sys/sys/tree.h

   1 /*      $NetBSD: tree.h,v 1.8 2004/03/28 19:38:30 provos Exp $  */
   2 /*      $OpenBSD: tree.h,v 1.7 2002/10/17 21:51:54 art Exp $    */
   3 /* $FreeBSD$ */
   4
   5 /*-
   6  * SPDX-License-Identifier: BSD-2-Clause-FreeBSD
   7  *
   8  * Copyright 2002 Niels Provos <provos@citi.umich.edu>
   9  * All rights reserved.
  10  *
  11  * Redistribution and use in source and binary forms, with or without
  12  * modification, are permitted provided that the following conditions
  13  * are met:
  14  * 1. Redistributions of source code must retain the above copyright
  15  *    notice, this list of conditions and the following disclaimer.
  16  * 2. Redistributions in binary form must reproduce the above copyright
  17  *    notice, this list of conditions and the following disclaimer in the
  18  *    documentation and/or other materials provided with the distribution.
  19  *
  20  * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
  21  * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
  22  * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
  23  * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
  24  * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
  25  * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
  26  * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
  27  * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
  28  * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
  29  * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
  30  */
  31
  32 #ifndef _SYS_TREE_H_
  33 #define _SYS_TREE_H_
  34
  35 #include <sys/cdefs.h>
  36
  37 /*
  38  * This file defines data structures for different types of trees:
  39  * splay trees and rank-balanced trees.
  40  *
  41  * A splay tree is a self-organizing data structure.  Every operation
  42  * on the tree causes a splay to happen.  The splay moves the requested
  43  * node to the root of the tree and partly rebalances it.
  44  *
  45  * This has the benefit that request locality causes faster lookups as
  46  * the requested nodes move to the top of the tree.  On the other hand,
  47  * every lookup causes memory writes.
  48  *
  49  * The Balance Theorem bounds the total access time for m operations
  50  * and n inserts on an initially empty tree as O((m + n)lg n).  The
  51  * amortized cost for a sequence of m accesses to a splay tree is O(lg n);
  52  *
  53  * A rank-balanced tree is a binary search tree with an integer
  54  * rank-difference as an attribute of each pointer from parent to child.
  55  * The sum of the rank-differences on any path from a node down to null is
  56  * the same, and defines the rank of that node. The rank of the null node
  57  * is -1.
  58  *
  59  * Different additional conditions define different sorts of balanced
  60  * trees, including "red-black" and "AVL" trees.  The set of conditions
  61  * applied here are the "weak-AVL" conditions of Haeupler, Sen and Tarjan:
  62  *      - every rank-difference is 1 or 2.
  63  *      - the rank of any leaf is 1.
  64  *
  65  * For historical reasons, rank differences that are even are associated
  66  * with the color red (Rank-Even-Difference), and the child that a red edge
  67  * points to is called a red child.
  68  *
  69  * Every operation on a rank-balanced tree is bounded as O(lg n).
  70  * The maximum height of a rank-balanced tree is 2lg (n+1).
  71  */
  72
  73 #define SPLAY_HEAD(name, type)                                          \
  74 struct name {                                                           \
  75         struct type *sph_root; /* root of the tree */                   \
  76 }
  77
  78 #define SPLAY_INITIALIZER(root)                                         \
  79         { NULL }
  80
  81 #define SPLAY_INIT(root) do {                                           \
  82         (root)->sph_root = NULL;                                        \
  83 } while (/*CONSTCOND*/ 0)
  84
  85 #define SPLAY_ENTRY(type)                                               \
  86 struct {                                                                \
  87         struct type *spe_left; /* left element */                       \
  88         struct type *spe_right; /* right element */                     \
  89 }
  90
  91 #define SPLAY_LEFT(elm, field)          (elm)->field.spe_left
  92 #define SPLAY_RIGHT(elm, field)         (elm)->field.spe_right
  93 #define SPLAY_ROOT(head)                (head)->sph_root
  94 #define SPLAY_EMPTY(head)               (SPLAY_ROOT(head) == NULL)
  95
  96 /* SPLAY_ROTATE_{LEFT,RIGHT} expect that tmp hold SPLAY_{RIGHT,LEFT} */
  97 #define SPLAY_ROTATE_RIGHT(head, tmp, field) do {                       \
  98         SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(tmp, field);  \
  99         SPLAY_RIGHT(tmp, field) = (head)->sph_root;                     \
 100         (head)->sph_root = tmp;                                         \
 101 } while (/*CONSTCOND*/ 0)
 102
 103 #define SPLAY_ROTATE_LEFT(head, tmp, field) do {                        \
 104         SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(tmp, field);  \
 105         SPLAY_LEFT(tmp, field) = (head)->sph_root;                      \
 106         (head)->sph_root = tmp;                                         \
 107 } while (/*CONSTCOND*/ 0)
 108
 109 #define SPLAY_LINKLEFT(head, tmp, field) do {                           \
 110         SPLAY_LEFT(tmp, field) = (head)->sph_root;                      \
 111         tmp = (head)->sph_root;                                         \
 112         (head)->sph_root = SPLAY_LEFT((head)->sph_root, field);         \
 113 } while (/*CONSTCOND*/ 0)
 114
 115 #define SPLAY_LINKRIGHT(head, tmp, field) do {                          \
 116         SPLAY_RIGHT(tmp, field) = (head)->sph_root;                     \
 117         tmp = (head)->sph_root;                                         \
 118         (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);        \
 119 } while (/*CONSTCOND*/ 0)
 120
 121 #define SPLAY_ASSEMBLE(head, node, left, right, field) do {             \
 122         SPLAY_RIGHT(left, field) = SPLAY_LEFT((head)->sph_root, field); \
 123         SPLAY_LEFT(right, field) = SPLAY_RIGHT((head)->sph_root, field);\
 124         SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(node, field); \
 125         SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(node, field); \
 126 } while (/*CONSTCOND*/ 0)
 127
 128 /* Generates prototypes and inline functions */
 129
 130 #define SPLAY_PROTOTYPE(name, type, field, cmp)                         \
 131 void name##_SPLAY(struct name *, struct type *);                        \
 132 void name##_SPLAY_MINMAX(struct name *, int);                           \
 133 struct type *name##_SPLAY_INSERT(struct name *, struct type *);         \
 134 struct type *name##_SPLAY_REMOVE(struct name *, struct type *);         \
