xref: /minix3/external/bsd/libevent/dist/WIN32-Code/tree.h (revision b80da2a01d0bb632707b7b4e974aa32eaebbcc6f)
1 /*	$NetBSD: tree.h,v 1.1.1.1 2013/04/11 16:43:33 christos Exp $	*/
2 /*	$OpenBSD: tree.h,v 1.7 2002/10/17 21:51:54 art Exp $	*/
3 /*
4  * Copyright 2002 Niels Provos <provos@citi.umich.edu>
5  * All rights reserved.
6  *
7  * Redistribution and use in source and binary forms, with or without
8  * modification, are permitted provided that the following conditions
9  * are met:
10  * 1. Redistributions of source code must retain the above copyright
11  *    notice, this list of conditions and the following disclaimer.
12  * 2. Redistributions in binary form must reproduce the above copyright
13  *    notice, this list of conditions and the following disclaimer in the
14  *    documentation and/or other materials provided with the distribution.
15  *
16  * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
17  * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
18  * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
19  * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
20  * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
21  * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
22  * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
23  * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
24  * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
25  * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
26  */
27 
28 #ifndef	_SYS_TREE_H_
29 #define	_SYS_TREE_H_
30 
31 /*
32  * This file defines data structures for different types of trees:
33  * splay trees and red-black trees.
34  *
35  * A splay tree is a self-organizing data structure.  Every operation
36  * on the tree causes a splay to happen.  The splay moves the requested
37  * node to the root of the tree and partly rebalances it.
38  *
39  * This has the benefit that request locality causes faster lookups as
40  * the requested nodes move to the top of the tree.  On the other hand,
41  * every lookup causes memory writes.
42  *
43  * The Balance Theorem bounds the total access time for m operations
44  * and n inserts on an initially empty tree as O((m + n)lg n).  The
45  * amortized cost for a sequence of m accesses to a splay tree is O(lg n);
46  *
47  * A red-black tree is a binary search tree with the node color as an
48  * extra attribute.  It fulfills a set of conditions:
49  *	- every search path from the root to a leaf consists of the
50  *	  same number of black nodes,
51  *	- each red node (except for the root) has a black parent,
52  *	- each leaf node is black.
53  *
54  * Every operation on a red-black tree is bounded as O(lg n).
55  * The maximum height of a red-black tree is 2lg (n+1).
56  */
57 
58 #define SPLAY_HEAD(name, type)						\
59 struct name {								\
60 	struct type *sph_root; /* root of the tree */			\
61 }
62 
63 #define SPLAY_INITIALIZER(root)						\
64 	{ NULL }
65 
66 #define SPLAY_INIT(root) do {						\
67 	(root)->sph_root = NULL;					\
68 } while (0)
69 
70 #define SPLAY_ENTRY(type)						\
71 struct {								\
72 	struct type *spe_left; /* left element */			\
