sys-tree.h

/*  $NetBSD: tree.h,v 1.8 2004/03/28 19:38:30 provos Exp $  */
/*  $OpenBSD: tree.h,v 1.7 2002/10/17 21:51:54 art Exp $    */
/* $FreeBSD: src/sys/sys/tree.h,v 1.9.2.1.2.1 2009/10/25 01:10:29 kensmith 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_

/* Ommit "struct" prefix if this code is built with C++,
 * so it can build. */
#ifdef __cplusplus
#define SYS_TREE_STRUCT
#else
#define SYS_TREE_STRUCT  struct
#endif

/*
 * 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 {                               \
    SYS_TREE_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 {                                \
    SYS_TREE_STRUCT type *spe_left; /* left element */           \
    SYS_TREE_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(SYS_TREE_STRUCT name *, SYS_TREE_STRUCT type *);            \
void name##_SPLAY_MINMAX(SYS_TREE_STRUCT name *, int);               \
SYS_TREE_STRUCT type *name##_SPLAY_INSERT(SYS_TREE_STRUCT name *, SYS_TREE_STRUCT type *);     \
SYS_TREE_STRUCT type *name##_SPLAY_REMOVE(SYS_TREE_STRUCT name *, SYS_TREE_STRUCT type *);     \
                                    \
/* Finds the node with the same key as elm */               \
static __inline SYS_TREE_STRUCT type *                       \
name##_SPLAY_FIND(SYS_TREE_STRUCT name *head, SYS_TREE_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 SYS_TREE_STRUCT type *                       \
name##_SPLAY_NEXT(SYS_TREE_STRUCT name *head, SYS_TREE_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 __inline SYS_TREE_STRUCT type *                       \
name##_SPLAY_MIN_MAX(SYS_TREE_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)              \
SYS_TREE_STRUCT type *                               \
name##_SPLAY_INSERT(SYS_TREE_STRUCT name *head, SYS_TREE_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);                          \
}                                   \
                                    \
SYS_TREE_STRUCT type *                               \
name##_SPLAY_REMOVE(SYS_TREE_STRUCT name *head, SYS_TREE_STRUCT type *elm)        \
{                                   \
    SYS_TREE_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(SYS_TREE_STRUCT name *head, SYS_TREE_STRUCT type *elm)           \
{                                   \
    SYS_TREE_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(SYS_TREE_STRUCT name *head, int __comp) \
{                                   \
    SYS_TREE_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 {                               \
    SYS_TREE_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 {                                \
    SYS_TREE_STRUCT type *rbe_left;      /* left element */      \
    SYS_TREE_STRUCT type *rbe_right;     /* right element */     \
    SYS_TREE_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 (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(SYS_TREE_STRUCT name *, SYS_TREE_STRUCT type *);     \
attr void name##_RB_REMOVE_COLOR(SYS_TREE_STRUCT name *, SYS_TREE_STRUCT type *, SYS_TREE_STRUCT type *);\
attr SYS_TREE_STRUCT type *name##_RB_REMOVE(SYS_TREE_STRUCT name *, SYS_TREE_STRUCT type *);   \
attr SYS_TREE_STRUCT type *name##_RB_INSERT(SYS_TREE_STRUCT name *, SYS_TREE_STRUCT type *);   \
attr SYS_TREE_STRUCT type *name##_RB_FIND(SYS_TREE_STRUCT name *, SYS_TREE_STRUCT type *);     \
attr SYS_TREE_STRUCT type *name##_RB_NFIND(SYS_TREE_STRUCT name *, SYS_TREE_STRUCT type *);    \
attr SYS_TREE_STRUCT type *name##_RB_NEXT(SYS_TREE_STRUCT type *);            \
attr SYS_TREE_STRUCT type *name##_RB_PREV(SYS_TREE_STRUCT type *);            \
attr SYS_TREE_STRUCT type *name##_RB_MINMAX(SYS_TREE_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(SYS_TREE_STRUCT name *head, SYS_TREE_STRUCT type *elm)     \
{                                   \
    SYS_TREE_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(SYS_TREE_STRUCT name *head, SYS_TREE_STRUCT type *parent, SYS_TREE_STRUCT type *elm) \
{                                   \
    SYS_TREE_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) {\
                    SYS_TREE_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) {\
                    SYS_TREE_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 SYS_TREE_STRUCT type *                          \
name##_RB_REMOVE(SYS_TREE_STRUCT name *head, SYS_TREE_STRUCT type *elm)           \
{                                   \
    SYS_TREE_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 {                              \
        SYS_TREE_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 SYS_TREE_STRUCT type *                          \
name##_RB_INSERT(SYS_TREE_STRUCT name *head, SYS_TREE_STRUCT type *elm)           \
{                                   \
    SYS_TREE_STRUCT type *tmp;                       \
    SYS_TREE_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 SYS_TREE_STRUCT type *                          \
name##_RB_FIND(SYS_TREE_STRUCT name *head, SYS_TREE_STRUCT type *elm)         \
{                                   \
    SYS_TREE_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 SYS_TREE_STRUCT type *                          \
name##_RB_NFIND(SYS_TREE_STRUCT name *head, SYS_TREE_STRUCT type *elm)            \
{                                   \
    SYS_TREE_STRUCT type *tmp = RB_ROOT(head);               \
    SYS_TREE_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 SYS_TREE_STRUCT type *                          \
name##_RB_NEXT(SYS_TREE_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 SYS_TREE_STRUCT type *                          \
name##_RB_PREV(SYS_TREE_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 SYS_TREE_STRUCT type *                          \
name##_RB_MINMAX(SYS_TREE_STRUCT name *head, int val)                \
{                                   \
    SYS_TREE_STRUCT type *tmp = RB_ROOT(head);               \
    SYS_TREE_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_ */