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 /* $FreeBSD$ */
   4
   5 /*-
   6  * Copyright 2002 Niels Provos <provos@citi.umich.edu>
   7  * All rights reserved.
   8  *
   9  * Redistribution and use in source and binary forms, with or without
  10  * modification, are permitted provided that the following conditions
  11  * are met:
  12  * 1. Redistributions of source code must retain the above copyright
  13  *    notice, this list of conditions and the following disclaimer.
  14  * 2. Redistributions in binary form must reproduce the above copyright
  15  *    notice, this list of conditions and the following disclaimer in the
  16  *    documentation and/or other materials provided with the distribution.
  17  *
  18  * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
  19  * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
  20  * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
  21  * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
  22  * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
  23  * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
  24  * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
  25  * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
  26  * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
  27  * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
  28  */
  29
  30 #ifndef _SYS_TREE_H_
  31 #define _SYS_TREE_H_
  32
  33 #include <sys/cdefs.h>
  34
  35 /*
  36  * This file defines data structures for different types of trees:
  37  * splay trees and red-black trees.
  38  *
  39  * A splay tree is a self-organizing data structure.  Every operation
  40  * on the tree causes a splay to happen.  The splay moves the requested
  41  * node to the root of the tree and partly rebalances it.
  42  *
  43  * This has the benefit that request locality causes faster lookups as
  44  * the requested nodes move to the top of the tree.  On the other hand,
  45  * every lookup causes memory writes.
  46  *
  47  * The Balance Theorem bounds the total access time for m operations
  48  * and n inserts on an initially empty tree as O((m + n)lg n).  The
  49  * amortized cost for a sequence of m accesses to a splay tree is O(lg n);
  50  *
  51  * A red-black tree is a binary search tree with the node color as an
  52  * extra attribute.  It fulfills a set of conditions:
  53  *      - every search path from the root to a leaf consists of the
  54  *        same number of black nodes,
  55  *      - each red node (except for the root) has a black parent,
  56  *      - each leaf node is black.
  57  *
  58  * Every operation on a red-black tree is bounded as O(lg n).
  59  * The maximum height of a red-black tree is 2lg (n+1).
  60  */
  61
  62 #define SPLAY_HEAD(name, type)                                          \
  63 struct name {                                                           \
  64         struct type *sph_root; /* root of the tree */                   \
  65 }
  66
  67 #define SPLAY_INITIALIZER(root)                                         \
  68         { NULL }
  69
  70 #define SPLAY_INIT(root) do {                                           \
  71         (root)->sph_root = NULL;                                        \
  72 } while (/*CONSTCOND*/ 0)
  73
  74 #define SPLAY_ENTRY(type)                                               \
  75 struct {                                                                \
  76         struct type *spe_left; /* left element */                       \
  77         struct type *spe_right; /* right element */                     \
  78 }
  79
  80 #define SPLAY_LEFT(elm, field)          (elm)->field.spe_left
  81 #define SPLAY_RIGHT(elm, field)         (elm)->field.spe_right
  82 #define SPLAY_ROOT(head)                (head)->sph_root
  83 #define SPLAY_EMPTY(head)               (SPLAY_ROOT(head) == NULL)
  84
  85 /* SPLAY_ROTATE_{LEFT,RIGHT} expect that tmp hold SPLAY_{RIGHT,LEFT} */
  86 #define SPLAY_ROTATE_RIGHT(head, tmp, field) do {                       \
  87         SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(tmp, field);  \
  88         SPLAY_RIGHT(tmp, field) = (head)->sph_root;                     \
  89         (head)->sph_root = tmp;                                         \
  90 } while (/*CONSTCOND*/ 0)
  91
  92 #define SPLAY_ROTATE_LEFT(head, tmp, field) do {                        \
  93         SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(tmp, field);  \
  94         SPLAY_LEFT(tmp, field) = (head)->sph_root;                      \
  95         (head)->sph_root = tmp;                                         \
  96 } while (/*CONSTCOND*/ 0)
  97
  98 #define SPLAY_LINKLEFT(head, tmp, field) do {                           \
  99         SPLAY_LEFT(tmp, field) = (head)->sph_root;                      \
 100         tmp = (head)->sph_root;                                         \
 101         (head)->sph_root = SPLAY_LEFT((head)->sph_root, field);         \
 102 } while (/*CONSTCOND*/ 0)
 103
 104 #define SPLAY_LINKRIGHT(head, tmp, field) do {                          \
 105         SPLAY_RIGHT(tmp, field) = (head)->sph_root;                     \
 106         tmp = (head)->sph_root;                                         \
 107         (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);        \
 108 } while (/*CONSTCOND*/ 0)
 109
 110 #define SPLAY_ASSEMBLE(head, node, left, right, field) do {             \
 111         SPLAY_RIGHT(left, field) = SPLAY_LEFT((head)->sph_root, field); \
 112         SPLAY_LEFT(right, field) = SPLAY_RIGHT((head)->sph_root, field);\
 113         SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(node, field); \
 114         SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(node, field); \
 115 } while (/*CONSTCOND*/ 0)
 116
 117 /* Generates prototypes and inline functions */
 118
 119 #define SPLAY_PROTOTYPE(name, type, field, cmp)                         \
 120 void name##_SPLAY(struct name *, struct type *);                        \
 121 void name##_SPLAY_MINMAX(struct name *, int);                           \
 122 struct type *name##_SPLAY_INSERT(struct name *, struct type *);         \
