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 /*      $OpenBSD: tree.h,v 1.6 2002/06/11 22:09:52 provos Exp $ */
    2 /*
    3  * Copyright 2002 Niels Provos <provos@citi.umich.edu>
    4  * All rights reserved.
    5  *
    6  * Redistribution and use in source and binary forms, with or without
    7  * modification, are permitted provided that the following conditions
    8  * are met:
    9  * 1. Redistributions of source code must retain the above copyright
   10  *    notice, this list of conditions and the following disclaimer.
   11  * 2. Redistributions in binary form must reproduce the above copyright
   12  *    notice, this list of conditions and the following disclaimer in the
   13  *    documentation and/or other materials provided with the distribution.
   14  *
   15  * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
   16  * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
   17  * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
   18  * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
   19  * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
   20  * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
   21  * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
   22  * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
   23  * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
   24  * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
   25  */
   26 
   27 #ifndef _SYS_TREE_H_
   28 #define _SYS_TREE_H_
   29 
   30 /*
   31  * This file defines data structures for different types of trees:
   32  * splay trees and red-black trees.
   33  *
   34  * A splay tree is a self-organizing data structure.  Every operation
   35  * on the tree causes a splay to happen.  The splay moves the requested
   36  * node to the root of the tree and partly rebalances it.
   37  *
   38  * This has the benefit that request locality causes faster lookups as
   39  * the requested nodes move to the top of the tree.  On the other hand,
   40  * every lookup causes memory writes.
   41  *
   42  * The Balance Theorem bounds the total access time for m operations
   43  * and n inserts on an initially empty tree as O((m + n)lg n).  The
   44  * amortized cost for a sequence of m accesses to a splay tree is O(lg n);
   45  *
   46  * A red-black tree is a binary search tree with the node color as an
   47  * extra attribute.  It fulfills a set of conditions:
   48  *      - every search path from the root to a leaf consists of the
   49  *        same number of black nodes,
   50  *      - each red node (except for the root) has a black parent,
   51  *      - each leaf node is black.
   52  *
   53  * Every operation on a red-black tree is bounded as O(lg n).
   54  * The maximum height of a red-black tree is 2lg (n+1).
   55  */
   56 
   57 #define SPLAY_HEAD(name, type)                                          \
   58 struct name {                                                           \
   59         struct type *sph_root; /* root of the tree */                   \
   60 }
   61 
   62 #define SPLAY_INITIALIZER(root)                                         \
   63         { NULL }
   64 
   65 #define SPLAY_INIT(root) do {                                           \
   66         (root)->sph_root = NULL;                                        \
   67 } while (0)
   68 
   69 #define SPLAY_ENTRY(type)                                               \
   70 struct {                                                                \
   71         struct type *spe_left; /* left element */                       \
   72         struct type *spe_right; /* right element */                     \
   73 }
   74 
   75 #define SPLAY_LEFT(elm, field)          (elm)->field.spe_left
   76 #define SPLAY_RIGHT(elm, field)         (elm)->field.spe_right
   77 #define SPLAY_ROOT(head)                (head)->sph_root
   78 #define SPLAY_EMPTY(head)               (SPLAY_ROOT(head) == NULL)
   79 
   80 /* SPLAY_ROTATE_{LEFT,RIGHT} expect that tmp hold SPLAY_{RIGHT,LEFT} */
   81 #define SPLAY_ROTATE_RIGHT(head, tmp, field) do {                       \
   82         SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(tmp, field);  \
   83         SPLAY_RIGHT(tmp, field) = (head)->sph_root;                     \
   84         (head)->sph_root = tmp;                                         \
   85 } while (0)
   86         
   87 #define SPLAY_ROTATE_LEFT(head, tmp, field) do {                        \
   88         SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(tmp, field);  \
   89         SPLAY_LEFT(tmp, field) = (head)->sph_root;                      \
   90         (head)->sph_root = tmp;                                         \
   91 } while (0)
   92 
   93 #define SPLAY_LINKLEFT(head, tmp, field) do {                           \
   94         SPLAY_LEFT(tmp, field) = (head)->sph_root;                      \
   95         tmp = (head)->sph_root;                                         \
   96         (head)->sph_root = SPLAY_LEFT((head)->sph_root, field);         \
   97 } while (0)
   98 
   99 #define SPLAY_LINKRIGHT(head, tmp, field) do {                          \
  100         SPLAY_RIGHT(tmp, field) = (head)->sph_root;                     \
  101         tmp = (head)->sph_root;                                         \
  102         (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);        \
  103 } while (0)
  104 
  105 #define SPLAY_ASSEMBLE(head, node, left, right, field) do {             \
  106         SPLAY_RIGHT(left, field) = SPLAY_LEFT((head)->sph_root, field); \
  107         SPLAY_LEFT(right, field) = SPLAY_RIGHT((head)->sph_root, field);\
  108         SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(node, field); \
  109         SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(node, field); \
  110 } while (0)
  111 
  112 /* Generates prototypes and inline functions */
