The Design and Implementation of the FreeBSD Operating System, Second Edition
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FreeBSD/Linux Kernel Cross Reference
sys/sys/tree.h

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    1 /*      $NetBSD: tree.h,v 1.8 2004/03/28 19:38:30 provos Exp $  */
    2 /*      $OpenBSD: tree.h,v 1.7 2002/10/17 21:51:54 art Exp $    */
    3 /*
    4  * Copyright 2002 Niels Provos <provos@citi.umich.edu>
    5  * All rights reserved.
    6  *
    7  * Redistribution and use in source and binary forms, with or without
    8  * modification, are permitted provided that the following conditions
    9  * are met:
   10  * 1. Redistributions of source code must retain the above copyright
   11  *    notice, this list of conditions and the following disclaimer.
   12  * 2. Redistributions in binary form must reproduce the above copyright
   13  *    notice, this list of conditions and the following disclaimer in the
   14  *    documentation and/or other materials provided with the distribution.
   15  *
   16  * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
   17  * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
   18  * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
   19  * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
   20  * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
   21  * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
   22  * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
   23  * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
   24  * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
   25  * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
   26  */
   27 
   28 #ifndef _SYS_TREE_H_
   29 #define _SYS_TREE_H_
   30 
   31 /*
   32  * This file defines data structures for different types of trees:
   33  * splay trees and red-black trees.
   34  *
   35  * A splay tree is a self-organizing data structure.  Every operation
   36  * on the tree causes a splay to happen.  The splay moves the requested
   37  * node to the root of the tree and partly rebalances it.
   38  *
   39  * This has the benefit that request locality causes faster lookups as
   40  * the requested nodes move to the top of the tree.  On the other hand,
   41  * every lookup causes memory writes.
   42  *
   43  * The Balance Theorem bounds the total access time for m operations
   44  * and n inserts on an initially empty tree as O((m + n)lg n).  The
   45  * amortized cost for a sequence of m accesses to a splay tree is O(lg n);
   46  *
   47  * A red-black tree is a binary search tree with the node color as an
   48  * extra attribute.  It fulfills a set of conditions:
   49  *      - every search path from the root to a leaf consists of the
   50  *        same number of black nodes,
   51  *      - each red node (except for the root) has a black parent,
   52  *      - each leaf node is black.
   53  *
   54  * Every operation on a red-black tree is bounded as O(lg n).
   55  * The maximum height of a red-black tree is 2lg (n+1).
   56  */
   57 
   58 #define SPLAY_HEAD(name, type)                                          \
   59 struct name {                                                           \
   60         struct type *sph_root; /* root of the tree */                   \
   61 }
   62 
   63 #define SPLAY_INITIALIZER(root)                                         \
   64         { NULL }
   65 
   66 #define SPLAY_INIT(root) do {                                           \
   67         (root)->sph_root = NULL;                                        \
   68 } while (/*CONSTCOND*/ 0)
   69 
   70 #define SPLAY_ENTRY(type)                                               \
   71 struct {                                                                \
   72         struct type *spe_left; /* left element */                       \
   73         struct type *spe_right; /* right element */                     \
   74 }
   75 
   76 #define SPLAY_LEFT(elm, field)          (elm)->field.spe_left
   77 #define SPLAY_RIGHT(elm, field)         (elm)->field.spe_right
   78 #define SPLAY_ROOT(head)                (head)->sph_root
   79 #define SPLAY_EMPTY(head)               (SPLAY_ROOT(head) == NULL)
   80 
   81 /* SPLAY_ROTATE_{LEFT,RIGHT} expect that tmp hold SPLAY_{RIGHT,LEFT} */
   82 #define SPLAY_ROTATE_RIGHT(head, tmp, field) do {                       \
   83         SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(tmp, field);  \
   84         SPLAY_RIGHT(tmp, field) = (head)->sph_root;                     \
   85         (head)->sph_root = tmp;                                         \