 123 struct type *name##_SPLAY_REMOVE(struct name *, struct type *);         \
 124                                                                         \
 125 /* Finds the node with the same key as elm */                           \
 126 static __inline struct type *                                           \
 127 name##_SPLAY_FIND(struct name *head, struct type *elm)                  \
 128 {                                                                       \
 129         if (SPLAY_EMPTY(head))                                          \
 130                 return(NULL);                                           \
 131         name##_SPLAY(head, elm);                                        \
 132         if ((cmp)(elm, (head)->sph_root) == 0)                          \
 133                 return (head->sph_root);                                \
 134         return (NULL);                                                  \
 135 }                                                                       \
 136                                                                         \
 137 static __inline struct type *                                           \
 138 name##_SPLAY_NEXT(struct name *head, struct type *elm)                  \
 139 {                                                                       \
 140         name##_SPLAY(head, elm);                                        \
 141         if (SPLAY_RIGHT(elm, field) != NULL) {                          \
 142                 elm = SPLAY_RIGHT(elm, field);                          \
 143                 while (SPLAY_LEFT(elm, field) != NULL) {                \
 144                         elm = SPLAY_LEFT(elm, field);                   \
 145                 }                                                       \
 146         } else                                                          \
 147                 elm = NULL;                                             \
 148         return (elm);                                                   \
 149 }                                                                       \
 150                                                                         \
 151 static __inline struct type *                                           \
 152 name##_SPLAY_MIN_MAX(struct name *head, int val)                        \
 153 {                                                                       \
 154         name##_SPLAY_MINMAX(head, val);                                 \
 155         return (SPLAY_ROOT(head));                                      \
 156 }
 157
 158 /* Main splay operation.
 159  * Moves node close to the key of elm to top
 160  */
 161 #define SPLAY_GENERATE(name, type, field, cmp)                          \
 162 struct type *                                                           \
 163 name##_SPLAY_INSERT(struct name *head, struct type *elm)                \
 164 {                                                                       \
 165     if (SPLAY_EMPTY(head)) {                                            \
 166             SPLAY_LEFT(elm, field) = SPLAY_RIGHT(elm, field) = NULL;    \
 167     } else {                                                            \
 168             int __comp;                                                 \
 169             name##_SPLAY(head, elm);                                    \
 170             __comp = (cmp)(elm, (head)->sph_root);                      \
 171             if(__comp < 0) {                                            \
 172                     SPLAY_LEFT(elm, field) = SPLAY_LEFT((head)->sph_root, field);\
 173                     SPLAY_RIGHT(elm, field) = (head)->sph_root;         \
 174                     SPLAY_LEFT((head)->sph_root, field) = NULL;         \
 175             } else if (__comp > 0) {                                    \
 176                     SPLAY_RIGHT(elm, field) = SPLAY_RIGHT((head)->sph_root, field);\
 177                     SPLAY_LEFT(elm, field) = (head)->sph_root;          \
 178                     SPLAY_RIGHT((head)->sph_root, field) = NULL;        \
 179             } else                                                      \
 180                     return ((head)->sph_root);                          \
 181     }                                                                   \
 182     (head)->sph_root = (elm);                                           \
 183     return (NULL);                                                      \
 184 }                                                                       \
 185                                                                         \
 186 struct type *                                                           \
 187 name##_SPLAY_REMOVE(struct name *head, struct type *elm)                \
 188 {                                                                       \
 189         struct type *__tmp;                                             \
 190         if (SPLAY_EMPTY(head))                                          \
 191                 return (NULL);                                          \
 192         name##_SPLAY(head, elm);                                        \
 193         if ((cmp)(elm, (head)->sph_root) == 0) {                        \
 194                 if (SPLAY_LEFT((head)->sph_root, field) == NULL) {      \
 195                         (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);\
 196                 } else {                                                \
 197                         __tmp = SPLAY_RIGHT((head)->sph_root, field);   \
 198                         (head)->sph_root = SPLAY_LEFT((head)->sph_root, field);\
 199                         name##_SPLAY(head, elm);                        \
 200                         SPLAY_RIGHT((head)->sph_root, field) = __tmp;   \
 201                 }                                                       \
 202                 return (elm);                                           \
 203         }                                                               \
 204         return (NULL);                                                  \
 205 }                                                                       \
