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 * Copyright 2002 Niels Provos <provos@citi.umich.edu>
9 * Redistribution and use in source and binary forms, with or without
10 * modification, are permitted provided that the following conditions
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.
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.
33 #include <sys/cdefs.h>
36 * This file defines data structures for different types of trees:
37 * splay trees and red-black trees.
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.
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.
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);
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.
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).
62 #define SPLAY_HEAD(name, type) \
64 struct type *sph_root; /* root of the tree */ \
67 #define SPLAY_INITIALIZER(root) \
70 #define SPLAY_INIT(root) do { \
71 (root)->sph_root = NULL; \
72 } while (/*CONSTCOND*/ 0)
74 #define SPLAY_ENTRY(type) \
76 struct type *spe_left; /* left element */ \
77 struct type *spe_right; /* right element */ \
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)
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)
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)
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)
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)
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)
117 /* Generates prototypes and inline functions */
119 #define SPLAY_PROTOTYPE(name, type, field, cmp) \
120 void name##_SPLAY(struct name *, struct type *); \
121 void name##_SPLAY_MINMAX(struct name *, int); \
122 struct type *name##_SPLAY_INSERT(struct name *, struct type *); \
123 struct type *name##_SPLAY_REMOVE(struct name *, struct type *); \
125 /* Finds the node with the same key as elm */ \
126 static __inline struct type * \
127 name##_SPLAY_FIND(struct name *head, struct type *elm) \
129 if (SPLAY_EMPTY(head)) \
131 name##_SPLAY(head, elm); \
132 if ((cmp)(elm, (head)->sph_root) == 0) \
133 return (head->sph_root); \
137 static __inline struct type * \
138 name##_SPLAY_NEXT(struct name *head, struct type *elm) \
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); \
151 static __inline struct type * \
152 name##_SPLAY_MIN_MAX(struct name *head, int val) \
154 name##_SPLAY_MINMAX(head, val); \
155 return (SPLAY_ROOT(head)); \
158 /* Main splay operation.
159 * Moves node close to the key of elm to top
161 #define SPLAY_GENERATE(name, type, field, cmp) \
163 name##_SPLAY_INSERT(struct name *head, struct type *elm) \
165 if (SPLAY_EMPTY(head)) { \
166 SPLAY_LEFT(elm, field) = SPLAY_RIGHT(elm, field) = NULL; \
169 name##_SPLAY(head, elm); \
170 __comp = (cmp)(elm, (head)->sph_root); \
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; \
180 return ((head)->sph_root); \
182 (head)->sph_root = (elm); \
187 name##_SPLAY_REMOVE(struct name *head, struct type *elm) \
189 struct type *__tmp; \
190 if (SPLAY_EMPTY(head)) \
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);\
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; \
208 name##_SPLAY(struct name *head, struct type *elm) \
210 struct type __node, *__left, *__right, *__tmp; \
213 SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
214 __left = __right = &__node; \
216 while ((__comp = (cmp)(elm, (head)->sph_root)) != 0) { \
218 __tmp = SPLAY_LEFT((head)->sph_root, field); \
221 if ((cmp)(elm, __tmp) < 0){ \
222 SPLAY_ROTATE_RIGHT(head, __tmp, field); \
223 if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
