sys/sys/tree.h

   1 /*      $NetBSD: tree.h,v 1.8 2004/03/28 19:38:30 provos Exp $  */
   2 /*      $OpenBSD: tree.h,v 1.7 2002/10/17 21:51:54 art Exp $    */
   3 /*      $DragonFly: src/sys/sys/tree.h,v 1.11 2008/01/07 01:22:30 corecode Exp $ */
   4 /*
   5  * Copyright 2002 Niels Provos <provos@citi.umich.edu>
   6  * All rights reserved.
   7  *
   8  * Redistribution and use in source and binary forms, with or without
   9  * modification, are permitted provided that the following conditions
  10  * are met:
  11  * 1. Redistributions of source code must retain the above copyright
  12  *    notice, this list of conditions and the following disclaimer.
  13  * 2. Redistributions in binary form must reproduce the above copyright
  14  *    notice, this list of conditions and the following disclaimer in the
  15  *    documentation and/or other materials provided with the distribution.
  16  *
  17  * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
  18  * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
  19  * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
  20  * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
  21  * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
  22  * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
  23  * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
  24  * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
  25  * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
  26  * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
  27  */
  28
  29 #ifndef _SYS_TREE_H_
  30 #define _SYS_TREE_H_
  31
  32 #ifndef _SYS_SPINLOCK_H_
  33 #include <sys/spinlock.h>
  34 #endif
  35
  36 void rb_spin_lock(struct spinlock *spin);
  37 void rb_spin_unlock(struct spinlock *spin);
  38
  39 /*
  40  * This file defines data structures for different types of trees:
  41  * splay trees and red-black trees.
  42  *
  43  * A splay tree is a self-organizing data structure.  Every operation
  44  * on the tree causes a splay to happen.  The splay moves the requested
  45  * node to the root of the tree and partly rebalances it.
  46  *
  47  * This has the benefit that request locality causes faster lookups as
  48  * the requested nodes move to the top of the tree.  On the other hand,
  49  * every lookup causes memory writes.
  50  *
  51  * The Balance Theorem bounds the total access time for m operations
  52  * and n inserts on an initially empty tree as O((m + n)lg n).  The
  53  * amortized cost for a sequence of m accesses to a splay tree is O(lg n);
  54  *
  55  * A red-black tree is a binary search tree with the node color as an
  56  * extra attribute.  It fulfills a set of conditions:
  57  *      - every search path from the root to a leaf consists of the
  58  *        same number of black nodes,
  59  *      - each red node (except for the root) has a black parent,
  60  *      - each leaf node is black.
  61  *
  62  * Every operation on a red-black tree is bounded as O(lg n).
  63  * The maximum height of a red-black tree is 2lg (n+1).
  64  */
  65
  66 #define SPLAY_HEAD(name, type)                                          \
  67 struct name {                                                           \
  68         struct type *sph_root; /* root of the tree */                   \
  69 }
  70
  71 #define SPLAY_INITIALIZER(root)                                         \
  72         { NULL }
  73
  74 #define SPLAY_INIT(root) do {                                           \
  75         (root)->sph_root = NULL;                                        \
  76 } while (/*CONSTCOND*/ 0)
  77
  78 #define SPLAY_ENTRY(type)                                               \
  79 struct {                                                                \
  80         struct type *spe_left; /* left element */                       \
  81         struct type *spe_right; /* right element */                     \
  82 }
  83
  84 #define SPLAY_LEFT(elm, field)          (elm)->field.spe_left
  85 #define SPLAY_RIGHT(elm, field)         (elm)->field.spe_right
  86 #define SPLAY_ROOT(head)                (head)->sph_root
  87 #define SPLAY_EMPTY(head)               (SPLAY_ROOT(head) == NULL)
  88
  89 /* SPLAY_ROTATE_{LEFT,RIGHT} expect that tmp hold SPLAY_{RIGHT,LEFT} */
  90 #define SPLAY_ROTATE_RIGHT(head, tmp, field) do {                       \
  91         SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(tmp, field);  \
  92         SPLAY_RIGHT(tmp, field) = (head)->sph_root;                     \
  93         (head)->sph_root = tmp;                                         \
  94 } while (/*CONSTCOND*/ 0)
  95
  96 #define SPLAY_ROTATE_LEFT(head, tmp, field) do {                        \
  97         SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(tmp, field);  \
  98         SPLAY_LEFT(tmp, field) = (head)->sph_root;                      \
  99         (head)->sph_root = tmp;                                         \
 100 } while (/*CONSTCOND*/ 0)
 101
 102 #define SPLAY_LINKLEFT(head, tmp, field) do {                           \
 103         SPLAY_LEFT(tmp, field) = (head)->sph_root;                      \
 104         tmp = (head)->sph_root;                                         \
 105         (head)->sph_root = SPLAY_LEFT((head)->sph_root, field);         \
 106 } while (/*CONSTCOND*/ 0)
 107
 108 #define SPLAY_LINKRIGHT(head, tmp, field) do {                          \
 109         SPLAY_RIGHT(tmp, field) = (head)->sph_root;                     \
 110         tmp = (head)->sph_root;                                         \
 111         (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);        \
 112 } while (/*CONSTCOND*/ 0)
 113
 114 #define SPLAY_ASSEMBLE(head, node, left, right, field) do {             \
 115         SPLAY_RIGHT(left, field) = SPLAY_LEFT((head)->sph_root, field); \
 116         SPLAY_LEFT(right, field) = SPLAY_RIGHT((head)->sph_root, field);\
 117         SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(node, field); \
 118         SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(node, field); \
 119 } while (/*CONSTCOND*/ 0)
 120
 121 /* Generates prototypes and inline functions */
 122
 123 #define SPLAY_PROTOTYPE(name, type, field, cmp)                         \
 124 void name##_SPLAY(struct name *, struct type *);                        \
 125 void name##_SPLAY_MINMAX(struct name *, int);                           \
 126 struct type *name##_SPLAY_INSERT(struct name *, struct type *);         \
 127 struct type *name##_SPLAY_REMOVE(struct name *, struct type *);         \
 128                                                                         \
 129 /* Finds the node with the same key as elm */                           \
 130 static __inline struct type *                                           \
 131 name##_SPLAY_FIND(struct name *head, struct type *elm)                  \
 132 {                                                                       \
 133         if (SPLAY_EMPTY(head))                                          \
 134                 return(NULL);                                           \
 135         name##_SPLAY(head, elm);                                        \
 136         if ((cmp)(elm, (head)->sph_root) == 0)                          \
 137                 return (head->sph_root);                                \
 138         return (NULL);                                                  \
 139 }                                                                       \
 140                                                                         \
 141 static __inline struct type *                                           \
 142 name##_SPLAY_NEXT(struct name *head, struct type *elm)                  \
 143 {                                                                       \
 144         name##_SPLAY(head, elm);                                        \
 145         if (SPLAY_RIGHT(elm, field) != NULL) {                          \
 146                 elm = SPLAY_RIGHT(elm, field);                          \
 147                 while (SPLAY_LEFT(elm, field) != NULL) {                \
 148                         elm = SPLAY_LEFT(elm, field);                   \
 149                 }                                                       \
 150         } else                                                          \
 151                 elm = NULL;                                             \
 152         return (elm);                                                   \
 153 }                                                                       \
 154                                                                         \
 155 static __inline struct type *                                           \
 156 name##_SPLAY_MIN_MAX(struct name *head, int val)                        \
 157 {                                                                       \
 158         name##_SPLAY_MINMAX(head, val);                                 \
 159         return (SPLAY_ROOT(head));                                      \
 160 }
 161
 162 /* Main splay operation.
