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 1.5 2006/03/28 22:17:05 dillon Exp $ */
   4 /*
   5  * Copyright 2002 Niels Provos <provos@citi.umich.edu>
   6  * All rights reserved.
   7  *
   8  * Redistribution and use in source and binary forms, with or without
   9  * modification, are permitted provided that the following conditions
  10  * are met:
  11  * 1. Redistributions of source code must retain the above copyright
  12  *    notice, this list of conditions and the following disclaimer.
  13  * 2. Redistributions in binary form must reproduce the above copyright
  14  *    notice, this list of conditions and the following disclaimer in the
  15  *    documentation and/or other materials provided with the distribution.
  16  *
  17  * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
  18  * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
  19  * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
  20  * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
  21  * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
  22  * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
  23  * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
  24  * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
  25  * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
  26  * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
  27  */
  28
  29 #ifndef _SYS_TREE_H_
  30 #define _SYS_TREE_H_
  31
  32 /*
  33  * This file defines data structures for different types of trees:
  34  * splay trees and red-black trees.
  35  *
  36  * A splay tree is a self-organizing data structure.  Every operation
  37  * on the tree causes a splay to happen.  The splay moves the requested
  38  * node to the root of the tree and partly rebalances it.
  39  *
  40  * This has the benefit that request locality causes faster lookups as
  41  * the requested nodes move to the top of the tree.  On the other hand,
  42  * every lookup causes memory writes.
  43  *
  44  * The Balance Theorem bounds the total access time for m operations
  45  * and n inserts on an initially empty tree as O((m + n)lg n).  The
  46  * amortized cost for a sequence of m accesses to a splay tree is O(lg n);
  47  *
  48  * A red-black tree is a binary search tree with the node color as an
  49  * extra attribute.  It fulfills a set of conditions:
  50  *      - every search path from the root to a leaf consists of the
  51  *        same number of black nodes,
  52  *      - each red node (except for the root) has a black parent,
  53  *      - each leaf node is black.
  54  *
  55  * Every operation on a red-black tree is bounded as O(lg n).
  56  * The maximum height of a red-black tree is 2lg (n+1).
  57  */
  58
  59 #define SPLAY_HEAD(name, type)                                          \
  60 struct name {                                                           \
  61         struct type *sph_root; /* root of the tree */                   \
  62 }
  63
  64 #define SPLAY_INITIALIZER(root)                                         \
  65         { NULL }
  66
  67 #define SPLAY_INIT(root) do {                                           \
  68         (root)->sph_root = NULL;                                        \
  69 } while (/*CONSTCOND*/ 0)
  70
  71 #define SPLAY_ENTRY(type)                                               \
  72 struct {                                                                \
  73         struct type *spe_left; /* left element */                       \
  74         struct type *spe_right; /* right element */                     \
  75 }
  76
  77 #define SPLAY_LEFT(elm, field)          (elm)->field.spe_left
  78 #define SPLAY_RIGHT(elm, field)         (elm)->field.spe_right
  79 #define SPLAY_ROOT(head)                (head)->sph_root
  80 #define SPLAY_EMPTY(head)               (SPLAY_ROOT(head) == NULL)
  81
  82 /* SPLAY_ROTATE_{LEFT,RIGHT} expect that tmp hold SPLAY_{RIGHT,LEFT} */
  83 #define SPLAY_ROTATE_RIGHT(head, tmp, field) do {                       \
  84         SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(tmp, field);  \
  85         SPLAY_RIGHT(tmp, field) = (head)->sph_root;                     \
  86         (head)->sph_root = tmp;                                         \
  87 } while (/*CONSTCOND*/ 0)
  88
  89 #define SPLAY_ROTATE_LEFT(head, tmp, field) do {                        \
  90         SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(tmp, field);  \
  91         SPLAY_LEFT(tmp, field) = (head)->sph_root;                      \
  92         (head)->sph_root = tmp;                                         \
  93 } while (/*CONSTCOND*/ 0)
  94
  95 #define SPLAY_LINKLEFT(head, tmp, field) do {                           \
  96         SPLAY_LEFT(tmp, field) = (head)->sph_root;                      \
  97         tmp = (head)->sph_root;                                         \
  98         (head)->sph_root = SPLAY_LEFT((head)->sph_root, field);         \
  99 } while (/*CONSTCOND*/ 0)
 100
 101 #define SPLAY_LINKRIGHT(head, tmp, field) do {                          \
 102         SPLAY_RIGHT(tmp, field) = (head)->sph_root;                     \
 103         tmp = (head)->sph_root;                                         \
 104         (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);        \
 105 } while (/*CONSTCOND*/ 0)
 106
 107 #define SPLAY_ASSEMBLE(head, node, left, right, field) do {             \
 108         SPLAY_RIGHT(left, field) = SPLAY_LEFT((head)->sph_root, field); \
 109         SPLAY_LEFT(right, field) = SPLAY_RIGHT((head)->sph_root, field);\
 110         SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(node, field); \
 111         SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(node, field); \
 112 } while (/*CONSTCOND*/ 0)
 113
 114 /* Generates prototypes and inline functions */
 115
 116 #define SPLAY_PROTOTYPE(name, type, field, cmp)                         \
 117 void name##_SPLAY(struct name *, struct type *);                        \
 118 void name##_SPLAY_MINMAX(struct name *, int);                           \
 119 struct type *name##_SPLAY_INSERT(struct name *, struct type *);         \
 120 struct type *name##_SPLAY_REMOVE(struct name *, struct type *);         \
 121                                                                         \
 122 /* Finds the node with the same key as elm */                           \
 123 static __inline struct type *                                           \
 124 name##_SPLAY_FIND(struct name *head, struct type *elm)                  \
 125 {                                                                       \
 126         if (SPLAY_EMPTY(head))                                          \
 127                 return(NULL);                                           \
 128         name##_SPLAY(head, elm);                                        \
 129         if ((cmp)(elm, (head)->sph_root) == 0)                          \
 130                 return (head->sph_root);                                \
 131         return (NULL);                                                  \
 132 }                                                                       \
 133                                                                         \
 134 static __inline struct type *                                           \
 135 name##_SPLAY_NEXT(struct name *head, struct type *elm)                  \
 136 {                                                                       \
 137         name##_SPLAY(head, elm);                                        \
 138         if (SPLAY_RIGHT(elm, field) != NULL) {                          \
 139                 elm = SPLAY_RIGHT(elm, field);                          \
 140                 while (SPLAY_LEFT(elm, field) != NULL) {                \
 141                         elm = SPLAY_LEFT(elm, field);                   \
 142                 }                                                       \
 143         } else                                                          \
 144                 elm = NULL;                                             \
 145         return (elm);                                                   \
 146 }                                                                       \
 147                                                                         \
 148 static __inline struct type *                                           \
 149 name##_SPLAY_MIN_MAX(struct name *head, int val)                        \
 150 {                                                                       \
 151         name##_SPLAY_MINMAX(head, val);                                 \
 152         return (SPLAY_ROOT(head));                                      \
 153 }
 154
 155 /* Main splay operation.
