sys/sys/tree.h

   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 /*      $DragonFly: src/sys/sys/tree.h,v 1.1 2004/08/19 20:38:33 joerg Exp $ */
   4 /*
   5  * Copyright 2002 Niels Provos <provos@citi.umich.edu>
   6  * All rights reserved.
   7  *
   8  * Redistribution and use in source and binary forms, with or without
   9  * modification, are permitted provided that the following conditions
  10  * are met:
  11  * 1. Redistributions of source code must retain the above copyright
  12  *    notice, this list of conditions and the following disclaimer.
  13  * 2. Redistributions in binary form must reproduce the above copyright
  14  *    notice, this list of conditions and the following disclaimer in the
  15  *    documentation and/or other materials provided with the distribution.
  16  *
  17  * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
  18  * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
  19  * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
  20  * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
  21  * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
  22  * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
  23  * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
  24  * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
  25  * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
  26  * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
  27  */
  28
  29 #ifndef _SYS_TREE_H_
  30 #define _SYS_TREE_H_
  31
  32 /*
  33  * This file defines data structures for different types of trees:
  34  * splay trees and red-black trees.
  35  *
  36  * A splay tree is a self-organizing data structure.  Every operation
  37  * on the tree causes a splay to happen.  The splay moves the requested
  38  * node to the root of the tree and partly rebalances it.
  39  *
  40  * This has the benefit that request locality causes faster lookups as
  41  * the requested nodes move to the top of the tree.  On the other hand,
  42  * every lookup causes memory writes.
  43  *
  44  * The Balance Theorem bounds the total access time for m operations
  45  * and n inserts on an initially empty tree as O((m + n)lg n).  The
  46  * amortized cost for a sequence of m accesses to a splay tree is O(lg n);
  47  *
  48  * A red-black tree is a binary search tree with the node color as an
  49  * extra attribute.  It fulfills a set of conditions:
  50  *      - every search path from the root to a leaf consists of the
  51  *        same number of black nodes,
  52  *      - each red node (except for the root) has a black parent,
  53  *      - each leaf node is black.
  54  *
  55  * Every operation on a red-black tree is bounded as O(lg n).
  56  * The maximum height of a red-black tree is 2lg (n+1).
  57  */
  58
  59 #define SPLAY_HEAD(name, type)                                          \
  60 struct name {                                                           \
  61         struct type *sph_root; /* root of the tree */                   \
  62 }
  63
  64 #define SPLAY_INITIALIZER(root)                                         \
  65         { NULL }
  66
  67 #define SPLAY_INIT(root) do {                                           \
  68         (root)->sph_root = NULL;                                        \
  69 } while (/*CONSTCOND*/ 0)
  70
  71 #define SPLAY_ENTRY(type)                                               \
  72 struct {                                                                \
  73         struct type *spe_left; /* left element */                       \
  74         struct type *spe_right; /* right element */                     \
  75 }
  76
  77 #define SPLAY_LEFT(elm, field)          (elm)->field.spe_left
  78 #define SPLAY_RIGHT(elm, field)         (elm)->field.spe_right
  79 #define SPLAY_ROOT(head)                (head)->sph_root
  80 #define SPLAY_EMPTY(head)               (SPLAY_ROOT(head) == NULL)
  81
  82 /* SPLAY_ROTATE_{LEFT,RIGHT} expect that tmp hold SPLAY_{RIGHT,LEFT} */
  83 #define SPLAY_ROTATE_RIGHT(head, tmp, field) do {                       \
  84         SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(tmp, field);  \
  85         SPLAY_RIGHT(tmp, field) = (head)->sph_root;                     \
  86         (head)->sph_root = tmp;                                         \
  87 } while (/*CONSTCOND*/ 0)
  88
  89 #define SPLAY_ROTATE_LEFT(head, tmp, field) do {                        \
  90         SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(tmp, field);  \
  91         SPLAY_LEFT(tmp, field) = (head)->sph_root;                      \
  92         (head)->sph_root = tmp;                                         \
  93 } while (/*CONSTCOND*/ 0)
  94
  95 #define SPLAY_LINKLEFT(head, tmp, field) do {                           \
  96         SPLAY_LEFT(tmp, field) = (head)->sph_root;                      \
  97         tmp = (head)->sph_root;                                         \
  98         (head)->sph_root = SPLAY_LEFT((head)->sph_root, field);         \
  99 } while (/*CONSTCOND*/ 0)
 100
 101 #define SPLAY_LINKRIGHT(head, tmp, field) do {                          \
 102         SPLAY_RIGHT(tmp, field) = (head)->sph_root;                     \
 103         tmp = (head)->sph_root;                                         \
 104         (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);        \
 105 } while (/*CONSTCOND*/ 0)
 106
 107 #define SPLAY_ASSEMBLE(head, node, left, right, field) do {             \
 108         SPLAY_RIGHT(left, field) = SPLAY_LEFT((head)->sph_root, field); \
 109         SPLAY_LEFT(right, field) = SPLAY_RIGHT((head)->sph_root, field);\
 110         SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(node, field); \
 111         SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(node, field); \
 112 } while (/*CONSTCOND*/ 0)
 113
 114 /* Generates prototypes and inline functions */