 206                                                                         \
 207 void                                                                    \
 208 name##_SPLAY(struct name *head, struct type *elm)                       \
 209 {                                                                       \
 210         struct type __node, *__left, *__right, *__tmp;                  \
 211         int __comp;                                                     \
 212 \
 213         SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
 214         __left = __right = &__node;                                     \
 215 \
 216         while ((__comp = (cmp)(elm, (head)->sph_root)) != 0) {          \
 217                 if (__comp < 0) {                                       \
 218                         __tmp = SPLAY_LEFT((head)->sph_root, field);    \
 219                         if (__tmp == NULL)                              \
 220                                 break;                                  \
 221                         if ((cmp)(elm, __tmp) < 0){                     \
 222                                 SPLAY_ROTATE_RIGHT(head, __tmp, field); \
 223                                 if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
 224                                         break;                          \
 225                         }                                               \
 226                         SPLAY_LINKLEFT(head, __right, field);           \
 227                 } else if (__comp > 0) {                                \
 228                         __tmp = SPLAY_RIGHT((head)->sph_root, field);   \
 229                         if (__tmp == NULL)                              \
 230                                 break;                                  \
 231                         if ((cmp)(elm, __tmp) > 0){                     \
 232                                 SPLAY_ROTATE_LEFT(head, __tmp, field);  \
 233                                 if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
 234                                         break;                          \
 235                         }                                               \
 236                         SPLAY_LINKRIGHT(head, __left, field);           \
 237                 }                                                       \
 238         }                                                               \
 239         SPLAY_ASSEMBLE(head, &__node, __left, __right, field);          \
 240 }                                                                       \
 241                                                                         \
 242 /* Splay with either the minimum or the maximum element                 \
 243  * Used to find minimum or maximum element in tree.                     \
 244  */                                                                     \
 245 void name##_SPLAY_MINMAX(struct name *head, int __comp) \
 246 {                                                                       \
 247         struct type __node, *__left, *__right, *__tmp;                  \
 248 \
 249         SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
 250         __left = __right = &__node;                                     \
 251 \
 252         while (1) {                                                     \
 253                 if (__comp < 0) {                                       \
 254                         __tmp = SPLAY_LEFT((head)->sph_root, field);    \
 255                         if (__tmp == NULL)                              \
 256                                 break;                                  \
 257                         if (__comp < 0){                                \
 258                                 SPLAY_ROTATE_RIGHT(head, __tmp, field); \
 259                                 if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
 260                                         break;                          \
 261                         }                                               \
 262                         SPLAY_LINKLEFT(head, __right, field);           \
 263                 } else if (__comp > 0) {                                \
 264                         __tmp = SPLAY_RIGHT((head)->sph_root, field);   \
 265                         if (__tmp == NULL)                              \
 266                                 break;                                  \
 267                         if (__comp > 0) {                               \
 268                                 SPLAY_ROTATE_LEFT(head, __tmp, field);  \
 269                                 if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
 270                                         break;                          \
 271                         }                                               \
 272                         SPLAY_LINKRIGHT(head, __left, field);           \
 273                 }                                                       \
 274         }                                                               \
 275         SPLAY_ASSEMBLE(head, &__node, __left, __right, field);          \
 276 }
 277
 278 #define SPLAY_NEGINF    -1
 279 #define SPLAY_INF       1
 280
 281 #define SPLAY_INSERT(name, x, y)        name##_SPLAY_INSERT(x, y)
 282 #define SPLAY_REMOVE(name, x, y)        name##_SPLAY_REMOVE(x, y)
 283 #define SPLAY_FIND(name, x, y)          name##_SPLAY_FIND(x, y)
 284 #define SPLAY_NEXT(name, x, y)          name##_SPLAY_NEXT(x, y)
 285 #define SPLAY_MIN(name, x)              (SPLAY_EMPTY(x) ? NULL  \
 286                                         : name##_SPLAY_MIN_MAX(x, SPLAY_NEGINF))
 287 #define SPLAY_MAX(name, x)              (SPLAY_EMPTY(x) ? NULL  \
 288                                         : name##_SPLAY_MIN_MAX(x, SPLAY_INF))
 289
 290 #define SPLAY_FOREACH(x, name, head)                                    \
 291         for ((x) = SPLAY_MIN(name, head);                               \
 292              (x) != NULL;                                               \
 293              (x) = SPLAY_NEXT(name, head, x))
