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: head/sys/sys/tree.h 347360 2019-05-08 18:47:00Z trasz $ */ 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_PARENT(dst, src, field) do { \ 329 RB_PARENT(dst, field) = src; \ 330 } while (/*CONSTCOND*/ 0) 331 332 #define RB_SET(elm, parent, field) do { \ 333 RB_SET_PARENT(elm, parent, field); \ 334 RB_LEFT(elm, field) = RB_RIGHT(elm, field) = NULL; \ 335 RB_COLOR(elm, field) = RB_RED; \ 336 } while (/*CONSTCOND*/ 0) 337 338 #define RB_SET_BLACKRED(black, red, field) do { \ 339 RB_COLOR(black, field) = RB_BLACK; \ 340 RB_COLOR(red, field) = RB_RED; \ 341 } while (/*CONSTCOND*/ 0) 342 343 /* 344 * Something to be invoked in a loop at the root of every modified subtree, 345 * from the bottom up to the root, to update augmented node data. 346 */ 347 #ifndef RB_AUGMENT 348 #define RB_AUGMENT(x) break 349 #endif 350 351 #define RB_SWAP_CHILD(head, out, in, field) do { \ 352 if (RB_PARENT(out, field) == NULL) \ 353 RB_ROOT(head) = (in); \ 354 else if ((out) == RB_LEFT(RB_PARENT(out, field), field)) \ 355 RB_LEFT(RB_PARENT(out, field), field) = (in); \ 356 else \ 357 RB_RIGHT(RB_PARENT(out, field), field) = (in); \ 358 } while (/*CONSTCOND*/ 0) 359 360 #define RB_ROTATE_LEFT(head, elm, tmp, field) do { \ 361 (tmp) = RB_RIGHT(elm, field); \ 362 if ((RB_RIGHT(elm, field) = RB_LEFT(tmp, field)) != NULL) { \ 363 RB_SET_PARENT(RB_RIGHT(elm, field), elm, field); \ 364 } \ 365 RB_SET_PARENT(tmp, RB_PARENT(elm, field), field); \ 366 RB_SWAP_CHILD(head, elm, tmp, field); \ 367 RB_LEFT(tmp, field) = (elm); \ 368 RB_SET_PARENT(elm, tmp, field); \ 369 RB_AUGMENT(elm); \ 370 } while (/*CONSTCOND*/ 0) 371 372 #define RB_ROTATE_RIGHT(head, elm, tmp, field) do { \ 373 (tmp) = RB_LEFT(elm, field); \ 374 if ((RB_LEFT(elm, field) = RB_RIGHT(tmp, field)) != NULL) { \ 375 RB_SET_PARENT(RB_LEFT(elm, field), elm, field); \ 376 } \ 377 RB_SET_PARENT(tmp, RB_PARENT(elm, field), field); \ 378 RB_SWAP_CHILD(head, elm, tmp, field); \ 379 RB_RIGHT(tmp, field) = (elm); \ 380 RB_SET_PARENT(elm, tmp, field); \ 381 RB_AUGMENT(elm); \ 382 } while (/*CONSTCOND*/ 0) 383 384 /* 385 * The RB_PARENT_ROTATE_LEFT() and RB_PARENT_ROTATE_RIGHT() rotations are 386 * specialized versions of RB_ROTATE_LEFT() and RB_ROTATE_RIGHT() which may be 387 * used if the parent node exists and the direction of the child element is 388 * known. 389 */ 390 391 #define RB_PARENT_ROTATE_LEFT(parent, left, tmp, field) do { \ 392 (tmp) = RB_RIGHT(left, field); \ 393 if ((RB_RIGHT(left, field) = RB_LEFT(tmp, field)) != NULL) { \ 394 RB_SET_PARENT(RB_RIGHT(left, field), left, field); \ 395 } \ 396 RB_SET_PARENT(tmp, parent, field); \ 397 RB_LEFT(parent, field) = (tmp); \ 398 RB_LEFT(tmp, field) = (left); \ 399 RB_SET_PARENT(left, tmp, field); \ 400 RB_AUGMENT(left); \ 401 } while (/*CONSTCOND*/ 0) 402 403 #define RB_PARENT_ROTATE_RIGHT(parent, right, tmp, field) do { \ 404 (tmp) = RB_LEFT(right, field); \ 405 if ((RB_LEFT(right, field) = RB_RIGHT(tmp, field)) != NULL) { \ 406 