 115
 116 #define SPLAY_PROTOTYPE(name, type, field, cmp)                         \
 117 void name##_SPLAY(struct name *, struct type *);                        \
 118 void name##_SPLAY_MINMAX(struct name *, int);                           \
 119 struct type *name##_SPLAY_INSERT(struct name *, struct type *);         \
 120 struct type *name##_SPLAY_REMOVE(struct name *, struct type *);         \
 121                                                                         \
 122 /* Finds the node with the same key as elm */                           \
 123 static __inline struct type *                                           \
 124 name##_SPLAY_FIND(struct name *head, struct type *elm)                  \
 125 {                                                                       \
 126         if (SPLAY_EMPTY(head))                                          \
 127                 return(NULL);                                           \
 128         name##_SPLAY(head, elm);                                        \
 129         if ((cmp)(elm, (head)->sph_root) == 0)                          \
 130                 return (head->sph_root);                                \
 131         return (NULL);                                                  \
 132 }                                                                       \
 133                                                                         \
 134 static __inline struct type *                                           \
 135 name##_SPLAY_NEXT(struct name *head, struct type *elm)                  \
 136 {                                                                       \
 137         name##_SPLAY(head, elm);                                        \
 138         if (SPLAY_RIGHT(elm, field) != NULL) {                          \
 139                 elm = SPLAY_RIGHT(elm, field);                          \
 140                 while (SPLAY_LEFT(elm, field) != NULL) {                \
 141                         elm = SPLAY_LEFT(elm, field);                   \
 142                 }                                                       \
 143         } else                                                          \
 144                 elm = NULL;                                             \
 145         return (elm);                                                   \
 146 }                                                                       \
 147                                                                         \
 148 static __inline struct type *                                           \
 149 name##_SPLAY_MIN_MAX(struct name *head, int val)                        \
 150 {                                                                       \
 151         name##_SPLAY_MINMAX(head, val);                                 \
 152         return (SPLAY_ROOT(head));                                      \
 153 }
 154
 155 /* Main splay operation.
 156  * Moves node close to the key of elm to top
 157  */
 158 #define SPLAY_GENERATE(name, type, field, cmp)                          \
 159 struct type *                                                           \
 160 name##_SPLAY_INSERT(struct name *head, struct type *elm)                \
 161 {                                                                       \
 162     if (SPLAY_EMPTY(head)) {                                            \
 163             SPLAY_LEFT(elm, field) = SPLAY_RIGHT(elm, field) = NULL;    \
 164     } else {                                                            \
 165             int __comp;                                                 \
 166             name##_SPLAY(head, elm);                                    \
 167             __comp = (cmp)(elm, (head)->sph_root);                      \
 168             if(__comp < 0) {                                            \
 169                     SPLAY_LEFT(elm, field) = SPLAY_LEFT((head)->sph_root, field);\
 170                     SPLAY_RIGHT(elm, field) = (head)->sph_root;         \
 171                     SPLAY_LEFT((head)->sph_root, field) = NULL;         \
 172             } else if (__comp > 0) {                                    \
 173                     SPLAY_RIGHT(elm, field) = SPLAY_RIGHT((head)->sph_root, field);\
 174                     SPLAY_LEFT(elm, field) = (head)->sph_root;          \
 175                     SPLAY_RIGHT((head)->sph_root, field) = NULL;        \
 176             } else                                                      \
 177                     return ((head)->sph_root);                          \
 178     }                                                                   \
 179     (head)->sph_root = (elm);                                           \
 180     return (NULL);                                                      \
 181 }                                                                       \
 182                                                                         \
 183 struct type *                                                           \
 184 name##_SPLAY_REMOVE(struct name *head, struct type *elm)                \
 185 {                                                                       \
 186         struct type *__tmp;                                             \
 187         if (SPLAY_EMPTY(head))                                          \
 188                 return (NULL);                                          \
 189         name##_SPLAY(head, elm);                                        \
 190         if ((cmp)(elm, (head)->sph_root) == 0) {                        \
 191                 if (SPLAY_LEFT((head)->sph_root, field) == NULL) {      \
 192                         (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);\
 193                 } else {                                                \