 163  * Moves node close to the key of elm to top
 164  */
 165 #define SPLAY_GENERATE(name, type, field, cmp)                          \
 166 struct type *                                                           \
 167 name##_SPLAY_INSERT(struct name *head, struct type *elm)                \
 168 {                                                                       \
 169     if (SPLAY_EMPTY(head)) {                                            \
 170             SPLAY_LEFT(elm, field) = SPLAY_RIGHT(elm, field) = NULL;    \
 171     } else {                                                            \
 172             int __comp;                                                 \
 173             name##_SPLAY(head, elm);                                    \
 174             __comp = (cmp)(elm, (head)->sph_root);                      \
 175             if(__comp < 0) {                                            \
 176                     SPLAY_LEFT(elm, field) = SPLAY_LEFT((head)->sph_root, field);\
 177                     SPLAY_RIGHT(elm, field) = (head)->sph_root;         \
 178                     SPLAY_LEFT((head)->sph_root, field) = NULL;         \
 179             } else if (__comp > 0) {                                    \
 180                     SPLAY_RIGHT(elm, field) = SPLAY_RIGHT((head)->sph_root, field);\
 181                     SPLAY_LEFT(elm, field) = (head)->sph_root;          \
 182                     SPLAY_RIGHT((head)->sph_root, field) = NULL;        \
 183             } else                                                      \
 184                     return ((head)->sph_root);                          \
 185     }                                                                   \
 186     (head)->sph_root = (elm);                                           \
 187     return (NULL);                                                      \
 188 }                                                                       \
 189                                                                         \
 190 struct type *                                                           \
 191 name##_SPLAY_REMOVE(struct name *head, struct type *elm)                \
 192 {                                                                       \
 193         struct type *__tmp;                                             \
 194         if (SPLAY_EMPTY(head))                                          \
 195                 return (NULL);                                          \
 196         name##_SPLAY(head, elm);                                        \
 197         if ((cmp)(elm, (head)->sph_root) == 0) {                        \
 198                 if (SPLAY_LEFT((head)->sph_root, field) == NULL) {      \
 199                         (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);\
 200                 } else {                                                \
 201                         __tmp = SPLAY_RIGHT((head)->sph_root, field);   \
 202                         (head)->sph_root = SPLAY_LEFT((head)->sph_root, field);\
 203                         name##_SPLAY(head, elm);                        \
 204                         SPLAY_RIGHT((head)->sph_root, field) = __tmp;   \
 205                 }                                                       \
 206                 return (elm);                                           \
 207         }                                                               \
 208         return (NULL);                                                  \
 209 }                                                                       \
 210                                                                         \
 211 void                                                                    \
 212 name##_SPLAY(struct name *head, struct type *elm)                       \
 213 {                                                                       \
 214         struct type __node, *__left, *__right, *__tmp;                  \
 215         int __comp;                                                     \
 216 \
 217         SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
 218         __left = __right = &__node;                                     \
 219 \
 220         while ((__comp = (cmp)(elm, (head)->sph_root)) != 0) {          \
 221                 if (__comp < 0) {                                       \
 222                         __tmp = SPLAY_LEFT((head)->sph_root, field);    \
 223                         if (__tmp == NULL)                              \
 224                                 break;                                  \
 225                         if ((cmp)(elm, __tmp) < 0){                     \
 226                                 SPLAY_ROTATE_RIGHT(head, __tmp, field); \
 227                                 if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
 228                                         break;                          \
 229                         }                                               \
 230                         SPLAY_LINKLEFT(head, __right, field);           \
 231                 } else if (__comp > 0) {                                \
 232                         __tmp = SPLAY_RIGHT((head)->sph_root, field);   \
 233                         if (__tmp == NULL)                              \
 234                                 break;                                  \
 235                         if ((cmp)(elm, __tmp) > 0){                     \
 236                                 SPLAY_ROTATE_LEFT(head, __tmp, field);  \
 237                                 if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
 238                                         break;                          \
 239                         }                                               \
 240                         SPLAY_LINKRIGHT(head, __left, field);           \
 241                 }                                                       \
 242         }                                                               \
 243         SPLAY_ASSEMBLE(head, &__node, __left, __right, field);          \
 244 }                                                                       \
 245                                                                         \
 246 /* Splay with either the minimum or the maximum element                 \
 247  * Used to find minimum or maximum element in tree.                     \
 248  */                                                                     \
 249 void name##_SPLAY_MINMAX(struct name *head, int __comp) \
 250 {                                                                       \
 251         struct type __node, *__left, *__right, *__tmp;                  \
 252 \
 253         SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
 254         __left = __right = &__node;                                     \
 255 \
 256         while (1) {                                                     \
 257                 if (__comp < 0) {                                       \
 258                         __tmp = SPLAY_LEFT((head)->sph_root, field);    \
 259                         if (__tmp == NULL)                              \
 260                                 break;                                  \
 261                         if (__comp < 0){                                \
 262                                 SPLAY_ROTATE_RIGHT(head, __tmp, field); \
 263                                 if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
 264                                         break;                          \
 265                         }                                               \
 266                         SPLAY_LINKLEFT(head, __right, field);           \
 267                 } else if (__comp > 0) {                                \
 268                         __tmp = SPLAY_RIGHT((head)->sph_root, field);   \
 269                         if (__tmp == NULL)                              \
 270                                 break;                                  \
 271                         if (__comp > 0) {                               \
 272                                 SPLAY_ROTATE_LEFT(head, __tmp, field);  \