RB_SET_PARENT(RB_LEFT(right, field), right, field); \ 407 } \ 408 RB_SET_PARENT(tmp, parent, field); \ 409 RB_RIGHT(parent, field) = (tmp); \ 410 RB_RIGHT(tmp, field) = (right); \ 411 RB_SET_PARENT(right, tmp, field); \ 412 RB_AUGMENT(right); \ 413 } while (/*CONSTCOND*/ 0) 414 415 /* 416 * The RB_RED_ROTATE_LEFT() and RB_RED_ROTATE_RIGHT() rotations are specialized 417 * versions of RB_ROTATE_LEFT() and RB_ROTATE_RIGHT() which may be used if we 418 * rotate an element with a red child which has a black sibling. Such a red 419 * node must have at least two child nodes so that the following red-black tree 420 * invariant is fulfilled: 421 * 422 * Every path from a given node to any of its descendant NULL nodes goes 423 * through the same number of black nodes. 424 * 425 * elm (could be the root) 426 * / \ 427 * BLACK RED (left or right child) 428 * / \ 429 * BLACK BLACK 430 */ 431 432 #define RB_RED_ROTATE_LEFT(head, elm, tmp, field) do { \ 433 (tmp) = RB_RIGHT(elm, field); \ 434 RB_RIGHT(elm, field) = RB_LEFT(tmp, field); \ 435 RB_SET_PARENT(RB_RIGHT(elm, field), elm, field); \ 436 RB_SET_PARENT(tmp, RB_PARENT(elm, field), field); \ 437 RB_SWAP_CHILD(head, elm, tmp, field); \ 438 RB_LEFT(tmp, field) = (elm); \ 439 RB_SET_PARENT(elm, tmp, field); \ 440 RB_AUGMENT(elm); \ 441 } while (/*CONSTCOND*/ 0) 442 443 #define RB_RED_ROTATE_RIGHT(head, elm, tmp, field) do { \ 444 (tmp) = RB_LEFT(elm, field); \ 445 RB_LEFT(elm, field) = RB_RIGHT(tmp, field); \ 446 RB_SET_PARENT(RB_LEFT(elm, field), elm, field); \ 447 RB_SET_PARENT(tmp, RB_PARENT(elm, field), field); \ 448 RB_SWAP_CHILD(head, elm, tmp, field); \ 449 RB_RIGHT(tmp, field) = (elm); \ 450 RB_SET_PARENT(elm, tmp, field); \ 451 RB_AUGMENT(elm); \ 452 } while (/*CONSTCOND*/ 0) 453 454 /* Generates prototypes and inline functions */ 455 #define RB_PROTOTYPE(name, type, field, cmp) \ 456 RB_PROTOTYPE_INTERNAL(name, type, field, cmp,) 457 #define RB_PROTOTYPE_STATIC(name, type, field, cmp) \ 458 RB_PROTOTYPE_INTERNAL(name, type, field, cmp, __unused static) 459 #define RB_PROTOTYPE_INTERNAL(name, type, field, cmp, attr) \ 460 RB_PROTOTYPE_INSERT_COLOR(name, type, attr); \ 461 RB_PROTOTYPE_REMOVE_COLOR(name, type, attr); \ 462 RB_PROTOTYPE_INSERT(name, type, attr); \ 463 RB_PROTOTYPE_REMOVE(name, type, attr); \ 464 RB_PROTOTYPE_FIND(name, type, attr); \ 465 RB_PROTOTYPE_NFIND(name, type, attr); \ 466 RB_PROTOTYPE_NEXT(name, type, attr); \ 467 RB_PROTOTYPE_PREV(name, type, attr); \ 468 RB_PROTOTYPE_MINMAX(name, type, attr); \ 469 RB_PROTOTYPE_REINSERT(name, type, attr); 470 #define RB_PROTOTYPE_INSERT_COLOR(name, type, attr) \ 471 attr void name##_RB_INSERT_COLOR(struct name *, struct type *) 472 #define RB_PROTOTYPE_REMOVE_COLOR(name, type, attr) \ 473 attr void name##_RB_REMOVE_COLOR(struct name *, struct type *) 474 #define RB_PROTOTYPE_REMOVE(name, type, attr) \ 475 attr struct type *name##_RB_REMOVE(struct name *, struct type *) 476 #define RB_PROTOTYPE_INSERT(name, type, attr) \ 477 attr struct type *name##_RB_INSERT(struct name *, struct type *) 478 #define