 156  * Moves node close to the key of elm to top
 157  */
 158 #define SPLAY_GENERATE(name, type, field, cmp)                          \
 159 struct type *                                                           \
 160 name##_SPLAY_INSERT(struct name *head, struct type *elm)                \
 161 {                                                                       \
 162     if (SPLAY_EMPTY(head)) {                                            \
 163             SPLAY_LEFT(elm, field) = SPLAY_RIGHT(elm, field) = NULL;    \
 164     } else {                                                            \
 165             int __comp;                                                 \
 166             name##_SPLAY(head, elm);                                    \
 167             __comp = (cmp)(elm, (head)->sph_root);                      \
 168             if(__comp < 0) {                                            \
 169                     SPLAY_LEFT(elm, field) = SPLAY_LEFT((head)->sph_root, field);\
 170                     SPLAY_RIGHT(elm, field) = (head)->sph_root;         \
 171                     SPLAY_LEFT((head)->sph_root, field) = NULL;         \
 172             } else if (__comp > 0) {                                    \
 173                     SPLAY_RIGHT(elm, field) = SPLAY_RIGHT((head)->sph_root, field);\
 174                     SPLAY_LEFT(elm, field) = (head)->sph_root;          \
 175                     SPLAY_RIGHT((head)->sph_root, field) = NULL;        \
 176             } else                                                      \
 177                     return ((head)->sph_root);                          \
 178     }                                                                   \
 179     (head)->sph_root = (elm);                                           \
 180     return (NULL);                                                      \
 181 }                                                                       \
 182                                                                         \
 183 struct type *                                                           \
 184 name##_SPLAY_REMOVE(struct name *head, struct type *elm)                \
 185 {                                                                       \
 186         struct type *__tmp;                                             \
 187         if (SPLAY_EMPTY(head))                                          \
 188                 return (NULL);                                          \
 189         name##_SPLAY(head, elm);                                        \
 190         if ((cmp)(elm, (head)->sph_root) == 0) {                        \
 191                 if (SPLAY_LEFT((head)->sph_root, field) == NULL) {      \
 192                         (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);\
 193                 } else {                                                \
 194                         __tmp = SPLAY_RIGHT((head)->sph_root, field);   \
 195                         (head)->sph_root = SPLAY_LEFT((head)->sph_root, field);\
 196                         name##_SPLAY(head, elm);                        \
 197                         SPLAY_RIGHT((head)->sph_root, field) = __tmp;   \
 198                 }                                                       \
 199                 return (elm);                                           \
 200         }                                                               \
 201         return (NULL);                                                  \
 202 }                                                                       \
 203                                                                         \
 204 void                                                                    \
 205 name##_SPLAY(struct name *head, struct type *elm)                       \
 206 {                                                                       \
 207         struct type __node, *__left, *__right, *__tmp;                  \
 208         int __comp;                                                     \
 209 \
 210         SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
 211         __left = __right = &__node;                                     \
 212 \
 213         while ((__comp = (cmp)(elm, (head)->sph_root)) != 0) {          \
 214                 if (__comp < 0) {                                       \
 215                         __tmp = SPLAY_LEFT((head)->sph_root, field);    \
 216                         if (__tmp == NULL)                              \
 217                                 break;                                  \
 218                         if ((cmp)(elm, __tmp) < 0){                     \
 219                                 SPLAY_ROTATE_RIGHT(head, __tmp, field); \
 220                                 if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
 221                                         break;                          \
 222                         }                                               \
 223                         SPLAY_LINKLEFT(head, __right, field);           \
 224                 } else if (__comp > 0) {                                \
 225                         __tmp = SPLAY_RIGHT((head)->sph_root, field);   \
 226                         if (__tmp == NULL)                              \
 227                                 break;                                  \
 228                         if ((cmp)(elm, __tmp) > 0){                     \
 229                                 SPLAY_ROTATE_LEFT(head, __tmp, field);  \
 230                                 if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
 231                                         break;                          \
