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tree.h
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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 1.9.2.1.4.1 2010/06/14 02:09:06 kensmith 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//#include <sys/cdefs.h>
34
35/*
36 * This file defines data structures for different types of trees:
37 * splay trees and red-black trees.
38 *
39 * A splay tree is a self-organizing data structure. Every operation
40 * on the tree causes a splay to happen. The splay moves the requested
41 * node to the root of the tree and partly rebalances it.
42 *
43 * This has the benefit that request locality causes faster lookups as
44 * the requested nodes move to the top of the tree. On the other hand,
45 * every lookup causes memory writes.
46 *
47 * The Balance Theorem bounds the total access time for m operations
48 * and n inserts on an initially empty tree as O((m + n)lg n). The
49 * amortized cost for a sequence of m accesses to a splay tree is O(lg n);
50 *
51 * A red-black tree is a binary search tree with the node color as an
52 * extra attribute. It fulfills a set of conditions:
53 * - every search path from the root to a leaf consists of the
54 * same number of black nodes,
55 * - each red node (except for the root) has a black parent,
56 * - each leaf node is black.
57 *
58 * Every operation on a red-black tree is bounded as O(lg n).
59 * The maximum height of a red-black tree is 2lg (n+1).
60 */
61
62#define SPLAY_HEAD(name, type) \
63struct name { \
64 struct type *sph_root; /* root of the tree */ \
65}
66
67#define SPLAY_INITIALIZER(root) \
68 { NULL }
69
70#define SPLAY_INIT(root) do { \
71 (root)->sph_root = NULL; \
72} while (/*CONSTCOND*/ 0)
73
74#define SPLAY_ENTRY(type) \
75struct { \
76 struct type *spe_left; /* left element */ \
77 struct type *spe_right; /* right element */ \
78}
79
80#define SPLAY_LEFT(elm, field) (elm)->field.spe_left
81#define SPLAY_RIGHT(elm, field) (elm)->field.spe_right
82#define SPLAY_ROOT(head) (head)->sph_root
83#define SPLAY_EMPTY(head) (SPLAY_ROOT(head) == NULL)
84
85/* SPLAY_ROTATE_{LEFT,RIGHT} expect that tmp hold SPLAY_{RIGHT,LEFT} */
86#define SPLAY_ROTATE_RIGHT(head, tmp, field) do { \
87 SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(tmp, field); \
88 SPLAY_RIGHT(tmp, field) = (head)->sph_root; \
89 (head)->sph_root = tmp; \
90} while (/*CONSTCOND*/ 0)
91
92#define SPLAY_ROTATE_LEFT(head, tmp, field) do { \
93 SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(tmp, field); \
94 SPLAY_LEFT(tmp, field) = (head)->sph_root; \
95 (head)->sph_root = tmp; \
96} while (/*CONSTCOND*/ 0)
97
98#define SPLAY_LINKLEFT(head, tmp, field) do { \
99 SPLAY_LEFT(tmp, field) = (head)->sph_root; \
100 tmp = (head)->sph_root; \
101 (head)->sph_root = SPLAY_LEFT((head)->sph_root, field); \
102} while (/*CONSTCOND*/ 0)
103
104#define SPLAY_LINKRIGHT(head, tmp, field) do { \
105 SPLAY_RIGHT(tmp, field) = (head)->sph_root; \
106 tmp = (head)->sph_root; \
107 (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field); \
108} while (/*CONSTCOND*/ 0)
109
110#define SPLAY_ASSEMBLE(head, node, left, right, field) do { \
111 SPLAY_RIGHT(left, field) = SPLAY_LEFT((head)->sph_root, field); \
112 SPLAY_LEFT(right, field) = SPLAY_RIGHT((head)->sph_root, field);\
113 SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(node, field); \
114 SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(node, field); \
115} while (/*CONSTCOND*/ 0)
116
117/* Generates prototypes and inline functions */
118
119#define SPLAY_PROTOTYPE(name, type, field, cmp) \
120void name##_SPLAY(struct name *, struct type *); \
121void name##_SPLAY_MINMAX(struct name *, int); \
122struct type *name##_SPLAY_INSERT(struct name *, struct type *); \
123struct type *name##_SPLAY_REMOVE(struct name *, struct type *); \
124 \
125/* Finds the node with the same key as elm */ \
126static __inline struct type * \
127name##_SPLAY_FIND(struct name *head, struct type *elm) \
128{ \
129 if (SPLAY_EMPTY(head)) \
130 return(NULL); \
131 name##_SPLAY(head, elm); \
132 if ((cmp)(elm, (head)->sph_root) == 0) \
133 return (head->sph_root); \
134 return (NULL); \
135} \
136 \
137static __inline struct type * \
138name##_SPLAY_NEXT(struct name *head, struct type *elm) \
139{ \
140 name##_SPLAY(head, elm); \
141 if (SPLAY_RIGHT(elm, field) != NULL) { \
142 elm = SPLAY_RIGHT(elm, field); \
143 while (SPLAY_LEFT(elm, field) != NULL) { \
144 elm = SPLAY_LEFT(elm, field); \
145 } \
146 } else \
147 elm = NULL; \
148 return (elm); \
149} \
150 \
151static __inline struct type * \
152name##_SPLAY_MIN_MAX(struct name *head, int val) \
153{ \
154 name##_SPLAY_MINMAX(head, val); \
155 return (SPLAY_ROOT(head)); \
156}
157
158/* Main splay operation.
