1 /*	$OpenBSD: tree.h,v 1.13 2011/07/09 00:19:45 pirofti Exp $	*/
2 /*
3  * Copyright 2002 Niels Provos <provos@citi.umich.edu>
4  * All rights reserved.
5  *
6  * Redistribution and use in source and binary forms, with or without
7  * modification, are permitted provided that the following conditions
8  * are met:
9  * 1. Redistributions of source code must retain the above copyright
10  *    notice, this list of conditions and the following disclaimer.
11  * 2. Redistributions in binary form must reproduce the above copyright
12  *    notice, this list of conditions and the following disclaimer in the
13  *    documentation and/or other materials provided with the distribution.
14  *
15  * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
16  * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
17  * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
18  * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
19  * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
20  * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
21  * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
22  * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
23  * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
24  * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
25  */
26 
27 /* OPENBSD ORIGINAL: sys/sys/tree.h */
28 
29 #include "config.h"
30 #ifdef NO_ATTRIBUTE_ON_RETURN_TYPE
31 # define __attribute__(x)
32 #endif
33 
34 #ifndef	_SYS_TREE_H_
35 #define	_SYS_TREE_H_
36 
37 /*
38  * This file defines data structures for different types of trees:
39  * splay trees and red-black trees.
40  *
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.
44  *
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.
48  *
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);
52  *
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.
59  *
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).
62  */
63 
64 #define SPLAY_HEAD(name, type)						\
65 struct name {								\
66 	struct type *sph_root; /* root of the tree */			\
67 }
68 
69 #define SPLAY_INITIALIZER(root)						\
70 	{ NULL }
71 
72 #define SPLAY_INIT(root) do {						\
73 	(root)->sph_root = NULL;					\
74 } while (0)
75 
76 #define SPLAY_ENTRY(type)						\
77 struct {								\
78 	struct type *spe_left; /* left element */			\
79 	struct type *spe_right; /* right element */			\
80 }
81 
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)
86 
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 (0)
93 
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 (0)
99 
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 (0)
105 
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 (0)
111 
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 (0)
118 
119 /* Generates prototypes and inline functions */
120 
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 *);		\
126 									\
127 /* Finds the node with the same key as elm */				\
128 static __inline struct type *						\
129 name##_SPLAY_FIND(struct name *head, struct type *elm)			\
130 {									\
131 	if (SPLAY_EMPTY(head))						\
132 		return(NULL);						\
133 	name##_SPLAY(head, elm);					\
134 	if ((cmp)(elm, (head)->sph_root) == 0)				\
135 		return (head->sph_root);				\
136 	return (NULL);							\
137 }									\
138 									\
139 static __inline struct type *						\
140 name##_SPLAY_NEXT(struct name *head, struct type *elm)			\
141 {									\
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);			\
147 		}							\
148 	} else								\
149 		elm = NULL;						\
150 	return (elm);							\
151 }									\
152 									\
153 static __inline struct type *						\
154 name##_SPLAY_MIN_MAX(struct name *head, int val)			\
155 {									\
156 	name##_SPLAY_MINMAX(head, val);					\
157         return (SPLAY_ROOT(head));					\
158 }
159 
160 /* Main splay operation.
