libbase/jemtree.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: src/sys/sys/tree.h,v 1.7 2007/12/28 07:03:26 jasone Exp $ */
   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         RB_PROTOTYPE_INTERNAL(name, type, field, cmp,)
 381 #define RB_PROTOTYPE_STATIC(name, type, field, cmp)                     \
 382         RB_PROTOTYPE_INTERNAL(name, type, field, cmp, __unused static)
 383 #define RB_PROTOTYPE_INTERNAL(name, type, field, cmp, attr)             \
 384 attr void name##_RB_INSERT_COLOR(struct name *, struct type *);         \
 385 attr void name##_RB_REMOVE_COLOR(struct name *, struct type *, struct type *);\
 386 attr struct type *name##_RB_REMOVE(struct name *, struct type *);       \
 387 attr struct type *name##_RB_INSERT(struct name *, struct type *);       \
 388 attr struct type *name##_RB_FIND(struct name *, struct type *);         \
 389 attr struct type *name##_RB_NFIND(struct name *, struct type *);        \
 390 attr struct type *name##_RB_NEXT(struct type *);                        \
 391 attr struct type *name##_RB_PREV(struct type *);                        \
 392 attr struct type *name##_RB_MINMAX(struct name *, int);                 \
 393                                                                         \
 394
 395 /* Main rb operation.
 396  * Moves node close to the key of elm to top
 397  */
 398 #define RB_GENERATE(name, type, field, cmp)                             \
 399         RB_GENERATE_INTERNAL(name, type, field, cmp,)
 400 #define RB_GENERATE_STATIC(name, type, field, cmp)                      \
 401         RB_GENERATE_INTERNAL(name, type, field, cmp, static)
 402 #define RB_GENERATE_INTERNAL(name, type, field, cmp, attr)              \
 403 attr void                                                               \
 404 name##_RB_INSERT_COLOR(struct name *head, struct type *elm)             \
 405 {                                                                       \
 406         struct type *parent, *gparent, *tmp;                            \
 407         while ((parent = RB_PARENT(elm, field)) != NULL &&              \
 408             RB_COLOR(parent, field) == RB_RED) {                        \
 409                 gparent = RB_PARENT(parent, field);                     \
 410                 if (parent == RB_LEFT(gparent, field)) {                \
 411                         tmp = RB_RIGHT(gparent, field);                 \
 412                         if (tmp && RB_COLOR(tmp, field) == RB_RED) {    \
 413                                 RB_COLOR(tmp, field) = RB_BLACK;        \
 414                                 RB_SET_BLACKRED(parent, gparent, field);\
 415                                 elm = gparent;                          \
 416                                 continue;                               \
 417                         }                                               \
 418                         if (RB_RIGHT(parent, field) == elm) {           \
 419                                 RB_ROTATE_LEFT(head, parent, tmp, field);\
 420                                 tmp = parent;                           \
 421                                 parent = elm;                           \
 422                                 elm = tmp;                              \
 423                         }                                               \
 424                         RB_SET_BLACKRED(parent, gparent, field);        \
 425                         RB_ROTATE_RIGHT(head, gparent, tmp, field);     \
 426                 } else {                                                \
 427                         tmp = RB_LEFT(gparent, field);                  \
 428                         if (tmp && RB_COLOR(tmp, field) == RB_RED) {    \
 429                                 RB_COLOR(tmp, field) = RB_BLACK;        \
 430                                 RB_SET_BLACKRED(parent, gparent, field);\
 431                                 elm = gparent;                          \
 432                                 continue;                               \
 433                         }                                               \
 434                         if (RB_LEFT(parent, field) == elm) {            \
 435                                 RB_ROTATE_RIGHT(head, parent, tmp, field);\
 436                                 tmp = parent;                           \
 437                                 parent = elm;                           \
 438                                 elm = tmp;                              \
 439                         }                                               \
 440                         RB_SET_BLACKRED(parent, gparent, field);        \
 441                         RB_ROTATE_LEFT(head, gparent, tmp, field);      \
 442                 }                                                       \
 443         }                                                               \
 444         RB_COLOR(head->rbh_root, field) = RB_BLACK;                     \
 445 }                                                                       \
 446                                                                         \
 447 attr void                                                               \
 448 name##_RB_REMOVE_COLOR(struct name *head, struct type *parent, struct type *elm) \
 449 {                                                                       \
 450         struct type *tmp;                                               \
 451         while ((elm == NULL || RB_COLOR(elm, field) == RB_BLACK) &&     \
 452             elm != RB_ROOT(head)) {                                     \
 453                 if (RB_LEFT(parent, field) == elm) {                    \
 454                         tmp = RB_RIGHT(parent, field);                  \
 455                         if (RB_COLOR(tmp, field) == RB_RED) {           \
 456                                 RB_SET_BLACKRED(tmp, parent, field);    \
 457                                 RB_ROTATE_LEFT(head, parent, tmp, field);\
 458                                 tmp = RB_RIGHT(parent, field);          \
 459                         }                                               \
 460                         if ((RB_LEFT(tmp, field) == NULL ||             \
 461                             RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
 462                             (RB_RIGHT(tmp, field) == NULL ||            \
 463                             RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
 464                                 RB_COLOR(tmp, field) = RB_RED;          \
 465                                 elm = parent;                           \
 466                                 parent = RB_PARENT(elm, field);         \
 467                         } else {                                        \
 468                                 if (RB_RIGHT(tmp, field) == NULL ||     \