 135                                                                         \
 136 /* Finds the node with the same key as elm */                           \
 137 static __unused __inline struct type *                                  \
 138 name##_SPLAY_FIND(struct name *head, struct type *elm)                  \
 139 {                                                                       \
 140         if (SPLAY_EMPTY(head))                                          \
 141                 return(NULL);                                           \
 142         name##_SPLAY(head, elm);                                        \
 143         if ((cmp)(elm, (head)->sph_root) == 0)                          \
 144                 return (head->sph_root);                                \
 145         return (NULL);                                                  \
 146 }                                                                       \
 147                                                                         \
 148 static __unused __inline struct type *                                  \
 149 name##_SPLAY_NEXT(struct name *head, struct type *elm)                  \
 150 {                                                                       \
 151         name##_SPLAY(head, elm);                                        \
 152         if (SPLAY_RIGHT(elm, field) != NULL) {                          \
 153                 elm = SPLAY_RIGHT(elm, field);                          \
 154                 while (SPLAY_LEFT(elm, field) != NULL) {                \
 155                         elm = SPLAY_LEFT(elm, field);                   \
 156                 }                                                       \
 157         } else                                                          \
 158                 elm = NULL;                                             \
 159         return (elm);                                                   \
 160 }                                                                       \
 161                                                                         \
 162 static __unused __inline struct type *                                  \
 163 name##_SPLAY_MIN_MAX(struct name *head, int val)                        \
 164 {                                                                       \
 165         name##_SPLAY_MINMAX(head, val);                                 \
 166         return (SPLAY_ROOT(head));                                      \
 167 }
 168
 169 /* Main splay operation.
 170  * Moves node close to the key of elm to top
 171  */
 172 #define SPLAY_GENERATE(name, type, field, cmp)                          \
 173 struct type *                                                           \
 174 name##_SPLAY_INSERT(struct name *head, struct type *elm)                \
 175 {                                                                       \
 176     if (SPLAY_EMPTY(head)) {                                            \
 177             SPLAY_LEFT(elm, field) = SPLAY_RIGHT(elm, field) = NULL;    \
 178     } else {                                                            \
 179             int __comp;                                                 \
 180             name##_SPLAY(head, elm);                                    \
 181             __comp = (cmp)(elm, (head)->sph_root);                      \
 182             if(__comp < 0) {                                            \
 183                     SPLAY_LEFT(elm, field) = SPLAY_LEFT((head)->sph_root, field);\
 184                     SPLAY_RIGHT(elm, field) = (head)->sph_root;         \
 185                     SPLAY_LEFT((head)->sph_root, field) = NULL;         \
 186             } else if (__comp > 0) {                                    \
 187                     SPLAY_RIGHT(elm, field) = SPLAY_RIGHT((head)->sph_root, field);\
 188                     SPLAY_LEFT(elm, field) = (head)->sph_root;          \
 189                     SPLAY_RIGHT((head)->sph_root, field) = NULL;        \
 190             } else                                                      \
 191                     return ((head)->sph_root);                          \
 192     }                                                                   \
 193     (head)->sph_root = (elm);                                           \
 194     return (NULL);                                                      \
 195 }                                                                       \
 196                                                                         \
 197 struct type *                                                           \
 198 name##_SPLAY_REMOVE(struct name *head, struct type *elm)                \
 199 {                                                                       \
 200         struct type *__tmp;                                             \
 201         if (SPLAY_EMPTY(head))                                          \
 202                 return (NULL);                                          \
 203         name##_SPLAY(head, elm);                                        \
 204         if ((cmp)(elm, (head)->sph_root) == 0) {                        \
 205                 if (SPLAY_LEFT((head)->sph_root, field) == NULL) {      \
 206                         (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);\
 207                 } else {                                                \
 208                         __tmp = SPLAY_RIGHT((head)->sph_root, field);   \
 209                         (head)->sph_root = SPLAY_LEFT((head)->sph_root, field);\
 210                         name##_SPLAY(head, elm);                        \
 211                         SPLAY_RIGHT((head)->sph_root, field) = __tmp;   \
 212                 }                                                       \
 213                 return (elm);                                           \
 214         }                                                               \
 215         return (NULL);                                                  \
 216 }                                                                       \
 217                                                                         \
 218 void                                                                    \
 219 name##_SPLAY(struct name *head, struct type *elm)                       \
 220 {                                                                       \
 221         struct type __node, *__left, *__right, *__tmp;                  \
 222         int __comp;                                                     \
 223 \
 224         SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
 225         __left = __right = &__node;                                     \
 226 \
 227         while ((__comp = (cmp)(elm, (head)->sph_root)) != 0) {          \
