Add implemenation of splay tree and red-black tree.
authorJoerg Sonnenberger <joerg@dragonflybsd.org>
Thu, 19 Aug 2004 20:38:33 +0000 (20:38 +0000)
committerJoerg Sonnenberger <joerg@dragonflybsd.org>
Thu, 19 Aug 2004 20:38:33 +0000 (20:38 +0000)
Obtained-from: NetBSD

share/man/man3/Makefile
share/man/man3/tree.3 [new file with mode: 0644]
sys/sys/tree.h [new file with mode: 0644]

index 9a1f6ea..feebc20 100644 (file)
@@ -1,9 +1,9 @@
 #      @(#)Makefile    8.2 (Berkeley) 12/13/93
 # $FreeBSD: src/share/man/man3/Makefile,v 1.15.2.3 2001/04/25 11:11:30 ru Exp $
-# $DragonFly: src/share/man/man3/Makefile,v 1.2 2003/06/17 04:36:58 dillon Exp $
+# $DragonFly: src/share/man/man3/Makefile,v 1.3 2004/08/19 20:38:33 joerg Exp $
 
 MAN=   assert.3 bitstring.3 end.3 fpgetround.3 intro.3 pthread.3 queue.3 \
-       stdarg.3 sysexits.3
+       stdarg.3 sysexits.3 tree.3
 MLINKS+=bitstring.3 bit_alloc.3 bitstring.3 bit_clear.3 \
        bitstring.3 bit_decl.3 bitstring.3 bit_ffc.3 bitstring.3 bit_ffs.3 \
        bitstring.3 bit_nclear.3 bitstring.3 bit_nset.3 bitstring.3 bit_set.3 \
diff --git a/share/man/man3/tree.3 b/share/man/man3/tree.3
new file mode 100644 (file)
index 0000000..f2e1d72
--- /dev/null
@@ -0,0 +1,461 @@
+.\"    $NetBSD: tree.3,v 1.3 2004/04/14 11:05:19 pooka Exp $
+.\"    $OpenBSD: tree.3,v 1.9 2003/05/20 09:13:38 jmc Exp $
+.\" $DragonFly: src/share/man/man3/tree.3,v 1.1 2004/08/19 20:38:33 joerg 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.
+.\" * 3. All advertising materials mentioning features or use of this software
+.\" *    must display the following acknowledgement:
+.\" *      This product includes software developed by Niels Provos.
+.\" * 4. The name of the author may not be used to endorse or promote products
+.\" *    derived from this software without specific prior written permission.
+.\" *
+.\" * 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.
+.\" */
+.Dd February 24, 2002
+.Dt TREE 3
+.Os
+.Sh NAME
+.Nm SPLAY_PROTOTYPE ,
+.Nm SPLAY_GENERATE ,
+.Nm SPLAY_ENTRY ,
+.Nm SPLAY_HEAD ,
+.Nm SPLAY_INITIALIZER ,
+.Nm SPLAY_ROOT ,
+.Nm SPLAY_EMPTY ,
+.Nm SPLAY_NEXT ,
+.Nm SPLAY_MIN ,
+.Nm SPLAY_MAX ,
+.Nm SPLAY_FIND ,
+.Nm SPLAY_LEFT ,
+.Nm SPLAY_RIGHT ,
+.Nm SPLAY_FOREACH ,
+.Nm SPLAY_INIT ,
+.Nm SPLAY_INSERT ,
+.Nm SPLAY_REMOVE ,
+.Nm RB_PROTOTYPE ,
+.Nm RB_GENERATE ,
+.Nm RB_ENTRY ,
+.Nm RB_HEAD ,
+.Nm RB_INITIALIZER ,