 294
 295 /* Macros that define a red-black tree */
 296 #define RB_HEAD(name, type)                                             \
 297 struct name {                                                           \
 298         struct type *rbh_root; /* root of the tree */                   \
 299 }
 300
 301 #define RB_INITIALIZER(root)                                            \
 302         { NULL }
 303
 304 #define RB_INIT(root) do {                                              \
 305         (root)->rbh_root = NULL;                                        \
 306 } while (/*CONSTCOND*/ 0)
 307
 308 #define RB_BLACK        0
 309 #define RB_RED          1
 310 #define RB_ENTRY(type)                                                  \
 311 struct {                                                                \
 312         struct type *rbe_left;          /* left element */              \
 313         struct type *rbe_right;         /* right element */             \
 314         struct type *rbe_parent;        /* parent element */            \
 315         int rbe_color;                  /* node color */                \
 316 }
 317
 318 #define RB_LEFT(elm, field)             (elm)->field.rbe_left
 319 #define RB_RIGHT(elm, field)            (elm)->field.rbe_right
 320 #define RB_PARENT(elm, field)           (elm)->field.rbe_parent
 321 #define RB_COLOR(elm, field)            (elm)->field.rbe_color
 322 #define RB_ROOT(head)                   (head)->rbh_root
 323 #define RB_EMPTY(head)                  (RB_ROOT(head) == NULL)
 324
 325 #define RB_SET(elm, parent, field) do {                                 \
 326         RB_PARENT(elm, field) = parent;                                 \
 327         RB_LEFT(elm, field) = RB_RIGHT(elm, field) = NULL;              \
 328         RB_COLOR(elm, field) = RB_RED;                                  \
 329 } while (/*CONSTCOND*/ 0)
 330
 331 #define RB_SET_BLACKRED(black, red, field) do {                         \
 332         RB_COLOR(black, field) = RB_BLACK;                              \
 333         RB_COLOR(red, field) = RB_RED;                                  \
 334 } while (/*CONSTCOND*/ 0)
 335
 336 #ifndef RB_AUGMENT
 337 #define RB_AUGMENT(x)   do {} while (0)
 338 #endif
 339
 340 #define RB_ROTATE_LEFT(head, elm, tmp, field) do {                      \
 341         (tmp) = RB_RIGHT(elm, field);                                   \
 342         if ((RB_RIGHT(elm, field) = RB_LEFT(tmp, field)) != NULL) {     \
 343                 RB_PARENT(RB_LEFT(tmp, field), field) = (elm);          \
 344         }                                                               \
 345         RB_AUGMENT(elm);                                                \
 346         if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) {  \
 347                 if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))     \
 348                         RB_LEFT(RB_PARENT(elm, field), field) = (tmp);  \
 349                 else                                                    \
 350                         RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \
 351         } else                                                          \
 352                 (head)->rbh_root = (tmp);                               \
 353         RB_LEFT(tmp, field) = (elm);                                    \
 354         RB_PARENT(elm, field) = (tmp);                                  \
 355         RB_AUGMENT(tmp);                                                \
 356         if ((RB_PARENT(tmp, field)))                                    \
 357                 RB_AUGMENT(RB_PARENT(tmp, field));                      \
 358 } while (/*CONSTCOND*/ 0)
 359
 360 #define RB_ROTATE_RIGHT(head, elm, tmp, field) do {                     \
 361         (tmp) = RB_LEFT(elm, field);                                    \
 362         if ((RB_LEFT(elm, field) = RB_RIGHT(tmp, field)) != NULL) {     \
 363                 RB_PARENT(RB_RIGHT(tmp, field), field) = (elm);         \
 364         }                                                               \
 365         RB_AUGMENT(elm);                                                \
 366         if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) {  \
 367                 if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))     \
 368                         RB_LEFT(RB_PARENT(elm, field), field) = (tmp);  \
 369                 else                                                    \
 370                         RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \
 371         } else                                                          \
 372                 (head)->rbh_root = (tmp);                               \
 373         RB_RIGHT(tmp, field) = (elm);                                   \
 374         RB_PARENT(elm, field) = (tmp);                                  \
 375         RB_AUGMENT(tmp);                                                \
 376         if ((RB_PARENT(tmp, field)))                                    \
 377                 RB_AUGMENT(RB_PARENT(tmp, field));                      \
 378 } while (/*CONSTCOND*/ 0)
 379
 380 /* Generates prototypes and inline functions */
 381 #define RB_PROTOTYPE(name, type, field, cmp)                            \
 382         RB_PROTOTYPE_INTERNAL(name, type, field, cmp,)
 383 #define RB_PROTOTYPE_STATIC(name, type, field, cmp)                     \
 384         RB_PROTOTYPE_INTERNAL(name, type, field, cmp, __unused static)
 385 #define RB_PROTOTYPE_INTERNAL(name, type, field, cmp, attr)             \
 386 attr void name##_RB_INSERT_COLOR(struct name *, struct type *);         \
 387 attr void name##_RB_REMOVE_COLOR(struct name *, struct type *, struct type *);\
 388 attr struct type *name##_RB_REMOVE(struct name *, struct type *);       \
 389 attr struct type *name##_RB_INSERT(struct name *, struct type *);       \
 390 attr struct type *name##_RB_FIND(struct name *, struct type *);         \
 391 attr struct type *name##_RB_NFIND(struct name *, struct type *);        \
 392 attr struct type *name##_RB_NEXT(struct type *);                        \
 393 attr struct type *name##_RB_MINMAX(struct name *, int);                 \
