libopenbsd/sys-tree.h

   1 /*      $OpenBSD: tree.h,v 1.13 2011/07/09 00:19:45 pirofti Exp $       */
   2 /*
   3  * Copyright 2002 Niels Provos <provos@citi.umich.edu>
   4  * All rights reserved.
   5  *
   6  * Redistribution and use in source and binary forms, with or without
   7  * modification, are permitted provided that the following conditions
   8  * are met:
   9  * 1. Redistributions of source code must retain the above copyright
  10  *    notice, this list of conditions and the following disclaimer.
  11  * 2. Redistributions in binary form must reproduce the above copyright
  12  *    notice, this list of conditions and the following disclaimer in the
  13  *    documentation and/or other materials provided with the distribution.
  14  *
  15  * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
  16  * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
  17  * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
  18  * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
  19  * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
  20  * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
  21  * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
  22  * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
  23  * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
  24  * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
  25  */
  26
  27 /* OPENBSD ORIGINAL: sys/sys/tree.h */
  28
  29 #ifdef NO_ATTRIBUTE_ON_RETURN_TYPE
  30 # define __attribute__(x)
  31 #endif
  32
  33 #ifndef _SYS_TREE_H_
  34 #define _SYS_TREE_H_
  35
  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 (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 (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 (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 (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 (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 (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))) {               \
 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 (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 (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 (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))) {             \
 344                 RB_PARENT(RB_LEFT(tmp, field), field) = (elm);          \
 345         }                                                               \
 346         RB_AUGMENT(elm);                                                \
 347         if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field))) {          \
 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 (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))) {             \
 364                 RB_PARENT(RB_RIGHT(tmp, field), field) = (elm);         \
 365         }                                                               \
 366         RB_AUGMENT(elm);                                                \
 367         if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field))) {          \
 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 (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, __attribute__((__unused__)) static)
 386 #define RB_PROTOTYPE_INTERNAL(name, type, field, cmp, attr)             \
 387 attr void name##_RB_INSERT_COLOR(struct name *, struct type *);         \
 388 attr void name##_RB_REMOVE_COLOR(struct name *, struct type *, struct type *);\
 389 attr struct type *name##_RB_REMOVE(struct name *, struct type *);       \
 390 attr struct type *name##_RB_INSERT(struct name *, struct type *);       \
 391 attr struct type *name##_RB_FIND(struct name *, struct type *);         \
 392 attr struct type *name##_RB_NFIND(struct name *, struct type *);        \
 393 attr struct type *name##_RB_NEXT(struct type *);                        \
 394 attr struct type *name##_RB_PREV(struct type *);                        \
 395 attr struct type *name##_RB_MINMAX(struct name *, int);                 \
 396                                                                         \
 397
 398 /* Main rb operation.
 399  * Moves node close to the key of elm to top
 400  */
 401 #define RB_GENERATE(name, type, field, cmp)                             \
 402         RB_GENERATE_INTERNAL(name, type, field, cmp,)
 403 #define RB_GENERATE_STATIC(name, type, field, cmp)                      \
 404         RB_GENERATE_INTERNAL(name, type, field, cmp, __attribute__((__unused__)) static)
 405 #define RB_GENERATE_INTERNAL(name, type, field, cmp, attr)              \
 406 attr void                                                               \
 407 name##_RB_INSERT_COLOR(struct name *head, struct type *elm)             \
 408 {                                                                       \
 409         struct type *parent, *gparent, *tmp;                            \
 410         while ((parent = RB_PARENT(elm, field)) &&                      \
 411             RB_COLOR(parent, field) == RB_RED) {                        \
 412                 gparent = RB_PARENT(parent, field);                     \
 413                 if (parent == RB_LEFT(gparent, field)) {                \
 414                         tmp = RB_RIGHT(gparent, field);                 \
 415                         if (tmp && RB_COLOR(tmp, field) == RB_RED) {    \
 416                                 RB_COLOR(tmp, field) = RB_BLACK;        \
 417                                 RB_SET_BLACKRED(parent, gparent, field);\
 418                                 elm = gparent;                          \
 419                                 continue;                               \
 420                         }                                               \
 421                         if (RB_RIGHT(parent, field) == elm) {           \
 422                                 RB_ROTATE_LEFT(head, parent, tmp, field);\
 423                                 tmp = parent;                           \
 424                                 parent = elm;                           \
 425                                 elm = tmp;                              \
 426                         }                                               \
 427                         RB_SET_BLACKRED(parent, gparent, field);        \