  113 
  114 #define SPLAY_PROTOTYPE(name, type, field, cmp)                         \
  115 void name##_SPLAY(struct name *, struct type *);                        \
  116 void name##_SPLAY_MINMAX(struct name *, int);                           \
  117 struct type *name##_SPLAY_INSERT(struct name *, struct type *);         \
  118 struct type *name##_SPLAY_REMOVE(struct name *, struct type *);         \
  119                                                                         \
  120 /* Finds the node with the same key as elm */                           \
  121 static __inline struct type *                                           \
  122 name##_SPLAY_FIND(struct name *head, struct type *elm)                  \
  123 {                                                                       \
  124         if (SPLAY_EMPTY(head))                                          \
  125                 return(NULL);                                           \
  126         name##_SPLAY(head, elm);                                        \
  127         if ((cmp)(elm, (head)->sph_root) == 0)                          \
  128                 return (head->sph_root);                                \
  129         return (NULL);                                                  \
  130 }                                                                       \
  131                                                                         \
  132 static __inline struct type *                                           \
  133 name##_SPLAY_NEXT(struct name *head, struct type *elm)                  \
  134 {                                                                       \
  135         name##_SPLAY(head, elm);                                        \
  136         if (SPLAY_RIGHT(elm, field) != NULL) {                          \
  137                 elm = SPLAY_RIGHT(elm, field);                          \
  138                 while (SPLAY_LEFT(elm, field) != NULL) {                \
  139                         elm = SPLAY_LEFT(elm, field);                   \
  140                 }                                                       \
  141         } else                                                          \
  142                 elm = NULL;                                             \
  143         return (elm);                                                   \
  144 }                                                                       \
  145                                                                         \
  146 static __inline struct type *                                           \
  147 name##_SPLAY_MIN_MAX(struct name *head, int val)                        \
  148 {                                                                       \
  149         name##_SPLAY_MINMAX(head, val);                                 \
  150         return (SPLAY_ROOT(head));                                      \
  151 }
  152 
  153 /* Main splay operation.
  154  * Moves node close to the key of elm to top
  155  */
  156 #define SPLAY_GENERATE(name, type, field, cmp)                          \
  157 struct type *                                                           \
  158 name##_SPLAY_INSERT(struct name *head, struct type *elm)                \
  159 {                                                                       \
  160     if (SPLAY_EMPTY(head)) {                                            \
  161             SPLAY_LEFT(elm, field) = SPLAY_RIGHT(elm, field) = NULL;    \
  162     } else {                                                            \
  163             int __comp;                                                 \
  164             name##_SPLAY(head, elm);                                    \
  165             __comp = (cmp)(elm, (head)->sph_root);                      \
  166             if(__comp < 0) {                                            \
  167                     SPLAY_LEFT(elm, field) = SPLAY_LEFT((head)->sph_root, field);\
  168                     SPLAY_RIGHT(elm, field) = (head)->sph_root;         \
  169                     SPLAY_LEFT((head)->sph_root, field) = NULL;         \
  170             } else if (__comp > 0) {                                    \
  171                     SPLAY_RIGHT(elm, field) = SPLAY_RIGHT((head)->sph_root, field);\
  172                     SPLAY_LEFT(elm, field) = (head)->sph_root;          \
  173                     SPLAY_RIGHT((head)->sph_root, field) = NULL;        \
  174             } else                                                      \
  175                     return ((head)->sph_root);                          \
  176     }                                                                   \
  177     (head)->sph_root = (elm);                                           \
  178     return (NULL);                                                      \
  179 }                                                                       \
  180                                                                         \
  181 struct type *                                                           \
  182 name##_SPLAY_REMOVE(struct name *head, struct type *elm)                \
  183 {                                                                       \
  184         struct type *__tmp;                                             \
  185         if (SPLAY_EMPTY(head))                                          \
  186                 return (NULL);                                          \
  187         name##_SPLAY(head, elm);                                        \
  188         if ((cmp)(elm, (head)->sph_root) == 0) {                        \
  189                 if (SPLAY_LEFT((head)->sph_root, field) == NULL) {      \
  190                         (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);\
  191                 } else {                                                \