RB_PROTOTYPE_FIND(name, type, attr) \ 479 attr struct type *name##_RB_FIND(struct name *, struct type *) 480 #define RB_PROTOTYPE_NFIND(name, type, attr) \ 481 attr struct type *name##_RB_NFIND(struct name *, struct type *) 482 #define RB_PROTOTYPE_NEXT(name, type, attr) \ 483 attr struct type *name##_RB_NEXT(struct type *) 484 #define RB_PROTOTYPE_PREV(name, type, attr) \ 485 attr struct type *name##_RB_PREV(struct type *) 486 #define RB_PROTOTYPE_MINMAX(name, type, attr) \ 487 attr struct type *name##_RB_MINMAX(struct name *, int) 488 #define RB_PROTOTYPE_REINSERT(name, type, attr) \ 489 attr struct type *name##_RB_REINSERT(struct name *, struct type *) 490 491 /* Main rb operation. 492 * Moves node close to the key of elm to top 493 */ 494 #define RB_GENERATE(name, type, field, cmp) \ 495 RB_GENERATE_INTERNAL(name, type, field, cmp,) 496 #define RB_GENERATE_STATIC(name, type, field, cmp) \ 497 RB_GENERATE_INTERNAL(name, type, field, cmp, __unused static) 498 #define RB_GENERATE_INTERNAL(name, type, field, cmp, attr) \ 499 RB_GENERATE_INSERT_COLOR(name, type, field, attr) \ 500 RB_GENERATE_REMOVE_COLOR(name, type, field, attr) \ 501 RB_GENERATE_INSERT(name, type, field, cmp, attr) \ 502 RB_GENERATE_REMOVE(name, type, field, attr) \ 503 RB_GENERATE_FIND(name, type, field, cmp, attr) \ 504 RB_GENERATE_NFIND(name, type, field, cmp, attr) \ 505 RB_GENERATE_NEXT(name, type, field, attr) \ 506 RB_GENERATE_PREV(name, type, field, attr) \ 507 RB_GENERATE_MINMAX(name, type, field, attr) \ 508 RB_GENERATE_REINSERT(name, type, field, cmp, attr) 509 510 511 #define RB_GENERATE_INSERT_COLOR(name, type, field, attr) \ 512 attr void \ 513 name##_RB_INSERT_COLOR(struct name *head, struct type *elm) \ 514 { \ 515 struct type *parent, *gparent, *tmp; \ 516 while (RB_ISRED((parent = RB_PARENT(elm, field)), field)) { \ 517 gparent = RB_PARENT(parent, field); \ 518 if (parent == RB_LEFT(gparent, field)) { \ 519 tmp = RB_RIGHT(gparent, field); \ 520 if (RB_ISRED(tmp, field)) { \ 521 RB_COLOR(tmp, field) = RB_BLACK; \ 522 RB_SET_BLACKRED(parent, gparent, field);\ 523 elm = gparent; \ 524 continue; \ 525 } \ 526 if (RB_RIGHT(parent, field) == elm) { \ 527 RB_PARENT_ROTATE_LEFT(gparent, parent, \ 528 tmp, field); \ 529 tmp = parent; \ 530 parent = elm; \ 531 elm = tmp; \ 532 } \ 533 RB_SET_BLACKRED(parent, gparent, field); \ 534 RB_ROTATE_RIGHT(head, gparent, tmp, field); \ 535 } else { \ 536 tmp = RB_LEFT(gparent, field); \ 537 if (RB_ISRED(tmp, field)) { \ 538 RB_COLOR(tmp, field) = RB_BLACK; \ 539 RB_SET_BLACKRED(parent, gparent, field);\ 540 elm = gparent; \ 541 continue; \ 542 } \ 543 if (RB_LEFT(parent, field) == elm) { \ 544 RB_PARENT_ROTATE_RIGHT(gparent, parent, \ 545 tmp, field); \ 546 tmp = parent; \ 547 parent = elm; \ 548 elm = tmp; \ 549 } \ 550 RB_SET_BLACKRED(parent, gparent, field); \ 551 RB_ROTATE_LEFT(head, gparent, tmp, field); \ 552 } \ 553 } \ 554 RB_COLOR(head->rbh_root, field) = RB_BLACK; \ 555 } 556 557 #define RB_GENERATE_REMOVE_COLOR(name, type, field, attr) \ 558 attr void \ 559 