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 #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 *, 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)
416 /* Main rb operation.
417 * Moves node close to the key of elm to top
419 #define RB_GENERATE(name, type, field, cmp) \
420 RB_GENERATE_INTERNAL(name, type, field, cmp,)
421 #define RB_GENERATE_STATIC(name, type, field, cmp) \
422 RB_GENERATE_INTERNAL(name, type, field, cmp, __unused static)
423 #define RB_GENERATE_INTERNAL(name, type, field, cmp, attr) \
424 RB_GENERATE_INSERT_COLOR(name, type, field, attr) \
425 RB_GENERATE_REMOVE_COLOR(name, type, field, attr) \
426 RB_GENERATE_INSERT(name, type, field, cmp, attr) \
427 RB_GENERATE_REMOVE(name, type, field, attr) \
428 RB_GENERATE_FIND(name, type, field, cmp, attr) \
429 RB_GENERATE_NFIND(name, type, field, cmp, attr) \
430 RB_GENERATE_NEXT(name, type, field, attr) \
431 RB_GENERATE_PREV(name, type, field, attr) \
432 RB_GENERATE_MINMAX(name, type, field, attr)
434 #define RB_GENERATE_INSERT_COLOR(name, type, field, attr) \
436 name##_RB_INSERT_COLOR(struct name *head, struct type *elm) \
438 struct type *parent, *gparent, *tmp; \
439 while ((parent = RB_PARENT(elm, field)) != NULL && \
440 RB_COLOR(parent, field) == RB_RED) { \
441 gparent = RB_PARENT(parent, field); \
442 if (parent == RB_LEFT(gparent, field)) { \
443 tmp = RB_RIGHT(gparent, field); \
444 if (tmp && RB_COLOR(tmp, field) == RB_RED) { \
445 RB_COLOR(tmp, field) = RB_BLACK; \
446 RB_SET_BLACKRED(parent, gparent, field);\
450 if (RB_RIGHT(parent, field) == elm) { \
451 RB_ROTATE_LEFT(head, parent, tmp, field);\
456 RB_SET_BLACKRED(parent, gparent, field); \
457 RB_ROTATE_RIGHT(head, gparent, tmp, field); \
459 tmp = RB_LEFT(gparent, field); \
460 if (tmp && RB_COLOR(tmp, field) == RB_RED) { \
461 RB_COLOR(tmp, field) = RB_BLACK; \
462 RB_SET_BLACKRED(parent, gparent, field);\
466 if (RB_LEFT(parent, field) == elm) { \
467 RB_ROTATE_RIGHT(head, parent, tmp, field);\
472 RB_SET_BLACKRED(parent, gparent, field); \
473 RB_ROTATE_LEFT(head, gparent, tmp, field); \
476 RB_COLOR(head->rbh_root, field) = RB_BLACK; \
479 #define RB_GENERATE_REMOVE_COLOR(name, type, field, attr) \
481 name##_RB_REMOVE_COLOR(struct name *head, struct type *parent, struct type *elm) \
484 while ((elm == NULL || RB_COLOR(elm, field) == RB_BLACK) && \
485 elm != RB_ROOT(head)) { \
486 if (RB_LEFT(parent, field) == elm) { \
487 tmp = RB_RIGHT(parent, field); \
488 if (RB_COLOR(tmp, field) == RB_RED) { \
489 RB_SET_BLACKRED(tmp, parent, field); \
490 RB_ROTATE_LEFT(head, parent, tmp, field);\
491 tmp = RB_RIGHT(parent, field); \
493 if ((RB_LEFT(tmp, field) == NULL || \
494 RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
495 (RB_RIGHT(tmp, field) == NULL || \
496 RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
497 RB_COLOR(tmp, field) = RB_RED; \
499 parent = RB_PARENT(elm, field); \
501 if (RB_RIGHT(tmp, field) == NULL || \
502 RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK) {\
503 struct type *oleft; \
504 if ((oleft = RB_LEFT(tmp, field)) \
506 RB_COLOR(oleft, field) = RB_BLACK;\
507 RB_COLOR(tmp, field) = RB_RED; \
508 RB_ROTATE_RIGHT(head, tmp, oleft, field);\
509 tmp = RB_RIGHT(parent, field); \
511 RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