 273                                 if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
 274                                         break;                          \
 275                         }                                               \
 276                         SPLAY_LINKRIGHT(head, __left, field);           \
 277                 }                                                       \
 278         }                                                               \
 279         SPLAY_ASSEMBLE(head, &__node, __left, __right, field);          \
 280 }
 281
 282 #define SPLAY_NEGINF    -1
 283 #define SPLAY_INF       1
 284
 285 #define SPLAY_INSERT(name, x, y)        name##_SPLAY_INSERT(x, y)
 286 #define SPLAY_REMOVE(name, x, y)        name##_SPLAY_REMOVE(x, y)
 287 #define SPLAY_FIND(name, x, y)          name##_SPLAY_FIND(x, y)
 288 #define SPLAY_NEXT(name, x, y)          name##_SPLAY_NEXT(x, y)
 289 #define SPLAY_MIN(name, x)              (SPLAY_EMPTY(x) ? NULL  \
 290                                         : name##_SPLAY_MIN_MAX(x, SPLAY_NEGINF))
 291 #define SPLAY_MAX(name, x)              (SPLAY_EMPTY(x) ? NULL  \
 292                                         : name##_SPLAY_MIN_MAX(x, SPLAY_INF))
 293
 294 #define SPLAY_FOREACH(x, name, head)                                    \
 295         for ((x) = SPLAY_MIN(name, head);                               \
 296              (x) != NULL;                                               \
 297              (x) = SPLAY_NEXT(name, head, x))
 298
 299 /*
 300  * Macros that define a red-black tree
 301  */
 302
 303 #define RB_SCAN_INFO(name, type)                                        \
 304 struct name##_scan_info {                                               \
 305         struct name##_scan_info *link;                                  \
 306         struct type     *node;                                          \
 307 }
 308
 309 #define RB_HEAD(name, type)                                             \
 310 struct name {                                                           \
 311         struct type *rbh_root;               /* root of the tree */     \
 312         struct name##_scan_info *rbh_inprog; /* scans in progress */    \
 313         struct spinlock rbh_spin;                                       \
 314 }
 315
 316 #define RB_INITIALIZER(root)                                            \
 317         { NULL, NULL, SPINLOCK_INITIALIZER(root.spin) }
 318
 319 #define RB_INIT(root) do {                                              \
 320         (root)->rbh_root = NULL;                                        \
 321         (root)->rbh_inprog = NULL;                                      \
 322 } while (/*CONSTCOND*/ 0)
 323
 324 #ifdef _KERNEL
 325 #define RB_SCAN_LOCK(spin)      rb_spin_lock(spin)
 326 #define RB_SCAN_UNLOCK(spin)    rb_spin_unlock(spin)
 327 #else
 328 #define RB_SCAN_LOCK(spin)
 329 #define RB_SCAN_UNLOCK(spin)
 330 #endif
 331
 332 #define RB_BLACK        0
 333 #define RB_RED          1
 334 #define RB_ENTRY(type)                                                  \
 335 struct {                                                                \
 336         struct type *rbe_left;          /* left element */              \
 337         struct type *rbe_right;         /* right element */             \
 338         struct type *rbe_parent;        /* parent element */            \
 339         int rbe_color;                  /* node color */                \
 340 }
 341
 342 #define RB_LEFT(elm, field)             (elm)->field.rbe_left
 343 #define RB_RIGHT(elm, field)            (elm)->field.rbe_right
 344 #define RB_PARENT(elm, field)           (elm)->field.rbe_parent
 345 #define RB_COLOR(elm, field)            (elm)->field.rbe_color
 346 #define RB_ROOT(head)                   (head)->rbh_root
 347 #define RB_INPROG(head)                 (head)->rbh_inprog
 348 #define RB_EMPTY(head)                  (RB_ROOT(head) == NULL)
 349
 350 #define RB_SET(elm, parent, field) do {                                 \
 351         RB_PARENT(elm, field) = parent;                                 \
 352         RB_LEFT(elm, field) = RB_RIGHT(elm, field) = NULL;              \
 353         RB_COLOR(elm, field) = RB_RED;                                  \
 354 } while (/*CONSTCOND*/ 0)
 355
 356 #define RB_SET_BLACKRED(black, red, field) do {                         \
 357         RB_COLOR(black, field) = RB_BLACK;                              \
 358         RB_COLOR(red, field) = RB_RED;                                  \
 359 } while (/*CONSTCOND*/ 0)
 360
 361 #ifndef RB_AUGMENT
 362 #define RB_AUGMENT(x)   do {} while (0)
 363 #endif
 364
 365 #define RB_ROTATE_LEFT(head, elm, tmp, field) do {                      \
 366         (tmp) = RB_RIGHT(elm, field);                                   \
 367         if ((RB_RIGHT(elm, field) = RB_LEFT(tmp, field)) != NULL) {     \
 368                 RB_PARENT(RB_LEFT(tmp, field), field) = (elm);          \
 369         }                                                               \
 370         RB_AUGMENT(elm);                                                \
 371         if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) {  \
 372                 if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))     \
 373                         RB_LEFT(RB_PARENT(elm, field), field) = (tmp);  \
 374                 else                                                    \
 375                         RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \
 376         } else                                                          \
 377                 (head)->rbh_root = (tmp);                               \
 378         RB_LEFT(tmp, field) = (elm);                                    \
 379         RB_PARENT(elm, field) = (tmp);                                  \
 380         RB_AUGMENT(tmp);                                                \
 381         if ((RB_PARENT(tmp, field)))                                    \
 382                 RB_AUGMENT(RB_PARENT(tmp, field));                      \
 383 } while (/*CONSTCOND*/ 0)
 384
 385 #define RB_ROTATE_RIGHT(head, elm, tmp, field) do {                     \
 386         (tmp) = RB_LEFT(elm, field);                                    \
 387         if ((RB_LEFT(elm, field) = RB_RIGHT(tmp, field)) != NULL) {     \
 388                 RB_PARENT(RB_RIGHT(tmp, field), field) = (elm);         \
 389         }                                                               \
 390         RB_AUGMENT(elm);                                                \
 391         if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) {  \
 392                 if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))     \
 393                         RB_LEFT(RB_PARENT(elm, field), field) = (tmp);  \
 394                 else                                                    \
 395                         RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \
 396         } else                                                          \
 397                 (head)->rbh_root = (tmp);                               \
 398         RB_RIGHT(tmp, field) = (elm);                                   \
 399         RB_PARENT(elm, field) = (tmp);                                  \
 400         RB_AUGMENT(tmp);                                                \
 401         if ((RB_PARENT(tmp, field)))                                    \
 402                 RB_AUGMENT(RB_PARENT(tmp, field));                      \
 403 } while (/*CONSTCOND*/ 0)
 404
 405 /* Generates prototypes and inline functions */
 406 #define RB_PROTOTYPE(name, type, field, cmp)                            \
 407         _RB_PROTOTYPE(name, type, field, cmp,)
 408 #define RB_PROTOTYPE_STATIC(name, type, field, cmp)                     \
 409         _RB_PROTOTYPE(name, type, field, cmp, __unused static)
 410
 411 #define _RB_PROTOTYPE(name, type, field, cmp, STORQUAL)                 \
 412 STORQUAL struct type *name##_RB_REMOVE(struct name *, struct type *);   \
 413 STORQUAL struct type *name##_RB_INSERT(struct name *, struct type *);   \
 414 STORQUAL struct type *name##_RB_FIND(struct name *, struct type *);     \
