xref: /titanic_41/usr/src/cmd/ssh/include/sys-tree.h (revision 1ae0874509b6811fdde1dfd46f0d93fd09867a3f)
1 /*	$OpenBSD: tree.h,v 1.6 2002/06/11 22:09:52 provos 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 #ifndef	_SYS_TREE_H
28 #define	_SYS_TREE_H
29 
30 #pragma ident	"%Z%%M%	%I%	%E% SMI"
31 
32 #ifdef __cplusplus
33 extern "C" {
34 #endif
35 
36 /*
37  * This file defines data structures for different types of trees:
38  * splay trees and red-black trees.
39  *
40  * A splay tree is a self-organizing data structure.  Every operation
41  * on the tree causes a splay to happen.  The splay moves the requested
42  * node to the root of the tree and partly rebalances it.
43  *
44  * This has the benefit that request locality causes faster lookups as
45  * the requested nodes move to the top of the tree.  On the other hand,
46  * every lookup causes memory writes.
47  *
48  * The Balance Theorem bounds the total access time for m operations
49  * and n inserts on an initially empty tree as O((m + n)lg n).  The
50  * amortized cost for a sequence of m accesses to a splay tree is O(lg n);
51  *
52  * A red-black tree is a binary search tree with the node color as an
53  * extra attribute.  It fulfills a set of conditions:
54  *	- every search path from the root to a leaf consists of the
55  *	  same number of black nodes,
56  *	- each red node (except for the root) has a black parent,
57  *	- each leaf node is black.
58  *
59  * Every operation on a red-black tree is bounded as O(lg n).
60  * The maximum height of a red-black tree is 2lg (n+1).
61  */
62 
63 #define SPLAY_HEAD(name, type)						\
64 struct name {								\
65 	struct type *sph_root; /* root of the tree */			\
66 }
67 
68 #define SPLAY_INITIALIZER(root)						\
69 	{ NULL }
70 
71 #define SPLAY_INIT(root) do {						\
72 	(root)->sph_root = NULL;					\
73 } while (0)
74 
75 #define SPLAY_ENTRY(type)						\
76 struct {								\
77 	struct type *spe_left; /* left element */			\
78 	struct type *spe_right; /* right element */			\
79 }
80 
81 #define SPLAY_LEFT(elm, field)		(elm)->field.spe_left
82 #define SPLAY_RIGHT(elm, field)		(elm)->field.spe_right
83 #define SPLAY_ROOT(head)		(head)->sph_root
84 #define SPLAY_EMPTY(head)		(SPLAY_ROOT(head) == NULL)
85 
86 /* SPLAY_ROTATE_{LEFT,RIGHT} expect that tmp hold SPLAY_{RIGHT,LEFT} */
87 #define SPLAY_ROTATE_RIGHT(head, tmp, field) do {			\
88 	SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(tmp, field);	\
89 	SPLAY_RIGHT(tmp, field) = (head)->sph_root;			\
90 	(head)->sph_root = tmp;						\
91 } while (0)
92 
93 #define SPLAY_ROTATE_LEFT(head, tmp, field) do {			\
94 	SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(tmp, field);	\
95 	SPLAY_LEFT(tmp, field) = (head)->sph_root;			\
96 	(head)->sph_root = tmp;						\
97 } while (0)
98 
99 #define SPLAY_LINKLEFT(head, tmp, field) do {				\
100 	SPLAY_LEFT(tmp, field) = (head)->sph_root;			\
101 	tmp = (head)->sph_root;						\
102 	(head)->sph_root = SPLAY_LEFT((head)->sph_root, field);		\
103 } while (0)
104 
105 #define SPLAY_LINKRIGHT(head, tmp, field) do {				\
106 	SPLAY_RIGHT(tmp, field) = (head)->sph_root;			\
107 	tmp = (head)->sph_root;						\
108 	(head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);	\
109 } while (0)
110 
111 #define SPLAY_ASSEMBLE(head, node, left, right, field) do {		\
112 	SPLAY_RIGHT(left, field) = SPLAY_LEFT((head)->sph_root, field);	\