512 RB_COLOR(parent, field) = RB_BLACK; \
513 if (RB_RIGHT(tmp, field)) \
514 RB_COLOR(RB_RIGHT(tmp, field), field) = RB_BLACK;\
515 RB_ROTATE_LEFT(head, parent, tmp, field);\
516 elm = RB_ROOT(head); \
520 tmp = RB_LEFT(parent, field); \
521 if (RB_COLOR(tmp, field) == RB_RED) { \
522 RB_SET_BLACKRED(tmp, parent, field); \
523 RB_ROTATE_RIGHT(head, parent, tmp, field);\
524 tmp = RB_LEFT(parent, field); \
526 if ((RB_LEFT(tmp, field) == NULL || \
527 RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
528 (RB_RIGHT(tmp, field) == NULL || \
529 RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
530 RB_COLOR(tmp, field) = RB_RED; \
532 parent = RB_PARENT(elm, field); \
534 if (RB_LEFT(tmp, field) == NULL || \
535 RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) {\
536 struct type *oright; \
537 if ((oright = RB_RIGHT(tmp, field)) \
539 RB_COLOR(oright, field) = RB_BLACK;\
540 RB_COLOR(tmp, field) = RB_RED; \
541 RB_ROTATE_LEFT(head, tmp, oright, field);\
542 tmp = RB_LEFT(parent, field); \
544 RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
545 RB_COLOR(parent, field) = RB_BLACK; \
546 if (RB_LEFT(tmp, field)) \
547 RB_COLOR(RB_LEFT(tmp, field), field) = RB_BLACK;\
548 RB_ROTATE_RIGHT(head, parent, tmp, field);\
549 elm = RB_ROOT(head); \
555 RB_COLOR(elm, field) = RB_BLACK; \
558 #define RB_GENERATE_REMOVE(name, type, field, attr) \
560 name##_RB_REMOVE(struct name *head, struct type *elm) \
562 struct type *child, *parent, *old = elm; \
564 if (RB_LEFT(elm, field) == NULL) \
565 child = RB_RIGHT(elm, field); \
566 else if (RB_RIGHT(elm, field) == NULL) \
567 child = RB_LEFT(elm, field); \
570 elm = RB_RIGHT(elm, field); \
571 while ((left = RB_LEFT(elm, field)) != NULL) \
573 child = RB_RIGHT(elm, field); \
574 parent = RB_PARENT(elm, field); \
575 color = RB_COLOR(elm, field); \
577 RB_PARENT(child, field) = parent; \
579 if (RB_LEFT(parent, field) == elm) \
580 RB_LEFT(parent, field) = child; \
582 RB_RIGHT(parent, field) = child; \
583 RB_AUGMENT(parent); \
585 RB_ROOT(head) = child; \
586 if (RB_PARENT(elm, field) == old) \
588 (elm)->field = (old)->field; \
589 if (RB_PARENT(old, field)) { \
590 if (RB_LEFT(RB_PARENT(old, field), field) == old)\
591 RB_LEFT(RB_PARENT(old, field), field) = elm;\
593 RB_RIGHT(RB_PARENT(old, field), field) = elm;\
594 RB_AUGMENT(RB_PARENT(old, field)); \
596 RB_ROOT(head) = elm; \
597 RB_PARENT(RB_LEFT(old, field), field) = elm; \
598 if (RB_RIGHT(old, field)) \
599 RB_PARENT(RB_RIGHT(old, field), field) = elm; \
604 } while ((left = RB_PARENT(left, field)) != NULL); \
608 parent = RB_PARENT(elm, field); \
609 color = RB_COLOR(elm, field); \
611 RB_PARENT(child, field) = parent; \
613 if (RB_LEFT(parent, field) == elm) \
614 RB_LEFT(parent, field) = child; \
616 RB_RIGHT(parent, field) = child; \
617 RB_AUGMENT(parent); \
619 RB_ROOT(head) = child; \
621 if (color == RB_BLACK) \
622 name##_RB_REMOVE_COLOR(head, parent, child); \
626 #define RB_GENERATE_INSERT(name, type, field, cmp, attr) \
627 /* Inserts a node into the RB tree */ \
629 name##_RB_INSERT(struct name *head, struct type *elm) \
632 struct type *parent = NULL; \
634 tmp = RB_ROOT(head); \
637 comp = (cmp)(elm, parent); \
639 tmp = RB_LEFT(tmp, field); \
641 tmp = RB_RIGHT(tmp, field); \
645 RB_SET(elm, parent, field); \
646 if (parent != NULL) { \