 415 STORQUAL int name##_RB_SCAN(struct name *, int (*)(struct type *, void *),\
 416                         int (*)(struct type *, void *), void *);        \
 417 STORQUAL struct type *name##_RB_NEXT(struct type *);                    \
 418 STORQUAL struct type *name##_RB_PREV(struct type *);                    \
 419 STORQUAL struct type *name##_RB_MINMAX(struct name *, int);             \
 420 RB_SCAN_INFO(name, type)                                                \
 421
 422 /*
 423  * A version which supplies a fast lookup routine for an exact match
 424  * on a numeric field.
 425  */
 426 #define RB_PROTOTYPE2(name, type, field, cmp, datatype)                 \
 427 RB_PROTOTYPE(name, type, field, cmp);                                   \
 428 struct type *name##_RB_LOOKUP(struct name *, datatype)                  \
 429
 430 /*
 431  * A version which supplies a fast lookup routine for a numeric
 432  * field which resides within a ranged object, either using (begin,end),
 433  * or using (begin,size).
 434  */
 435 #define RB_PROTOTYPE3(name, type, field, cmp, datatype)                 \
 436 RB_PROTOTYPE2(name, type, field, cmp, datatype);                        \
 437 struct type *name##_RB_RLOOKUP(struct name *, datatype)                 \
 438
 439 #define RB_PROTOTYPE4(name, type, field, cmp, datatype)                 \
 440 RB_PROTOTYPE2(name, type, field, cmp, datatype);                        \
 441 struct type *name##_RB_RLOOKUP(struct name *, datatype)                 \
 442
 443 #define RB_PROTOTYPEX(name, ext, type, field, cmp, datatype)            \
 444 RB_PROTOTYPE(name, type, field, cmp);                                   \
 445 struct type *name##_RB_LOOKUP_##ext (struct name *, datatype)           \
 446
 447 /* Main rb operation.
 448  * Moves node close to the key of elm to top
 449  */
 450 #define RB_GENERATE(name, type, field, cmp)                             \
 451         _RB_GENERATE(name, type, field, cmp,)
 452
 453 #define RB_GENERATE_STATIC(name, type, field, cmp)                      \
 454         _RB_GENERATE(name, type, field, cmp, __unused static)
 455
 456 #define _RB_GENERATE(name, type, field, cmp, STORQUAL)                  \
 457 static void                                                             \
 458 name##_RB_INSERT_COLOR(struct name *head, struct type *elm)             \
 459 {                                                                       \
 460         struct type *parent, *gparent, *tmp;                            \
 461         while ((parent = RB_PARENT(elm, field)) != NULL &&              \
 462             RB_COLOR(parent, field) == RB_RED) {                        \
 463                 gparent = RB_PARENT(parent, field);                     \
 464                 if (parent == RB_LEFT(gparent, field)) {                \
 465                         tmp = RB_RIGHT(gparent, field);                 \
 466                         if (tmp && RB_COLOR(tmp, field) == RB_RED) {    \
 467                                 RB_COLOR(tmp, field) = RB_BLACK;        \
 468                                 RB_SET_BLACKRED(parent, gparent, field);\
 469                                 elm = gparent;                          \
 470                                 continue;                               \
 471                         }                                               \
 472                         if (RB_RIGHT(parent, field) == elm) {           \
 473                                 RB_ROTATE_LEFT(head, parent, tmp, field);\
 474                                 tmp = parent;                           \
 475                                 parent = elm;                           \
 476                                 elm = tmp;                              \
 477                         }                                               \
 478                         RB_SET_BLACKRED(parent, gparent, field);        \
 479                         RB_ROTATE_RIGHT(head, gparent, tmp, field);     \
 480                 } else {                                                \
 481                         tmp = RB_LEFT(gparent, field);                  \
 482                         if (tmp && RB_COLOR(tmp, field) == RB_RED) {    \
 483                                 RB_COLOR(tmp, field) = RB_BLACK;        \
 484                                 RB_SET_BLACKRED(parent, gparent, field);\
 485                                 elm = gparent;                          \
 486                                 continue;                               \
 487                         }                                               \
 488                         if (RB_LEFT(parent, field) == elm) {            \
 489                                 RB_ROTATE_RIGHT(head, parent, tmp, field);\
 490                                 tmp = parent;                           \
 491                                 parent = elm;                           \
 492                                 elm = tmp;                              \
 493                         }                                               \
 494                         RB_SET_BLACKRED(parent, gparent, field);        \
 495                         RB_ROTATE_LEFT(head, gparent, tmp, field);      \
 496                 }                                                       \
 497         }                                                               \
 498         RB_COLOR(head->rbh_root, field) = RB_BLACK;                     \
 499 }                                                                       \
 500                                                                         \
 501 static void                                                             \
 502 name##_RB_REMOVE_COLOR(struct name *head, struct type *parent,          \
 503                         struct type *elm)                               \
 504 {                                                                       \
 505         struct type *tmp;                                               \
 506         while ((elm == NULL || RB_COLOR(elm, field) == RB_BLACK) &&     \
 507             elm != RB_ROOT(head)) {                                     \
 508                 if (RB_LEFT(parent, field) == elm) {                    \
 509                         tmp = RB_RIGHT(parent, field);                  \
 510                         if (RB_COLOR(tmp, field) == RB_RED) {           \
 511                                 RB_SET_BLACKRED(tmp, parent, field);    \
 512                                 RB_ROTATE_LEFT(head, parent, tmp, field);\
 513                                 tmp = RB_RIGHT(parent, field);          \
 514                         }                                               \
 515                         if ((RB_LEFT(tmp, field) == NULL ||             \
 516                             RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
 517                             (RB_RIGHT(tmp, field) == NULL ||            \
 518                             RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
 519                                 RB_COLOR(tmp, field) = RB_RED;          \
 520                                 elm = parent;                           \
 521                                 parent = RB_PARENT(elm, field);         \
 522                         } else {                                        \
 523                                 if (RB_RIGHT(tmp, field) == NULL ||     \
 524                                     RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK) {\
 525                                         struct type *oleft;             \
 526                                         if ((oleft = RB_LEFT(tmp, field)) \
 527                                             != NULL)                    \
 528                                                 RB_COLOR(oleft, field) = RB_BLACK;\
 529                                         RB_COLOR(tmp, field) = RB_RED;  \
 530                                         RB_ROTATE_RIGHT(head, tmp, oleft, field);\
 531                                         tmp = RB_RIGHT(parent, field);  \
 532                                 }                                       \
 533                                 RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