226 SPLAY_LINKLEFT(head, __right, field); \
227 } else if (__comp > 0) { \
228 __tmp = SPLAY_RIGHT((head)->sph_root, field); \
231 if ((cmp)(elm, __tmp) > 0){ \
232 SPLAY_ROTATE_LEFT(head, __tmp, field); \
233 if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
236 SPLAY_LINKRIGHT(head, __left, field); \
239 SPLAY_ASSEMBLE(head, &__node, __left, __right, field); \
242 /* Splay with either the minimum or the maximum element \
243 * Used to find minimum or maximum element in tree. \
245 void name##_SPLAY_MINMAX(struct name *head, int __comp) \
247 struct type __node, *__left, *__right, *__tmp; \
249 SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
250 __left = __right = &__node; \
254 __tmp = SPLAY_LEFT((head)->sph_root, field); \
258 SPLAY_ROTATE_RIGHT(head, __tmp, field); \
259 if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
262 SPLAY_LINKLEFT(head, __right, field); \
263 } else if (__comp > 0) { \
264 __tmp = SPLAY_RIGHT((head)->sph_root, field); \
268 SPLAY_ROTATE_LEFT(head, __tmp, field); \
269 if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
272 SPLAY_LINKRIGHT(head, __left, field); \
275 SPLAY_ASSEMBLE(head, &__node, __left, __right, field); \
278 #define SPLAY_NEGINF -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))
290 #define SPLAY_FOREACH(x, name, head) \
291 for ((x) = SPLAY_MIN(name, head); \
293 (x) = SPLAY_NEXT(name, head, x))
295 /* Macros that define a red-black tree */
296 #define RB_HEAD(name, type) \
298 struct type *rbh_root; /* root of the tree */ \
301 #define RB_INITIALIZER(root) \
304 #define RB_INIT(root) do { \
305 (root)->rbh_root = NULL; \
306 } while (/*CONSTCOND*/ 0)
310 #define RB_ENTRY(type) \
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)
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)
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)
337 #define RB_AUGMENT(x) do {} while (0)
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); \
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); \
350 RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \
352 (head)->rbh_root = (tmp); \
353 RB_LEFT(tmp, field) = (elm); \
354 RB_PARENT(elm, field) = (tmp); \
356 if ((RB_PARENT(tmp, field))) \
357 RB_AUGMENT(RB_PARENT(tmp, field)); \
358 } while (/*CONSTCOND*/ 0)
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); \
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); \
370 RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \
372 (head)->rbh_root = (tmp); \
373 RB_RIGHT(tmp, field) = (elm); \
374 RB_PARENT(elm, field) = (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) \
386 attr void name##_RB_INSERT_COLOR(struct name *, struct type *); \
387 attr void name##_RB_REMOVE_COLOR(struct name *, struct type *, struct type *);\
388 attr struct type *name##_RB_REMOVE(struct name *, struct type *); \
389 attr struct type *name##_RB_INSERT(struct name *, struct type *); \
390 attr struct type *name##_RB_FIND(struct name *, struct type *); \
391 attr struct type *name##_RB_NFIND(struct name *, struct type *); \
392 attr struct type *name##_RB_NEXT(struct type *); \
393 attr struct type *name##_RB_MINMAX(struct name *, int); \
396 /* Main rb operation.
397 * Moves node close to the key of elm to top
399 #define RB_GENERATE(name, type, field, cmp) \
400 RB_GENERATE_INTERNAL(name, type, field, cmp,)
401 #define RB_GENERATE_STATIC(name, type, field, cmp) \
402 RB_GENERATE_INTERNAL(name, type, field, cmp, __unused static)
403 #define RB_GENERATE_INTERNAL(name, type, field, cmp, attr) \
405 name##_RB_INSERT_COLOR(struct name *head, struct type *elm) \