 394                                                                         \
 395
 396 /* Main rb operation.
 397  * Moves node close to the key of elm to top
 398  */
 399 #define RB_GENERATE(name, type, field, cmp)                             \
 400         RB_GENERATE_INTERNAL(name, type, field, cmp,)
 401 #define RB_GENERATE_STATIC(name, type, field, cmp)                      \
 402         RB_GENERATE_INTERNAL(name, type, field, cmp, __unused static)
 403 #define RB_GENERATE_INTERNAL(name, type, field, cmp, attr)              \
 404 attr void                                                               \
 405 name##_RB_INSERT_COLOR(struct name *head, struct type *elm)             \
 406 {                                                                       \
 407         struct type *parent, *gparent, *tmp;                            \
 408         while ((parent = RB_PARENT(elm, field)) != NULL &&              \
 409             RB_COLOR(parent, field) == RB_RED) {                        \
 410                 gparent = RB_PARENT(parent, field);                     \
 411                 if (parent == RB_LEFT(gparent, field)) {                \
 412                         tmp = RB_RIGHT(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_RIGHT(parent, field) == elm) {           \
 420                                 RB_ROTATE_LEFT(head, parent, tmp, field);\
 421                                 tmp = parent;                           \
 422                                 parent = elm;                           \
 423                                 elm = tmp;                              \
 424                         }                                               \
 425                         RB_SET_BLACKRED(parent, gparent, field);        \
 426                         RB_ROTATE_RIGHT(head, gparent, tmp, field);     \
 427                 } else {                                                \
 428                         tmp = RB_LEFT(gparent, field);                  \
 429                         if (tmp && RB_COLOR(tmp, field) == RB_RED) {    \
 430                                 RB_COLOR(tmp, field) = RB_BLACK;        \
 431                                 RB_SET_BLACKRED(parent, gparent, field);\
 432                                 elm = gparent;                          \
 433                                 continue;                               \
 434                         }                                               \
 435                         if (RB_LEFT(parent, field) == elm) {            \
 436                                 RB_ROTATE_RIGHT(head, parent, tmp, field);\
 437                                 tmp = parent;                           \
 438                                 parent = elm;                           \
 439                                 elm = tmp;                              \
 440                         }                                               \
 441                         RB_SET_BLACKRED(parent, gparent, field);        \
 442                         RB_ROTATE_LEFT(head, gparent, tmp, field);      \
 443                 }                                                       \
 444         }                                                               \
 445         RB_COLOR(head->rbh_root, field) = RB_BLACK;                     \
 446 }                                                                       \
 447                                                                         \
 448 attr void                                                               \
 449 name##_RB_REMOVE_COLOR(struct name *head, struct type *parent, struct type *elm) \
 450 {                                                                       \
 451         struct type *tmp;                                               \
 452         while ((elm == NULL || RB_COLOR(elm, field) == RB_BLACK) &&     \
 453             elm != RB_ROOT(head)) {                                     \
 454                 if (RB_LEFT(parent, field) == elm) {                    \
 455                         tmp = RB_RIGHT(parent, field);                  \
 456                         if (RB_COLOR(tmp, field) == RB_RED) {           \
 457                                 RB_SET_BLACKRED(tmp, parent, field);    \
 458                                 RB_ROTATE_LEFT(head, parent, tmp, field);\
 459                                 tmp = RB_RIGHT(parent, field);          \
 460                         }                                               \
 461                         if ((RB_LEFT(tmp, field) == NULL ||             \
 462                             RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
 463                             (RB_RIGHT(tmp, field) == NULL ||            \
 464                             RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
 465                                 RB_COLOR(tmp, field) = RB_RED;          \
 466                                 elm = parent;                           \
 467                                 parent = RB_PARENT(elm, field);         \
 468                         } else {                                        \
 469                                 if (RB_RIGHT(tmp, field) == NULL ||     \
 470                                     RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK) {\
 471                                         struct type *oleft;             \
 472                                         if ((oleft = RB_LEFT(tmp, field)) \
 473                                             != NULL)                    \
 474                                                 RB_COLOR(oleft, field) = RB_BLACK;\
 475                                         RB_COLOR(tmp, field) = RB_RED;  \
 476                                         RB_ROTATE_RIGHT(head, tmp, oleft, field);\
 477                                         tmp = RB_RIGHT(parent, field);  \
 478                                 }                                       \
 479                                 RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
 480                                 RB_COLOR(parent, field) = RB_BLACK;     \