  192                         __tmp = SPLAY_RIGHT((head)->sph_root, field);   \
  193                         (head)->sph_root = SPLAY_LEFT((head)->sph_root, field);\
  194                         name##_SPLAY(head, elm);                        \
  195                         SPLAY_RIGHT((head)->sph_root, field) = __tmp;   \
  196                 }                                                       \
  197                 return (elm);                                           \
  198         }                                                               \
  199         return (NULL);                                                  \
  200 }                                                                       \
  201                                                                         \
  202 void                                                                    \
  203 name##_SPLAY(struct name *head, struct type *elm)                       \
  204 {                                                                       \
  205         struct type __node, *__left, *__right, *__tmp;                  \
  206         int __comp;                                                     \
  207 \
  208         SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
  209         __left = __right = &__node;                                     \
  210 \
  211         while ((__comp = (cmp)(elm, (head)->sph_root))) {               \
  212                 if (__comp < 0) {                                       \
  213                         __tmp = SPLAY_LEFT((head)->sph_root, field);    \
  214                         if (__tmp == NULL)                              \
  215                                 break;                                  \
  216                         if ((cmp)(elm, __tmp) < 0){                     \
  217                                 SPLAY_ROTATE_RIGHT(head, __tmp, field); \
  218                                 if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
  219                                         break;                          \
  220                         }                                               \
  221                         SPLAY_LINKLEFT(head, __right, field);           \
  222                 } else if (__comp > 0) {                                \
  223                         __tmp = SPLAY_RIGHT((head)->sph_root, field);   \
  224                         if (__tmp == NULL)                              \
  225                                 break;                                  \
  226                         if ((cmp)(elm, __tmp) > 0){                     \
  227                                 SPLAY_ROTATE_LEFT(head, __tmp, field);  \
  228                                 if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
  229                                         break;                          \
  230                         }                                               \
  231                         SPLAY_LINKRIGHT(head, __left, field);           \
  232                 }                                                       \
  233         }                                                               \
  234         SPLAY_ASSEMBLE(head, &__node, __left, __right, field);          \
  235 }                                                                       \
  236                                                                         \
  237 /* Splay with either the minimum or the maximum element                 \
  238  * Used to find minimum or maximum element in tree.                     \
  239  */                                                                     \
  240 void name##_SPLAY_MINMAX(struct name *head, int __comp) \
  241 {                                                                       \
  242         struct type __node, *__left, *__right, *__tmp;                  \
  243 \
  244         SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
  245         __left = __right = &__node;                                     \
  246 \
  247         while (1) {                                                     \
  248                 if (__comp < 0) {                                       \
  249                         __tmp = SPLAY_LEFT((head)->sph_root, field);    \
  250                         if (__tmp == NULL)                              \
  251                                 break;                                  \
  252                         if (__comp < 0){                                \
  253                                 SPLAY_ROTATE_RIGHT(head, __tmp, field); \
  254                                 if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
  255                                         break;                          \
  256                         }                                               \
  257                         SPLAY_LINKLEFT(head, __right, field);           \
  258                 } else if (__comp > 0) {                                \
  259                         __tmp = SPLAY_RIGHT((head)->sph_root, field);   \
  260                         if (__tmp == NULL)                              \
  261                                 break;                                  \
  262                         if (__comp > 0) {                               \
  263                                 SPLAY_ROTATE_LEFT(head, __tmp, field);  \
  264                                 if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
  265                                         break;                          \
  266                         }                                               \
  267                         SPLAY_LINKRIGHT(head, __left, field);           \
  268                 }                                                       \
