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 1.3 2006/03/03 20:25:46 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_MINMAX(struct name *, int);                      \
 396 RB_SCAN_INFO(name, type)                                                \
 397
 398 #define RB_PROTOTYPE2(name, type, field, cmp, datatype, datacmp)        \
 399 RB_PROTOTYPE(name, type, field, cmp);                                   \
 400 struct type *name##_RB_LOOKUP(struct name *, datatype value)            \
 401
 402 /* Main rb operation.
 403  * Moves node close to the key of elm to top
 404  */
 405 #define RB_GENERATE(name, type, field, cmp)                             \
 406 static void                                                             \
 407 name##_RB_INSERT_COLOR(struct name *head, struct type *elm)             \
 408 {                                                                       \
 409         struct type *parent, *gparent, *tmp;                            \
 410         while ((parent = RB_PARENT(elm, field)) != NULL &&              \
 411             RB_COLOR(parent, field) == RB_RED) {                        \
 412                 gparent = RB_PARENT(parent, field);                     \
 413                 if (parent == RB_LEFT(gparent, field)) {                \
 414                         tmp = RB_RIGHT(gparent, field);                 \
 415                         if (tmp && RB_COLOR(tmp, field) == RB_RED) {    \
 416                                 RB_COLOR(tmp, field) = RB_BLACK;        \
 417                                 RB_SET_BLACKRED(parent, gparent, field);\
 418                                 elm = gparent;                          \
 419                                 continue;                               \
 420                         }                                               \
 421                         if (RB_RIGHT(parent, field) == elm) {           \
 422                                 RB_ROTATE_LEFT(head, parent, tmp, field);\
 423                                 tmp = parent;                           \
 424                                 parent = elm;                           \
 425                                 elm = tmp;                              \
 426                         }                                               \
 427                         RB_SET_BLACKRED(parent, gparent, field);        \
 428                         RB_ROTATE_RIGHT(head, gparent, tmp, field);     \
 429                 } else {                                                \
 430                         tmp = RB_LEFT(gparent, field);                  \
 431                         if (tmp && RB_COLOR(tmp, field) == RB_RED) {    \
 432                                 RB_COLOR(tmp, field) = RB_BLACK;        \
 433                                 RB_SET_BLACKRED(parent, gparent, field);\
 434                                 elm = gparent;                          \
 435                                 continue;                               \
 436                         }                                               \
 437                         if (RB_LEFT(parent, field) == elm) {            \
 438                                 RB_ROTATE_RIGHT(head, parent, tmp, field);\
 439                                 tmp = parent;                           \
 440                                 parent = elm;                           \
 441                                 elm = tmp;                              \
 442                         }                                               \
 443                         RB_SET_BLACKRED(parent, gparent, field);        \
 444                         RB_ROTATE_LEFT(head, gparent, tmp, field);      \
 445                 }                                                       \
 446         }                                                               \
 447         RB_COLOR(head->rbh_root, field) = RB_BLACK;                     \
 448 }                                                                       \
 449                                                                         \
 450 static void                                                             \
 451 name##_RB_REMOVE_COLOR(struct name *head, struct type *parent,          \
 452                         struct type *elm)                               \
 453 {                                                                       \
 454         struct type *tmp;                                               \
 455         while ((elm == NULL || RB_COLOR(elm, field) == RB_BLACK) &&     \
 456             elm != RB_ROOT(head)) {                                     \
 457                 if (RB_LEFT(parent, field) == elm) {                    \
 458                         tmp = RB_RIGHT(parent, field);                  \
 459                         if (RB_COLOR(tmp, field) == RB_RED) {           \
 460                                 RB_SET_BLACKRED(tmp, parent, field);    \
 461                                 RB_ROTATE_LEFT(head, parent, tmp, field);\
 462                                 tmp = RB_RIGHT(parent, field);          \
 463                         }                                               \
 464                         if ((RB_LEFT(tmp, field) == NULL ||             \
 465                             RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
 466                             (RB_RIGHT(tmp, field) == NULL ||            \
 467                             RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
 468                                 RB_COLOR(tmp, field) = RB_RED;          \
 469                                 elm = parent;                           \
 470                                 parent = RB_PARENT(elm, field);         \
 471                         } else {                                        \
 472                                 if (RB_RIGHT(tmp, field) == NULL ||     \
 473                                     RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK) {\
 474                                         struct type *oleft;             \
 475                                         if ((oleft = RB_LEFT(tmp, field)) \
 476                                             != NULL)                    \
 477                                                 RB_COLOR(oleft, field) = RB_BLACK;\
 478                                         RB_COLOR(tmp, field) = RB_RED;  \
 479                                         RB_ROTATE_RIGHT(head, tmp, oleft, field);\
 480                                         tmp = RB_RIGHT(parent, field);  \
 481                                 }                                       \
 482                                 RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
 483                                 RB_COLOR(parent, field) = RB_BLACK;     \
 484                                 if (RB_RIGHT(tmp, field))               \
 485                                         RB_COLOR(RB_RIGHT(tmp, field), field) = RB_BLACK;\
 486                                 RB_ROTATE_LEFT(head, parent, tmp, field);\