   86 } while (/*CONSTCOND*/ 0)
   87         
   88 #define SPLAY_ROTATE_LEFT(head, tmp, field) do {                        \
   89         SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(tmp, field);  \
   90         SPLAY_LEFT(tmp, field) = (head)->sph_root;                      \
   91         (head)->sph_root = tmp;                                         \
   92 } while (/*CONSTCOND*/ 0)
   93 
   94 #define SPLAY_LINKLEFT(head, tmp, field) do {                           \
   95         SPLAY_LEFT(tmp, field) = (head)->sph_root;                      \
   96         tmp = (head)->sph_root;                                         \
   97         (head)->sph_root = SPLAY_LEFT((head)->sph_root, field);         \
   98 } while (/*CONSTCOND*/ 0)
   99 
  100 #define SPLAY_LINKRIGHT(head, tmp, field) do {                          \
  101         SPLAY_RIGHT(tmp, field) = (head)->sph_root;                     \
  102         tmp = (head)->sph_root;                                         \
  103         (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);        \
  104 } while (/*CONSTCOND*/ 0)
  105 
  106 #define SPLAY_ASSEMBLE(head, node, left, right, field) do {             \
  107         SPLAY_RIGHT(left, field) = SPLAY_LEFT((head)->sph_root, field); \
  108         SPLAY_LEFT(right, field) = SPLAY_RIGHT((head)->sph_root, field);\
  109         SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(node, field); \
  110         SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(node, field); \
  111 } while (/*CONSTCOND*/ 0)
  112 
  113 /* Generates prototypes and inline functions */
  114 
  115 #define SPLAY_PROTOTYPE(name, type, field, cmp)                         \
  116 void name##_SPLAY(struct name *, struct type *);                        \
  117 void name##_SPLAY_MINMAX(struct name *, int);                           \
  118 struct type *name##_SPLAY_INSERT(struct name *, struct type *);         \
  119 struct type *name##_SPLAY_REMOVE(struct name *, struct type *);         \
  120                                                                         \
  121 /* Finds the node with the same key as elm */                           \
  122 static __inline struct type *                                           \
  123 name##_SPLAY_FIND(struct name *head, struct type *elm)                  \
  124 {                                                                       \
  125         if (SPLAY_EMPTY(head))                                          \
  126                 return(NULL);                                           \
  127         name##_SPLAY(head, elm);                                        \
  128         if ((cmp)(elm, (head)->sph_root) == 0)                          \
  129                 return (head->sph_root);                                \
  130         return (NULL);                                                  \
  131 }                                                                       \
  132                                                                         \
  133 static __inline struct type *                                           \
  134 name##_SPLAY_NEXT(struct name *head, struct type *elm)                  \
  135 {                                                                       \
  136         name##_SPLAY(head, elm);                                        \
  137         if (SPLAY_RIGHT(elm, field) != NULL) {                          \
  138                 elm = SPLAY_RIGHT(elm, field);                          \
  139                 while (SPLAY_LEFT(elm, field) != NULL) {                \
  140                         elm = SPLAY_LEFT(elm, field);                   \
  141                 }                                                       \
  142         } else                                                          \
  143                 elm = NULL;                                             \
  144         return (elm);                                                   \
  145 }                                                                       \
  146                                                                         \
  147 static __inline struct type *                                           \
  148 name##_SPLAY_MIN_MAX(struct name *head, int val)                        \
  149 {                                                                       \
  150         name##_SPLAY_MINMAX(head, val);                                 \
  151         return (SPLAY_ROOT(head));                                      \
  152 }
  153 
  154 /* Main splay operation.
