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 $ */
6 * SPDX-License-Identifier: BSD-2-Clause-FreeBSD
8 * Copyright 2002 Niels Provos <provos@citi.umich.edu>
11 * Redistribution and use in source and binary forms, with or without
12 * modification, are permitted provided that the following conditions
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.
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.
35 #include <sys/cdefs.h>
38 * This file defines data structures for different types of trees:
39 * splay trees and red-black trees.
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.
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.
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);
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.
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).
64 #define SPLAY_HEAD(name, type) \
66 struct type *sph_root; /* root of the tree */ \
69 #define SPLAY_INITIALIZER(root) \
72 #define SPLAY_INIT(root) do { \
73 (root)->sph_root = NULL; \
74 } while (/*CONSTCOND*/ 0)
76 #define SPLAY_ENTRY(type) \
78 struct type *spe_left; /* left element */ \
79 struct type *spe_right; /* right element */ \
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)
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)
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)
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)
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)
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)
119 /* Generates prototypes and inline functions */
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 *); \
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) \
131 if (SPLAY_EMPTY(head)) \
133 name##_SPLAY(head, elm); \
134 if ((cmp)(elm, (head)->sph_root) == 0) \
135 return (head->sph_root); \
139 static __unused __inline struct type * \
140 name##_SPLAY_NEXT(struct name *head, struct type *elm) \
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); \
153 static __unused __inline struct type * \
154 name##_SPLAY_MIN_MAX(struct name *head, int val) \
156 name##_SPLAY_MINMAX(head, val); \
157 return (SPLAY_ROOT(head)); \
160 /* Main splay operation.
161 * Moves node close to the key of elm to top
163 #define SPLAY_GENERATE(name, type, field, cmp) \
165 name##_SPLAY_INSERT(struct name *head, struct type *elm) \
167 if (SPLAY_EMPTY(head)) { \
168 SPLAY_LEFT(elm, field) = SPLAY_RIGHT(elm, field) = NULL; \
171 name##_SPLAY(head, elm); \
172 __comp = (cmp)(elm, (head)->sph_root); \
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; \
182 return ((head)->sph_root); \
184 (head)->sph_root = (elm); \
189 name##_SPLAY_REMOVE(struct name *head, struct type *elm) \
191 struct type *__tmp; \
192 if (SPLAY_EMPTY(head)) \
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);\
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; \
210 name##_SPLAY(struct name *head, struct type *elm) \
212 struct type __node, *__left, *__right, *__tmp; \
215 SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
216 __left = __right = &__node; \
218 while ((__comp = (cmp)(elm, (head)->sph_root)) != 0) { \