 232                         }                                               \
 233                         SPLAY_LINKRIGHT(head, __left, field);           \
 234                 }                                                       \
 235         }                                                               \
 236         SPLAY_ASSEMBLE(head, &__node, __left, __right, field);          \
 237 }                                                                       \
 238                                                                         \
 239 /* Splay with either the minimum or the maximum element                 \
 240  * Used to find minimum or maximum element in tree.                     \
 241  */                                                                     \
 242 void name##_SPLAY_MINMAX(struct name *head, int __comp) \
 243 {                                                                       \
 244         struct type __node, *__left, *__right, *__tmp;                  \
 245 \
 246         SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
 247         __left = __right = &__node;                                     \
 248 \
 249         while (1) {                                                     \
 250                 if (__comp < 0) {                                       \
 251                         __tmp = SPLAY_LEFT((head)->sph_root, field);    \
 252                         if (__tmp == NULL)                              \
 253                                 break;                                  \
 254                         if (__comp < 0){                                \
 255                                 SPLAY_ROTATE_RIGHT(head, __tmp, field); \
 256                                 if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
 257                                         break;                          \
 258                         }                                               \
 259                         SPLAY_LINKLEFT(head, __right, field);           \
 260                 } else if (__comp > 0) {                                \
 261                         __tmp = SPLAY_RIGHT((head)->sph_root, field);   \
 262                         if (__tmp == NULL)                              \
 263                                 break;                                  \
 264                         if (__comp > 0) {                               \
 265                                 SPLAY_ROTATE_LEFT(head, __tmp, field);  \
 266                                 if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
 267                                         break;                          \
 268                         }                                               \
 269                         SPLAY_LINKRIGHT(head, __left, field);           \
 270                 }                                                       \
 271         }                                                               \
 272         SPLAY_ASSEMBLE(head, &__node, __left, __right, field);          \
 273 }
 274
 275 #define SPLAY_NEGINF    -1
 276 #define SPLAY_INF       1
 277
 278 #define SPLAY_INSERT(name, x, y)        name##_SPLAY_INSERT(x, y)
 279 #define SPLAY_REMOVE(name, x, y)        name##_SPLAY_REMOVE(x, y)
 280 #define SPLAY_FIND(name, x, y)          name##_SPLAY_FIND(x, y)
 281 #define SPLAY_NEXT(name, x, y)          name##_SPLAY_NEXT(x, y)
 282 #define SPLAY_MIN(name, x)              (SPLAY_EMPTY(x) ? NULL  \
 283                                         : name##_SPLAY_MIN_MAX(x, SPLAY_NEGINF))
 284 #define SPLAY_MAX(name, x)              (SPLAY_EMPTY(x) ? NULL  \
 285                                         : name##_SPLAY_MIN_MAX(x, SPLAY_INF))
 286
 287 #define SPLAY_FOREACH(x, name, head)                                    \
 288         for ((x) = SPLAY_MIN(name, head);                               \
 289              (x) != NULL;                                               \
 290              (x) = SPLAY_NEXT(name, head, x))
 291
 292 /* Macros that define a red-black tree */
 293
 294 #define RB_SCAN_INFO(name, type)                                        \
 295 struct name##_scan_info {                                               \
 296         struct name##_scan_info *link;                                  \
 297         struct type     *node;                                          \
 298 }
 299
 300 #define RB_HEAD(name, type)                                             \
 301 struct name {                                                           \
 302         struct type *rbh_root;               /* root of the tree */     \
 303         struct name##_scan_info *rbh_inprog; /* scans in progress */    \
 304 }
 305
 306 #define RB_INITIALIZER(root)                                            \
 307         { NULL, NULL }
 308
 309 #define RB_INIT(root) do {                                              \
 310         (root)->rbh_root = NULL;                                        \
 311         (root)->rbh_inprog = NULL;                                      \
 312 } while (/*CONSTCOND*/ 0)
 313
 314 #define RB_BLACK        0
 315 #define RB_RED          1
 316 #define RB_ENTRY(type)                                                  \
 317 struct {                                                                \
 318         struct type *rbe_left;          /* left element */              \
 319         struct type *rbe_right;         /* right element */             \
 320         struct type *rbe_parent;        /* parent element */            \
 321         int rbe_color;                  /* node color */                \
 322 }
 323
 324 #define RB_LEFT(elm, field)             (elm)->field.rbe_left
 325 #define RB_RIGHT(elm, field)            (elm)->field.rbe_right