 481                                 if (RB_RIGHT(tmp, field))               \
 482                                         RB_COLOR(RB_RIGHT(tmp, field), field) = RB_BLACK;\
 483                                 RB_ROTATE_LEFT(head, parent, tmp, field);\
 484                                 elm = RB_ROOT(head);                    \
 485                                 break;                                  \
 486                         }                                               \
 487                 } else {                                                \
 488                         tmp = RB_LEFT(parent, field);                   \
 489                         if (RB_COLOR(tmp, field) == RB_RED) {           \
 490                                 RB_SET_BLACKRED(tmp, parent, field);    \
 491                                 RB_ROTATE_RIGHT(head, parent, tmp, field);\
 492                                 tmp = RB_LEFT(parent, field);           \
 493                         }                                               \
 494                         if ((RB_LEFT(tmp, field) == NULL ||             \
 495                             RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
 496                             (RB_RIGHT(tmp, field) == NULL ||            \
 497                             RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
 498                                 RB_COLOR(tmp, field) = RB_RED;          \
 499                                 elm = parent;                           \
 500                                 parent = RB_PARENT(elm, field);         \
 501                         } else {                                        \
 502                                 if (RB_LEFT(tmp, field) == NULL ||      \
 503                                     RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) {\
 504                                         struct type *oright;            \
 505                                         if ((oright = RB_RIGHT(tmp, field)) \
 506                                             != NULL)                    \
 507                                                 RB_COLOR(oright, field) = RB_BLACK;\
 508                                         RB_COLOR(tmp, field) = RB_RED;  \
 509                                         RB_ROTATE_LEFT(head, tmp, oright, field);\
 510                                         tmp = RB_LEFT(parent, field);   \
 511                                 }                                       \
 512                                 RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
 513                                 RB_COLOR(parent, field) = RB_BLACK;     \
 514                                 if (RB_LEFT(tmp, field))                \
 515                                         RB_COLOR(RB_LEFT(tmp, field), field) = RB_BLACK;\
 516                                 RB_ROTATE_RIGHT(head, parent, tmp, field);\
 517                                 elm = RB_ROOT(head);                    \
 518                                 break;                                  \
 519                         }                                               \
 520                 }                                                       \
 521         }                                                               \
 522         if (elm)                                                        \
 523                 RB_COLOR(elm, field) = RB_BLACK;                        \
 524 }                                                                       \
 525                                                                         \
 526 attr struct type *                                                      \
 527 name##_RB_REMOVE(struct name *head, struct type *elm)                   \
 528 {                                                                       \
 529         struct type *child, *parent, *old = elm;                        \
 530         int color;                                                      \
 531         if (RB_LEFT(elm, field) == NULL)                                \
 532                 child = RB_RIGHT(elm, field);                           \
 533         else if (RB_RIGHT(elm, field) == NULL)                          \
 534                 child = RB_LEFT(elm, field);                            \
 535         else {                                                          \
 536                 struct type *left;                                      \
 537                 elm = RB_RIGHT(elm, field);                             \
 538                 while ((left = RB_LEFT(elm, field)) != NULL)            \
 539                         elm = left;                                     \
 540                 child = RB_RIGHT(elm, field);                           \
 541                 parent = RB_PARENT(elm, field);                         \
 542                 color = RB_COLOR(elm, field);                           \
 543                 if (child)                                              \
 544                         RB_PARENT(child, field) = parent;               \
 545                 if (parent) {                                           \
 546                         if (RB_LEFT(parent, field) == elm)              \
 547                                 RB_LEFT(parent, field) = child;         \
 548                         else                                            \
 549                                 RB_RIGHT(parent, field) = child;        \
 550                         RB_AUGMENT(parent);                             \
 551                 } else                                                  \
 552                         RB_ROOT(head) = child;                          \
 553                 if (RB_PARENT(elm, field) == old)                       \
 554                         parent = elm;                                   \
 555                 (elm)->field = (old)->field;                            \
 556                 if (RB_PARENT(old, field)) {                            \
 557                         if (RB_LEFT(RB_PARENT(old, field), field) == old)\