407 struct type *parent, *gparent, *tmp; \
408 while ((parent = RB_PARENT(elm, field)) != NULL && \
409 RB_COLOR(parent, field) == RB_RED) { \
410 gparent = RB_PARENT(parent, field); \
411 if (parent == RB_LEFT(gparent, field)) { \
412 tmp = RB_RIGHT(gparent, field); \
413 if (tmp && RB_COLOR(tmp, field) == RB_RED) { \
414 RB_COLOR(tmp, field) = RB_BLACK; \
415 RB_SET_BLACKRED(parent, gparent, field);\
419 if (RB_RIGHT(parent, field) == elm) { \
420 RB_ROTATE_LEFT(head, parent, tmp, field);\
425 RB_SET_BLACKRED(parent, gparent, field); \
426 RB_ROTATE_RIGHT(head, gparent, tmp, field); \
428 tmp = RB_LEFT(gparent, field); \
429 if (tmp && RB_COLOR(tmp, field) == RB_RED) { \
430 RB_COLOR(tmp, field) = RB_BLACK; \
431 RB_SET_BLACKRED(parent, gparent, field);\
435 if (RB_LEFT(parent, field) == elm) { \
436 RB_ROTATE_RIGHT(head, parent, tmp, field);\
441 RB_SET_BLACKRED(parent, gparent, field); \
442 RB_ROTATE_LEFT(head, gparent, tmp, field); \
445 RB_COLOR(head->rbh_root, field) = RB_BLACK; \
449 name##_RB_REMOVE_COLOR(struct name *head, struct type *parent, struct type *elm) \
452 while ((elm == NULL || RB_COLOR(elm, field) == RB_BLACK) && \
453 elm != RB_ROOT(head)) { \
454 if (RB_LEFT(parent, field) == elm) { \
455 tmp = RB_RIGHT(parent, field); \
456 if (RB_COLOR(tmp, field) == RB_RED) { \
457 RB_SET_BLACKRED(tmp, parent, field); \
458 RB_ROTATE_LEFT(head, parent, tmp, field);\
459 tmp = RB_RIGHT(parent, field); \
461 if ((RB_LEFT(tmp, field) == NULL || \
462 RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
463 (RB_RIGHT(tmp, field) == NULL || \
464 RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
465 RB_COLOR(tmp, field) = RB_RED; \
467 parent = RB_PARENT(elm, field); \
469 if (RB_RIGHT(tmp, field) == NULL || \
470 RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK) {\
471 struct type *oleft; \
472 if ((oleft = RB_LEFT(tmp, field)) \
474 RB_COLOR(oleft, field) = RB_BLACK;\
475 RB_COLOR(tmp, field) = RB_RED; \
476 RB_ROTATE_RIGHT(head, tmp, oleft, field);\
477 tmp = RB_RIGHT(parent, field); \
479 RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
480 RB_COLOR(parent, field) = RB_BLACK; \
481 if (RB_RIGHT(tmp, field)) \
482 RB_COLOR(RB_RIGHT(tmp, field), field) = RB_BLACK;\
483 RB_ROTATE_LEFT(head, parent, tmp, field);\
484 elm = RB_ROOT(head); \
488 tmp = RB_LEFT(parent, field); \
489 if (RB_COLOR(tmp, field) == RB_RED) { \
490 RB_SET_BLACKRED(tmp, parent, field); \
491 RB_ROTATE_RIGHT(head, parent, tmp, field);\
492 tmp = RB_LEFT(parent, field); \
494 if ((RB_LEFT(tmp, field) == NULL || \
495 RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
496 (RB_RIGHT(tmp, field) == NULL || \
497 RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
498 RB_COLOR(tmp, field) = RB_RED; \
500 parent = RB_PARENT(elm, field); \
502 if (RB_LEFT(tmp, field) == NULL || \
503 RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) {\
504 struct type *oright; \
505 if ((oright = RB_RIGHT(tmp, field)) \
507 RB_COLOR(oright, field) = RB_BLACK;\
508 RB_COLOR(tmp, field) = RB_RED; \
509 RB_ROTATE_LEFT(head, tmp, oright, field);\
510 tmp = RB_LEFT(parent, field); \
512 RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
513 RB_COLOR(parent, field) = RB_BLACK; \
514 if (RB_LEFT(tmp, field)) \
515 RB_COLOR(RB_LEFT(tmp, field), field) = RB_BLACK;\
516 RB_ROTATE_RIGHT(head, parent, tmp, field);\
517 elm = RB_ROOT(head); \
523 RB_COLOR(elm, field) = RB_BLACK; \
527 name##_RB_REMOVE(struct name *head, struct type *elm) \
529 struct type *child, *parent, *old = elm; \
531 if (RB_LEFT(elm, field) == NULL) \
532 child = RB_RIGHT(elm, field); \