 534                                 RB_COLOR(parent, field) = RB_BLACK;     \
 535                                 if (RB_RIGHT(tmp, field))               \
 536                                         RB_COLOR(RB_RIGHT(tmp, field), field) = RB_BLACK;\
 537                                 RB_ROTATE_LEFT(head, parent, tmp, field);\
 538                                 elm = RB_ROOT(head);                    \
 539                                 break;                                  \
 540                         }                                               \
 541                 } else {                                                \
 542                         tmp = RB_LEFT(parent, field);                   \
 543                         if (RB_COLOR(tmp, field) == RB_RED) {           \
 544                                 RB_SET_BLACKRED(tmp, parent, field);    \
 545                                 RB_ROTATE_RIGHT(head, parent, tmp, field);\
 546                                 tmp = RB_LEFT(parent, field);           \
 547                         }                                               \
 548                         if ((RB_LEFT(tmp, field) == NULL ||             \
 549                             RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
 550                             (RB_RIGHT(tmp, field) == NULL ||            \
 551                             RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
 552                                 RB_COLOR(tmp, field) = RB_RED;          \
 553                                 elm = parent;                           \
 554                                 parent = RB_PARENT(elm, field);         \
 555                         } else {                                        \
 556                                 if (RB_LEFT(tmp, field) == NULL ||      \
 557                                     RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) {\
 558                                         struct type *oright;            \
 559                                         if ((oright = RB_RIGHT(tmp, field)) \
 560                                             != NULL)                    \
 561                                                 RB_COLOR(oright, field) = RB_BLACK;\
 562                                         RB_COLOR(tmp, field) = RB_RED;  \
 563                                         RB_ROTATE_LEFT(head, tmp, oright, field);\
 564                                         tmp = RB_LEFT(parent, field);   \
 565                                 }                                       \
 566                                 RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
 567                                 RB_COLOR(parent, field) = RB_BLACK;     \
 568                                 if (RB_LEFT(tmp, field))                \
 569                                         RB_COLOR(RB_LEFT(tmp, field), field) = RB_BLACK;\
 570                                 RB_ROTATE_RIGHT(head, parent, tmp, field);\
 571                                 elm = RB_ROOT(head);                    \
 572                                 break;                                  \
 573                         }                                               \
 574                 }                                                       \
 575         }                                                               \
 576         if (elm)                                                        \
 577                 RB_COLOR(elm, field) = RB_BLACK;                        \
 578 }                                                                       \
 579                                                                         \
 580 STORQUAL struct type *                                                  \
 581 name##_RB_REMOVE(struct name *head, struct type *elm)                   \
 582 {                                                                       \
 583         struct type *child, *parent, *old;                              \
 584         struct name##_scan_info *inprog;                                \
 585         int color;                                                      \
 586                                                                         \
 587         for (inprog = RB_INPROG(head); inprog; inprog = inprog->link) { \
 588                 if (inprog->node == elm)                                \
 589                         inprog->node = RB_NEXT(name, head, elm);        \
 590         }                                                               \
 591                                                                         \
 592         old = elm;                                                      \
 593         if (RB_LEFT(elm, field) == NULL)                                \
 594                 child = RB_RIGHT(elm, field);                           \
 595         else if (RB_RIGHT(elm, field) == NULL)                          \
 596                 child = RB_LEFT(elm, field);                            \
 597         else {                                                          \
 598                 struct type *left;                                      \
 599                 elm = RB_RIGHT(elm, field);                             \
 600                 while ((left = RB_LEFT(elm, field)) != NULL)            \
 601                         elm = left;                                     \
 602                 child = RB_RIGHT(elm, field);                           \
 603                 parent = RB_PARENT(elm, field);                         \
 604                 color = RB_COLOR(elm, field);                           \
 605                 if (child)                                              \
 606                         RB_PARENT(child, field) = parent;               \
 607                 if (parent) {                                           \
 608                         if (RB_LEFT(parent, field) == elm)              \
 609                                 RB_LEFT(parent, field) = child;         \
 610                         else                                            \
 611                                 RB_RIGHT(parent, field) = child;        \
 612                         RB_AUGMENT(parent);                             \
 613                 } else                                                  \
 614                         RB_ROOT(head) = child;                          \
 615                 if (RB_PARENT(elm, field) == old)                       \
 616                         parent = elm;                                   \
 617                 (elm)->field = (old)->field;                            \
 618                 if (RB_PARENT(old, field)) {                            \
 619                         if (RB_LEFT(RB_PARENT(old, field), field) == old)\
 620                                 RB_LEFT(RB_PARENT(old, field), field) = elm;\
 621                         else                                            \
 622                                 RB_RIGHT(RB_PARENT(old, field), field) = elm;\
 623                         RB_AUGMENT(RB_PARENT(old, field));              \
 624                 } else                                                  \
 625                         RB_ROOT(head) = elm;                            \
 626                 RB_PARENT(RB_LEFT(old, field), field) = elm;            \
 627                 if (RB_RIGHT(old, field))                               \
 628                         RB_PARENT(RB_RIGHT(old, field), field) = elm;   \
 629                 if (parent) {                                           \
 630                         left = parent;                                  \
 631                         do {                                            \
 632                                 RB_AUGMENT(left);                       \
 633                         } while ((left = RB_PARENT(left, field)) != NULL); \
 634                 }                                                       \
 635                 goto color;                                             \
 636         }                                                               \
 637         parent = RB_PARENT(elm, field);                                 \