 558                                 RB_LEFT(RB_PARENT(old, field), field) = elm;\
 559                         else                                            \
 560                                 RB_RIGHT(RB_PARENT(old, field), field) = elm;\
 561                         RB_AUGMENT(RB_PARENT(old, field));              \
 562                 } else                                                  \
 563                         RB_ROOT(head) = elm;                            \
 564                 RB_PARENT(RB_LEFT(old, field), field) = elm;            \
 565                 if (RB_RIGHT(old, field))                               \
 566                         RB_PARENT(RB_RIGHT(old, field), field) = elm;   \
 567                 if (parent) {                                           \
 568                         left = parent;                                  \
 569                         do {                                            \
 570                                 RB_AUGMENT(left);                       \
 571                         } while ((left = RB_PARENT(left, field)) != NULL); \
 572                 }                                                       \
 573                 goto color;                                             \
 574         }                                                               \
 575         parent = RB_PARENT(elm, field);                                 \
 576         color = RB_COLOR(elm, field);                                   \
 577         if (child)                                                      \
 578                 RB_PARENT(child, field) = parent;                       \
 579         if (parent) {                                                   \
 580                 if (RB_LEFT(parent, field) == elm)                      \
 581                         RB_LEFT(parent, field) = child;                 \
 582                 else                                                    \
 583                         RB_RIGHT(parent, field) = child;                \
 584                 RB_AUGMENT(parent);                                     \
 585         } else                                                          \
 586                 RB_ROOT(head) = child;                                  \
 587 color:                                                                  \
 588         if (color == RB_BLACK)                                          \
 589                 name##_RB_REMOVE_COLOR(head, parent, child);            \
 590         return (old);                                                   \
 591 }                                                                       \
 592                                                                         \
 593 /* Inserts a node into the RB tree */                                   \
 594 attr struct type *                                                      \
 595 name##_RB_INSERT(struct name *head, struct type *elm)                   \
 596 {                                                                       \
 597         struct type *tmp;                                               \
 598         struct type *parent = NULL;                                     \
 599         int comp = 0;                                                   \
 600         tmp = RB_ROOT(head);                                            \
 601         while (tmp) {                                                   \
 602                 parent = tmp;                                           \
 603                 comp = (cmp)(elm, parent);                              \
 604                 if (comp < 0)                                           \
 605                         tmp = RB_LEFT(tmp, field);                      \
 606                 else if (comp > 0)                                      \
 607                         tmp = RB_RIGHT(tmp, field);                     \
 608                 else                                                    \
 609                         return (tmp);                                   \
 610         }                                                               \
 611         RB_SET(elm, parent, field);                                     \
 612         if (parent != NULL) {                                           \
 613                 if (comp < 0)                                           \
 614                         RB_LEFT(parent, field) = elm;                   \
 615                 else                                                    \
 616                         RB_RIGHT(parent, field) = elm;                  \
 617                 RB_AUGMENT(parent);                                     \
 618         } else                                                          \
 619                 RB_ROOT(head) = elm;                                    \
 620         name##_RB_INSERT_COLOR(head, elm);                              \
 621         return (NULL);                                                  \
 622 }                                                                       \
 623                                                                         \
 624 /* Finds the node with the same key as elm */                           \
 625 attr struct type *                                                      \
 626 name##_RB_FIND(struct name *head, struct type *elm)                     \
 627 {                                                                       \
 628         struct type *tmp = RB_ROOT(head);                               \
 629         int comp;                                                       \
 630         while (tmp) {                                                   \
 631                 comp = cmp(elm, tmp);                                   \
 632                 if (comp < 0)                                           \
 633                         tmp = RB_LEFT(tmp, field);                      \
 634                 else if (comp > 0)                                      \
 635                         tmp = RB_RIGHT(tmp, field);                     \
 636                 else                                                    \