  155  * Moves node close to the key of elm to top
  156  */
  157 #define SPLAY_GENERATE(name, type, field, cmp)                          \
  158 struct type *                                                           \
  159 name##_SPLAY_INSERT(struct name *head, struct type *elm)                \
  160 {                                                                       \
  161     if (SPLAY_EMPTY(head)) {                                            \
  162             SPLAY_LEFT(elm, field) = SPLAY_RIGHT(elm, field) = NULL;    \
  163     } else {                                                            \
  164             int __comp;                                                 \
  165             name##_SPLAY(head, elm);                                    \
  166             __comp = (cmp)(elm, (head)->sph_root);                      \
  167             if(__comp < 0) {                                            \
  168                     SPLAY_LEFT(elm, field) = SPLAY_LEFT((head)->sph_root, field);\
  169                     SPLAY_RIGHT(elm, field) = (head)->sph_root;         \
  170                     SPLAY_LEFT((head)->sph_root, field) = NULL;         \
  171             } else if (__comp > 0) {                                    \
  172                     SPLAY_RIGHT(elm, field) = SPLAY_RIGHT((head)->sph_root, field);\
  173                     SPLAY_LEFT(elm, field) = (head)->sph_root;          \
  174                     SPLAY_RIGHT((head)->sph_root, field) = NULL;        \
  175             } else                                                      \
  176                     return ((head)->sph_root);                          \
  177     }                                                                   \
  178     (head)->sph_root = (elm);                                           \
  179     return (NULL);                                                      \
  180 }                                                                       \
  181                                                                         \
  182 struct type *                                                           \
  183 name##_SPLAY_REMOVE(struct name *head, struct type *elm)                \
  184 {                                                                       \
  185         struct type *__tmp;                                             \
  186         if (SPLAY_EMPTY(head))                                          \
  187                 return (NULL);                                          \
  188         name##_SPLAY(head, elm);                                        \
  189         if ((cmp)(elm, (head)->sph_root) == 0) {                        \
  190                 if (SPLAY_LEFT((head)->sph_root, field) == NULL) {      \
  191                         (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);\
  192                 } else {                                                \
  193                         __tmp = SPLAY_RIGHT((head)->sph_root, field);   \
  194                         (head)->sph_root = SPLAY_LEFT((head)->sph_root, field);\
  195                         name##_SPLAY(head, elm);                        \
  196                         SPLAY_RIGHT((head)->sph_root, field) = __tmp;   \
  197                 }                                                       \
  198                 return (elm);                                           \
  199         }                                                               \
  200         return (NULL);                                                  \
  201 }                                                                       \
  202                                                                         \
  203 void                                                                    \
  204 name##_SPLAY(struct name *head, struct type *elm)                       \
  205 {                                                                       \
  206         struct type __node, *__left, *__right, *__tmp;                  \
  207         int __comp;                                                     \
  208 \
  209         SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
  210         __left = __right = &__node;                                     \
  211 \
  212         while ((__comp = (cmp)(elm, (head)->sph_root)) != 0) {          \
  213                 if (__comp < 0) {                                       \
  214                         __tmp = SPLAY_LEFT((head)->sph_root, field);    \
  215                         if (__tmp == NULL)                              \
  216                                 break;                                  \
  217                         if ((cmp)(elm, __tmp) < 0){                     \
  218                                 SPLAY_ROTATE_RIGHT(head, __tmp, field); \
  219                                 if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
  220                                         break;                          \
  221                         }                                               \
  222                         SPLAY_LINKLEFT(head, __right, field);           \
  223                 } else if (__comp > 0) {                                \
  224                         __tmp = SPLAY_RIGHT((head)->sph_root, field);   \
  225                         if (__tmp == NULL)                              \
  226                                 break;                                  \
  227                         if ((cmp)(elm, __tmp) > 0){                     \
  228                                 SPLAY_ROTATE_LEFT(head, __tmp, field);  \
  229                                 if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
  230                                         break;                          \
  231                         }                                               \
  232                         SPLAY_LINKRIGHT(head, __left, field);           \
  233                 }                                                       \
  234         }                                                               \
  235         SPLAY_ASSEMBLE(head, &__node, __left, __right, field);          \
  236 }                                                                       \
  237                                                                         \
  238 /* Splay with either the minimum or the maximum element                 \