533 else if (RB_RIGHT(elm, field) == NULL) \
534 child = RB_LEFT(elm, field); \
537 elm = RB_RIGHT(elm, field); \
538 while ((left = RB_LEFT(elm, field)) != NULL) \
540 child = RB_RIGHT(elm, field); \
541 parent = RB_PARENT(elm, field); \
542 color = RB_COLOR(elm, field); \
544 RB_PARENT(child, field) = parent; \
546 if (RB_LEFT(parent, field) == elm) \
547 RB_LEFT(parent, field) = child; \
549 RB_RIGHT(parent, field) = child; \
550 RB_AUGMENT(parent); \
552 RB_ROOT(head) = child; \
553 if (RB_PARENT(elm, field) == old) \
555 (elm)->field = (old)->field; \
556 if (RB_PARENT(old, field)) { \
557 if (RB_LEFT(RB_PARENT(old, field), field) == old)\
558 RB_LEFT(RB_PARENT(old, field), field) = elm;\
560 RB_RIGHT(RB_PARENT(old, field), field) = elm;\
561 RB_AUGMENT(RB_PARENT(old, field)); \
563 RB_ROOT(head) = elm; \
564 RB_PARENT(RB_LEFT(old, field), field) = elm; \
565 if (RB_RIGHT(old, field)) \
566 RB_PARENT(RB_RIGHT(old, field), field) = elm; \
571 } while ((left = RB_PARENT(left, field)) != NULL); \
575 parent = RB_PARENT(elm, field); \
576 color = RB_COLOR(elm, field); \
578 RB_PARENT(child, field) = parent; \
580 if (RB_LEFT(parent, field) == elm) \
581 RB_LEFT(parent, field) = child; \
583 RB_RIGHT(parent, field) = child; \
584 RB_AUGMENT(parent); \
586 RB_ROOT(head) = child; \
588 if (color == RB_BLACK) \
589 name##_RB_REMOVE_COLOR(head, parent, child); \
593 /* Inserts a node into the RB tree */ \
595 name##_RB_INSERT(struct name *head, struct type *elm) \
598 struct type *parent = NULL; \
600 tmp = RB_ROOT(head); \
603 comp = (cmp)(elm, parent); \
605 tmp = RB_LEFT(tmp, field); \
607 tmp = RB_RIGHT(tmp, field); \
611 RB_SET(elm, parent, field); \
612 if (parent != NULL) { \
614 RB_LEFT(parent, field) = elm; \
616 RB_RIGHT(parent, field) = elm; \
617 RB_AUGMENT(parent); \
619 RB_ROOT(head) = elm; \
620 name##_RB_INSERT_COLOR(head, elm); \
624 /* Finds the node with the same key as elm */ \
626 name##_RB_FIND(struct name *head, struct type *elm) \
628 struct type *tmp = RB_ROOT(head); \
631 comp = cmp(elm, tmp); \
633 tmp = RB_LEFT(tmp, field); \
635 tmp = RB_RIGHT(tmp, field); \
642 /* Finds the first node greater than or equal to the search key */ \
644 name##_RB_NFIND(struct name *head, struct type *elm) \
646 struct type *tmp = RB_ROOT(head); \
647 struct type *res = NULL; \
650 comp = cmp(elm, tmp); \
653 tmp = RB_LEFT(tmp, field); \
656 tmp = RB_RIGHT(tmp, field); \
665 name##_RB_NEXT(struct type *elm) \
667 if (RB_RIGHT(elm, field)) { \
668 elm = RB_RIGHT(elm, field); \
669 while (RB_LEFT(elm, field)) \
670 elm = RB_LEFT(elm, field); \
672 if (RB_PARENT(elm, field) && \
673 (elm == RB_LEFT(RB_PARENT(elm, field), field))) \
674 elm = RB_PARENT(elm, field); \
676 while (RB_PARENT(elm, field) && \
677 (elm == RB_RIGHT(RB_PARENT(elm, field), field)))\
678 elm = RB_PARENT(elm, field); \
679 elm = RB_PARENT(elm, field); \
686 name##_RB_MINMAX(struct name *head, int val) \
688 struct type *tmp = RB_ROOT(head); \
689 struct type *parent = NULL; \
693 tmp = RB_LEFT(tmp, field); \
695 tmp = RB_RIGHT(tmp, field); \
703 #define RB_INSERT(name, x, y) name##_RB_INSERT(x, y)
704 #define RB_REMOVE(name, x, y) name##_RB_REMOVE(x, y)
705 #define RB_FIND(name, x, y) name##_RB_FIND(x, y)
706 #define RB_NFIND(name, x, y) name##_RB_NFIND(x, y)
707 #define RB_NEXT(name, x, y) name##_RB_NEXT(y)
708 #define RB_MIN(name, x) name##_RB_MINMAX(x, RB_NEGINF)
709 #define RB_MAX(name, x) name##_RB_MINMAX(x, RB_INF)
711 #define RB_FOREACH(x, name, head) \
712 for ((x) = RB_MIN(name, head); \
714 (x) = name##_RB_NEXT(x))
716 #endif /* _SYS_TREE_H_ */