648 RB_LEFT(parent, field) = elm; \
650 RB_RIGHT(parent, field) = elm; \
651 RB_AUGMENT(parent); \
653 RB_ROOT(head) = elm; \
654 name##_RB_INSERT_COLOR(head, elm); \
658 #define RB_GENERATE_FIND(name, type, field, cmp, attr) \
659 /* Finds the node with the same key as elm */ \
661 name##_RB_FIND(struct name *head, struct type *elm) \
663 struct type *tmp = RB_ROOT(head); \
666 comp = cmp(elm, tmp); \
668 tmp = RB_LEFT(tmp, field); \
670 tmp = RB_RIGHT(tmp, field); \
677 #define RB_GENERATE_NFIND(name, type, field, cmp, attr) \
678 /* Finds the first node greater than or equal to the search key */ \
680 name##_RB_NFIND(struct name *head, struct type *elm) \
682 struct type *tmp = RB_ROOT(head); \
683 struct type *res = NULL; \
686 comp = cmp(elm, tmp); \
689 tmp = RB_LEFT(tmp, field); \
692 tmp = RB_RIGHT(tmp, field); \
699 #define RB_GENERATE_NEXT(name, type, field, attr) \
702 name##_RB_NEXT(struct type *elm) \
704 if (RB_RIGHT(elm, field)) { \
705 elm = RB_RIGHT(elm, field); \
706 while (RB_LEFT(elm, field)) \
707 elm = RB_LEFT(elm, field); \
709 if (RB_PARENT(elm, field) && \
710 (elm == RB_LEFT(RB_PARENT(elm, field), field))) \
711 elm = RB_PARENT(elm, field); \
713 while (RB_PARENT(elm, field) && \
714 (elm == RB_RIGHT(RB_PARENT(elm, field), field)))\
715 elm = RB_PARENT(elm, field); \
716 elm = RB_PARENT(elm, field); \
722 #define RB_GENERATE_PREV(name, type, field, attr) \
725 name##_RB_PREV(struct type *elm) \
727 if (RB_LEFT(elm, field)) { \
728 elm = RB_LEFT(elm, field); \
729 while (RB_RIGHT(elm, field)) \
730 elm = RB_RIGHT(elm, field); \
732 if (RB_PARENT(elm, field) && \
733 (elm == RB_RIGHT(RB_PARENT(elm, field), field))) \
734 elm = RB_PARENT(elm, field); \
736 while (RB_PARENT(elm, field) && \
737 (elm == RB_LEFT(RB_PARENT(elm, field), field)))\
738 elm = RB_PARENT(elm, field); \
739 elm = RB_PARENT(elm, field); \
745 #define RB_GENERATE_MINMAX(name, type, field, attr) \
747 name##_RB_MINMAX(struct name *head, int val) \
749 struct type *tmp = RB_ROOT(head); \
750 struct type *parent = NULL; \
754 tmp = RB_LEFT(tmp, field); \
756 tmp = RB_RIGHT(tmp, field); \
764 #define RB_INSERT(name, x, y) name##_RB_INSERT(x, y)
765 #define RB_REMOVE(name, x, y) name##_RB_REMOVE(x, y)
766 #define RB_FIND(name, x, y) name##_RB_FIND(x, y)
767 #define RB_NFIND(name, x, y) name##_RB_NFIND(x, y)
768 #define RB_NEXT(name, x, y) name##_RB_NEXT(y)
769 #define RB_PREV(name, x, y) name##_RB_PREV(y)
770 #define RB_MIN(name, x) name##_RB_MINMAX(x, RB_NEGINF)
771 #define RB_MAX(name, x) name##_RB_MINMAX(x, RB_INF)
773 #define RB_FOREACH(x, name, head) \
774 for ((x) = RB_MIN(name, head); \
776 (x) = name##_RB_NEXT(x))
778 #define RB_FOREACH_FROM(x, name, y) \
780 ((x) != NULL) && ((y) = name##_RB_NEXT(x), (x) != NULL); \
783 #define RB_FOREACH_SAFE(x, name, head, y) \
784 for ((x) = RB_MIN(name, head); \
785 ((x) != NULL) && ((y) = name##_RB_NEXT(x), (x) != NULL); \
788 #define RB_FOREACH_REVERSE(x, name, head) \
789 for ((x) = RB_MAX(name, head); \
791 (x) = name##_RB_PREV(x))
793 #define RB_FOREACH_REVERSE_FROM(x, name, y) \
795 ((x) != NULL) && ((y) = name##_RB_PREV(x), (x) != NULL); \
798 #define RB_FOREACH_REVERSE_SAFE(x, name, head, y) \
799 for ((x) = RB_MAX(name, head); \
800 ((x) != NULL) && ((y) = name##_RB_PREV(x), (x) != NULL); \
803 #endif /* _SYS_TREE_H_ */