lwext4/tree.h

   1 /*      $NetBSD: tree.h,v 1.8 2004/03/28 19:38:30 provos Exp $  */
   2 /*      $OpenBSD: tree.h,v 1.7 2002/10/17 21:51:54 art Exp $    */
   3 /* $FreeBSD$ */
   4
   5 /*-
   6  * Copyright 2002 Niels Provos <provos@citi.umich.edu>
   7  * All rights reserved.
   8  *
   9  * Redistribution and use in source and binary forms, with or without
  10  * modification, are permitted provided that the following conditions
  11  * are met:
  12  * 1. Redistributions of source code must retain the above copyright
  13  *    notice, this list of conditions and the following disclaimer.
  14  * 2. Redistributions in binary form must reproduce the above copyright
  15  *    notice, this list of conditions and the following disclaimer in the
  16  *    documentation and/or other materials provided with the distribution.
  17  *
  18  * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
  19  * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
  20  * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
  21  * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
  22  * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
  23  * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
  24  * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
  25  * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
  26  * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
  27  * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
  28  */
  29
  30 #ifndef _SYS_TREE_H_
  31 #define _SYS_TREE_H_
  32
  33 #ifdef __GNUC__
  34 #define __unused __attribute__ ((__unused__))
  35 #endif
  36 /*
  37  * This file defines data structures for different types of trees:
  38  * splay trees and red-black trees.
  39  *
  40  * A splay tree is a self-organizing data structure.  Every operation
  41  * on the tree causes a splay to happen.  The splay moves the requested
  42  * node to the root of the tree and partly rebalances it.
  43  *
  44  * This has the benefit that request locality causes faster lookups as
  45  * the requested nodes move to the top of the tree.  On the other hand,
  46  * every lookup causes memory writes.
  47  *
  48  * The Balance Theorem bounds the total access time for m operations
  49  * and n inserts on an initially empty tree as O((m + n)lg n).  The
  50  * amortized cost for a sequence of m accesses to a splay tree is O(lg n);
  51  *
  52  * A red-black tree is a binary search tree with the node color as an
  53  * extra attribute.  It fulfills a set of conditions:
  54  *      - every search path from the root to a leaf consists of the
  55  *        same number of black nodes,
  56  *      - each red node (except for the root) has a black parent,
  57  *      - each leaf node is black.
  58  *
  59  * Every operation on a red-black tree is bounded as O(lg n).
  60  * The maximum height of a red-black tree is 2lg (n+1).
  61  */
  62
  63 #define SPLAY_HEAD(name, type)                                          \
  64 struct name {                                                           \
  65         struct type *sph_root; /* root of the tree */                   \
  66 }
  67
  68 #define SPLAY_INITIALIZER(root)                                         \
  69         { NULL }
  70
  71 #define SPLAY_INIT(root) do {                                           \
  72         (root)->sph_root = NULL;                                        \
  73 } while (/*CONSTCOND*/ 0)
  74
  75 #define SPLAY_ENTRY(type)                                               \
  76 struct {                                                                \
  77         struct type *spe_left; /* left element */                       \
  78         struct type *spe_right; /* right element */                     \
  79 }
  80
  81 #define SPLAY_LEFT(elm, field)          (elm)->field.spe_left
  82 #define SPLAY_RIGHT(elm, field)         (elm)->field.spe_right
  83 #define SPLAY_ROOT(head)                (head)->sph_root
  84 #define SPLAY_EMPTY(head)               (SPLAY_ROOT(head) == NULL)
  85
  86 /* SPLAY_ROTATE_{LEFT,RIGHT} expect that tmp hold SPLAY_{RIGHT,LEFT} */
  87 #define SPLAY_ROTATE_RIGHT(head, tmp, field) do {                       \
  88         SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(tmp, field);  \
  89         SPLAY_RIGHT(tmp, field) = (head)->sph_root;                     \
  90         (head)->sph_root = tmp;                                         \
  91 } while (/*CONSTCOND*/ 0)
  92
  93 #define SPLAY_ROTATE_LEFT(head, tmp, field) do {                        \
  94         SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(tmp, field);  \
  95         SPLAY_LEFT(tmp, field) = (head)->sph_root;                      \
  96         (head)->sph_root = tmp;                                         \
  97 } while (/*CONSTCOND*/ 0)
  98
  99 #define SPLAY_LINKLEFT(head, tmp, field) do {                           \
 100         SPLAY_LEFT(tmp, field) = (head)->sph_root;                      \
 101         tmp = (head)->sph_root;                                         \
 102         (head)->sph_root = SPLAY_LEFT((head)->sph_root, field);         \
 103 } while (/*CONSTCOND*/ 0)
 104
 105 #define SPLAY_LINKRIGHT(head, tmp, field) do {                          \
 106         SPLAY_RIGHT(tmp, field) = (head)->sph_root;                     \
 107         tmp = (head)->sph_root;                                         \
 108         (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);        \
 109 } while (/*CONSTCOND*/ 0)
 110
 111 #define SPLAY_ASSEMBLE(head, node, left, right, field) do {             \
 112         SPLAY_RIGHT(left, field) = SPLAY_LEFT((head)->sph_root, field); \
 113         SPLAY_LEFT(right, field) = SPLAY_RIGHT((head)->sph_root, field);\
 114         SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(node, field); \
 115         SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(node, field); \
 116 } while (/*CONSTCOND*/ 0)
 117
 118 /* Generates prototypes and inline functions */
 119
 120 #define SPLAY_PROTOTYPE(name, type, field, cmp)                         \
 121 void name##_SPLAY(struct name *, struct type *);                        \
 122 void name##_SPLAY_MINMAX(struct name *, int);                           \
 123 struct type *name##_SPLAY_INSERT(struct name *, struct type *);         \
 124 struct type *name##_SPLAY_REMOVE(struct name *, struct type *);         \
 125                                                                         \
 126 /* Finds the node with the same key as elm */                           \
 127 static __inline struct type *                                           \