159 * Moves node close to the key of elm to top
160 */
161#define SPLAY_GENERATE(name, type, field, cmp) \
162struct type * \
163name##_SPLAY_INSERT(struct name *head, struct type *elm) \
164{ \
165 if (SPLAY_EMPTY(head)) { \
166 SPLAY_LEFT(elm, field) = SPLAY_RIGHT(elm, field) = NULL; \
167 } else { \
168 int __comp; \
169 name##_SPLAY(head, elm); \
170 __comp = (cmp)(elm, (head)->sph_root); \
171 if(__comp < 0) { \
172 SPLAY_LEFT(elm, field) = SPLAY_LEFT((head)->sph_root, field);\
173 SPLAY_RIGHT(elm, field) = (head)->sph_root; \
174 SPLAY_LEFT((head)->sph_root, field) = NULL; \
175 } else if (__comp > 0) { \
176 SPLAY_RIGHT(elm, field) = SPLAY_RIGHT((head)->sph_root, field);\
177 SPLAY_LEFT(elm, field) = (head)->sph_root; \
178 SPLAY_RIGHT((head)->sph_root, field) = NULL; \
179 } else \
180 return ((head)->sph_root); \
181 } \
182 (head)->sph_root = (elm); \
183 return (NULL); \
184} \
185 \
186struct type * \
187name##_SPLAY_REMOVE(struct name *head, struct type *elm) \
188{ \
189 struct type *__tmp; \
190 if (SPLAY_EMPTY(head)) \
191 return (NULL); \
192 name##_SPLAY(head, elm); \
193 if ((cmp)(elm, (head)->sph_root) == 0) { \
194 if (SPLAY_LEFT((head)->sph_root, field) == NULL) { \
195 (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);\
196 } else { \
197 __tmp = SPLAY_RIGHT((head)->sph_root, field); \
198 (head)->sph_root = SPLAY_LEFT((head)->sph_root, field);\
199 name##_SPLAY(head, elm); \
200 SPLAY_RIGHT((head)->sph_root, field) = __tmp; \
201 } \
202 return (elm); \
203 } \
204 return (NULL); \
205} \
206 \
207void \
208name##_SPLAY(struct name *head, struct type *elm) \
209{ \
210 struct type __node, *__left, *__right, *__tmp; \
211 int __comp; \
212\
213 SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
214 __left = __right = &__node; \
215\
216 while ((__comp = (cmp)(elm, (head)->sph_root)) != 0) { \
217 if (__comp < 0) { \
218 __tmp = SPLAY_LEFT((head)->sph_root, field); \
219 if (__tmp == NULL) \
220 break; \
221 if ((cmp)(elm, __tmp) < 0){ \
222 SPLAY_ROTATE_RIGHT(head, __tmp, field); \
223 if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
224 break; \
225 } \
226 SPLAY_LINKLEFT(head, __right, field); \
227 } else if (__comp > 0) { \
228 __tmp = SPLAY_RIGHT((head)->sph_root, field); \
229 if (__tmp == NULL) \
230 break; \
231 if ((cmp)(elm, __tmp) > 0){ \
232 SPLAY_ROTATE_LEFT(head, __tmp, field); \
233 if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
234 break; \
235 } \
236 SPLAY_LINKRIGHT(head, __left, field); \
237 } \
238 } \
239 SPLAY_ASSEMBLE(head, &__node, __left, __right, field); \
240} \
241 \
242/* Splay with either the minimum or the maximum element \
243 * Used to find minimum or maximum element in tree. \
244 */ \
245void name##_SPLAY_MINMAX(struct name *head, int __comp) \
246{ \
247 struct type __node, *__left, *__right, *__tmp; \
248\
249 SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
250 __left = __right = &__node; \
251\
252 while (1) { \
253 if (__comp < 0) { \
254 __tmp = SPLAY_LEFT((head)->sph_root, field); \
255 if (__tmp == NULL) \
256 break; \
257 if (__comp < 0){ \
258 SPLAY_ROTATE_RIGHT(head, __tmp, field); \