 638         color = RB_COLOR(elm, field);                                   \
 639         if (child)                                                      \
 640                 RB_PARENT(child, field) = parent;                       \
 641         if (parent) {                                                   \
 642                 if (RB_LEFT(parent, field) == elm)                      \
 643                         RB_LEFT(parent, field) = child;                 \
 644                 else                                                    \
 645                         RB_RIGHT(parent, field) = child;                \
 646                 RB_AUGMENT(parent);                                     \
 647         } else                                                          \
 648                 RB_ROOT(head) = child;                                  \
 649 color:                                                                  \
 650         if (color == RB_BLACK)                                          \
 651                 name##_RB_REMOVE_COLOR(head, parent, child);            \
 652         return (old);                                                   \
 653 }                                                                       \
 654                                                                         \
 655 /* Inserts a node into the RB tree */                                   \
 656 STORQUAL struct type *                                                  \
 657 name##_RB_INSERT(struct name *head, struct type *elm)                   \
 658 {                                                                       \
 659         struct type *tmp;                                               \
 660         struct type *parent = NULL;                                     \
 661         int comp = 0;                                                   \
 662         tmp = RB_ROOT(head);                                            \
 663         while (tmp) {                                                   \
 664                 parent = tmp;                                           \
 665                 comp = (cmp)(elm, parent);                              \
 666                 if (comp < 0)                                           \
 667                         tmp = RB_LEFT(tmp, field);                      \
 668                 else if (comp > 0)                                      \
 669                         tmp = RB_RIGHT(tmp, field);                     \
 670                 else                                                    \
 671                         return(tmp);                                    \
 672         }                                                               \
 673         RB_SET(elm, parent, field);                                     \
 674         if (parent != NULL) {                                           \
 675                 if (comp < 0)                                           \
 676                         RB_LEFT(parent, field) = elm;                   \
 677                 else                                                    \
 678                         RB_RIGHT(parent, field) = elm;                  \
 679                 RB_AUGMENT(parent);                                     \
 680         } else                                                          \
 681                 RB_ROOT(head) = elm;                                    \
 682         name##_RB_INSERT_COLOR(head, elm);                              \
 683         return (NULL);                                                  \
 684 }                                                                       \
 685                                                                         \
 686 /* Finds the node with the same key as elm */                           \
 687 STORQUAL struct type *                                                  \
 688 name##_RB_FIND(struct name *head, struct type *elm)                     \
 689 {                                                                       \
 690         struct type *tmp = RB_ROOT(head);                               \
 691         int comp;                                                       \
 692         while (tmp) {                                                   \
 693                 comp = cmp(elm, tmp);                                   \
 694                 if (comp < 0)                                           \
 695                         tmp = RB_LEFT(tmp, field);                      \
 696                 else if (comp > 0)                                      \
 697                         tmp = RB_RIGHT(tmp, field);                     \
 698                 else                                                    \
 699                         return (tmp);                                   \
 700         }                                                               \
 701         return (NULL);                                                  \
 702 }                                                                       \
 703                                                                         \
 704 /*                                                                      \
 705  * Issue a callback for all matching items.  The scan function must     \
 706  * return < 0 for items below the desired range, 0 for items within     \
 707  * the range, and > 0 for items beyond the range.   Any item may be     \
 708  * deleted while the scan is in progress.                               \
 709  */                                                                     \
 710 static int                                                              \
 711 name##_SCANCMP_ALL(struct type *type __unused, void *data __unused)     \
 712 {                                                                       \
 713         return(0);                                                      \
 714 }                                                                       \
 715                                                                         \
 716 static __inline void                                                    \
 717 name##_scan_info_link(struct name##_scan_info *scan, struct name *head) \
 718 {                                                                       \
 719         RB_SCAN_LOCK(&head->rbh_spin);                                  \
 720         scan->link = RB_INPROG(head);                                   \
 721         RB_INPROG(head) = scan;                                         \
 722         RB_SCAN_UNLOCK(&head->rbh_spin);                                \
 723 }                                                                       \
 724                                                                         \
 725 static __inline void                                                    \
 726 name##_scan_info_done(struct name##_scan_info *scan, struct name *head) \
 727 {                                                                       \
 728         struct name##_scan_info **infopp;                               \
 729                                                                         \
 730         RB_SCAN_LOCK(&head->rbh_spin);                                  \
 731         infopp = &RB_INPROG(head);                                      \
 732         while (*infopp != scan)                                         \
 733                 infopp = &(*infopp)->link;                              \
 734         *infopp = scan->link;                                           \
 735         RB_SCAN_UNLOCK(&head->rbh_spin);                                \
 736 }                                                                       \
 737                                                                         \
 738 STORQUAL int                                                            \
 739 name##_RB_SCAN(struct name *head,                                       \
 740                 int (*scancmp)(struct type *, void *),                  \
 741                 int (*callback)(struct type *, void *),                 \
 742                 void *data)                                             \
 743 {                                                                       \