  239  * Used to find minimum or maximum element in tree.                     \
  240  */                                                                     \
  241 void name##_SPLAY_MINMAX(struct name *head, int __comp) \
  242 {                                                                       \
  243         struct type __node, *__left, *__right, *__tmp;                  \
  244 \
  245         SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
  246         __left = __right = &__node;                                     \
  247 \
  248         while (1) {                                                     \
  249                 if (__comp < 0) {                                       \
  250                         __tmp = SPLAY_LEFT((head)->sph_root, field);    \
  251                         if (__tmp == NULL)                              \
  252                                 break;                                  \
  253                         if (__comp < 0){                                \
  254                                 SPLAY_ROTATE_RIGHT(head, __tmp, field); \
  255                                 if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
  256                                         break;                          \
  257                         }                                               \
  258                         SPLAY_LINKLEFT(head, __right, field);           \
  259                 } else if (__comp > 0) {                                \
  260                         __tmp = SPLAY_RIGHT((head)->sph_root, field);   \
  261                         if (__tmp == NULL)                              \
  262                                 break;                                  \
  263                         if (__comp > 0) {                               \
  264                                 SPLAY_ROTATE_LEFT(head, __tmp, field);  \
  265                                 if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
  266                                         break;                          \
  267                         }                                               \
  268                         SPLAY_LINKRIGHT(head, __left, field);           \
  269                 }                                                       \
  270         }                                                               \
  271         SPLAY_ASSEMBLE(head, &__node, __left, __right, field);          \
  272 }
  273 
  274 #define SPLAY_NEGINF    -1
  275 #define SPLAY_INF       1
  276 
  277 #define SPLAY_INSERT(name, x, y)        name##_SPLAY_INSERT(x, y)
  278 #define SPLAY_REMOVE(name, x, y)        name##_SPLAY_REMOVE(x, y)
  279 #define SPLAY_FIND(name, x, y)          name##_SPLAY_FIND(x, y)
  280 #define SPLAY_NEXT(name, x, y)          name##_SPLAY_NEXT(x, y)
  281 #define SPLAY_MIN(name, x)              (SPLAY_EMPTY(x) ? NULL  \
  282                                         : name##_SPLAY_MIN_MAX(x, SPLAY_NEGINF))
  283 #define SPLAY_MAX(name, x)              (SPLAY_EMPTY(x) ? NULL  \
  284                                         : name##_SPLAY_MIN_MAX(x, SPLAY_INF))
  285 
  286 #define SPLAY_FOREACH(x, name, head)                                    \
  287         for ((x) = SPLAY_MIN(name, head);                               \
  288              (x) != NULL;                                               \
  289              (x) = SPLAY_NEXT(name, head, x))
  290 
  291 /* Macros that define a red-black tree */
  292 #define RB_HEAD(name, type)                                             \
  293 struct name {                                                           \
  294         struct type *rbh_root; /* root of the tree */                   \
  295 }
  296 
  297 #define RB_INITIALIZER(root)                                            \
  298         { NULL }
  299 
  300 #define RB_INIT(root) do {                                              \
  301         (root)->rbh_root = NULL;                                        \
  302 } while (/*CONSTCOND*/ 0)
  303 
  304 #define RB_BLACK        0
  305 #define RB_RED          1
  306 #define RB_ENTRY(type)                                                  \
  307 struct {                                                                \
  308         struct type *rbe_left;          /* left element */              \
  309         struct type *rbe_right;         /* right element */             \
  310         struct type *rbe_parent;        /* parent element */            \
  311         int rbe_color;                  /* node color */                \
  312 }
  313 
  314 #define RB_LEFT(elm, field)             (elm)->field.rbe_left
  315 #define RB_RIGHT(elm, field)            (elm)->field.rbe_right
  316 #define RB_PARENT(elm, field)           (elm)->field.rbe_parent
  317 #define RB_COLOR(elm, field)            (elm)->field.rbe_color
  318 #define RB_ROOT(head)                   (head)->rbh_root
  319 #define RB_EMPTY(head)                  (RB_ROOT(head) == NULL)
  320 
  321 #define RB_SET(elm, parent, field) do {                                 \
  322         RB_PARENT(elm, field) = parent;                                 \
  323         RB_LEFT(elm, field) = RB_RIGHT(elm, field) = NULL;              \
  324         RB_COLOR(elm, field) = RB_RED;                                  \
  325 } while (/*CONSTCOND*/ 0)
  326 
  327 #define RB_SET_BLACKRED(black, red, field) do {                         \
  328         RB_COLOR(black, field) = RB_BLACK;                              \
  329         RB_COLOR(red, field) = RB_RED;                                  \
  330 } while (/*CONSTCOND*/ 0)
  331 
  332 #ifndef RB_AUGMENT
  333 #define RB_AUGMENT(x)
  334 #endif
  335 
  336 #define RB_ROTATE_LEFT(head, elm, tmp, field) do {                      \
  337         (tmp) = RB_RIGHT(elm, field);                                   \
  338         if ((RB_RIGHT(elm, field) = RB_LEFT(tmp, field)) != NULL) {     \
  339                 RB_PARENT(RB_LEFT(tmp, field), field) = (elm);          \
  340         }                                                               \
  341         RB_AUGMENT(elm);                                                \
  342         if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) {  \
  343                 if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))     \
  344                         RB_LEFT(RB_PARENT(elm, field), field) = (tmp);  \