113 	SPLAY_LEFT(right, field) = SPLAY_RIGHT((head)->sph_root, field);\
114 	SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(node, field);	\
115 	SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(node, field);	\
116 } while (0)
117 
118 /* Generates prototypes and inline functions */
119 
120 #define SPLAY_PROTOTYPE(name, type, field, cmp)				\
121 void name##_SPLAY(struct name *, struct type *);			\
122 void name##_SPLAY_MINMAX(struct name *, int);				\
123 struct type *name##_SPLAY_INSERT(struct name *, struct type *);		\
124 struct type *name##_SPLAY_REMOVE(struct name *, struct type *);		\
125 									\
126 /* Finds the node with the same key as elm */				\
127 static __inline struct type *						\
128 name##_SPLAY_FIND(struct name *head, struct type *elm)			\
129 {									\
130 	if (SPLAY_EMPTY(head))						\
131 		return(NULL);						\
132 	name##_SPLAY(head, elm);					\
133 	if ((cmp)(elm, (head)->sph_root) == 0)				\
134 		return (head->sph_root);				\
135 	return (NULL);							\
136 }									\
137 									\
138 static __inline struct type *						\
139 name##_SPLAY_NEXT(struct name *head, struct type *elm)			\
140 {									\
141 	name##_SPLAY(head, elm);					\
142 	if (SPLAY_RIGHT(elm, field) != NULL) {				\
143 		elm = SPLAY_RIGHT(elm, field);				\
144 		while (SPLAY_LEFT(elm, field) != NULL) {		\
145 			elm = SPLAY_LEFT(elm, field);			\
146 		}							\
147 	} else								\
148 		elm = NULL;						\
149 	return (elm);							\
150 }									\
151 									\
152 static __inline struct type *						\
153 name##_SPLAY_MIN_MAX(struct name *head, int val)			\
154 {									\
155 	name##_SPLAY_MINMAX(head, val);					\
156         return (SPLAY_ROOT(head));					\
157 }
158 
159 /* Main splay operation.
160  * Moves node close to the key of elm to top
161  */
162 #define SPLAY_GENERATE(name, type, field, cmp)				\
163 struct type *								\
164 name##_SPLAY_INSERT(struct name *head, struct type *elm)		\
165 {									\
166     if (SPLAY_EMPTY(head)) {						\
167 	    SPLAY_LEFT(elm, field) = SPLAY_RIGHT(elm, field) = NULL;	\
168     } else {								\
169 	    int __comp;							\
170 	    name##_SPLAY(head, elm);					\
171 	    __comp = (cmp)(elm, (head)->sph_root);			\
172 	    if(__comp < 0) {						\
173 		    SPLAY_LEFT(elm, field) = SPLAY_LEFT((head)->sph_root, field);\
174 		    SPLAY_RIGHT(elm, field) = (head)->sph_root;		\
175 		    SPLAY_LEFT((head)->sph_root, field) = NULL;		\
176 	    } else if (__comp > 0) {					\
177 		    SPLAY_RIGHT(elm, field) = SPLAY_RIGHT((head)->sph_root, field);\
178 		    SPLAY_LEFT(elm, field) = (head)->sph_root;		\
179 		    SPLAY_RIGHT((head)->sph_root, field) = NULL;	\
180 	    } else							\
181 		    return ((head)->sph_root);				\
182     }									\
183     (head)->sph_root = (elm);						\
184     return (NULL);							\
185 }									\
186 									\
187 struct type *								\
188 name##_SPLAY_REMOVE(struct name *head, struct type *elm)		\
189 {									\
190 	struct type *__tmp;						\
191 	if (SPLAY_EMPTY(head))						\
192 		return (NULL);						\
193 	name##_SPLAY(head, elm);					\
194 	if ((cmp)(elm, (head)->sph_root) == 0) {			\
195 		if (SPLAY_LEFT((head)->sph_root, field) == NULL) {	\
196 			(head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);\
197 		} else {						\
198 			__tmp = SPLAY_RIGHT((head)->sph_root, field);	\
199 			(head)->sph_root = SPLAY_LEFT((head)->sph_root, field);\
200 			name##_SPLAY(head, elm);			\
