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_ISRED(elm, field) ((elm) != NULL && RB_COLOR(elm, field) == RB_RED) 325 #define RB_ROOT(head) (head)->rbh_root 326 #define RB_EMPTY(head) (RB_ROOT(head) == NULL) 327 328 #define RB_SET(elm, parent, field) do { \ 329 RB_PARENT(elm, field) = parent; \ 330 RB_LEFT(elm, field) = RB_RIGHT(elm, field) = NULL; \ 331 RB_COLOR(elm, field) = RB_RED; \ 332 } while (/*CONSTCOND*/ 0) 333 334 #define RB_SET_BLACKRED(black, red, field) do { \ 335 RB_COLOR(black, field) = RB_BLACK; \ 336 RB_COLOR(red, field) = RB_RED; \ 337 } while (/*CONSTCOND*/ 0) 338 339 /* 340 * Something to be invoked in a loop at the root of every modified subtree, 341 * from the bottom up to the root, to update augmented node data. 342 */ 343 #ifndef RB_AUGMENT 344 #define RB_AUGMENT(x) break 345 #endif 346 347 #define RB_ROTATE_LEFT(head, elm, tmp, field) do { \ 348 (tmp) = RB_RIGHT(elm, field); \ 349 if ((RB_RIGHT(elm, field) = RB_LEFT(tmp, field)) != NULL) { \ 350 RB_PARENT(RB_LEFT(tmp, field), field) = (elm); \ 351 } \ 352 if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) { \ 353 if ((elm) == RB_LEFT(RB_PARENT(elm, field), field)) \ 354 RB_LEFT(RB_PARENT(elm, field), field) = (tmp); \ 355 else \ 356 RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \ 357 } else \ 358 (head)->rbh_root = (tmp); \ 359 RB_LEFT(tmp, field) = (elm); \ 360 RB_PARENT(elm, field) = (tmp); \ 361 RB_AUGMENT(elm); \ 362 } while (/*CONSTCOND*/ 0) 363 364 #define RB_ROTATE_RIGHT(head, elm, tmp, field) do { \ 365 (tmp) = RB_LEFT(elm, field); \ 366 if ((RB_LEFT(elm, field) = RB_RIGHT(tmp, field)) != NULL) { \ 367 RB_PARENT(RB_RIGHT(tmp, field), field) = (elm); \ 368 } \ 369 if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) { \ 370 if ((elm) == RB_LEFT(RB_PARENT(elm, field), field)) \ 371 RB_LEFT(RB_PARENT(elm, field), field) = (tmp); \ 372 else \ 373 RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \ 374 } else \ 375 (head)->rbh_root = (tmp); \ 376 RB_RIGHT(tmp, field) = (elm); \ 377 RB_PARENT(elm, field) = (tmp); \ 378 RB_AUGMENT(elm); \ 379 } while (/*CONSTCOND*/ 0) 380 381 /* Generates prototypes and inline functions */ 382 #define RB_PROTOTYPE(name, type, field, cmp) \ 383 RB_PROTOTYPE_INTERNAL(name, type, field, cmp,) 384 #define RB_PROTOTYPE_STATIC(name, type, field, cmp) \ 385 RB_PROTOTYPE_INTERNAL(name, type, field, cmp, __unused static) 386 #define RB_PROTOTYPE_INTERNAL(name, type, field, cmp, attr) \ 387 RB_PROTOTYPE_INSERT_COLOR(name, type, attr); \ 388 RB_PROTOTYPE_REMOVE_COLOR(name, type, attr); \ 389 RB_PROTOTYPE_INSERT(name, type, attr); \ 390 RB_PROTOTYPE_REMOVE(name, type, attr); \ 391 RB_PROTOTYPE_FIND(name, type, attr); \ 392 RB_PROTOTYPE_NFIND(name, type, attr); \ 393 RB_PROTOTYPE_NEXT(name, type, attr); \ 394 RB_PROTOTYPE_PREV(name, type, attr); \ 395 RB_PROTOTYPE_MINMAX(name, type, attr); \ 396 RB_PROTOTYPE_REINSERT(name, type, attr); 397 #define RB_PROTOTYPE_INSERT_COLOR(name, type, attr) \ 