  345                 else                                                    \
  346                         RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \
  347         } else                                                          \
  348                 (head)->rbh_root = (tmp);                               \
  349         RB_LEFT(tmp, field) = (elm);                                    \
  350         RB_PARENT(elm, field) = (tmp);                                  \
  351         RB_AUGMENT(tmp);                                                \
  352         if ((RB_PARENT(tmp, field)))                                    \
  353                 RB_AUGMENT(RB_PARENT(tmp, field));                      \
  354 } while (/*CONSTCOND*/ 0)
  355 
  356 #define RB_ROTATE_RIGHT(head, elm, tmp, field) do {                     \
  357         (tmp) = RB_LEFT(elm, field);                                    \
  358         if ((RB_LEFT(elm, field) = RB_RIGHT(tmp, field)) != NULL) {     \
  359                 RB_PARENT(RB_RIGHT(tmp, field), field) = (elm);         \
  360         }                                                               \
  361         RB_AUGMENT(elm);                                                \
  362         if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) {  \
  363                 if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))     \
  364                         RB_LEFT(RB_PARENT(elm, field), field) = (tmp);  \
  365                 else                                                    \
  366                         RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \
  367         } else                                                          \
  368                 (head)->rbh_root = (tmp);                               \
  369         RB_RIGHT(tmp, field) = (elm);                                   \
  370         RB_PARENT(elm, field) = (tmp);                                  \
  371         RB_AUGMENT(tmp);                                                \
  372         if ((RB_PARENT(tmp, field)))                                    \
  373                 RB_AUGMENT(RB_PARENT(tmp, field));                      \
  374 } while (/*CONSTCOND*/ 0)
  375 
  376 /* Generates prototypes and inline functions */
  377 #define RB_PROTOTYPE(name, type, field, cmp)                            \
  378 void name##_RB_INSERT_COLOR(struct name *, struct type *);      \
  379 void name##_RB_REMOVE_COLOR(struct name *, struct type *, struct type *);\
  380 struct type *name##_RB_REMOVE(struct name *, struct type *);            \
  381 struct type *name##_RB_INSERT(struct name *, struct type *);            \
  382 struct type *name##_RB_FIND(struct name *, struct type *);              \
  383 struct type *name##_RB_NEXT(struct type *);                             \
  384 struct type *name##_RB_MINMAX(struct name *, int);                      \
  385                                                                         \
  386 
  387 /* Main rb operation.
  388  * Moves node close to the key of elm to top
  389  */
  390 #define RB_GENERATE(name, type, field, cmp)                             \
  391 void                                                                    \
  392 name##_RB_INSERT_COLOR(struct name *head, struct type *elm)             \
  393 {                                                                       \
  394         struct type *parent, *gparent, *tmp;                            \
  395         while ((parent = RB_PARENT(elm, field)) != NULL &&              \
  396             RB_COLOR(parent, field) == RB_RED) {                        \
  397                 gparent = RB_PARENT(parent, field);                     \
  398                 if (parent == RB_LEFT(gparent, field)) {                \
  399                         tmp = RB_RIGHT(gparent, field);                 \
  400                         if (tmp && RB_COLOR(tmp, field) == RB_RED) {    \
  401                                 RB_COLOR(tmp, field) = RB_BLACK;        \
  402                                 RB_SET_BLACKRED(parent, gparent, field);\
  403                                 elm = gparent;                          \
  404                                 continue;                               \
  405                         }                                               \
  406                         if (RB_RIGHT(parent, field) == elm) {           \
  407                                 RB_ROTATE_LEFT(head, parent, tmp, field);\
  408                                 tmp = parent;                           \
  409                                 parent = elm;                           \
  410                                 elm = tmp;                              \
  411                         }                                               \
  412                         RB_SET_BLACKRED(parent, gparent, field);        \
  413                         RB_ROTATE_RIGHT(head, gparent, tmp, field);     \
  414                 } else {                                                \
  415                         tmp = RB_LEFT(gparent, field);                  \
  416                         if (tmp && RB_COLOR(tmp, field) == RB_RED) {    \
  417                                 RB_COLOR(tmp, field) = RB_BLACK;        \
  418                                 RB_SET_BLACKRED(parent, gparent, field);\
  419                                 elm = gparent;                          \
  420                                 continue;                               \
  421                         }                                               \
  422                         if (RB_LEFT(parent, field) == elm) {            \
  423                                 RB_ROTATE_RIGHT(head, parent, tmp, field);\
  424                                 tmp = parent;                           \
  425                                 parent = elm;                           \
  426                                 elm = tmp;                              \
  427                         }                                               \
  428                         RB_SET_BLACKRED(parent, gparent, field);        \
  429                         RB_ROTATE_LEFT(head, gparent, tmp, field);      \
  430                 }                                                       \
  431         }                                                               \
  432         RB_COLOR(head->rbh_root, field) = RB_BLACK;                     \
