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