+.Nm RB_ROOT ,
+.Nm RB_EMPTY ,
+.Nm RB_NEXT ,
+.Nm RB_MIN ,
+.Nm RB_MAX ,
+.Nm RB_FIND ,
+.Nm RB_LEFT ,
+.Nm RB_RIGHT ,
+.Nm RB_PARENT ,
+.Nm RB_FOREACH ,
+.Nm RB_INIT ,
+.Nm RB_INSERT ,
+.Nm RB_REMOVE
+.Nd implementations of splay and red-black trees
+.Sh SYNOPSIS
+.In sys/tree.h
+.Fn SPLAY_PROTOTYPE "NAME" "TYPE" "FIELD" "CMP"
+.Fn SPLAY_GENERATE "NAME" "TYPE" "FIELD" "CMP"
+.Fn SPLAY_ENTRY "TYPE"
+.Fn SPLAY_HEAD "HEADNAME" "TYPE"
+.Ft "struct TYPE *"
+.Fn SPLAY_INITIALIZER "SPLAY_HEAD *head"
+.Fn SPLAY_ROOT "SPLAY_HEAD *head"
+.Ft "bool"
+.Fn SPLAY_EMPTY "SPLAY_HEAD *head"
+.Ft "struct TYPE *"
+.Fn SPLAY_NEXT "NAME" "SPLAY_HEAD *head" "struct TYPE *elm"
+.Ft "struct TYPE *"
+.Fn SPLAY_MIN "NAME" "SPLAY_HEAD *head"
+.Ft "struct TYPE *"
+.Fn SPLAY_MAX "NAME" "SPLAY_HEAD *head"
+.Ft "struct TYPE *"
+.Fn SPLAY_FIND "NAME" "SPLAY_HEAD *head" "struct TYPE *elm"
+.Ft "struct TYPE *"
+.Fn SPLAY_LEFT "struct TYPE *elm" "SPLAY_ENTRY NAME"
+.Ft "struct TYPE *"
+.Fn SPLAY_RIGHT "struct TYPE *elm" "SPLAY_ENTRY NAME"
+.Fn SPLAY_FOREACH "VARNAME" "NAME" "SPLAY_HEAD *head"
+.Ft void
+.Fn SPLAY_INIT "SPLAY_HEAD *head"
+.Ft "struct TYPE *"
+.Fn SPLAY_INSERT "NAME" "SPLAY_HEAD *head" "struct TYPE *elm"
+.Ft "struct TYPE *"
+.Fn SPLAY_REMOVE "NAME" "SPLAY_HEAD *head" "struct TYPE *elm"
+.Pp
+.Fn RB_PROTOTYPE "NAME" "TYPE" "FIELD" "CMP"
+.Fn RB_GENERATE "NAME" "TYPE" "FIELD" "CMP"
+.Fn RB_ENTRY "TYPE"
+.Fn RB_HEAD "HEADNAME" "TYPE"
+.Fn RB_INITIALIZER "RB_HEAD *head"
+.Ft "struct TYPE *"
+.Fn RB_ROOT "RB_HEAD *head"
+.Ft "bool"
+.Fn RB_EMPTY "RB_HEAD *head"
+.Ft "struct TYPE *"
+.Fn RB_NEXT "NAME" "RB_HEAD *head" "struct TYPE *elm"
+.Ft "struct TYPE *"
+.Fn RB_MIN "NAME" "RB_HEAD *head"
+.Ft "struct TYPE *"
+.Fn RB_MAX "NAME" "RB_HEAD *head"
+.Ft "struct TYPE *"
+.Fn RB_FIND "NAME" "RB_HEAD *head" "struct TYPE *elm"
+.Ft "struct TYPE *"
+.Fn RB_LEFT "struct TYPE *elm" "RB_ENTRY NAME"
+.Ft "struct TYPE *"
+.Fn RB_RIGHT "struct TYPE *elm" "RB_ENTRY NAME"
+.Ft "struct TYPE *"
+.Fn RB_PARENT "struct TYPE *elm" "RB_ENTRY NAME"
+.Fn RB_FOREACH "VARNAME" "NAME" "RB_HEAD *head"
+.Ft void
+.Fn RB_INIT "RB_HEAD *head"
+.Ft "struct TYPE *"
+.Fn RB_INSERT "NAME" "RB_HEAD *head" "struct TYPE *elm"
+.Ft "struct TYPE *"
+.Fn RB_REMOVE "NAME" "RB_HEAD *head" "struct TYPE *elm"
+.Sh DESCRIPTION
+These macros define data structures for different types of trees:
+splay trees and red-black trees.
