT((head)->sph_root, field);		\

} while (/*CONSTCOND*/ 0)

#define SPLAY_LINKRIGHT(head, tmp, field) do {				\

	SPLAY_RIGHT(tmp, field) = (head)->sph_root;			\

	tmp = (head)->sph_root;						\

	(head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);	\

} while (/*CONSTCOND*/ 0)

#define SPLAY_ASSEMBLE(head, node, left, right, field) do {		\

	SPLAY_RIGHT(left, field) = SPLAY_LEFT((head)->sph_root, field);	\

	SPLAY_LEFT(right, field) = SPLAY_RIGHT((head)->sph_root, field);\

	SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(node, field);	\

	SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(node, field);	\

} while (/*CONSTCOND*/ 0)

/* Generates prototypes and inline functions */

#define SPLAY_PROTOTYPE(name, type, field, cmp)				\

void name##_SPLAY(struct name *, struct type *);			\

void name##_SPLAY_MINMAX(struct name *, int);				\

struct type *name##_SPLAY_INSERT(struct name *, struct type *);		\

struct type *name##_SPLAY_REMOVE(struct name *, struct type *);		\

									\

/* Finds the node with the same key as elm */				\

static __inline struct type *						\

name##_SPLAY_FIND(struct name *head, struct type *elm)			\

{									\

	if (SPLAY_EMPTY(head))						\

		return(NULL);						\

	name##_SPLAY(head, elm);					\

	if ((cmp)(elm, (head)->sph_root) == 0)				\

		return (head->sph_root);				\

	return (NULL);							\

}									\

									\

static __inline __unused struct type *					\

name##_SPLAY_NEXT(struct name *head, struct type *elm)			\

{									\

	name##_SPLAY(head, elm);					\

	if (SPLAY_RIGHT(elm, field) != NULL) {				\

		elm = SPLAY_RIGHT(elm, field);				\

		while (SPLAY_LEFT(elm, field) != NULL) {		\

			elm = SPLAY_LEFT(elm, field);			\

		}							\

	} else								\

		elm = NULL;						\

	return (elm);							\

}									\

									\

static __unused __inline struct type *					\

name##_SPLAY_MIN_MAX(struct name *head, int val)			\

{									\

	name##_SPLAY_MINMAX(head, val);					\

        return (SPLAY_ROOT(head));					\

}

/* Main splay operation.