 428                         RB_ROTATE_RIGHT(head, gparent, tmp, field);     \
 429                 } else {                                                \
 430                         tmp = RB_LEFT(gparent, field);                  \
 431                         if (tmp && RB_COLOR(tmp, field) == RB_RED) {    \
 432                                 RB_COLOR(tmp, field) = RB_BLACK;        \
 433                                 RB_SET_BLACKRED(parent, gparent, field);\
 434                                 elm = gparent;                          \
 435                                 continue;                               \
 436                         }                                               \
 437                         if (RB_LEFT(parent, field) == elm) {            \
 438                                 RB_ROTATE_RIGHT(head, parent, tmp, field);\
 439                                 tmp = parent;                           \
 440                                 parent = elm;                           \
 441                                 elm = tmp;                              \
 442                         }                                               \
 443                         RB_SET_BLACKRED(parent, gparent, field);        \
 444                         RB_ROTATE_LEFT(head, gparent, tmp, field);      \
 445                 }                                                       \
 446         }                                                               \
 447         RB_COLOR(head->rbh_root, field) = RB_BLACK;                     \
 448 }                                                                       \
 449                                                                         \
 450 attr void                                                               \
 451 name##_RB_REMOVE_COLOR(struct name *head, struct type *parent, struct type *elm) \
 452 {                                                                       \
 453         struct type *tmp;                                               \
 454         while ((elm == NULL || RB_COLOR(elm, field) == RB_BLACK) &&     \
 455             elm != RB_ROOT(head)) {                                     \
 456                 if (RB_LEFT(parent, field) == elm) {                    \
 457                         tmp = RB_RIGHT(parent, field);                  \
 458                         if (RB_COLOR(tmp, field) == RB_RED) {           \
 459                                 RB_SET_BLACKRED(tmp, parent, field);    \
 460                                 RB_ROTATE_LEFT(head, parent, tmp, field);\
 461                                 tmp = RB_RIGHT(parent, field);          \
 462                         }                                               \
 463                         if ((RB_LEFT(tmp, field) == NULL ||             \
 464                             RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
 465                             (RB_RIGHT(tmp, field) == NULL ||            \
 466                             RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
 467                                 RB_COLOR(tmp, field) = RB_RED;          \
 468                                 elm = parent;                           \
 469                                 parent = RB_PARENT(elm, field);         \
 470                         } else {                                        \
 471                                 if (RB_RIGHT(tmp, field) == NULL ||     \
 472                                     RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK) {\
 473                                         struct type *oleft;             \
 474                                         if ((oleft = RB_LEFT(tmp, field)))\
 475                                                 RB_COLOR(oleft, field) = RB_BLACK;\
 476                                         RB_COLOR(tmp, field) = RB_RED;  \
 477                                         RB_ROTATE_RIGHT(head, tmp, oleft, field);\
 478                                         tmp = RB_RIGHT(parent, field);  \
 479                                 }                                       \
 480                                 RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
 481                                 RB_COLOR(parent, field) = RB_BLACK;     \
 482                                 if (RB_RIGHT(tmp, field))               \
 483                                         RB_COLOR(RB_RIGHT(tmp, field), field) = RB_BLACK;\
 484                                 RB_ROTATE_LEFT(head, parent, tmp, field);\
 485                                 elm = RB_ROOT(head);                    \
 486                                 break;                                  \
 487                         }                                               \
 488                 } else {                                                \
 489                         tmp = RB_LEFT(parent, field);                   \
 490                         if (RB_COLOR(tmp, field) == RB_RED) {           \
 491                                 RB_SET_BLACKRED(tmp, parent, field);    \
 492                                 RB_ROTATE_RIGHT(head, parent, tmp, field);\
 493                                 tmp = RB_LEFT(parent, field);           \
 494                         }                                               \
 495                         if ((RB_LEFT(tmp, field) == NULL ||             \
 496                             RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
 497                             (RB_RIGHT(tmp, field) == NULL ||            \
 498                             RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
 499                                 RB_COLOR(tmp, field) = RB_RED;          \
 500                                 elm = parent;                           \
 501                                 parent = RB_PARENT(elm, field);         \
 502                         } else {                                        \
 503                                 if (RB_LEFT(tmp, field) == NULL ||      \
 504                                     RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) {\