 469                                     RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK) {\
 470                                         struct type *oleft;             \
 471                                         if ((oleft = RB_LEFT(tmp, field)) \
 472                                             != NULL)                    \
 473                                                 RB_COLOR(oleft, field) = RB_BLACK;\
 474                                         RB_COLOR(tmp, field) = RB_RED;  \
 475                                         RB_ROTATE_RIGHT(head, tmp, oleft, field);\
 476                                         tmp = RB_RIGHT(parent, field);  \
 477                                 }                                       \
 478                                 RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
 479                                 RB_COLOR(parent, field) = RB_BLACK;     \
 480                                 if (RB_RIGHT(tmp, field))               \
 481                                         RB_COLOR(RB_RIGHT(tmp, field), field) = RB_BLACK;\
 482                                 RB_ROTATE_LEFT(head, parent, tmp, field);\
 483                                 elm = RB_ROOT(head);                    \
 484                                 break;                                  \
 485                         }                                               \
 486                 } else {                                                \
 487                         tmp = RB_LEFT(parent, field);                   \
 488                         if (RB_COLOR(tmp, field) == RB_RED) {           \
 489                                 RB_SET_BLACKRED(tmp, parent, field);    \
 490                                 RB_ROTATE_RIGHT(head, parent, tmp, field);\
 491                                 tmp = RB_LEFT(parent, field);           \
 492                         }                                               \
 493                         if ((RB_LEFT(tmp, field) == NULL ||             \
 494                             RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
 495                             (RB_RIGHT(tmp, field) == NULL ||            \
 496                             RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
 497                                 RB_COLOR(tmp, field) = RB_RED;          \
 498                                 elm = parent;                           \
 499                                 parent = RB_PARENT(elm, field);         \
 500                         } else {                                        \
 501                                 if (RB_LEFT(tmp, field) == NULL ||      \
 502                                     RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) {\
 503                                         struct type *oright;            \
 504                                         if ((oright = RB_RIGHT(tmp, field)) \
 505                                             != NULL)                    \
 506                                                 RB_COLOR(oright, field) = RB_BLACK;\
 507                                         RB_COLOR(tmp, field) = RB_RED;  \
 508                                         RB_ROTATE_LEFT(head, tmp, oright, field);\
 509                                         tmp = RB_LEFT(parent, field);   \
 510                                 }                                       \
 511                                 RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
 512                                 RB_COLOR(parent, field) = RB_BLACK;     \
 513                                 if (RB_LEFT(tmp, field))                \
 514                                         RB_COLOR(RB_LEFT(tmp, field), field) = RB_BLACK;\
 515                                 RB_ROTATE_RIGHT(head, parent, tmp, field);\
 516                                 elm = RB_ROOT(head);                    \
 517                                 break;                                  \
 518                         }                                               \
 519                 }                                                       \
 520         }                                                               \
 521         if (elm)                                                        \
 522                 RB_COLOR(elm, field) = RB_BLACK;                        \
 523 }                                                                       \
 524                                                                         \
 525 attr struct type *                                                      \
 526 name##_RB_REMOVE(struct name *head, struct type *elm)                   \
 527 {                                                                       \
 528         struct type *child, *parent, *old = elm;                        \
 529         int color;                                                      \
 530         if (RB_LEFT(elm, field) == NULL)                                \
 531                 child = RB_RIGHT(elm, field);                           \
 532         else if (RB_RIGHT(elm, field) == NULL)                          \
 533                 child = RB_LEFT(elm, field);                            \
 534         else {                                                          \
 535                 struct type *left;                                      \
 536                 elm = RB_RIGHT(elm, field);                             \
 537                 while ((left = RB_LEFT(elm, field)) != NULL)            \
 538                         elm = left;                                     \
 539                 child = RB_RIGHT(elm, field);                           \
 540                 parent = RB_PARENT(elm, field);                         \
 541                 color = RB_COLOR(elm, field);                           \
 542                 if (child)                                              \
 543                         RB_PARENT(child, field) = parent;               \
 544                 if (parent) {                                           \
 545                         if (RB_LEFT(parent, field) == elm)              \
 546                                 RB_LEFT(parent, field) = child;         \
 547                         else                                            \
 548                                 RB_RIGHT(parent, field) = child;        \
 549                         RB_AUGMENT(parent);                             \
 550                 } else                                                  \
 551                         RB_ROOT(head) = child;                          \
 552                 if (RB_PARENT(elm, field) == old)                       \
 553                         parent = elm;                                   \
 554                 (elm)->field = (old)->field;                            \
 555                 if (RB_PARENT(old, field)) {                            \