259 if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
260 break; \
261 } \
262 SPLAY_LINKLEFT(head, __right, field); \
263 } else if (__comp > 0) { \
264 __tmp = SPLAY_RIGHT((head)->sph_root, field); \
265 if (__tmp == NULL) \
266 break; \
267 if (__comp > 0) { \
268 SPLAY_ROTATE_LEFT(head, __tmp, field); \
269 if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
270 break; \
271 } \
272 SPLAY_LINKRIGHT(head, __left, field); \
273 } \
274 } \
275 SPLAY_ASSEMBLE(head, &__node, __left, __right, field); \
278#define SPLAY_NEGINF -1
279#define SPLAY_INF 1
281#define SPLAY_INSERT(name, x, y) name##_SPLAY_INSERT(x, y)
282#define SPLAY_REMOVE(name, x, y) name##_SPLAY_REMOVE(x, y)
283#define SPLAY_FIND(name, x, y) name##_SPLAY_FIND(x, y)
284#define SPLAY_NEXT(name, x, y) name##_SPLAY_NEXT(x, y)
285#define SPLAY_MIN(name, x) (SPLAY_EMPTY(x) ? NULL \
286 : name##_SPLAY_MIN_MAX(x, SPLAY_NEGINF))
287#define SPLAY_MAX(name, x) (SPLAY_EMPTY(x) ? NULL \
288 : name##_SPLAY_MIN_MAX(x, SPLAY_INF))
289
290#define SPLAY_FOREACH(x, name, head) \
291 for ((x) = SPLAY_MIN(name, head); \
292 (x) != NULL; \
293 (x) = SPLAY_NEXT(name, head, x))
295/* Macros that define a red-black tree */
296#define RB_HEAD(name, type) \
297struct name { \
298 struct type *rbh_root; /* root of the tree */ \
300
301#define RB_INITIALIZER(root) \
302 { NULL }
303
304#define RB_INIT(root) do { \
305 (root)->rbh_root = NULL; \
306} while (/*CONSTCOND*/ 0)
308#define RB_BLACK 0
309#define RB_RED 1
310#define RB_ENTRY(type) \
311struct { \
312 struct type *rbe_left; /* left element */ \
313 struct type *rbe_right; /* right element */ \
314 struct type *rbe_parent; /* parent element */ \
315 int rbe_color; /* node color */ \
318#define RB_LEFT(elm, field) (elm)->field.rbe_left
319#define RB_RIGHT(elm, field) (elm)->field.rbe_right
320#define RB_PARENT(elm, field) (elm)->field.rbe_parent
321#define RB_COLOR(elm, field) (elm)->field.rbe_color
322#define RB_ROOT(head) (head)->rbh_root
323#define RB_EMPTY(head) (RB_ROOT(head) == NULL)
324
325#define RB_SET(elm, parent, field) do { \
326 RB_PARENT(elm, field) = parent; \
327 RB_LEFT(elm, field) = RB_RIGHT(elm, field) = NULL; \
328 RB_COLOR(elm, field) = RB_RED; \
329} while (/*CONSTCOND*/ 0)
330
331#define RB_SET_BLACKRED(black, red, field) do { \
332 RB_COLOR(black, field) = RB_BLACK; \
333 RB_COLOR(red, field) = RB_RED; \
334} while (/*CONSTCOND*/ 0)
336#ifndef RB_AUGMENT
337#define RB_AUGMENT(x) do {} while (0)
338#endif
339
340#define RB_ROTATE_LEFT(head, elm, tmp, field) do { \
341 (tmp) = RB_RIGHT(elm, field); \
342 if ((RB_RIGHT(elm, field) = RB_LEFT(tmp, field)) != NULL) { \
343 RB_PARENT(RB_LEFT(tmp, field), field) = (elm); \
344 } \
345 RB_AUGMENT(elm); \
346 if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) { \
347 if ((elm) == RB_LEFT(RB_PARENT(elm, field), field)) \
348 RB_LEFT(RB_PARENT(elm, field), field) = (tmp); \
349 else \
350 RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \
351 } else \
352 (head)->rbh_root = (tmp); \
353 RB_LEFT(tmp, field) = (elm); \
354 RB_PARENT(elm, field) = (tmp); \
355 RB_AUGMENT(tmp); \