 228                 if (__comp < 0) {                                       \
 229                         __tmp = SPLAY_LEFT((head)->sph_root, field);    \
 230                         if (__tmp == NULL)                              \
 231                                 break;                                  \
 232                         if ((cmp)(elm, __tmp) < 0){                     \
 233                                 SPLAY_ROTATE_RIGHT(head, __tmp, field); \
 234                                 if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
 235                                         break;                          \
 236                         }                                               \
 237                         SPLAY_LINKLEFT(head, __right, field);           \
 238                 } else if (__comp > 0) {                                \
 239                         __tmp = SPLAY_RIGHT((head)->sph_root, field);   \
 240                         if (__tmp == NULL)                              \
 241                                 break;                                  \
 242                         if ((cmp)(elm, __tmp) > 0){                     \
 243                                 SPLAY_ROTATE_LEFT(head, __tmp, field);  \
 244                                 if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
 245                                         break;                          \
 246                         }                                               \
 247                         SPLAY_LINKRIGHT(head, __left, field);           \
 248                 }                                                       \
 249         }                                                               \
 250         SPLAY_ASSEMBLE(head, &__node, __left, __right, field);          \
 251 }                                                                       \
 252                                                                         \
 253 /* Splay with either the minimum or the maximum element                 \
 254  * Used to find minimum or maximum element in tree.                     \
 255  */                                                                     \
 256 void name##_SPLAY_MINMAX(struct name *head, int __comp) \
 257 {                                                                       \
 258         struct type __node, *__left, *__right, *__tmp;                  \
 259 \
 260         SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
 261         __left = __right = &__node;                                     \
 262 \
 263         while (1) {                                                     \
 264                 if (__comp < 0) {                                       \
 265                         __tmp = SPLAY_LEFT((head)->sph_root, field);    \
 266                         if (__tmp == NULL)                              \
 267                                 break;                                  \
 268                         if (__comp < 0){                                \
 269                                 SPLAY_ROTATE_RIGHT(head, __tmp, field); \
 270                                 if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
 271                                         break;                          \
 272                         }                                               \
 273                         SPLAY_LINKLEFT(head, __right, field);           \
 274                 } else if (__comp > 0) {                                \
 275                         __tmp = SPLAY_RIGHT((head)->sph_root, field);   \
 276                         if (__tmp == NULL)                              \
 277                                 break;                                  \
 278                         if (__comp > 0) {                               \
 279                                 SPLAY_ROTATE_LEFT(head, __tmp, field);  \
 280                                 if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
 281                                         break;                          \
 282                         }                                               \
 283                         SPLAY_LINKRIGHT(head, __left, field);           \
 284                 }                                                       \
 285         }                                                               \
 286         SPLAY_ASSEMBLE(head, &__node, __left, __right, field);          \
 287 }
 288
 289 #define SPLAY_NEGINF    -1
 290 #define SPLAY_INF       1
 291
 292 #define SPLAY_INSERT(name, x, y)        name##_SPLAY_INSERT(x, y)
 293 #define SPLAY_REMOVE(name, x, y)        name##_SPLAY_REMOVE(x, y)
 294 #define SPLAY_FIND(name, x, y)          name##_SPLAY_FIND(x, y)
 295 #define SPLAY_NEXT(name, x, y)          name##_SPLAY_NEXT(x, y)
 296 #define SPLAY_MIN(name, x)              (SPLAY_EMPTY(x) ? NULL  \
 297                                         : name##_SPLAY_MIN_MAX(x, SPLAY_NEGINF))
 298 #define SPLAY_MAX(name, x)              (SPLAY_EMPTY(x) ? NULL  \
 299                                         : name##_SPLAY_MIN_MAX(x, SPLAY_INF))
 300
 301 #define SPLAY_FOREACH(x, name, head)                                    \
 302         for ((x) = SPLAY_MIN(name, head);                               \
 303              (x) != NULL;                                               \
 304              (x) = SPLAY_NEXT(name, head, x))
 305
 306 /* Macros that define a rank-balanced tree */
 307 #define RB_HEAD(name, type)                                             \
 308 struct name {                                                           \
 309         struct type *rbh_root; /* root of the tree */                   \
 310 }
 311
 312 #define RB_INITIALIZER(root)                                            \
 313         { NULL }
 314
 315 #define RB_INIT(root) do {                                              \
 316         (root)->rbh_root = NULL;                                        \
 317 } while (/*CONSTCOND*/ 0)
 318
 319 #define RB_ENTRY(type)                                                  \
 320 struct {                                                                \
 321         struct type *rbe_left;          /* left element */              \
 322         struct type *rbe_right;         /* right element */             \
 323         struct type *rbe_parent;        /* parent element */            \
 324 }
 325
 326 #define RB_LEFT(elm, field)             (elm)->field.rbe_left
 327 #define RB_RIGHT(elm, field)            (elm)->field.rbe_right
 328
 329 /*
 330  * With the expectation that any object of struct type has an
 331  * address that is a multiple of 4, and that therefore the
 332  * 2 least significant bits of a pointer to struct type are
 333  * always zero, this implementation sets those bits to indicate
 334  * that the left or right child of the tree node is "red".