 505                                         struct type *oright;            \
 506                                         if ((oright = RB_RIGHT(tmp, field)))\
 507                                                 RB_COLOR(oright, field) = RB_BLACK;\
 508                                         RB_COLOR(tmp, field) = RB_RED;  \
 509                                         RB_ROTATE_LEFT(head, tmp, oright, field);\
 510                                         tmp = RB_LEFT(parent, field);   \
 511                                 }                                       \
 512                                 RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
 513                                 RB_COLOR(parent, field) = RB_BLACK;     \
 514                                 if (RB_LEFT(tmp, field))                \
 515                                         RB_COLOR(RB_LEFT(tmp, field), field) = RB_BLACK;\
 516                                 RB_ROTATE_RIGHT(head, parent, tmp, field);\
 517                                 elm = RB_ROOT(head);                    \
 518                                 break;                                  \
 519                         }                                               \
 520                 }                                                       \
 521         }                                                               \
 522         if (elm)                                                        \
 523                 RB_COLOR(elm, field) = RB_BLACK;                        \
 524 }                                                                       \
 525                                                                         \
 526 attr struct type *                                                      \
 527 name##_RB_REMOVE(struct name *head, struct type *elm)                   \
 528 {                                                                       \
 529         struct type *child, *parent, *old = elm;                        \
 530         int color;                                                      \
 531         if (RB_LEFT(elm, field) == NULL)                                \
 532                 child = RB_RIGHT(elm, field);                           \
 533         else if (RB_RIGHT(elm, field) == NULL)                          \
 534                 child = RB_LEFT(elm, field);                            \
 535         else {                                                          \
 536                 struct type *left;                                      \
 537                 elm = RB_RIGHT(elm, field);                             \
 538                 while ((left = RB_LEFT(elm, field)))                    \
 539                         elm = left;                                     \
 540                 child = RB_RIGHT(elm, field);                           \
 541                 parent = RB_PARENT(elm, field);                         \
 542                 color = RB_COLOR(elm, field);                           \
 543                 if (child)                                              \
 544                         RB_PARENT(child, field) = parent;               \
 545                 if (parent) {                                           \
 546                         if (RB_LEFT(parent, field) == elm)              \
 547                                 RB_LEFT(parent, field) = child;         \
 548                         else                                            \
 549                                 RB_RIGHT(parent, field) = child;        \
 550                         RB_AUGMENT(parent);                             \
 551                 } else                                                  \
 552                         RB_ROOT(head) = child;                          \
 553                 if (RB_PARENT(elm, field) == old)                       \
 554                         parent = elm;                                   \
 555                 (elm)->field = (old)->field;                            \
 556                 if (RB_PARENT(old, field)) {                            \
 557                         if (RB_LEFT(RB_PARENT(old, field), field) == old)\
 558                                 RB_LEFT(RB_PARENT(old, field), field) = elm;\
 559                         else                                            \
 560                                 RB_RIGHT(RB_PARENT(old, field), field) = elm;\
 561                         RB_AUGMENT(RB_PARENT(old, field));              \
 562                 } else                                                  \
 563                         RB_ROOT(head) = elm;                            \
 564                 RB_PARENT(RB_LEFT(old, field), field) = elm;            \
 565                 if (RB_RIGHT(old, field))                               \
 566                         RB_PARENT(RB_RIGHT(old, field), field) = elm;   \
 567                 if (parent) {                                           \
 568                         left = parent;                                  \
 569                         do {                                            \
 570                                 RB_AUGMENT(left);                       \
 571                         } while ((left = RB_PARENT(left, field)));      \
 572                 }                                                       \
 573                 goto color;                                             \
 574         }                                                               \
 575         parent = RB_PARENT(elm, field);                                 \
 576         color = RB_COLOR(elm, field);                                   \
 577         if (child)                                                      \
 578                 RB_PARENT(child, field) = parent;                       \
 579         if (parent) {                                                   \
 580                 if (RB_LEFT(parent, field) == elm)                      \
 581                         RB_LEFT(parent, field) = child;                 \
 582                 else                                                    \