 194                         __tmp = SPLAY_RIGHT((head)->sph_root, field);   \
 195                         (head)->sph_root = SPLAY_LEFT((head)->sph_root, field);\
 196                         name##_SPLAY(head, elm);                        \
 197                         SPLAY_RIGHT((head)->sph_root, field) = __tmp;   \
 198                 }                                                       \
 199                 return (elm);                                           \
 200         }                                                               \
 201         return (NULL);                                                  \
 202 }                                                                       \
 203                                                                         \
 204 void                                                                    \
 205 name##_SPLAY(struct name *head, struct type *elm)                       \
 206 {                                                                       \
 207         struct type __node, *__left, *__right, *__tmp;                  \
 208         int __comp;                                                     \
 209 \
 210         SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
 211         __left = __right = &__node;                                     \
 212 \
 213         while ((__comp = (cmp)(elm, (head)->sph_root)) != 0) {          \
 214                 if (__comp < 0) {                                       \
 215                         __tmp = SPLAY_LEFT((head)->sph_root, field);    \
 216                         if (__tmp == NULL)                              \
 217                                 break;                                  \
 218                         if ((cmp)(elm, __tmp) < 0){                     \
 219                                 SPLAY_ROTATE_RIGHT(head, __tmp, field); \
 220                                 if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
 221                                         break;                          \
 222                         }                                               \
 223                         SPLAY_LINKLEFT(head, __right, field);           \
 224                 } else if (__comp > 0) {                                \
 225                         __tmp = SPLAY_RIGHT((head)->sph_root, field);   \
 226                         if (__tmp == NULL)                              \
 227                                 break;                                  \
 228                         if ((cmp)(elm, __tmp) > 0){                     \
 229                                 SPLAY_ROTATE_LEFT(head, __tmp, field);  \
 230                                 if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
 231                                         break;                          \
 232                         }                                               \
 233                         SPLAY_LINKRIGHT(head, __left, field);           \
 234                 }                                                       \
 235         }                                                               \
 236         SPLAY_ASSEMBLE(head, &__node, __left, __right, field);          \
 237 }                                                                       \
 238                                                                         \
 239 /* Splay with either the minimum or the maximum element                 \
 240  * Used to find minimum or maximum element in tree.                     \
 241  */                                                                     \
 242 void name##_SPLAY_MINMAX(struct name *head, int __comp) \
 243 {                                                                       \
 244         struct type __node, *__left, *__right, *__tmp;                  \
 245 \
 246         SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
 247         __left = __right = &__node;                                     \
 248 \
 249         while (1) {                                                     \
 250                 if (__comp < 0) {                                       \
 251                         __tmp = SPLAY_LEFT((head)->sph_root, field);    \
 252                         if (__tmp == NULL)                              \
 253                                 break;                                  \
 254                         if (__comp < 0){                                \
 255                                 SPLAY_ROTATE_RIGHT(head, __tmp, field); \
 256                                 if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
 257                                         break;                          \
 258                         }                                               \
 259                         SPLAY_LINKLEFT(head, __right, field);           \
 260                 } else if (__comp > 0) {                                \
 261                         __tmp = SPLAY_RIGHT((head)->sph_root, field);   \
 262                         if (__tmp == NULL)                              \
 263                                 break;                                  \
 264                         if (__comp > 0) {                               \
 265                                 SPLAY_ROTATE_LEFT(head, __tmp, field);  \
 266                                 if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
 267                                         break;                          \
 268                         }                                               \
 269                         SPLAY_LINKRIGHT(head, __left, field);           \
 270                 }                                                       \
 271         }                                                               \
 272         SPLAY_ASSEMBLE(head, &__node, __left, __right, field);          \