161  * Moves node close to the key of elm to top
162  */
163 #define SPLAY_GENERATE(name, type, field, cmp)				\
164 struct type *								\
165 name##_SPLAY_INSERT(struct name *head, struct type *elm)		\
166 {									\
167     if (SPLAY_EMPTY(head)) {						\
168 	    SPLAY_LEFT(elm, field) = SPLAY_RIGHT(elm, field) = NULL;	\
169     } else {								\
170 	    int __comp;							\
171 	    name##_SPLAY(head, elm);					\
172 	    __comp = (cmp)(elm, (head)->sph_root);			\
173 	    if(__comp < 0) {						\
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;	\
181 	    } else							\
182 		    return ((head)->sph_root);				\
183     }									\
184     (head)->sph_root = (elm);						\
185     return (NULL);							\
186 }									\
187 									\
188 struct type *								\
189 name##_SPLAY_REMOVE(struct name *head, struct type *elm)		\
190 {									\
191 	struct type *__tmp;						\
192 	if (SPLAY_EMPTY(head))						\
193 		return (NULL);						\
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);\
198 		} else {						\
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;	\
203 		}							\
204 		return (elm);						\
205 	}								\
206 	return (NULL);							\
207 }									\
208 									\
209 void									\
210 name##_SPLAY(struct name *head, struct type *elm)			\
211 {									\
212 	struct type __node, *__left, *__right, *__tmp;			\
213 	int __comp;							\
214 \
215 	SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
216 	__left = __right = &__node;					\
217 \
218 	while ((__comp = (cmp)(elm, (head)->sph_root))) {		\
219 		if (__comp < 0) {					\
220 			__tmp = SPLAY_LEFT((head)->sph_root, field);	\
221 			if (__tmp == NULL)				\
222 				break;					\
223 			if ((cmp)(elm, __tmp) < 0){			\
224 				SPLAY_ROTATE_RIGHT(head, __tmp, field);	\
225 				if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
226 					break;				\
227 			}						\
228 			SPLAY_LINKLEFT(head, __right, field);		\
229 		} else if (__comp > 0) {				\
230 			__tmp = SPLAY_RIGHT((head)->sph_root, field);	\
231 			if (__tmp == NULL)				\
232 				break;					\
233 			if ((cmp)(elm, __tmp) > 0){			\
234 				SPLAY_ROTATE_LEFT(head, __tmp, field);	\
235 				if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
236 					break;				\
237 			}						\
238 			SPLAY_LINKRIGHT(head, __left, field);		\
239 		}							\
240 	}								\
241 	SPLAY_ASSEMBLE(head, &__node, __left, __right, field);		\
242 }									\
243 									\
244 /* Splay with either the minimum or the maximum element			\
245  * Used to find minimum or maximum element in tree.			\
246  */									\
247 void name##_SPLAY_MINMAX(struct name *head, int __comp) \
248 {									\
249 	struct type __node, *__left, *__right, *__tmp;			\
250 \
251 	SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
252 	__left = __right = &__node;					\
253 \
254 	while (1) {							\
255 		if (__comp < 0) {					\
256 			__tmp = SPLAY_LEFT((head)->sph_root, field);	\
257 			if (__tmp == NULL)				\
258 				break;					\
259 			if (__comp < 0){				\
260 				SPLAY_ROTATE_RIGHT(head, __tmp, field);	\
261 				if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
262 					break;				\
263 			}						\
264 			SPLAY_LINKLEFT(head, __right, field);		\
265 		} else if (__comp > 0) {				\
266 			__tmp = SPLAY_RIGHT((head)->sph_root, field);	\
267 			if (__tmp == NULL)				\
268 				break;					\
269 			if (__comp > 0) {				\
270 				SPLAY_ROTATE_LEFT(head, __tmp, field);	\
271 				if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
272 					break;				\
273 			}						\
274 			SPLAY_LINKRIGHT(head, __left, field);		\
275 		}							\
276 	}								\
277 	SPLAY_ASSEMBLE(head, &__node, __left, __right, field);		\
278 }
279 
280 #define SPLAY_NEGINF	-1
281 #define SPLAY_INF	1
282 
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))
291 
292 #define SPLAY_FOREACH(x, name, head)					\
293 	for ((x) = SPLAY_MIN(name, head);				\
294 	     (x) != NULL;						\
295 	     (x) = SPLAY_NEXT(name, head, x))
296 
297 /* Macros that define a red-black tree */
298 #define RB_HEAD(name, type)						\
299 struct name {								\
300 	struct type *rbh_root; /* root of the tree */			\
301 }
302 
303 #define RB_INITIALIZER(root)						\
304 	{ NULL }
305 
306 #define RB_INIT(root) do {						\
307 	(root)->rbh_root = NULL;					\
308 } while (0)
309 
310 #define RB_BLACK	0
311 #define RB_RED		1