201 			SPLAY_RIGHT((head)->sph_root, field) = __tmp;	\
202 		}							\
203 		return (elm);						\
204 	}								\
205 	return (NULL);							\
206 }									\
207 									\
208 void									\
209 name##_SPLAY(struct name *head, struct type *elm)			\
210 {									\
211 	struct type __node, *__left, *__right, *__tmp;			\
212 	int __comp;							\
213 \
214 	SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
215 	__left = __right = &__node;					\
216 \
217 	while ((__comp = (cmp)(elm, (head)->sph_root))) {		\
218 		if (__comp < 0) {					\
219 			__tmp = SPLAY_LEFT((head)->sph_root, field);	\
220 			if (__tmp == NULL)				\
221 				break;					\
222 			if ((cmp)(elm, __tmp) < 0){			\
223 				SPLAY_ROTATE_RIGHT(head, __tmp, field);	\
224 				if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
225 					break;				\
226 			}						\
227 			SPLAY_LINKLEFT(head, __right, field);		\
228 		} else if (__comp > 0) {				\
229 			__tmp = SPLAY_RIGHT((head)->sph_root, field);	\
230 			if (__tmp == NULL)				\
231 				break;					\
232 			if ((cmp)(elm, __tmp) > 0){			\
233 				SPLAY_ROTATE_LEFT(head, __tmp, field);	\
234 				if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
235 					break;				\
236 			}						\
237 			SPLAY_LINKRIGHT(head, __left, field);		\
238 		}							\
239 	}								\
240 	SPLAY_ASSEMBLE(head, &__node, __left, __right, field);		\
241 }									\
242 									\
243 /* Splay with either the minimum or the maximum element			\
244  * Used to find minimum or maximum element in tree.			\
245  */									\
246 void name##_SPLAY_MINMAX(struct name *head, int __comp) \
247 {									\
248 	struct type __node, *__left, *__right, *__tmp;			\
249 \
250 	SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
251 	__left = __right = &__node;					\
252 \
253 	while (1) {							\
254 		if (__comp < 0) {					\
255 			__tmp = SPLAY_LEFT((head)->sph_root, field);	\
256 			if (__tmp == NULL)				\
257 				break;					\
258 			if (__comp < 0){				\
259 				SPLAY_ROTATE_RIGHT(head, __tmp, field);	\
260 				if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
261 					break;				\
262 			}						\
263 			SPLAY_LINKLEFT(head, __right, field);		\
264 		} else if (__comp > 0) {				\
265 			__tmp = SPLAY_RIGHT((head)->sph_root, field);	\
266 			if (__tmp == NULL)				\
267 				break;					\
268 			if (__comp > 0) {				\
269 				SPLAY_ROTATE_LEFT(head, __tmp, field);	\
270 				if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
271 					break;				\
272 			}						\
273 			SPLAY_LINKRIGHT(head, __left, field);		\
274 		}							\
275 	}								\
276 	SPLAY_ASSEMBLE(head, &__node, __left, __right, field);		\
277 }
278 
279 #define SPLAY_NEGINF	-1
280 #define SPLAY_INF	1
281 
282 #define SPLAY_INSERT(name, x, y)	name##_SPLAY_INSERT(x, y)
283 #define SPLAY_REMOVE(name, x, y)	name##_SPLAY_REMOVE(x, y)
284 #define SPLAY_FIND(name, x, y)		name##_SPLAY_FIND(x, y)
285 #define SPLAY_NEXT(name, x, y)		name##_SPLAY_NEXT(x, y)
286 #define SPLAY_MIN(name, x)		(SPLAY_EMPTY(x) ? NULL	\
287 					: name##_SPLAY_MIN_MAX(x, SPLAY_NEGINF))
288 #define SPLAY_MAX(name, x)		(SPLAY_EMPTY(x) ? NULL	\
289 					: name##_SPLAY_MIN_MAX(x, SPLAY_INF))
290 
291 #define SPLAY_FOREACH(x, name, head)					\
292 	for ((x) = SPLAY_MIN(name, head);				\
293 	     (x) != NULL;						\
294 	     (x) = SPLAY_NEXT(name, head, x))
295 
296 /* Macros that define a red-back tree */
297 #define RB_HEAD(name, type)						\