 583                         RB_RIGHT(parent, field) = child;                \
 584                 RB_AUGMENT(parent);                                     \
 585         } else                                                          \
 586                 RB_ROOT(head) = child;                                  \
 587 color:                                                                  \
 588         if (color == RB_BLACK)                                          \
 589                 name##_RB_REMOVE_COLOR(head, parent, child);            \
 590         return (old);                                                   \
 591 }                                                                       \
 592                                                                         \
 593 /* Inserts a node into the RB tree */                                   \
 594 attr struct type *                                                      \
 595 name##_RB_INSERT(struct name *head, struct type *elm)                   \
 596 {                                                                       \
 597         struct type *tmp;                                               \
 598         struct type *parent = NULL;                                     \
 599         int comp = 0;                                                   \
 600         tmp = RB_ROOT(head);                                            \
 601         while (tmp) {                                                   \
 602                 parent = tmp;                                           \
 603                 comp = (cmp)(elm, parent);                              \
 604                 if (comp < 0)                                           \
 605                         tmp = RB_LEFT(tmp, field);                      \
 606                 else if (comp > 0)                                      \
 607                         tmp = RB_RIGHT(tmp, field);                     \
 608                 else                                                    \
 609                         return (tmp);                                   \
 610         }                                                               \
 611         RB_SET(elm, parent, field);                                     \
 612         if (parent != NULL) {                                           \
 613                 if (comp < 0)                                           \
 614                         RB_LEFT(parent, field) = elm;                   \
 615                 else                                                    \
 616                         RB_RIGHT(parent, field) = elm;                  \
 617                 RB_AUGMENT(parent);                                     \
 618         } else                                                          \
 619                 RB_ROOT(head) = elm;                                    \
 620         name##_RB_INSERT_COLOR(head, elm);                              \
 621         return (NULL);                                                  \
 622 }                                                                       \
 623                                                                         \
 624 /* Finds the node with the same key as elm */                           \
 625 attr struct type *                                                      \
 626 name##_RB_FIND(struct name *head, struct type *elm)                     \
 627 {                                                                       \
 628         struct type *tmp = RB_ROOT(head);                               \
 629         int comp;                                                       \
 630         while (tmp) {                                                   \
 631                 comp = cmp(elm, tmp);                                   \
 632                 if (comp < 0)                                           \
 633                         tmp = RB_LEFT(tmp, field);                      \
 634                 else if (comp > 0)                                      \
 635                         tmp = RB_RIGHT(tmp, field);                     \
 636                 else                                                    \
 637                         return (tmp);                                   \
 638         }                                                               \
 639         return (NULL);                                                  \
 640 }                                                                       \
 641                                                                         \
 642 /* Finds the first node greater than or equal to the search key */      \
 643 attr struct type *                                                      \
 644 name##_RB_NFIND(struct name *head, struct type *elm)                    \
 645 {                                                                       \
 646         struct type *tmp = RB_ROOT(head);                               \
 647         struct type *res = NULL;                                        \
 648         int comp;                                                       \
 649         while (tmp) {                                                   \
 650                 comp = cmp(elm, tmp);                                   \
 651                 if (comp < 0) {                                         \
 652                         res = tmp;                                      \
 653                         tmp = RB_LEFT(tmp, field);                      \
 654                 }                                                       \
 655                 else if (comp > 0)                                      \
 656                         tmp = RB_RIGHT(tmp, field);                     \
 657                 else                                                    \
 658                         return (tmp);                                   \
 659         }                                                               \
 660         return (res);                                                   \
 661 }                                                                       \
 662                                                                         \