 128 name##_SPLAY_FIND(struct name *head, struct type *elm)                  \
 129 {                                                                       \
 130         if (SPLAY_EMPTY(head))                                          \
 131                 return(NULL);                                           \
 132         name##_SPLAY(head, elm);                                        \
 133         if ((cmp)(elm, (head)->sph_root) == 0)                          \
 134                 return (head->sph_root);                                \
 135         return (NULL);                                                  \
 136 }                                                                       \
 137                                                                         \
 138 static __inline struct type *                                           \
 139 name##_SPLAY_NEXT(struct name *head, struct type *elm)                  \
 140 {                                                                       \
 141         name##_SPLAY(head, elm);                                        \
 142         if (SPLAY_RIGHT(elm, field) != NULL) {                          \
 143                 elm = SPLAY_RIGHT(elm, field);                          \
 144                 while (SPLAY_LEFT(elm, field) != NULL) {                \
 145                         elm = SPLAY_LEFT(elm, field);                   \
 146                 }                                                       \
 147         } else                                                          \
 148                 elm = NULL;                                             \
 149         return (elm);                                                   \
 150 }                                                                       \
 151                                                                         \
 152 static __inline struct type *                                           \
 153 name##_SPLAY_MIN_MAX(struct name *head, int val)                        \
 154 {                                                                       \
 155         name##_SPLAY_MINMAX(head, val);                                 \
 156         return (SPLAY_ROOT(head));                                      \
 157 }
 158
 159 /* Main splay operation.
 160  * Moves node close to the key of elm to top
 161  */
 162 #define SPLAY_GENERATE(name, type, field, cmp)                          \
 163 struct type *                                                           \
 164 name##_SPLAY_INSERT(struct name *head, struct type *elm)                \
 165 {                                                                       \
 166     if (SPLAY_EMPTY(head)) {                                            \
 167             SPLAY_LEFT(elm, field) = SPLAY_RIGHT(elm, field) = NULL;    \
 168     } else {                                                            \
 169             int __comp;                                                 \
 170             name##_SPLAY(head, elm);                                    \
 171             __comp = (cmp)(elm, (head)->sph_root);                      \
 172             if(__comp < 0) {                                            \
 173                     SPLAY_LEFT(elm, field) = SPLAY_LEFT((head)->sph_root, field);\
 174                     SPLAY_RIGHT(elm, field) = (head)->sph_root;         \
 175                     SPLAY_LEFT((head)->sph_root, field) = NULL;         \
 176             } else if (__comp > 0) {                                    \
 177                     SPLAY_RIGHT(elm, field) = SPLAY_RIGHT((head)->sph_root, field);\
 178                     SPLAY_LEFT(elm, field) = (head)->sph_root;          \
 179                     SPLAY_RIGHT((head)->sph_root, field) = NULL;        \
 180             } else                                                      \
 181                     return ((head)->sph_root);                          \
 182     }                                                                   \
 183     (head)->sph_root = (elm);                                           \
 184     return (NULL);                                                      \
 185 }                                                                       \
 186                                                                         \
 187 struct type *                                                           \
 188 name##_SPLAY_REMOVE(struct name *head, struct type *elm)                \
 189 {                                                                       \
 190         struct type *__tmp;                                             \
 191         if (SPLAY_EMPTY(head))                                          \
 192                 return (NULL);                                          \
 193         name##_SPLAY(head, elm);                                        \
 194         if ((cmp)(elm, (head)->sph_root) == 0) {                        \
 195                 if (SPLAY_LEFT((head)->sph_root, field) == NULL) {      \
 196                         (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);\
 197                 } else {                                                \
 198                         __tmp = SPLAY_RIGHT((head)->sph_root, field);   \
 199                         (head)->sph_root = SPLAY_LEFT((head)->sph_root, field);\
 200                         name##_SPLAY(head, elm);                        \
 201                         SPLAY_RIGHT((head)->sph_root, field) = __tmp;   \
 202                 }                                                       \
 203                 return (elm);                                           \
 204         }                                                               \
 205         return (NULL);                                                  \
 206 }                                                                       \
 207                                                                         \
 208 void                                                                    \
 209 name##_SPLAY(struct name *head, struct type *elm)                       \
 210 {                                                                       \
 211         struct type __node, *__left, *__right, *__tmp;                  \
 212         int __comp;                                                     \
 213 \
 214         SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
 215         __left = __right = &__node;                                     \
 216 \