356 if ((RB_PARENT(tmp, field))) \
357 RB_AUGMENT(RB_PARENT(tmp, field)); \
358} while (/*CONSTCOND*/ 0)
359
360#define RB_ROTATE_RIGHT(head, elm, tmp, field) do { \
361 (tmp) = RB_LEFT(elm, field); \
362 if ((RB_LEFT(elm, field) = RB_RIGHT(tmp, field)) != NULL) { \
363 RB_PARENT(RB_RIGHT(tmp, field), field) = (elm); \
364 } \
365 RB_AUGMENT(elm); \
366 if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) { \
367 if ((elm) == RB_LEFT(RB_PARENT(elm, field), field)) \
368 RB_LEFT(RB_PARENT(elm, field), field) = (tmp); \
369 else \
370 RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \
371 } else \
372 (head)->rbh_root = (tmp); \
373 RB_RIGHT(tmp, field) = (elm); \
374 RB_PARENT(elm, field) = (tmp); \
375 RB_AUGMENT(tmp); \
376 if ((RB_PARENT(tmp, field))) \
377 RB_AUGMENT(RB_PARENT(tmp, field)); \
378} while (/*CONSTCOND*/ 0)
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) \
386attr void name##_RB_INSERT_COLOR(struct name *, struct type *); \
387attr void name##_RB_REMOVE_COLOR(struct name *, struct type *, struct type *);\
388attr struct type *name##_RB_REMOVE(struct name *, struct type *); \
389attr struct type *name##_RB_INSERT(struct name *, struct type *); \
390attr struct type *name##_RB_FIND(struct name *, struct type *); \
391attr struct type *name##_RB_NFIND(struct name *, struct type *); \
392attr struct type *name##_RB_NEXT(struct type *); \
393attr struct type *name##_RB_PREV(struct type *); \
394attr struct type *name##_RB_MINMAX(struct name *, int); \
395 \
396
397/* Main rb operation.
398 * Moves node close to the key of elm to top
399 */
400#define RB_GENERATE(name, type, field, cmp) \
401 RB_GENERATE_INTERNAL(name, type, field, cmp,)
402#define RB_GENERATE_STATIC(name, type, field, cmp) \
403 RB_GENERATE_INTERNAL(name, type, field, cmp, __unused static)
404#define RB_GENERATE_INTERNAL(name, type, field, cmp, attr) \
405attr void \
406name##_RB_INSERT_COLOR(struct name *head, struct type *elm) \
407{ \
408 struct type *parent, *gparent, *tmp; \
409 while ((parent = RB_PARENT(elm, field)) != NULL && \
410 RB_COLOR(parent, field) == RB_RED) { \
411 gparent = RB_PARENT(parent, field); \
412 if (parent == RB_LEFT(gparent, field)) { \
413 tmp = RB_RIGHT(gparent, field); \
414 if (tmp && RB_COLOR(tmp, field) == RB_RED) { \
415 RB_COLOR(tmp, field) = RB_BLACK; \
416 RB_SET_BLACKRED(parent, gparent, field);\
417 elm = gparent; \
418 continue; \
419 } \
420 if (RB_RIGHT(parent, field) == elm) { \
421 RB_ROTATE_LEFT(head, parent, tmp, field);\
422 tmp = parent; \
423 parent = elm; \
424 elm = tmp; \
425 } \
426 RB_SET_BLACKRED(parent, gparent, field); \
427 RB_ROTATE_RIGHT(head, gparent, tmp, field); \
428 } else { \
429 tmp = RB_LEFT(gparent, field); \
430 if (tmp && RB_COLOR(tmp, field) == RB_RED) { \
431 RB_COLOR(tmp, field) = RB_BLACK; \
432 RB_SET_BLACKRED(parent, gparent, field);\
433 elm = gparent; \
434 continue; \
435 } \
436 if (RB_LEFT(parent, field) == elm) { \
437 RB_ROTATE_RIGHT(head, parent, tmp, field);\
438 tmp = parent; \
439 parent = elm; \
440 elm = tmp; \
441 } \
442 RB_SET_BLACKRED(parent, gparent, field); \
443 RB_ROTATE_LEFT(head, gparent, tmp, field); \
