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  * SPDX-License-Identifier: BSD-2-Clause-FreeBSD
   7  *
   8  * Copyright 2002 Niels Provos <provos@citi.umich.edu>
   9  * All rights reserved.
  10  *
  11  * Redistribution and use in source and binary forms, with or without
  12  * modification, are permitted provided that the following conditions
  13  * are met:
  14  * 1. Redistributions of source code must retain the above copyright
  15  *    notice, this list of conditions and the following disclaimer.
  16  * 2. Redistributions in binary form must reproduce the above copyright
  17  *    notice, this list of conditions and the following disclaimer in the
  18  *    documentation and/or other materials provided with the distribution.
  19  *
  20  * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
  21  * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
  22  * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
  23  * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
  24  * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
  25  * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
  26  * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
  27  * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
  28  * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
  29  * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
  30  */
  31
  32 #ifndef _SYS_TREE_H_
  33 #define _SYS_TREE_H_
  34
  35 #include <sys/cdefs.h>
  36
  37 /*
  38  * This file defines data structures for different types of trees:
  39  * splay trees and red-black trees.
  40  *
  41  * A splay tree is a self-organizing data structure.  Every operation
  42  * on the tree causes a splay to happen.  The splay moves the requested
  43  * node to the root of the tree and partly rebalances it.
  44  *
  45  * This has the benefit that request locality causes faster lookups as
  46  * the requested nodes move to the top of the tree.  On the other hand,
  47  * every lookup causes memory writes.
  48  *
  49  * The Balance Theorem bounds the total access time for m operations
  50  * and n inserts on an initially empty tree as O((m + n)lg n).  The
  51  * amortized cost for a sequence of m accesses to a splay tree is O(lg n);
  52  *
  53  * A red-black tree is a binary search tree with the node color as an
  54  * extra attribute.  It fulfills a set of conditions:
  55  *      - every search path from the root to a leaf consists of the
  56  *        same number of black nodes,
  57  *      - each red node (except for the root) has a black parent,
  58  *      - each leaf node is black.
  59  *
  60  * Every operation on a red-black tree is bounded as O(lg n).
  61  * The maximum height of a red-black tree is 2lg (n+1).
  62  */
  63
  64 #define SPLAY_HEAD(name, type)                                          \
  65 struct name {                                                           \
  66         struct type *sph_root; /* root of the tree */                   \
  67 }
  68
  69 #define SPLAY_INITIALIZER(root)                                         \
  70         { NULL }
  71
  72 #define SPLAY_INIT(root) do {                                           \
  73         (root)->sph_root = NULL;                                        \
  74 } while (/*CONSTCOND*/ 0)
  75
  76 #define SPLAY_ENTRY(type)                                               \
  77 struct {                                                                \
  78         struct type *spe_left; /* left element */                       \
  79         struct type *spe_right; /* right element */                     \
  80 }
  81
  82 #define SPLAY_LEFT(elm, field)          (elm)->field.spe_left
  83 #define SPLAY_RIGHT(elm, field)         (elm)->field.spe_right
  84 #define SPLAY_ROOT(head)                (head)->sph_root
  85 #define SPLAY_EMPTY(head)               (SPLAY_ROOT(head) == NULL)
  86
  87 /* SPLAY_ROTATE_{LEFT,RIGHT} expect that tmp hold SPLAY_{RIGHT,LEFT} */
  88 #define SPLAY_ROTATE_RIGHT(head, tmp, field) do {                       \
  89         SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(tmp, field);  \
  90         SPLAY_RIGHT(tmp, field) = (head)->sph_root;                     \
  91         (head)->sph_root = tmp;                                         \
  92 } while (/*CONSTCOND*/ 0)
  93
  94 #define SPLAY_ROTATE_LEFT(head, tmp, field) do {                        \
  95         SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(tmp, field);  \
  96         SPLAY_LEFT(tmp, field) = (head)->sph_root;                      \
  97         (head)->sph_root = tmp;                                         \
  98 } while (/*CONSTCOND*/ 0)
  99
 100 #define SPLAY_LINKLEFT(head, tmp, field) do {                           \
 101         SPLAY_LEFT(tmp, field) = (head)->sph_root;                      \
 102         tmp = (head)->sph_root;                                         \
 103         (head)->sph_root = SPLAY_LEFT((head)->sph_root, field);         \
 104 } while (/*CONSTCOND*/ 0)
 105
 106 #define SPLAY_LINKRIGHT(head, tmp, field) do {                          \
 107         SPLAY_RIGHT(tmp, field) = (head)->sph_root;                     \
 108         tmp = (head)->sph_root;                                         \
 109         (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);        \
 110 } while (/*CONSTCOND*/ 0)
 111
 112 #define SPLAY_ASSEMBLE(head, node, left, right, field) do {             \
 113         SPLAY_RIGHT(left, field) = SPLAY_LEFT((head)->sph_root, field); \
 114         SPLAY_LEFT(right, field) = SPLAY_RIGHT((head)->sph_root, field);\
 115         SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(node, field); \
 116         SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(node, field); \
 117 } while (/*CONSTCOND*/ 0)
 118
 119 /* Generates prototypes and inline functions */
 120
 121 #define SPLAY_PROTOTYPE(name, type, field, cmp)                         \
 122 void name##_SPLAY(struct name *, struct type *);                        \
 123 void name##_SPLAY_MINMAX(struct name *, int);                           \
 124 struct type *name##_SPLAY_INSERT(struct name *, struct type *);         \
 125 struct type *name##_SPLAY_REMOVE(struct name *, struct type *);         \
 126                                                                         \
 127 /* Finds the node with the same key as elm */                           \
 128 static __unused __inline struct type *                                  \
 129 name##_SPLAY_FIND(struct name *head, struct type *elm)                  \
 130 {                                                                       \
 131         if (SPLAY_EMPTY(head))                                          \
 132                 return(NULL);                                           \
 133         name##_SPLAY(head, elm);                                        \
 134         if ((cmp)(elm, (head)->sph_root) == 0)                          \
