include/sys/tree.h

   1 /*      $NetBSD: tree.h,v 1.16 2008/03/21 13:07:15 ad Exp $     */
   2 /*      $OpenBSD: tree.h,v 1.7 2002/10/17 21:51:54 art Exp $    */
   3 /*
   4  * Copyright 2002 Niels Provos <provos@citi.umich.edu>
   5  * All rights reserved.
   6  *
   7  * Redistribution and use in source and binary forms, with or without
   8  * modification, are permitted provided that the following conditions
   9  * are met:
  10  * 1. Redistributions of source code must retain the above copyright
  11  *    notice, this list of conditions and the following disclaimer.
  12  * 2. Redistributions in binary form must reproduce the above copyright
  13  *    notice, this list of conditions and the following disclaimer in the
  14  *    documentation and/or other materials provided with the distribution.
  15  *
  16  * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
  17  * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
  18  * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
  19  * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
  20  * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
  21  * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
  22  * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
  23  * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
  24  * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
  25  * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
  26  */
  27
  28 #ifndef _SYS_TREE_H_
  29 #define _SYS_TREE_H_
  30
  31 /*
  32  * This file defines data structures for different types of trees:
  33  * splay trees and red-black trees.
  34  *
  35  * A splay tree is a self-organizing data structure.  Every operation
  36  * on the tree causes a splay to happen.  The splay moves the requested
  37  * node to the root of the tree and partly rebalances it.
  38  *
  39  * This has the benefit that request locality causes faster lookups as
  40  * the requested nodes move to the top of the tree.  On the other hand,
  41  * every lookup causes memory writes.
  42  *
  43  * The Balance Theorem bounds the total access time for m operations
  44  * and n inserts on an initially empty tree as O((m + n)lg n).  The
  45  * amortized cost for a sequence of m accesses to a splay tree is O(lg n);
  46  *
  47  * A red-black tree is a binary search tree with the node color as an
  48  * extra attribute.  It fulfills a set of conditions:
  49  *      - every search path from the root to a leaf consists of the
  50  *        same number of black nodes,
  51  *      - each red node (except for the root) has a black parent,
  52  *      - each leaf node is black.
  53  *
  54  * Every operation on a red-black tree is bounded as O(lg n).
  55  * The maximum height of a red-black tree is 2lg (n+1).
  56  */
  57
  58 #define SPLAY_HEAD(name, type)                                          \
  59 struct name {                                                           \
  60         struct type *sph_root; /* root of the tree */                   \
  61 }
  62
  63 #define SPLAY_INITIALIZER(root)                                         \
  64         { NULL }
  65
  66 #define SPLAY_INIT(root) do {                                           \
  67         (root)->sph_root = NULL;                                        \
  68 } while (/*CONSTCOND*/ 0)
  69
  70 #define SPLAY_ENTRY(type)                                               \
  71 struct {                                                                \
  72         struct type *spe_left; /* left element */                       \
  73         struct type *spe_right; /* right element */                     \
  74 }
  75
  76 #define SPLAY_LEFT(elm, field)          (elm)->field.spe_left
  77 #define SPLAY_RIGHT(elm, field)         (elm)->field.spe_right
  78 #define SPLAY_ROOT(head)                (head)->sph_root
  79 #define SPLAY_EMPTY(head)               (SPLAY_ROOT(head) == NULL)
  80
  81 /* SPLAY_ROTATE_{LEFT,RIGHT} expect that tmp hold SPLAY_{RIGHT,LEFT} */
  82 #define SPLAY_ROTATE_RIGHT(head, tmp, field) do {                       \
  83         SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(tmp, field);  \
  84         SPLAY_RIGHT(tmp, field) = (head)->sph_root;                     \
  85         (head)->sph_root = tmp;                                         \
  86 } while (/*CONSTCOND*/ 0)