 487                                 elm = RB_ROOT(head);                    \
 488                                 break;                                  \
 489                         }                                               \
 490                 } else {                                                \
 491                         tmp = RB_LEFT(parent, field);                   \
 492                         if (RB_COLOR(tmp, field) == RB_RED) {           \
 493                                 RB_SET_BLACKRED(tmp, parent, field);    \
 494                                 RB_ROTATE_RIGHT(head, parent, tmp, field);\
 495                                 tmp = RB_LEFT(parent, field);           \
 496                         }                                               \
 497                         if ((RB_LEFT(tmp, field) == NULL ||             \
 498                             RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
 499                             (RB_RIGHT(tmp, field) == NULL ||            \
 500                             RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
 501                                 RB_COLOR(tmp, field) = RB_RED;          \
 502                                 elm = parent;                           \
 503                                 parent = RB_PARENT(elm, field);         \
 504                         } else {                                        \
 505                                 if (RB_LEFT(tmp, field) == NULL ||      \
 506                                     RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) {\
 507                                         struct type *oright;            \
 508                                         if ((oright = RB_RIGHT(tmp, field)) \
 509                                             != NULL)                    \
 510                                                 RB_COLOR(oright, field) = RB_BLACK;\
 511                                         RB_COLOR(tmp, field) = RB_RED;  \
 512                                         RB_ROTATE_LEFT(head, tmp, oright, field);\
 513                                         tmp = RB_LEFT(parent, field);   \
 514                                 }                                       \
 515                                 RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
 516                                 RB_COLOR(parent, field) = RB_BLACK;     \
 517                                 if (RB_LEFT(tmp, field))                \
 518                                         RB_COLOR(RB_LEFT(tmp, field), field) = RB_BLACK;\
 519                                 RB_ROTATE_RIGHT(head, parent, tmp, field);\
 520                                 elm = RB_ROOT(head);                    \
 521                                 break;                                  \
 522                         }                                               \
 523                 }                                                       \
 524         }                                                               \
 525         if (elm)                                                        \
 526                 RB_COLOR(elm, field) = RB_BLACK;                        \
 527 }                                                                       \
 528                                                                         \
 529 struct type *                                                           \
 530 name##_RB_REMOVE(struct name *head, struct type *elm)                   \
 531 {                                                                       \
 532         struct type *child, *parent, *old;                              \
 533         struct name##_scan_info *inprog;                                \
 534         int color;                                                      \
 535                                                                         \
 536         for (inprog = RB_INPROG(head); inprog; inprog = inprog->link) { \
 537                 if (inprog->node == elm)                                \
 538                         inprog->node = RB_NEXT(name, head, elm);        \
 539         }                                                               \
 540                                                                         \
 541         old = elm;                                                      \
 542         if (RB_LEFT(elm, field) == NULL)                                \
 543                 child = RB_RIGHT(elm, field);                           \
 544         else if (RB_RIGHT(elm, field) == NULL)                          \
 545                 child = RB_LEFT(elm, field);                            \
 546         else {                                                          \
 547                 struct type *left;                                      \
 548                 elm = RB_RIGHT(elm, field);                             \
 549                 while ((left = RB_LEFT(elm, field)) != NULL)            \
 550                         elm = left;                                     \
 551                 child = RB_RIGHT(elm, field);                           \
 552                 parent = RB_PARENT(elm, field);                         \
 553                 color = RB_COLOR(elm, field);                           \
 554                 if (child)                                              \
 555                         RB_PARENT(child, field) = parent;               \
 556                 if (parent) {                                           \
 557                         if (RB_LEFT(parent, field) == elm)              \
 558                                 RB_LEFT(parent, field) = child;         \
 559                         else                                            \
 560                                 RB_RIGHT(parent, field) = child;        \
 561                         RB_AUGMENT(parent);                             \
 562                 } else                                                  \
 563                         RB_ROOT(head) = child;                          \
 564                 if (RB_PARENT(elm, field) == old)                       \
 565                         parent = elm;                                   \
 566                 (elm)->field = (old)->field;                            \
 567                 if (RB_PARENT(old, field)) {                            \
 568                         if (RB_LEFT(RB_PARENT(old, field), field) == old)\
 569                                 RB_LEFT(RB_PARENT(old, field), field) = elm;\
 570                         else                                            \
 571                                 RB_RIGHT(RB_PARENT(old, field), field) = elm;\
 572                         RB_AUGMENT(RB_PARENT(old, field));              \
 573                 } else                                                  \
 574                         RB_ROOT(head) = elm;                            \
 575                 RB_PARENT(RB_LEFT(old, field), field) = elm;            \
