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.
34 * This file defines data structures for different types of trees:
35 * splay trees and red-black trees.
37 * A splay tree is a self-organizing data structure. Every operation
38 * on the tree causes a splay to happen. The splay moves the requested
39 * node to the root of the tree and partly rebalances it.
41 * This has the benefit that request locality causes faster lookups as
42 * the requested nodes move to the top of the tree. On the other hand,
43 * every lookup causes memory writes.
45 * The Balance Theorem bounds the total access time for m operations
46 * and n inserts on an initially empty tree as O((m + n)lg n). The
47 * amortized cost for a sequence of m accesses to a splay tree is O(lg n);
49 * A red-black tree is a binary search tree with the node color as an
50 * extra attribute. It fulfills a set of conditions:
51 * - every search path from the root to a leaf consists of the
52 * same number of black nodes,
53 * - each red node (except for the root) has a black parent,
54 * - each leaf node is black.
56 * Every operation on a red-black tree is bounded as O(lg n).
57 * The maximum height of a red-black tree is 2lg (n+1).
60 #define SPLAY_HEAD(name, type) \
62 struct type *sph_root; /* root of the tree */ \
65 #define SPLAY_INITIALIZER(root) \
68 #define SPLAY_INIT(root) do { \
69 (root)->sph_root = NULL; \
70 } while (/*CONSTCOND*/ 0)
72 #define SPLAY_ENTRY(type) \
74 struct type *spe_left; /* left element */ \
75 struct type *spe_right; /* right element */ \
78 #define SPLAY_LEFT(elm, field) (elm)->field.spe_left
79 #define SPLAY_RIGHT(elm, field) (elm)->field.spe_right
80 #define SPLAY_ROOT(head) (head)->sph_root
81 #define SPLAY_EMPTY(head) (SPLAY_ROOT(head) == NULL)
83 /* SPLAY_ROTATE_{LEFT,RIGHT} expect that tmp hold SPLAY_{RIGHT,LEFT} */
84 #define SPLAY_ROTATE_RIGHT(head, tmp, field) do { \
85 SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(tmp, field); \
86 SPLAY_RIGHT(tmp, field) = (head)->sph_root; \
87 (head)->sph_root = tmp; \
88 } while (/*CONSTCOND*/ 0)
90 #define SPLAY_ROTATE_LEFT(head, tmp, field) do { \
91 SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(tmp, field); \
92 SPLAY_LEFT(tmp, field) = (head)->sph_root; \
93 (head)->sph_root = tmp; \
94 } while (/*CONSTCOND*/ 0)
96 #define SPLAY_LINKLEFT(head, tmp, field) do { \
97 SPLAY_LEFT(tmp, field) = (head)->sph_root; \
98 tmp = (head)->sph_root; \
99 (head)->sph_root = SPLAY_LEFT((head)->sph_root, field); \
100 } while (/*CONSTCOND*/ 0)
102 #define SPLAY_LINKRIGHT(head, tmp, field) do { \
103 SPLAY_RIGHT(tmp, field) = (head)->sph_root; \
104 tmp = (head)->sph_root; \
105 (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field); \
106 } while (/*CONSTCOND*/ 0)
108 #define SPLAY_ASSEMBLE(head, node, left, right, field) do { \
109 SPLAY_RIGHT(left, field) = SPLAY_LEFT((head)->sph_root, field); \
110 SPLAY_LEFT(right, field) = SPLAY_RIGHT((head)->sph_root, field);\
111 SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(node, field); \
112 SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(node, field); \
113 } while (/*CONSTCOND*/ 0)
115 /* Generates prototypes and inline functions */
117 #define SPLAY_PROTOTYPE(name, type, field, cmp) \
118 void name##_SPLAY(struct name *, struct type *); \
119 void name##_SPLAY_MINMAX(struct name *, int); \
120 struct type *name##_SPLAY_INSERT(struct name *, struct type *); \
121 struct type *name##_SPLAY_REMOVE(struct name *, struct type *); \
123 /* Finds the node with the same key as elm */ \
124 static __inline struct type * \
125 name##_SPLAY_FIND(struct name *head, struct type *elm) \
127 if (SPLAY_EMPTY(head)) \
129 name##_SPLAY(head, elm); \
130 if ((cmp)(elm, (head)->sph_root) == 0) \
131 return (head->sph_root); \
135 static __inline struct type * \
136 name##_SPLAY_NEXT(struct name *head, struct type *elm) \
138 name##_SPLAY(head, elm); \
139 if (SPLAY_RIGHT(elm, field) != NULL) { \
140 elm = SPLAY_RIGHT(elm, field); \
141 while (SPLAY_LEFT(elm, field) != NULL) { \
142 elm = SPLAY_LEFT(elm, field); \
149 static __inline struct type * \
150 name##_SPLAY_MIN_MAX(struct name *head, int val) \
152 name##_SPLAY_MINMAX(head, val); \
153 return (SPLAY_ROOT(head)); \
156 /* Main splay operation.