 217         while ((__comp = (cmp)(elm, (head)->sph_root)) != 0) {          \
 218                 if (__comp < 0) {                                       \
 219                         __tmp = SPLAY_LEFT((head)->sph_root, field);    \
 220                         if (__tmp == NULL)                              \
 221                                 break;                                  \
 222                         if ((cmp)(elm, __tmp) < 0){                     \
 223                                 SPLAY_ROTATE_RIGHT(head, __tmp, field); \
 224                                 if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
 225                                         break;                          \
 226                         }                                               \
 227                         SPLAY_LINKLEFT(head, __right, field);           \
 228                 } else if (__comp > 0) {                                \
 229                         __tmp = SPLAY_RIGHT((head)->sph_root, field);   \
 230                         if (__tmp == NULL)                              \
 231                                 break;                                  \
 232                         if ((cmp)(elm, __tmp) > 0){                     \
 233                                 SPLAY_ROTATE_LEFT(head, __tmp, field);  \
 234                                 if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
 235                                         break;                          \
 236                         }                                               \
 237                         SPLAY_LINKRIGHT(head, __left, field);           \
 238                 }                                                       \
 239         }                                                               \
 240         SPLAY_ASSEMBLE(head, &__node, __left, __right, field);          \
 241 }                                                                       \
 242                                                                         \
 243 /* Splay with either the minimum or the maximum element                 \
 244  * Used to find minimum or maximum element in tree.                     \
 245  */                                                                     \
 246 void name##_SPLAY_MINMAX(struct name *head, int __comp) \
 247 {                                                                       \
 248         struct type __node, *__left, *__right, *__tmp;                  \
 249 \
 250         SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
 251         __left = __right = &__node;                                     \
 252 \
 253         while (1) {                                                     \
 254                 if (__comp < 0) {                                       \
 255                         __tmp = SPLAY_LEFT((head)->sph_root, field);    \
 256                         if (__tmp == NULL)                              \
 257                                 break;                                  \
 258                         if (__comp < 0){                                \
 259                                 SPLAY_ROTATE_RIGHT(head, __tmp, field); \
 260                                 if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
 261                                         break;                          \
 262                         }                                               \
 263                         SPLAY_LINKLEFT(head, __right, field);           \
 264                 } else if (__comp > 0) {                                \
 265                         __tmp = SPLAY_RIGHT((head)->sph_root, field);   \
 266                         if (__tmp == NULL)                              \
 267                                 break;                                  \
 268                         if (__comp > 0) {                               \
 269                                 SPLAY_ROTATE_LEFT(head, __tmp, field);  \
 270                                 if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
 271                                         break;                          \
 272                         }                                               \
 273                         SPLAY_LINKRIGHT(head, __left, field);           \
 274                 }                                                       \
 275         }                                                               \
 276         SPLAY_ASSEMBLE(head, &__node, __left, __right, field);          \
 277 }
 278
 279 #define SPLAY_NEGINF    -1
 280 #define SPLAY_INF       1
 281
 282 #define SPLAY_INSERT(name, x, y)        name##_SPLAY_INSERT(x, y)
 283 #define SPLAY_REMOVE(name, x, y)        name##_SPLAY_REMOVE(x, y)
 284 #define SPLAY_FIND(name, x, y)          name##_SPLAY_FIND(x, y)
 285 #define SPLAY_NEXT(name, x, y)          name##_SPLAY_NEXT(x, y)
 286 #define SPLAY_MIN(name, x)              (SPLAY_EMPTY(x) ? NULL  \
 287                                         : name##_SPLAY_MIN_MAX(x, SPLAY_NEGINF))
 288 #define SPLAY_MAX(name, x)              (SPLAY_EMPTY(x) ? NULL  \
 289                                         : name##_SPLAY_MIN_MAX(x, SPLAY_INF))
 290
 291 #define SPLAY_FOREACH(x, name, head)                                    \
 292         for ((x) = SPLAY_MIN(name, head);                               \
 293              (x) != NULL;                                               \
 294              (x) = SPLAY_NEXT(name, head, x))
 295
 296 /* Macros that define a red-black tree */
 297 #define RB_HEAD(name, type)                                             \
 298 struct name {                                                           \
 299         struct type *rbh_root; /* root of the tree */                   \
 300 }
 301
 302 #define RB_INITIALIZER(root)                                            \
 303         { NULL }
 304
 305 #define RB_INIT(root) do {                                              \
 306         (root)->rbh_root = NULL;                                        \
 307 } while (/*CONSTCOND*/ 0)
 308
 309 #define RB_BLACK        0
 310 #define RB_RED          1
 311 #define RB_ENTRY(type)                                                  \
 312 struct {                                                                \
 313         struct type *rbe_left;          /* left element */              \
 314         struct type *rbe_right;         /* right element */             \
 315         struct type *rbe_parent;        /* parent element */            \