 273 }
 274
 275 #define SPLAY_NEGINF    -1
 276 #define SPLAY_INF       1
 277
 278 #define SPLAY_INSERT(name, x, y)        name##_SPLAY_INSERT(x, y)
 279 #define SPLAY_REMOVE(name, x, y)        name##_SPLAY_REMOVE(x, y)
 280 #define SPLAY_FIND(name, x, y)          name##_SPLAY_FIND(x, y)
 281 #define SPLAY_NEXT(name, x, y)          name##_SPLAY_NEXT(x, y)
 282 #define SPLAY_MIN(name, x)              (SPLAY_EMPTY(x) ? NULL  \
 283                                         : name##_SPLAY_MIN_MAX(x, SPLAY_NEGINF))
 284 #define SPLAY_MAX(name, x)              (SPLAY_EMPTY(x) ? NULL  \
 285                                         : name##_SPLAY_MIN_MAX(x, SPLAY_INF))
 286
 287 #define SPLAY_FOREACH(x, name, head)                                    \
 288         for ((x) = SPLAY_MIN(name, head);                               \
 289              (x) != NULL;                                               \
 290              (x) = SPLAY_NEXT(name, head, x))
 291
 292 /* Macros that define a red-black tree */
 293 #define RB_HEAD(name, type)                                             \
 294 struct name {                                                           \
 295         struct type *rbh_root; /* root of the tree */                   \
 296 }
 297
 298 #define RB_INITIALIZER(root)                                            \
 299         { NULL }
 300
 301 #define RB_INIT(root) do {                                              \
 302         (root)->rbh_root = NULL;                                        \
 303 } while (/*CONSTCOND*/ 0)
 304
 305 #define RB_BLACK        0
 306 #define RB_RED          1
 307 #define RB_ENTRY(type)                                                  \
 308 struct {                                                                \
 309         struct type *rbe_left;          /* left element */              \
 310         struct type *rbe_right;         /* right element */             \
 311         struct type *rbe_parent;        /* parent element */            \
 312         int rbe_color;                  /* node color */                \
 313 }
 314
 315 #define RB_LEFT(elm, field)             (elm)->field.rbe_left
 316 #define RB_RIGHT(elm, field)            (elm)->field.rbe_right
 317 #define RB_PARENT(elm, field)           (elm)->field.rbe_parent
 318 #define RB_COLOR(elm, field)            (elm)->field.rbe_color
 319 #define RB_ROOT(head)                   (head)->rbh_root
 320 #define RB_EMPTY(head)                  (RB_ROOT(head) == NULL)
 321
 322 #define RB_SET(elm, parent, field) do {                                 \
 323         RB_PARENT(elm, field) = parent;                                 \
 324         RB_LEFT(elm, field) = RB_RIGHT(elm, field) = NULL;              \
 325         RB_COLOR(elm, field) = RB_RED;                                  \
 326 } while (/*CONSTCOND*/ 0)
 327
 328 #define RB_SET_BLACKRED(black, red, field) do {                         \
 329         RB_COLOR(black, field) = RB_BLACK;                              \
 330         RB_COLOR(red, field) = RB_RED;                                  \
 331 } while (/*CONSTCOND*/ 0)
 332
 333 #ifndef RB_AUGMENT
 334 #define RB_AUGMENT(x)
 335 #endif
 336
 337 #define RB_ROTATE_LEFT(head, elm, tmp, field) do {                      \
 338         (tmp) = RB_RIGHT(elm, field);                                   \
 339         if ((RB_RIGHT(elm, field) = RB_LEFT(tmp, field)) != NULL) {     \
 340                 RB_PARENT(RB_LEFT(tmp, field), field) = (elm);          \
 341         }                                                               \
 342         RB_AUGMENT(elm);                                                \
 343         if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) {  \
 344                 if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))     \
 345                         RB_LEFT(RB_PARENT(elm, field), field) = (tmp);  \
 346                 else                                                    \
 347                         RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \
 348         } else                                                          \
 349                 (head)->rbh_root = (tmp);                               \
 350         RB_LEFT(tmp, field) = (elm);                                    \
 351         RB_PARENT(elm, field) = (tmp);                                  \
 352         RB_AUGMENT(tmp);                                                \
 353         if ((RB_PARENT(tmp, field)))                                    \
 354                 RB_AUGMENT(RB_PARENT(tmp, field));                      \
 355 } while (/*CONSTCOND*/ 0)
 356
 357 #define RB_ROTATE_RIGHT(head, elm, tmp, field) do {                     \
 358         (tmp) = RB_LEFT(elm, field);                                    \
 359         if ((RB_LEFT(elm, field) = RB_RIGHT(tmp, field)) != NULL) {     \
 360                 RB_PARENT(RB_RIGHT(tmp, field), field) = (elm);         \
 361         }                                                               \
 362         RB_AUGMENT(elm);                                                \
 363         if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) {  \
 364                 if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))     \
 365                         RB_LEFT(RB_PARENT(elm, field), field) = (tmp);  \
 366                 else                                                    \
 367                         RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \
 368         } else                                                          \
 369                 (head)->rbh_root = (tmp);                               \
 370         RB_RIGHT(tmp, field) = (elm);                                   \
 371         RB_PARENT(elm, field) = (tmp);                                  \