73 	struct type *spe_right; /* right element */			\
74 }
75 
76 #define SPLAY_LEFT(elm, field)		(elm)->field.spe_left
77 #define SPLAY_RIGHT(elm, field)		(elm)->field.spe_right
78 #define SPLAY_ROOT(head)		(head)->sph_root
79 #define SPLAY_EMPTY(head)		(SPLAY_ROOT(head) == NULL)
80 
81 /* SPLAY_ROTATE_{LEFT,RIGHT} expect that tmp hold SPLAY_{RIGHT,LEFT} */
82 #define SPLAY_ROTATE_RIGHT(head, tmp, field) do {			\
83 	SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(tmp, field);	\
84 	SPLAY_RIGHT(tmp, field) = (head)->sph_root;			\
85 	(head)->sph_root = tmp;						\
86 } while (0)
87 
88 #define SPLAY_ROTATE_LEFT(head, tmp, field) do {			\
89 	SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(tmp, field);	\
90 	SPLAY_LEFT(tmp, field) = (head)->sph_root;			\
91 	(head)->sph_root = tmp;						\
92 } while (0)
93 
94 #define SPLAY_LINKLEFT(head, tmp, field) do {				\
95 	SPLAY_LEFT(tmp, field) = (head)->sph_root;			\
96 	tmp = (head)->sph_root;						\
97 	(head)->sph_root = SPLAY_LEFT((head)->sph_root, field);		\
98 } while (0)
99 
100 #define SPLAY_LINKRIGHT(head, tmp, field) do {				\
101 	SPLAY_RIGHT(tmp, field) = (head)->sph_root;			\
102 	tmp = (head)->sph_root;						\
103 	(head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);	\
104 } while (0)
105 
106 #define SPLAY_ASSEMBLE(head, node, left, right, field) do {		\
107 	SPLAY_RIGHT(left, field) = SPLAY_LEFT((head)->sph_root, field);	\
108 	SPLAY_LEFT(right, field) = SPLAY_RIGHT((head)->sph_root, field);\
109 	SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(node, field);	\
110 	SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(node, field);	\
111 } while (0)
112 
113 /* Generates prototypes and inline functions */
114 
115 #define SPLAY_PROTOTYPE(name, type, field, cmp)				\
116 void name##_SPLAY(struct name *, struct type *);			\
117 void name##_SPLAY_MINMAX(struct name *, int);				\
118 struct type *name##_SPLAY_INSERT(struct name *, struct type *);		\
119 struct type *name##_SPLAY_REMOVE(struct name *, struct type *);		\
120 									\
121 /* Finds the node with the same key as elm */				\
122 static __inline struct type *						\
123 name##_SPLAY_FIND(struct name *head, struct type *elm)			\
124 {									\
125 	if (SPLAY_EMPTY(head))						\
126 		return(NULL);						\
127 	name##_SPLAY(head, elm);					\
128 	if ((cmp)(elm, (head)->sph_root) == 0)				\
129 		return (head->sph_root);				\
130 	return (NULL);							\
131 }									\
132 									\
133 static __inline struct type *						\
134 name##_SPLAY_NEXT(struct name *head, struct type *elm)			\
135 {									\
136 	name##_SPLAY(head, elm);					\
137 	if (SPLAY_RIGHT(elm, field) != NULL) {				\
138 		elm = SPLAY_RIGHT(elm, field);				\
139 		while (SPLAY_LEFT(elm, field) != NULL) {		\
140 			elm = SPLAY_LEFT(elm, field);			\
141 		}							\
142 	} else								\
143 		elm = NULL;						\
144 	return (elm);							\
145 }									\
146 									\
147 static __inline struct type *						\
148 name##_SPLAY_MIN_MAX(struct name *head, int val)			\
149 {									\
150 	name##_SPLAY_MINMAX(head, val);					\
151 	return (SPLAY_ROOT(head));					\
152 }
153 
154 /* Main splay operation.