+.Pp
+In the macro definitions,
+.Fa TYPE
+is the name tag of a user defined structure that must contain a field of type
+.Li SPLAY_ENTRY ,
+or
+.Li RB_ENTRY ,
+named
+.Fa ENTRYNAME .
+The argument
+.Fa HEADNAME
+is the name tag of a user defined structure that must be declared
+using the macros
+.Fn SPLAY_HEAD
+or
+.Fn RB_HEAD .
+The argument
+.Fa NAME
+has to be a unique name prefix for every tree that is defined.
+.Pp
+The function prototypes are declared with either
+.Li SPLAY_PROTOTYPE
+or
+.Li RB_PROTOTYPE .
+The function bodies are generated with either
+.Li SPLAY_GENERATE
+or
+.Li RB_GENERATE .
+See the examples below for further explanation of how these macros are used.
+.Sh SPLAY 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.
+.Pp
+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.
+.Pp
+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).
+.Pp
+A splay tree is headed by a structure defined by the
+.Fn SPLAY_HEAD
+macro.
+A
+.Fa SPLAY_HEAD
+structure is declared as follows:
+.Bd -literal -offset indent
+SPLAY_HEAD(HEADNAME, TYPE) head;
+.Ed
+.Pp
+where
+.Fa HEADNAME
+is the name of the structure to be defined, and struct
+.Fa TYPE
+is the type of the elements to be inserted into the tree.
+.Pp
+The
+.Fn SPLAY_ENTRY
+macro declares a structure that allows elements to be connected in the tree.
+.Pp
+In order to use the functions that manipulate the tree structure,
+their prototypes need to be declared with the
+.Fn SPLAY_PROTOTYPE
+macro,
+where
+.Fa NAME
+is a unique identifier for this particular tree.
+The
+.Fa TYPE
+argument is the type of the structure that is being managed
+by the tree.
+The
+.Fa FIELD
+argument is the name of the element defined by
+.Fn SPLAY_ENTRY .
+.Pp
+The function bodies are generated with the
+.Fn SPLAY_GENERATE
+macro.
+It takes the same arguments as the
+.Fn SPLAY_PROTOTYPE
+macro, but should be used only once.
+.Pp
+Finally,
+the
+.Fa CMP
+argument is the name of a function used to compare trees noded
+with each other.
+The function takes two arguments of type
+.Fa "struct TYPE *" .
+If the first argument is smaller than the second, the function returns a
+value smaller than zero.
+If they are equal, the function returns zero.
+Otherwise, it should return a value greater than zero.
+The compare function defines the order of the tree elements.
+.Pp
+The
+.Fn SPLAY_INIT
+macro initializes the tree referenced by
+.Fa head .
+.Pp
+The splay tree can also be initialized statically by using the
+.Fn SPLAY_INITIALIZER
+macro like this:
+.Bd -literal -offset indent
+SPLAY_HEAD(HEADNAME, TYPE) head = SPLAY_INITIALIZER(\*[Am]head);
+.Ed
+.Pp
+The
+.Fn SPLAY_INSERT
+macro inserts the new element
+.Fa elm
+into the tree.
+.Pp
+The
+.Fn SPLAY_REMOVE
+macro removes the element
+.Fa elm
+from the tree pointed by
+.Fa head .
+.Pp
+The
+.Fn SPLAY_FIND
+macro can be used to find a particular element in the tree.