444 } \
445 } \
446 RB_COLOR(head->rbh_root, field) = RB_BLACK; \
447} \
448 \
449attr void \
450name##_RB_REMOVE_COLOR(struct name *head, struct type *parent, struct type *elm) \
451{ \
452 struct type *tmp; \
453 while ((elm == NULL || RB_COLOR(elm, field) == RB_BLACK) && \
454 elm != RB_ROOT(head)) { \
455 if (RB_LEFT(parent, field) == elm) { \
456 tmp = RB_RIGHT(parent, field); \
457 if (RB_COLOR(tmp, field) == RB_RED) { \
458 RB_SET_BLACKRED(tmp, parent, field); \
459 RB_ROTATE_LEFT(head, parent, tmp, field);\
460 tmp = RB_RIGHT(parent, field); \
461 } \
462 if ((RB_LEFT(tmp, field) == NULL || \
463 RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
464 (RB_RIGHT(tmp, field) == NULL || \
465 RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
466 RB_COLOR(tmp, field) = RB_RED; \
467 elm = parent; \
468 parent = RB_PARENT(elm, field); \
469 } else { \
470 if (RB_RIGHT(tmp, field) == NULL || \
471 RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK) {\
472 struct type *oleft; \
473 if ((oleft = RB_LEFT(tmp, field)) \
474 != NULL) \
475 RB_COLOR(oleft, field) = RB_BLACK;\
476 RB_COLOR(tmp, field) = RB_RED; \
477 RB_ROTATE_RIGHT(head, tmp, oleft, field);\
478 tmp = RB_RIGHT(parent, field); \
479 } \
480 RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
481 RB_COLOR(parent, field) = RB_BLACK; \
482 if (RB_RIGHT(tmp, field)) \
483 RB_COLOR(RB_RIGHT(tmp, field), field) = RB_BLACK;\
484 RB_ROTATE_LEFT(head, parent, tmp, field);\
485 elm = RB_ROOT(head); \
486 break; \
487 } \
488 } else { \
489 tmp = RB_LEFT(parent, field); \
490 if (RB_COLOR(tmp, field) == RB_RED) { \
491 RB_SET_BLACKRED(tmp, parent, field); \
492 RB_ROTATE_RIGHT(head, parent, tmp, field);\
493 tmp = RB_LEFT(parent, field); \
494 } \
495 if ((RB_LEFT(tmp, field) == NULL || \
496 RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
497 (RB_RIGHT(tmp, field) == NULL || \
498 RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
499 RB_COLOR(tmp, field) = RB_RED; \
500 elm = parent; \
501 parent = RB_PARENT(elm, field); \
502 } else { \
503 if (RB_LEFT(tmp, field) == NULL || \
504 RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) {\
505 struct type *oright; \
506 if ((oright = RB_RIGHT(tmp, field)) \
507 != NULL) \
508 RB_COLOR(oright, field) = RB_BLACK;\
509 RB_COLOR(tmp, field) = RB_RED; \
510 RB_ROTATE_LEFT(head, tmp, oright, field);\
511 tmp = RB_LEFT(parent, field); \
512 } \
513 RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
514 RB_COLOR(parent, field) = RB_BLACK; \
515 if (RB_LEFT(tmp, field)) \
516 RB_COLOR(RB_LEFT(tmp, field), field) = RB_BLACK;\
517 RB_ROTATE_RIGHT(head, parent, tmp, field);\
518 elm = RB_ROOT(head); \
519 break; \
520 } \
521 } \
522 } \
523 if (elm) \
524 RB_COLOR(elm, field) = RB_BLACK; \
525} \
526 \
527attr struct type * \
528name##_RB_REMOVE(struct name *head, struct type *elm) \
529{ \
530 struct type *child, *parent, *old = elm; \
531 int color; \
532 if (RB_LEFT(elm, field) == NULL) \
533 child = RB_RIGHT(elm, field); \
534 else if (RB_RIGHT(elm, field) == NULL) \
535 child = RB_LEFT(elm, field); \
536 else { \
537 struct type *left; \