 135                 return (head->sph_root);                                \
 136         return (NULL);                                                  \
 137 }                                                                       \
 138                                                                         \
 139 static __unused __inline struct type *                                  \
 140 name##_SPLAY_NEXT(struct name *head, struct type *elm)                  \
 141 {                                                                       \
 142         name##_SPLAY(head, elm);                                        \
 143         if (SPLAY_RIGHT(elm, field) != NULL) {                          \
 144                 elm = SPLAY_RIGHT(elm, field);                          \
 145                 while (SPLAY_LEFT(elm, field) != NULL) {                \
 146                         elm = SPLAY_LEFT(elm, field);                   \
 147                 }                                                       \
 148         } else                                                          \
 149                 elm = NULL;                                             \
 150         return (elm);                                                   \
 151 }                                                                       \
 152                                                                         \
 153 static __unused __inline struct type *                                  \
 154 name##_SPLAY_MIN_MAX(struct name *head, int val)                        \
 155 {                                                                       \
 156         name##_SPLAY_MINMAX(head, val);                                 \
 157         return (SPLAY_ROOT(head));                                      \
 158 }
 159
 160 /* Main splay operation.
 161  * Moves node close to the key of elm to top
 162  */
 163 #define SPLAY_GENERATE(name, type, field, cmp)                          \
 164 struct type *                                                           \
 165 name##_SPLAY_INSERT(struct name *head, struct type *elm)                \
 166 {                                                                       \
 167     if (SPLAY_EMPTY(head)) {                                            \
 168             SPLAY_LEFT(elm, field) = SPLAY_RIGHT(elm, field) = NULL;    \
 169     } else {                                                            \
 170             int __comp;                                                 \
 171             name##_SPLAY(head, elm);                                    \
 172             __comp = (cmp)(elm, (head)->sph_root);                      \
 173             if(__comp < 0) {                                            \
 174                     SPLAY_LEFT(elm, field) = SPLAY_LEFT((head)->sph_root, field);\
 175                     SPLAY_RIGHT(elm, field) = (head)->sph_root;         \
 176                     SPLAY_LEFT((head)->sph_root, field) = NULL;         \
 177             } else if (__comp > 0) {                                    \
 178                     SPLAY_RIGHT(elm, field) = SPLAY_RIGHT((head)->sph_root, field);\
 179                     SPLAY_LEFT(elm, field) = (head)->sph_root;          \
 180                     SPLAY_RIGHT((head)->sph_root, field) = NULL;        \
 181             } else                                                      \
 182                     return ((head)->sph_root);                          \
 183     }                                                                   \
 184     (head)->sph_root = (elm);                                           \
 185     return (NULL);                                                      \
 186 }                                                                       \
 187                                                                         \
 188 struct type *                                                           \
 189 name##_SPLAY_REMOVE(struct name *head, struct type *elm)                \
 190 {                                                                       \
 191         struct type *__tmp;                                             \
 192         if (SPLAY_EMPTY(head))                                          \
 193                 return (NULL);                                          \
 194         name##_SPLAY(head, elm);                                        \
 195         if ((cmp)(elm, (head)->sph_root) == 0) {                        \
 196                 if (SPLAY_LEFT((head)->sph_root, field) == NULL) {      \
 197                         (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);\
 198                 } else {                                                \
 199                         __tmp = SPLAY_RIGHT((head)->sph_root, field);   \
 200                         (head)->sph_root = SPLAY_LEFT((head)->sph_root, field);\
 201                         name##_SPLAY(head, elm);                        \
 202                         SPLAY_RIGHT((head)->sph_root, field) = __tmp;   \
 203                 }                                                       \
 204                 return (elm);                                           \
 205         }                                                               \
 206         return (NULL);                                                  \
 207 }                                                                       \
 208                                                                         \
 209 void                                                                    \
 210 name##_SPLAY(struct name *head, struct type *elm)                       \
 211 {                                                                       \
 212         struct type __node, *__left, *__right, *__tmp;                  \
 213         int __comp;                                                     \
 214 \
 215         SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
 216         __left = __right = &__node;                                     \
 217 \
 218         while ((__comp = (cmp)(elm, (head)->sph_root)) != 0) {          \
 219                 if (__comp < 0) {                                       \
 220                         __tmp = SPLAY_LEFT((head)->sph_root, field);    \
 221                         if (__tmp == NULL)                              \
 222                                 break;                                  \
 223                         if ((cmp)(elm, __tmp) < 0){                     \
 224                                 SPLAY_ROTATE_RIGHT(head, __tmp, field); \
 225                                 if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
 226                                         break;                          \
 227                         }                                               \
 228                         SPLAY_LINKLEFT(head, __right, field);           \