 * Moves node close to the key of elm to top

 */

#define SPLAY_GENERATE(name, type, field, cmp)				\

struct type *								\

name##_SPLAY_INSERT(struct name *head, struct type *elm)		\

{									\

    if (SPLAY_EMPTY(head)) {						\

	    SPLAY_LEFT(elm, field) = SPLAY_RIGHT(elm, field) = NULL;	\

    } else {								\

	    int __comp;							\

	    name##_SPLAY(head, elm);					\

	    __comp = (cmp)(elm, (head)->sph_root);			\

	    if(__comp < 0) {						\

		    SPLAY_LEFT(elm, field) = SPLAY_LEFT((head)->sph_root, field);\

		    SPLAY_RIGHT(elm, field) = (head)->sph_root;		\

		    SPLAY_LEFT((head)->sph_root, field) = NULL;		\

	    } else if (__comp > 0) {					\

		    SPLAY_RIGHT(elm, field) = SPLAY_RIGHT((head)->sph_root, field);\

		    SPLAY_LEFT(elm, field) = (head)->sph_root;		\

		    SPLAY_RIGHT((head)->sph_root, field) = NULL;	\

	    } else							\

		    return ((head)->sph_root);				\

    }									\

    (head)->sph_root = (elm);						\

    return (NULL);							\

}									\

									\

struct type *								\

name##_SPLAY_REMOVE(struct name *head, struct type *elm)		\

{									\

	struct type *__tmp;						\

	if (SPLAY_EMPTY(head))						\

		return (NULL);						\

	name##_SPLAY(head, elm);					\

	if ((cmp)(elm, (head)->sph_root) == 0) {			\

		if (SPLAY_LEFT((head)->sph_root, field) == NULL) {	\

			(head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);\

		} else {						\

			__tmp = SPLAY_RIGHT((head)->sph_root, field);	\

			(head)->sph_root = SPLAY_LEFT((head)->sph_root, field);\

			name##_SPLAY(head, elm);			\

			SPLAY_RIGHT((head)->sph_root, field) = __tmp;	\

		}							\

		return (elm);						\

	}								\

	return (NULL);							\

}									\

									\

void									\

name##_SPLAY(struct name *head, struct type *elm)			\

{									\

	struct type __node, *__left, *__right, *__tmp;			\

	int __comp;							\

\

	SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\

	__left = __right = &__node;					\

\

	while ((__comp = (cmp)(elm, (head)->sph_root)) != 0) {		\

		if (__comp < 0) {					\

			__tmp = SPLAY_LEFT((head)->sph_root, field);	\

			if (__tmp == NULL)				\

				break;					\

			if ((cmp)(elm, __tmp) < 0){			\

				SPLAY_ROTATE_RIGHT(head, __tmp, field);	\

				if (SPLAY_LEFT((head)->sph_root, field) == NULL)\

					break;				\

			}						\

			SPLAY_LINKLEFT(head, __right, field);		\

		} else if (__comp > 0) {				\

			__tmp = SPLAY_RIGHT((head)->sph_root, field);	\

			if (__tmp == NULL)				\

				break;					\

			if ((cmp)(elm, __tmp) > 0){			\

				SPLAY_ROTATE_LEFT(head, __tmp, field);	\

				if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\

					break;				\

			}						\

			SPLAY_LINKRIGHT(head, __left, field);		\

		}							\

	}								\

	SPLAY_ASSEMBLE(head, &__node, __left, __right, field);		\

}									\

									\

/* Splay with either the minimum or the maximum element			\

 * Used to find minimum or maximum element in tree.			\

 */									\

void name##_SPLAY_MINMAX(struct name *head, int __comp) \

{									\

	struct type __node, *__left, *__right, *__tmp;			\

\

	SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\

	__left = __right = &__node;					\

\

	while (1) {							\

		if (__comp < 0) {					\

			__tmp = SPLAY_LEFT((head)->sph_root, field);	\

			if (__tmp == NULL)				\

				break;					\

			if (__comp < 0){				\

				SPLAY_ROTATE_RIGHT(head, __tmp, field);	\

				if (SPLAY_LEFT((head)->sph_root, field) == NULL)\

					break;				\

			}						\

			SPLAY_LINKLEFT(head, __right, field);		\

		} else if (__comp > 0) {				\

			__tmp = SPLAY_RIGHT((head)->sph_root, field);	\

			if (__tmp == NULL)				\

				break;					\

			if (__comp > 0) {				\

				SPLAY_ROTATE_LEFT(head, __tmp, field);	\

				if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\

					break;				\

			}						\

			SPLAY_LINKRIGHT(head, __left, field);		\

		}							\

	}								\

	SPLAY_ASSEMBLE(head, &__node, __left, __right, field);		\

}

#define SPLAY_NEGINF	-1

#define SPLAY_INF	1

#define SPLAY_INSERT(name, x, y)	name##_SPLAY_INSERT(x, y)

#define SPLAY_REMOVE(name, x, y)	name##_SPLAY_REMOVE(x, y)

#define SPLAY_FIND(name, x, y)		name##_SPLAY_FIND(x, y)

#define SPLAY_NEXT(name, x, y)		name##_SPLAY_NEXT(x, y)

#define SPLAY_MIN(name, x)		(SPLAY_EMPTY(x) ? NULL	\

					: name##_SPLAY_MIN_MAX(x, SPLAY_NEGINF))

#define SPLAY_MAX(name, x)		(SPLAY_EMPTY(x) ? NULL	\

					: name##_SPLAY_MIN_MAX(x, SPLAY_INF))

#define SPLAY_FOREACH(x, name, head)					\

	for ((x) = SPLAY_MIN(name, head);				\

	     (x) != NULL;						\

	     (x) = SPLAY_NEXT(name, head, x))