220 __tmp = SPLAY_LEFT((head)->sph_root, field); \
223 if ((cmp)(elm, __tmp) < 0){ \
224 SPLAY_ROTATE_RIGHT(head, __tmp, field); \
225 if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
228 SPLAY_LINKLEFT(head, __right, field); \
229 } else if (__comp > 0) { \
230 __tmp = SPLAY_RIGHT((head)->sph_root, field); \
233 if ((cmp)(elm, __tmp) > 0){ \
234 SPLAY_ROTATE_LEFT(head, __tmp, field); \
235 if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
238 SPLAY_LINKRIGHT(head, __left, field); \
241 SPLAY_ASSEMBLE(head, &__node, __left, __right, field); \
244 /* Splay with either the minimum or the maximum element \
245 * Used to find minimum or maximum element in tree. \
247 void name##_SPLAY_MINMAX(struct name *head, int __comp) \
249 struct type __node, *__left, *__right, *__tmp; \
251 SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
252 __left = __right = &__node; \
256 __tmp = SPLAY_LEFT((head)->sph_root, field); \
260 SPLAY_ROTATE_RIGHT(head, __tmp, field); \
261 if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
264 SPLAY_LINKLEFT(head, __right, field); \
265 } else if (__comp > 0) { \
266 __tmp = SPLAY_RIGHT((head)->sph_root, field); \
270 SPLAY_ROTATE_LEFT(head, __tmp, field); \
271 if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
274 SPLAY_LINKRIGHT(head, __left, field); \
277 SPLAY_ASSEMBLE(head, &__node, __left, __right, field); \
280 #define SPLAY_NEGINF -1
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))
292 #define SPLAY_FOREACH(x, name, head) \
293 for ((x) = SPLAY_MIN(name, head); \
295 (x) = SPLAY_NEXT(name, head, x))
297 /* Macros that define a red-black tree */
298 #define RB_HEAD(name, type) \
300 struct type *rbh_root; /* root of the tree */ \
303 #define RB_INITIALIZER(root) \
306 #define RB_INIT(root) do { \
307 (root)->rbh_root = NULL; \
308 } while (/*CONSTCOND*/ 0)
312 #define RB_ENTRY(type) \
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 */ \
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)
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)
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)
339 #define RB_AUGMENT(x) do {} while (0)
342 #define RB_ROTATE_LEFT(head, elm, tmp, field) do { \
343 (tmp) = RB_RIGHT(elm, field); \
344 if ((RB_RIGHT(elm, field) = RB_LEFT(tmp, field)) != NULL) { \
345 RB_PARENT(RB_LEFT(tmp, field), field) = (elm); \
348 if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) { \
349 if ((elm) == RB_LEFT(RB_PARENT(elm, field), field)) \
350 RB_LEFT(RB_PARENT(elm, field), field) = (tmp); \
352 RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \
354 (head)->rbh_root = (tmp); \
355 RB_LEFT(tmp, field) = (elm); \
356 RB_PARENT(elm, field) = (tmp); \
358 if ((RB_PARENT(tmp, field))) \
359 RB_AUGMENT(RB_PARENT(tmp, field)); \
360 } while (/*CONSTCOND*/ 0)
362 #define RB_ROTATE_RIGHT(head, elm, tmp, field) do { \
363 (tmp) = RB_LEFT(elm, field); \
364 if ((RB_LEFT(elm, field) = RB_RIGHT(tmp, field)) != NULL) { \
365 RB_PARENT(RB_RIGHT(tmp, field), field) = (elm); \
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); \
372 RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \
374 (head)->rbh_root = (tmp); \
375 RB_RIGHT(tmp, field) = (elm); \
376 RB_PARENT(elm, field) = (tmp); \
378 if ((RB_PARENT(tmp, field))) \
379 RB_AUGMENT(RB_PARENT(tmp, field)); \
380 } while (/*CONSTCOND*/ 0)
382 /* Generates prototypes and inline functions */
383 #define RB_PROTOTYPE(name, type, field, cmp) \
384 RB_PROTOTYPE_INTERNAL(name, type, field, cmp,)
385 #define RB_PROTOTYPE_STATIC(name, type, field, cmp) \
386 RB_PROTOTYPE_INTERNAL(name, type, field, cmp, __unused static)
387 #define RB_PROTOTYPE_INTERNAL(name, type, field, cmp, attr) \
388 RB_PROTOTYPE_INSERT_COLOR(name, type, attr); \
389 RB_PROTOTYPE_REMOVE_COLOR(name, type, attr); \
390 RB_PROTOTYPE_INSERT(name, type, attr); \
391 RB_PROTOTYPE_REMOVE(name, type, attr); \
392 RB_PROTOTYPE_FIND(name, type, attr); \
393 RB_PROTOTYPE_NFIND(name, type, attr); \
394 RB_PROTOTYPE_NEXT(name, type, attr); \
395 RB_PROTOTYPE_PREV(name, type, attr); \
396 RB_PROTOTYPE_MINMAX(name, type, attr); \
397 RB_PROTOTYPE_REINSERT(name, type, attr);
398 #define RB_PROTOTYPE_INSERT_COLOR(name, type, attr) \
399 attr void name##_RB_INSERT_COLOR(struct name *, struct type *)
400 #define RB_PROTOTYPE_REMOVE_COLOR(name, type, attr) \
401 attr void name##_RB_REMOVE_COLOR(struct name *, struct type *, struct type *)
402 #define RB_PROTOTYPE_REMOVE(name, type, attr) \
403 attr struct type *name##_RB_REMOVE(struct name *, struct type *)
404 #define RB_PROTOTYPE_INSERT(name, type, attr) \
405 attr struct type *name##_RB_INSERT(struct name *, struct type *)
406 #define RB_PROTOTYPE_FIND(name, type, attr) \
407 attr struct type *name##_RB_FIND(struct name *, struct type *)
408 #define RB_PROTOTYPE_NFIND(name, type, attr) \
409 attr struct type *name##_RB_NFIND(struct name *, struct type *)
410 #define RB_PROTOTYPE_NEXT(name, type, attr) \
411 attr struct type *name##_RB_NEXT(struct type *)
412 #define RB_PROTOTYPE_PREV(name, type, attr) \
413 attr struct type *name##_RB_PREV(struct type *)
414 #define RB_PROTOTYPE_MINMAX(name, type, attr) \
415 attr struct type *name##_RB_MINMAX(struct name *, int)
416 #define RB_PROTOTYPE_REINSERT(name, type, attr) \
417 attr struct type *name##_RB_REINSERT(struct name *, struct type *)
419 /* Main rb operation.
420 * Moves node close to the key of elm to top
422 #define RB_GENERATE(name, type, field, cmp) \
423 RB_GENERATE_INTERNAL(name, type, field, cmp,)
424 #define RB_GENERATE_STATIC(name, type, field, cmp) \
425 RB_GENERATE_INTERNAL(name, type, field, cmp, __unused static)
426 #define RB_GENERATE_INTERNAL(name, type, field, cmp, attr) \
427 RB_GENERATE_INSERT_COLOR(name, type, field, attr) \
428 RB_GENERATE_REMOVE_COLOR(name, type, field, attr) \
429 RB_GENERATE_INSERT(name, type, field, cmp, attr) \
430 RB_GENERATE_REMOVE(name, type, field, attr) \
431 RB_GENERATE_FIND(name, type, field, cmp, attr) \
432 RB_GENERATE_NFIND(name, type, field, cmp, attr) \
433 RB_GENERATE_NEXT(name, type, field, attr) \
434 RB_GENERATE_PREV(name, type, field, attr) \
435 RB_GENERATE_MINMAX(name, type, field, attr) \
436 RB_GENERATE_REINSERT(name, type, field, cmp, attr)
439 #define RB_GENERATE_INSERT_COLOR(name, type, field, attr) \