 372         RB_AUGMENT(tmp);                                                \
 373         if ((RB_PARENT(tmp, field)))                                    \
 374                 RB_AUGMENT(RB_PARENT(tmp, field));                      \
 375 } while (/*CONSTCOND*/ 0)
 376
 377 /* Generates prototypes and inline functions */
 378 #define RB_PROTOTYPE(name, type, field, cmp)                            \
 379 void name##_RB_INSERT_COLOR(struct name *, struct type *);      \
 380 void name##_RB_REMOVE_COLOR(struct name *, struct type *, struct type *);\
 381 struct type *name##_RB_REMOVE(struct name *, struct type *);            \
 382 struct type *name##_RB_INSERT(struct name *, struct type *);            \
 383 struct type *name##_RB_FIND(struct name *, struct type *);              \
 384 struct type *name##_RB_NEXT(struct type *);                             \
 385 struct type *name##_RB_MINMAX(struct name *, int);                      \
 386                                                                         \
 387
 388 /* Main rb operation.
 389  * Moves node close to the key of elm to top
 390  */
 391 #define RB_GENERATE(name, type, field, cmp)                             \
 392 void                                                                    \
 393 name##_RB_INSERT_COLOR(struct name *head, struct type *elm)             \
 394 {                                                                       \
 395         struct type *parent, *gparent, *tmp;                            \
 396         while ((parent = RB_PARENT(elm, field)) != NULL &&              \
 397             RB_COLOR(parent, field) == RB_RED) {                        \
 398                 gparent = RB_PARENT(parent, field);                     \
 399                 if (parent == RB_LEFT(gparent, field)) {                \
 400                         tmp = RB_RIGHT(gparent, field);                 \
 401                         if (tmp && RB_COLOR(tmp, field) == RB_RED) {    \
 402                                 RB_COLOR(tmp, field) = RB_BLACK;        \
 403                                 RB_SET_BLACKRED(parent, gparent, field);\
 404                                 elm = gparent;                          \
 405                                 continue;                               \
 406                         }                                               \
 407                         if (RB_RIGHT(parent, field) == elm) {           \
 408                                 RB_ROTATE_LEFT(head, parent, tmp, field);\
 409                                 tmp = parent;                           \
 410                                 parent = elm;                           \
 411                                 elm = tmp;                              \
 412                         }                                               \
 413                         RB_SET_BLACKRED(parent, gparent, field);        \
 414                         RB_ROTATE_RIGHT(head, gparent, tmp, field);     \
 415                 } else {                                                \
 416                         tmp = RB_LEFT(gparent, field);                  \
 417                         if (tmp && RB_COLOR(tmp, field) == RB_RED) {    \
 418                                 RB_COLOR(tmp, field) = RB_BLACK;        \
 419                                 RB_SET_BLACKRED(parent, gparent, field);\
 420                                 elm = gparent;                          \
 421                                 continue;                               \
 422                         }                                               \
 423                         if (RB_LEFT(parent, field) == elm) {            \
 424                                 RB_ROTATE_RIGHT(head, parent, tmp, field);\
 425                                 tmp = parent;                           \
 426                                 parent = elm;                           \
 427                                 elm = tmp;                              \
 428                         }                                               \
 429                         RB_SET_BLACKRED(parent, gparent, field);        \
 430                         RB_ROTATE_LEFT(head, gparent, tmp, field);      \
 431                 }                                                       \
 432         }                                                               \
 433         RB_COLOR(head->rbh_root, field) = RB_BLACK;                     \
 434 }                                                                       \
 435                                                                         \
 436 void                                                                    \
 437 name##_RB_REMOVE_COLOR(struct name *head, struct type *parent, struct type *elm) \
 438 {                                                                       \
 439         struct type *tmp;                                               \
 440         while ((elm == NULL || RB_COLOR(elm, field) == RB_BLACK) &&     \
 441             elm != RB_ROOT(head)) {                                     \
 442                 if (RB_LEFT(parent, field) == elm) {                    \
 443                         tmp = RB_RIGHT(parent, field);                  \
 444                         if (RB_COLOR(tmp, field) == RB_RED) {           \
 445                                 RB_SET_BLACKRED(tmp, parent, field);    \
 446                                 RB_ROTATE_LEFT(head, parent, tmp, field);\
 447                                 tmp = RB_RIGHT(parent, field);          \
 448                         }                                               \
 449                         if ((RB_LEFT(tmp, field) == NULL ||             \
 450                             RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
 451                             (RB_RIGHT(tmp, field) == NULL ||            \