312 #define RB_ENTRY(type)							\
313 struct {								\
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 */		\
318 }
319 
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)
326 
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 (0)
332 
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 (0)
337 
338 #ifndef RB_AUGMENT
339 #define RB_AUGMENT(x)	do {} while (0)
340 #endif
341 
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))) {		\
345 		RB_PARENT(RB_LEFT(tmp, field), field) = (elm);		\
346 	}								\
347 	RB_AUGMENT(elm);						\
348 	if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field))) {		\
349 		if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))	\
350 			RB_LEFT(RB_PARENT(elm, field), field) = (tmp);	\
351 		else							\
352 			RB_RIGHT(RB_PARENT(elm, field), field) = (tmp);	\
353 	} else								\
354 		(head)->rbh_root = (tmp);				\
355 	RB_LEFT(tmp, field) = (elm);					\
356 	RB_PARENT(elm, field) = (tmp);					\
357 	RB_AUGMENT(tmp);						\
358 	if ((RB_PARENT(tmp, field)))					\
359 		RB_AUGMENT(RB_PARENT(tmp, field));			\
360 } while (0)
361 
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))) {		\
365 		RB_PARENT(RB_RIGHT(tmp, field), field) = (elm);		\
366 	}								\
367 	RB_AUGMENT(elm);						\
368 	if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field))) {		\
369 		if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))	\
370 			RB_LEFT(RB_PARENT(elm, field), field) = (tmp);	\
371 		else							\
372 			RB_RIGHT(RB_PARENT(elm, field), field) = (tmp);	\
373 	} else								\
374 		(head)->rbh_root = (tmp);				\
375 	RB_RIGHT(tmp, field) = (elm);					\
376 	RB_PARENT(elm, field) = (tmp);					\
377 	RB_AUGMENT(tmp);						\
378 	if ((RB_PARENT(tmp, field)))					\
379 		RB_AUGMENT(RB_PARENT(tmp, field));			\
380 } while (0)
381 
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, __attribute__((__unused__)) static)
387 #define RB_PROTOTYPE_INTERNAL(name, type, field, cmp, attr)		\
388 attr void name##_RB_INSERT_COLOR(struct name *, struct type *);		\
389 attr void name##_RB_REMOVE_COLOR(struct name *, struct type *, struct type *);\
390 attr struct type *name##_RB_REMOVE(struct name *, struct type *);	\
391 attr struct type *name##_RB_INSERT(struct name *, struct type *);	\
392 attr struct type *name##_RB_FIND(struct name *, struct type *);		\
393 attr struct type *name##_RB_NFIND(struct name *, struct type *);	\
394 attr struct type *name##_RB_NEXT(struct type *);			\
395 attr struct type *name##_RB_PREV(struct type *);			\
396 attr struct type *name##_RB_MINMAX(struct name *, int);			\
397 									\
398 
399 /* Main rb operation.
400  * Moves node close to the key of elm to top
401  */
402 #define	RB_GENERATE(name, type, field, cmp)				\
403 	RB_GENERATE_INTERNAL(name, type, field, cmp,)
404 #define	RB_GENERATE_STATIC(name, type, field, cmp)			\
405 	RB_GENERATE_INTERNAL(name, type, field, cmp, __attribute__((__unused__)) static)
406 #define RB_GENERATE_INTERNAL(name, type, field, cmp, attr)		\
407 attr void								\
408 name##_RB_INSERT_COLOR(struct name *head, struct type *elm)		\
409 {									\
410 	struct type *parent, *gparent, *tmp;				\
411 	while ((parent = RB_PARENT(elm, field)) &&			\
412 	    RB_COLOR(parent, field) == RB_RED) {			\
413 		gparent = RB_PARENT(parent, field);			\
414 		if (parent == RB_LEFT(gparent, field)) {		\
415 			tmp = RB_RIGHT(gparent, field);			\
416 			if (tmp && RB_COLOR(tmp, field) == RB_RED) {	\
417 				RB_COLOR(tmp, field) = RB_BLACK;	\
418 				RB_SET_BLACKRED(parent, gparent, field);\
419 				elm = gparent;				\
420 				continue;				\
421 			}						\
422 			if (RB_RIGHT(parent, field) == elm) {		\
423 				RB_ROTATE_LEFT(head, parent, tmp, field);\
424 				tmp = parent;				\
425 				parent = elm;				\
426 				elm = tmp;				\
427 			}						\
428 			RB_SET_BLACKRED(parent, gparent, field);	\
429 			RB_ROTATE_RIGHT(head, gparent, tmp, field);	\
430 		} else {						\
431 			tmp = RB_LEFT(gparent, field);			\
432 			if (tmp && RB_COLOR(tmp, field) == RB_RED) {	\
433 				RB_COLOR(tmp, field) = RB_BLACK;	\
434 				RB_SET_BLACKRED(parent, gparent, field);\
435 				elm = gparent;				\
436 				continue;				\
437 			}						\
438 			if (RB_LEFT(parent, field) == elm) {		\
439 				RB_ROTATE_RIGHT(head, parent, tmp, field);\
440 				tmp = parent;				\
441 				parent = elm;				\
442 				elm = tmp;				\