 316         int rbe_color;                  /* node color */                \
 317 }
 318
 319 #define RB_LEFT(elm, field)             (elm)->field.rbe_left
 320 #define RB_RIGHT(elm, field)            (elm)->field.rbe_right
 321 #define RB_PARENT(elm, field)           (elm)->field.rbe_parent
 322 #define RB_COLOR(elm, field)            (elm)->field.rbe_color
 323 #define RB_ROOT(head)                   (head)->rbh_root
 324 #define RB_EMPTY(head)                  (RB_ROOT(head) == NULL)
 325
 326 #define RB_SET(elm, parent, field) do {                                 \
 327         RB_PARENT(elm, field) = parent;                                 \
 328         RB_LEFT(elm, field) = RB_RIGHT(elm, field) = NULL;              \
 329         RB_COLOR(elm, field) = RB_RED;                                  \
 330 } while (/*CONSTCOND*/ 0)
 331
 332 #define RB_SET_BLACKRED(black, red, field) do {                         \
 333         RB_COLOR(black, field) = RB_BLACK;                              \
 334         RB_COLOR(red, field) = RB_RED;                                  \
 335 } while (/*CONSTCOND*/ 0)
 336
 337 #ifndef RB_AUGMENT
 338 #define RB_AUGMENT(x)   do {} while (0)
 339 #endif
 340
 341 #define RB_ROTATE_LEFT(head, elm, tmp, field) do {                      \
 342         (tmp) = RB_RIGHT(elm, field);                                   \
 343         if ((RB_RIGHT(elm, field) = RB_LEFT(tmp, field)) != NULL) {     \
 344                 RB_PARENT(RB_LEFT(tmp, field), field) = (elm);          \
 345         }                                                               \
 346         RB_AUGMENT(elm);                                                \
 347         if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) {  \
 348                 if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))     \
 349                         RB_LEFT(RB_PARENT(elm, field), field) = (tmp);  \
 350                 else                                                    \
 351                         RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \
 352         } else                                                          \
 353                 (head)->rbh_root = (tmp);                               \
 354         RB_LEFT(tmp, field) = (elm);                                    \
 355         RB_PARENT(elm, field) = (tmp);                                  \
 356         RB_AUGMENT(tmp);                                                \
 357         if ((RB_PARENT(tmp, field)))                                    \
 358                 RB_AUGMENT(RB_PARENT(tmp, field));                      \
 359 } while (/*CONSTCOND*/ 0)
 360
 361 #define RB_ROTATE_RIGHT(head, elm, tmp, field) do {                     \
 362         (tmp) = RB_LEFT(elm, field);                                    \
 363         if ((RB_LEFT(elm, field) = RB_RIGHT(tmp, field)) != NULL) {     \
 364                 RB_PARENT(RB_RIGHT(tmp, field), field) = (elm);         \
 365         }                                                               \
 366         RB_AUGMENT(elm);                                                \
 367         if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) {  \
 368                 if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))     \
 369                         RB_LEFT(RB_PARENT(elm, field), field) = (tmp);  \
 370                 else                                                    \
 371                         RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \
 372         } else                                                          \
 373                 (head)->rbh_root = (tmp);                               \
 374         RB_RIGHT(tmp, field) = (elm);                                   \
 375         RB_PARENT(elm, field) = (tmp);                                  \
 376         RB_AUGMENT(tmp);                                                \
 377         if ((RB_PARENT(tmp, field)))                                    \
 378                 RB_AUGMENT(RB_PARENT(tmp, field));                      \
 379 } while (/*CONSTCOND*/ 0)
 380
 381 /* Generates prototypes and inline functions */
 382 #define RB_PROTOTYPE(name, type, field, cmp)                            \
 383         RB_PROTOTYPE_INTERNAL(name, type, field, cmp,)
 384 #define RB_PROTOTYPE_STATIC(name, type, field, cmp)                     \
 385         RB_PROTOTYPE_INTERNAL(name, type, field, cmp, __unused static)
 386 #define RB_PROTOTYPE_INTERNAL(name, type, field, cmp, attr)             \
 387         RB_PROTOTYPE_INSERT_COLOR(name, type, attr);                    \
 388         RB_PROTOTYPE_REMOVE_COLOR(name, type, attr);                    \
 389         RB_PROTOTYPE_INSERT(name, type, attr);                          \
 390         RB_PROTOTYPE_REMOVE(name, type, attr);                          \
 391         RB_PROTOTYPE_FIND(name, type, attr);                            \
 392         RB_PROTOTYPE_NFIND(name, type, attr);                           \
 393         RB_PROTOTYPE_NEXT(name, type, attr);                            \
 394         RB_PROTOTYPE_PREV(name, type, attr);                            \
 395         RB_PROTOTYPE_MINMAX(name, type, attr);
 396 #define RB_PROTOTYPE_INSERT_COLOR(name, type, attr)                     \
 397         attr void name##_RB_INSERT_COLOR(struct name *, struct type *)
 398 #define RB_PROTOTYPE_REMOVE_COLOR(name, type, attr)                     \
 399         attr void name##_RB_REMOVE_COLOR(struct name *, struct type *, struct type *)
 400 #define RB_PROTOTYPE_REMOVE(name, type, attr)                           \
 401         attr struct type *name##_RB_REMOVE(struct name *, struct type *)
 402 #define RB_PROTOTYPE_INSERT(name, type, attr)                           \
 403         attr struct type *name##_RB_INSERT(struct name *, struct type *)
 404 #define RB_PROTOTYPE_FIND(name, type, attr)                             \
 405         attr struct type *name##_RB_FIND(struct name *, struct type *)
 406 #define RB_PROTOTYPE_NFIND(name, type, attr)                            \
 407         attr struct type *name##_RB_NFIND(struct name *, struct type *)
 408 #define RB_PROTOTYPE_NEXT(name, type, attr)                             \
 409         attr struct type *name##_RB_NEXT(struct type *)
 410 #define RB_PROTOTYPE_PREV(name, type, attr)                             \
 411         attr struct type *name##_RB_PREV(struct type *)
 412 #define RB_PROTOTYPE_MINMAX(name, type, attr)                           \
 413         attr struct type *name##_RB_MINMAX(struct name *, int)
 414
 415 /* Main rb operation.