  433 }                                                                       \
  434                                                                         \
  435 void                                                                    \
  436 name##_RB_REMOVE_COLOR(struct name *head, struct type *parent, struct type *elm) \
  437 {                                                                       \
  438         struct type *tmp;                                               \
  439         while ((elm == NULL || RB_COLOR(elm, field) == RB_BLACK) &&     \
  440             elm != RB_ROOT(head)) {                                     \
  441                 if (RB_LEFT(parent, field) == elm) {                    \
  442                         tmp = RB_RIGHT(parent, field);                  \
  443                         if (RB_COLOR(tmp, field) == RB_RED) {           \
  444                                 RB_SET_BLACKRED(tmp, parent, field);    \
  445                                 RB_ROTATE_LEFT(head, parent, tmp, field);\
  446                                 tmp = RB_RIGHT(parent, field);          \
  447                         }                                               \
  448                         if ((RB_LEFT(tmp, field) == NULL ||             \
  449                             RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
  450                             (RB_RIGHT(tmp, field) == NULL ||            \
  451                             RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
  452                                 RB_COLOR(tmp, field) = RB_RED;          \
  453                                 elm = parent;                           \
  454                                 parent = RB_PARENT(elm, field);         \
  455                         } else {                                        \
  456                                 if (RB_RIGHT(tmp, field) == NULL ||     \
  457                                     RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK) {\
  458                                         struct type *oleft;             \
  459                                         if ((oleft = RB_LEFT(tmp, field)) \
  460                                             != NULL)                    \
  461                                                 RB_COLOR(oleft, field) = RB_BLACK;\
  462                                         RB_COLOR(tmp, field) = RB_RED;  \
  463                                         RB_ROTATE_RIGHT(head, tmp, oleft, field);\
  464                                         tmp = RB_RIGHT(parent, field);  \
  465                                 }                                       \
  466                                 RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
  467                                 RB_COLOR(parent, field) = RB_BLACK;     \
  468                                 if (RB_RIGHT(tmp, field))               \
  469                                         RB_COLOR(RB_RIGHT(tmp, field), field) = RB_BLACK;\
  470                                 RB_ROTATE_LEFT(head, parent, tmp, field);\
  471                                 elm = RB_ROOT(head);                    \
  472                                 break;                                  \
  473                         }                                               \
  474                 } else {                                                \
  475                         tmp = RB_LEFT(parent, field);                   \
  476                         if (RB_COLOR(tmp, field) == RB_RED) {           \
  477                                 RB_SET_BLACKRED(tmp, parent, field);    \
  478                                 RB_ROTATE_RIGHT(head, parent, tmp, field);\
  479                                 tmp = RB_LEFT(parent, field);           \
  480                         }                                               \
  481                         if ((RB_LEFT(tmp, field) == NULL ||             \
  482                             RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
  483                             (RB_RIGHT(tmp, field) == NULL ||            \
  484                             RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
  485                                 RB_COLOR(tmp, field) = RB_RED;          \
  486                                 elm = parent;                           \
  487                                 parent = RB_PARENT(elm, field);         \
  488                         } else {                                        \
  489                                 if (RB_LEFT(tmp, field) == NULL ||      \
  490                                     RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) {\
  491                                         struct type *oright;            \
  492                                         if ((oright = RB_RIGHT(tmp, field)) \
  493                                             != NULL)                    \
  494                                                 RB_COLOR(oright, field) = RB_BLACK;\
  495                                         RB_COLOR(tmp, field) = RB_RED;  \
  496                                         RB_ROTATE_LEFT(head, tmp, oright, field);\
  497                                         tmp = RB_LEFT(parent, field);   \
  498                                 }                                       \
  499                                 RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
  500                                 RB_COLOR(parent, field) = RB_BLACK;     \
  501                                 if (RB_LEFT(tmp, field))                \
  502                                         RB_COLOR(RB_LEFT(tmp, field), field) = RB_BLACK;\
  503                                 RB_ROTATE_RIGHT(head, parent, tmp, field);\
  504                                 elm = RB_ROOT(head);                    \
  505                                 break;                                  \
  506                         }                                               \
  507                 }                                                       \
  508         }                                                               \
  509         if (elm)                                                        \
  510                 RB_COLOR(elm, field) = RB_BLACK;                        \
  511 }                                                                       \