 335  */
 336 #define RB_UP(elm, field)               (elm)->field.rbe_parent
 337 #define RB_BITS(elm, field)             (*(__uintptr_t *)&RB_UP(elm, field))
 338 #define RB_RED_L                        ((__uintptr_t)1)
 339 #define RB_RED_R                        ((__uintptr_t)2)
 340 #define RB_RED_MASK                     ((__uintptr_t)3)
 341 #define RB_FLIP_LEFT(elm, field)        (RB_BITS(elm, field) ^= RB_RED_L)
 342 #define RB_FLIP_RIGHT(elm, field)       (RB_BITS(elm, field) ^= RB_RED_R)
 343 #define RB_RED_LEFT(elm, field)         ((RB_BITS(elm, field) & RB_RED_L) != 0)
 344 #define RB_RED_RIGHT(elm, field)        ((RB_BITS(elm, field) & RB_RED_R) != 0)
 345 #define RB_PARENT(elm, field)           ((__typeof(RB_UP(elm, field)))  \
 346                                          (RB_BITS(elm, field) & ~RB_RED_MASK))
 347 #define RB_ROOT(head)                   (head)->rbh_root
 348 #define RB_EMPTY(head)                  (RB_ROOT(head) == NULL)
 349
 350 #define RB_SET_PARENT(dst, src, field) do {                             \
 351         RB_BITS(dst, field) &= RB_RED_MASK;                             \
 352         RB_BITS(dst, field) |= (__uintptr_t)src;                        \
 353 } while (/*CONSTCOND*/ 0)
 354
 355 #define RB_SET(elm, parent, field) do {                                 \
 356         RB_UP(elm, field) = parent;                                     \
 357         RB_LEFT(elm, field) = RB_RIGHT(elm, field) = NULL;              \
 358 } while (/*CONSTCOND*/ 0)
 359
 360 #define RB_COLOR(elm, field)    (RB_PARENT(elm, field) == NULL ? 0 :    \
 361                                 RB_LEFT(RB_PARENT(elm, field), field) == elm ? \
 362                                 RB_RED_LEFT(RB_PARENT(elm, field), field) : \
 363                                 RB_RED_RIGHT(RB_PARENT(elm, field), field))
 364
 365 /*
 366  * Something to be invoked in a loop at the root of every modified subtree,
 367  * from the bottom up to the root, to update augmented node data.
 368  */
 369 #ifndef RB_AUGMENT
 370 #define RB_AUGMENT(x)   break
 371 #endif
 372
 373 #define RB_SWAP_CHILD(head, out, in, field) do {                        \
 374         if (RB_PARENT(out, field) == NULL)                              \
 375                 RB_ROOT(head) = (in);                                   \
 376         else if ((out) == RB_LEFT(RB_PARENT(out, field), field))        \
 377                 RB_LEFT(RB_PARENT(out, field), field) = (in);           \
 378         else                                                            \
 379                 RB_RIGHT(RB_PARENT(out, field), field) = (in);          \
 380 } while (/*CONSTCOND*/ 0)
 381
 382 #define RB_ROTATE_LEFT(head, elm, tmp, field) do {                      \
 383         (tmp) = RB_RIGHT(elm, field);                                   \
 384         if ((RB_RIGHT(elm, field) = RB_LEFT(tmp, field)) != NULL) {     \
 385                 RB_SET_PARENT(RB_RIGHT(elm, field), elm, field);        \
 386         }                                                               \
 387         RB_SET_PARENT(tmp, RB_PARENT(elm, field), field);               \
 388         RB_SWAP_CHILD(head, elm, tmp, field);                           \
 389         RB_LEFT(tmp, field) = (elm);                                    \
 390         RB_SET_PARENT(elm, tmp, field);                                 \
 391         RB_AUGMENT(elm);                                                \
 392 } while (/*CONSTCOND*/ 0)
 393
 394 #define RB_ROTATE_RIGHT(head, elm, tmp, field) do {                     \
 395         (tmp) = RB_LEFT(elm, field);                                    \
 396         if ((RB_LEFT(elm, field) = RB_RIGHT(tmp, field)) != NULL) {     \
 397                 RB_SET_PARENT(RB_LEFT(elm, field), elm, field);         \
 398         }                                                               \
 399         RB_SET_PARENT(tmp, RB_PARENT(elm, field), field);               \
 400         RB_SWAP_CHILD(head, elm, tmp, field);                           \
 401         RB_RIGHT(tmp, field) = (elm);                                   \
 402         RB_SET_PARENT(elm, tmp, field);                                 \
 403         RB_AUGMENT(elm);                                                \
 404 } while (/*CONSTCOND*/ 0)
 405
 406 /* Generates prototypes and inline functions */
 407 #define RB_PROTOTYPE(name, type, field, cmp)                            \
 408         RB_PROTOTYPE_INTERNAL(name, type, field, cmp,)
 409 #define RB_PROTOTYPE_STATIC(name, type, field, cmp)                     \
 410         RB_PROTOTYPE_INTERNAL(name, type, field, cmp, __unused static)
 411 #define RB_PROTOTYPE_INTERNAL(name, type, field, cmp, attr)             \
 412         RB_PROTOTYPE_INSERT_COLOR(name, type, attr);                    \
 413         RB_PROTOTYPE_REMOVE_COLOR(name, type, attr);                    \
 414         RB_PROTOTYPE_INSERT(name, type, attr);                          \
 415         RB_PROTOTYPE_REMOVE(name, type, attr);                          \
 416         RB_PROTOTYPE_FIND(name, type, attr);                            \
 417         RB_PROTOTYPE_NFIND(name, type, attr);                           \
 418         RB_PROTOTYPE_NEXT(name, type, attr);                            \
 419         RB_PROTOTYPE_PREV(name, type, attr);                            \
 420         RB_PROTOTYPE_MINMAX(name, type, attr);                          \
 421         RB_PROTOTYPE_REINSERT(name, type, attr);
 422 #define RB_PROTOTYPE_INSERT_COLOR(name, type, attr)                     \
 423         attr void name##_RB_INSERT_COLOR(struct name *, struct type *)
 424 #define RB_PROTOTYPE_REMOVE_COLOR(name, type, attr)                     \
 425         attr void name##_RB_REMOVE_COLOR(struct name *,                 \
 426             struct type *, struct type *)
 427 #define RB_PROTOTYPE_REMOVE(name, type, attr)                           \
 428         attr struct type *name##_RB_REMOVE(struct name *, struct type *)
 429 #define RB_PROTOTYPE_INSERT(name, type, attr)                           \
 430         attr struct type *name##_RB_INSERT(struct name *, struct type *)
 431 #define RB_PROTOTYPE_FIND(name, type, attr)                             \
 432         attr struct type *name##_RB_FIND(struct name *, struct type *)
 433 #define RB_PROTOTYPE_NFIND(name, type, attr)                            \
 434         attr struct type *name##_RB_NFIND(struct name *, struct type *)
 435 #define RB_PROTOTYPE_NEXT(name, type, attr)                             \
 436         attr struct type *name##_RB_NEXT(struct type *)
 437 #define RB_PROTOTYPE_PREV(name, type, attr)                             \
 438         attr struct type *name##_RB_PREV(struct type *)
 439 #define RB_PROTOTYPE_MINMAX(name, type, attr)                           \
 440         attr struct type *name##_RB_MINMAX(struct name *, int)
 441 #define RB_PROTOTYPE_REINSERT(name, type, attr)                 \
