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rbtree.h

/*    $OpenBSD: tree.h,v 1.6 2002/06/11 22:09:52 provos 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-back 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)
#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); \
            RB_AUGMENT(RB_PARENT(elm, field));              \
      } else                                                \
            (head)->rbh_root = (tmp);                       \
      RB_LEFT(tmp, field) = (elm);                          \
      RB_PARENT(elm, field) = (tmp);                              \
      RB_AUGMENT(tmp);                                \
} 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); \
            RB_AUGMENT(RB_PARENT(elm, field));              \
      } else                                                \
            (head)->rbh_root = (tmp);                       \
      RB_RIGHT(tmp, field) = (elm);                         \
      RB_PARENT(elm, field) = (tmp);                              \
      RB_AUGMENT(tmp);                                \
} while (0)

/* Generates prototypes and inline functions */
#define RB_PROTOTYPE(name, type, field, cmp)                      \
void name##_RB_INSERT_COLOR(struct name *, struct type *);  \
void name##_RB_REMOVE_COLOR(struct name *, struct type *, struct type *);\
struct type *name##_RB_REMOVE(struct name *, struct type *);            \
struct type *name##_RB_INSERT(struct name *, struct type *);            \
struct type *name##_RB_FIND(struct name *, struct type *);        \
struct type *name##_RB_NEXT(struct name *, struct type *);        \
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)                       \
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;                 \
}                                                     \
                                                      \
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;                \
}                                                     \
                                                      \
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 */                             \
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 */                     \
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);                                        \
}                                                     \
                                                      \
struct type *                                               \
name##_RB_NEXT(struct name *head, 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);                                         \
}                                                     \
                                                      \
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_NEXT(name, x, y)   name##_RB_NEXT(x, 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(head, x))

#endif /* _SYS_TREE_H_ */

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