 326 #define RB_PARENT(elm, field)           (elm)->field.rbe_parent
 327 #define RB_COLOR(elm, field)            (elm)->field.rbe_color
 328 #define RB_ROOT(head)                   (head)->rbh_root
 329 #define RB_INPROG(head)                 (head)->rbh_inprog
 330 #define RB_EMPTY(head)                  (RB_ROOT(head) == NULL)
 331
 332 #define RB_SET(elm, parent, field) do {                                 \
 333         RB_PARENT(elm, field) = parent;                                 \
 334         RB_LEFT(elm, field) = RB_RIGHT(elm, field) = NULL;              \
 335         RB_COLOR(elm, field) = RB_RED;                                  \
 336 } while (/*CONSTCOND*/ 0)
 337
 338 #define RB_SET_BLACKRED(black, red, field) do {                         \
 339         RB_COLOR(black, field) = RB_BLACK;                              \
 340         RB_COLOR(red, field) = RB_RED;                                  \
 341 } while (/*CONSTCOND*/ 0)
 342
 343 #ifndef RB_AUGMENT
 344 #define RB_AUGMENT(x)
 345 #endif
 346
 347 #define RB_ROTATE_LEFT(head, elm, tmp, field) do {                      \
 348         (tmp) = RB_RIGHT(elm, field);                                   \
 349         if ((RB_RIGHT(elm, field) = RB_LEFT(tmp, field)) != NULL) {     \
 350                 RB_PARENT(RB_LEFT(tmp, field), field) = (elm);          \
 351         }                                                               \
 352         RB_AUGMENT(elm);                                                \
 353         if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) {  \
 354                 if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))     \
 355                         RB_LEFT(RB_PARENT(elm, field), field) = (tmp);  \
 356                 else                                                    \
 357                         RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \
 358         } else                                                          \
 359                 (head)->rbh_root = (tmp);                               \
 360         RB_LEFT(tmp, field) = (elm);                                    \
 361         RB_PARENT(elm, field) = (tmp);                                  \
 362         RB_AUGMENT(tmp);                                                \
 363         if ((RB_PARENT(tmp, field)))                                    \
 364                 RB_AUGMENT(RB_PARENT(tmp, field));                      \
 365 } while (/*CONSTCOND*/ 0)
 366
 367 #define RB_ROTATE_RIGHT(head, elm, tmp, field) do {                     \
 368         (tmp) = RB_LEFT(elm, field);                                    \
 369         if ((RB_LEFT(elm, field) = RB_RIGHT(tmp, field)) != NULL) {     \
 370                 RB_PARENT(RB_RIGHT(tmp, field), field) = (elm);         \
 371         }                                                               \
 372         RB_AUGMENT(elm);                                                \
 373         if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) {  \
 374                 if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))     \
 375                         RB_LEFT(RB_PARENT(elm, field), field) = (tmp);  \
 376                 else                                                    \
 377                         RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \
 378         } else                                                          \
 379                 (head)->rbh_root = (tmp);                               \
 380         RB_RIGHT(tmp, field) = (elm);                                   \
 381         RB_PARENT(elm, field) = (tmp);                                  \
 382         RB_AUGMENT(tmp);                                                \
 383         if ((RB_PARENT(tmp, field)))                                    \
 384                 RB_AUGMENT(RB_PARENT(tmp, field));                      \
 385 } while (/*CONSTCOND*/ 0)
 386
 387 /* Generates prototypes and inline functions */
 388 #define RB_PROTOTYPE(name, type, field, cmp)                            \
 389 struct type *name##_RB_REMOVE(struct name *, struct type *);            \
 390 struct type *name##_RB_INSERT(struct name *, struct type *);            \
 391 struct type *name##_RB_FIND(struct name *, struct type *);              \
 392 int name##_RB_SCAN(struct name *, int (*)(struct type *, void *),       \
 393                         int (*)(struct type *, void *), void *);        \
 394 struct type *name##_RB_NEXT(struct type *);                             \
 395 struct type *name##_RB_PREV(struct type *);                             \
 396 struct type *name##_RB_MINMAX(struct name *, int);                      \
 397 RB_SCAN_INFO(name, type)                                                \
 398
 399 /*
 400  * A version which supplies a fast lookup routine for an exact match
 401  * on a numeric field.
 402  */
 403 #define RB_PROTOTYPE2(name, type, field, cmp, datatype)                 \
 404 RB_PROTOTYPE(name, type, field, cmp);                                   \
 405 struct type *name##_RB_LOOKUP(struct name *, datatype)                  \
 406
 407 /*
 408  * A version which supplies a fast lookup routine for a numeric
 409  * field which resides within a ranged object, either using (begin,end),
 410  * or using (begin,size).
 411  */
 412 #define RB_PROTOTYPE3(name, type, field, cmp, datatype)                 \
 413 RB_PROTOTYPE2(name, type, field, cmp, datatype);                        \
 414 struct type *name##_RB_RLOOKUP(struct name *, datatype)                 \
 415
 416 #define RB_PROTOTYPE4(name, type, field, cmp, datatype)                 \
 417 RB_PROTOTYPE2(name, type, field, cmp, datatype);                        \
 418 struct type *name##_RB_RLOOKUP(struct name *, datatype)                 \
 419
 420 /* Main rb operation.