 442         attr struct type *name##_RB_REINSERT(struct name *, struct type *)
 443
 444 /* Main rb operation.
 445  * Moves node close to the key of elm to top
 446  */
 447 #define RB_GENERATE(name, type, field, cmp)                             \
 448         RB_GENERATE_INTERNAL(name, type, field, cmp,)
 449 #define RB_GENERATE_STATIC(name, type, field, cmp)                      \
 450         RB_GENERATE_INTERNAL(name, type, field, cmp, __unused static)
 451 #define RB_GENERATE_INTERNAL(name, type, field, cmp, attr)              \
 452         RB_GENERATE_INSERT_COLOR(name, type, field, attr)               \
 453         RB_GENERATE_REMOVE_COLOR(name, type, field, attr)               \
 454         RB_GENERATE_INSERT(name, type, field, cmp, attr)                \
 455         RB_GENERATE_REMOVE(name, type, field, attr)                     \
 456         RB_GENERATE_FIND(name, type, field, cmp, attr)                  \
 457         RB_GENERATE_NFIND(name, type, field, cmp, attr)                 \
 458         RB_GENERATE_NEXT(name, type, field, attr)                       \
 459         RB_GENERATE_PREV(name, type, field, attr)                       \
 460         RB_GENERATE_MINMAX(name, type, field, attr)                     \
 461         RB_GENERATE_REINSERT(name, type, field, cmp, attr)
 462
 463 #define RB_GENERATE_INSERT_COLOR(name, type, field, attr)               \
 464 attr void                                                               \
 465 name##_RB_INSERT_COLOR(struct name *head, struct type *elm)             \
 466 {                                                                       \
 467         struct type *child, *parent;                                    \
 468         while ((parent = RB_PARENT(elm, field)) != NULL) {              \
 469                 if (RB_LEFT(parent, field) == elm) {                    \
 470                         if (RB_RED_LEFT(parent, field)) {               \
 471                                 RB_FLIP_LEFT(parent, field);            \
 472                                 return;                                 \
 473                         }                                               \
 474                         RB_FLIP_RIGHT(parent, field);                   \
 475                         if (RB_RED_RIGHT(parent, field)) {              \
 476                                 elm = parent;                           \
 477                                 continue;                               \
 478                         }                                               \
 479                         if (!RB_RED_RIGHT(elm, field)) {                \
 480                                 RB_FLIP_LEFT(elm, field);               \
 481                                 RB_ROTATE_LEFT(head, elm, child, field);\
 482                                 if (RB_RED_LEFT(child, field))          \
 483                                         RB_FLIP_RIGHT(elm, field);      \
 484                                 else if (RB_RED_RIGHT(child, field))    \
 485                                         RB_FLIP_LEFT(parent, field);    \
 486                                 elm = child;                            \
 487                         }                                               \
 488                         RB_ROTATE_RIGHT(head, parent, elm, field);      \
 489                 } else {                                                \
 490                         if (RB_RED_RIGHT(parent, field)) {              \
 491                                 RB_FLIP_RIGHT(parent, field);           \
 492                                 return;                                 \
 493                         }                                               \
 494                         RB_FLIP_LEFT(parent, field);                    \
 495                         if (RB_RED_LEFT(parent, field)) {               \
 496                                 elm = parent;                           \
 497                                 continue;                               \
 498                         }                                               \
 499                         if (!RB_RED_LEFT(elm, field)) {                 \
 500                                 RB_FLIP_RIGHT(elm, field);              \
 501                                 RB_ROTATE_RIGHT(head, elm, child, field);\
 502                                 if (RB_RED_RIGHT(child, field))         \
 503                                         RB_FLIP_LEFT(elm, field);       \
 504                                 else if (RB_RED_LEFT(child, field))     \
 505                                         RB_FLIP_RIGHT(parent, field);   \
 506                                 elm = child;                            \
 507                         }                                               \
 508                         RB_ROTATE_LEFT(head, parent, elm, field);       \
 509                 }                                                       \
 510                 RB_BITS(elm, field) &= ~RB_RED_MASK;                    \
 511                 break;                                                  \
 512         }                                                               \
 513 }
 514
 515 #define RB_GENERATE_REMOVE_COLOR(name, type, field, attr)               \
 516 attr void                                                               \
 517 name##_RB_REMOVE_COLOR(struct name *head,                               \
 518     struct type *parent, struct type *elm)                              \
 519 {                                                                       \
 520         struct type *sib;                                               \
 521         if (RB_LEFT(parent, field) == elm &&                            \
 522             RB_RIGHT(parent, field) == elm) {                           \
 523                 RB_BITS(parent, field) &= ~RB_RED_MASK;                 \
 524                 elm = parent;                                           \
 525                 parent = RB_PARENT(elm, field);                         \
 526                 if (parent == NULL)                                     \
 527                         return;                                         \
 528         }                                                               \
 529         do  {                                                           \
 530                 if (RB_LEFT(parent, field) == elm) {                    \
 531                         if (!RB_RED_LEFT(parent, field)) {              \
 532                                 RB_FLIP_LEFT(parent, field);            \
 533                                 return;                                 \
 534                         }                                               \
 535                         if (RB_RED_RIGHT(parent, field)) {              \
 536                                 RB_FLIP_RIGHT(parent, field);           \