 576                 if (RB_RIGHT(old, field))                               \
 577                         RB_PARENT(RB_RIGHT(old, field), field) = elm;   \
 578                 if (parent) {                                           \
 579                         left = parent;                                  \
 580                         do {                                            \
 581                                 RB_AUGMENT(left);                       \
 582                         } while ((left = RB_PARENT(left, field)) != NULL); \
 583                 }                                                       \
 584                 goto color;                                             \
 585         }                                                               \
 586         parent = RB_PARENT(elm, field);                                 \
 587         color = RB_COLOR(elm, field);                                   \
 588         if (child)                                                      \
 589                 RB_PARENT(child, field) = parent;                       \
 590         if (parent) {                                                   \
 591                 if (RB_LEFT(parent, field) == elm)                      \
 592                         RB_LEFT(parent, field) = child;                 \
 593                 else                                                    \
 594                         RB_RIGHT(parent, field) = child;                \
 595                 RB_AUGMENT(parent);                                     \
 596         } else                                                          \
 597                 RB_ROOT(head) = child;                                  \
 598 color:                                                                  \
 599         if (color == RB_BLACK)                                          \
 600                 name##_RB_REMOVE_COLOR(head, parent, child);            \
 601         return (old);                                                   \
 602 }                                                                       \
 603                                                                         \
 604 /* Inserts a node into the RB tree */                                   \
 605 struct type *                                                           \
 606 name##_RB_INSERT(struct name *head, struct type *elm)                   \
 607 {                                                                       \
 608         struct type *tmp;                                               \
 609         struct type *parent = NULL;                                     \
 610         int comp = 0;                                                   \
 611         tmp = RB_ROOT(head);                                            \
 612         while (tmp) {                                                   \
 613                 parent = tmp;                                           \
 614                 comp = (cmp)(elm, parent);                              \
 615                 if (comp < 0)                                           \
 616                         tmp = RB_LEFT(tmp, field);                      \
 617                 else if (comp > 0)                                      \
 618                         tmp = RB_RIGHT(tmp, field);                     \
 619                 else                                                    \
 620                         return(tmp);                                    \
 621         }                                                               \
 622         RB_SET(elm, parent, field);                                     \
 623         if (parent != NULL) {                                           \
 624                 if (comp < 0)                                           \
 625                         RB_LEFT(parent, field) = elm;                   \
 626                 else                                                    \
 627                         RB_RIGHT(parent, field) = elm;                  \
 628                 RB_AUGMENT(parent);                                     \
 629         } else                                                          \
 630                 RB_ROOT(head) = elm;                                    \
 631         name##_RB_INSERT_COLOR(head, elm);                              \
 632         return (NULL);                                                  \
 633 }                                                                       \
 634                                                                         \
 635 /* Finds the node with the same key as elm */                           \
 636 struct type *                                                           \
 637 name##_RB_FIND(struct name *head, struct type *elm)                     \
 638 {                                                                       \
 639         struct type *tmp = RB_ROOT(head);                               \
 640         int comp;                                                       \
 641         while (tmp) {                                                   \
 642                 comp = cmp(elm, tmp);                                   \
 643                 if (comp < 0)                                           \
 644                         tmp = RB_LEFT(tmp, field);                      \
 645                 else if (comp > 0)                                      \
 646                         tmp = RB_RIGHT(tmp, field);                     \
 647                 else                                                    \
 648                         return (tmp);                                   \
 649         }                                                               \
 650         return (NULL);                                                  \
 651 }                                                                       \
 652                                                                         \
 653 /*                                                                      \
 654  * Issue a callback for all matching items.  The scan function must     \
 655  * return < 0 for items below the desired range, 0 for items within     \
 656  * the range, and > 0 for items beyond the range.   Any item may be     \
 657  * deleted while the scan is in progress.                               \
 658  */                                                                     \
 659 static int                                                              \
 660 name##_SCANCMP_ALL(struct type *type, void *data)                       \
 661 {                                                                       \
 662         return(0);                                                      \
 663 }                                                                       \
 664                                                                         \
 665 int                                                                     \
 666 name##_RB_SCAN(struct name *head,                                       \