 421  * Moves node close to the key of elm to top
 422  */
 423 #define RB_GENERATE(name, type, field, cmp)                             \
 424 static void                                                             \
 425 name##_RB_INSERT_COLOR(struct name *head, struct type *elm)             \
 426 {                                                                       \
 427         struct type *parent, *gparent, *tmp;                            \
 428         while ((parent = RB_PARENT(elm, field)) != NULL &&              \
 429             RB_COLOR(parent, field) == RB_RED) {                        \
 430                 gparent = RB_PARENT(parent, field);                     \
 431                 if (parent == RB_LEFT(gparent, field)) {                \
 432                         tmp = RB_RIGHT(gparent, field);                 \
 433                         if (tmp && RB_COLOR(tmp, field) == RB_RED) {    \
 434                                 RB_COLOR(tmp, field) = RB_BLACK;        \
 435                                 RB_SET_BLACKRED(parent, gparent, field);\
 436                                 elm = gparent;                          \
 437                                 continue;                               \
 438                         }                                               \
 439                         if (RB_RIGHT(parent, field) == elm) {           \
 440                                 RB_ROTATE_LEFT(head, parent, tmp, field);\
 441                                 tmp = parent;                           \
 442                                 parent = elm;                           \
 443                                 elm = tmp;                              \
 444                         }                                               \
 445                         RB_SET_BLACKRED(parent, gparent, field);        \
 446                         RB_ROTATE_RIGHT(head, gparent, tmp, field);     \
 447                 } else {                                                \
 448                         tmp = RB_LEFT(gparent, field);                  \
 449                         if (tmp && RB_COLOR(tmp, field) == RB_RED) {    \
 450                                 RB_COLOR(tmp, field) = RB_BLACK;        \
 451                                 RB_SET_BLACKRED(parent, gparent, field);\
 452                                 elm = gparent;                          \
 453                                 continue;                               \
 454                         }                                               \
 455                         if (RB_LEFT(parent, field) == elm) {            \
 456                                 RB_ROTATE_RIGHT(head, parent, tmp, field);\
 457                                 tmp = parent;                           \
 458                                 parent = elm;                           \
 459                                 elm = tmp;                              \
 460                         }                                               \
 461                         RB_SET_BLACKRED(parent, gparent, field);        \
 462                         RB_ROTATE_LEFT(head, gparent, tmp, field);      \
 463                 }                                                       \
 464         }                                                               \
 465         RB_COLOR(head->rbh_root, field) = RB_BLACK;                     \
 466 }                                                                       \
 467                                                                         \
 468 static void                                                             \
 469 name##_RB_REMOVE_COLOR(struct name *head, struct type *parent,          \
 470                         struct type *elm)                               \
 471 {                                                                       \
 472         struct type *tmp;                                               \
 473         while ((elm == NULL || RB_COLOR(elm, field) == RB_BLACK) &&     \
 474             elm != RB_ROOT(head)) {                                     \
 475                 if (RB_LEFT(parent, field) == elm) {                    \
 476                         tmp = RB_RIGHT(parent, field);                  \
 477                         if (RB_COLOR(tmp, field) == RB_RED) {           \
 478                                 RB_SET_BLACKRED(tmp, parent, field);    \
 479                                 RB_ROTATE_LEFT(head, parent, tmp, field);\
 480                                 tmp = RB_RIGHT(parent, field);          \
 481                         }                                               \
 482                         if ((RB_LEFT(tmp, field) == NULL ||             \
 483                             RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
 484                             (RB_RIGHT(tmp, field) == NULL ||            \
 485                             RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
 486                                 RB_COLOR(tmp, field) = RB_RED;          \
 487                                 elm = parent;                           \
 488                                 parent = RB_PARENT(elm, field);         \
 489                         } else {                                        \
 490                                 if (RB_RIGHT(tmp, field) == NULL ||     \
 491                                     RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK) {\
 492                                         struct type *oleft;             \
 493                                         if ((oleft = RB_LEFT(tmp, field)) \
 494                                             != NULL)                    \
 495                                                 RB_COLOR(oleft, field) = RB_BLACK;\
 496                                         RB_COLOR(tmp, field) = RB_RED;  \
 497                                         RB_ROTATE_RIGHT(head, tmp, oleft, field);\
 498                                         tmp = RB_RIGHT(parent, field);  \
 499                                 }                                       \
 500                                 RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
 501                                 RB_COLOR(parent, field) = RB_BLACK;     \
 502                                 if (RB_RIGHT(tmp, field))               \
 503                                         RB_COLOR(RB_RIGHT(tmp, field), field) = RB_BLACK;\
 504                                 RB_ROTATE_LEFT(head, parent, tmp, field);\
 505                                 elm = RB_ROOT(head);                    \
 506                                 break;                                  \
 507                         }                                               \
 508                 } else {                                                \
 509                         tmp = RB_LEFT(parent, field);                   \
 510                         if (RB_COLOR(tmp, field) == RB_RED) {           \
 511                                 RB_SET_BLACKRED(tmp, parent, field);    \
 512                                 RB_ROTATE_RIGHT(head, parent, tmp, field);\
 513                                 tmp = RB_LEFT(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_LEFT(tmp, field) == NULL ||      \
 524                                     RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) {\
 525                                         struct type *oright;            \
 526                                         if ((oright = RB_RIGHT(tmp, field)) \
 527                                             != NULL)                    \
 528                                                 RB_COLOR(oright, field) = RB_BLACK;\
 529                                         RB_COLOR(tmp, field) = RB_RED;  \
 530                                         RB_ROTATE_LEFT(head, tmp, oright, field);\
 531                                         tmp = RB_LEFT(parent, field);   \
 532                                 }                                       \
 533                                 RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
 534                                 RB_COLOR(parent, field) = RB_BLACK;     \
 535                                 if (RB_LEFT(tmp, field))                \
 536                                         RB_COLOR(RB_LEFT(tmp, field), field) = RB_BLACK;\
 537                                 RB_ROTATE_RIGHT(head, parent, tmp, field);\
 538                                 elm = RB_ROOT(head);                    \
 539                                 break;                                  \
 540                         }                                               \
 541                 }                                                       \
 542         }                                                               \
 543         if (elm)                                                        \
 544                 RB_COLOR(elm, field) = RB_BLACK;                        \
 545 }                                                                       \
 546                                                                         \
 547 struct type *                                                           \
 548 name##_RB_REMOVE(struct name *head, struct type *elm)                   \
 549 {                                                                       \
 550         struct type *child, *parent, *old;                              \
 551         struct name##_scan_info *inprog;                                \