  269         }                                                               \
  270         SPLAY_ASSEMBLE(head, &__node, __left, __right, field);          \
  271 }
  272 
  273 #define SPLAY_NEGINF    -1
  274 #define SPLAY_INF       1
  275 
  276 #define SPLAY_INSERT(name, x, y)        name##_SPLAY_INSERT(x, y)
  277 #define SPLAY_REMOVE(name, x, y)        name##_SPLAY_REMOVE(x, y)
  278 #define SPLAY_FIND(name, x, y)          name##_SPLAY_FIND(x, y)
  279 #define SPLAY_NEXT(name, x, y)          name##_SPLAY_NEXT(x, y)
  280 #define SPLAY_MIN(name, x)              (SPLAY_EMPTY(x) ? NULL  \
  281                                         : name##_SPLAY_MIN_MAX(x, SPLAY_NEGINF))
  282 #define SPLAY_MAX(name, x)              (SPLAY_EMPTY(x) ? NULL  \
  283                                         : name##_SPLAY_MIN_MAX(x, SPLAY_INF))
  284 
  285 #define SPLAY_FOREACH(x, name, head)                                    \
  286         for ((x) = SPLAY_MIN(name, head);                               \
  287              (x) != NULL;                                               \
  288              (x) = SPLAY_NEXT(name, head, x))
  289 
  290 /* Macros that define a red-back tree */
  291 #define RB_HEAD(name, type)                                             \
  292 struct name {                                                           \
  293         struct type *rbh_root; /* root of the tree */                   \
  294 }
  295 
  296 #define RB_INITIALIZER(root)                                            \
  297         { NULL }
  298 
  299 #define RB_INIT(root) do {                                              \
  300         (root)->rbh_root = NULL;                                        \
  301 } while (0)
  302 
  303 #define RB_BLACK        0
  304 #define RB_RED          1
  305 #define RB_ENTRY(type)                                                  \
  306 struct {                                                                \
  307         struct type *rbe_left;          /* left element */              \
  308         struct type *rbe_right;         /* right element */             \
  309         struct type *rbe_parent;        /* parent element */            \
  310         int rbe_color;                  /* node color */                \
  311 }
  312 
  313 #define RB_LEFT(elm, field)             (elm)->field.rbe_left
  314 #define RB_RIGHT(elm, field)            (elm)->field.rbe_right
  315 #define RB_PARENT(elm, field)           (elm)->field.rbe_parent
  316 #define RB_COLOR(elm, field)            (elm)->field.rbe_color
  317 #define RB_ROOT(head)                   (head)->rbh_root
  318 #define RB_EMPTY(head)                  (RB_ROOT(head) == NULL)
  319 
  320 #define RB_SET(elm, parent, field) do {                                 \
  321         RB_PARENT(elm, field) = parent;                                 \
  322         RB_LEFT(elm, field) = RB_RIGHT(elm, field) = NULL;              \
  323         RB_COLOR(elm, field) = RB_RED;                                  \
  324 } while (0)
  325 
  326 #define RB_SET_BLACKRED(black, red, field) do {                         \
  327         RB_COLOR(black, field) = RB_BLACK;                              \
  328         RB_COLOR(red, field) = RB_RED;                                  \
  329 } while (0)
  330 
  331 #ifndef RB_AUGMENT
  332 #define RB_AUGMENT(x)
  333 #endif
  334 
  335 #define RB_ROTATE_LEFT(head, elm, tmp, field) do {                      \
  336         (tmp) = RB_RIGHT(elm, field);                                   \
  337         if ((RB_RIGHT(elm, field) = RB_LEFT(tmp, field))) {             \
  338                 RB_PARENT(RB_LEFT(tmp, field), field) = (elm);          \
  339         }                                                               \
  340         RB_AUGMENT(elm);                                                \
  341         if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field))) {          \
  342                 if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))     \
  343                         RB_LEFT(RB_PARENT(elm, field), field) = (tmp);  \
  344                 else                                                    \
  345                         RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \
  346                 RB_AUGMENT(RB_PARENT(elm, field));                      \
  347         } else                                                          \
  348                 (head)->rbh_root = (tmp);                               \
  349         RB_LEFT(tmp, field) = (elm);                                    \
  350         RB_PARENT(elm, field) = (tmp);                                  \
  351         RB_AUGMENT(tmp);                                                \
  352 } while (0)
  353 
  354 #define RB_ROTATE_RIGHT(head, elm, tmp, field) do {                     \
  355         (tmp) = RB_LEFT(elm, field);                                    \
  356         if ((RB_LEFT(elm, field) = RB_RIGHT(tmp, field))) {             \
  357                 RB_PARENT(RB_RIGHT(tmp, field), field) = (elm);         \
  358         }                                                               \
  359         RB_AUGMENT(elm);                                                \
  360         if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field))) {          \
  361                 if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))     \
  362                         RB_LEFT(RB_PARENT(elm, field), field) = (tmp);  \
  363                 else                                                    \
  364                         RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \
  365                 RB_AUGMENT(RB_PARENT(elm, field));                      \
  366         } else                                                          \
  367                 (head)->rbh_root = (tmp);                               \