/* Macros that define a red-black tree */

#define RB_HEAD(name, type)						\

struct name {								\

	struct type *rbh_root; /* root of the tree */			\

}

#define RB_INITIALIZER(root)						\

	{ NULL }

#define RB_INIT(root) do {						\

	(root)->rbh_root = NULL;					\

} while (/*CONSTCOND*/ 0)

#define RB_BLACK	0

#define RB_RED		1

#define RB_ENTRY(type)							\

struct {								\

	struct type *rbe_left;		/* left element */		\

	struct type *rbe_right;		/* right element */		\

	struct type *rbe_parent;	/* parent element */		\

	int rbe_color;			/* node color */		\

}

#define RB_LEFT(elm, field)		(elm)->field.rbe_left

#define RB_RIGHT(elm, field)		(elm)->field.rbe_right

#define RB_PARENT(elm, field)		(elm)->field.rbe_parent

#define RB_COLOR(elm, field)		(elm)->field.rbe_color

#define RB_ROOT(head)			(head)->rbh_root

#define RB_EMPTY(head)			(RB_ROOT(head) == NULL)

#define RB_SET(elm, parent, field) do {					\

	RB_PARENT(elm, field) = parent;					\

	RB_LEFT(elm, field) = RB_RIGHT(elm, field) = NULL;		\

	RB_COLOR(elm, field) = RB_RED;					\

} while (/*CONSTCOND*/ 0)

#define RB_SET_BLACKRED(black, red, field) do {				\

	RB_COLOR(black, field) = RB_BLACK;				\

	RB_COLOR(red, field) = RB_RED;					\

} while (/*CONSTCOND*/ 0)

#ifndef RB_AUGMENT

#define RB_AUGMENT(x)	do {} while (/*CONSTCOND*/ 0)

#endif

#define RB_ROTATE_LEFT(head, elm, tmp, field) do {			\

	(tmp) = RB_RIGHT(elm, field);					\

	if ((RB_RIGHT(elm, field) = RB_LEFT(tmp, field)) != NULL) {	\

		RB_PARENT(RB_LEFT(tmp, field), field) = (elm);		\

	}								\

	RB_AUGMENT(elm);						\

	if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) {	\

		if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))	\

			RB_LEFT(RB_PARENT(elm, field), field) = (tmp);	\

		else							\

			RB_RIGHT(RB_PARENT(elm, field), field) = (tmp);	\

	} else								\

		(head)->rbh_root = (tmp);				\

	RB_LEFT(tmp, field) = (elm);					\

	RB_PARENT(elm, field) = (tmp);					\

	RB_AUGMENT(tmp);						\

	if ((RB_PARENT(tmp, field)))					\

		RB_AUGMENT(RB_PARENT(tmp, field));			\

} while (/*CONSTCOND*/ 0)

#define RB_ROTATE_RIGHT(head, elm, tmp, field) do {			\

	(tmp) = RB_LEFT(elm, field);					\

	if ((RB_LEFT(elm, field) = RB_RIGHT(tmp, field)) != NULL) {	\

		RB_PARENT(RB_RIGHT(tmp, field), field) = (elm);		\

	}								\

	RB_AUGMENT(elm);						\

	if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) {	\

		if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))	\

			RB_LEFT(RB_PARENT(elm, field), field) = (tmp);	\

		else							\

			RB_RIGHT(RB_PARENT(elm, field), field) = (tmp);	\

	} else								\

		(head)->rbh_root = (tmp);				\

	RB_RIGHT(tmp, field) = (elm);					\

	RB_PARENT(elm, field) = (tmp);					\

	RB_AUGMENT(tmp);						\

	if ((RB_PARENT(tmp, field)))					\

		RB_AUGMENT(RB_PARENT(tmp, field));			\

} while (/*CONSTCOND*/ 0)

/* Generates prototypes and inline functions */

#define RB_PROTOTYPE(name, type, field, cmp)				\

	RB_PROTOTYPE_INTERNAL(name, type, field, cmp,)