 663 /* ARGSUSED */                                                          \
 664 attr struct type *                                                      \
 665 name##_RB_NEXT(struct type *elm)                                        \
 666 {                                                                       \
 667         if (RB_RIGHT(elm, field)) {                                     \
 668                 elm = RB_RIGHT(elm, field);                             \
 669                 while (RB_LEFT(elm, field))                             \
 670                         elm = RB_LEFT(elm, field);                      \
 671         } else {                                                        \
 672                 if (RB_PARENT(elm, field) &&                            \
 673                     (elm == RB_LEFT(RB_PARENT(elm, field), field)))     \
 674                         elm = RB_PARENT(elm, field);                    \
 675                 else {                                                  \
 676                         while (RB_PARENT(elm, field) &&                 \
 677                             (elm == RB_RIGHT(RB_PARENT(elm, field), field)))\
 678                                 elm = RB_PARENT(elm, field);            \
 679                         elm = RB_PARENT(elm, field);                    \
 680                 }                                                       \
 681         }                                                               \
 682         return (elm);                                                   \
 683 }                                                                       \
 684                                                                         \
 685 /* ARGSUSED */                                                          \
 686 attr struct type *                                                      \
 687 name##_RB_PREV(struct type *elm)                                        \
 688 {                                                                       \
 689         if (RB_LEFT(elm, field)) {                                      \
 690                 elm = RB_LEFT(elm, field);                              \
 691                 while (RB_RIGHT(elm, field))                            \
 692                         elm = RB_RIGHT(elm, field);                     \
 693         } else {                                                        \
 694                 if (RB_PARENT(elm, field) &&                            \
 695                     (elm == RB_RIGHT(RB_PARENT(elm, field), field)))    \
 696                         elm = RB_PARENT(elm, field);                    \
 697                 else {                                                  \
 698                         while (RB_PARENT(elm, field) &&                 \
 699                             (elm == RB_LEFT(RB_PARENT(elm, field), field)))\
 700                                 elm = RB_PARENT(elm, field);            \
 701                         elm = RB_PARENT(elm, field);                    \
 702                 }                                                       \
 703         }                                                               \
 704         return (elm);                                                   \
 705 }                                                                       \
 706                                                                         \
 707 attr struct type *                                                      \
 708 name##_RB_MINMAX(struct name *head, int val)                            \
 709 {                                                                       \
 710         struct type *tmp = RB_ROOT(head);                               \
 711         struct type *parent = NULL;                                     \
 712         while (tmp) {                                                   \
 713                 parent = tmp;                                           \
 714                 if (val < 0)                                            \
 715                         tmp = RB_LEFT(tmp, field);                      \
 716                 else                                                    \
 717                         tmp = RB_RIGHT(tmp, field);                     \
 718         }                                                               \
 719         return (parent);                                                \
 720 }
 721
 722 #define RB_NEGINF       -1
 723 #define RB_INF  1
 724
 725 #define RB_INSERT(name, x, y)   name##_RB_INSERT(x, y)
 726 #define RB_REMOVE(name, x, y)   name##_RB_REMOVE(x, y)
 727 #define RB_FIND(name, x, y)     name##_RB_FIND(x, y)
 728 #define RB_NFIND(name, x, y)    name##_RB_NFIND(x, y)
 729 #define RB_NEXT(name, x, y)     name##_RB_NEXT(y)
 730 #define RB_PREV(name, x, y)     name##_RB_PREV(y)
 731 #define RB_MIN(name, x)         name##_RB_MINMAX(x, RB_NEGINF)
 732 #define RB_MAX(name, x)         name##_RB_MINMAX(x, RB_INF)
 733
 734 #define RB_FOREACH(x, name, head)                                       \
 735         for ((x) = RB_MIN(name, head);                                  \
 736              (x) != NULL;                                               \
 737              (x) = name##_RB_NEXT(x))
 738
 739 #define RB_FOREACH_SAFE(x, name, head, y)                               \
 740         for ((x) = RB_MIN(name, head);                                  \
 741             ((x) != NULL) && ((y) = name##_RB_NEXT(x), 1);              \
 742              (x) = (y))
 743
 744 #define RB_FOREACH_REVERSE(x, name, head)                               \
 745         for ((x) = RB_MAX(name, head);                                  \
 746              (x) != NULL;                                               \
 747              (x) = name##_RB_PREV(x))
 748
 749 #define RB_FOREACH_REVERSE_SAFE(x, name, head, y)                       \
 750         for ((x) = RB_MAX(name, head);                                  \
 751             ((x) != NULL) && ((y) = name##_RB_PREV(x), 1);              \
 752              (x) = (y))
 753
 754 #endif  /* _SYS_TREE_H_ */