443 			}						\
444 			RB_SET_BLACKRED(parent, gparent, field);	\
445 			RB_ROTATE_LEFT(head, gparent, tmp, field);	\
446 		}							\
447 	}								\
448 	RB_COLOR(head->rbh_root, field) = RB_BLACK;			\
449 }									\
450 									\
451 attr void								\
452 name##_RB_REMOVE_COLOR(struct name *head, struct type *parent, struct type *elm) \
453 {									\
454 	struct type *tmp;						\
455 	while ((elm == NULL || RB_COLOR(elm, field) == RB_BLACK) &&	\
456 	    elm != RB_ROOT(head)) {					\
457 		if (RB_LEFT(parent, field) == elm) {			\
458 			tmp = RB_RIGHT(parent, field);			\
459 			if (RB_COLOR(tmp, field) == RB_RED) {		\
460 				RB_SET_BLACKRED(tmp, parent, field);	\
461 				RB_ROTATE_LEFT(head, parent, tmp, field);\
462 				tmp = RB_RIGHT(parent, field);		\
463 			}						\
464 			if ((RB_LEFT(tmp, field) == NULL ||		\
465 			    RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
466 			    (RB_RIGHT(tmp, field) == NULL ||		\
467 			    RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
468 				RB_COLOR(tmp, field) = RB_RED;		\
469 				elm = parent;				\
470 				parent = RB_PARENT(elm, field);		\
471 			} else {					\
472 				if (RB_RIGHT(tmp, field) == NULL ||	\
473 				    RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK) {\
474 					struct type *oleft;		\
475 					if ((oleft = RB_LEFT(tmp, field)))\
476 						RB_COLOR(oleft, field) = RB_BLACK;\
477 					RB_COLOR(tmp, field) = RB_RED;	\
478 					RB_ROTATE_RIGHT(head, tmp, oleft, field);\
479 					tmp = RB_RIGHT(parent, field);	\
480 				}					\
481 				RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
482 				RB_COLOR(parent, field) = RB_BLACK;	\
483 				if (RB_RIGHT(tmp, field))		\
484 					RB_COLOR(RB_RIGHT(tmp, field), field) = RB_BLACK;\
485 				RB_ROTATE_LEFT(head, parent, tmp, field);\
486 				elm = RB_ROOT(head);			\
487 				break;					\
488 			}						\
489 		} else {						\
490 			tmp = RB_LEFT(parent, field);			\
491 			if (RB_COLOR(tmp, field) == RB_RED) {		\
492 				RB_SET_BLACKRED(tmp, parent, field);	\
493 				RB_ROTATE_RIGHT(head, parent, tmp, field);\
494 				tmp = RB_LEFT(parent, field);		\
495 			}						\
496 			if ((RB_LEFT(tmp, field) == NULL ||		\
497 			    RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
498 			    (RB_RIGHT(tmp, field) == NULL ||		\
499 			    RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
500 				RB_COLOR(tmp, field) = RB_RED;		\
501 				elm = parent;				\
502 				parent = RB_PARENT(elm, field);		\
503 			} else {					\
504 				if (RB_LEFT(tmp, field) == NULL ||	\
505 				    RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) {\
506 					struct type *oright;		\
507 					if ((oright = RB_RIGHT(tmp, field)))\
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 									\
527 attr struct type *							\
528 name##_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)))			\
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)));	\
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;					\
588 color:									\
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 */					\
595 attr struct type *							\
596 name##_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 */				\
626 attr struct type *							\
627 name##_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 */	\
644 attr struct type *							\
645 name##_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 */								\
665 attr struct type *							\
666 name##_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 */								\
687 attr struct type *							\
688 name##_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 									\
708 attr struct type *							\
709 name##_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);						\
721 }
722 
723 #define RB_NEGINF	-1
724 #define RB_INF	1
725 
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_SAFE(x, name, head, y)				\
741 	for ((x) = RB_MIN(name, head);					\
742 	    ((x) != NULL) && ((y) = name##_RB_NEXT(x), 1);		\
743 	     (x) = (y))
744 
745 #define RB_FOREACH_REVERSE(x, name, head)				\
746 	for ((x) = RB_MAX(name, head);					\
747 	     (x) != NULL;						\
748 	     (x) = name##_RB_PREV(x))
749 
750 #define RB_FOREACH_REVERSE_SAFE(x, name, head, y)			\
751 	for ((x) = RB_MAX(name, head);					\
752 	    ((x) != NULL) && ((y) = name##_RB_PREV(x), 1);		\
753 	     (x) = (y))
754 
755 #endif	/* _SYS_TREE_H_ */
756