 416  * Moves node close to the key of elm to top
 417  */
 418 #define RB_GENERATE(name, type, field, cmp)                             \
 419         RB_GENERATE_INTERNAL(name, type, field, cmp,)
 420 #define RB_GENERATE_STATIC(name, type, field, cmp)                      \
 421         RB_GENERATE_INTERNAL(name, type, field, cmp, __unused static)
 422 #define RB_GENERATE_INTERNAL(name, type, field, cmp, attr)              \
 423         RB_GENERATE_INSERT_COLOR(name, type, field, attr)               \
 424         RB_GENERATE_REMOVE_COLOR(name, type, field, attr)               \
 425         RB_GENERATE_INSERT(name, type, field, cmp, attr)                \
 426         RB_GENERATE_REMOVE(name, type, field, attr)                     \
 427         RB_GENERATE_FIND(name, type, field, cmp, attr)                  \
 428         RB_GENERATE_NFIND(name, type, field, cmp, attr)                 \
 429         RB_GENERATE_NEXT(name, type, field, attr)                       \
 430         RB_GENERATE_PREV(name, type, field, attr)                       \
 431         RB_GENERATE_MINMAX(name, type, field, attr)
 432
 433 #define RB_GENERATE_INSERT_COLOR(name, type, field, attr)               \
 434 attr void                                                               \
 435 name##_RB_INSERT_COLOR(struct name *head, struct type *elm)             \
 436 {                                                                       \
 437         struct type *parent, *gparent, *tmp;                            \
 438         while ((parent = RB_PARENT(elm, field)) != NULL &&              \
 439             RB_COLOR(parent, field) == RB_RED) {                        \
 440                 gparent = RB_PARENT(parent, field);                     \
 441                 if (parent == RB_LEFT(gparent, field)) {                \
 442                         tmp = RB_RIGHT(gparent, field);                 \
 443                         if (tmp && RB_COLOR(tmp, field) == RB_RED) {    \
 444                                 RB_COLOR(tmp, field) = RB_BLACK;        \
 445                                 RB_SET_BLACKRED(parent, gparent, field);\
 446                                 elm = gparent;                          \
 447                                 continue;                               \
 448                         }                                               \
 449                         if (RB_RIGHT(parent, field) == elm) {           \
 450                                 RB_ROTATE_LEFT(head, parent, tmp, field);\
 451                                 tmp = parent;                           \
 452                                 parent = elm;                           \
 453                                 elm = tmp;                              \
 454                         }                                               \
 455                         RB_SET_BLACKRED(parent, gparent, field);        \
 456                         RB_ROTATE_RIGHT(head, gparent, tmp, field);     \
 457                 } else {                                                \
 458                         tmp = RB_LEFT(gparent, field);                  \
 459                         if (tmp && RB_COLOR(tmp, field) == RB_RED) {    \
 460                                 RB_COLOR(tmp, field) = RB_BLACK;        \
 461                                 RB_SET_BLACKRED(parent, gparent, field);\
 462                                 elm = gparent;                          \
 463                                 continue;                               \
 464                         }                                               \
 465                         if (RB_LEFT(parent, field) == elm) {            \
 466                                 RB_ROTATE_RIGHT(head, parent, tmp, field);\
 467                                 tmp = parent;                           \
 468                                 parent = elm;                           \
 469                                 elm = tmp;                              \
 470                         }                                               \
 471                         RB_SET_BLACKRED(parent, gparent, field);        \
 472                         RB_ROTATE_LEFT(head, gparent, tmp, field);      \
 473                 }                                                       \
 474         }                                                               \
 475         RB_COLOR(head->rbh_root, field) = RB_BLACK;                     \
 476 }
 477
 478 #define RB_GENERATE_REMOVE_COLOR(name, type, field, attr)               \
 479 attr void                                                               \
 480 name##_RB_REMOVE_COLOR(struct name *head, struct type *parent, struct type *elm) \
 481 {                                                                       \
 482         struct type *tmp;                                               \
 483         while ((elm == NULL || RB_COLOR(elm, field) == RB_BLACK) &&     \
 484             elm != RB_ROOT(head)) {                                     \
 485                 if (RB_LEFT(parent, field) == elm) {                    \
 486                         tmp = RB_RIGHT(parent, field);                  \
 487                         if (RB_COLOR(tmp, field) == RB_RED) {           \
 488                                 RB_SET_BLACKRED(tmp, parent, field);    \
 489                                 RB_ROTATE_LEFT(head, parent, tmp, field);\
 490                                 tmp = RB_RIGHT(parent, field);          \
 491                         }                                               \
 492                         if ((RB_LEFT(tmp, field) == NULL ||             \
 493                             RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
 494                             (RB_RIGHT(tmp, field) == NULL ||            \
 495                             RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
 496                                 RB_COLOR(tmp, field) = RB_RED;          \
 497                                 elm = parent;                           \
 498                                 parent = RB_PARENT(elm, field);         \
 499                         } else {                                        \
 500                                 if (RB_RIGHT(tmp, field) == NULL ||     \
 501                                     RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK) {\
 502                                         struct type *oleft;             \
 503                                         if ((oleft = RB_LEFT(tmp, field)) \
 504                                             != NULL)                    \
 505                                                 RB_COLOR(oleft, field) = RB_BLACK;\
 506                                         RB_COLOR(tmp, field) = RB_RED;  \
 507                                         RB_ROTATE_RIGHT(head, tmp, oleft, field);\
 508                                         tmp = RB_RIGHT(parent, field);  \