+.Bd -literal -offset indent
+struct TYPE find, *res;
+find.key = 30;
+res = SPLAY_FIND(NAME, head, \*[Am]find);
+.Ed
+.Pp
+The
+.Fn SPLAY_ROOT ,
+.Fn SPLAY_MIN ,
+.Fn SPLAY_MAX ,
+and
+.Fn SPLAY_NEXT
+macros can be used to traverse the tree:
+.Bd -literal -offset indent
+for (np = SPLAY_MIN(NAME, \*[Am]head); np != NULL; np = SPLAY_NEXT(NAME, \*[Am]head, np))
+.Ed
+.Pp
+Or, for simplicity, one can use the
+.Fn SPLAY_FOREACH
+macro:
+.Bd -literal -offset indent
+SPLAY_FOREACH(np, NAME, head)
+.Ed
+.Pp
+The
+.Fn SPLAY_EMPTY
+macro should be used to check whether a splay tree is empty.
+.Sh RED-BLACK TREES
+A red-black tree is a binary search tree with the node color as an
+extra attribute.
+It fulfills a set of conditions:
+.Bl -enum -compact -offset indent
+.It
+every search path from the root to a leaf consists of the same number of
+black nodes,
+.It
+each red node (except for the root) has a black parent,
+.It
+each leaf node is black.
+.El
+.Pp
+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).
+.Pp
+A red-black tree is headed by a structure defined by the
+.Fn RB_HEAD
+macro.
+A
+.Fa RB_HEAD
+structure is declared as follows:
+.Bd -literal -offset indent
+RB_HEAD(HEADNAME, TYPE) head;
+.Ed
+.Pp
+where
+.Fa HEADNAME
+is the name of the structure to be defined, and struct
+.Fa TYPE
+is the type of the elements to be inserted into the tree.
+.Pp
+The
+.Fn RB_ENTRY
+macro declares a structure that allows elements to be connected in the tree.
+.Pp
+In order to use the functions that manipulate the tree structure,
+their prototypes need to be declared with the
+.Fn RB_PROTOTYPE
+macro,
+where
+.Fa NAME
+is a unique identifier for this particular tree.
+The
+.Fa TYPE
+argument is the type of the structure that is being managed
+by the tree.
+The
+.Fa FIELD
+argument is the name of the element defined by
+.Fn RB_ENTRY .
+.Pp
+The function bodies are generated with the
+.Fn RB_GENERATE
+macro.
+It takes the same arguments as the
+.Fn RB_PROTOTYPE
+macro, but should be used only once.
+.Pp
+Finally,
+the
+.Fa CMP
+argument is the name of a function used to compare trees noded
+with each other.
+The function takes two arguments of type
+.Fa "struct TYPE *" .
+If the first argument is smaller than the second, the function returns a
+value smaller than zero.
+If they are equal, the function returns zero.
+Otherwise, it should return a value greater than zero.
+The compare function defines the order of the tree elements.
+.Pp
+The
+.Fn RB_INIT
+macro initializes the tree referenced by
+.Fa head .
+.Pp
+The redblack tree can also be initialized statically by using the
+.Fn RB_INITIALIZER
+macro like this:
+.Bd -literal -offset indent
+RB_HEAD(HEADNAME, TYPE) head = RB_INITIALIZER(\*[Am]head);
+.Ed
+.Pp
+The
+.Fn RB_INSERT
+macro inserts the new element
+.Fa elm
+into the tree.
+.Pp
+The
+.Fn RB_REMOVE
+macro removes the element
+.Fa elm
+from the tree pointed by
+.Fa head .
+.Pp
+The
+.Fn RB_FIND
+macro can be used to find a particular element in the tree.