 452                             RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
 453                                 RB_COLOR(tmp, field) = RB_RED;          \
 454                                 elm = parent;                           \
 455                                 parent = RB_PARENT(elm, field);         \
 456                         } else {                                        \
 457                                 if (RB_RIGHT(tmp, field) == NULL ||     \
 458                                     RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK) {\
 459                                         struct type *oleft;             \
 460                                         if ((oleft = RB_LEFT(tmp, field)) \
 461                                             != NULL)                    \
 462                                                 RB_COLOR(oleft, field) = RB_BLACK;\
 463                                         RB_COLOR(tmp, field) = RB_RED;  \
 464                                         RB_ROTATE_RIGHT(head, tmp, oleft, field);\
 465                                         tmp = RB_RIGHT(parent, field);  \
 466                                 }                                       \
 467                                 RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
 468                                 RB_COLOR(parent, field) = RB_BLACK;     \
 469                                 if (RB_RIGHT(tmp, field))               \
 470                                         RB_COLOR(RB_RIGHT(tmp, field), field) = RB_BLACK;\
 471                                 RB_ROTATE_LEFT(head, parent, tmp, field);\
 472                                 elm = RB_ROOT(head);                    \
 473                                 break;                                  \
 474                         }                                               \
 475                 } else {                                                \
 476                         tmp = RB_LEFT(parent, field);                   \
 477                         if (RB_COLOR(tmp, field) == RB_RED) {           \
 478                                 RB_SET_BLACKRED(tmp, parent, field);    \
 479                                 RB_ROTATE_RIGHT(head, parent, tmp, field);\
 480                                 tmp = RB_LEFT(parent, field);           \
 481                         }                                               \
 482                         if ((RB_LEFT(tmp, field) == NULL ||             \
 483                             RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
 484                             (RB_RIGHT(tmp, field) == NULL ||            \
 485                             RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
 486                                 RB_COLOR(tmp, field) = RB_RED;          \
 487                                 elm = parent;                           \
 488                                 parent = RB_PARENT(elm, field);         \
 489                         } else {                                        \
 490                                 if (RB_LEFT(tmp, field) == NULL ||      \
 491                                     RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) {\
 492                                         struct type *oright;            \
 493                                         if ((oright = RB_RIGHT(tmp, field)) \
 494                                             != NULL)                    \
 495                                                 RB_COLOR(oright, field) = RB_BLACK;\
 496                                         RB_COLOR(tmp, field) = RB_RED;  \
 497                                         RB_ROTATE_LEFT(head, tmp, oright, field);\
 498                                         tmp = RB_LEFT(parent, field);   \
 499                                 }                                       \
 500                                 RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
 501                                 RB_COLOR(parent, field) = RB_BLACK;     \
 502                                 if (RB_LEFT(tmp, field))                \
 503                                         RB_COLOR(RB_LEFT(tmp, field), field) = RB_BLACK;\
 504                                 RB_ROTATE_RIGHT(head, parent, tmp, field);\
 505                                 elm = RB_ROOT(head);                    \
 506                                 break;                                  \
 507                         }                                               \
 508                 }                                                       \
 509         }                                                               \
 510         if (elm)                                                        \
 511                 RB_COLOR(elm, field) = RB_BLACK;                        \
 512 }                                                                       \
 513                                                                         \
 514 struct type *                                                           \
 515 name##_RB_REMOVE(struct name *head, struct type *elm)                   \
 516 {                                                                       \
 517         struct type *child, *parent, *old = elm;                        \
 518         int color;                                                      \
 519         if (RB_LEFT(elm, field) == NULL)                                \
 520                 child = RB_RIGHT(elm, field);                           \
 521         else if (RB_RIGHT(elm, field) == NULL)                          \
 522                 child = RB_LEFT(elm, field);                            \
 523         else {                                                          \
 524                 struct type *left;                                      \