 537                                 elm = parent;                           \
 538                                 continue;                               \
 539                         }                                               \
 540                         sib = RB_RIGHT(parent, field);                  \
 541                         if ((~RB_BITS(sib, field) & RB_RED_MASK) == 0) {\
 542                                 RB_BITS(sib, field) &= ~RB_RED_MASK;    \
 543                                 elm = parent;                           \
 544                                 continue;                               \
 545                         }                                               \
 546                         RB_FLIP_RIGHT(sib, field);                      \
 547                         if (RB_RED_LEFT(sib, field))                    \
 548                                 RB_FLIP_LEFT(parent, field);            \
 549                         else if (!RB_RED_RIGHT(sib, field)) {           \
 550                                 RB_FLIP_LEFT(parent, field);            \
 551                                 RB_ROTATE_RIGHT(head, sib, elm, field); \
 552                                 if (RB_RED_RIGHT(elm, field))           \
 553                                         RB_FLIP_LEFT(sib, field);       \
 554                                 if (RB_RED_LEFT(elm, field))            \
 555                                         RB_FLIP_RIGHT(parent, field);   \
 556                                 RB_BITS(elm, field) |= RB_RED_MASK;     \
 557                                 sib = elm;                              \
 558                         }                                               \
 559                         RB_ROTATE_LEFT(head, parent, sib, field);       \
 560                 } else {                                                \
 561                         if (!RB_RED_RIGHT(parent, field)) {             \
 562                                 RB_FLIP_RIGHT(parent, field);           \
 563                                 return;                                 \
 564                         }                                               \
 565                         if (RB_RED_LEFT(parent, field)) {               \
 566                                 RB_FLIP_LEFT(parent, field);            \
 567                                 elm = parent;                           \
 568                                 continue;                               \
 569                         }                                               \
 570                         sib = RB_LEFT(parent, field);                   \
 571                         if ((~RB_BITS(sib, field) & RB_RED_MASK) == 0) {\
 572                                 RB_BITS(sib, field) &= ~RB_RED_MASK;    \
 573                                 elm = parent;                           \
 574                                 continue;                               \
 575                         }                                               \
 576                         RB_FLIP_LEFT(sib, field);                       \
 577                         if (RB_RED_RIGHT(sib, field))                   \
 578                                 RB_FLIP_RIGHT(parent, field);           \
 579                         else if (!RB_RED_LEFT(sib, field)) {            \
 580                                 RB_FLIP_RIGHT(parent, field);           \
 581                                 RB_ROTATE_LEFT(head, sib, elm, field);  \
 582                                 if (RB_RED_LEFT(elm, field))            \
 583                                         RB_FLIP_RIGHT(sib, field);      \
 584                                 if (RB_RED_RIGHT(elm, field))           \
 585                                         RB_FLIP_LEFT(parent, field);    \
 586                                 RB_BITS(elm, field) |= RB_RED_MASK;     \
 587                                 sib = elm;                              \
 588                         }                                               \
 589                         RB_ROTATE_RIGHT(head, parent, sib, field);      \
 590                 }                                                       \
 591                 break;                                                  \
 592         } while ((parent = RB_PARENT(elm, field)) != NULL);             \
 593 }
 594
 595 #define RB_GENERATE_REMOVE(name, type, field, attr)                     \
 596 attr struct type *                                                      \
 597 name##_RB_REMOVE(struct name *head, struct type *elm)                   \
 598 {                                                                       \
 599         struct type *child, *old, *parent, *right;                      \
 600                                                                         \
 601         old = elm;                                                      \
 602         parent = RB_PARENT(elm, field);                                 \
 603         right = RB_RIGHT(elm, field);                                   \
 604         if (RB_LEFT(elm, field) == NULL)                                \
 605                 elm = child = right;                                    \
 606         else if (right == NULL)                                         \
 607                 elm = child = RB_LEFT(elm, field);                      \
 608         else {                                                          \
 609                 if ((child = RB_LEFT(right, field)) == NULL) {          \
 610                         child = RB_RIGHT(right, field);                 \
 611                         RB_RIGHT(old, field) = child;                   \
 612                         parent = elm = right;                           \
 613                 } else {                                                \
 614                         do                                              \
 615                                 elm = child;                            \
 616                         while ((child = RB_LEFT(elm, field)) != NULL);  \
 617                         child = RB_RIGHT(elm, field);                   \
 618                         parent = RB_PARENT(elm, field);                 \
 619                         RB_LEFT(parent, field) = child;                 \
 620                         RB_SET_PARENT(RB_RIGHT(old, field), elm, field);\
 621                 }                                                       \
 622                 RB_SET_PARENT(RB_LEFT(old, field), elm, field);         \
 623                 elm->field = old->field;                                \
 624         }                                                               \
 625         RB_SWAP_CHILD(head, old, elm, field);                           \
 626         if (child != NULL)                                              \
 627                 RB_SET_PARENT(child, parent, field);                    \