 229                 } else if (__comp > 0) {                                \
 230                         __tmp = SPLAY_RIGHT((head)->sph_root, field);   \
 231                         if (__tmp == NULL)                              \
 232                                 break;                                  \
 233                         if ((cmp)(elm, __tmp) > 0){                     \
 234                                 SPLAY_ROTATE_LEFT(head, __tmp, field);  \
 235                                 if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
 236                                         break;                          \
 237                         }                                               \
 238                         SPLAY_LINKRIGHT(head, __left, field);           \
 239                 }                                                       \
 240         }                                                               \
 241         SPLAY_ASSEMBLE(head, &__node, __left, __right, field);          \
 242 }                                                                       \
 243                                                                         \
 244 /* Splay with either the minimum or the maximum element                 \
 245  * Used to find minimum or maximum element in tree.                     \
 246  */                                                                     \
 247 void name##_SPLAY_MINMAX(struct name *head, int __comp) \
 248 {                                                                       \
 249         struct type __node, *__left, *__right, *__tmp;                  \
 250 \
 251         SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
 252         __left = __right = &__node;                                     \
 253 \
 254         while (1) {                                                     \
 255                 if (__comp < 0) {                                       \
 256                         __tmp = SPLAY_LEFT((head)->sph_root, field);    \
 257                         if (__tmp == NULL)                              \
 258                                 break;                                  \
 259                         if (__comp < 0){                                \
 260                                 SPLAY_ROTATE_RIGHT(head, __tmp, field); \
 261                                 if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
 262                                         break;                          \
 263                         }                                               \
 264                         SPLAY_LINKLEFT(head, __right, field);           \
 265                 } else if (__comp > 0) {                                \
 266                         __tmp = SPLAY_RIGHT((head)->sph_root, field);   \
 267                         if (__tmp == NULL)                              \
 268                                 break;                                  \
 269                         if (__comp > 0) {                               \
 270                                 SPLAY_ROTATE_LEFT(head, __tmp, field);  \
 271                                 if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
 272                                         break;                          \
 273                         }                                               \
 274                         SPLAY_LINKRIGHT(head, __left, field);           \
 275                 }                                                       \
 276         }                                                               \
 277         SPLAY_ASSEMBLE(head, &__node, __left, __right, field);          \
 278 }
 279
 280 #define SPLAY_NEGINF    -1
 281 #define SPLAY_INF       1
 282
 283 #define SPLAY_INSERT(name, x, y)        name##_SPLAY_INSERT(x, y)
 284 #define SPLAY_REMOVE(name, x, y)        name##_SPLAY_REMOVE(x, y)
 285 #define SPLAY_FIND(name, x, y)          name##_SPLAY_FIND(x, y)
 286 #define SPLAY_NEXT(name, x, y)          name##_SPLAY_NEXT(x, y)
 287 #define SPLAY_MIN(name, x)              (SPLAY_EMPTY(x) ? NULL  \
 288                                         : name##_SPLAY_MIN_MAX(x, SPLAY_NEGINF))
 289 #define SPLAY_MAX(name, x)              (SPLAY_EMPTY(x) ? NULL  \
 290                                         : name##_SPLAY_MIN_MAX(x, SPLAY_INF))
 291
 292 #define SPLAY_FOREACH(x, name, head)                                    \
 293         for ((x) = SPLAY_MIN(name, head);                               \
 294              (x) != NULL;                                               \
 295              (x) = SPLAY_NEXT(name, head, x))
 296
 297 /* Macros that define a red-black tree */
 298 #define RB_HEAD(name, type)                                             \
 299 struct name {                                                           \
 300         struct type *rbh_root; /* root of the tree */                   \
 301 }
 302
 303 #define RB_INITIALIZER(root)                                            \
 304         { NULL }
 305
 306 #define RB_INIT(root) do {                                              \
 307         (root)->rbh_root = NULL;                                        \
 308 } while (/*CONSTCOND*/ 0)
 309
 310 #define RB_BLACK        0
 311 #define RB_RED          1
 312 #define RB_ENTRY(type)                                                  \
 313 struct {                                                                \
 314         struct type *rbe_left;          /* left element */              \
 315         struct type *rbe_right;         /* right element */             \
 316         struct type *rbe_parent;        /* parent element */            \
 317         int rbe_color;                  /* node color */                \
 318 }
 319
 320 #define RB_LEFT(elm, field)             (elm)->field.rbe_left
 321 #define RB_RIGHT(elm, field)            (elm)->field.rbe_right
 322 #define RB_PARENT(elm, field)           (elm)->field.rbe_parent
 323 #define RB_COLOR(elm, field)            (elm)->field.rbe_color
 324 #define RB_ROOT(head)                   (head)->rbh_root
 325 #define RB_EMPTY(head)                  (RB_ROOT(head) == NULL)
 326
 327 #define RB_SET(elm, parent, field) do {                                 \
 328         RB_PARENT(elm, field) = parent;                                 \
 329         RB_LEFT(elm, field) = RB_RIGHT(elm, field) = NULL;              \
 330         RB_COLOR(elm, field) = RB_RED;                                  \
 331 } while (/*CONSTCOND*/ 0)
 332
 333 #define RB_SET_BLACKRED(black, red, field) do {                         \
 334         RB_COLOR(black, field) = RB_BLACK;                              \
 335         RB_COLOR(red, field) = RB_RED;                                  \
 336 } while (/*CONSTCOND*/ 0)
 337
 338 /*
 339  * Something to be invoked in a loop at the root of every modified subtree,
 340  * from the bottom up to the root, to update augmented node data.