 637                         return (tmp);                                   \
 638         }                                                               \
 639         return (NULL);                                                  \
 640 }                                                                       \
 641                                                                         \
 642 /* Finds the first node greater than or equal to the search key */      \
 643 attr struct type *                                                      \
 644 name##_RB_NFIND(struct name *head, struct type *elm)                    \
 645 {                                                                       \
 646         struct type *ret = RB_ROOT(head);                               \
 647         struct type *tmp;                                               \
 648         int comp;                                                       \
 649         while (ret && (comp = cmp(elm, ret)) != 0) {                    \
 650                 if (comp < 0) {                                         \
 651                         if ((tmp = RB_LEFT(ret, field)) == NULL)        \
 652                                 break;                                  \
 653                         ret = tmp;                                      \
 654                 } else {                                                \
 655                         if ((tmp = RB_RIGHT(ret, field)) == NULL) {     \
 656                                 tmp = ret;                              \
 657                                 ret = RB_PARENT(ret, field);            \
 658                                 while (ret && tmp == RB_RIGHT(ret,      \
 659                                     field)) {                           \
 660                                         tmp = ret;                      \
 661                                         ret = RB_PARENT(ret, field);    \
 662                                 }                                       \
 663                                 break;                                  \
 664                         }                                               \
 665                         ret = tmp;                                      \
 666                 }                                                       \
 667         }                                                               \
 668         return (ret);                                                   \
 669 }                                                                       \
 670                                                                         \
 671 /* ARGSUSED */                                                          \
 672 attr struct type *                                                      \
 673 name##_RB_NEXT(struct type *elm)                                        \
 674 {                                                                       \
 675         if (RB_RIGHT(elm, field)) {                                     \
 676                 elm = RB_RIGHT(elm, field);                             \
 677                 while (RB_LEFT(elm, field))                             \
 678                         elm = RB_LEFT(elm, field);                      \
 679         } else {                                                        \
 680                 if (RB_PARENT(elm, field) &&                            \
 681                     (elm == RB_LEFT(RB_PARENT(elm, field), field)))     \
 682                         elm = RB_PARENT(elm, field);                    \
 683                 else {                                                  \
 684                         while (RB_PARENT(elm, field) &&                 \
 685                             (elm == RB_RIGHT(RB_PARENT(elm, field), field)))\
 686                                 elm = RB_PARENT(elm, field);            \
 687                         elm = RB_PARENT(elm, field);                    \
 688                 }                                                       \
 689         }                                                               \
 690         return (elm);                                                   \
 691 }                                                                       \
 692                                                                         \
 693 attr struct type *                                                      \
 694 name##_RB_MINMAX(struct name *head, int val)                            \
 695 {                                                                       \
 696         struct type *tmp = RB_ROOT(head);                               \
 697         struct type *parent = NULL;                                     \
 698         while (tmp) {                                                   \
 699                 parent = tmp;                                           \
 700                 if (val < 0)                                            \
 701                         tmp = RB_LEFT(tmp, field);                      \
 702                 else                                                    \
 703                         tmp = RB_RIGHT(tmp, field);                     \
 704         }                                                               \
 705         return (parent);                                                \
 706 }
 707
 708 #define RB_NEGINF       -1
 709 #define RB_INF  1
 710
 711 #define RB_INSERT(name, x, y)   name##_RB_INSERT(x, y)
 712 #define RB_REMOVE(name, x, y)   name##_RB_REMOVE(x, y)
 713 #define RB_FIND(name, x, y)     name##_RB_FIND(x, y)
 714 #define RB_NFIND(name, x, y)    name##_RB_NFIND(x, y)
 715 #define RB_NEXT(name, x, y)     name##_RB_NEXT(y)
 716 #define RB_MIN(name, x)         name##_RB_MINMAX(x, RB_NEGINF)
 717 #define RB_MAX(name, x)         name##_RB_MINMAX(x, RB_INF)
 718
 719 #define RB_FOREACH(x, name, head)                                       \
 720         for ((x) = RB_MIN(name, head);                                  \
 721              (x) != NULL;                                               \
 722              (x) = name##_RB_NEXT(x))
 723
 724 #endif  /* _SYS_TREE_H_ */