 556                         if (RB_LEFT(RB_PARENT(old, field), field) == old)\
 557                                 RB_LEFT(RB_PARENT(old, field), field) = elm;\
 558                         else                                            \
 559                                 RB_RIGHT(RB_PARENT(old, field), field) = elm;\
 560                         RB_AUGMENT(RB_PARENT(old, field));              \
 561                 } else                                                  \
 562                         RB_ROOT(head) = elm;                            \
 563                 RB_PARENT(RB_LEFT(old, field), field) = elm;            \
 564                 if (RB_RIGHT(old, field))                               \
 565                         RB_PARENT(RB_RIGHT(old, field), field) = elm;   \
 566                 if (parent) {                                           \
 567                         left = parent;                                  \
 568                         do {                                            \
 569                                 RB_AUGMENT(left);                       \
 570                         } while ((left = RB_PARENT(left, field)) != NULL); \
 571                 }                                                       \
 572                 goto color;                                             \
 573         }                                                               \
 574         parent = RB_PARENT(elm, field);                                 \
 575         color = RB_COLOR(elm, field);                                   \
 576         if (child)                                                      \
 577                 RB_PARENT(child, field) = parent;                       \
 578         if (parent) {                                                   \
 579                 if (RB_LEFT(parent, field) == elm)                      \
 580                         RB_LEFT(parent, field) = child;                 \
 581                 else                                                    \
 582                         RB_RIGHT(parent, field) = child;                \
 583                 RB_AUGMENT(parent);                                     \
 584         } else                                                          \
 585                 RB_ROOT(head) = child;                                  \
 586 color:                                                                  \
 587         if (color == RB_BLACK)                                          \
 588                 name##_RB_REMOVE_COLOR(head, parent, child);            \
 589         return (old);                                                   \
 590 }                                                                       \
 591                                                                         \
 592 /* Inserts a node into the RB tree */                                   \
 593 attr struct type *                                                      \
 594 name##_RB_INSERT(struct name *head, struct type *elm)                   \
 595 {                                                                       \
 596         struct type *tmp;                                               \
 597         struct type *parent = NULL;                                     \
 598         int comp = 0;                                                   \
 599         tmp = RB_ROOT(head);                                            \
 600         while (tmp) {                                                   \
 601                 parent = tmp;                                           \
 602                 comp = (cmp)(elm, parent);                              \
 603                 if (comp < 0)                                           \
 604                         tmp = RB_LEFT(tmp, field);                      \
 605                 else if (comp > 0)                                      \
 606                         tmp = RB_RIGHT(tmp, field);                     \
 607                 else                                                    \
 608                         return (tmp);                                   \
 609         }                                                               \
 610         RB_SET(elm, parent, field);                                     \
 611         if (parent != NULL) {                                           \
 612                 if (comp < 0)                                           \
 613                         RB_LEFT(parent, field) = elm;                   \
 614                 else                                                    \
 615                         RB_RIGHT(parent, field) = elm;                  \
 616                 RB_AUGMENT(parent);                                     \
 617         } else                                                          \
 618                 RB_ROOT(head) = elm;                                    \
 619         name##_RB_INSERT_COLOR(head, elm);                              \
 620         return (NULL);                                                  \
 621 }                                                                       \
 622                                                                         \
 623 /* Finds the node with the same key as elm */                           \
 624 attr struct type *                                                      \
 625 name##_RB_FIND(struct name *head, struct type *elm)                     \
 626 {                                                                       \
 627         struct type *tmp = RB_ROOT(head);                               \
 628         int comp;                                                       \
 629         while (tmp) {                                                   \
 630                 comp = cmp(elm, tmp);                                   \
 631                 if (comp < 0)                                           \
 632                         tmp = RB_LEFT(tmp, field);                      \
 633                 else if (comp > 0)                                      \
 634                         tmp = RB_RIGHT(tmp, field);                     \
 635                 else                                                    \
 636                         return (tmp);                                   \
 637         }                                                               \
 638         return (NULL);                                                  \
 639 }                                                                       \
 640                                                                         \
 641 /* Finds the first node greater than or equal to the search key */      \
 642 attr struct type *                                                      \
 643 name##_RB_NFIND(struct name *head, struct type *elm)                    \
 644 {                                                                       \