398 attr void name##_RB_INSERT_COLOR(struct name *, struct type *) 399 #define RB_PROTOTYPE_REMOVE_COLOR(name, type, attr) \ 400 attr void name##_RB_REMOVE_COLOR(struct name *, struct type *) 401 #define RB_PROTOTYPE_REMOVE(name, type, attr) \ 402 attr struct type *name##_RB_REMOVE(struct name *, struct type *) 403 #define RB_PROTOTYPE_INSERT(name, type, attr) \ 404 attr struct type *name##_RB_INSERT(struct name *, struct type *) 405 #define RB_PROTOTYPE_FIND(name, type, attr) \ 406 attr struct type *name##_RB_FIND(struct name *, struct type *) 407 #define RB_PROTOTYPE_NFIND(name, type, attr) \ 408 attr struct type *name##_RB_NFIND(struct name *, struct type *) 409 #define RB_PROTOTYPE_NEXT(name, type, attr) \ 410 attr struct type *name##_RB_NEXT(struct type *) 411 #define RB_PROTOTYPE_PREV(name, type, attr) \ 412 attr struct type *name##_RB_PREV(struct type *) 413 #define RB_PROTOTYPE_MINMAX(name, type, attr) \ 414 attr struct type *name##_RB_MINMAX(struct name *, int) 415 #define RB_PROTOTYPE_REINSERT(name, type, attr) \ 416 attr struct type *name##_RB_REINSERT(struct name *, struct type *) 417 418 /* Main rb operation. 419 * Moves node close to the key of elm to top 420 */ 421 #define RB_GENERATE(name, type, field, cmp) \ 422 RB_GENERATE_INTERNAL(name, type, field, cmp,) 423 #define RB_GENERATE_STATIC(name, type, field, cmp) \ 424 RB_GENERATE_INTERNAL(name, type, field, cmp, __unused static) 425 #define RB_GENERATE_INTERNAL(name, type, field, cmp, attr) \ 426 RB_GENERATE_INSERT_COLOR(name, type, field, attr) \ 427 RB_GENERATE_REMOVE_COLOR(name, type, field, attr) \ 428 RB_GENERATE_INSERT(name, type, field, cmp, attr) \ 429 RB_GENERATE_REMOVE(name, type, field, attr) \ 430 RB_GENERATE_FIND(name, type, field, cmp, attr) \ 431 RB_GENERATE_NFIND(name, type, field, cmp, attr) \ 432 RB_GENERATE_NEXT(name, type, field, attr) \ 433 RB_GENERATE_PREV(name, type, field, attr) \ 434 RB_GENERATE_MINMAX(name, type, field, attr) \ 435 RB_GENERATE_REINSERT(name, type, field, cmp, attr) 436 437 438 #define RB_GENERATE_INSERT_COLOR(name, type, field, attr) \ 439 attr void \ 440 name##_RB_INSERT_COLOR(struct name *head, struct type *elm) \ 441 { \ 442 struct type *parent, *gparent, *tmp; \ 443 while (RB_ISRED((parent = RB_PARENT(elm, field)), field)) { \ 444 gparent = RB_PARENT(parent, field); \ 445 if (parent == RB_LEFT(gparent, field)) { \ 446 tmp = RB_RIGHT(gparent, field); \ 447 if (RB_ISRED(tmp, field)) { \ 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 (RB_ISRED(tmp, field)) { \ 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) \ 485 { \ 486 struct type *elm, *tmp; \ 487 elm = NULL; \ 488 do { \ 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_ISRED(RB_LEFT(tmp, field), field)) { \ 497 struct type *oleft; \ 498 oleft = RB_LEFT(tmp, field); \ 499 RB_COLOR(oleft, field) = RB_BLACK; \ 500 RB_COLOR(tmp, field) = RB_RED; \ 501 RB_ROTATE_RIGHT(head, tmp, oleft, field); \ 502 tmp = RB_RIGHT(parent, field); \ 503 } else if (!RB_ISRED(RB_RIGHT(tmp, field), field)) { \ 504 RB_COLOR(tmp, field) = RB_RED; \ 505 elm = parent; \ 506 parent = RB_PARENT(elm, field); \ 507 continue; \ 508 } \ 509 if (RB_ISRED(RB_RIGHT(tmp, field), field)) \ 510 RB_COLOR(RB_RIGHT(tmp, field), field) = RB_BLACK; \ 511 RB_COLOR(tmp, field) = RB_COLOR(parent, field); \ 512 RB_COLOR(parent, field) = RB_BLACK; \ 513 RB_ROTATE_LEFT(head, parent, tmp, field); \ 514 elm = RB_ROOT(head); \ 515 break; \ 516 } else { \ 517 tmp = RB_LEFT(parent, field); \ 518 if (RB_COLOR(tmp, field) == RB_RED) { \ 519 RB_SET_BLACKRED(tmp, parent, field); \ 520 RB_ROTATE_RIGHT(head, parent, tmp, field);\ 521 tmp = RB_LEFT(parent, field); \ 522 } \ 523 if (RB_ISRED(RB_RIGHT(tmp, field), field)) { \ 524 struct type *oright; \ 525 oright = RB_RIGHT(tmp, field); \ 526 RB_COLOR(oright, field) = RB_BLACK; \ 527 RB_COLOR(tmp, field) = RB_RED; \ 528 RB_ROTATE_LEFT(head, tmp, oright, field); \ 529 tmp = RB_LEFT(parent, field); \ 530 } else if (!RB_ISRED(RB_LEFT(tmp, field), field)) { \ 531 RB_COLOR(tmp, field) = RB_RED; \ 532 elm = parent; \ 533 parent = RB_PARENT(elm, field); \ 534 continue; \ 535 } \ 536 if (RB_ISRED(RB_LEFT(tmp, field), field)) \ 537 RB_COLOR(RB_LEFT(tmp, field), field) = RB_BLACK; \ 538 RB_COLOR(tmp, field) = RB_COLOR(parent, field); \ 539 RB_COLOR(parent, field) = RB_BLACK; \ 540 RB_ROTATE_RIGHT(head, parent, tmp, field); \ 541 elm = RB_ROOT(head); \ 542 break; \ 543 } \ 544 } while (!RB_ISRED(elm, field) && parent != NULL); \ 545 RB_COLOR(elm, field) = RB_BLACK; \ 546 } 547 548 #define RB_GENERATE_REMOVE(name, type, field, attr) \ 549 attr struct type * \ 550 name##_RB_REMOVE(struct name *head, struct type *elm) \ 551 { \ 552 struct type *child, *old, *parent, *parent_old, *right; \ 553 int color; \ 554 \ 555 old = elm; \ 556 parent_old = parent = RB_PARENT(elm, field); \ 557 right = RB_RIGHT(elm, field); \ 558 color = RB_COLOR(elm, field); \ 559 if (RB_LEFT(elm, field) == NULL) \ 560 elm = child = right; \ 561 else if (right == NULL) \ 562 elm = child = RB_LEFT(elm, field); \ 563 else { \ 564 if ((child = RB_LEFT(right, field)) == NULL) { \ 565 child = RB_RIGHT(right, field); \ 566 RB_RIGHT(old, field) = child; \ 567 parent = elm = right; \ 568 } else { \ 569 do \ 570 elm = child; \ 571 while ((child = RB_LEFT(elm, field)) != NULL); \ 572 child = RB_RIGHT(elm, field); \ 573 parent = RB_PARENT(elm, field); \ 574 RB_LEFT(parent, field) = child; \ 575 RB_PARENT(RB_RIGHT(old, field), field) = elm; \ 576 } \ 577 RB_PARENT(RB_LEFT(old, field), field) = elm; \ 578 color = RB_COLOR(elm, field); \ 579 elm->field = old->field; \ 580 } \ 581 if (parent_old == NULL) \ 582 RB_ROOT(head) = elm; \ 583 else if (RB_LEFT(parent_old, field) == old) \ 584 RB_LEFT(parent_old, field) = elm; \ 585 else \ 586 RB_RIGHT(parent_old, field) = elm; \ 587 if (child != NULL) { \ 588 RB_PARENT(child, field) = parent; \ 589 RB_COLOR(child, field) = RB_BLACK; \ 