441 name##_RB_INSERT_COLOR(struct name *head, struct type *elm) \
443 struct type *parent, *gparent, *tmp; \
444 while ((parent = RB_PARENT(elm, field)) != NULL && \
445 RB_COLOR(parent, field) == RB_RED) { \
446 gparent = RB_PARENT(parent, field); \
447 if (parent == RB_LEFT(gparent, field)) { \
448 tmp = RB_RIGHT(gparent, field); \
449 if (tmp && RB_COLOR(tmp, field) == RB_RED) { \
450 RB_COLOR(tmp, field) = RB_BLACK; \
451 RB_SET_BLACKRED(parent, gparent, field);\
455 if (RB_RIGHT(parent, field) == elm) { \
456 RB_ROTATE_LEFT(head, parent, tmp, field);\
461 RB_SET_BLACKRED(parent, gparent, field); \
462 RB_ROTATE_RIGHT(head, gparent, tmp, field); \
464 tmp = RB_LEFT(gparent, field); \
465 if (tmp && RB_COLOR(tmp, field) == RB_RED) { \
466 RB_COLOR(tmp, field) = RB_BLACK; \
467 RB_SET_BLACKRED(parent, gparent, field);\
471 if (RB_LEFT(parent, field) == elm) { \
472 RB_ROTATE_RIGHT(head, parent, tmp, field);\
477 RB_SET_BLACKRED(parent, gparent, field); \
478 RB_ROTATE_LEFT(head, gparent, tmp, field); \
481 RB_COLOR(head->rbh_root, field) = RB_BLACK; \
484 #define RB_GENERATE_REMOVE_COLOR(name, type, field, attr) \
486 name##_RB_REMOVE_COLOR(struct name *head, struct type *parent, struct type *elm) \
489 while ((elm == NULL || RB_COLOR(elm, field) == RB_BLACK) && \
490 elm != RB_ROOT(head)) { \
491 if (RB_LEFT(parent, field) == elm) { \
492 tmp = RB_RIGHT(parent, field); \
493 if (RB_COLOR(tmp, field) == RB_RED) { \
494 RB_SET_BLACKRED(tmp, parent, field); \
495 RB_ROTATE_LEFT(head, parent, tmp, field);\
496 tmp = RB_RIGHT(parent, field); \
498 if ((RB_LEFT(tmp, field) == NULL || \
499 RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
500 (RB_RIGHT(tmp, field) == NULL || \
501 RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
502 RB_COLOR(tmp, field) = RB_RED; \
504 parent = RB_PARENT(elm, field); \
506 if (RB_RIGHT(tmp, field) == NULL || \
507 RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK) {\
508 struct type *oleft; \
509 if ((oleft = RB_LEFT(tmp, field)) \
511 RB_COLOR(oleft, field) = RB_BLACK;\
512 RB_COLOR(tmp, field) = RB_RED; \
513 RB_ROTATE_RIGHT(head, tmp, oleft, field);\
514 tmp = RB_RIGHT(parent, field); \
516 RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
517 RB_COLOR(parent, field) = RB_BLACK; \
518 if (RB_RIGHT(tmp, field)) \
519 RB_COLOR(RB_RIGHT(tmp, field), field) = RB_BLACK;\
520 RB_ROTATE_LEFT(head, parent, tmp, field);\
521 elm = RB_ROOT(head); \
525 tmp = RB_LEFT(parent, field); \
526 if (RB_COLOR(tmp, field) == RB_RED) { \
527 RB_SET_BLACKRED(tmp, parent, field); \
528 RB_ROTATE_RIGHT(head, parent, tmp, field);\
529 tmp = RB_LEFT(parent, field); \
531 if ((RB_LEFT(tmp, field) == NULL || \
532 RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
533 (RB_RIGHT(tmp, field) == NULL || \
534 RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
535 RB_COLOR(tmp, field) = RB_RED; \
537 parent = RB_PARENT(elm, field); \
539 if (RB_LEFT(tmp, field) == NULL || \
540 RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) {\
541 struct type *oright; \
542 if ((oright = RB_RIGHT(tmp, field)) \
544 RB_COLOR(oright, field) = RB_BLACK;\
