/****************************************************************************
 * include/nuttx/tree.h
 *
 * 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.
 *
 ****************************************************************************/

/* 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 fulfils 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).
 */

/****************************************************************************
 * Included Files
 ****************************************************************************/

#ifndef __INCLUDE_NUTTX_TREE_H
#define __INCLUDE_NUTTX_TREE_H

/****************************************************************************
 * Pre-processor Definitions
 ****************************************************************************/

#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_SAFE(x, name, head, y) \
  for ((x) = RB_MIN(name, head); \
      ((x) != NULL) && ((y) = name##_RB_NEXT(x), 1); \
       (x) = (y))

#define RB_FOREACH_REVERSE(x, name, head) \
  for ((x) = RB_MAX(name, head); \
       (x) != NULL; \
       (x) = name##_RB_PREV(x))

#define RB_FOREACH_REVERSE_SAFE(x, name, head, y) \
  for ((x) = RB_MAX(name, head); \
      ((x) != NULL) && ((y) = name##_RB_PREV(x), 1); \
       (x) = (y))

#endif    /* __INCLUDE_NUTTX_TREE_H */