name##_RB_REMOVE_COLOR(struct name *head, struct type *parent) \ 560 { \ 561 struct type *elm, *tmp; \ 562 elm = NULL; \ 563 do { \ 564 if (RB_LEFT(parent, field) == elm) { \ 565 tmp = RB_RIGHT(parent, field); \ 566 if (RB_COLOR(tmp, field) == RB_RED) { \ 567 RB_SET_BLACKRED(tmp, parent, field); \ 568 RB_RED_ROTATE_LEFT(head, parent, tmp, field); \ 569 tmp = RB_RIGHT(parent, field); \ 570 } \ 571 if (RB_ISRED(RB_RIGHT(tmp, field), field)) \ 572 RB_COLOR(RB_RIGHT(tmp, field), field) = RB_BLACK; \ 573 else if (RB_ISRED(RB_LEFT(tmp, field), field)) { \ 574 struct type *oleft; \ 575 RB_PARENT_ROTATE_RIGHT(parent, tmp, \ 576 oleft, field); \ 577 RB_COLOR(oleft, field) = RB_BLACK; \ 578 tmp = oleft; \ 579 } else { \ 580 RB_COLOR(tmp, field) = RB_RED; \ 581 elm = parent; \ 582 parent = RB_PARENT(elm, field); \ 583 continue; \ 584 } \ 585 RB_COLOR(tmp, field) = RB_COLOR(parent, field); \ 586 RB_COLOR(parent, field) = RB_BLACK; \ 587 RB_ROTATE_LEFT(head, parent, tmp, field); \ 588 elm = RB_ROOT(head); \ 589 break; \ 590 } else { \ 591 tmp = RB_LEFT(parent, field); \ 592 if (RB_COLOR(tmp, field) == RB_RED) { \ 593 RB_SET_BLACKRED(tmp, parent, field); \ 594 RB_RED_ROTATE_RIGHT(head, parent, tmp, field); \ 595 tmp = RB_LEFT(parent, field); \ 596 } \ 597 if (RB_ISRED(RB_LEFT(tmp, field), field)) \ 598 RB_COLOR(RB_LEFT(tmp, field), field) = RB_BLACK; \ 599 else if (RB_ISRED(RB_RIGHT(tmp, field), field)) { \ 600 struct type *oright; \ 601 RB_PARENT_ROTATE_LEFT(parent, tmp, \ 602 oright, field); \ 603 RB_COLOR(oright, field) = RB_BLACK; \ 604 tmp = oright; \ 605 } else { \ 606 RB_COLOR(tmp, field) = RB_RED; \ 607 elm = parent; \ 608 parent = RB_PARENT(elm, field); \ 609 continue; \ 610 } \ 611 RB_COLOR(tmp, field) = RB_COLOR(parent, field); \ 612 RB_COLOR(parent, field) = RB_BLACK; \ 613 RB_ROTATE_RIGHT(head, parent, tmp, field); \ 614 elm = RB_ROOT(head); \ 615 break; \ 616 } \ 617 } while (RB_COLOR(elm, field) == RB_BLACK && parent != NULL); \ 618 RB_COLOR(elm, field) = RB_BLACK; \ 619 } 620 621 #define RB_GENERATE_REMOVE(name, type, field, attr) \ 622 attr struct type * \ 623 name##_RB_REMOVE(struct name *head, struct type *elm) \ 624 { \ 625 struct type *child, *old, *parent, *right; \ 626 int color; \ 627 \ 628 old = elm; \ 629 parent = RB_PARENT(elm, field); \ 630 right = RB_RIGHT(elm, field); \ 631 color = RB_COLOR(elm, field); \ 632 if (RB_LEFT(elm, field) == NULL) \ 633 elm = child = right; \ 634 else if (right == NULL) \ 635 elm = child = RB_LEFT(elm, field); \ 636 else { \ 637 if ((child = RB_LEFT(right, field)) == NULL) { \ 638 child = RB_RIGHT(right, field); \ 639 RB_RIGHT(old, field) = child; \ 640 parent = elm = right; \ 641 } else { \ 642 do \ 643 elm = child; \ 644 while ((child = RB_LEFT(elm, field)) != NULL); \ 645 child = RB_RIGHT(elm, field); \ 646 parent = RB_PARENT(elm, field); \ 647 RB_LEFT(parent, field) = child; \ 648 RB_SET_PARENT(RB_RIGHT(old, field), elm, field); \ 649 } \ 650 RB_SET_PARENT(RB_LEFT(old, field), elm, field); \ 651 color = RB_COLOR(elm, field); \ 652 elm->field = old->field; \ 653 } \ 654 RB_SWAP_CHILD(head, old, elm, field); \ 655 if (child != NULL) { \ 656 RB_SET_PARENT(child, parent, field); \ 657 RB_COLOR(child, field) = RB_BLACK; \ 658 } else if (color != RB_RED && parent != NULL) \ 659 name##_RB_REMOVE_COLOR(head, parent); \ 660 while (parent != NULL) { \ 661 RB_AUGMENT(parent); \ 662 parent = RB_PARENT(parent, field); \ 663 } \ 664 return (old); \ 665 } 666 667 #define RB_GENERATE_INSERT(name, type, field, cmp, attr) \ 668 /* Inserts a node into the RB tree */ \ 669 attr struct type * \ 670 name##_RB_INSERT(struct name *head, struct type *elm) \ 671 { \ 672 struct type *tmp; \ 673 struct type *parent = NULL; \ 674 int comp = 0; \ 675 tmp = RB_ROOT(head); \ 676 while (tmp) { \ 677 parent = tmp; \ 678 comp = (cmp)(elm, parent); \ 679 if (comp < 0) \ 680 tmp = RB_LEFT(tmp, field); \ 681 else if (comp > 0) \ 682 tmp = RB_RIGHT(tmp, field); \ 683 else \ 684 return (tmp); \ 685 } \ 686 RB_SET(elm, parent, field); \ 687 if (parent != NULL) { \ 688 if (comp < 0) \ 689 RB_LEFT(parent, field) = elm; \ 690 else \ 691 RB_RIGHT(parent, field) = elm; \ 692 } else \ 693 RB_ROOT(head) = elm; \ 694 name##_RB_INSERT_COLOR(head, elm); \ 695 while (elm != NULL) { \ 696 RB_AUGMENT(elm); \ 697 elm = RB_PARENT(elm, field); \ 698 } \ 699 return (NULL); \ 700 } 701 702 #define RB_GENERATE_FIND(name, type, field, cmp, attr) \ 703 /* Finds the node with the same key as elm */ \ 704 attr struct type * \ 705 name##_RB_FIND(struct name *head, struct type *elm) \ 706 { \ 707 struct type *tmp = RB_ROOT(head); \ 708 int comp; \ 709 while (tmp) { \ 710 comp = cmp(elm, tmp); \ 711 if (comp < 0) \ 712 tmp = RB_LEFT(tmp, field); \ 713 else if (comp > 0) \ 714 tmp = RB_RIGHT(tmp, field); \ 715 else \ 716 return (tmp); \ 717 } \ 718 return (NULL); \ 719 } 720 721 #define RB_GENERATE_NFIND(name, type, field, cmp, attr) \ 722 /* Finds the first node greater than or equal to the search key */ \ 723 attr struct type * \ 724 name##_RB_NFIND(struct name *head, struct type *elm) \ 725 { \ 726 struct type *tmp = RB_ROOT(head); \ 727 struct type *res = NULL; \ 728 int comp; \ 729 while (tmp) { \ 730 comp = cmp(elm, tmp); \ 731 if (comp < 0) { \ 732 res = tmp; \ 733 tmp = RB_LEFT(tmp, field); \ 734 } \ 735 else if (comp > 0) \ 736 tmp = RB_RIGHT(tmp, field); \ 737 else \ 738 return (tmp); \ 739 } \ 740 return (res); \ 741 } 742 743 #define RB_GENERATE_NEXT(name, type, field, attr) \ 744 /* ARGSUSED */ \ 745 attr struct type * \ 746 name##_RB_NEXT(struct type *elm) \ 747 { \ 748 if (RB_RIGHT(elm, field)) { \ 749 elm = RB_RIGHT(elm, field); \ 750 while (RB_LEFT(elm, field)) \ 751 elm = RB_LEFT(elm, field); \ 752 } else { \ 753 if (RB_PARENT(elm, field) && \ 754 (elm == RB_LEFT(RB_PARENT(elm, field), field))) \ 755 elm = RB_PARENT(elm, field); \ 756 else { \ 757 while (RB_PARENT(elm, field) && \ 758 (elm == RB_RIGHT(RB_PARENT(elm, field), field)))\ 759 elm = RB_PARENT(elm, field); \ 760 elm = RB_PARENT(elm, field); \ 761 } \ 762 } \ 763 return (elm); \ 764 } 765 766 #define