 341  */
 342 #ifndef RB_AUGMENT
 343 #define RB_AUGMENT(x)   break
 344 #endif
 345
 346 #define RB_ROTATE_LEFT(head, elm, tmp, field) do {                      \
 347         (tmp) = RB_RIGHT(elm, field);                                   \
 348         if ((RB_RIGHT(elm, field) = RB_LEFT(tmp, field)) != NULL) {     \
 349                 RB_PARENT(RB_LEFT(tmp, field), field) = (elm);          \
 350         }                                                               \
 351         if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) {  \
 352                 if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))     \
 353                         RB_LEFT(RB_PARENT(elm, field), field) = (tmp);  \
 354                 else                                                    \
 355                         RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \
 356         } else                                                          \
 357                 (head)->rbh_root = (tmp);                               \
 358         RB_LEFT(tmp, field) = (elm);                                    \
 359         RB_PARENT(elm, field) = (tmp);                                  \
 360         RB_AUGMENT(elm);                                                \
 361 } while (/*CONSTCOND*/ 0)
 362
 363 #define RB_ROTATE_RIGHT(head, elm, tmp, field) do {                     \
 364         (tmp) = RB_LEFT(elm, field);                                    \
 365         if ((RB_LEFT(elm, field) = RB_RIGHT(tmp, field)) != NULL) {     \
 366                 RB_PARENT(RB_RIGHT(tmp, field), field) = (elm);         \
 367         }                                                               \
 368         if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) {  \
 369                 if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))     \
 370                         RB_LEFT(RB_PARENT(elm, field), field) = (tmp);  \
 371                 else                                                    \
 372                         RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \
 373         } else                                                          \
 374                 (head)->rbh_root = (tmp);                               \
 375         RB_RIGHT(tmp, field) = (elm);                                   \
 376         RB_PARENT(elm, field) = (tmp);                                  \
 377         RB_AUGMENT(elm);                                                \
 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         RB_PROTOTYPE_INSERT_COLOR(name, type, attr);                    \
 387         RB_PROTOTYPE_REMOVE_COLOR(name, type, attr);                    \
 388         RB_PROTOTYPE_INSERT(name, type, attr);                          \
 389         RB_PROTOTYPE_REMOVE(name, type, attr);                          \
 390         RB_PROTOTYPE_FIND(name, type, attr);                            \
 391         RB_PROTOTYPE_NFIND(name, type, attr);                           \
 392         RB_PROTOTYPE_NEXT(name, type, attr);                            \
 393         RB_PROTOTYPE_PREV(name, type, attr);                            \
 394         RB_PROTOTYPE_MINMAX(name, type, attr);                          \
 395         RB_PROTOTYPE_REINSERT(name, type, attr);
 396 #define RB_PROTOTYPE_INSERT_COLOR(name, type, attr)                     \
 397         attr void name##_RB_INSERT_COLOR(struct name *, struct type *)
 398 #define RB_PROTOTYPE_REMOVE_COLOR(name, type, attr)                     \
 399         attr void name##_RB_REMOVE_COLOR(struct name *, struct type *, struct type *)
 400 #define RB_PROTOTYPE_REMOVE(name, type, attr)                           \
 401         attr struct type *name##_RB_REMOVE(struct name *, struct type *)
 402 #define RB_PROTOTYPE_INSERT(name, type, attr)                           \
 403         attr struct type *name##_RB_INSERT(struct name *, struct type *)
 404 #define RB_PROTOTYPE_FIND(name, type, attr)                             \
 405         attr struct type *name##_RB_FIND(struct name *, struct type *)
 406 #define RB_PROTOTYPE_NFIND(name, type, attr)                            \
 407         attr struct type *name##_RB_NFIND(struct name *, struct type *)
 408 #define RB_PROTOTYPE_NEXT(name, type, attr)                             \
 409         attr struct type *name##_RB_NEXT(struct type *)
 410 #define RB_PROTOTYPE_PREV(name, type, attr)                             \
 411         attr struct type *name##_RB_PREV(struct type *)
 412 #define RB_PROTOTYPE_MINMAX(name, type, attr)                           \
 413         attr struct type *name##_RB_MINMAX(struct name *, int)
 414 #define RB_PROTOTYPE_REINSERT(name, type, attr)                 \
 415         attr struct type *name##_RB_REINSERT(struct name *, struct type *)
 416
 417 /* Main rb operation.