298 struct name {								\
299 	struct type *rbh_root; /* root of the tree */			\
300 }
301 
302 #define RB_INITIALIZER(root)						\
303 	{ NULL }
304 
305 #define RB_INIT(root) do {						\
306 	(root)->rbh_root = NULL;					\
307 } while (0)
308 
309 #define RB_BLACK	0
310 #define RB_RED		1
311 #define RB_ENTRY(type)							\
312 struct {								\
313 	struct type *rbe_left;		/* left element */		\
314 	struct type *rbe_right;		/* right element */		\
315 	struct type *rbe_parent;	/* parent element */		\
316 	int rbe_color;			/* node color */		\
317 }
318 
319 #define RB_LEFT(elm, field)		(elm)->field.rbe_left
320 #define RB_RIGHT(elm, field)		(elm)->field.rbe_right
321 #define RB_PARENT(elm, field)		(elm)->field.rbe_parent
322 #define RB_COLOR(elm, field)		(elm)->field.rbe_color
323 #define RB_ROOT(head)			(head)->rbh_root
324 #define RB_EMPTY(head)			(RB_ROOT(head) == NULL)
325 
326 #define RB_SET(elm, parent, field) do {					\
327 	RB_PARENT(elm, field) = parent;					\
328 	RB_LEFT(elm, field) = RB_RIGHT(elm, field) = NULL;		\
329 	RB_COLOR(elm, field) = RB_RED;					\
330 } while (0)
331 
332 #define RB_SET_BLACKRED(black, red, field) do {				\
333 	RB_COLOR(black, field) = RB_BLACK;				\
334 	RB_COLOR(red, field) = RB_RED;					\
335 } while (0)
336 
337 #ifndef RB_AUGMENT
338 #define RB_AUGMENT(x)
339 #endif
340 
341 #define RB_ROTATE_LEFT(head, elm, tmp, field) do {			\
342 	(tmp) = RB_RIGHT(elm, field);					\
343 	if ((RB_RIGHT(elm, field) = RB_LEFT(tmp, field))) {		\
344 		RB_PARENT(RB_LEFT(tmp, field), field) = (elm);		\
345 	}								\
346 	RB_AUGMENT(elm);						\
347 	if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field))) {		\
348 		if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))	\
349 			RB_LEFT(RB_PARENT(elm, field), field) = (tmp);	\
350 		else							\
351 			RB_RIGHT(RB_PARENT(elm, field), field) = (tmp);	\
352 		RB_AUGMENT(RB_PARENT(elm, field));			\
353 	} else								\
354 		(head)->rbh_root = (tmp);				\
355 	RB_LEFT(tmp, field) = (elm);					\
356 	RB_PARENT(elm, field) = (tmp);					\
357 	RB_AUGMENT(tmp);						\
358 } while (0)
359 
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))) {		\
363 		RB_PARENT(RB_RIGHT(tmp, field), field) = (elm);		\
364 	}								\
365 	RB_AUGMENT(elm);						\
366 	if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field))) {		\
367 		if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))	\
368 			RB_LEFT(RB_PARENT(elm, field), field) = (tmp);	\
369 		else							\
370 			RB_RIGHT(RB_PARENT(elm, field), field) = (tmp);	\
371 		RB_AUGMENT(RB_PARENT(elm, field));			\
372 	} else								\
373 		(head)->rbh_root = (tmp);				\
374 	RB_RIGHT(tmp, field) = (elm);					\
375 	RB_PARENT(elm, field) = (tmp);					\
376 	RB_AUGMENT(tmp);						\
377 } while (0)
378 
379 /* Generates prototypes and inline functions */
380 #define RB_PROTOTYPE(name, type, field, cmp)				\
381 void name##_RB_INSERT_COLOR(struct name *, struct type *);	\
382 void name##_RB_REMOVE_COLOR(struct name *, struct type *, struct type *);\
383 struct type *name##_RB_REMOVE(struct name *, struct type *);		\
384 struct type *name##_RB_INSERT(struct name *, struct type *);		\
385 struct type *name##_RB_FIND(struct name *, struct type *);		\
386 struct type *name##_RB_NEXT(struct name *, struct type *);		\
387 struct type *name##_RB_MINMAX(struct name *, int);			\
388 									\
389 
390 /* Main rb operation.