  87
  88 #define SPLAY_ROTATE_LEFT(head, tmp, field) do {                        \
  89         SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(tmp, field);  \
  90         SPLAY_LEFT(tmp, field) = (head)->sph_root;                      \
  91         (head)->sph_root = tmp;                                         \
  92 } while (/*CONSTCOND*/ 0)
  93
  94 #define SPLAY_LINKLEFT(head, tmp, field) do {                           \
  95         SPLAY_LEFT(tmp, field) = (head)->sph_root;                      \
  96         tmp = (head)->sph_root;                                         \
  97         (head)->sph_root = SPLAY_LEFT((head)->sph_root, field);         \
  98 } while (/*CONSTCOND*/ 0)
  99
 100 #define SPLAY_LINKRIGHT(head, tmp, field) do {                          \
 101         SPLAY_RIGHT(tmp, field) = (head)->sph_root;                     \
 102         tmp = (head)->sph_root;                                         \
 103         (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);        \
 104 } while (/*CONSTCOND*/ 0)
 105
 106 #define SPLAY_ASSEMBLE(head, node, left, right, field) do {             \
 107         SPLAY_RIGHT(left, field) = SPLAY_LEFT((head)->sph_root, field); \
 108         SPLAY_LEFT(right, field) = SPLAY_RIGHT((head)->sph_root, field);\
 109         SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(node, field); \
 110         SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(node, field); \
 111 } while (/*CONSTCOND*/ 0)
 112
 113 /* Generates prototypes and inline functions */
 114
 115 void name##_SPLAY_MINMAX(struct name *, int);                           \
 116 struct type *name##_SPLAY_INSERT(struct name *, struct type *);         \
 117 struct type *name##_SPLAY_REMOVE(struct name *, struct type *);         \
 118                                                                         \
 119 /* Finds the node with the same key as elm */                           \
 120 static __inline struct type *                                           \
 121 name##_SPLAY_FIND(struct name *head, struct type *elm)                  \
 122 {                                                                       \
 123         if (SPLAY_EMPTY(head))                                          \
 124                 return(NULL);                                           \
 125         name##_SPLAY(head, elm);                                        \
 126         if ((cmp)(elm, (head)->sph_root) == 0)                          \
 127                 return (head->sph_root);                                \
 128         return (NULL);                                                  \
 129 }                                                                       \
 130                                                                         \
 131 static __inline struct type *                                           \
 132 name##_SPLAY_NEXT(struct name *head, struct type *elm)                  \
 133 {                                                                       \
 134         name##_SPLAY(head, elm);                                        \
 135         if (SPLAY_RIGHT(elm, field) != NULL) {                          \
 136                 elm = SPLAY_RIGHT(elm, field);                          \
 137                 while (SPLAY_LEFT(elm, field) != NULL) {                \
 138                         elm = SPLAY_LEFT(elm, field);                   \
 139                 }                                                       \
 140         } else                                                          \
 141                 elm = NULL;                                             \
 142         return (elm);                                                   \
 143 }                                                                       \
 144                                                                         \
 145 static __inline struct type *                                           \
 146 name##_SPLAY_MIN_MAX(struct name *head, int val)                        \
 147 {                                                                       \
 148         name##_SPLAY_MINMAX(head, val);                                 \
 149         return (SPLAY_ROOT(head));                                      \
 150 }
 151
 152 /* Main splay operation.