#define	RB_PROTOTYPE_STATIC(name, type, field, cmp)			\

	RB_PROTOTYPE_INTERNAL(name, type, field, cmp, __unused static)

#define RB_PROTOTYPE_INTERNAL(name, type, field, cmp, attr)		\

attr void name##_RB_INSERT_COLOR(struct name *, struct type *);		\

attr void name##_RB_REMOVE_COLOR(struct name *, struct type *, struct type *);\

attr struct type *name##_RB_REMOVE(struct name *, struct type *);	\

attr struct type *name##_RB_INSERT(struct name *, struct type *);	\

attr struct type *name##_RB_FIND(struct name *, struct type *);		\

attr struct type *name##_RB_NFIND(struct name *, struct type *);	\

attr struct type *name##_RB_NEXT(struct type *);			\

attr struct type *name##_RB_PREV(struct type *);			\

attr struct type *name##_RB_MINMAX(struct name *, int);			\

									\

/* Main rb operation.

 * Moves node close to the key of elm to top

 */

#define	RB_GENERATE(name, type, field, cmp)				\

	RB_GENERATE_INTERNAL(name, type, field, cmp,)

#define	RB_GENERATE_STATIC(name, type, field, cmp)			\

	RB_GENERATE_INTERNAL(name, type, field, cmp, __unused static)

#define RB_GENERATE_INTERNAL(name, type, field, cmp, attr)		\

attr void								\

name##_RB_INSERT_COLOR(struct name *head, struct type *elm)		\

{									\

	struct type *parent, *gparent, *tmp;				\

	while ((parent = RB_PARENT(elm, field)) != NULL &&		\

	    RB_COLOR(parent, field) == RB_RED) {			\

		gparent = RB_PARENT(parent, field);			\

		if (parent == RB_LEFT(gparent, field)) {		\

			tmp = RB_RIGHT(gparent, field);			\

			if (tmp && RB_COLOR(tmp, field) == RB_RED) {	\

				RB_COLOR(tmp, field) = RB_BLACK;	\

				RB_SET_BLACKRED(parent, gparent, field);\

				elm = gparent;				\

				continue;				\

			}						\

			if (RB_RIGHT(parent, field) == elm) {		\

				RB_ROTATE_LEFT(head, parent, tmp, field);\

				tmp = parent;				\

				parent = elm;				\

				elm = tmp;				\

			}						\

			RB_SET_BLACKRED(parent, gparent, field);	\

			RB_ROTATE_RIGHT(head, gparent, tmp, field);	\

		} else {						\

			tmp = RB_LEFT(gparent, field);			\

			if (tmp && RB_COLOR(tmp, field) == RB_RED) {	\

				RB_COLOR(tmp, field) = RB_BLACK;	\

				RB_SET_BLACKRED(parent, gparent, field);\

				elm = gparent;				\

				continue;				\

			}						\

			if (RB_LEFT(parent, field) == elm) {		\

				RB_ROTATE_RIGHT(head, parent, tmp, field);\

				tmp = parent;				\

				parent = elm;				\

				elm = tmp;				\

			}						\

			RB_SET_BLACKRED(parent, gparent, field);	\

			RB_ROTATE_LEFT(head, gparent, tmp, field);	\

		}							\

	}								\

	RB_COLOR(head->rbh_root, field) = RB_BLACK;			\

}									\

									\

attr void								\

name##_RB_REMOVE_COLOR(struct name *head, struct type *parent, struct type *elm) \