 744         struct name##_scan_info info;                                   \
 745         struct type *best;                                              \
 746         struct type *tmp;                                               \
 747         int count;                                                      \
 748         int comp;                                                       \
 749                                                                         \
 750         if (scancmp == NULL)                                            \
 751                 scancmp = name##_SCANCMP_ALL;                           \
 752                                                                         \
 753         /*                                                              \
 754          * Locate the first element.                                    \
 755          */                                                             \
 756         tmp = RB_ROOT(head);                                            \
 757         best = NULL;                                                    \
 758         while (tmp) {                                                   \
 759                 comp = scancmp(tmp, data);                              \
 760                 if (comp < 0) {                                         \
 761                         tmp = RB_RIGHT(tmp, field);                     \
 762                 } else if (comp > 0) {                                  \
 763                         tmp = RB_LEFT(tmp, field);                      \
 764                 } else {                                                \
 765                         best = tmp;                                     \
 766                         if (RB_LEFT(tmp, field) == NULL)                \
 767                                 break;                                  \
 768                         tmp = RB_LEFT(tmp, field);                      \
 769                 }                                                       \
 770         }                                                               \
 771         count = 0;                                                      \
 772         if (best) {                                                     \
 773                 info.node = RB_NEXT(name, head, best);                  \
 774                 name##_scan_info_link(&info, head);                     \
 775                 while ((comp = callback(best, data)) >= 0) {            \
 776                         count += comp;                                  \
 777                         best = info.node;                               \
 778                         if (best == NULL || scancmp(best, data) != 0)   \
 779                                 break;                                  \
 780                         info.node = RB_NEXT(name, head, best);          \
 781                 }                                                       \
 782                 name##_scan_info_done(&info, head);                     \
 783                 if (comp < 0)   /* error or termination */              \
 784                         count = comp;                                   \
 785         }                                                               \
 786         return(count);                                                  \
 787 }                                                                       \
 788                                                                         \
 789 /* ARGSUSED */                                                          \
 790 STORQUAL struct type *                                                  \
 791 name##_RB_NEXT(struct type *elm)                                        \
 792 {                                                                       \
 793         if (RB_RIGHT(elm, field)) {                                     \
 794                 elm = RB_RIGHT(elm, field);                             \
 795                 while (RB_LEFT(elm, field))                             \
 796                         elm = RB_LEFT(elm, field);                      \
 797         } else {                                                        \
 798                 if (RB_PARENT(elm, field) &&                            \
 799                     (elm == RB_LEFT(RB_PARENT(elm, field), field)))     \
 800                         elm = RB_PARENT(elm, field);                    \
 801                 else {                                                  \
 802                         while (RB_PARENT(elm, field) &&                 \
 803                             (elm == RB_RIGHT(RB_PARENT(elm, field), field)))\
 804                                 elm = RB_PARENT(elm, field);            \
 805                         elm = RB_PARENT(elm, field);                    \
 806                 }                                                       \
 807         }                                                               \
 808         return (elm);                                                   \
 809 }                                                                       \
 810                                                                         \
 811 /* ARGSUSED */                                                          \
 812 STORQUAL struct type *                                                  \
 813 name##_RB_PREV(struct type *elm)                                        \
 814 {                                                                       \
 815         if (RB_LEFT(elm, field)) {                                      \
 816                 elm = RB_LEFT(elm, field);                              \
 817                 while (RB_RIGHT(elm, field))                            \
 818                         elm = RB_RIGHT(elm, field);                     \
 819         } else {                                                        \
 820                 if (RB_PARENT(elm, field) &&                            \
 821                     (elm == RB_RIGHT(RB_PARENT(elm, field), field)))    \
 822                         elm = RB_PARENT(elm, field);                    \
 823                 else {                                                  \
 824                         while (RB_PARENT(elm, field) &&                 \
 825                             (elm == RB_LEFT(RB_PARENT(elm, field), field)))\
 826                                 elm = RB_PARENT(elm, field);            \
 827                         elm = RB_PARENT(elm, field);                    \
 828                 }                                                       \
 829         }                                                               \
 830         return (elm);                                                   \
 831 }                                                                       \
 832                                                                         \
 833 STORQUAL struct type *                                                  \
 834 name##_RB_MINMAX(struct name *head, int val)                            \
 835 {                                                                       \
 836         struct type *tmp = RB_ROOT(head);                               \
 837         struct type *parent = NULL;                                     \
 838         while (tmp) {                                                   \
 839                 parent = tmp;                                           \
 840                 if (val < 0)                                            \
 841                         tmp = RB_LEFT(tmp, field);                      \
 842                 else                                                    \
 843                         tmp = RB_RIGHT(tmp, field);                     \
 844         }                                                               \
 845         return (parent);                                                \
 846 }
 847
 848 /*
 849  * This extended version implements a fast LOOKUP function given
 850  * a numeric data type.
 851  *
 852  * The element whos index/offset field is exactly the specified value
 853  * will be returned, or NULL.