  368         RB_RIGHT(tmp, field) = (elm);                                   \
  369         RB_PARENT(elm, field) = (tmp);                                  \
  370         RB_AUGMENT(tmp);                                                \
  371 } while (0)
  372 
  373 /* Generates prototypes and inline functions */
  374 #define RB_PROTOTYPE(name, type, field, cmp)                            \
  375 void name##_RB_INSERT_COLOR(struct name *, struct type *);      \
  376 void name##_RB_REMOVE_COLOR(struct name *, struct type *, struct type *);\
  377 struct type *name##_RB_REMOVE(struct name *, struct type *);            \
  378 struct type *name##_RB_INSERT(struct name *, struct type *);            \
  379 struct type *name##_RB_FIND(struct name *, struct type *);              \
  380 struct type *name##_RB_NEXT(struct name *, struct type *);              \
  381 struct type *name##_RB_MINMAX(struct name *, int);                      \
  382                                                                         \
  383 
  384 /* Main rb operation.
  385  * Moves node close to the key of elm to top
  386  */
  387 #define RB_GENERATE(name, type, field, cmp)                             \
  388 void                                                                    \
  389 name##_RB_INSERT_COLOR(struct name *head, struct type *elm)             \
  390 {                                                                       \
  391         struct type *parent, *gparent, *tmp;                            \
  392         while ((parent = RB_PARENT(elm, field)) &&                      \
  393             RB_COLOR(parent, field) == RB_RED) {                        \
  394                 gparent = RB_PARENT(parent, field);                     \
  395                 if (parent == RB_LEFT(gparent, field)) {                \
  396                         tmp = RB_RIGHT(gparent, field);                 \
  397                         if (tmp && RB_COLOR(tmp, field) == RB_RED) {    \
  398                                 RB_COLOR(tmp, field) = RB_BLACK;        \
  399                                 RB_SET_BLACKRED(parent, gparent, field);\
  400                                 elm = gparent;                          \
  401                                 continue;                               \
  402                         }                                               \
  403                         if (RB_RIGHT(parent, field) == elm) {           \
  404                                 RB_ROTATE_LEFT(head, parent, tmp, field);\
  405                                 tmp = parent;                           \
  406                                 parent = elm;                           \
  407                                 elm = tmp;                              \
  408                         }                                               \
  409                         RB_SET_BLACKRED(parent, gparent, field);        \
  410                         RB_ROTATE_RIGHT(head, gparent, tmp, field);     \
  411                 } else {                                                \
  412                         tmp = RB_LEFT(gparent, field);                  \
  413                         if (tmp && RB_COLOR(tmp, field) == RB_RED) {    \
  414                                 RB_COLOR(tmp, field) = RB_BLACK;        \
  415                                 RB_SET_BLACKRED(parent, gparent, field);\
  416                                 elm = gparent;                          \
  417                                 continue;                               \
  418                         }                                               \
  419                         if (RB_LEFT(parent, field) == elm) {            \
  420                                 RB_ROTATE_RIGHT(head, parent, tmp, field);\
  421                                 tmp = parent;                           \
  422                                 parent = elm;                           \
  423                                 elm = tmp;                              \
  424                         }                                               \
  425                         RB_SET_BLACKRED(parent, gparent, field);        \
  426                         RB_ROTATE_LEFT(head, gparent, tmp, field);      \
  427                 }                                                       \
  428         }                                                               \
  429         RB_COLOR(head->rbh_root, field) = RB_BLACK;                     \
  430 }                                                                       \
  431                                                                         \
  432 void                                                                    \
  433 name##_RB_REMOVE_COLOR(struct name *head, struct type *parent, struct type *elm) \
  434 {                                                                       \
  435         struct type *tmp;                                               \
  436         while ((elm == NULL || RB_COLOR(elm, field) == RB_BLACK) &&     \
  437             elm != RB_ROOT(head)) {                                     \
  438                 if (RB_LEFT(parent, field) == elm) {                    \
  439                         tmp = RB_RIGHT(parent, field);                  \
  440                         if (RB_COLOR(tmp, field) == RB_RED) {           \
  441                                 RB_SET_BLACKRED(tmp, parent, field);    \
  442                                 RB_ROTATE_LEFT(head, parent, tmp, field);\
  443                                 tmp = RB_RIGHT(parent, field);          \
  444                         }                                               \
  445                         if ((RB_LEFT(tmp, field) == NULL ||             \
  446                             RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
  447                             (RB_RIGHT(tmp, field) == NULL ||            \