545 RB_COLOR(tmp, field) = RB_RED; \
546 RB_ROTATE_LEFT(head, tmp, oright, field);\
547 tmp = RB_LEFT(parent, field); \
549 RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
550 RB_COLOR(parent, field) = RB_BLACK; \
551 if (RB_LEFT(tmp, field)) \
552 RB_COLOR(RB_LEFT(tmp, field), field) = RB_BLACK;\
553 RB_ROTATE_RIGHT(head, parent, tmp, field);\
554 elm = RB_ROOT(head); \
560 RB_COLOR(elm, field) = RB_BLACK; \
563 #define RB_GENERATE_REMOVE(name, type, field, attr) \
565 name##_RB_REMOVE(struct name *head, struct type *elm) \
567 struct type *child, *parent, *old = elm; \
569 if (RB_LEFT(elm, field) == NULL) \
570 child = RB_RIGHT(elm, field); \
571 else if (RB_RIGHT(elm, field) == NULL) \
572 child = RB_LEFT(elm, field); \
575 elm = RB_RIGHT(elm, field); \
576 while ((left = RB_LEFT(elm, field)) != NULL) \
578 child = RB_RIGHT(elm, field); \
579 parent = RB_PARENT(elm, field); \
580 color = RB_COLOR(elm, field); \
582 RB_PARENT(child, field) = parent; \
584 if (RB_LEFT(parent, field) == elm) \
585 RB_LEFT(parent, field) = child; \
587 RB_RIGHT(parent, field) = child; \
588 RB_AUGMENT(parent); \
590 RB_ROOT(head) = child; \
591 if (RB_PARENT(elm, field) == old) \
593 (elm)->field = (old)->field; \
594 if (RB_PARENT(old, field)) { \
595 if (RB_LEFT(RB_PARENT(old, field), field) == old)\
596 RB_LEFT(RB_PARENT(old, field), field) = elm;\
598 RB_RIGHT(RB_PARENT(old, field), field) = elm;\
599 RB_AUGMENT(RB_PARENT(old, field)); \
601 RB_ROOT(head) = elm; \
602 RB_PARENT(RB_LEFT(old, field), field) = elm; \
603 if (RB_RIGHT(old, field)) \
604 RB_PARENT(RB_RIGHT(old, field), field) = elm; \
609 } while ((left = RB_PARENT(left, field)) != NULL); \
613 parent = RB_PARENT(elm, field); \
614 color = RB_COLOR(elm, field); \
616 RB_PARENT(child, field) = parent; \
618 if (RB_LEFT(parent, field) == elm) \
619 RB_LEFT(parent, field) = child; \
621 RB_RIGHT(parent, field) = child; \
622 RB_AUGMENT(parent); \
624 RB_ROOT(head) = child; \
626 if (color == RB_BLACK) \
627 name##_RB_REMOVE_COLOR(head, parent, child); \
631 #define RB_GENERATE_INSERT(name, type, field, cmp, attr) \
632 /* Inserts a node into the RB tree */ \
634 name##_RB_INSERT(struct name *head, struct type *elm) \
637 struct type *parent = NULL; \
639 tmp = RB_ROOT(head); \
642 comp = (cmp)(elm, parent); \
644 tmp = RB_LEFT(tmp, field); \
646 tmp = RB_RIGHT(tmp, field); \
650 RB_SET(elm, parent, field); \
651 if (parent != NULL) { \
653 RB_LEFT(parent, field) = elm; \
655 RB_RIGHT(parent, field) = elm; \
656 RB_AUGMENT(parent); \
658 RB_ROOT(head) = elm; \
659 name##_RB_INSERT_COLOR(head, elm); \
663 #define RB_GENERATE_FIND(name, type, field, cmp, attr) \
664 /* Finds the node with the same key as elm */ \
666 name##_RB_FIND(struct name *head, struct type *elm) \
668 struct type *tmp = RB_ROOT(head); \
671 comp = cmp(elm, tmp); \
673 tmp = RB_LEFT(tmp, field); \
675 tmp = RB_RIGHT(tmp, field); \
682 #define RB_GENERATE_NFIND(name, type, field, cmp, attr) \
683 /* Finds the first node greater than or equal to the search key */ \
685 name##_RB_NFIND(struct name *head, struct type *elm) \
687 struct type *tmp = RB_ROOT(head); \