 509                                 }                                       \
 510                                 RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
 511                                 RB_COLOR(parent, field) = RB_BLACK;     \
 512                                 if (RB_RIGHT(tmp, field))               \
 513                                         RB_COLOR(RB_RIGHT(tmp, field), field) = RB_BLACK;\
 514                                 RB_ROTATE_LEFT(head, parent, tmp, field);\
 515                                 elm = RB_ROOT(head);                    \
 516                                 break;                                  \
 517                         }                                               \
 518                 } else {                                                \
 519                         tmp = RB_LEFT(parent, field);                   \
 520                         if (RB_COLOR(tmp, field) == RB_RED) {           \
 521                                 RB_SET_BLACKRED(tmp, parent, field);    \
 522                                 RB_ROTATE_RIGHT(head, parent, tmp, field);\
 523                                 tmp = RB_LEFT(parent, field);           \
 524                         }                                               \
 525                         if ((RB_LEFT(tmp, field) == NULL ||             \
 526                             RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
 527                             (RB_RIGHT(tmp, field) == NULL ||            \
 528                             RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
 529                                 RB_COLOR(tmp, field) = RB_RED;          \
 530                                 elm = parent;                           \
 531                                 parent = RB_PARENT(elm, field);         \
 532                         } else {                                        \
 533                                 if (RB_LEFT(tmp, field) == NULL ||      \
 534                                     RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) {\
 535                                         struct type *oright;            \
 536                                         if ((oright = RB_RIGHT(tmp, field)) \
 537                                             != NULL)                    \
 538                                                 RB_COLOR(oright, field) = RB_BLACK;\
 539                                         RB_COLOR(tmp, field) = RB_RED;  \
 540                                         RB_ROTATE_LEFT(head, tmp, oright, field);\
 541                                         tmp = RB_LEFT(parent, field);   \
 542                                 }                                       \
 543                                 RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
 544                                 RB_COLOR(parent, field) = RB_BLACK;     \
 545                                 if (RB_LEFT(tmp, field))                \
 546                                         RB_COLOR(RB_LEFT(tmp, field), field) = RB_BLACK;\
 547                                 RB_ROTATE_RIGHT(head, parent, tmp, field);\
 548                                 elm = RB_ROOT(head);                    \
 549                                 break;                                  \
 550                         }                                               \
 551                 }                                                       \
 552         }                                                               \
 553         if (elm)                                                        \
 554                 RB_COLOR(elm, field) = RB_BLACK;                        \
 555 }
 556
 557 #define RB_GENERATE_REMOVE(name, type, field, attr)                     \
 558 attr struct type *                                                      \
 559 name##_RB_REMOVE(struct name *head, struct type *elm)                   \
 560 {                                                                       \
 561         struct type *child, *parent, *old = elm;                        \
 562         int color;                                                      \
 563         if (RB_LEFT(elm, field) == NULL)                                \
 564                 child = RB_RIGHT(elm, field);                           \
 565         else if (RB_RIGHT(elm, field) == NULL)                          \
 566                 child = RB_LEFT(elm, field);                            \
 567         else {                                                          \
 568                 struct type *left;                                      \
 569                 elm = RB_RIGHT(elm, field);                             \
 570                 while ((left = RB_LEFT(elm, field)) != NULL)            \
 571                         elm = left;                                     \
 572                 child = RB_RIGHT(elm, field);                           \
 573                 parent = RB_PARENT(elm, field);                         \
 574                 color = RB_COLOR(elm, field);                           \
 575                 if (child)                                              \
 576                         RB_PARENT(child, field) = parent;               \
 577                 if (parent) {                                           \
 578                         if (RB_LEFT(parent, field) == elm)              \
 579                                 RB_LEFT(parent, field) = child;         \
 580                         else                                            \
 581                                 RB_RIGHT(parent, field) = child;        \
 582                         RB_AUGMENT(parent);                             \
 583                 } else                                                  \
 584                         RB_ROOT(head) = child;                          \
 585                 if (RB_PARENT(elm, field) == old)                       \
 586                         parent = elm;                                   \
 587                 (elm)->field = (old)->field;                            \
 588                 if (RB_PARENT(old, field)) {                            \
 589                         if (RB_LEFT(RB_PARENT(old, field), field) == old)\
 590                                 RB_LEFT(RB_PARENT(old, field), field) = elm;\
 591                         else                                            \
 592                                 RB_RIGHT(RB_PARENT(old, field), field) = elm;\
 593                         RB_AUGMENT(RB_PARENT(old, field));              \
 594                 } else                                                  \
 595                         RB_ROOT(head) = elm;                            \
 596                 RB_PARENT(RB_LEFT(old, field), field) = elm;            \
 597                 if (RB_RIGHT(old, field))                               \