+.Bd -literal -offset indent
+struct TYPE find, *res;
+find.key = 30;
+res = RB_FIND(NAME, head, \*[Am]find);
+.Ed
+.Pp
+The
+.Fn RB_ROOT ,
+.Fn RB_MIN ,
+.Fn RB_MAX ,
+and
+.Fn RB_NEXT
+macros can be used to traverse the tree:
+.Bd -literal -offset indent
+for (np = RB_MIN(NAME, \*[Am]head); np != NULL; np = RB_NEXT(NAME, \*[Am]head, np))
+.Ed
+.Pp
+Or, for simplicity, one can use the
+.Fn RB_FOREACH
+macro:
+.Bd -literal -offset indent
+RB_FOREACH(np, NAME, head)
+.Ed
+.Pp
+The
+.Fn RB_EMPTY
+macro should be used to check whether a red-black tree is empty.
+.Sh NOTES
+Trying to free a tree in the following way is a common error:
+.Bd -literal -offset indent
+SPLAY_FOREACH(var, NAME, head) {
+       SPLAY_REMOVE(NAME, head, var);
+       free(var);
+}
+free(head);
+.Ed
+.Pp
+Since
+.Va var
+is free'd, the
+.Fn FOREACH
+macro refers to a pointer that may have been reallocated already.
+Proper code needs a second variable.
+.Bd -literal -offset indent
+for (var = SPLAY_MIN(NAME, head); var != NULL; var = nxt) {
+       nxt = SPLAY_NEXT(NAME, head, var);
+       SPLAY_REMOVE(NAME, head, var);
+       free(var);
+}
+.Ed
+.Pp
+Both
+.Fn RB_INSERT
+and
+.Fn SPLAY_INSERT
+return
+.Dv NULL
+if the element was inserted in the tree successfully, otherwise they
+return a pointer to the element with the colliding key.
+.Pp
+Accordingly,
+.Fn RB_REMOVE
+and
+.Fn SPLAY_REMOVE
+return the pointer to the removed element, otherwise they return
+.Dv NULL
+to indicate an error.
+.Sh AUTHORS
+The author of the tree macros is
+.An Niels Provos .
diff --git a/sys/sys/tree.h b/sys/sys/tree.h
new file mode 100644 (file)
index 0000000..717bed8
--- /dev/null
@@ -0,0 +1,682 @@
+/*     $NetBSD: tree.h,v 1.8 2004/03/28 19:38:30 provos Exp $  */
+/*     $OpenBSD: tree.h,v 1.7 2002/10/17 21:51:54 art Exp $    */
+/*     $DragonFly: src/sys/sys/tree.h,v 1.1 2004/08/19 20:38:33 joerg 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 (/*CONSTCOND*/ 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 (/*CONSTCOND*/ 0)
+       
+#define SPLAY_ROTATE_LEFT(head, tmp, field) do {                       \
+       SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(tmp, field);  \
+       SPLAY_LEFT(tmp, field) = (head)->sph_root;                      \
+       (head)->sph_root = tmp;                                         \
+} while (/*CONSTCOND*/ 0)
+
+#define SPLAY_LINKLEFT(head, tmp, field) do {                          \
+       SPLAY_LEFT(tmp, field) = (head)->sph_root;                      \
+       tmp = (head)->sph_root;                                         \
+       (head)->sph_root = SPLAY_LEFT((head)->sph_root, field);         \
+} while (/*CONSTCOND*/ 0)
+
+#define SPLAY_LINKRIGHT(head, tmp, field) do {                         \
+       SPLAY_RIGHT(tmp, field) = (head)->sph_root;                     \
+       tmp = (head)->sph_root;                                         \
+       (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);        \
+} while (/*CONSTCOND*/ 0)
+
+#define SPLAY_ASSEMBLE(head, node, left, right, field) do {            \
+       SPLAY_RIGHT(left, field) = SPLAY_LEFT((head)->sph_root, field); \
+       SPLAY_LEFT(right, field) = SPLAY_RIGHT((head)->sph_root, field);\
+       SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(node, field); \
+       SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(node, field); \
+} while (/*CONSTCOND*/ 0)
+
+/* Generates prototypes and inline functions */
+
+#define SPLAY_PROTOTYPE(name, type, field, cmp)                                \
+void name##_SPLAY(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)) != 0) {          \
+               if (__comp < 0) {                                       \
+                       __tmp = SPLAY_LEFT((head)->sph_root, field);    \
+                       if (__tmp == NULL)                              \
+                               break;                                  \
+                       if ((cmp)(elm, __tmp) < 0){                     \
+                               SPLAY_ROTATE_RIGHT(head, __tmp, field); \
+                               if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
+                                       break;                          \
+                       }                                               \
+                       SPLAY_LINKLEFT(head, __right, field);           \
+               } else if (__comp > 0) {                                \
+                       __tmp = SPLAY_RIGHT((head)->sph_root, field);   \
+                       if (__tmp == NULL)                              \
+                               break;                                  \
+                       if ((cmp)(elm, __tmp) > 0){                     \
+                               SPLAY_ROTATE_LEFT(head, __tmp, field);  \
+                               if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
+                                       break;                          \
+                       }                                               \
+                       SPLAY_LINKRIGHT(head, __left, field);           \
+               }                                                       \
+       }                                                               \