538 elm = RB_RIGHT(elm, field); \
539 while ((left = RB_LEFT(elm, field)) != NULL) \
540 elm = left; \
541 child = RB_RIGHT(elm, field); \
542 parent = RB_PARENT(elm, field); \
543 color = RB_COLOR(elm, field); \
544 if (child) \
545 RB_PARENT(child, field) = parent; \
546 if (parent) { \
547 if (RB_LEFT(parent, field) == elm) \
548 RB_LEFT(parent, field) = child; \
549 else \
550 RB_RIGHT(parent, field) = child; \
551 RB_AUGMENT(parent); \
552 } else \
553 RB_ROOT(head) = child; \
554 if (RB_PARENT(elm, field) == old) \
555 parent = elm; \
556 (elm)->field = (old)->field; \
557 if (RB_PARENT(old, field)) { \
558 if (RB_LEFT(RB_PARENT(old, field), field) == old)\
559 RB_LEFT(RB_PARENT(old, field), field) = elm;\
560 else \
561 RB_RIGHT(RB_PARENT(old, field), field) = elm;\
562 RB_AUGMENT(RB_PARENT(old, field)); \
563 } else \
564 RB_ROOT(head) = elm; \
565 RB_PARENT(RB_LEFT(old, field), field) = elm; \
566 if (RB_RIGHT(old, field)) \
567 RB_PARENT(RB_RIGHT(old, field), field) = elm; \
568 if (parent) { \
569 left = parent; \
570 do { \
571 RB_AUGMENT(left); \
572 } while ((left = RB_PARENT(left, field)) != NULL); \
573 } \
574 goto color; \
575 } \
576 parent = RB_PARENT(elm, field); \
577 color = RB_COLOR(elm, field); \
578 if (child) \
579 RB_PARENT(child, field) = parent; \
580 if (parent) { \
581 if (RB_LEFT(parent, field) == elm) \
582 RB_LEFT(parent, field) = child; \
583 else \
584 RB_RIGHT(parent, field) = child; \
585 RB_AUGMENT(parent); \
586 } else \
587 RB_ROOT(head) = child; \
588color: \
589 if (color == RB_BLACK) \
590 name##_RB_REMOVE_COLOR(head, parent, child); \
591 return (old); \
592} \
593 \
594/* Inserts a node into the RB tree */ \
595attr struct type * \
596name##_RB_INSERT(struct name *head, struct type *elm) \
597{ \
598 struct type *tmp; \
599 struct type *parent = NULL; \
600 int comp = 0; \
601 tmp = RB_ROOT(head); \
602 while (tmp) { \
603 parent = tmp; \
604 comp = (cmp)(elm, parent); \
605 if (comp < 0) \
606 tmp = RB_LEFT(tmp, field); \
607 else if (comp > 0) \
608 tmp = RB_RIGHT(tmp, field); \
609 else \
610 return (tmp); \
611 } \
612 RB_SET(elm, parent, field); \
613 if (parent != NULL) { \
614 if (comp < 0) \
615 RB_LEFT(parent, field) = elm; \
616 else \
617 RB_RIGHT(parent, field) = elm; \
618 RB_AUGMENT(parent); \
619 } else \
620 RB_ROOT(head) = elm; \
621 name##_RB_INSERT_COLOR(head, elm); \
622 return (NULL); \
623} \
624 \
625/* Finds the node with the same key as elm */ \
626attr struct type * \
627name##_RB_FIND(struct name *head, struct type *elm) \
628{ \
629 struct type *tmp = RB_ROOT(head); \
630 int comp; \
631 while (tmp) { \
632 comp = cmp(elm, tmp); \
633 if (comp < 0) \
634 tmp = RB_LEFT(tmp, field); \
635 else if (comp > 0) \
636 tmp = RB_RIGHT(tmp, field); \
637 else \
638 return (tmp); \
639 } \
640 return (NULL); \
641} \
642 \
643/* Finds the first node greater than or equal to the search key */ \
644attr struct type * \
645name##_RB_NFIND(struct name *head, struct type *elm) \
646{ \
647 struct type *tmp = RB_ROOT(head); \
648 struct type *res = NULL; \
649 int comp; \
650 while (tmp) { \
651 comp = cmp(elm, tmp); \