157 * Moves node close to the key of elm to top
159 #define SPLAY_GENERATE(name, type, field, cmp) \
161 name##_SPLAY_INSERT(struct name *head, struct type *elm) \
163 if (SPLAY_EMPTY(head)) { \
164 SPLAY_LEFT(elm, field) = SPLAY_RIGHT(elm, field) = NULL; \
167 name##_SPLAY(head, elm); \
168 __comp = (cmp)(elm, (head)->sph_root); \
170 SPLAY_LEFT(elm, field) = SPLAY_LEFT((head)->sph_root, field);\
171 SPLAY_RIGHT(elm, field) = (head)->sph_root; \
172 SPLAY_LEFT((head)->sph_root, field) = NULL; \
173 } else if (__comp > 0) { \
174 SPLAY_RIGHT(elm, field) = SPLAY_RIGHT((head)->sph_root, field);\
175 SPLAY_LEFT(elm, field) = (head)->sph_root; \
176 SPLAY_RIGHT((head)->sph_root, field) = NULL; \
178 return ((head)->sph_root); \
180 (head)->sph_root = (elm); \
185 name##_SPLAY_REMOVE(struct name *head, struct type *elm) \
187 struct type *__tmp; \
188 if (SPLAY_EMPTY(head)) \
190 name##_SPLAY(head, elm); \
191 if ((cmp)(elm, (head)->sph_root) == 0) { \
192 if (SPLAY_LEFT((head)->sph_root, field) == NULL) { \
193 (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);\
195 __tmp = SPLAY_RIGHT((head)->sph_root, field); \
196 (head)->sph_root = SPLAY_LEFT((head)->sph_root, field);\
197 name##_SPLAY(head, elm); \
198 SPLAY_RIGHT((head)->sph_root, field) = __tmp; \
206 name##_SPLAY(struct name *head, struct type *elm) \
208 struct type __node, *__left, *__right, *__tmp; \
211 SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
212 __left = __right = &__node; \
214 while ((__comp = (cmp)(elm, (head)->sph_root)) != 0) { \
216 __tmp = SPLAY_LEFT((head)->sph_root, field); \
219 if ((cmp)(elm, __tmp) < 0){ \
220 SPLAY_ROTATE_RIGHT(head, __tmp, field); \
221 if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
224 SPLAY_LINKLEFT(head, __right, field); \
225 } else if (__comp > 0) { \
226 __tmp = SPLAY_RIGHT((head)->sph_root, field); \
229 if ((cmp)(elm, __tmp) > 0){ \
230 SPLAY_ROTATE_LEFT(head, __tmp, field); \
231 if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
234 SPLAY_LINKRIGHT(head, __left, field); \
237 SPLAY_ASSEMBLE(head, &__node, __left, __right, field); \
240 /* Splay with either the minimum or the maximum element \
241 * Used to find minimum or maximum element in tree. \
243 void name##_SPLAY_MINMAX(struct name *head, int __comp) \
245 struct type __node, *__left, *__right, *__tmp; \
247 SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
248 __left = __right = &__node; \
252 __tmp = SPLAY_LEFT((head)->sph_root, field); \
256 SPLAY_ROTATE_RIGHT(head, __tmp, field); \
257 if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
260 SPLAY_LINKLEFT(head, __right, field); \
261 } else if (__comp > 0) { \
262 __tmp = SPLAY_RIGHT((head)->sph_root, field); \