 854  */
 855 #define RB_GENERATE2(name, type, field, cmp, datatype, indexfield)      \
 856 RB_GENERATE(name, type, field, cmp)                                     \
 857                                                                         \
 858 struct type *                                                           \
 859 name##_RB_LOOKUP(struct name *head, datatype value)                     \
 860 {                                                                       \
 861         struct type *tmp;                                               \
 862                                                                         \
 863         tmp = RB_ROOT(head);                                            \
 864         while (tmp) {                                                   \
 865                 if (value > tmp->indexfield)                            \
 866                         tmp = RB_RIGHT(tmp, field);                     \
 867                 else if (value < tmp->indexfield)                       \
 868                         tmp = RB_LEFT(tmp, field);                      \
 869                 else                                                    \
 870                         return(tmp);                                    \
 871         }                                                               \
 872         return(NULL);                                                   \
 873 }                                                                       \
 874
 875 /*
 876  * This extended version implements a fast ranged-based LOOKUP function
 877  * given a numeric data type, for data types with a beginning and end
 878  * (end is inclusive).
 879  *
 880  * The element whos range contains the specified value is returned, or NULL
 881  */
 882 #define RB_GENERATE3(name, type, field, cmp, datatype, begfield, endfield) \
 883 RB_GENERATE2(name, type, field, cmp, datatype, begfield)                \
 884                                                                         \
 885 struct type *                                                           \
 886 name##_RB_RLOOKUP(struct name *head, datatype value)                    \
 887 {                                                                       \
 888         struct type *tmp;                                               \
 889                                                                         \
 890         tmp = RB_ROOT(head);                                            \
 891         while (tmp) {                                                   \
 892                 if (value >= tmp->begfield && value <= tmp->endfield)   \
 893                         return(tmp);                                    \
 894                 if (value > tmp->begfield)                              \
 895                         tmp = RB_RIGHT(tmp, field);                     \
 896                 else                                                    \
 897                         tmp = RB_LEFT(tmp, field);                      \
 898         }                                                               \
 899         return(NULL);                                                   \
 900 }                                                                       \
 901
 902 /*
 903  * This extended version implements a fast ranged-based LOOKUP function
 904  * given a numeric data type, for data types with a beginning and size.
 905  *
 906  * WARNING: The full range of the data type is not supported due to a
 907  * boundary condition at the end, where (beginning + size) might overflow.
 908  *
 909  * The element whos range contains the specified value is returned, or NULL
 910  */
 911 #define RB_GENERATE4(name, type, field, cmp, datatype, begfield, sizefield) \
 912 RB_GENERATE2(name, type, field, cmp, datatype, begfield)                \
 913                                                                         \
 914 struct type *                                                           \
 915 name##_RB_RLOOKUP(struct name *head, datatype value)                    \
 916 {                                                                       \
 917         struct type *tmp;                                               \
 918                                                                         \
 919         tmp = RB_ROOT(head);                                            \
 920         while (tmp) {                                                   \
 921                 if (value >= tmp->begfield &&                           \
 922                     value < tmp->begfield + tmp->sizefield) {           \
 923                         return(tmp);                                    \
 924                 }                                                       \
 925                 if (value > tmp->begfield)                              \
 926                         tmp = RB_RIGHT(tmp, field);                     \
 927                 else                                                    \
 928                         tmp = RB_LEFT(tmp, field);                      \
 929         }                                                               \
 930         return(NULL);                                                   \
 931 }                                                                       \
 932
 933 /*
 934  * This generates a custom lookup function for a red-black tree.
 935  * Note that the macro may be used with a storage qualifier.
 936  */
 937
 938 #define RB_GENERATE_XLOOKUP(name, ext, type, field, xcmp, datatype)        \
 939         _RB_GENERATE_XLOOKUP(name, ext, type, field, xcmp, datatype,)
 940 #define RB_GENERATE_XLOOKUP_STATIC(name, ext, type, field, xcmp, datatype) \
 941         _RB_GENERATE_XLOOKUP(name, ext, type, field, xcmp, datatype, __unused static)
 942
 943 #define _RB_GENERATE_XLOOKUP(name, ext, type, field, xcmp, datatype, STORQUAL)\
 944                                                                         \
 945 STORQUAL struct type *                                                  \
 946 name##_RB_LOOKUP_##ext (struct name *head, datatype value)              \
 947 {                                                                       \
 948         struct type *tmp;                                               \
 949         int r;                                                          \
 950                                                                         \
 951         tmp = RB_ROOT(head);                                            \
 952         while (tmp) {                                                   \
 953                 r = xcmp(value, tmp);                                   \
 954                 if (r == 0)                                             \
 955                         return(tmp);                                    \
 956                 if (r > 0)                                              \
 957                         tmp = RB_RIGHT(tmp, field);                     \
 958                 else                                                    \
 959                         tmp = RB_LEFT(tmp, field);                      \
 960         }                                                               \
 961         return(NULL);                                                   \
 962 }                                                                       \
 963
 964
 965 #define RB_NEGINF       -1
 966 #define RB_INF  1
 967
 968 #define RB_INSERT(name, root, elm)      name##_RB_INSERT(root, elm)
 969 #define RB_REMOVE(name, root, elm)      name##_RB_REMOVE(root, elm)
 970 #define RB_FIND(name, root, elm)        name##_RB_FIND(root, elm)
 971 #define RB_LOOKUP(name, root, value)    name##_RB_LOOKUP(root, value)
 972 #define RB_RLOOKUP(name, root, value)   name##_RB_RLOOKUP(root, value)
 973 #define RB_SCAN(name, root, cmp, callback, data)                        \
 974                                 name##_RB_SCAN(root, cmp, callback, data)
 975 #define RB_FIRST(name, root)            name##_RB_MINMAX(root, RB_NEGINF)
 976 #define RB_NEXT(name, root, elm)        name##_RB_NEXT(elm)
 977 #define RB_PREV(name, root, elm)        name##_RB_PREV(elm)
 978 #define RB_MIN(name, root)              name##_RB_MINMAX(root, RB_NEGINF)
 979 #define RB_MAX(name, root)              name##_RB_MINMAX(root, RB_INF)
 980
 981 #define RB_FOREACH(x, name, head)                                       \
 982         for ((x) = RB_MIN(name, head);                                  \
 983              (x) != NULL;                                               \
 984              (x) = name##_RB_NEXT(x))
 985
 986 #endif  /* _SYS_TREE_H_ */