{									\

	struct type *tmp;						\

	while ((elm == NULL || RB_COLOR(elm, field) == RB_BLACK) &&	\

	    elm != RB_ROOT(head)) {					\

		if (RB_LEFT(parent, field) == elm) {			\

			tmp = RB_RIGHT(parent, field);			\

			if (RB_COLOR(tmp, field) == RB_RED) {		\

				RB_SET_BLACKRED(tmp, parent, field);	\

				RB_ROTATE_LEFT(head, parent, tmp, field);\

				tmp = RB_RIGHT(parent, field);		\

			}						\

			if ((RB_LEFT(tmp, field) == NULL ||		\

			    RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\

			    (RB_RIGHT(tmp, field) == NULL ||		\

			    RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\

				RB_COLOR(tmp, field) = RB_RED;		\

				elm = parent;				\

				parent = RB_PARENT(elm, field);		\

			} else {					\

				if (RB_RIGHT(tmp, field) == NULL ||	\

				    RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK) {\

					struct type *oleft;		\

					if ((oleft = RB_LEFT(tmp, field)) \

					    != NULL)			\

						RB_COLOR(oleft, field) = RB_BLACK;\

					RB_COLOR(tmp, field) = RB_RED;	\

					RB_ROTATE_RIGHT(head, tmp, oleft, field);\

					tmp = RB_RIGHT(parent, field);	\

				}					\

				RB_COLOR(tmp, field) = RB_COLOR(parent, field);\

				RB_COLOR(parent, field) = RB_BLACK;	\

				if (RB_RIGHT(tmp, field))		\

					RB_COLOR(RB_RIGHT(tmp, field), field) = RB_BLACK;\

				RB_ROTATE_LEFT(head, parent, tmp, field);\

				elm = RB_ROOT(head);			\

				break;					\

			}						\

		} else {						\

			tmp = RB_LEFT(parent, field);			\

			if (RB_COLOR(tmp, field) == RB_RED) {		\

				RB_SET_BLACKRED(tmp, parent, field);	\

				RB_ROTATE_RIGHT(head, parent, tmp, field);\

				tmp = RB_LEFT(parent, field);		\

			}						\

			if ((RB_LEFT(tmp, field) == NULL ||		\

			    RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\

			    (RB_RIGHT(tmp, field) == NULL ||		\

			    RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\

				RB_COLOR(tmp, field) = RB_RED;		\

				elm = parent;				\

				parent = RB_PARENT(elm, field);		\

			} else {					\

				if (RB_LEFT(tmp, field) == NULL ||	\

				    RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) {\

					struct type *oright;		\

					if ((oright = RB_RIGHT(tmp, field)) \

					    != NULL)			\

						RB_COLOR(oright, field) = RB_BLACK;\

					RB_COLOR(tmp, field) = RB_RED;	\

					RB_ROTATE_LEFT(head, tmp, oright, field);\

					tmp = RB_LEFT(parent, field);	\

				}					\

				RB_COLOR(tmp, field) = RB_COLOR(parent, field);\

				RB_COLOR(parent, field) = RB_BLACK;	\

				if (RB_LEFT(tmp, field))		\

					RB_COLOR(RB_LEFT(tmp, field), field) = RB_BLACK;\

				RB_ROTATE_RIGHT(head, parent, tmp, field);\

				elm = RB_ROOT(head);			\

				break;					\

			}						\

		}							\

	}								\

	if (elm)							\

		RB_COLOR(elm, field) = RB_BLACK;			\

}									\

									\

attr struct type *							\

name##_RB_REMOVE(struct name *head, struct type *elm)			\

{									\

	struct type *child, *parent, *old = elm;			\

	int color;							\

	if (RB_LEFT(elm, field) == NULL)				\

		child = RB_RIGHT(elm, field);				\

	else if (RB_RIGHT(elm, field) == NULL)				\

		child = RB_LEFT(elm, field);				\

	else {								\

		struct type *left;					\

		elm = RB_RIGHT(elm, field);				\

		while ((left = RB_LEFT(elm, field)) != NULL)		\

			elm = left;					\

		child = RB_RIGHT(elm, field);				\