  512                                                                         \
  513 struct type *                                                           \
  514 name##_RB_REMOVE(struct name *head, struct type *elm)                   \
  515 {                                                                       \
  516         struct type *child, *parent, *old = elm;                        \
  517         int color;                                                      \
  518         if (RB_LEFT(elm, field) == NULL)                                \
  519                 child = RB_RIGHT(elm, field);                           \
  520         else if (RB_RIGHT(elm, field) == NULL)                          \
  521                 child = RB_LEFT(elm, field);                            \
  522         else {                                                          \
  523                 struct type *left;                                      \
  524                 elm = RB_RIGHT(elm, field);                             \
  525                 while ((left = RB_LEFT(elm, field)) != NULL)            \
  526                         elm = left;                                     \
  527                 child = RB_RIGHT(elm, field);                           \
  528                 parent = RB_PARENT(elm, field);                         \
  529                 color = RB_COLOR(elm, field);                           \
  530                 if (child)                                              \
  531                         RB_PARENT(child, field) = parent;               \
  532                 if (parent) {                                           \
  533                         if (RB_LEFT(parent, field) == elm)              \
  534                                 RB_LEFT(parent, field) = child;         \
  535                         else                                            \
  536                                 RB_RIGHT(parent, field) = child;        \
  537                         RB_AUGMENT(parent);                             \
  538                 } else                                                  \
  539                         RB_ROOT(head) = child;                          \
  540                 if (RB_PARENT(elm, field) == old)                       \
  541                         parent = elm;                                   \
  542                 (elm)->field = (old)->field;                            \
  543                 if (RB_PARENT(old, field)) {                            \
  544                         if (RB_LEFT(RB_PARENT(old, field), field) == old)\
  545                                 RB_LEFT(RB_PARENT(old, field), field) = elm;\
  546                         else                                            \
  547                                 RB_RIGHT(RB_PARENT(old, field), field) = elm;\
  548                         RB_AUGMENT(RB_PARENT(old, field));              \
  549                 } else                                                  \
  550                         RB_ROOT(head) = elm;                            \
  551                 RB_PARENT(RB_LEFT(old, field), field) = elm;            \
  552                 if (RB_RIGHT(old, field))                               \
  553                         RB_PARENT(RB_RIGHT(old, field), field) = elm;   \
  554                 if (parent) {                                           \
  555                         left = parent;                                  \
  556                         do {                                            \
  557                                 RB_AUGMENT(left);                       \
  558                         } while ((left = RB_PARENT(left, field)) != NULL); \
  559                 }                                                       \
  560                 goto color;                                             \
  561         }                                                               \
  562         parent = RB_PARENT(elm, field);                                 \
  563         color = RB_COLOR(elm, field);                                   \
  564         if (child)                                                      \
  565                 RB_PARENT(child, field) = parent;                       \
  566         if (parent) {                                                   \
  567                 if (RB_LEFT(parent, field) == elm)                      \
  568                         RB_LEFT(parent, field) = child;                 \
  569                 else                                                    \
  570                         RB_RIGHT(parent, field) = child;                \
  571                 RB_AUGMENT(parent);                                     \
  572         } else                                                          \
  573                 RB_ROOT(head) = child;                                  \
  574 color:                                                                  \
  575         if (color == RB_BLACK)                                          \
  576                 name##_RB_REMOVE_COLOR(head, parent, child);            \
  577         return (old);                                                   \
  578 }                                                                       \
  579                                                                         \
  580 /* Inserts a node into the RB tree */                                   \
  581 struct type *                                                           \
  582 name##_RB_INSERT(struct name *head, struct type *elm)                   \
  583 {                                                                       \
  584         struct type *tmp;                                               \
  585         struct type *parent = NULL;                                     \
  586         int comp = 0;                                                   \
  587         tmp = RB_ROOT(head);                                            \
  588         while (tmp) {                                                   \
  589                 parent = tmp;                                           \
  590                 comp = (cmp)(elm, parent);                              \
  591                 if (comp < 0)                                           \
  592                         tmp = RB_LEFT(tmp, field);                      \