 153  * Moves node close to the key of elm to top
 154  */
 155 #define SPLAY_GENERATE(name, type, field, cmp)                          \
 156 struct type *                                                           \
 157 name##_SPLAY_INSERT(struct name *head, struct type *elm)                \
 158 {                                                                       \
 159     if (SPLAY_EMPTY(head)) {                                            \
 160             SPLAY_LEFT(elm, field) = SPLAY_RIGHT(elm, field) = NULL;    \
 161     } else {                                                            \
 162             int __comp;                                                 \
 163             name##_SPLAY(head, elm);                                    \
 164             __comp = (cmp)(elm, (head)->sph_root);                      \
 165             if(__comp < 0) {                                            \
 166                     SPLAY_LEFT(elm, field) = SPLAY_LEFT((head)->sph_root, field);\
 167                     SPLAY_RIGHT(elm, field) = (head)->sph_root;         \
 168                     SPLAY_LEFT((head)->sph_root, field) = NULL;         \
 169             } else if (__comp > 0) {                                    \
 170                     SPLAY_RIGHT(elm, field) = SPLAY_RIGHT((head)->sph_root, field);\
 171                     SPLAY_LEFT(elm, field) = (head)->sph_root;          \
 172                     SPLAY_RIGHT((head)->sph_root, field) = NULL;        \
 173             } else                                                      \
 174                     return ((head)->sph_root);                          \
 175     }                                                                   \
 176     (head)->sph_root = (elm);                                           \
 177     return (NULL);                                                      \
 178 }                                                                       \
 179                                                                         \
 180 struct type *                                                           \
 181 name##_SPLAY_REMOVE(struct name *head, struct type *elm)                \
 182 {                                                                       \
 183         struct type *__tmp;                                             \
 184         if (SPLAY_EMPTY(head))                                          \
 185                 return (NULL);                                          \
 186         name##_SPLAY(head, elm);                                        \
 187         if ((cmp)(elm, (head)->sph_root) == 0) {                        \
 188                 if (SPLAY_LEFT((head)->sph_root, field) == NULL) {      \
 189                         (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);\
 190                 } else {                                                \
 191                         __tmp = SPLAY_RIGHT((head)->sph_root, field);   \
 192                         (head)->sph_root = SPLAY_LEFT((head)->sph_root, field);\
 193                         name##_SPLAY(head, elm);                        \
 194                         SPLAY_RIGHT((head)->sph_root, field) = __tmp;   \
 195                 }                                                       \
 196                 return (elm);                                           \
 197         }                                                               \
 198         return (NULL);                                                  \
 199 }                                                                       \
 200                                                                         \
 201 void                                                                    \
 202 name##_SPLAY(struct name *head, struct type *elm)                       \
 203 {                                                                       \
 204         struct type __node, *__left, *__right, *__tmp;                  \
 205         int __comp;                                                     \
 206 \
 207         SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
 208         __left = __right = &__node;                                     \
 209 \
 210         while ((__comp = (cmp)(elm, (head)->sph_root)) != 0) {          \
 211                 if (__comp < 0) {                                       \
 212                         __tmp = SPLAY_LEFT((head)->sph_root, field);    \
 213                         if (__tmp == NULL)                              \
 214                                 break;                                  \
 215                         if ((cmp)(elm, __tmp) < 0){                     \
 216                                 SPLAY_ROTATE_RIGHT(head, __tmp, field); \
 217                                 if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
 218                                         break;                          \
 219                         }                                               \
 220                         SPLAY_LINKLEFT(head, __right, field);           \
 221                 } else if (__comp > 0) {                                \
 222                         __tmp = SPLAY_RIGHT((head)->sph_root, field);   \
 223                         if (__tmp == NULL)                              \
 224                                 break;                                  \
 225                         if ((cmp)(elm, __tmp) > 0){                     \
 226                                 SPLAY_ROTATE_LEFT(head, __tmp, field);  \
 227                                 if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
 228                                         break;                          \
 229                         }                                               \
 230                         SPLAY_LINKRIGHT(head, __left, field);           \