RB_GENERATE_PREV(name, type, field, attr) \ 767 /* ARGSUSED */ \ 768 attr struct type * \ 769 name##_RB_PREV(struct type *elm) \ 770 { \ 771 if (RB_LEFT(elm, field)) { \ 772 elm = RB_LEFT(elm, field); \ 773 while (RB_RIGHT(elm, field)) \ 774 elm = RB_RIGHT(elm, field); \ 775 } else { \ 776 if (RB_PARENT(elm, field) && \ 777 (elm == RB_RIGHT(RB_PARENT(elm, field), field))) \ 778 elm = RB_PARENT(elm, field); \ 779 else { \ 780 while (RB_PARENT(elm, field) && \ 781 (elm == RB_LEFT(RB_PARENT(elm, field), field)))\ 782 elm = RB_PARENT(elm, field); \ 783 elm = RB_PARENT(elm, field); \ 784 } \ 785 } \ 786 return (elm); \ 787 } 788 789 #define RB_GENERATE_MINMAX(name, type, field, attr) \ 790 attr struct type * \ 791 name##_RB_MINMAX(struct name *head, int val) \ 792 { \ 793 struct type *tmp = RB_ROOT(head); \ 794 struct type *parent = NULL; \ 795 while (tmp) { \ 796 parent = tmp; \ 797 if (val < 0) \ 798 tmp = RB_LEFT(tmp, field); \ 799 else \ 800 tmp = RB_RIGHT(tmp, field); \ 801 } \ 802 return (parent); \ 803 } 804 805 #define RB_GENERATE_REINSERT(name, type, field, cmp, attr) \ 806 attr struct type * \ 807 name##_RB_REINSERT(struct name *head, struct type *elm) \ 808 { \ 809 struct type *cmpelm; \ 810 if (((cmpelm = RB_PREV(name, head, elm)) != NULL && \ 811 cmp(cmpelm, elm) >= 0) || \ 812 ((cmpelm = RB_NEXT(name, head, elm)) != NULL && \ 813 cmp(elm, cmpelm) >= 0)) { \ 814 /* XXXLAS: Remove/insert is heavy handed. */ \ 815 RB_REMOVE(name, head, elm); \ 816 return (RB_INSERT(name, head, elm)); \ 817 } \ 818 return (NULL); \ 819 } \ 820 821 #define RB_NEGINF -1 822 #define RB_INF 1 823 824 #define RB_INSERT(name, x, y) name##_RB_INSERT(x, y) 825 #define RB_REMOVE(name, x, y) name##_RB_REMOVE(x, y) 826 #define RB_FIND(name, x, y) name##_RB_FIND(x, y) 827 #define RB_NFIND(name, x, y) name##_RB_NFIND(x, y) 828 #define RB_NEXT(name, x, y) name##_RB_NEXT(y) 829 #define RB_PREV(name, x, y) name##_RB_PREV(y) 830 #define RB_MIN(name, x) name##_RB_MINMAX(x, RB_NEGINF) 831 #define RB_MAX(name, x) name##_RB_MINMAX(x, RB_INF) 832 #define RB_REINSERT(name, x, y) name##_RB_REINSERT(x, y) 833 834 #define RB_FOREACH(x, name, head) \ 835 for ((x) = RB_MIN(name, head); \ 836 (x) != NULL; \ 837 (x) = name##_RB_NEXT(x)) 838 839 #define RB_FOREACH_FROM(x, name, y) \ 840 for ((x) = (y); \ 841 ((x) != NULL) && ((y) = name##_RB_NEXT(x), (x) != NULL); \ 842 (x) = (y)) 843 844 #define RB_FOREACH_SAFE(x, name, head, y) \ 845 for ((x) = RB_MIN(name, head); \ 846 ((x) != NULL) && ((y) = name##_RB_NEXT(x), (x) != NULL); \ 847 (x) = (y)) 848 849 #define RB_FOREACH_REVERSE(x, name, head) \ 850 for ((x) = RB_MAX(name, head); \ 851 (x) != NULL; \ 852 (x) = name##_RB_PREV(x)) 853 854 #define RB_FOREACH_REVERSE_FROM(x, name, y) \ 855 for ((x) = (y); \ 856 ((x) != NULL) && ((y) = name##_RB_PREV(x), (x) != NULL); \ 857 (x) = (y)) 858 859 #define RB_FOREACH_REVERSE_SAFE(x, name, head, y) \ 860 for ((x) = RB_MAX(name, head); \ 861 ((x) != NULL) && ((y) = name##_RB_PREV(x), (x) != NULL); \ 862 (x) = (y)) 863 864 #endif /* _SYS_TREE_H_ */ 865