+       SPLAY_ASSEMBLE(head, &__node, __left, __right, field);          \
+}                                                                      \
+                                                                       \
+/* Splay with either the minimum or the maximum element                        \
+ * Used to find minimum or maximum element in tree.                    \
+ */                                                                    \
+void name##_SPLAY_MINMAX(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 (/*CONSTCOND*/ 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 (/*CONSTCOND*/ 0)
+
+#define RB_SET_BLACKRED(black, red, field) do {                                \
+       RB_COLOR(black, field) = RB_BLACK;                              \
+       RB_COLOR(red, field) = RB_RED;                                  \
+} while (/*CONSTCOND*/ 0)
+
+#ifndef RB_AUGMENT
+#define RB_AUGMENT(x)
+#endif
+
+#define RB_ROTATE_LEFT(head, elm, tmp, field) do {                     \
+       (tmp) = RB_RIGHT(elm, field);                                   \
+       if ((RB_RIGHT(elm, field) = RB_LEFT(tmp, field)) != NULL) {     \
+               RB_PARENT(RB_LEFT(tmp, field), field) = (elm);          \
+       }                                                               \
+       RB_AUGMENT(elm);                                                \
+       if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) {  \
+               if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))     \
+                       RB_LEFT(RB_PARENT(elm, field), field) = (tmp);  \
+               else                                                    \
+                       RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \
+       } else                                                          \
+               (head)->rbh_root = (tmp);                               \
+       RB_LEFT(tmp, field) = (elm);                                    \
+       RB_PARENT(elm, field) = (tmp);                                  \
+       RB_AUGMENT(tmp);                                                \
+       if ((RB_PARENT(tmp, field)))                                    \
+               RB_AUGMENT(RB_PARENT(tmp, field));                      \
+} while (/*CONSTCOND*/ 0)
+
+#define RB_ROTATE_RIGHT(head, elm, tmp, field) do {                    \
+       (tmp) = RB_LEFT(elm, field);                                    \
+       if ((RB_LEFT(elm, field) = RB_RIGHT(tmp, field)) != NULL) {     \
+               RB_PARENT(RB_RIGHT(tmp, field), field) = (elm);         \
+       }                                                               \
+       RB_AUGMENT(elm);                                                \
+       if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) {  \
+               if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))     \
+                       RB_LEFT(RB_PARENT(elm, field), field) = (tmp);  \
+               else                                                    \
+                       RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \
+       } else                                                          \
+               (head)->rbh_root = (tmp);                               \
+       RB_RIGHT(tmp, field) = (elm);                                   \
+       RB_PARENT(elm, field) = (tmp);                                  \
+       RB_AUGMENT(tmp);                                                \
+       if ((RB_PARENT(tmp, field)))                                    \
+               RB_AUGMENT(RB_PARENT(tmp, field));                      \
+} while (/*CONSTCOND*/ 0)
+
+/* Generates prototypes and inline functions */
+#define RB_PROTOTYPE(name, type, field, cmp)                           \
+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 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)) != NULL &&              \
+           RB_COLOR(parent, field) == RB_RED) {                        \
+               gparent = RB_PARENT(parent, field);                     \
+               if (parent == RB_LEFT(gparent, field)) {                \
+                       tmp = RB_RIGHT(gparent, field);                 \
+                       if (tmp && RB_COLOR(tmp, field) == RB_RED) {    \
+                               RB_COLOR(tmp, field) = RB_BLACK;        \
+                               RB_SET_BLACKRED(parent, gparent, field);\
+                               elm = gparent;                          \
+                               continue;                               \
+                       }                                               \
+                       if (RB_RIGHT(parent, field) == elm) {           \
+                               RB_ROTATE_LEFT(head, parent, tmp, field);\
+                               tmp = parent;                           \
+                               parent = elm;                           \
+                               elm = tmp;                              \
+                       }                                               \
+                       RB_SET_BLACKRED(parent, gparent, field);        \
+                       RB_ROTATE_RIGHT(head, gparent, tmp, field);     \