 667                 int (*scancmp)(struct type *, void *),                  \
 668                 int (*callback)(struct type *, void *),                 \
 669                 void *data)                                             \
 670 {                                                                       \
 671         struct name##_scan_info info;                                   \
 672         struct name##_scan_info **infopp;                               \
 673         struct type *best;                                              \
 674         struct type *tmp;                                               \
 675         int count;                                                      \
 676         int comp;                                                       \
 677                                                                         \
 678         if (scancmp == NULL)                                            \
 679                 scancmp = name##_SCANCMP_ALL;                           \
 680                                                                         \
 681         /*                                                              \
 682          * Locate the first element.                                    \
 683          */                                                             \
 684         tmp = RB_ROOT(head);                                            \
 685         best = NULL;                                                    \
 686         while (tmp) {                                                   \
 687                 comp = scancmp(tmp, data);                              \
 688                 if (comp < 0) {                                         \
 689                         tmp = RB_RIGHT(tmp, field);                     \
 690                 } else if (comp > 0) {                                  \
 691                         tmp = RB_LEFT(tmp, field);                      \
 692                 } else {                                                \
 693                         best = tmp;                                     \
 694                         if (RB_LEFT(tmp, field) == NULL)                \
 695                                 break;                                  \
 696                         tmp = RB_LEFT(tmp, field);                      \
 697                 }                                                       \
 698         }                                                               \
 699         count = 0;                                                      \
 700         if (best) {                                                     \
 701                 info.node = RB_NEXT(name, head, best);                  \
 702                 info.link = RB_INPROG(head);                            \
 703                 RB_INPROG(head) = &info;                                \
 704                 while ((comp = callback(best, data)) >= 0) {            \
 705                         count += comp;                                  \
 706                         best = info.node;                               \
 707                         if (best == NULL || scancmp(best, data) != 0)   \
 708                                 break;                                  \
 709                         info.node = RB_NEXT(name, head, best);          \
 710                 }                                                       \
 711                 if (comp < 0)   /* error or termination */              \
 712                         count = comp;                                   \
 713                 infopp = &RB_INPROG(head);                              \
 714                 while (*infopp != &info)                                \
 715                         infopp = &(*infopp)->link;                      \
 716                 *infopp = info.link;                                    \
 717         }                                                               \
 718         return(count);                                                  \
 719 }                                                                       \
 720                                                                         \
 721 /* ARGSUSED */                                                          \
 722 struct type *                                                           \
 723 name##_RB_NEXT(struct type *elm)                                        \
 724 {                                                                       \
 725         if (RB_RIGHT(elm, field)) {                                     \
 726                 elm = RB_RIGHT(elm, field);                             \
 727                 while (RB_LEFT(elm, field))                             \
 728                         elm = RB_LEFT(elm, field);                      \
 729         } else {                                                        \
 730                 if (RB_PARENT(elm, field) &&                            \
 731                     (elm == RB_LEFT(RB_PARENT(elm, field), field)))     \
 732                         elm = RB_PARENT(elm, field);                    \
 733                 else {                                                  \
 734                         while (RB_PARENT(elm, field) &&                 \
 735                             (elm == RB_RIGHT(RB_PARENT(elm, field), field)))\
 736                                 elm = RB_PARENT(elm, field);            \
 737                         elm = RB_PARENT(elm, field);                    \
 738                 }                                                       \
 739         }                                                               \
 740         return (elm);                                                   \
 741 }                                                                       \
 742                                                                         \
 743 struct type *                                                           \
 744 name##_RB_MINMAX(struct name *head, int val)                            \
 745 {                                                                       \
 746         struct type *tmp = RB_ROOT(head);                               \
 747         struct type *parent = NULL;                                     \
 748         while (tmp) {                                                   \
 749                 parent = tmp;                                           \
 750                 if (val < 0)                                            \
 751                         tmp = RB_LEFT(tmp, field);                      \
 752                 else                                                    \
 753                         tmp = RB_RIGHT(tmp, field);                     \
 754         }                                                               \
 755         return (parent);                                                \
 756 }
 757
 758 /*
 759  * This extended version implements a fast LOOKUP function given
 760  * a numeric data type.