 418  * Moves node close to the key of elm to top
 419  */
 420 #define RB_GENERATE(name, type, field, cmp)                             \
 421         RB_GENERATE_INTERNAL(name, type, field, cmp,)
 422 #define RB_GENERATE_STATIC(name, type, field, cmp)                      \
 423         RB_GENERATE_INTERNAL(name, type, field, cmp, __unused static)
 424 #define RB_GENERATE_INTERNAL(name, type, field, cmp, attr)              \
 425         RB_GENERATE_INSERT_COLOR(name, type, field, attr)               \
 426         RB_GENERATE_REMOVE_COLOR(name, type, field, attr)               \
 427         RB_GENERATE_INSERT(name, type, field, cmp, attr)                \
 428         RB_GENERATE_REMOVE(name, type, field, attr)                     \
 429         RB_GENERATE_FIND(name, type, field, cmp, attr)                  \
 430         RB_GENERATE_NFIND(name, type, field, cmp, attr)                 \
 431         RB_GENERATE_NEXT(name, type, field, attr)                       \
 432         RB_GENERATE_PREV(name, type, field, attr)                       \
 433         RB_GENERATE_MINMAX(name, type, field, attr)                     \
 434         RB_GENERATE_REINSERT(name, type, field, cmp, attr)
 435
 436
 437 #define RB_GENERATE_INSERT_COLOR(name, type, field, attr)               \
 438 attr void                                                               \
 439 name##_RB_INSERT_COLOR(struct name *head, struct type *elm)             \
 440 {                                                                       \
 441         struct type *parent, *gparent, *tmp;                            \
 442         while ((parent = RB_PARENT(elm, field)) != NULL &&              \
 443             RB_COLOR(parent, field) == RB_RED) {                        \
 444                 gparent = RB_PARENT(parent, field);                     \
 445                 if (parent == RB_LEFT(gparent, field)) {                \
 446                         tmp = RB_RIGHT(gparent, field);                 \
 447                         if (tmp && RB_COLOR(tmp, field) == RB_RED) {    \
 448                                 RB_COLOR(tmp, field) = RB_BLACK;        \
 449                                 RB_SET_BLACKRED(parent, gparent, field);\
 450                                 elm = gparent;                          \
 451                                 continue;                               \
 452                         }                                               \
 453                         if (RB_RIGHT(parent, field) == elm) {           \
 454                                 RB_ROTATE_LEFT(head, parent, tmp, field);\
 455                                 tmp = parent;                           \
 456                                 parent = elm;                           \
 457                                 elm = tmp;                              \
 458                         }                                               \
 459                         RB_SET_BLACKRED(parent, gparent, field);        \
 460                         RB_ROTATE_RIGHT(head, gparent, tmp, field);     \
 461                 } else {                                                \
 462                         tmp = RB_LEFT(gparent, field);                  \
 463                         if (tmp && RB_COLOR(tmp, field) == RB_RED) {    \
 464                                 RB_COLOR(tmp, field) = RB_BLACK;        \
 465                                 RB_SET_BLACKRED(parent, gparent, field);\
 466                                 elm = gparent;                          \
 467                                 continue;                               \
 468                         }                                               \
 469                         if (RB_LEFT(parent, field) == elm) {            \
 470                                 RB_ROTATE_RIGHT(head, parent, tmp, field);\
 471                                 tmp = parent;                           \
 472                                 parent = elm;                           \
 473                                 elm = tmp;                              \
 474                         }                                               \
 475                         RB_SET_BLACKRED(parent, gparent, field);        \
 476                         RB_ROTATE_LEFT(head, gparent, tmp, field);      \
 477                 }                                                       \
 478         }                                                               \
 479         RB_COLOR(head->rbh_root, field) = RB_BLACK;                     \
 480 }
 481
 482 #define RB_GENERATE_REMOVE_COLOR(name, type, field, attr)               \
 483 attr void                                                               \
 484 name##_RB_REMOVE_COLOR(struct name *head, struct type *parent, struct type *elm) \
 485 {                                                                       \
 486         struct type *tmp;                                               \
 487         while ((elm == NULL || RB_COLOR(elm, field) == RB_BLACK) &&     \
 488             elm != RB_ROOT(head)) {                                     \
 489                 if (RB_LEFT(parent, field) == elm) {                    \
 490                         tmp = RB_RIGHT(parent, field);                  \
 491                         if (RB_COLOR(tmp, field) == RB_RED) {           \
 492                                 RB_SET_BLACKRED(tmp, parent, field);    \
 493                                 RB_ROTATE_LEFT(head, parent, tmp, field);\
 494                                 tmp = RB_RIGHT(parent, field);          \
 495                         }                                               \
 496                         if ((RB_LEFT(tmp, field) == NULL ||             \
 497                             RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
 498                             (RB_RIGHT(tmp, field) == NULL ||            \
 499                             RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
 500                                 RB_COLOR(tmp, field) = RB_RED;          \
 501                                 elm = parent;                           \
 502                                 parent = RB_PARENT(elm, field);         \
 503                         } else {                                        \
 504                                 if (RB_RIGHT(tmp, field) == NULL ||     \
 505                                     RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK) {\
 506                                         struct type *oleft;             \
 507                                         if ((oleft = RB_LEFT(tmp, field)) \
 508                                             != NULL)                    \
 509                                                 RB_COLOR(oleft, field) = RB_BLACK;\
 510                                         RB_COLOR(tmp, field) = RB_RED;  \
 511                                         RB_ROTATE_RIGHT(head, tmp, oleft, field);\
 512                                         tmp = RB_RIGHT(parent, field);  \