590 } else if (color != RB_RED && parent != NULL) \ 591 name##_RB_REMOVE_COLOR(head, parent); \ 592 while (parent != NULL) { \ 593 RB_AUGMENT(parent); \ 594 parent = RB_PARENT(parent, field); \ 595 } \ 596 return (old); \ 597 } 598 599 #define RB_GENERATE_INSERT(name, type, field, cmp, attr) \ 600 /* Inserts a node into the RB tree */ \ 601 attr struct type * \ 602 name##_RB_INSERT(struct name *head, struct type *elm) \ 603 { \ 604 struct type *tmp; \ 605 struct type *parent = NULL; \ 606 int comp = 0; \ 607 tmp = RB_ROOT(head); \ 608 while (tmp) { \ 609 parent = tmp; \ 610 comp = (cmp)(elm, parent); \ 611 if (comp < 0) \ 612 tmp = RB_LEFT(tmp, field); \ 613 else if (comp > 0) \ 614 tmp = RB_RIGHT(tmp, field); \ 615 else \ 616 return (tmp); \ 617 } \ 618 RB_SET(elm, parent, field); \ 619 if (parent != NULL) { \ 620 if (comp < 0) \ 621 RB_LEFT(parent, field) = elm; \ 622 else \ 623 RB_RIGHT(parent, field) = elm; \ 624 } else \ 625 RB_ROOT(head) = elm; \ 626 name##_RB_INSERT_COLOR(head, elm); \ 627 while (elm != NULL) { \ 628 RB_AUGMENT(elm); \ 629 elm = RB_PARENT(elm, field); \ 630 } \ 631 return (NULL); \ 632 } 633 634 #define RB_GENERATE_FIND(name, type, field, cmp, attr) \ 635 /* Finds the node with the same key as elm */ \ 636 attr struct type * \ 637 name##_RB_FIND(struct name *head, struct type *elm) \ 638 { \ 639 struct type *tmp = RB_ROOT(head); \ 640 int comp; \ 641 while (tmp) { \ 642 comp = cmp(elm, tmp); \ 643 if (comp < 0) \ 644 tmp = RB_LEFT(tmp, field); \ 645 else if (comp > 0) \ 646 tmp = RB_RIGHT(tmp, field); \ 647 else \ 648 return (tmp); \ 649 } \ 650 return (NULL); \ 651 } 652 653 #define RB_GENERATE_NFIND(name, type, field, cmp, attr) \ 654 /* Finds the first node greater than or equal to the search key */ \ 655 attr struct type * \ 656 name##_RB_NFIND(struct name *head, struct type *elm) \ 657 { \ 658 struct type *tmp = RB_ROOT(head); \ 659 struct type *res = NULL; \ 660 int comp; \ 661 while (tmp) { \ 662 comp = cmp(elm, tmp); \ 663 if (comp < 0) { \ 664 res = tmp; \ 665 tmp = RB_LEFT(tmp, field); \ 666 } \ 667 else if (comp > 0) \ 668 tmp = RB_RIGHT(tmp, field); \ 669 else \ 670 return (tmp); \ 671 } \ 672 return (res); \ 673 } 674 675 #define RB_GENERATE_NEXT(name, type, field, attr) \ 676 /* ARGSUSED */ \ 677 attr struct type * \ 678 name##_RB_NEXT(struct type *elm) \ 679 { \ 680 if (RB_RIGHT(elm, field)) { \ 681 elm = RB_RIGHT(elm, field); \ 682 while (RB_LEFT(elm, field)) \ 683 elm = RB_LEFT(elm, field); \ 684 } else { \ 685 if (RB_PARENT(elm, field) && \ 686 (elm == RB_LEFT(RB_PARENT(elm, field), field))) \ 687 elm = RB_PARENT(elm, field); \ 688 else { \ 689 while (RB_PARENT(elm, field) && \ 690 (elm == RB_RIGHT(RB_PARENT(elm, field), field)))\ 691 elm = RB_PARENT(elm, field); \ 692 elm = RB_PARENT(elm, field); \ 693 } \ 694 } \ 695 return (elm); \ 696 } 697 698 #define RB_GENERATE_PREV(name, type, field, attr) \ 699 /* ARGSUSED */ \ 700 attr struct type * \ 701 