266 SPLAY_ROTATE_LEFT(head, __tmp, field); \
267 if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
270 SPLAY_LINKRIGHT(head, __left, field); \
273 SPLAY_ASSEMBLE(head, &__node, __left, __right, field); \
276 #define SPLAY_NEGINF -1
279 #define SPLAY_INSERT(name, x, y) name##_SPLAY_INSERT(x, y)
280 #define SPLAY_REMOVE(name, x, y) name##_SPLAY_REMOVE(x, y)
281 #define SPLAY_FIND(name, x, y) name##_SPLAY_FIND(x, y)
282 #define SPLAY_NEXT(name, x, y) name##_SPLAY_NEXT(x, y)
283 #define SPLAY_MIN(name, x) (SPLAY_EMPTY(x) ? NULL \
284 : name##_SPLAY_MIN_MAX(x, SPLAY_NEGINF))
285 #define SPLAY_MAX(name, x) (SPLAY_EMPTY(x) ? NULL \
286 : name##_SPLAY_MIN_MAX(x, SPLAY_INF))
288 #define SPLAY_FOREACH(x, name, head) \
289 for ((x) = SPLAY_MIN(name, head); \
291 (x) = SPLAY_NEXT(name, head, x))
293 /* Macros that define a red-black tree */
294 #define RB_HEAD(name, type) \
296 struct type *rbh_root; /* root of the tree */ \
299 #define RB_INITIALIZER(root) \
302 #define RB_INIT(root) do { \
303 (root)->rbh_root = NULL; \
304 } while (/*CONSTCOND*/ 0)
308 #define RB_ENTRY(type) \
310 struct type *rbe_left; /* left element */ \
311 struct type *rbe_right; /* right element */ \
312 struct type *rbe_parent; /* parent element */ \
313 int rbe_color; /* node color */ \
316 #define RB_LEFT(elm, field) (elm)->field.rbe_left
317 #define RB_RIGHT(elm, field) (elm)->field.rbe_right
318 #define RB_PARENT(elm, field) (elm)->field.rbe_parent
319 #define RB_COLOR(elm, field) (elm)->field.rbe_color
320 #define RB_ROOT(head) (head)->rbh_root
321 #define RB_EMPTY(head) (RB_ROOT(head) == NULL)
323 #define RB_SET(elm, parent, field) do { \
324 RB_PARENT(elm, field) = parent; \
325 RB_LEFT(elm, field) = RB_RIGHT(elm, field) = NULL; \
326 RB_COLOR(elm, field) = RB_RED; \
327 } while (/*CONSTCOND*/ 0)
329 #define RB_SET_BLACKRED(black, red, field) do { \
330 RB_COLOR(black, field) = RB_BLACK; \
331 RB_COLOR(red, field) = RB_RED; \
332 } while (/*CONSTCOND*/ 0)
335 #define RB_AUGMENT(x) do {} while (0)
338 #define RB_ROTATE_LEFT(head, elm, tmp, field) do { \
339 (tmp) = RB_RIGHT(elm, field); \
340 if ((RB_RIGHT(elm, field) = RB_LEFT(tmp, field)) != NULL) { \
341 RB_PARENT(RB_LEFT(tmp, field), field) = (elm); \
344 if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) { \
345 if ((elm) == RB_LEFT(RB_PARENT(elm, field), field)) \
346 RB_LEFT(RB_PARENT(elm, field), field) = (tmp); \
348 RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \
350 (head)->rbh_root = (tmp); \
351 RB_LEFT(tmp, field) = (elm); \
352 RB_PARENT(elm, field) = (tmp); \
354 if ((RB_PARENT(tmp, field))) \
355 RB_AUGMENT(RB_PARENT(tmp, field)); \
356 } while (/*CONSTCOND*/ 0)
358 #define RB_ROTATE_RIGHT(head, elm, tmp, field) do { \