		parent = RB_PARENT(elm, field);				\

		color = RB_COLOR(elm, field);				\

		if (child)						\

			RB_PARENT(child, field) = parent;		\

		if (parent) {						\

			if (RB_LEFT(parent, field) == elm)		\

				RB_LEFT(parent, field) = child;		\

			else						\

				RB_RIGHT(parent, field) = child;	\

			RB_AUGMENT(parent);				\

		} else							\

			RB_ROOT(head) = child;				\

		if (RB_PARENT(elm, field) == old)			\

			parent = elm;					\

		(elm)->field = (old)->field;				\

		if (RB_PARENT(old, field)) {				\

			if (RB_LEFT(RB_PARENT(old, field), field) == old)\

				RB_LEFT(RB_PARENT(old, field), field) = elm;\

			else						\

				RB_RIGHT(RB_PARENT(old, field), field) = elm;\

			RB_AUGMENT(RB_PARENT(old, field));		\

		} else							\

			RB_ROOT(head) = elm;				\

		RB_PARENT(RB_LEFT(old, field), field) = elm;		\

		if (RB_RIGHT(old, field))				\

			RB_PARENT(RB_RIGHT(old, field), field) = elm;	\

		if (parent) {						\

			left = parent;					\

			do {						\

				RB_AUGMENT(left);			\

			} while ((left = RB_PARENT(left, field)) != NULL); \

		}							\

		goto color;						\

	}								\

	parent = RB_PARENT(elm, field);					\

	color = RB_COLOR(elm, field);					\

	if (child)							\

		RB_PARENT(child, field) = parent;			\

	if (parent) {							\

		if (RB_LEFT(parent, field) == elm)			\

			RB_LEFT(parent, field) = child;			\

		else							\

			RB_RIGHT(parent, field) = child;		\

		RB_AUGMENT(parent);					\

	} else								\

		RB_ROOT(head) = child;					\

color:									\

	if (color == RB_BLACK)						\

		name##_RB_REMOVE_COLOR(head, parent, child);		\

	return (old);							\

}									\

									\

/* Inserts a node into the RB tree */					\

attr struct type *							\

name##_RB_INSERT(struct name *head, struct type *elm)			\

{									\

	struct type *tmp;						\

	struct type *parent = NULL;					\

	int comp = 0;							\

	tmp = RB_ROOT(head);						\

	while (tmp) {							\

		parent = tmp;						\

		comp = (cmp)(elm, parent);				\

		if (comp < 0)						\

			tmp = RB_LEFT(tmp, field);			\

		else if (comp > 0)					\

			tmp = RB_RIGHT(tmp, field);			\

		else							\

			return (tmp);					\

	}								\

	RB_SET(elm, parent, field);					\

	if (parent != NULL) {						\

		if (comp < 0)						\

			RB_LEFT(parent, field) = elm;			\

		else							\

			RB_RIGHT(parent, field) = elm;			\

		RB_AUGMENT(parent);					\

	} else								\

		RB_ROOT(head) = elm;					\

	name##_RB_INSERT_COLOR(head, elm);				\

	return (NULL);							\

}									\

									\

/* Finds the node with the same key as elm */				\

attr struct type *							\

name##_RB_FIND(struct name *head, struct type *elm)			\

{									\

	struct type *tmp = RB_ROOT(head);				\

	int comp;							\

	while (tmp) {							\

		comp = cmp(elm, tmp);					\

		if (comp < 0)						\

			tmp = RB_LEFT(tmp, field);			\

		else if (comp > 0)					\

			tmp = RB_RIGHT(tmp, field);			\

		else							\

			return (tmp);					\

	}								\

	return (NULL);							\

}									\

									\

/* Finds the first node greater than or equal to the search key */	\

attr struct type *							\

name##_RB_NFIND(struct name *head, struct type *elm)			\

{									\

	struct type *tmp = RB_ROOT(head);				\

	struct type *res = NULL;					\

	int comp;							\

	while (tmp) {							\

		comp = cmp(elm, tmp);					\

		if (comp < 0) {						\