  448                             RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
  449                                 RB_COLOR(tmp, field) = RB_RED;          \
  450                                 elm = parent;                           \
  451                                 parent = RB_PARENT(elm, field);         \
  452                         } else {                                        \
  453                                 if (RB_RIGHT(tmp, field) == NULL ||     \
  454                                     RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK) {\
  455                                         struct type *oleft;             \
  456                                         if ((oleft = RB_LEFT(tmp, field)))\
  457                                                 RB_COLOR(oleft, field) = RB_BLACK;\
  458                                         RB_COLOR(tmp, field) = RB_RED;  \
  459                                         RB_ROTATE_RIGHT(head, tmp, oleft, field);\
  460                                         tmp = RB_RIGHT(parent, field);  \
  461                                 }                                       \
  462                                 RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
  463                                 RB_COLOR(parent, field) = RB_BLACK;     \
  464                                 if (RB_RIGHT(tmp, field))               \
  465                                         RB_COLOR(RB_RIGHT(tmp, field), field) = RB_BLACK;\
  466                                 RB_ROTATE_LEFT(head, parent, tmp, field);\
  467                                 elm = RB_ROOT(head);                    \
  468                                 break;                                  \
  469                         }                                               \
  470                 } else {                                                \
  471                         tmp = RB_LEFT(parent, field);                   \
  472                         if (RB_COLOR(tmp, field) == RB_RED) {           \
  473                                 RB_SET_BLACKRED(tmp, parent, field);    \
  474                                 RB_ROTATE_RIGHT(head, parent, tmp, field);\
  475                                 tmp = RB_LEFT(parent, field);           \
  476                         }                                               \
  477                         if ((RB_LEFT(tmp, field) == NULL ||             \
  478                             RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
  479                             (RB_RIGHT(tmp, field) == NULL ||            \
  480                             RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
  481                                 RB_COLOR(tmp, field) = RB_RED;          \
  482                                 elm = parent;                           \
  483                                 parent = RB_PARENT(elm, field);         \
  484                         } else {                                        \
  485                                 if (RB_LEFT(tmp, field) == NULL ||      \
  486                                     RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) {\
  487                                         struct type *oright;            \
  488                                         if ((oright = RB_RIGHT(tmp, field)))\
  489                                                 RB_COLOR(oright, field) = RB_BLACK;\
  490                                         RB_COLOR(tmp, field) = RB_RED;  \
  491                                         RB_ROTATE_LEFT(head, tmp, oright, field);\
  492                                         tmp = RB_LEFT(parent, field);   \
  493                                 }                                       \
  494                                 RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
  495                                 RB_COLOR(parent, field) = RB_BLACK;     \
  496                                 if (RB_LEFT(tmp, field))                \
  497                                         RB_COLOR(RB_LEFT(tmp, field), field) = RB_BLACK;\
  498                                 RB_ROTATE_RIGHT(head, parent, tmp, field);\
  499                                 elm = RB_ROOT(head);                    \
  500                                 break;                                  \
  501                         }                                               \
  502                 }                                                       \
  503         }                                                               \
  504         if (elm)                                                        \
  505                 RB_COLOR(elm, field) = RB_BLACK;                        \
  506 }                                                                       \
  507                                                                         \
  508 struct type *                                                           \
  509 name##_RB_REMOVE(struct name *head, struct type *elm)                   \
  510 {                                                                       \
  511         struct type *child, *parent, *old = elm;                        \
  512         int color;                                                      \
  513         if (RB_LEFT(elm, field) == NULL)                                \
  514                 child = RB_RIGHT(elm, field);                           \
  515         else if (RB_RIGHT(elm, field) == NULL)                          \
  516                 child = RB_LEFT(elm, field);                            \
  517         else {                                                          \
  518                 struct type *left;                                      \
  519                 elm = RB_RIGHT(elm, field);                             \