359 (tmp) = RB_LEFT(elm, field); \
360 if ((RB_LEFT(elm, field) = RB_RIGHT(tmp, field)) != NULL) { \
361 RB_PARENT(RB_RIGHT(tmp, field), field) = (elm); \
364 if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) { \
365 if ((elm) == RB_LEFT(RB_PARENT(elm, field), field)) \
366 RB_LEFT(RB_PARENT(elm, field), field) = (tmp); \
368 RB_RIGHT(RB_PARENT(elm, field), field) = (tmp); \
370 (head)->rbh_root = (tmp); \
371 RB_RIGHT(tmp, field) = (elm); \
372 RB_PARENT(elm, field) = (tmp); \
374 if ((RB_PARENT(tmp, field))) \
375 RB_AUGMENT(RB_PARENT(tmp, field)); \
376 } while (/*CONSTCOND*/ 0)
378 /* Generates prototypes and inline functions */
379 #define RB_PROTOTYPE(name, type, field, cmp) \
380 void name##_RB_INSERT_COLOR(struct name *, struct type *); \
381 void name##_RB_REMOVE_COLOR(struct name *, struct type *, struct type *);\
382 struct type *name##_RB_REMOVE(struct name *, struct type *); \
383 struct type *name##_RB_INSERT(struct name *, struct type *); \
384 struct type *name##_RB_FIND(struct name *, struct type *); \
385 struct type *name##_RB_NEXT(struct type *); \
386 struct type *name##_RB_MINMAX(struct name *, int); \
389 /* Main rb operation.
390 * Moves node close to the key of elm to top
392 #define RB_GENERATE(name, type, field, cmp) \
394 name##_RB_INSERT_COLOR(struct name *head, struct type *elm) \
396 struct type *parent, *gparent, *tmp; \
397 while ((parent = RB_PARENT(elm, field)) != NULL && \
398 RB_COLOR(parent, field) == RB_RED) { \
399 gparent = RB_PARENT(parent, field); \
400 if (parent == RB_LEFT(gparent, field)) { \
401 tmp = RB_RIGHT(gparent, field); \
402 if (tmp && RB_COLOR(tmp, field) == RB_RED) { \
403 RB_COLOR(tmp, field) = RB_BLACK; \
404 RB_SET_BLACKRED(parent, gparent, field);\
408 if (RB_RIGHT(parent, field) == elm) { \
409 RB_ROTATE_LEFT(head, parent, tmp, field);\
414 RB_SET_BLACKRED(parent, gparent, field); \
415 RB_ROTATE_RIGHT(head, gparent, tmp, field); \
417 tmp = RB_LEFT(gparent, field); \
418 if (tmp && RB_COLOR(tmp, field) == RB_RED) { \
419 RB_COLOR(tmp, field) = RB_BLACK; \
420 RB_SET_BLACKRED(parent, gparent, field);\
424 if (RB_LEFT(parent, field) == elm) { \
425 RB_ROTATE_RIGHT(head, parent, tmp, field);\
430 RB_SET_BLACKRED(parent, gparent, field); \
431 RB_ROTATE_LEFT(head, gparent, tmp, field); \
434 RB_COLOR(head->rbh_root, field) = RB_BLACK; \
438 name##_RB_REMOVE_COLOR(struct name *head, struct type *parent, struct type *elm) \
441 while ((elm == NULL || RB_COLOR(elm, field) == RB_BLACK) && \
442 elm != RB_ROOT(head)) { \
443 if (RB_LEFT(parent, field) == elm) { \
444 tmp = RB_RIGHT(parent, field); \
445 if (RB_COLOR(tmp, field) == RB_RED) { \
446 RB_SET_BLACKRED(tmp, parent, field); \
447 RB_ROTATE_LEFT(head, parent, tmp, field);\
