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