 525                 elm = RB_RIGHT(elm, field);                             \
 526                 while ((left = RB_LEFT(elm, field)) != NULL)            \
 527                         elm = left;                                     \
 528                 child = RB_RIGHT(elm, field);                           \
 529                 parent = RB_PARENT(elm, field);                         \
 530                 color = RB_COLOR(elm, field);                           \
 531                 if (child)                                              \
 532                         RB_PARENT(child, field) = parent;               \
 533                 if (parent) {                                           \
 534                         if (RB_LEFT(parent, field) == elm)              \
 535                                 RB_LEFT(parent, field) = child;         \
 536                         else                                            \
 537                                 RB_RIGHT(parent, field) = child;        \
 538                         RB_AUGMENT(parent);                             \
 539                 } else                                                  \
 540                         RB_ROOT(head) = child;                          \
 541                 if (RB_PARENT(elm, field) == old)                       \
 542                         parent = elm;                                   \
 543                 (elm)->field = (old)->field;                            \
 544                 if (RB_PARENT(old, field)) {                            \
 545                         if (RB_LEFT(RB_PARENT(old, field), field) == old)\
 546                                 RB_LEFT(RB_PARENT(old, field), field) = elm;\
 547                         else                                            \
 548                                 RB_RIGHT(RB_PARENT(old, field), field) = elm;\
 549                         RB_AUGMENT(RB_PARENT(old, field));              \
 550                 } else                                                  \
 551                         RB_ROOT(head) = elm;                            \
 552                 RB_PARENT(RB_LEFT(old, field), field) = elm;            \
 553                 if (RB_RIGHT(old, field))                               \
 554                         RB_PARENT(RB_RIGHT(old, field), field) = elm;   \
 555                 if (parent) {                                           \
 556                         left = parent;                                  \
 557                         do {                                            \
 558                                 RB_AUGMENT(left);                       \
 559                         } while ((left = RB_PARENT(left, field)) != NULL); \
 560                 }                                                       \
 561                 goto color;                                             \
 562         }                                                               \
 563         parent = RB_PARENT(elm, field);                                 \
 564         color = RB_COLOR(elm, field);                                   \
 565         if (child)                                                      \
 566                 RB_PARENT(child, field) = parent;                       \
 567         if (parent) {                                                   \
 568                 if (RB_LEFT(parent, field) == elm)                      \
 569                         RB_LEFT(parent, field) = child;                 \
 570                 else                                                    \
 571                         RB_RIGHT(parent, field) = child;                \
 572                 RB_AUGMENT(parent);                                     \
 573         } else                                                          \
 574                 RB_ROOT(head) = child;                                  \
 575 color:                                                                  \
 576         if (color == RB_BLACK)                                          \
 577                 name##_RB_REMOVE_COLOR(head, parent, child);            \
 578         return (old);                                                   \
 579 }                                                                       \
 580                                                                         \
 581 /* Inserts a node into the RB tree */                                   \
 582 struct type *                                                           \
 583 name##_RB_INSERT(struct name *head, struct type *elm)                   \
 584 {                                                                       \
 585         struct type *tmp;                                               \
 586         struct type *parent = NULL;                                     \
 587         int comp = 0;                                                   \
 588         tmp = RB_ROOT(head);                                            \
 589         while (tmp) {                                                   \
 590                 parent = tmp;                                           \
 591                 comp = (cmp)(elm, parent);                              \
 592                 if (comp < 0)                                           \
 593                         tmp = RB_LEFT(tmp, field);                      \
 594                 else if (comp > 0)                                      \
 595                         tmp = RB_RIGHT(tmp, field);                     \
 596                 else                                                    \
 597                         return (tmp);                                   \
 598         }                                                               \
 599         RB_SET(elm, parent, field);                                     \