 598                         RB_PARENT(RB_RIGHT(old, field), field) = elm;   \
 599                 if (parent) {                                           \
 600                         left = parent;                                  \
 601                         do {                                            \
 602                                 RB_AUGMENT(left);                       \
 603                         } while ((left = RB_PARENT(left, field)) != NULL); \
 604                 }                                                       \
 605                 goto color;                                             \
 606         }                                                               \
 607         parent = RB_PARENT(elm, field);                                 \
 608         color = RB_COLOR(elm, field);                                   \
 609         if (child)                                                      \
 610                 RB_PARENT(child, field) = parent;                       \
 611         if (parent) {                                                   \
 612                 if (RB_LEFT(parent, field) == elm)                      \
 613                         RB_LEFT(parent, field) = child;                 \
 614                 else                                                    \
 615                         RB_RIGHT(parent, field) = child;                \
 616                 RB_AUGMENT(parent);                                     \
 617         } else                                                          \
 618                 RB_ROOT(head) = child;                                  \
 619 color:                                                                  \
 620         if (color == RB_BLACK)                                          \
 621                 name##_RB_REMOVE_COLOR(head, parent, child);            \
 622         return (old);                                                   \
 623 }                                                                       \
 624
 625 #define RB_GENERATE_INSERT(name, type, field, cmp, attr)                \
 626 /* Inserts a node into the RB tree */                                   \
 627 attr struct type *                                                      \
 628 name##_RB_INSERT(struct name *head, struct type *elm)                   \
 629 {                                                                       \
 630         struct type *tmp;                                               \
 631         struct type *parent = NULL;                                     \
 632         int comp = 0;                                                   \
 633         tmp = RB_ROOT(head);                                            \
 634         while (tmp) {                                                   \
 635                 parent = tmp;                                           \
 636                 comp = (cmp)(elm, parent);                              \
 637                 if (comp < 0)                                           \
 638                         tmp = RB_LEFT(tmp, field);                      \
 639                 else if (comp > 0)                                      \
 640                         tmp = RB_RIGHT(tmp, field);                     \
 641                 else                                                    \
 642                         return (tmp);                                   \
 643         }                                                               \
 644         RB_SET(elm, parent, field);                                     \
 645         if (parent != NULL) {                                           \
 646                 if (comp < 0)                                           \
 647                         RB_LEFT(parent, field) = elm;                   \
 648                 else                                                    \
 649                         RB_RIGHT(parent, field) = elm;                  \
 650                 RB_AUGMENT(parent);                                     \
 651         } else                                                          \
 652                 RB_ROOT(head) = elm;                                    \
 653         name##_RB_INSERT_COLOR(head, elm);                              \
 654         return (NULL);                                                  \
 655 }
 656
 657 #define RB_GENERATE_FIND(name, type, field, cmp, attr)                  \
 658 /* Finds the node with the same key as elm */                           \
 659 attr struct type *                                                      \
 660 name##_RB_FIND(struct name *head, struct type *elm)                     \
 661 {                                                                       \
 662         struct type *tmp = RB_ROOT(head);                               \
 663         int comp;                                                       \
 664         while (tmp) {                                                   \
 665                 comp = cmp(elm, tmp);                                   \
 666                 if (comp < 0)                                           \
 667                         tmp = RB_LEFT(tmp, field);                      \
 668                 else if (comp > 0)                                      \
 669                         tmp = RB_RIGHT(tmp, field);                     \
 670                 else                                                    \
 671                         return (tmp);                                   \
 672         }                                                               \
 673         return (NULL);                                                  \
 674 }
 675
 676 #define RB_GENERATE_NFIND(name, type, field, cmp, attr)                 \
 677 /* Finds the first node greater than or equal to the search key */      \
 678 attr struct type *                                                      \
 679 name##_RB_NFIND(struct name *head, struct type *elm)                    \
 680 {                                                                       \
 681         struct type *tmp = RB_ROOT(head);                               \
 682         struct type *res = NULL;                                        \
 683         int comp;                                                       \
 684         while (tmp) {                                                   \
 685                 comp = cmp(elm, tmp);                                   \
 686                 if (comp < 0) {                                         \
 687                         res = tmp;                                      \
 688                         tmp = RB_LEFT(tmp, field);                      \
 689                 }                                                       \
 690                 else if (comp > 0)                                      \
 691                         tmp = RB_RIGHT(tmp, field);                     \