+               } else {                                                \
+                       tmp = RB_LEFT(gparent, field);                  \
+                       if (tmp && RB_COLOR(tmp, field) == RB_RED) {    \
+                               RB_COLOR(tmp, field) = RB_BLACK;        \
+                               RB_SET_BLACKRED(parent, gparent, field);\
+                               elm = gparent;                          \
+                               continue;                               \
+                       }                                               \
+                       if (RB_LEFT(parent, field) == elm) {            \
+                               RB_ROTATE_RIGHT(head, parent, tmp, field);\
+                               tmp = parent;                           \
+                               parent = elm;                           \
+                               elm = tmp;                              \
+                       }                                               \
+                       RB_SET_BLACKRED(parent, gparent, field);        \
+                       RB_ROTATE_LEFT(head, gparent, tmp, field);      \
+               }                                                       \
+       }                                                               \
+       RB_COLOR(head->rbh_root, field) = RB_BLACK;                     \
+}                                                                      \
+                                                                       \
+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)) \
+                                           != NULL)                    \
+                                               RB_COLOR(oleft, field) = RB_BLACK;\
+                                       RB_COLOR(tmp, field) = RB_RED;  \
+                                       RB_ROTATE_RIGHT(head, tmp, oleft, field);\
+                                       tmp = RB_RIGHT(parent, field);  \
+                               }                                       \
+                               RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
+                               RB_COLOR(parent, field) = RB_BLACK;     \
+                               if (RB_RIGHT(tmp, field))               \
+                                       RB_COLOR(RB_RIGHT(tmp, field), field) = RB_BLACK;\
+                               RB_ROTATE_LEFT(head, parent, tmp, field);\
+                               elm = RB_ROOT(head);                    \
+                               break;                                  \
+                       }                                               \
+               } else {                                                \
+                       tmp = RB_LEFT(parent, field);                   \
+                       if (RB_COLOR(tmp, field) == RB_RED) {           \
+                               RB_SET_BLACKRED(tmp, parent, field);    \
+                               RB_ROTATE_RIGHT(head, parent, tmp, field);\
+                               tmp = RB_LEFT(parent, field);           \
+                       }                                               \
+                       if ((RB_LEFT(tmp, field) == NULL ||             \
+                           RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
+                           (RB_RIGHT(tmp, field) == NULL ||            \
+                           RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
+                               RB_COLOR(tmp, field) = RB_RED;          \
+                               elm = parent;                           \
+                               parent = RB_PARENT(elm, field);         \
+                       } else {                                        \
+                               if (RB_LEFT(tmp, field) == NULL ||      \
+                                   RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) {\
+                                       struct type *oright;            \
+                                       if ((oright = RB_RIGHT(tmp, field)) \
+                                           != NULL)                    \
+                                               RB_COLOR(oright, field) = RB_BLACK;\
+                                       RB_COLOR(tmp, field) = RB_RED;  \
+                                       RB_ROTATE_LEFT(head, tmp, oright, field);\
+                                       tmp = RB_LEFT(parent, field);   \
+                               }                                       \
+                               RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
+                               RB_COLOR(parent, field) = RB_BLACK;     \
+                               if (RB_LEFT(tmp, field))                \
+                                       RB_COLOR(RB_LEFT(tmp, field), field) = RB_BLACK;\
+                               RB_ROTATE_RIGHT(head, parent, tmp, field);\
+                               elm = RB_ROOT(head);                    \
+                               break;                                  \
+                       }                                               \
+               }                                                       \