 600         if (parent != NULL) {                                           \
 601                 if (comp < 0)                                           \
 602                         RB_LEFT(parent, field) = elm;                   \
 603                 else                                                    \
 604                         RB_RIGHT(parent, field) = elm;                  \
 605                 RB_AUGMENT(parent);                                     \
 606         } else                                                          \
 607                 RB_ROOT(head) = elm;                                    \
 608         name##_RB_INSERT_COLOR(head, elm);                              \
 609         return (NULL);                                                  \
 610 }                                                                       \
 611                                                                         \
 612 /* Finds the node with the same key as elm */                           \
 613 struct type *                                                           \
 614 name##_RB_FIND(struct name *head, struct type *elm)                     \
 615 {                                                                       \
 616         struct type *tmp = RB_ROOT(head);                               \
 617         int comp;                                                       \
 618         while (tmp) {                                                   \
 619                 comp = cmp(elm, tmp);                                   \
 620                 if (comp < 0)                                           \
 621                         tmp = RB_LEFT(tmp, field);                      \
 622                 else if (comp > 0)                                      \
 623                         tmp = RB_RIGHT(tmp, field);                     \
 624                 else                                                    \
 625                         return (tmp);                                   \
 626         }                                                               \
 627         return (NULL);                                                  \
 628 }                                                                       \
 629                                                                         \
 630 /* ARGSUSED */                                                          \
 631 struct type *                                                           \
 632 name##_RB_NEXT(struct type *elm)                                        \
 633 {                                                                       \
 634         if (RB_RIGHT(elm, field)) {                                     \
 635                 elm = RB_RIGHT(elm, field);                             \
 636                 while (RB_LEFT(elm, field))                             \
 637                         elm = RB_LEFT(elm, field);                      \
 638         } else {                                                        \
 639                 if (RB_PARENT(elm, field) &&                            \
 640                     (elm == RB_LEFT(RB_PARENT(elm, field), field)))     \
 641                         elm = RB_PARENT(elm, field);                    \
 642                 else {                                                  \
 643                         while (RB_PARENT(elm, field) &&                 \
 644                             (elm == RB_RIGHT(RB_PARENT(elm, field), field)))\
 645                                 elm = RB_PARENT(elm, field);            \
 646                         elm = RB_PARENT(elm, field);                    \
 647                 }                                                       \
 648         }                                                               \
 649         return (elm);                                                   \
 650 }                                                                       \
 651                                                                         \
 652 struct type *                                                           \
 653 name##_RB_MINMAX(struct name *head, int val)                            \
 654 {                                                                       \
 655         struct type *tmp = RB_ROOT(head);                               \
 656         struct type *parent = NULL;                                     \
 657         while (tmp) {                                                   \
 658                 parent = tmp;                                           \
 659                 if (val < 0)                                            \
 660                         tmp = RB_LEFT(tmp, field);                      \
 661                 else                                                    \
 662                         tmp = RB_RIGHT(tmp, field);                     \
 663         }                                                               \
 664         return (parent);                                                \
 665 }
 666
 667 #define RB_NEGINF       -1
 668 #define RB_INF  1
 669
 670 #define RB_INSERT(name, x, y)   name##_RB_INSERT(x, y)
 671 #define RB_REMOVE(name, x, y)   name##_RB_REMOVE(x, y)
 672 #define RB_FIND(name, x, y)     name##_RB_FIND(x, y)
 673 #define RB_NEXT(name, x, y)     name##_RB_NEXT(y)
 674 #define RB_MIN(name, x)         name##_RB_MINMAX(x, RB_NEGINF)
 675 #define RB_MAX(name, x)         name##_RB_MINMAX(x, RB_INF)
 676
 677 #define RB_FOREACH(x, name, head)                                       \
 678         for ((x) = RB_MIN(name, head);                                  \
 679              (x) != NULL;                                               \
 680              (x) = name##_RB_NEXT(x))
 681
 682 #endif  /* _SYS_TREE_H_ */