 692                 else                                                    \
 693                         return (tmp);                                   \
 694         }                                                               \
 695         return (res);                                                   \
 696 }
 697
 698 #define RB_GENERATE_NEXT(name, type, field, attr)                       \
 699 /* ARGSUSED */                                                          \
 700 attr struct type *                                                      \
 701 name##_RB_NEXT(struct type *elm)                                        \
 702 {                                                                       \
 703         if (RB_RIGHT(elm, field)) {                                     \
 704                 elm = RB_RIGHT(elm, field);                             \
 705                 while (RB_LEFT(elm, field))                             \
 706                         elm = RB_LEFT(elm, field);                      \
 707         } else {                                                        \
 708                 if (RB_PARENT(elm, field) &&                            \
 709                     (elm == RB_LEFT(RB_PARENT(elm, field), field)))     \
 710                         elm = RB_PARENT(elm, field);                    \
 711                 else {                                                  \
 712                         while (RB_PARENT(elm, field) &&                 \
 713                             (elm == RB_RIGHT(RB_PARENT(elm, field), field)))\
 714                                 elm = RB_PARENT(elm, field);            \
 715                         elm = RB_PARENT(elm, field);                    \
 716                 }                                                       \
 717         }                                                               \
 718         return (elm);                                                   \
 719 }
 720
 721 #define RB_GENERATE_PREV(name, type, field, attr)                       \
 722 /* ARGSUSED */                                                          \
 723 attr struct type *                                                      \
 724 name##_RB_PREV(struct type *elm)                                        \
 725 {                                                                       \
 726         if (RB_LEFT(elm, field)) {                                      \
 727                 elm = RB_LEFT(elm, field);                              \
 728                 while (RB_RIGHT(elm, field))                            \
 729                         elm = RB_RIGHT(elm, field);                     \
 730         } else {                                                        \
 731                 if (RB_PARENT(elm, field) &&                            \
 732                     (elm == RB_RIGHT(RB_PARENT(elm, field), field)))    \
 733                         elm = RB_PARENT(elm, field);                    \
 734                 else {                                                  \
 735                         while (RB_PARENT(elm, field) &&                 \
 736                             (elm == RB_LEFT(RB_PARENT(elm, field), field)))\
 737                                 elm = RB_PARENT(elm, field);            \
 738                         elm = RB_PARENT(elm, field);                    \
 739                 }                                                       \
 740         }                                                               \
 741         return (elm);                                                   \
 742 }
 743
 744 #define RB_GENERATE_MINMAX(name, type, field, attr)                     \
 745 attr struct type *                                                      \
 746 name##_RB_MINMAX(struct name *head, int val)                            \
 747 {                                                                       \
 748         struct type *tmp = RB_ROOT(head);                               \
 749         struct type *parent = NULL;                                     \
 750         while (tmp) {                                                   \
 751                 parent = tmp;                                           \
 752                 if (val < 0)                                            \
 753                         tmp = RB_LEFT(tmp, field);                      \
 754                 else                                                    \
 755                         tmp = RB_RIGHT(tmp, field);                     \
 756         }                                                               \
 757         return (parent);                                                \
 758 }
 759
 760 #define RB_NEGINF       -1
 761 #define RB_INF  1
 762
 763 #define RB_INSERT(name, x, y)   name##_RB_INSERT(x, y)
 764 #define RB_REMOVE(name, x, y)   name##_RB_REMOVE(x, y)
 765 #define RB_FIND(name, x, y)     name##_RB_FIND(x, y)
 766 #define RB_NFIND(name, x, y)    name##_RB_NFIND(x, y)
 767 #define RB_NEXT(name, x, y)     name##_RB_NEXT(y)
 768 #define RB_PREV(name, x, y)     name##_RB_PREV(y)
 769 #define RB_MIN(name, x)         name##_RB_MINMAX(x, RB_NEGINF)
 770 #define RB_MAX(name, x)         name##_RB_MINMAX(x, RB_INF)
 771
 772 #define RB_FOREACH(x, name, head)                                       \
 773         for ((x) = RB_MIN(name, head);                                  \
 774              (x) != NULL;                                               \
 775              (x) = name##_RB_NEXT(x))
 776
 777 #define RB_FOREACH_FROM(x, name, y)                                     \
 778         for ((x) = (y);                                                 \
 779             ((x) != NULL) && ((y) = name##_RB_NEXT(x), (x) != NULL);    \
 780              (x) = (y))
 781
 782 #define RB_FOREACH_SAFE(x, name, head, y)                               \
 783         for ((x) = RB_MIN(name, head);                                  \
 784             ((x) != NULL) && ((y) = name##_RB_NEXT(x), (x) != NULL);    \
 785              (x) = (y))
 786
 787 #define RB_FOREACH_REVERSE(x, name, head)                               \
 788         for ((x) = RB_MAX(name, head);                                  \
 789              (x) != NULL;                                               \
 790              (x) = name##_RB_PREV(x))
 791
 792 #define RB_FOREACH_REVERSE_FROM(x, name, y)                             \
 793         for ((x) = (y);                                                 \
 794             ((x) != NULL) && ((y) = name##_RB_PREV(x), (x) != NULL);    \
 795              (x) = (y))
 796
 797 #define RB_FOREACH_REVERSE_SAFE(x, name, head, y)                       \
 798         for ((x) = RB_MAX(name, head);                                  \
 799             ((x) != NULL) && ((y) = name##_RB_PREV(x), (x) != NULL);    \
 800              (x) = (y))
 801
 802 #endif  /* _SYS_TREE_H_ */