+       }                                                               \
+       if (elm)                                                        \
+               RB_COLOR(elm, field) = RB_BLACK;                        \
+}                                                                      \
+                                                                       \
+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)) != NULL)            \
+                       elm = left;                                     \
+               child = RB_RIGHT(elm, field);                           \
+               parent = RB_PARENT(elm, field);                         \
+               color = RB_COLOR(elm, field);                           \
+               if (child)                                              \
+                       RB_PARENT(child, field) = parent;               \
+               if (parent) {                                           \
+                       if (RB_LEFT(parent, field) == elm)              \
+                               RB_LEFT(parent, field) = child;         \
+                       else                                            \
+                               RB_RIGHT(parent, field) = child;        \
+                       RB_AUGMENT(parent);                             \
+               } else                                                  \
+                       RB_ROOT(head) = child;                          \
+               if (RB_PARENT(elm, field) == old)                       \
+                       parent = elm;                                   \
+               (elm)->field = (old)->field;                            \
+               if (RB_PARENT(old, field)) {                            \
+                       if (RB_LEFT(RB_PARENT(old, field), field) == old)\
+                               RB_LEFT(RB_PARENT(old, field), field) = elm;\
+                       else                                            \
+                               RB_RIGHT(RB_PARENT(old, field), field) = elm;\
+                       RB_AUGMENT(RB_PARENT(old, field));              \
+               } else                                                  \
+                       RB_ROOT(head) = elm;                            \
+               RB_PARENT(RB_LEFT(old, field), field) = elm;            \
+               if (RB_RIGHT(old, field))                               \
+                       RB_PARENT(RB_RIGHT(old, field), field) = elm;   \
+               if (parent) {                                           \
+                       left = parent;                                  \
+                       do {                                            \
+                               RB_AUGMENT(left);                       \
+                       } while ((left = RB_PARENT(left, field)) != NULL); \
+               }                                                       \
+               goto color;                                             \
+       }                                                               \
+       parent = RB_PARENT(elm, field);                                 \
+       color = RB_COLOR(elm, field);                                   \
+       if (child)                                                      \
+               RB_PARENT(child, field) = parent;                       \
+       if (parent) {                                                   \
+               if (RB_LEFT(parent, field) == elm)                      \
+                       RB_LEFT(parent, field) = child;                 \
+               else                                                    \
+                       RB_RIGHT(parent, field) = child;                \
+               RB_AUGMENT(parent);                                     \
+       } else                                                          \
+               RB_ROOT(head) = child;                                  \
+color:                                                                 \
+       if (color == RB_BLACK)                                          \
+               name##_RB_REMOVE_COLOR(head, parent, child);            \
+       return (old);                                                   \
+}                                                                      \
+                                                                       \
+/* Inserts a node into the RB tree */                                  \
+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);                                                  \
+}                                                                      \
+                                                                       \
+/* ARGSUSED */                                                         \
+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);                                                   \
+}                                                                      \
+                                                                       \
+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(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))
+
+#endif /* _SYS_TREE_H_ */