652 if (comp < 0) { \
653 res = tmp; \
654 tmp = RB_LEFT(tmp, field); \
655 } \
656 else if (comp > 0) \
657 tmp = RB_RIGHT(tmp, field); \
658 else \
659 return (tmp); \
660 } \
661 return (res); \
662} \
663 \
664/* ARGSUSED */ \
665attr struct type * \
666name##_RB_NEXT(struct type *elm) \
667{ \
668 if (RB_RIGHT(elm, field)) { \
669 elm = RB_RIGHT(elm, field); \
670 while (RB_LEFT(elm, field)) \
671 elm = RB_LEFT(elm, field); \
672 } else { \
673 if (RB_PARENT(elm, field) && \
674 (elm == RB_LEFT(RB_PARENT(elm, field), field))) \
675 elm = RB_PARENT(elm, field); \
676 else { \
677 while (RB_PARENT(elm, field) && \
678 (elm == RB_RIGHT(RB_PARENT(elm, field), field)))\
679 elm = RB_PARENT(elm, field); \
680 elm = RB_PARENT(elm, field); \
681 } \
682 } \
683 return (elm); \
684} \
685 \
686/* ARGSUSED */ \
687attr struct type * \
688name##_RB_PREV(struct type *elm) \
689{ \
690 if (RB_LEFT(elm, field)) { \
691 elm = RB_LEFT(elm, field); \
692 while (RB_RIGHT(elm, field)) \
693 elm = RB_RIGHT(elm, field); \
694 } else { \
695 if (RB_PARENT(elm, field) && \
696 (elm == RB_RIGHT(RB_PARENT(elm, field), field))) \
697 elm = RB_PARENT(elm, field); \
698 else { \
699 while (RB_PARENT(elm, field) && \
700 (elm == RB_LEFT(RB_PARENT(elm, field), field)))\
701 elm = RB_PARENT(elm, field); \
702 elm = RB_PARENT(elm, field); \
703 } \
704 } \
705 return (elm); \
706} \
707 \
708attr struct type * \
709name##_RB_MINMAX(struct name *head, int val) \
710{ \
711 struct type *tmp = RB_ROOT(head); \
712 struct type *parent = NULL; \
713 while (tmp) { \
714 parent = tmp; \
715 if (val < 0) \
716 tmp = RB_LEFT(tmp, field); \
717 else \
718 tmp = RB_RIGHT(tmp, field); \
719 } \
720 return (parent); \
723#define RB_NEGINF -1
724#define RB_INF 1
726#define RB_INSERT(name, x, y) name##_RB_INSERT(x, y)
727#define RB_REMOVE(name, x, y) name##_RB_REMOVE(x, y)
728#define RB_FIND(name, x, y) name##_RB_FIND(x, y)
729#define RB_NFIND(name, x, y) name##_RB_NFIND(x, y)
730#define RB_NEXT(name, x, y) name##_RB_NEXT(y)
731#define RB_PREV(name, x, y) name##_RB_PREV(y)
732#define RB_MIN(name, x) name##_RB_MINMAX(x, RB_NEGINF)
733#define RB_MAX(name, x) name##_RB_MINMAX(x, RB_INF)
734
735#define RB_FOREACH(x, name, head) \
736 for ((x) = RB_MIN(name, head); \
737 (x) != NULL; \
738 (x) = name##_RB_NEXT(x))
739
740#define RB_FOREACH_FROM(x, name, y) \
741 for ((x) = (y); \
742 ((x) != NULL) && ((y) = name##_RB_NEXT(x), (x) != NULL); \
743 (x) = (y))
744
745#define RB_FOREACH_SAFE(x, name, head, y) \
746 for ((x) = RB_MIN(name, head); \
747 ((x) != NULL) && ((y) = name##_RB_NEXT(x), (x) != NULL); \
748 (x) = (y))
749
750#define RB_FOREACH_REVERSE(x, name, head) \
751 for ((x) = RB_MAX(name, head); \
752 (x) != NULL; \
753 (x) = name##_RB_PREV(x))
754
755#define RB_FOREACH_REVERSE_FROM(x, name, y) \
756 for ((x) = (y); \
757 ((x) != NULL) && ((y) = name##_RB_PREV(x), (x) != NULL); \
758 (x) = (y))
759
760#define RB_FOREACH_REVERSE_SAFE(x, name, head, y) \
761 for ((x) = RB_MAX(name, head); \
762 ((x) != NULL) && ((y) = name##_RB_PREV(x), (x) != NULL); \
763 (x) = (y))
764
765#endif /* _SYS_TREE_H_ */