 645         struct type *tmp = RB_ROOT(head);                               \
 646         struct type *res = NULL;                                        \
 647         int comp;                                                       \
 648         while (tmp) {                                                   \
 649                 comp = cmp(elm, tmp);                                   \
 650                 if (comp < 0) {                                         \
 651                         res = tmp;                                      \
 652                         tmp = RB_LEFT(tmp, field);                      \
 653                 }                                                       \
 654                 else if (comp > 0)                                      \
 655                         tmp = RB_RIGHT(tmp, field);                     \
 656                 else                                                    \
 657                         return (tmp);                                   \
 658         }                                                               \
 659         return (res);                                                   \
 660 }                                                                       \
 661                                                                         \
 662 /* ARGSUSED */                                                          \
 663 attr struct type *                                                      \
 664 name##_RB_NEXT(struct type *elm)                                        \
 665 {                                                                       \
 666         if (RB_RIGHT(elm, field)) {                                     \
 667                 elm = RB_RIGHT(elm, field);                             \
 668                 while (RB_LEFT(elm, field))                             \
 669                         elm = RB_LEFT(elm, field);                      \
 670         } else {                                                        \
 671                 if (RB_PARENT(elm, field) &&                            \
 672                     (elm == RB_LEFT(RB_PARENT(elm, field), field)))     \
 673                         elm = RB_PARENT(elm, field);                    \
 674                 else {                                                  \
 675                         while (RB_PARENT(elm, field) &&                 \
 676                             (elm == RB_RIGHT(RB_PARENT(elm, field), field)))\
 677                                 elm = RB_PARENT(elm, field);            \
 678                         elm = RB_PARENT(elm, field);                    \
 679                 }                                                       \
 680         }                                                               \
 681         return (elm);                                                   \
 682 }                                                                       \
 683                                                                         \
 684 /* ARGSUSED */                                                          \
 685 attr struct type *                                                      \
 686 name##_RB_PREV(struct type *elm)                                        \
 687 {                                                                       \
 688         if (RB_LEFT(elm, field)) {                                      \
 689                 elm = RB_LEFT(elm, field);                              \
 690                 while (RB_RIGHT(elm, field))                            \
 691                         elm = RB_RIGHT(elm, field);                     \
 692         } else {                                                        \
 693                 if (RB_PARENT(elm, field) &&                            \
 694                     (elm == RB_RIGHT(RB_PARENT(elm, field), field)))    \
 695                         elm = RB_PARENT(elm, field);                    \
 696                 else {                                                  \
 697                         while (RB_PARENT(elm, field) &&                 \
 698                             (elm == RB_LEFT(RB_PARENT(elm, field), field)))\
 699                                 elm = RB_PARENT(elm, field);            \
 700                         elm = RB_PARENT(elm, field);                    \
 701                 }                                                       \
 702         }                                                               \
 703         return (elm);                                                   \
 704 }                                                                       \
 705                                                                         \
 706 attr struct type *                                                      \
 707 name##_RB_MINMAX(struct name *head, int val)                            \
 708 {                                                                       \
 709         struct type *tmp = RB_ROOT(head);                               \
 710         struct type *parent = NULL;                                     \
 711         while (tmp) {                                                   \
 712                 parent = tmp;                                           \
 713                 if (val < 0)                                            \
 714                         tmp = RB_LEFT(tmp, field);                      \
 715                 else                                                    \
 716                         tmp = RB_RIGHT(tmp, field);                     \
 717         }                                                               \
 718         return (parent);                                                \
 719 }
 720
 721 #define RB_NEGINF       -1
 722 #define RB_INF  1
 723
 724 #define RB_INSERT(name, x, y)   name##_RB_INSERT(x, y)
 725 #define RB_REMOVE(name, x, y)   name##_RB_REMOVE(x, y)
 726 #define RB_FIND(name, x, y)     name##_RB_FIND(x, y)
 727 #define RB_NFIND(name, x, y)    name##_RB_NFIND(x, y)
 728 #define RB_NEXT(name, x, y)     name##_RB_NEXT(y)
 729 #define RB_PREV(name, x, y)     name##_RB_PREV(y)
 730 #define RB_MIN(name, x)         name##_RB_MINMAX(x, RB_NEGINF)
 731 #define RB_MAX(name, x)         name##_RB_MINMAX(x, RB_INF)
 732
 733 #define RB_FOREACH(x, name, head)                                       \
 734         for ((x) = RB_MIN(name, head);                                  \
 735              (x) != NULL;                                               \
 736              (x) = name##_RB_NEXT(x))
 737
 738 #define RB_FOREACH_REVERSE(x, name, head)                               \
 739         for ((x) = RB_MAX(name, head);                                  \
 740              (x) != NULL;                                               \
 741              (x) = name##_RB_PREV(x))
 742
 743 #endif  /* _SYS_TREE_H_ */