  520                 while ((left = RB_LEFT(elm, field)))                    \
  521                         elm = left;                                     \
  522                 child = RB_RIGHT(elm, field);                           \
  523                 parent = RB_PARENT(elm, field);                         \
  524                 color = RB_COLOR(elm, field);                           \
  525                 if (child)                                              \
  526                         RB_PARENT(child, field) = parent;               \
  527                 if (parent) {                                           \
  528                         if (RB_LEFT(parent, field) == elm)              \
  529                                 RB_LEFT(parent, field) = child;         \
  530                         else                                            \
  531                                 RB_RIGHT(parent, field) = child;        \
  532                         RB_AUGMENT(parent);                             \
  533                 } else                                                  \
  534                         RB_ROOT(head) = child;                          \
  535                 if (RB_PARENT(elm, field) == old)                       \
  536                         parent = elm;                                   \
  537                 (elm)->field = (old)->field;                            \
  538                 if (RB_PARENT(old, field)) {                            \
  539                         if (RB_LEFT(RB_PARENT(old, field), field) == old)\
  540                                 RB_LEFT(RB_PARENT(old, field), field) = elm;\
  541                         else                                            \
  542                                 RB_RIGHT(RB_PARENT(old, field), field) = elm;\
  543                         RB_AUGMENT(RB_PARENT(old, field));              \
  544                 } else                                                  \
  545                         RB_ROOT(head) = elm;                            \
  546                 RB_PARENT(RB_LEFT(old, field), field) = elm;            \
  547                 if (RB_RIGHT(old, field))                               \
  548                         RB_PARENT(RB_RIGHT(old, field), field) = elm;   \
  549                 if (parent) {                                           \
  550                         left = parent;                                  \
  551                         do {                                            \
  552                                 RB_AUGMENT(left);                       \
  553                         } while ((left = RB_PARENT(left, field)));      \
  554                 }                                                       \
  555                 goto color;                                             \
  556         }                                                               \
  557         parent = RB_PARENT(elm, field);                                 \
  558         color = RB_COLOR(elm, field);                                   \
  559         if (child)                                                      \
  560                 RB_PARENT(child, field) = parent;                       \
  561         if (parent) {                                                   \
  562                 if (RB_LEFT(parent, field) == elm)                      \
  563                         RB_LEFT(parent, field) = child;                 \
  564                 else                                                    \
  565                         RB_RIGHT(parent, field) = child;                \
  566                 RB_AUGMENT(parent);                                     \
  567         } else                                                          \
  568                 RB_ROOT(head) = child;                                  \
  569 color:                                                                  \
  570         if (color == RB_BLACK)                                          \
  571                 name##_RB_REMOVE_COLOR(head, parent, child);            \
  572         return (old);                                                   \
  573 }                                                                       \
  574                                                                         \
  575 /* Inserts a node into the RB tree */                                   \
  576 struct type *                                                           \
  577 name##_RB_INSERT(struct name *head, struct type *elm)                   \
  578 {                                                                       \
  579         struct type *tmp;                                               \
  580         struct type *parent = NULL;                                     \
  581         int comp = 0;                                                   \
  582         tmp = RB_ROOT(head);                                            \
  583         while (tmp) {                                                   \
  584                 parent = tmp;                                           \
  585                 comp = (cmp)(elm, parent);                              \
  586                 if (comp < 0)                                           \
  587                         tmp = RB_LEFT(tmp, field);                      \
  588                 else if (comp > 0)                                      \
  589                         tmp = RB_RIGHT(tmp, field);                     \
  590                 else                                                    \
  591                         return (tmp);                                   \
  592         }                                                               \
  593         RB_SET(elm, parent, field);                                     \