 761  *
 762  * The element whos index/offset field is exactly the specified value
 763  * will be returned, or NULL.
 764  */
 765 #define RB_GENERATE2(name, type, field, cmp, datatype, indexfield)      \
 766 RB_GENERATE(name, type, field, cmp)                                     \
 767                                                                         \
 768 struct type *                                                           \
 769 name##_RB_LOOKUP(struct name *head, datatype value)                     \
 770 {                                                                       \
 771         struct type *tmp;                                               \
 772                                                                         \
 773         tmp = RB_ROOT(head);                                            \
 774         while (tmp) {                                                   \
 775                 if (value > tmp->indexfield)                            \
 776                         tmp = RB_RIGHT(tmp, field);                     \
 777                 else if (value < tmp->indexfield)                       \
 778                         tmp = RB_LEFT(tmp, field);                      \
 779                 else                                                    \
 780                         return(tmp);                                    \
 781         }                                                               \
 782         return(NULL);                                                   \
 783 }                                                                       \
 784
 785 /*
 786  * This extended version implements a fast ranged-based LOOKUP function
 787  * given a numeric data type, for data types with a beginning and end
 788  * (end non-inclusive).
 789  *
 790  * The element whos range contains the specified value is returned, or NULL
 791  */
 792 #define RB_GENERATE3(name, type, field, cmp, datatype, begfield, endfield) \
 793 RB_GENERATE2(name, type, field, cmp, datatype, begfield)                \
 794                                                                         \
 795 struct type *                                                           \
 796 name##_RB_RANGED_LOOKUP(struct name *head, datatype value)              \
 797 {                                                                       \
 798         struct type *tmp;                                               \
 799                                                                         \
 800         tmp = RB_ROOT(head);                                            \
 801         while (tmp) {                                                   \
 802                 if (value >= tmp->begfield && value < tmp->endfield)    \
 803                         return(tmp);                                    \
 804                 if (value > tmp->begfield)                              \
 805                         tmp = RB_RIGHT(tmp, field);                     \
 806                 else                                                    \
 807                         tmp = RB_LEFT(tmp, field);                      \
 808         }                                                               \
 809         return(NULL);                                                   \
 810 }                                                                       \
 811
 812 #define RB_NEGINF       -1
 813 #define RB_INF  1
 814
 815 #define RB_INSERT(name, x, y)   name##_RB_INSERT(x, y)
 816 #define RB_REMOVE(name, x, y)   name##_RB_REMOVE(x, y)
 817 #define RB_FIND(name, x, y)     name##_RB_FIND(x, y)
 818 #define RB_SCAN(name, root, cmp, callback, data)                \
 819                                 name##_RB_SCAN(root, cmp, callback, data)
 820 #define RB_NEXT(name, x, y)     name##_RB_NEXT(y)
 821 #define RB_MIN(name, x)         name##_RB_MINMAX(x, RB_NEGINF)
 822 #define RB_MAX(name, x)         name##_RB_MINMAX(x, RB_INF)
 823
 824 #define RB_FOREACH(x, name, head)                                       \
 825         for ((x) = RB_MIN(name, head);                                  \
 826              (x) != NULL;                                               \
 827              (x) = name##_RB_NEXT(x))
 828
 829 #endif  /* _SYS_TREE_H_ */