 552         int color;                                                      \
 553                                                                         \
 554         for (inprog = RB_INPROG(head); inprog; inprog = inprog->link) { \
 555                 if (inprog->node == elm)                                \
 556                         inprog->node = RB_NEXT(name, head, elm);        \
 557         }                                                               \
 558                                                                         \
 559         old = elm;                                                      \
 560         if (RB_LEFT(elm, field) == NULL)                                \
 561                 child = RB_RIGHT(elm, field);                           \
 562         else if (RB_RIGHT(elm, field) == NULL)                          \
 563                 child = RB_LEFT(elm, field);                            \
 564         else {                                                          \
 565                 struct type *left;                                      \
 566                 elm = RB_RIGHT(elm, field);                             \
 567                 while ((left = RB_LEFT(elm, field)) != NULL)            \
 568                         elm = left;                                     \
 569                 child = RB_RIGHT(elm, field);                           \
 570                 parent = RB_PARENT(elm, field);                         \
 571                 color = RB_COLOR(elm, field);                           \
 572                 if (child)                                              \
 573                         RB_PARENT(child, field) = parent;               \
 574                 if (parent) {                                           \
 575                         if (RB_LEFT(parent, field) == elm)              \
 576                                 RB_LEFT(parent, field) = child;         \
 577                         else                                            \
 578                                 RB_RIGHT(parent, field) = child;        \
 579                         RB_AUGMENT(parent);                             \
 580                 } else                                                  \
 581                         RB_ROOT(head) = child;                          \
 582                 if (RB_PARENT(elm, field) == old)                       \
 583                         parent = elm;                                   \
 584                 (elm)->field = (old)->field;                            \
 585                 if (RB_PARENT(old, field)) {                            \
 586                         if (RB_LEFT(RB_PARENT(old, field), field) == old)\
 587                                 RB_LEFT(RB_PARENT(old, field), field) = elm;\
 588                         else                                            \
 589                                 RB_RIGHT(RB_PARENT(old, field), field) = elm;\
 590                         RB_AUGMENT(RB_PARENT(old, field));              \
 591                 } else                                                  \
 592                         RB_ROOT(head) = elm;                            \
 593                 RB_PARENT(RB_LEFT(old, field), field) = elm;            \
 594                 if (RB_RIGHT(old, field))                               \
 595                         RB_PARENT(RB_RIGHT(old, field), field) = elm;   \
 596                 if (parent) {                                           \
 597                         left = parent;                                  \
 598                         do {                                            \
 599                                 RB_AUGMENT(left);                       \
 600                         } while ((left = RB_PARENT(left, field)) != NULL); \
 601                 }                                                       \
 602                 goto color;                                             \
 603         }                                                               \
 604         parent = RB_PARENT(elm, field);                                 \
 605         color = RB_COLOR(elm, field);                                   \
 606         if (child)                                                      \
 607                 RB_PARENT(child, field) = parent;                       \
 608         if (parent) {                                                   \
 609                 if (RB_LEFT(parent, field) == elm)                      \
 610                         RB_LEFT(parent, field) = child;                 \
 611                 else                                                    \
 612                         RB_RIGHT(parent, field) = child;                \
 613                 RB_AUGMENT(parent);                                     \
 614         } else                                                          \
 615                 RB_ROOT(head) = child;                                  \
 616 color:                                                                  \
 617         if (color == RB_BLACK)                                          \
 618                 name##_RB_REMOVE_COLOR(head, parent, child);            \
 619         return (old);                                                   \
 620 }                                                                       \
 621                                                                         \
 622 /* Inserts a node into the RB tree */                                   \
 623 struct type *                                                           \
 624 name##_RB_INSERT(struct name *head, struct type *elm)                   \
 625 {                                                                       \
 626         struct type *tmp;                                               \
 627         struct type *parent = NULL;                                     \
 628         int comp = 0;                                                   \
 629         tmp = RB_ROOT(head);                                            \
 630         while (tmp) {                                                   \
 631                 parent = tmp;                                           \
 632                 comp = (cmp)(elm, parent);                              \
 633                 if (comp < 0)                                           \
 634                         tmp = RB_LEFT(tmp, field);                      \
 635                 else if (comp > 0)                                      \
 636                         tmp = RB_RIGHT(tmp, field);                     \
 637                 else                                                    \
 638                         return(tmp);                                    \
 639         }                                                               \
 640         RB_SET(elm, parent, field);                                     \
 641         if (parent != NULL) {                                           \
 642                 if (comp < 0)                                           \
 643                         RB_LEFT(parent, field) = elm;                   \
 644                 else                                                    \
 645                         RB_RIGHT(parent, field) = elm;                  \
 646                 RB_AUGMENT(parent);                                     \
 647         } else                                                          \
 648                 RB_ROOT(head) = elm;                                    \
 649         name##_RB_INSERT_COLOR(head, elm);                              \
 650         return (NULL);                                                  \
 651 }                                                                       \
 652                                                                         \
 653 /* Finds the node with the same key as elm */                           \
 654 struct type *                                                           \
 655 name##_RB_FIND(struct name *head, struct type *elm)                     \
 656 {                                                                       \
 657         struct type *tmp = RB_ROOT(head);                               \
 658         int comp;                                                       \
 659         while (tmp) {                                                   \
 660                 comp = cmp(elm, tmp);                                   \
 661                 if (comp < 0)                                           \
 662                         tmp = RB_LEFT(tmp, field);                      \
 663                 else if (comp > 0)                                      \
 664                         tmp = RB_RIGHT(tmp, field);                     \
 665                 else                                                    \
 666                         return (tmp);                                   \
 667         }                                                               \
 668         return (NULL);                                                  \
 669 }                                                                       \
 670                                                                         \
 671 /*                                                                      \
 672  * Issue a callback for all matching items.  The scan function must     \
 673  * return < 0 for items below the desired range, 0 for items within     \
 674  * the range, and > 0 for items beyond the range.   Any item may be     \