name##_RB_PREV(struct type *elm) \ 702 { \ 703 if (RB_LEFT(elm, field)) { \ 704 elm = RB_LEFT(elm, field); \ 705 while (RB_RIGHT(elm, field)) \ 706 elm = RB_RIGHT(elm, field); \ 707 } else { \ 708 if (RB_PARENT(elm, field) && \ 709 (elm == RB_RIGHT(RB_PARENT(elm, field), field))) \ 710 elm = RB_PARENT(elm, field); \ 711 else { \ 712 while (RB_PARENT(elm, field) && \ 713 (elm == RB_LEFT(RB_PARENT(elm, field), field)))\ 714 elm = RB_PARENT(elm, field); \ 715 elm = RB_PARENT(elm, field); \ 716 } \ 717 } \ 718 return (elm); \ 719 } 720 721 #define RB_GENERATE_MINMAX(name, type, field, attr) \ 722 attr struct type * \ 723 name##_RB_MINMAX(struct name *head, int val) \ 724 { \ 725 struct type *tmp = RB_ROOT(head); \ 726 struct type *parent = NULL; \ 727 while (tmp) { \ 728 parent = tmp; \ 729 if (val < 0) \ 730 tmp = RB_LEFT(tmp, field); \ 731 else \ 732 tmp = RB_RIGHT(tmp, field); \ 733 } \ 734 return (parent); \ 735 } 736 737 #define RB_GENERATE_REINSERT(name, type, field, cmp, attr) \ 738 attr struct type * \ 739 name##_RB_REINSERT(struct name *head, struct type *elm) \ 740 { \ 741 struct type *cmpelm; \ 742 if (((cmpelm = RB_PREV(name, head, elm)) != NULL && \ 743 cmp(cmpelm, elm) >= 0) || \ 744 ((cmpelm = RB_NEXT(name, head, elm)) != NULL && \ 745 cmp(elm, cmpelm) >= 0)) { \ 746 /* XXXLAS: Remove/insert is heavy handed. */ \ 747 RB_REMOVE(name, head, elm); \ 748 return (RB_INSERT(name, head, elm)); \ 749 } \ 750 return (NULL); \ 751 } \ 752 753 #define RB_NEGINF -1 754 #define RB_INF 1 755 756 #define RB_INSERT(name, x, y) name##_RB_INSERT(x, y) 757 #define RB_REMOVE(name, x, y) name##_RB_REMOVE(x, y) 758 #define RB_FIND(name, x, y) name##_RB_FIND(x, y) 759 #define RB_NFIND(name, x, y) name##_RB_NFIND(x, y) 760 #define RB_NEXT(name, x, y) name##_RB_NEXT(y) 761 #define RB_PREV(name, x, y) name##_RB_PREV(y) 762 #define RB_MIN(name, x) name##_RB_MINMAX(x, RB_NEGINF) 763 #define RB_MAX(name, x) name##_RB_MINMAX(x, RB_INF) 764 #define RB_REINSERT(name, x, y) name##_RB_REINSERT(x, y) 765 766 #define RB_FOREACH(x, name, head) \ 767 for ((x) = RB_MIN(name, head); \ 768 (x) != NULL; \ 769 (x) = name##_RB_NEXT(x)) 770 771 #define RB_FOREACH_FROM(x, name, y) \ 772 for ((x) = (y); \ 773 ((x) != NULL) && ((y) = name##_RB_NEXT(x), (x) != NULL); \ 774 (x) = (y)) 775 776 #define RB_FOREACH_SAFE(x, name, head, y) \ 777 for ((x) = RB_MIN(name, head); \ 778 ((x) != NULL) && ((y) = name##_RB_NEXT(x), (x) != NULL); \ 779 (x) = (y)) 780 781 #define RB_FOREACH_REVERSE(x, name, head) \ 782 for ((x) = RB_MAX(name, head); \ 783 (x) != NULL; \ 784 (x) = name##_RB_PREV(x)) 785 786 #define RB_FOREACH_REVERSE_FROM(x, name, y) \ 787 for ((x) = (y); \ 788 ((x) != NULL) && ((y) = name##_RB_PREV(x), (x) != NULL); \ 789 (x) = (y)) 790 791 #define RB_FOREACH_REVERSE_SAFE(x, name, head, y) \ 792 for ((x) = RB_MAX(name, head); \ 793 ((x) != NULL) && ((y) = name##_RB_PREV(x), (x) != NULL); \ 794 (x) = (y)) 795 796 #endif /* _SYS_TREE_H_ */ 797