448 tmp = RB_RIGHT(parent, field); \
450 if ((RB_LEFT(tmp, field) == NULL || \
451 RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
452 (RB_RIGHT(tmp, field) == NULL || \
453 RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
454 RB_COLOR(tmp, field) = RB_RED; \
456 parent = RB_PARENT(elm, field); \
458 if (RB_RIGHT(tmp, field) == NULL || \
459 RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK) {\
460 struct type *oleft; \
461 if ((oleft = RB_LEFT(tmp, field)) \
463 RB_COLOR(oleft, field) = RB_BLACK;\
464 RB_COLOR(tmp, field) = RB_RED; \
465 RB_ROTATE_RIGHT(head, tmp, oleft, field);\
466 tmp = RB_RIGHT(parent, field); \
468 RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
469 RB_COLOR(parent, field) = RB_BLACK; \
470 if (RB_RIGHT(tmp, field)) \
471 RB_COLOR(RB_RIGHT(tmp, field), field) = RB_BLACK;\
472 RB_ROTATE_LEFT(head, parent, tmp, field);\
473 elm = RB_ROOT(head); \
477 tmp = RB_LEFT(parent, field); \
478 if (RB_COLOR(tmp, field) == RB_RED) { \
479 RB_SET_BLACKRED(tmp, parent, field); \
480 RB_ROTATE_RIGHT(head, parent, tmp, field);\
481 tmp = RB_LEFT(parent, field); \
483 if ((RB_LEFT(tmp, field) == NULL || \
484 RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
485 (RB_RIGHT(tmp, field) == NULL || \
486 RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
487 RB_COLOR(tmp, field) = RB_RED; \
489 parent = RB_PARENT(elm, field); \
491 if (RB_LEFT(tmp, field) == NULL || \
492 RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) {\
493 struct type *oright; \
494 if ((oright = RB_RIGHT(tmp, field)) \
496 RB_COLOR(oright, field) = RB_BLACK;\
497 RB_COLOR(tmp, field) = RB_RED; \
498 RB_ROTATE_LEFT(head, tmp, oright, field);\
499 tmp = RB_LEFT(parent, field); \
501 RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
502 RB_COLOR(parent, field) = RB_BLACK; \
503 if (RB_LEFT(tmp, field)) \
504 RB_COLOR(RB_LEFT(tmp, field), field) = RB_BLACK;\
505 RB_ROTATE_RIGHT(head, parent, tmp, field);\
506 elm = RB_ROOT(head); \
512 RB_COLOR(elm, field) = RB_BLACK; \
516 name##_RB_REMOVE(struct name *head, struct type *elm) \
518 struct type *child, *parent, *old = elm; \
520 if (RB_LEFT(elm, field) == NULL) \
521 child = RB_RIGHT(elm, field); \
522 else if (RB_RIGHT(elm, field) == NULL) \
523 child = RB_LEFT(elm, field); \
526 elm = RB_RIGHT(elm, field); \
527 while ((left = RB_LEFT(elm, field)) != NULL) \
529 child = RB_RIGHT(elm, field); \
530 parent = RB_PARENT(elm, field); \
531 color = RB_COLOR(elm, field); \
533 RB_PARENT(child, field) = parent; \
535 if (RB_LEFT(parent, field) == elm) \
536 RB_LEFT(parent, field) = child; \
538 RB_RIGHT(parent, field) = child; \
539 RB_AUGMENT(parent); \
541 RB_ROOT(head) = child; \
542 if (RB_PARENT(elm, field) == old) \