 513                                 }                                       \
 514                                 RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
 515                                 RB_COLOR(parent, field) = RB_BLACK;     \
 516                                 if (RB_RIGHT(tmp, field))               \
 517                                         RB_COLOR(RB_RIGHT(tmp, field), field) = RB_BLACK;\
 518                                 RB_ROTATE_LEFT(head, parent, tmp, field);\
 519                                 elm = RB_ROOT(head);                    \
 520                                 break;                                  \
 521                         }                                               \
 522                 } else {                                                \
 523                         tmp = RB_LEFT(parent, field);                   \
 524                         if (RB_COLOR(tmp, field) == RB_RED) {           \
 525                                 RB_SET_BLACKRED(tmp, parent, field);    \
 526                                 RB_ROTATE_RIGHT(head, parent, tmp, field);\
 527                                 tmp = RB_LEFT(parent, field);           \
 528                         }                                               \
 529                         if ((RB_LEFT(tmp, field) == NULL ||             \
 530                             RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
 531                             (RB_RIGHT(tmp, field) == NULL ||            \
 532                             RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
 533                                 RB_COLOR(tmp, field) = RB_RED;          \
 534                                 elm = parent;                           \
 535                                 parent = RB_PARENT(elm, field);         \
 536                         } else {                                        \
 537                                 if (RB_LEFT(tmp, field) == NULL ||      \
 538                                     RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) {\
 539                                         struct type *oright;            \
 540                                         if ((oright = RB_RIGHT(tmp, field)) \
 541                                             != NULL)                    \
 542                                                 RB_COLOR(oright, field) = RB_BLACK;\
 543                                         RB_COLOR(tmp, field) = RB_RED;  \
 544                                         RB_ROTATE_LEFT(head, tmp, oright, field);\
 545                                         tmp = RB_LEFT(parent, field);   \
 546                                 }                                       \
 547                                 RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
 548                                 RB_COLOR(parent, field) = RB_BLACK;     \
 549                                 if (RB_LEFT(tmp, field))                \
 550                                         RB_COLOR(RB_LEFT(tmp, field), field) = RB_BLACK;\
 551                                 RB_ROTATE_RIGHT(head, parent, tmp, field);\
 552                                 elm = RB_ROOT(head);                    \
 553                                 break;                                  \
 554                         }                                               \
 555                 }                                                       \
 556         }                                                               \
 557         if (elm)                                                        \
 558                 RB_COLOR(elm, field) = RB_BLACK;                        \
 559 }
 560
 561 #define RB_GENERATE_REMOVE(name, type, field, attr)                     \
 562 attr struct type *                                                      \
 563 name##_RB_REMOVE(struct name *head, struct type *elm)                   \
 564 {                                                                       \
 565         struct type *child, *parent, *old = elm;                        \
 566         int color;                                                      \
 567         if (RB_LEFT(elm, field) == NULL)                                \
 568                 child = RB_RIGHT(elm, field);                           \
 569         else if (RB_RIGHT(elm, field) == NULL)                          \
 570                 child = RB_LEFT(elm, field);                            \
 571         else {                                                          \
 572                 elm = RB_RIGHT(old, field);                             \
 573                 if ((child = RB_LEFT(elm, field)) == NULL) {            \
 574                         child = RB_RIGHT(elm, field);                   \
 575                         RB_RIGHT(old, field) = child;                   \
 576                         RB_PARENT(elm, field) = elm;                    \
 577                 } else {                                                \
 578                         do                                              \
 579                                 elm = child;                            \
 580                         while ((child = RB_LEFT(elm, field)) != NULL);  \
 581                         child = RB_RIGHT(elm, field);                   \
 582                         RB_PARENT(RB_RIGHT(old, field), field) = elm;   \
 583                 }                                                       \
 584                 RB_PARENT(RB_LEFT(old, field), field) = elm;            \
 585                 parent = RB_PARENT(old, field);                         \
 586                 if (parent != NULL) {                                   \
 587                         if (RB_LEFT(parent, field) == old)              \
 588                                 RB_LEFT(parent, field) = elm;           \
 589                         else                                            \
 590                                 RB_RIGHT(parent, field) = elm;          \
 591                 } else                                                  \
 592                         RB_ROOT(head) = elm;                            \
 593         }                                                               \
 594         parent = RB_PARENT(elm, field);                                 \
 595         color = RB_COLOR(elm, field);                                   \
 596         if (child != NULL)                                              \
 597                 RB_PARENT(child, field) = parent;                       \
 598         if (parent != NULL) {                                           \
 599                 if (RB_LEFT(parent, field) == elm)                      \
 600                         RB_LEFT(parent, field) = child;                 \
 601                 else                                                    \
 602                         RB_RIGHT(parent, field) = child;                \
 603         } else                                                          \