  593                 else if (comp > 0)                                      \
  594                         tmp = RB_RIGHT(tmp, field);                     \
  595                 else                                                    \
  596                         return (tmp);                                   \
  597         }                                                               \
  598         RB_SET(elm, parent, field);                                     \
  599         if (parent != NULL) {                                           \
  600                 if (comp < 0)                                           \
  601                         RB_LEFT(parent, field) = elm;                   \
  602                 else                                                    \
  603                         RB_RIGHT(parent, field) = elm;                  \
  604                 RB_AUGMENT(parent);                                     \
  605         } else                                                          \
  606                 RB_ROOT(head) = elm;                                    \
  607         name##_RB_INSERT_COLOR(head, elm);                              \
  608         return (NULL);                                                  \
  609 }                                                                       \
  610                                                                         \
  611 /* Finds the node with the same key as elm */                           \
  612 struct type *                                                           \
  613 name##_RB_FIND(struct name *head, struct type *elm)                     \
  614 {                                                                       \
  615         struct type *tmp = RB_ROOT(head);                               \
  616         int comp;                                                       \
  617         while (tmp) {                                                   \
  618                 comp = cmp(elm, tmp);                                   \
  619                 if (comp < 0)                                           \
  620                         tmp = RB_LEFT(tmp, field);                      \
  621                 else if (comp > 0)                                      \
  622                         tmp = RB_RIGHT(tmp, field);                     \
  623                 else                                                    \
  624                         return (tmp);                                   \
  625         }                                                               \
  626         return (NULL);                                                  \
  627 }                                                                       \
  628                                                                         \
  629 /* ARGSUSED */                                                          \
  630 struct type *                                                           \
  631 name##_RB_NEXT(struct type *elm)                                        \
  632 {                                                                       \
  633         if (RB_RIGHT(elm, field)) {                                     \
  634                 elm = RB_RIGHT(elm, field);                             \
  635                 while (RB_LEFT(elm, field))                             \
  636                         elm = RB_LEFT(elm, field);                      \
  637         } else {                                                        \
  638                 if (RB_PARENT(elm, field) &&                            \
  639                     (elm == RB_LEFT(RB_PARENT(elm, field), field)))     \
  640                         elm = RB_PARENT(elm, field);                    \
  641                 else {                                                  \
  642                         while (RB_PARENT(elm, field) &&                 \
  643                             (elm == RB_RIGHT(RB_PARENT(elm, field), field)))\
  644                                 elm = RB_PARENT(elm, field);            \
  645                         elm = RB_PARENT(elm, field);                    \
  646                 }                                                       \
  647         }                                                               \
  648         return (elm);                                                   \
  649 }                                                                       \
  650                                                                         \
  651 struct type *                                                           \
  652 name##_RB_MINMAX(struct name *head, int val)                            \
  653 {                                                                       \
  654         struct type *tmp = RB_ROOT(head);                               \
  655         struct type *parent = NULL;                                     \
  656         while (tmp) {                                                   \
  657                 parent = tmp;                                           \
  658                 if (val < 0)                                            \
  659                         tmp = RB_LEFT(tmp, field);                      \
  660                 else                                                    \
  661                         tmp = RB_RIGHT(tmp, field);                     \
  662         }                                                               \
  663         return (parent);                                                \
  664 }
  665 
  666 #define RB_NEGINF       -1
  667 #define RB_INF  1
  668 
  669 #define RB_INSERT(name, x, y)   name##_RB_INSERT(x, y)
  670 #define RB_REMOVE(name, x, y)   name##_RB_REMOVE(x, y)
  671 #define RB_FIND(name, x, y)     name##_RB_FIND(x, y)
  672 #define RB_NEXT(name, x, y)     name##_RB_NEXT(y)
  673 #define RB_MIN(name, x)         name##_RB_MINMAX(x, RB_NEGINF)
  674 #define RB_MAX(name, x)         name##_RB_MINMAX(x, RB_INF)
  675 
  676 #define RB_FOREACH(x, name, head)                                       \
  677         for ((x) = RB_MIN(name, head);                                  \
  678              (x) != NULL;                                               \
  679              (x) = name##_RB_NEXT(x))
  680 
  681 #endif  /* _SYS_TREE_H_ */

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