544 (elm)->field = (old)->field; \
545 if (RB_PARENT(old, field)) { \
546 if (RB_LEFT(RB_PARENT(old, field), field) == old)\
547 RB_LEFT(RB_PARENT(old, field), field) = elm;\
549 RB_RIGHT(RB_PARENT(old, field), field) = elm;\
550 RB_AUGMENT(RB_PARENT(old, field)); \
552 RB_ROOT(head) = elm; \
553 RB_PARENT(RB_LEFT(old, field), field) = elm; \
554 if (RB_RIGHT(old, field)) \
555 RB_PARENT(RB_RIGHT(old, field), field) = elm; \
560 } while ((left = RB_PARENT(left, field)) != NULL); \
564 parent = RB_PARENT(elm, field); \
565 color = RB_COLOR(elm, field); \
567 RB_PARENT(child, field) = parent; \
569 if (RB_LEFT(parent, field) == elm) \
570 RB_LEFT(parent, field) = child; \
572 RB_RIGHT(parent, field) = child; \
573 RB_AUGMENT(parent); \
575 RB_ROOT(head) = child; \
577 if (color == RB_BLACK) \
578 name##_RB_REMOVE_COLOR(head, parent, child); \
582 /* Inserts a node into the RB tree */ \
584 name##_RB_INSERT(struct name *head, struct type *elm) \
587 struct type *parent = NULL; \
589 tmp = RB_ROOT(head); \
592 comp = (cmp)(elm, parent); \
594 tmp = RB_LEFT(tmp, field); \
596 tmp = RB_RIGHT(tmp, field); \
600 RB_SET(elm, parent, field); \
601 if (parent != NULL) { \
603 RB_LEFT(parent, field) = elm; \
605 RB_RIGHT(parent, field) = elm; \
606 RB_AUGMENT(parent); \
608 RB_ROOT(head) = elm; \
609 name##_RB_INSERT_COLOR(head, elm); \
613 /* Finds the node with the same key as elm */ \
615 name##_RB_FIND(struct name *head, struct type *elm) \
617 struct type *tmp = RB_ROOT(head); \
620 comp = cmp(elm, tmp); \
622 tmp = RB_LEFT(tmp, field); \
624 tmp = RB_RIGHT(tmp, field); \
633 name##_RB_NEXT(struct type *elm) \
635 if (RB_RIGHT(elm, field)) { \
636 elm = RB_RIGHT(elm, field); \
637 while (RB_LEFT(elm, field)) \
638 elm = RB_LEFT(elm, field); \
640 if (RB_PARENT(elm, field) && \
641 (elm == RB_LEFT(RB_PARENT(elm, field), field))) \
642 elm = RB_PARENT(elm, field); \
644 while (RB_PARENT(elm, field) && \
645 (elm == RB_RIGHT(RB_PARENT(elm, field), field)))\
646 elm = RB_PARENT(elm, field); \
647 elm = RB_PARENT(elm, field); \
654 name##_RB_MINMAX(struct name *head, int val) \
656 struct type *tmp = RB_ROOT(head); \
657 struct type *parent = NULL; \
661 tmp = RB_LEFT(tmp, field); \
663 tmp = RB_RIGHT(tmp, field); \
671 #define RB_INSERT(name, x, y) name##_RB_INSERT(x, y)
672 #define RB_REMOVE(name, x, y) name##_RB_REMOVE(x, y)
673 #define RB_FIND(name, x, y) name##_RB_FIND(x, y)
674 #define RB_NEXT(name, x, y) name##_RB_NEXT(y)
675 #define RB_MIN(name, x) name##_RB_MINMAX(x, RB_NEGINF)
676 #define RB_MAX(name, x) name##_RB_MINMAX(x, RB_INF)
678 #define RB_FOREACH(x, name, head) \
679 for ((x) = RB_MIN(name, head); \
681 (x) = name##_RB_NEXT(x))
683 #endif /* _SYS_TREE_H_ */