 604                 RB_ROOT(head) = child;                                  \
 605         if (elm != old)                                                 \
 606                 (elm)->field = (old)->field;                            \
 607         if (color == RB_BLACK)                                          \
 608                 name##_RB_REMOVE_COLOR(head, parent, child);            \
 609         while (parent != NULL) {                                        \
 610                 RB_AUGMENT(parent);                                     \
 611                 parent = RB_PARENT(parent, field);                      \
 612         }                                                               \
 613         return (old);                                                   \
 614 }
 615
 616 #define RB_GENERATE_INSERT(name, type, field, cmp, attr)                \
 617 /* Inserts a node into the RB tree */                                   \
 618 attr struct type *                                                      \
 619 name##_RB_INSERT(struct name *head, struct type *elm)                   \
 620 {                                                                       \
 621         struct type *tmp;                                               \
 622         struct type *parent = NULL;                                     \
 623         int comp = 0;                                                   \
 624         tmp = RB_ROOT(head);                                            \
 625         while (tmp) {                                                   \
 626                 parent = tmp;                                           \
 627                 comp = (cmp)(elm, parent);                              \
 628                 if (comp < 0)                                           \
 629                         tmp = RB_LEFT(tmp, field);                      \
 630                 else if (comp > 0)                                      \
 631                         tmp = RB_RIGHT(tmp, field);                     \
 632                 else                                                    \
 633                         return (tmp);                                   \
 634         }                                                               \
 635         RB_SET(elm, parent, field);                                     \
 636         if (parent != NULL) {                                           \
 637                 if (comp < 0)                                           \
 638                         RB_LEFT(parent, field) = elm;                   \
 639                 else                                                    \
 640                         RB_RIGHT(parent, field) = elm;                  \
 641         } else                                                          \
 642                 RB_ROOT(head) = elm;                                    \
 643         name##_RB_INSERT_COLOR(head, elm);                              \
 644         while (elm != NULL) {                                           \
 645                 RB_AUGMENT(elm);                                        \
 646                 elm = RB_PARENT(elm, field);                            \
 647         }                                                               \
 648         return (NULL);                                                  \
 649 }
 650
 651 #define RB_GENERATE_FIND(name, type, field, cmp, attr)                  \
 652 /* Finds the node with the same key as elm */                           \
 653 attr struct type *                                                      \
 654 name##_RB_FIND(struct name *head, struct type *elm)                     \
 655 {                                                                       \
 656         struct type *tmp = RB_ROOT(head);                               \
 657         int comp;                                                       \
 658         while (tmp) {                                                   \
 659                 comp = cmp(elm, tmp);                                   \
 660                 if (comp < 0)                                           \
 661                         tmp = RB_LEFT(tmp, field);                      \
 662                 else if (comp > 0)                                      \
 663                         tmp = RB_RIGHT(tmp, field);                     \
 664                 else                                                    \
 665                         return (tmp);                                   \
 666         }                                                               \
 667         return (NULL);                                                  \
 668 }
 669
 670 #define RB_GENERATE_NFIND(name, type, field, cmp, attr)                 \
 671 /* Finds the first node greater than or equal to the search key */      \
 672 attr struct type *                                                      \
 673 name##_RB_NFIND(struct name *head, struct type *elm)                    \
 674 {                                                                       \
 675         struct type *tmp = RB_ROOT(head);                               \
 676         struct type *res = NULL;                                        \
 677         int comp;                                                       \
 678         while (tmp) {                                                   \
 679                 comp = cmp(elm, tmp);                                   \
 680                 if (comp < 0) {                                         \
 681                         res = tmp;                                      \
 682                         tmp = RB_LEFT(tmp, field);                      \
 683                 }                                                       \
 684                 else if (comp > 0)                                      \
 685                         tmp = RB_RIGHT(tmp, field);                     \
 686                 else                                                    \
 687                         return (tmp);                                   \
 688         }                                                               \
 689         return (res);                                                   \
 690 }
 691
 692 #define RB_GENERATE_NEXT(name, type, field, attr)                       \
 693 /* ARGSUSED */                                                          \
 694 attr struct type *                                                      \
 695 name##_RB_NEXT(struct type *elm)                                        \
 696 {                                                                       \
 697         if (RB_RIGHT(elm, field)) {                                     \
 698                 elm = RB_RIGHT(elm, field);                             \
 699                 while (RB_LEFT(elm, field))                             \
 700                         elm = RB_LEFT(elm, field);                      \
 701         } else {                                                        \