			res = tmp;					\

			tmp = RB_LEFT(tmp, field);			\

		}							\

		else if (comp > 0)					\

			tmp = RB_RIGHT(tmp, field);			\

		else							\

			return (tmp);					\

	}								\

	return (res);							\

}									\

									\

/* ARGSUSED */								\

attr struct type *							\

name##_RB_NEXT(struct type *elm)					\

{									\

	if (RB_RIGHT(elm, field)) {					\

		elm = RB_RIGHT(elm, field);				\

		while (RB_LEFT(elm, field))				\

			elm = RB_LEFT(elm, field);			\

	} else {							\

		if (RB_PARENT(elm, field) &&				\

		    (elm == RB_LEFT(RB_PARENT(elm, field), field)))	\

			elm = RB_PARENT(elm, field);			\

		else {							\

			while (RB_PARENT(elm, field) &&			\

			    (elm == RB_RIGHT(RB_PARENT(elm, field), field)))\

				elm = RB_PARENT(elm, field);		\

			elm = RB_PARENT(elm, field);			\

		}							\

	}								\

	return (elm);							\

}									\

									\

/* ARGSUSED */								\

attr struct type *							\

name##_RB_PREV(struct type *elm)					\

{									\

	if (RB_LEFT(elm, field)) {					\

		elm = RB_LEFT(elm, field);				\

		while (RB_RIGHT(elm, field))				\

			elm = RB_RIGHT(elm, field);			\

	} else {							\

		if (RB_PARENT(elm, field) &&				\

		    (elm == RB_RIGHT(RB_PARENT(elm, field), field)))	\

			elm = RB_PARENT(elm, field);			\

		else {							\

			while (RB_PARENT(elm, field) &&			\

			    (elm == RB_LEFT(RB_PARENT(elm, field), field)))\

				elm = RB_PARENT(elm, field);		\

			elm = RB_PARENT(elm, field);			\

		}							\

	}								\

	return (elm);							\

}									\

									\

attr struct type *							\

name##_RB_MINMAX(struct name *head, int val)				\

{									\

	struct type *tmp = RB_ROOT(head);				\

	struct type *parent = NULL;					\

	while (tmp) {							\

		parent = tmp;						\

		if (val < 0)						\

			tmp = RB_LEFT(tmp, field);			\

		else							\

			tmp = RB_RIGHT(tmp, field);			\

	}								\

	return (parent);						\

}

#define RB_NEGINF	-1

#define RB_INF	1

#define RB_INSERT(name, x, y)	name##_RB_INSERT(x, y)

#define RB_REMOVE(name, x, y)	name##_RB_REMOVE(x, y)

#define RB_FIND(name, x, y)	name##_RB_FIND(x, y)

#define RB_NFIND(name, x, y)	name##_RB_NFIND(x, y)

#define RB_NEXT(name, x, y)	name##_RB_NEXT(y)

#define RB_PREV(name, x, y)	name##_RB_PREV(y)

#define RB_MIN(name, x)		name##_RB_MINMAX(x, RB_NEGINF)

#define RB_MAX(name, x)		name##_RB_MINMAX(x, RB_INF)

#define RB_FOREACH(x, name, head)					\

	for ((x) = RB_MIN(name, head);					\

	     (x) != NULL;						\

	     (x) = name##_RB_NEXT(x))

#define RB_FOREACH_FROM(x, name, y)					\

	for ((x) = (y);							\

	    ((x) != NULL) && ((y) = name##_RB_NEXT(x), (x) != NULL);	\

	     (x) = (y))

#define RB_FOREACH_SAFE(x, name, head, y)				\

	for ((x) = RB_MIN(name, head);					\

	    ((x) != NULL) && ((y) = name##_RB_NEXT(x), (x) != NULL);	\

	     (x) = (y))

#define RB_FOREACH_REVERSE(x, name, head)				\

	for ((x) = RB_MAX(name, head);					\

	     (x) != NULL;						\

	     (x) = name##_RB_PREV(x))

#define RB_FOREACH_REVERSE_FROM(x, name, y)				\

	for ((x) = (y);							\

	    ((x) != NULL) && ((y) = name##_RB_PREV(x), (x) != NULL);	\

	     (x) = (y))

#define RB_FOREACH_REVERSE_SAFE(x, name, head, y)			\

	for ((x) = RB_MAX(name, head);					\

	    ((x) != NULL) && ((y) = name##_RB_PREV(x), (x) != NULL);	\

	     (x) = (y))

#endif	/* _SYS_TREE_H_ */