 231                 }                                                       \
 232         }                                                               \
 233         SPLAY_ASSEMBLE(head, &__node, __left, __right, field);          \
 234 }                                                                       \
 235                                                                         \
 236 /* Splay with either the minimum or the maximum element                 \
 237  * Used to find minimum or maximum element in tree.                     \
 238  */                                                                     \
 239 void name##_SPLAY_MINMAX(struct name *head, int __comp) \
 240 {                                                                       \
 241         struct type __node, *__left, *__right, *__tmp;                  \
 242 \
 243         SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
 244         __left = __right = &__node;                                     \
 245 \
 246         while (1) {                                                     \
 247                 if (__comp < 0) {                                       \
 248                         __tmp = SPLAY_LEFT((head)->sph_root, field);    \
 249                         if (__tmp == NULL)                              \
 250                                 break;                                  \
 251                         if (__comp < 0){                                \
 252                                 SPLAY_ROTATE_RIGHT(head, __tmp, field); \
 253                                 if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
 254                                         break;                          \
 255                         }                                               \
 256                         SPLAY_LINKLEFT(head, __right, field);           \
 257                 } else if (__comp > 0) {                                \
 258                         __tmp = SPLAY_RIGHT((head)->sph_root, field);   \
 259                         if (__tmp == NULL)                              \
 260                                 break;                                  \
 261                         if (__comp > 0) {                               \
 262                                 SPLAY_ROTATE_LEFT(head, __tmp, field);  \
 263                                 if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
 264                                         break;                          \
 265                         }                                               \
 266                         SPLAY_LINKRIGHT(head, __left, field);           \
 267                 }                                                       \
 268         }                                                               \
 269         SPLAY_ASSEMBLE(head, &__node, __left, __right, field);          \
 270 }
 271
 272 #define SPLAY_NEGINF    -1
 273 #define SPLAY_INF       1
 274
 275 #define SPLAY_INSERT(name, x, y)        name##_SPLAY_INSERT(x, y)
 276 #define SPLAY_REMOVE(name, x, y)        name##_SPLAY_REMOVE(x, y)
 277 #define SPLAY_FIND(name, x, y)          name##_SPLAY_FIND(x, y)
 278 #define SPLAY_NEXT(name, x, y)          name##_SPLAY_NEXT(x, y)
 279 #define SPLAY_MIN(name, x)              (SPLAY_EMPTY(x) ? NULL  \
 280                                         : name##_SPLAY_MIN_MAX(x, SPLAY_NEGINF))
 281 #define SPLAY_MAX(name, x)              (SPLAY_EMPTY(x) ? NULL  \
 282                                         : name##_SPLAY_MIN_MAX(x, SPLAY_INF))
 283
 284 #define SPLAY_FOREACH(x, name, head)                                    \
 285         for ((x) = SPLAY_MIN(name, head);                               \
 286              (x) != NULL;                                               \
 287              (x) = SPLAY_NEXT(name, head, x))
 288
 289 /* Macros that define a red-black tree */
 290 #define RB_HEAD(name, type)                                             \
 291 struct name {                                                           \
 292         struct type *rbh_root; /* root of the tree */                   \
 293 }
 294
 295 #define RB_INITIALIZER(root)                                            \
 296         { NULL }
 297
 298 #define RB_INIT(root) do {                                              \
 299         (root)->rbh_root = NULL;                                        \
 300 } while (/*CONSTCOND*/ 0)
 301
 302 #define RB_BLACK        0
 303 #define RB_RED          1
 304 #define RB_ENTRY(type)                                                  \
 305 struct {                                                                \
 306         struct type *rbe_left;          /* left element */              \
 307         struct type *rbe_right;         /* right element */             \
 308         struct type *rbe_parent;        /* parent element */            \
 309         int rbe_color;                  /* node color */                \
 310 }
 311
 312 #define RB_LEFT(elm, field)             (elm)->field.rbe_left
 313 #define RB_RIGHT(elm, field)            (elm)->field.rbe_right
 314 #define RB_PARENT(elm, field)           (elm)->field.rbe_parent
 315 #define RB_COLOR(elm, field)            (elm)->field.rbe_color
 316 #define RB_ROOT(head)                   (head)->rbh_root
 317 #define RB_EMPTY(head)                  (RB_ROOT(head) == NULL)
 318
 319 #define RB_SET(elm, parent, field) do {                                 \
 320         RB_PARENT(elm, field) = parent;                                 \
 321         RB_LEFT(elm, field) = RB_RIGHT(elm, field) = NULL;              \
 322         RB_COLOR(elm, field) = RB_RED;                                  \
 323 } while (/*CONSTCOND*/ 0)
 324
 325 #define RB_SET_BLACKRED(black, red, field) do {                         \
 326         RB_COLOR(black, field) = RB_BLACK;                              \