 628         if (parent != NULL)                                             \
 629                 name##_RB_REMOVE_COLOR(head, parent, child);            \
 630         while (parent != NULL) {                                        \
 631                 RB_AUGMENT(parent);                                     \
 632                 parent = RB_PARENT(parent, field);                      \
 633         }                                                               \
 634         return (old);                                                   \
 635 }
 636
 637 #define RB_GENERATE_INSERT(name, type, field, cmp, attr)                \
 638 /* Inserts a node into the RB tree */                                   \
 639 attr struct type *                                                      \
 640 name##_RB_INSERT(struct name *head, struct type *elm)                   \
 641 {                                                                       \
 642         struct type *tmp;                                               \
 643         struct type *parent = NULL;                                     \
 644         int comp = 0;                                                   \
 645         tmp = RB_ROOT(head);                                            \
 646         while (tmp) {                                                   \
 647                 parent = tmp;                                           \
 648                 comp = (cmp)(elm, parent);                              \
 649                 if (comp < 0)                                           \
 650                         tmp = RB_LEFT(tmp, field);                      \
 651                 else if (comp > 0)                                      \
 652                         tmp = RB_RIGHT(tmp, field);                     \
 653                 else                                                    \
 654                         return (tmp);                                   \
 655         }                                                               \
 656         RB_SET(elm, parent, field);                                     \
 657         if (parent == NULL)                                             \
 658                 RB_ROOT(head) = elm;                                    \
 659         else if (comp < 0)                                              \
 660                 RB_LEFT(parent, field) = elm;                           \
 661         else                                                            \
 662                 RB_RIGHT(parent, field) = elm;                          \
 663         name##_RB_INSERT_COLOR(head, elm);                              \
 664         while (elm != NULL) {                                           \
 665                 RB_AUGMENT(elm);                                        \
 666                 elm = RB_PARENT(elm, field);                            \
 667         }                                                               \
 668         return (NULL);                                                  \
 669 }
 670
 671 #define RB_GENERATE_FIND(name, type, field, cmp, attr)                  \
 672 /* Finds the node with the same key as elm */                           \
 673 attr struct type *                                                      \
 674 name##_RB_FIND(struct name *head, struct type *elm)                     \
 675 {                                                                       \
 676         struct type *tmp = RB_ROOT(head);                               \
 677         int comp;                                                       \
 678         while (tmp) {                                                   \
 679                 comp = cmp(elm, tmp);                                   \
 680                 if (comp < 0)                                           \
 681                         tmp = RB_LEFT(tmp, field);                      \
 682                 else if (comp > 0)                                      \
 683                         tmp = RB_RIGHT(tmp, field);                     \
 684                 else                                                    \
 685                         return (tmp);                                   \
 686         }                                                               \
 687         return (NULL);                                                  \
 688 }
 689
 690 #define RB_GENERATE_NFIND(name, type, field, cmp, attr)                 \
 691 /* Finds the first node greater than or equal to the search key */      \
 692 attr struct type *                                                      \
 693 name##_RB_NFIND(struct name *head, struct type *elm)                    \
 694 {                                                                       \
 695         struct type *tmp = RB_ROOT(head);                               \
 696         struct type *res = NULL;                                        \
 697         int comp;                                                       \
 698         while (tmp) {                                                   \
 699                 comp = cmp(elm, tmp);                                   \
 700                 if (comp < 0) {                                         \
 701                         res = tmp;                                      \
 702                         tmp = RB_LEFT(tmp, field);                      \
 703                 }                                                       \
 704                 else if (comp > 0)                                      \
 705                         tmp = RB_RIGHT(tmp, field);                     \
 706                 else                                                    \
 707                         return (tmp);                                   \
 708         }                                                               \
 709         return (res);                                                   \
 710 }
 711
 712 #define RB_GENERATE_NEXT(name, type, field, attr)                       \
 713 /* ARGSUSED */                                                          \
 714 attr struct type *                                                      \
 715 name##_RB_NEXT(struct type *elm)                                        \
 716 {                                                                       \
 717         if (RB_RIGHT(elm, field)) {                                     \
 718                 elm = RB_RIGHT(elm, field);                             \
 719                 while (RB_LEFT(elm, field))                             \
 720                         elm = RB_LEFT(elm, field);                      \
 721         } else {                                                        \
 722                 if (RB_PARENT(elm, field) &&                            \
 723                     (elm == RB_LEFT(RB_PARENT(elm, field), field)))     \
