text: /****************************************************************************
   * 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, unused_code static)
  #define RB_PROTOTYPE_INTERNAL(name, type, field, cmp, attr) \
    attr void name##_RB_INSERT_COLOR(struct name *, struct type *); \
    attr void name##_RB_REMOVE_COLOR(struct name *, struct type *, struct type *); \
    attr struct type *name##_RB_REMOVE(struct name *, struct type *); \
    attr struct type *name##_RB_INSERT(struct name *, struct type *); \
    attr struct type *name##_RB_FIND(struct name *, struct type *); \
    attr struct type *name##_RB_NFIND(struct name *, struct type *); \
    attr struct type *name##_RB_NEXT(struct type *); \
    attr struct type *name##_RB_PREV(struct type *); \
    attr struct type *name##_RB_MINMAX(struct name *, int);
  
  /* Main rb operation.
   * Moves node close to the key of elm to top
   */
  
  #define RB_GENERATE(name, type, field, cmp) \
    RB_GENERATE_INTERNAL(name, type, field, cmp,)
  
  #define RB_GENERATE_STATIC(name, type, field, cmp) \
    RB_GENERATE_INTERNAL(name, type, field, cmp, unused_code 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 */
  