 327         RB_COLOR(red, field) = RB_RED;                                  \
 328 } while (/*CONSTCOND*/ 0)
 329
 330 #ifndef RB_AUGMENT
 331 #define RB_AUGMENT(x) (void)(x)
 332 #endif
 333
 334 #define RB_ROTATE_LEFT(head, elm, tmp, field) do {                      \
 335         (tmp) = RB_RIGHT(elm, field);                                   \
 336         if ((RB_RIGHT(elm, field) = RB_LEFT(tmp, field)) != NULL) {     \
 337                 RB_PARENT(RB_LEFT(tmp, field), field) = (elm);          \
 338         }                                                               \
 339         RB_AUGMENT(elm);                                                \
 340         if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) {  \
 341                 if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))     \
 342                         RB_LEFT(RB_PARENT(elm, field), field) = (tmp);  \
 343                 else                                                    \
 344                         RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \
 345         } else                                                          \
 346                 (head)->rbh_root = (tmp);                               \
 347         RB_LEFT(tmp, field) = (elm);                                    \
 348         RB_PARENT(elm, field) = (tmp);                                  \
 349         RB_AUGMENT(tmp);                                                \
 350         if ((RB_PARENT(tmp, field)))                                    \
 351                 RB_AUGMENT(RB_PARENT(tmp, field));                      \
 352 } while (/*CONSTCOND*/ 0)
 353
 354 #define RB_ROTATE_RIGHT(head, elm, tmp, field) do {                     \
 355         (tmp) = RB_LEFT(elm, field);                                    \
 356         if ((RB_LEFT(elm, field) = RB_RIGHT(tmp, field)) != NULL) {     \
 357                 RB_PARENT(RB_RIGHT(tmp, field), field) = (elm);         \
 358         }                                                               \
 359         RB_AUGMENT(elm);                                                \
 360         if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) {  \
 361                 if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))     \
 362                         RB_LEFT(RB_PARENT(elm, field), field) = (tmp);  \
 363                 else                                                    \
 364                         RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \
 365         } else                                                          \
 366                 (head)->rbh_root = (tmp);                               \
 367         RB_RIGHT(tmp, field) = (elm);                                   \
 368         RB_PARENT(elm, field) = (tmp);                                  \
 369         RB_AUGMENT(tmp);                                                \
 370         if ((RB_PARENT(tmp, field)))                                    \
 371                 RB_AUGMENT(RB_PARENT(tmp, field));                      \
 372 } while (/*CONSTCOND*/ 0)
 373
 374 /* Generates prototypes and inline functions */
 375 attr void name##_RB_REMOVE_COLOR(struct name *, struct type *, struct type *);\
 376 attr struct type *name##_RB_REMOVE(struct name *, struct type *);       \
 377 attr struct type *name##_RB_INSERT(struct name *, struct type *);       \
 378 attr struct type *name##_RB_FIND(struct name *, struct type *);         \
 379 attr struct type *name##_RB_NFIND(struct name *, struct type *);        \
 380 attr struct type *name##_RB_NEXT(struct type *);                        \
 381 attr struct type *name##_RB_PREV(struct type *);                        \
 382 attr struct type *name##_RB_MINMAX(struct name *, int);                 \
 383                                                                         \
 384
 385 /* Main rb operation.
 386  * Moves node close to the key of elm to top
 387  */
 388 #define RB_GENERATE(name, type, field, cmp)                             \
 389         RB_GENERATE_INTERNAL(name, type, field, cmp,)
 390 #define RB_GENERATE_STATIC(name, type, field, cmp)                      \
 391         RB_GENERATE_INTERNAL(name, type, field, cmp, __unused static)
 392 #define RB_GENERATE_INTERNAL(name, type, field, cmp, attr)              \
 393 attr 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 attr 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 attr 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 attr 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 attr 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 /* Finds the first node greater than or equal to the search key */      \
 632 attr struct type *                                                      \
 633 name##_RB_NFIND(struct name *head, struct type *elm)                    \
 634 {                                                                       \
 635         struct type *tmp = RB_ROOT(head);                               \
 636         struct type *res = NULL;                                        \
 637         int comp;                                                       \
 638         while (tmp) {                                                   \
 639                 comp = cmp(elm, tmp);                                   \
 640                 if (comp < 0) {                                         \
 641                         res = tmp;                                      \
 642                         tmp = RB_LEFT(tmp, field);                      \
 643                 }                                                       \
 644                 else if (comp > 0)                                      \
 645                         tmp = RB_RIGHT(tmp, field);                     \
 646                 else                                                    \
 647                         return (tmp);                                   \