  594         if (parent != NULL) {                                           \
  595                 if (comp < 0)                                           \
  596                         RB_LEFT(parent, field) = elm;                   \
  597                 else                                                    \
  598                         RB_RIGHT(parent, field) = elm;                  \
  599                 RB_AUGMENT(parent);                                     \
  600         } else                                                          \
  601                 RB_ROOT(head) = elm;                                    \
  602         name##_RB_INSERT_COLOR(head, elm);                              \
  603         return (NULL);                                                  \
  604 }                                                                       \
  605                                                                         \
  606 /* Finds the node with the same key as elm */                           \
  607 struct type *                                                           \
  608 name##_RB_FIND(struct name *head, struct type *elm)                     \
  609 {                                                                       \
  610         struct type *tmp = RB_ROOT(head);                               \
  611         int comp;                                                       \
  612         while (tmp) {                                                   \
  613                 comp = cmp(elm, tmp);                                   \
  614                 if (comp < 0)                                           \
  615                         tmp = RB_LEFT(tmp, field);                      \
  616                 else if (comp > 0)                                      \
  617                         tmp = RB_RIGHT(tmp, field);                     \
  618                 else                                                    \
  619                         return (tmp);                                   \
  620         }                                                               \
  621         return (NULL);                                                  \
  622 }                                                                       \
  623                                                                         \
  624 struct type *                                                           \
  625 name##_RB_NEXT(struct name *head, struct type *elm)                     \
  626 {                                                                       \
  627         if (RB_RIGHT(elm, field)) {                                     \
  628                 elm = RB_RIGHT(elm, field);                             \
  629                 while (RB_LEFT(elm, field))                             \
  630                         elm = RB_LEFT(elm, field);                      \
  631         } else {                                                        \
  632                 if (RB_PARENT(elm, field) &&                            \
  633                     (elm == RB_LEFT(RB_PARENT(elm, field), field)))     \
  634                         elm = RB_PARENT(elm, field);                    \
  635                 else {                                                  \
  636                         while (RB_PARENT(elm, field) &&                 \
  637                             (elm == RB_RIGHT(RB_PARENT(elm, field), field)))\
  638                                 elm = RB_PARENT(elm, field);            \
  639                         elm = RB_PARENT(elm, field);                    \
  640                 }                                                       \
  641         }                                                               \
  642         return (elm);                                                   \
  643 }                                                                       \
  644                                                                         \
  645 struct type *                                                           \
  646 name##_RB_MINMAX(struct name *head, int val)                            \
  647 {                                                                       \
  648         struct type *tmp = RB_ROOT(head);                               \
  649         struct type *parent = NULL;                                     \
  650         while (tmp) {                                                   \
  651                 parent = tmp;                                           \
  652                 if (val < 0)                                            \
  653                         tmp = RB_LEFT(tmp, field);                      \
  654                 else                                                    \
  655                         tmp = RB_RIGHT(tmp, field);                     \
  656         }                                                               \
  657         return (parent);                                                \
  658 }
  659 
  660 #define RB_NEGINF       -1
  661 #define RB_INF  1
  662 
  663 #define RB_INSERT(name, x, y)   name##_RB_INSERT(x, y)
  664 #define RB_REMOVE(name, x, y)   name##_RB_REMOVE(x, y)
  665 #define RB_FIND(name, x, y)     name##_RB_FIND(x, y)
  666 #define RB_NEXT(name, x, y)     name##_RB_NEXT(x, y)
  667 #define RB_MIN(name, x)         name##_RB_MINMAX(x, RB_NEGINF)
  668 #define RB_MAX(name, x)         name##_RB_MINMAX(x, RB_INF)
  669 
  670 #define RB_FOREACH(x, name, head)                                       \
  671         for ((x) = RB_MIN(name, head);                                  \
  672              (x) != NULL;                                               \
  673              (x) = name##_RB_NEXT(head, x))
  674 
  675 #endif  /* _SYS_TREE_H_ */

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