 702                 if (RB_PARENT(elm, field) &&                            \
 703                     (elm == RB_LEFT(RB_PARENT(elm, field), field)))     \
 704                         elm = RB_PARENT(elm, field);                    \
 705                 else {                                                  \
 706                         while (RB_PARENT(elm, field) &&                 \
 707                             (elm == RB_RIGHT(RB_PARENT(elm, field), field)))\
 708                                 elm = RB_PARENT(elm, field);            \
 709                         elm = RB_PARENT(elm, field);                    \
 710                 }                                                       \
 711         }                                                               \
 712         return (elm);                                                   \
 713 }
 714
 715 #define RB_GENERATE_PREV(name, type, field, attr)                       \
 716 /* ARGSUSED */                                                          \
 717 attr struct type *                                                      \
 718 name##_RB_PREV(struct type *elm)                                        \
 719 {                                                                       \
 720         if (RB_LEFT(elm, field)) {                                      \
 721                 elm = RB_LEFT(elm, field);                              \
 722                 while (RB_RIGHT(elm, field))                            \
 723                         elm = RB_RIGHT(elm, field);                     \
 724         } else {                                                        \
 725                 if (RB_PARENT(elm, field) &&                            \
 726                     (elm == RB_RIGHT(RB_PARENT(elm, field), field)))    \
 727                         elm = RB_PARENT(elm, field);                    \
 728                 else {                                                  \
 729                         while (RB_PARENT(elm, field) &&                 \
 730                             (elm == RB_LEFT(RB_PARENT(elm, field), field)))\
 731                                 elm = RB_PARENT(elm, field);            \
 732                         elm = RB_PARENT(elm, field);                    \
 733                 }                                                       \
 734         }                                                               \
 735         return (elm);                                                   \
 736 }
 737
 738 #define RB_GENERATE_MINMAX(name, type, field, attr)                     \
 739 attr struct type *                                                      \
 740 name##_RB_MINMAX(struct name *head, int val)                            \
 741 {                                                                       \
 742         struct type *tmp = RB_ROOT(head);                               \
 743         struct type *parent = NULL;                                     \
 744         while (tmp) {                                                   \
 745                 parent = tmp;                                           \
 746                 if (val < 0)                                            \
 747                         tmp = RB_LEFT(tmp, field);                      \
 748                 else                                                    \
 749                         tmp = RB_RIGHT(tmp, field);                     \
 750         }                                                               \
 751         return (parent);                                                \
 752 }
 753
 754 #define RB_GENERATE_REINSERT(name, type, field, cmp, attr)              \
 755 attr struct type *                                                      \
 756 name##_RB_REINSERT(struct name *head, struct type *elm)                 \
 757 {                                                                       \
 758         struct type *cmpelm;                                            \
 759         if (((cmpelm = RB_PREV(name, head, elm)) != NULL &&             \
 760             cmp(cmpelm, elm) >= 0) ||                                   \
 761             ((cmpelm = RB_NEXT(name, head, elm)) != NULL &&             \
 762             cmp(elm, cmpelm) >= 0)) {                                   \
 763                 /* XXXLAS: Remove/insert is heavy handed. */            \
 764                 RB_REMOVE(name, head, elm);                             \
 765                 return (RB_INSERT(name, head, elm));                    \
 766         }                                                               \
 767         return (NULL);                                                  \
 768 }                                                                       \
 769
 770 #define RB_NEGINF       -1
 771 #define RB_INF  1
 772
 773 #define RB_INSERT(name, x, y)   name##_RB_INSERT(x, y)
 774 #define RB_REMOVE(name, x, y)   name##_RB_REMOVE(x, y)
 775 #define RB_FIND(name, x, y)     name##_RB_FIND(x, y)
 776 #define RB_NFIND(name, x, y)    name##_RB_NFIND(x, y)
 777 #define RB_NEXT(name, x, y)     name##_RB_NEXT(y)
 778 #define RB_PREV(name, x, y)     name##_RB_PREV(y)
 779 #define RB_MIN(name, x)         name##_RB_MINMAX(x, RB_NEGINF)
 780 #define RB_MAX(name, x)         name##_RB_MINMAX(x, RB_INF)
 781 #define RB_REINSERT(name, x, y) name##_RB_REINSERT(x, y)
 782
 783 #define RB_FOREACH(x, name, head)                                       \
 784         for ((x) = RB_MIN(name, head);                                  \
 785              (x) != NULL;                                               \
 786              (x) = name##_RB_NEXT(x))
 787
 788 #define RB_FOREACH_FROM(x, name, y)                                     \
 789         for ((x) = (y);                                                 \
 790             ((x) != NULL) && ((y) = name##_RB_NEXT(x), (x) != NULL);    \
 791              (x) = (y))
 792
 793 #define RB_FOREACH_SAFE(x, name, head, y)                               \
 794         for ((x) = RB_MIN(name, head);                                  \
 795             ((x) != NULL) && ((y) = name##_RB_NEXT(x), (x) != NULL);    \
 796              (x) = (y))
 797
 798 #define RB_FOREACH_REVERSE(x, name, head)                               \
 799         for ((x) = RB_MAX(name, head);                                  \
 800              (x) != NULL;                                               \
 801              (x) = name##_RB_PREV(x))
 802
 803 #define RB_FOREACH_REVERSE_FROM(x, name, y)                             \
 804         for ((x) = (y);                                                 \
 805             ((x) != NULL) && ((y) = name##_RB_PREV(x), (x) != NULL);    \
 806              (x) = (y))
 807
 808 #define RB_FOREACH_REVERSE_SAFE(x, name, head, y)                       \
 809         for ((x) = RB_MAX(name, head);                                  \
 810             ((x) != NULL) && ((y) = name##_RB_PREV(x), (x) != NULL);    \
 811              (x) = (y))
 812
 813 #endif  /* _SYS_TREE_H_ */