 648         }                                                               \
 649         return (res);                                                   \
 650 }                                                                       \
 651                                                                         \
 652 /* ARGSUSED */                                                          \
 653 attr struct type *                                                      \
 654 name##_RB_NEXT(struct type *elm)                                        \
 655 {                                                                       \
 656         if (RB_RIGHT(elm, field)) {                                     \
 657                 elm = RB_RIGHT(elm, field);                             \
 658                 while (RB_LEFT(elm, field))                             \
 659                         elm = RB_LEFT(elm, field);                      \
 660         } else {                                                        \
 661                 if (RB_PARENT(elm, field) &&                            \
 662                     (elm == RB_LEFT(RB_PARENT(elm, field), field)))     \
 663                         elm = RB_PARENT(elm, field);                    \
 664                 else {                                                  \
 665                         while (RB_PARENT(elm, field) &&                 \
 666                             (elm == RB_RIGHT(RB_PARENT(elm, field), field)))\
 667                                 elm = RB_PARENT(elm, field);            \
 668                         elm = RB_PARENT(elm, field);                    \
 669                 }                                                       \
 670         }                                                               \
 671         return (elm);                                                   \
 672 }                                                                       \
 673                                                                         \
 674 /* ARGSUSED */                                                          \
 675 attr struct type *                                                      \
 676 name##_RB_PREV(struct type *elm)                                        \
 677 {                                                                       \
 678         if (RB_LEFT(elm, field)) {                                      \
 679                 elm = RB_LEFT(elm, field);                              \
 680                 while (RB_RIGHT(elm, field))                            \
 681                         elm = RB_RIGHT(elm, field);                     \
 682         } else {                                                        \
 683                 if (RB_PARENT(elm, field) &&                            \
 684                     (elm == RB_RIGHT(RB_PARENT(elm, field), field)))    \
 685                         elm = RB_PARENT(elm, field);                    \
 686                 else {                                                  \
 687                         while (RB_PARENT(elm, field) &&                 \
 688                             (elm == RB_LEFT(RB_PARENT(elm, field), field)))\
 689                                 elm = RB_PARENT(elm, field);            \
 690                         elm = RB_PARENT(elm, field);                    \
 691                 }                                                       \
 692         }                                                               \
 693         return (elm);                                                   \
 694 }                                                                       \
 695                                                                         \
 696 attr struct type *                                                      \
 697 name##_RB_MINMAX(struct name *head, int val)                            \
 698 {                                                                       \
 699         struct type *tmp = RB_ROOT(head);                               \
 700         struct type *parent = NULL;                                     \
 701         while (tmp) {                                                   \
 702                 parent = tmp;                                           \
 703                 if (val < 0)                                            \
 704                         tmp = RB_LEFT(tmp, field);                      \
 705                 else                                                    \
 706                         tmp = RB_RIGHT(tmp, field);                     \
 707         }                                                               \
 708         return (parent);                                                \
 709 }
 710
 711 #define RB_NEGINF       -1
 712 #define RB_INF  1
 713
 714 #define RB_INSERT(name, x, y)   name##_RB_INSERT(x, y)
 715 #define RB_REMOVE(name, x, y)   name##_RB_REMOVE(x, y)
 716 #define RB_FIND(name, x, y)     name##_RB_FIND(x, y)
 717 #define RB_NFIND(name, x, y)    name##_RB_NFIND(x, y)
 718 #define RB_NEXT(name, x, y)     name##_RB_NEXT(y)
 719 #define RB_PREV(name, x, y)     name##_RB_PREV(y)
 720 #define RB_MIN(name, x)         name##_RB_MINMAX(x, RB_NEGINF)
 721 #define RB_MAX(name, x)         name##_RB_MINMAX(x, RB_INF)
 722
 723 #define RB_FOREACH(x, name, head)                                       \
 724         for ((x) = RB_MIN(name, head);                                  \
 725              (x) != NULL;                                               \
 726              (x) = name##_RB_NEXT(x))
 727
 728 #define RB_FOREACH_REVERSE(x, name, head)                               \
 729         for ((x) = RB_MAX(name, head);                                  \
 730              (x) != NULL;                                               \
 731              (x) = name##_RB_PREV(x))
 732
 733 #endif  /* _SYS_TREE_H_ */