688 struct type *res = NULL; \
691 comp = cmp(elm, tmp); \
694 tmp = RB_LEFT(tmp, field); \
697 tmp = RB_RIGHT(tmp, field); \
704 #define RB_GENERATE_NEXT(name, type, field, attr) \
707 name##_RB_NEXT(struct type *elm) \
709 if (RB_RIGHT(elm, field)) { \
710 elm = RB_RIGHT(elm, field); \
711 while (RB_LEFT(elm, field)) \
712 elm = RB_LEFT(elm, field); \
714 if (RB_PARENT(elm, field) && \
715 (elm == RB_LEFT(RB_PARENT(elm, field), field))) \
716 elm = RB_PARENT(elm, field); \
718 while (RB_PARENT(elm, field) && \
719 (elm == RB_RIGHT(RB_PARENT(elm, field), field)))\
720 elm = RB_PARENT(elm, field); \
721 elm = RB_PARENT(elm, field); \
727 #define RB_GENERATE_PREV(name, type, field, attr) \
730 name##_RB_PREV(struct type *elm) \
732 if (RB_LEFT(elm, field)) { \
733 elm = RB_LEFT(elm, field); \
734 while (RB_RIGHT(elm, field)) \
735 elm = RB_RIGHT(elm, field); \
737 if (RB_PARENT(elm, field) && \
738 (elm == RB_RIGHT(RB_PARENT(elm, field), field))) \
739 elm = RB_PARENT(elm, field); \
741 while (RB_PARENT(elm, field) && \
742 (elm == RB_LEFT(RB_PARENT(elm, field), field)))\
743 elm = RB_PARENT(elm, field); \
744 elm = RB_PARENT(elm, field); \
750 #define RB_GENERATE_MINMAX(name, type, field, attr) \
752 name##_RB_MINMAX(struct name *head, int val) \
754 struct type *tmp = RB_ROOT(head); \
755 struct type *parent = NULL; \
759 tmp = RB_LEFT(tmp, field); \
761 tmp = RB_RIGHT(tmp, field); \
766 #define RB_GENERATE_REINSERT(name, type, field, cmp, attr) \
768 name##_RB_REINSERT(struct name *head, struct type *elm) \
770 struct type *cmpelm; \
771 if (((cmpelm = RB_PREV(name, head, elm)) != NULL && \
772 cmp(cmpelm, elm) >= 0) || \
773 ((cmpelm = RB_NEXT(name, head, elm)) != NULL && \
774 cmp(elm, cmpelm) >= 0)) { \
775 /* XXXLAS: Remove/insert is heavy handed. */ \
776 RB_REMOVE(name, head, elm); \
777 return (RB_INSERT(name, head, elm)); \
785 #define RB_INSERT(name, x, y) name##_RB_INSERT(x, y)
786 #define RB_REMOVE(name, x, y) name##_RB_REMOVE(x, y)
787 #define RB_FIND(name, x, y) name##_RB_FIND(x, y)
788 #define RB_NFIND(name, x, y) name##_RB_NFIND(x, y)
789 #define RB_NEXT(name, x, y) name##_RB_NEXT(y)
790 #define RB_PREV(name, x, y) name##_RB_PREV(y)
791 #define RB_MIN(name, x) name##_RB_MINMAX(x, RB_NEGINF)
792 #define RB_MAX(name, x) name##_RB_MINMAX(x, RB_INF)
793 #define RB_REINSERT(name, x, y) name##_RB_REINSERT(x, y)
795 #define RB_FOREACH(x, name, head) \
796 for ((x) = RB_MIN(name, head); \
798 (x) = name##_RB_NEXT(x))
800 #define RB_FOREACH_FROM(x, name, y) \
802 ((x) != NULL) && ((y) = name##_RB_NEXT(x), (x) != NULL); \
805 #define RB_FOREACH_SAFE(x, name, head, y) \
806 for ((x) = RB_MIN(name, head); \
807 ((x) != NULL) && ((y) = name##_RB_NEXT(x), (x) != NULL); \
810 #define RB_FOREACH_REVERSE(x, name, head) \
811 for ((x) = RB_MAX(name, head); \
813 (x) = name##_RB_PREV(x))
815 #define RB_FOREACH_REVERSE_FROM(x, name, y) \
817 ((x) != NULL) && ((y) = name##_RB_PREV(x), (x) != NULL); \
820 #define RB_FOREACH_REVERSE_SAFE(x, name, head, y) \
821 for ((x) = RB_MAX(name, head); \
822 ((x) != NULL) && ((y) = name##_RB_PREV(x), (x) != NULL); \
825 #endif /* _SYS_TREE_H_ */