391  * Moves node close to the key of elm to top
392  */
393 #define RB_GENERATE(name, type, field, cmp)				\
394 void									\
395 name##_RB_INSERT_COLOR(struct name *head, struct type *elm)		\
396 {									\
397 	struct type *parent, *gparent, *tmp;				\
398 	while ((parent = RB_PARENT(elm, field)) &&			\
399 	    RB_COLOR(parent, field) == RB_RED) {			\
400 		gparent = RB_PARENT(parent, field);			\
401 		if (parent == RB_LEFT(gparent, field)) {		\
402 			tmp = RB_RIGHT(gparent, field);			\
403 			if (tmp && RB_COLOR(tmp, field) == RB_RED) {	\
404 				RB_COLOR(tmp, field) = RB_BLACK;	\
405 				RB_SET_BLACKRED(parent, gparent, field);\
406 				elm = gparent;				\
407 				continue;				\
408 			}						\
409 			if (RB_RIGHT(parent, field) == elm) {		\
410 				RB_ROTATE_LEFT(head, parent, tmp, field);\
411 				tmp = parent;				\
412 				parent = elm;				\
413 				elm = tmp;				\
414 			}						\
415 			RB_SET_BLACKRED(parent, gparent, field);	\
416 			RB_ROTATE_RIGHT(head, gparent, tmp, field);	\
417 		} else {						\
418 			tmp = RB_LEFT(gparent, field);			\
419 			if (tmp && RB_COLOR(tmp, field) == RB_RED) {	\
420 				RB_COLOR(tmp, field) = RB_BLACK;	\
421 				RB_SET_BLACKRED(parent, gparent, field);\
422 				elm = gparent;				\
423 				continue;				\
424 			}						\
425 			if (RB_LEFT(parent, field) == elm) {		\
426 				RB_ROTATE_RIGHT(head, parent, tmp, field);\
427 				tmp = parent;				\
428 				parent = elm;				\
429 				elm = tmp;				\
430 			}						\
431 			RB_SET_BLACKRED(parent, gparent, field);	\
432 			RB_ROTATE_LEFT(head, gparent, tmp, field);	\
433 		}							\
434 	}								\
435 	RB_COLOR(head->rbh_root, field) = RB_BLACK;			\
436 }									\
437 									\
438 void									\
439 name##_RB_REMOVE_COLOR(struct name *head, struct type *parent, struct type *elm) \
440 {									\
441 	struct type *tmp;						\
442 	while ((elm == NULL || RB_COLOR(elm, field) == RB_BLACK) &&	\
443 	    elm != RB_ROOT(head)) {					\
444 		if (RB_LEFT(parent, field) == elm) {			\
445 			tmp = RB_RIGHT(parent, field);			\
446 			if (RB_COLOR(tmp, field) == RB_RED) {		\
447 				RB_SET_BLACKRED(tmp, parent, field);	\
448 				RB_ROTATE_LEFT(head, parent, tmp, field);\
449 				tmp = RB_RIGHT(parent, field);		\
450 			}						\
451 			if ((RB_LEFT(tmp, field) == NULL ||		\
452 			    RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
453 			    (RB_RIGHT(tmp, field) == NULL ||		\
454 			    RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
455 				RB_COLOR(tmp, field) = RB_RED;		\
456 				elm = parent;				\
457 				parent = RB_PARENT(elm, field);		\
458 			} else {					\
459 				if (RB_RIGHT(tmp, field) == NULL ||	\
460 				    RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK) {\
461 					struct type *oleft;		\
462 					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);	\
467 				}					\
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);			\
474 				break;					\
475 			}						\
476 		} else {						\
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);		\
482 			}						\
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;		\
488 				elm = parent;				\
489 				parent = RB_PARENT(elm, field);		\
