/*
 * OPENBSD ORIGINAL: sys/sys/tree.h
 */

/*
 * $OpenBSD: tree.h,v 1.12 2009/03/02 09:42:55 mikeb 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 (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 (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 (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 (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 (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 (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 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 __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))) {                                    \
                    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 (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 (0)

#define RB_SET_BLACKRED(black, red, field) do { \
    RB_COLOR(black, field) = RB_BLACK;          \
    RB_COLOR(red, field)   = RB_RED;            \
} while (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))) {                 \
             RB_PARENT(RB_LEFT(tmp, field), field) = (elm);             \
         }                                                              \
         RB_AUGMENT(elm);                                               \
         if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field))) {         \
                  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 (0)

#define RB_ROTATE_RIGHT(head, elm, tmp, field) do {                     \
    (tmp) = RB_LEFT(elm, field);                                        \
    if ((RB_LEFT(elm, field) = RB_RIGHT(tmp, field))) {                 \
             RB_PARENT(RB_RIGHT(tmp, field), field) = (elm);            \
         }                                                              \
         RB_AUGMENT(elm);                                               \
         if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field))) {         \
                  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 (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, __attribute__((__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, __attribute__((__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)) &&                                                                                                    \
                         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))) {                                                                              \
                                             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))) {                                                           \
                                                              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))) {                                              \
                                                                              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)));                                      \
                                                                                }                                                                     \
                                                                                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_REVERSE(x, name, head) \
    for ((x) = RB_MAX(name, head);        \
         (x) != NULL;                     \
         (x) = name ## _RB_PREV(x))

#endif                          /* _SYS_TREE_H_ */