 724                         elm = RB_PARENT(elm, field);                    \
 725                 else {                                                  \
 726                         while (RB_PARENT(elm, field) &&                 \
 727                             (elm == RB_RIGHT(RB_PARENT(elm, field), field)))\
 728                                 elm = RB_PARENT(elm, field);            \
 729                         elm = RB_PARENT(elm, field);                    \
 730                 }                                                       \
 731         }                                                               \
 732         return (elm);                                                   \
 733 }
 734
 735 #define RB_GENERATE_PREV(name, type, field, attr)                       \
 736 /* ARGSUSED */                                                          \
 737 attr struct type *                                                      \
 738 name##_RB_PREV(struct type *elm)                                        \
 739 {                                                                       \
 740         if (RB_LEFT(elm, field)) {                                      \
 741                 elm = RB_LEFT(elm, field);                              \
 742                 while (RB_RIGHT(elm, field))                            \
 743                         elm = RB_RIGHT(elm, field);                     \
 744         } else {                                                        \
 745                 if (RB_PARENT(elm, field) &&                            \
 746                     (elm == RB_RIGHT(RB_PARENT(elm, field), field)))    \
 747                         elm = RB_PARENT(elm, field);                    \
 748                 else {                                                  \
 749                         while (RB_PARENT(elm, field) &&                 \
 750                             (elm == RB_LEFT(RB_PARENT(elm, field), field)))\
 751                                 elm = RB_PARENT(elm, field);            \
 752                         elm = RB_PARENT(elm, field);                    \
 753                 }                                                       \
 754         }                                                               \
 755         return (elm);                                                   \
 756 }
 757
 758 #define RB_GENERATE_MINMAX(name, type, field, attr)                     \
 759 attr struct type *                                                      \
 760 name##_RB_MINMAX(struct name *head, int val)                            \
 761 {                                                                       \
 762         struct type *tmp = RB_ROOT(head);                               \
 763         struct type *parent = NULL;                                     \
 764         while (tmp) {                                                   \
 765                 parent = tmp;                                           \
 766                 if (val < 0)                                            \
 767                         tmp = RB_LEFT(tmp, field);                      \
 768                 else                                                    \
 769                         tmp = RB_RIGHT(tmp, field);                     \
 770         }                                                               \
 771         return (parent);                                                \
 772 }
 773
 774 #define RB_GENERATE_REINSERT(name, type, field, cmp, attr)              \
 775 attr struct type *                                                      \
 776 name##_RB_REINSERT(struct name *head, struct type *elm)                 \
 777 {                                                                       \
 778         struct type *cmpelm;                                            \
 779         if (((cmpelm = RB_PREV(name, head, elm)) != NULL &&             \
 780             cmp(cmpelm, elm) >= 0) ||                                   \
 781             ((cmpelm = RB_NEXT(name, head, elm)) != NULL &&             \
 782             cmp(elm, cmpelm) >= 0)) {                                   \
 783                 /* XXXLAS: Remove/insert is heavy handed. */            \
 784                 RB_REMOVE(name, head, elm);                             \
 785                 return (RB_INSERT(name, head, elm));                    \
 786         }                                                               \
 787         return (NULL);                                                  \
 788 }                                                                       \
 789
 790 #define RB_NEGINF       -1
 791 #define RB_INF  1
 792
 793 #define RB_INSERT(name, x, y)   name##_RB_INSERT(x, y)
 794 #define RB_REMOVE(name, x, y)   name##_RB_REMOVE(x, y)
 795 #define RB_FIND(name, x, y)     name##_RB_FIND(x, y)
 796 #define RB_NFIND(name, x, y)    name##_RB_NFIND(x, y)
 797 #define RB_NEXT(name, x, y)     name##_RB_NEXT(y)
 798 #define RB_PREV(name, x, y)     name##_RB_PREV(y)
 799 #define RB_MIN(name, x)         name##_RB_MINMAX(x, RB_NEGINF)
 800 #define RB_MAX(name, x)         name##_RB_MINMAX(x, RB_INF)
 801 #define RB_REINSERT(name, x, y) name##_RB_REINSERT(x, y)
 802
 803 #define RB_FOREACH(x, name, head)                                       \
 804         for ((x) = RB_MIN(name, head);                                  \
 805              (x) != NULL;                                               \
 806              (x) = name##_RB_NEXT(x))
 807
 808 #define RB_FOREACH_FROM(x, name, y)                                     \
 809         for ((x) = (y);                                                 \
 810             ((x) != NULL) && ((y) = name##_RB_NEXT(x), (x) != NULL);    \
 811              (x) = (y))
 812
 813 #define RB_FOREACH_SAFE(x, name, head, y)                               \
 814         for ((x) = RB_MIN(name, head);                                  \
 815             ((x) != NULL) && ((y) = name##_RB_NEXT(x), (x) != NULL);    \
 816              (x) = (y))
 817
 818 #define RB_FOREACH_REVERSE(x, name, head)                               \
 819         for ((x) = RB_MAX(name, head);                                  \
 820              (x) != NULL;                                               \
 821              (x) = name##_RB_PREV(x))
 822
 823 #define RB_FOREACH_REVERSE_FROM(x, name, y)                             \
 824         for ((x) = (y);                                                 \
 825             ((x) != NULL) && ((y) = name##_RB_PREV(x), (x) != NULL);    \
 826              (x) = (y))
 827
 828 #define RB_FOREACH_REVERSE_SAFE(x, name, head, y)                       \
 829         for ((x) = RB_MAX(name, head);                                  \
 830             ((x) != NULL) && ((y) = name##_RB_PREV(x), (x) != NULL);    \
 831              (x) = (y))
 832
 833 #endif  /* _SYS_TREE_H_ */