 675  * deleted while the scan is in progress.                               \
 676  */                                                                     \
 677 static int                                                              \
 678 name##_SCANCMP_ALL(struct type *type, void *data)                       \
 679 {                                                                       \
 680         return(0);                                                      \
 681 }                                                                       \
 682                                                                         \
 683 int                                                                     \
 684 name##_RB_SCAN(struct name *head,                                       \
 685                 int (*scancmp)(struct type *, void *),                  \
 686                 int (*callback)(struct type *, void *),                 \
 687                 void *data)                                             \
 688 {                                                                       \
 689         struct name##_scan_info info;                                   \
 690         struct name##_scan_info **infopp;                               \
 691         struct type *best;                                              \
 692         struct type *tmp;                                               \
 693         int count;                                                      \
 694         int comp;                                                       \
 695                                                                         \
 696         if (scancmp == NULL)                                            \
 697                 scancmp = name##_SCANCMP_ALL;                           \
 698                                                                         \
 699         /*                                                              \
 700          * Locate the first element.                                    \
 701          */                                                             \
 702         tmp = RB_ROOT(head);                                            \
 703         best = NULL;                                                    \
 704         while (tmp) {                                                   \
 705                 comp = scancmp(tmp, data);                              \
 706                 if (comp < 0) {                                         \
 707                         tmp = RB_RIGHT(tmp, field);                     \
 708                 } else if (comp > 0) {                                  \
 709                         tmp = RB_LEFT(tmp, field);                      \
 710                 } else {                                                \
 711                         best = tmp;                                     \
 712                         if (RB_LEFT(tmp, field) == NULL)                \
 713                                 break;                                  \
 714                         tmp = RB_LEFT(tmp, field);                      \
 715                 }                                                       \
 716         }                                                               \
 717         count = 0;                                                      \
 718         if (best) {                                                     \
 719                 info.node = RB_NEXT(name, head, best);                  \
 720                 info.link = RB_INPROG(head);                            \
 721                 RB_INPROG(head) = &info;                                \
 722                 while ((comp = callback(best, data)) >= 0) {            \
 723                         count += comp;                                  \
 724                         best = info.node;                               \
 725                         if (best == NULL || scancmp(best, data) != 0)   \
 726                                 break;                                  \
 727                         info.node = RB_NEXT(name, head, best);          \
 728                 }                                                       \
 729                 if (comp < 0)   /* error or termination */              \
 730                         count = comp;                                   \
 731                 infopp = &RB_INPROG(head);                              \
 732                 while (*infopp != &info)                                \
 733                         infopp = &(*infopp)->link;                      \
 734                 *infopp = info.link;                                    \
 735         }                                                               \
 736         return(count);                                                  \
 737 }                                                                       \
 738                                                                         \
 739 /* ARGSUSED */                                                          \
 740 struct type *                                                           \
 741 name##_RB_NEXT(struct type *elm)                                        \
 742 {                                                                       \
 743         if (RB_RIGHT(elm, field)) {                                     \
 744                 elm = RB_RIGHT(elm, field);                             \
 745                 while (RB_LEFT(elm, field))                             \
 746                         elm = RB_LEFT(elm, field);                      \
 747         } else {                                                        \
 748                 if (RB_PARENT(elm, field) &&                            \
 749                     (elm == RB_LEFT(RB_PARENT(elm, field), field)))     \
 750                         elm = RB_PARENT(elm, field);                    \
 751                 else {                                                  \
 752                         while (RB_PARENT(elm, field) &&                 \
 753                             (elm == RB_RIGHT(RB_PARENT(elm, field), field)))\
 754                                 elm = RB_PARENT(elm, field);            \
 755                         elm = RB_PARENT(elm, field);                    \
 756                 }                                                       \
 757         }                                                               \
 758         return (elm);                                                   \
 759 }                                                                       \
 760                                                                         \
 761 /* ARGSUSED */                                                          \
 762 struct type *                                                           \
 763 name##_RB_PREV(struct type *elm)                                        \
 764 {                                                                       \
 765         if (RB_LEFT(elm, field)) {                                      \
 766                 elm = RB_LEFT(elm, field);                              \
 767                 while (RB_RIGHT(elm, field))                            \
 768                         elm = RB_RIGHT(elm, field);                     \
 769         } else {                                                        \
 770                 if (RB_PARENT(elm, field) &&                            \
 771                     (elm == RB_RIGHT(RB_PARENT(elm, field), field)))    \
 772                         elm = RB_PARENT(elm, field);                    \
 773                 else {                                                  \
 774                         while (RB_PARENT(elm, field) &&                 \
 775                             (elm == RB_LEFT(RB_PARENT(elm, field), field)))\
 776                                 elm = RB_PARENT(elm, field);            \
 777                         elm = RB_PARENT(elm, field);                    \
 778                 }                                                       \
 779         }                                                               \
 780         return (elm);                                                   \
 781 }                                                                       \
 782                                                                         \
 783 struct type *                                                           \
 784 name##_RB_MINMAX(struct name *head, int val)                            \
 785 {                                                                       \
 786         struct type *tmp = RB_ROOT(head);                               \
 787         struct type *parent = NULL;                                     \
 788         while (tmp) {                                                   \
 789                 parent = tmp;                                           \
 790                 if (val < 0)                                            \
 791                         tmp = RB_LEFT(tmp, field);                      \
 792                 else                                                    \
 793                         tmp = RB_RIGHT(tmp, field);                     \
 794         }                                                               \
 795         return (parent);                                                \
 796 }
 797
 798 /*
 799  * This extended version implements a fast LOOKUP function given
 800  * a numeric data type.