490 			} else {					\
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)))\
495 						RB_COLOR(oright, field) = RB_BLACK;\
496 					RB_COLOR(tmp, field) = RB_RED;	\
497 					RB_ROTATE_LEFT(head, tmp, oright, field);\
498 					tmp = RB_LEFT(parent, field);	\
499 				}					\
500 				RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
501 				RB_COLOR(parent, field) = RB_BLACK;	\
502 				if (RB_LEFT(tmp, field))		\
503 					RB_COLOR(RB_LEFT(tmp, field), field) = RB_BLACK;\
504 				RB_ROTATE_RIGHT(head, parent, tmp, field);\
505 				elm = RB_ROOT(head);			\
506 				break;					\
507 			}						\
508 		}							\
509 	}								\
510 	if (elm)							\
511 		RB_COLOR(elm, field) = RB_BLACK;			\
512 }									\
513 									\
514 struct type *								\
515 name##_RB_REMOVE(struct name *head, struct type *elm)			\
516 {									\
517 	struct type *child, *parent, *old = elm;			\
518 	int color;							\
519 	if (RB_LEFT(elm, field) == NULL)				\
520 		child = RB_RIGHT(elm, field);				\
521 	else if (RB_RIGHT(elm, field) == NULL)				\
522 		child = RB_LEFT(elm, field);				\
523 	else {								\
524 		struct type *left;					\
525 		elm = RB_RIGHT(elm, field);				\
526 		while ((left = RB_LEFT(elm, field)))			\
527 			elm = left;					\
528 		child = RB_RIGHT(elm, field);				\
529 		parent = RB_PARENT(elm, field);				\
530 		color = RB_COLOR(elm, field);				\
531 		if (child)						\
532 			RB_PARENT(child, field) = parent;		\
533 		if (parent) {						\
534 			if (RB_LEFT(parent, field) == elm)		\
535 				RB_LEFT(parent, field) = child;		\
536 			else						\
537 				RB_RIGHT(parent, field) = child;	\
538 			RB_AUGMENT(parent);				\
539 		} else							\
540 			RB_ROOT(head) = child;				\
541 		if (RB_PARENT(elm, field) == old)			\
542 			parent = elm;					\
543 		(elm)->field = (old)->field;				\
544 		if (RB_PARENT(old, field)) {				\
545 			if (RB_LEFT(RB_PARENT(old, field), field) == old)\
546 				RB_LEFT(RB_PARENT(old, field), field) = elm;\
547 			else						\
548 				RB_RIGHT(RB_PARENT(old, field), field) = elm;\
549 			RB_AUGMENT(RB_PARENT(old, field));		\
550 		} else							\
551 			RB_ROOT(head) = elm;				\
552 		RB_PARENT(RB_LEFT(old, field), field) = elm;		\
553 		if (RB_RIGHT(old, field))				\
554 			RB_PARENT(RB_RIGHT(old, field), field) = elm;	\
555 		if (parent) {						\
556 			left = parent;					\
557 			do {						\
558 				RB_AUGMENT(left);			\
559 			} while ((left = RB_PARENT(left, field)));	\
560 		}							\
561 		goto color;						\
562 	}								\
563 	parent = RB_PARENT(elm, field);					\
564 	color = RB_COLOR(elm, field);					\
565 	if (child)							\
566 		RB_PARENT(child, field) = parent;			\
567 	if (parent) {							\
568 		if (RB_LEFT(parent, field) == elm)			\
569 			RB_LEFT(parent, field) = child;			\
570 		else							\
571 			RB_RIGHT(parent, field) = child;		\
572 		RB_AUGMENT(parent);					\
573 	} else								\
574 		RB_ROOT(head) = child;					\
575 color:									\
576 	if (color == RB_BLACK)						\
577 		name##_RB_REMOVE_COLOR(head, parent, child);		\
578 	return (old);							\
579 }									\
580 									\
581 /* Inserts a node into the RB tree */					\
582 struct type *								\
583 name##_RB_INSERT(struct name *head, struct type *elm)			\
584 {									\
585 	struct type *tmp;						\
586 	struct type *parent = NULL;					\
587 	int comp = 0;							\
588 	tmp = RB_ROOT(head);						\
589 	while (tmp) {							\
590 		parent = tmp;						\
591 		comp = (cmp)(elm, parent);				\
592 		if (comp < 0)						\
593 			tmp = RB_LEFT(tmp, field);			\
594 		else if (comp > 0)					\
595 			tmp = RB_RIGHT(tmp, field);			\
596 		else							\
597 			return (tmp);					\
598 	}								\
599 	RB_SET(elm, parent, field);					\
600 	if (parent != NULL) {						\
601 		if (comp < 0)						\
602 			RB_LEFT(parent, field) = elm;			\
603 		else							\
604 			RB_RIGHT(parent, field) = elm;			\
605 		RB_AUGMENT(parent);					\
606 	} else								\
607 		RB_ROOT(head) = elm;					\
608 	name##_RB_INSERT_COLOR(head, elm);				\
609 	return (NULL);							\
610 }									\
611 									\
612 /* Finds the node with the same key as elm */				\
613 struct type *								\
614 name##_RB_FIND(struct name *head, struct type *elm)			\
615 {									\
616 	struct type *tmp = RB_ROOT(head);				\
617 	int comp;							\
618 	while (tmp) {							\
619 		comp = cmp(elm, tmp);					\
620 		if (comp < 0)						\
621 			tmp = RB_LEFT(tmp, field);			\
622 		else if (comp > 0)					\
623 			tmp = RB_RIGHT(tmp, field);			\
624 		else							\
625 			return (tmp);					\
626 	}								\
627 	return (NULL);							\
628 }									\
629 									\
630 struct type *								\
631 name##_RB_NEXT(struct name *head, struct type *elm)			\
632 {									\
633 	if (RB_RIGHT(elm, field)) {					\
634 		elm = RB_RIGHT(elm, field);				\
635 		while (RB_LEFT(elm, field))				\
636 			elm = RB_LEFT(elm, field);			\
637 	} else {							\
638 		if (RB_PARENT(elm, field) &&				\
639 		    (elm == RB_LEFT(RB_PARENT(elm, field), field)))	\
640 			elm = RB_PARENT(elm, field);			\
641 		else {							\
642 			while (RB_PARENT(elm, field) &&			\
643 			    (elm == RB_RIGHT(RB_PARENT(elm, field), field)))\
644 				elm = RB_PARENT(elm, field);		\
645 			elm = RB_PARENT(elm, field);			\
646 		}							\
647 	}								\
648 	return (elm);							\
649 }									\
650 									\
651 struct type *								\
652 name##_RB_MINMAX(struct name *head, int val)				\
653 {									\
654 	struct type *tmp = RB_ROOT(head);				\
655 	struct type *parent = NULL;					\
656 	while (tmp) {							\
657 		parent = tmp;						\
658 		if (val < 0)						\
659 			tmp = RB_LEFT(tmp, field);			\
660 		else							\
661 			tmp = RB_RIGHT(tmp, field);			\
662 	}								\
663 	return (parent);						\
664 }
665 
666 #define RB_NEGINF	-1
667 #define RB_INF	1
668 
669 #define RB_INSERT(name, x, y)	name##_RB_INSERT(x, y)
670 #define RB_REMOVE(name, x, y)	name##_RB_REMOVE(x, y)
671 #define RB_FIND(name, x, y)	name##_RB_FIND(x, y)
672 #define RB_NEXT(name, x, y)	name##_RB_NEXT(x, y)
673 #define RB_MIN(name, x)		name##_RB_MINMAX(x, RB_NEGINF)
674 #define RB_MAX(name, x)		name##_RB_MINMAX(x, RB_INF)
675 
676 #define RB_FOREACH(x, name, head)					\
677 	for ((x) = RB_MIN(name, head);					\
678 	     (x) != NULL;						\
679 	     (x) = name##_RB_NEXT(head, x))
680 
681 #ifdef __cplusplus
682 }
683 #endif
684 
685 #endif /* _SYS_TREE_H */
686