 801  *
 802  * The element whos index/offset field is exactly the specified value
 803  * will be returned, or NULL.
 804  */
 805 #define RB_GENERATE2(name, type, field, cmp, datatype, indexfield)      \
 806 RB_GENERATE(name, type, field, cmp)                                     \
 807                                                                         \
 808 struct type *                                                           \
 809 name##_RB_LOOKUP(struct name *head, datatype value)                     \
 810 {                                                                       \
 811         struct type *tmp;                                               \
 812                                                                         \
 813         tmp = RB_ROOT(head);                                            \
 814         while (tmp) {                                                   \
 815                 if (value > tmp->indexfield)                            \
 816                         tmp = RB_RIGHT(tmp, field);                     \
 817                 else if (value < tmp->indexfield)                       \
 818                         tmp = RB_LEFT(tmp, field);                      \
 819                 else                                                    \
 820                         return(tmp);                                    \
 821         }                                                               \
 822         return(NULL);                                                   \
 823 }                                                                       \
 824
 825 /*
 826  * This extended version implements a fast ranged-based LOOKUP function
 827  * given a numeric data type, for data types with a beginning and end
 828  * (end is inclusive).
 829  *
 830  * The element whos range contains the specified value is returned, or NULL
 831  */
 832 #define RB_GENERATE3(name, type, field, cmp, datatype, begfield, endfield) \
 833 RB_GENERATE2(name, type, field, cmp, datatype, begfield)                \
 834                                                                         \
 835 struct type *                                                           \
 836 name##_RB_RLOOKUP(struct name *head, datatype value)                    \
 837 {                                                                       \
 838         struct type *tmp;                                               \
 839                                                                         \
 840         tmp = RB_ROOT(head);                                            \
 841         while (tmp) {                                                   \
 842                 if (value >= tmp->begfield && value <= tmp->endfield)   \
 843                         return(tmp);                                    \
 844                 if (value > tmp->begfield)                              \
 845                         tmp = RB_RIGHT(tmp, field);                     \
 846                 else                                                    \
 847                         tmp = RB_LEFT(tmp, field);                      \
 848         }                                                               \
 849         return(NULL);                                                   \
 850 }                                                                       \
 851
 852 /*
 853  * This extended version implements a fast ranged-based LOOKUP function
 854  * given a numeric data type, for data types with a beginning and size.
 855  *
 856  * WARNING: The full range of the data type is not supported due to a
 857  * boundary condition at the end, where (beginning + size) might overflow.
 858  *
 859  * The element whos range contains the specified value is returned, or NULL
 860  */
 861 #define RB_GENERATE4(name, type, field, cmp, datatype, begfield, sizefield) \
 862 RB_GENERATE2(name, type, field, cmp, datatype, begfield)                \
 863                                                                         \
 864 struct type *                                                           \
 865 name##_RB_RLOOKUP(struct name *head, datatype value)                    \
 866 {                                                                       \
 867         struct type *tmp;                                               \
 868                                                                         \
 869         tmp = RB_ROOT(head);                                            \
 870         while (tmp) {                                                   \
 871                 if (value >= tmp->begfield &&                           \
 872                     value < tmp->begfield + tmp->sizefield) {           \
 873                         return(tmp);                                    \
 874                 }                                                       \
 875                 if (value > tmp->begfield)                              \
 876                         tmp = RB_RIGHT(tmp, field);                     \
 877                 else                                                    \
 878                         tmp = RB_LEFT(tmp, field);                      \
 879         }                                                               \
 880         return(NULL);                                                   \
 881 }                                                                       \
 882
 883
 884 #define RB_NEGINF       -1
 885 #define RB_INF  1
 886
 887 #define RB_INSERT(name, root, elm)      name##_RB_INSERT(root, elm)
 888 #define RB_REMOVE(name, root, elm)      name##_RB_REMOVE(root, elm)
 889 #define RB_FIND(name, root, elm)        name##_RB_FIND(root, elm)
 890 #define RB_LOOKUP(name, root, value)    name##_RB_LOOKUP(root, value)
 891 #define RB_RLOOKUP(name, root, value)   name##_RB_RLOOKUP(root, value)
 892 #define RB_SCAN(name, root, cmp, callback, data)                        \
 893                                 name##_RB_SCAN(root, cmp, callback, data)
 894 #define RB_NEXT(name, root, elm)        name##_RB_NEXT(elm)
 895 #define RB_PREV(name, root, elm)        name##_RB_PREV(elm)
 896 #define RB_MIN(name, root)              name##_RB_MINMAX(root, RB_NEGINF)
 897 #define RB_MAX(name, root)              name##_RB_MINMAX(root, RB_INF)
 898
 899 #define RB_FOREACH(x, name, head)                                       \
 900         for ((x) = RB_MIN(name, head);                                  \
 901              (x) != NULL;                                               \
 902              (x) = name##_RB_NEXT(x))
 903
 904 #endif  /* _SYS_TREE_H_ */