155  * Moves node close to the key of elm to top
156  */
157 #define SPLAY_GENERATE(name, type, field, cmp)				\
158 struct type *								\
159 name##_SPLAY_INSERT(struct name *head, struct type *elm)		\
160 {									\
161     if (SPLAY_EMPTY(head)) {						\
162 	    SPLAY_LEFT(elm, field) = SPLAY_RIGHT(elm, field) = NULL;	\
163     } else {								\
164 	    int __comp;							\
165 	    name##_SPLAY(head, elm);					\
166 	    __comp = (cmp)(elm, (head)->sph_root);			\
167 	    if(__comp < 0) {						\
168 		    SPLAY_LEFT(elm, field) = SPLAY_LEFT((head)->sph_root, field);\
169 		    SPLAY_RIGHT(elm, field) = (head)->sph_root;		\
170 		    SPLAY_LEFT((head)->sph_root, field) = NULL;		\
171 	    } else if (__comp > 0) {					\
172 		    SPLAY_RIGHT(elm, field) = SPLAY_RIGHT((head)->sph_root, field);\
173 		    SPLAY_LEFT(elm, field) = (head)->sph_root;		\
174 		    SPLAY_RIGHT((head)->sph_root, field) = NULL;	\
175 	    } else							\
176 		    return ((head)->sph_root);				\
177     }									\
178     (head)->sph_root = (elm);						\
179     return (NULL);							\
180 }									\
181 									\
182 struct type *								\
183 name##_SPLAY_REMOVE(struct name *head, struct type *elm)		\
184 {									\
185 	struct type *__tmp;						\
186 	if (SPLAY_EMPTY(head))						\
187 		return (NULL);						\
188 	name##_SPLAY(head, elm);					\
189 	if ((cmp)(elm, (head)->sph_root) == 0) {			\
190 		if (SPLAY_LEFT((head)->sph_root, field) == NULL) {	\
191 			(head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);\
192 		} else {						\
193 			__tmp = SPLAY_RIGHT((head)->sph_root, field);	\
194 			(head)->sph_root = SPLAY_LEFT((head)->sph_root, field);\
195 			name##_SPLAY(head, elm);			\
196 			SPLAY_RIGHT((head)->sph_root, field) = __tmp;	\
197 		}							\
198 		return (elm);						\
199 	}								\
200 	return (NULL);							\
201 }									\
202 									\
203 void									\
204 name##_SPLAY(struct name *head, struct type *elm)			\
205 {									\
206 	struct type __node, *__left, *__right, *__tmp;			\
207 	int __comp;							\
208 \
209 	SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
210 	__left = __right = &__node;					\
211 \
212 	while ((__comp = (cmp)(elm, (head)->sph_root))) {		\
213 		if (__comp < 0) {					\
214 			__tmp = SPLAY_LEFT((head)->sph_root, field);	\
215 			if (__tmp == NULL)				\
216 				break;					\
217 			if ((cmp)(elm, __tmp) < 0){			\
218 				SPLAY_ROTATE_RIGHT(head, __tmp, field);	\
219 				if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
220 					break;				\
221 			}						\
222 			SPLAY_LINKLEFT(head, __right, field);		\
223 		} else if (__comp > 0) {				\
224 			__tmp = SPLAY_RIGHT((head)->sph_root, field);	\
225 			if (__tmp == NULL)				\
226 				break;					\
227 			if ((cmp)(elm, __tmp) > 0){			\
228 				SPLAY_ROTATE_LEFT(head, __tmp, field);	\
229 				if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
230 					break;				\
231 			}						\
232 			SPLAY_LINKRIGHT(head, __left, field);		\
233 		}							\
234 	}								\
235 	SPLAY_ASSEMBLE(head, &__node, __left, __right, field);		\
236 }									\
237 									\
238 /* Splay with either the minimum or the maximum element			\
239  * Used to find minimum or maximum element in tree.			\
240  */									\
241 void name##_SPLAY_MINMAX(struct name *head, int __comp) \
242 {									\
243 	struct type __node, *__left, *__right, *__tmp;			\
244 \
245 	SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
246 	__left = __right = &__node;					\
247 \
248 	while (1) {							\
249 		if (__comp < 0) {					\
250 			__tmp = SPLAY_LEFT((head)->sph_root, field);	\
251 			if (__tmp == NULL)				\
252 				break;					\
253 			if (__comp < 0){				\
254 				SPLAY_ROTATE_RIGHT(head, __tmp, field);	\
255 				if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
256 					break;				\
257 			}						\
258 			SPLAY_LINKLEFT(head, __right, field);		\
259 		} else if (__comp > 0) {				\
260 			__tmp = SPLAY_RIGHT((head)->sph_root, field);	\
261 			if (__tmp == NULL)				\
262 				break;					\
263 			if (__comp > 0) {				\
264 				SPLAY_ROTATE_LEFT(head, __tmp, field);	\
265 				if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
266 					break;				\
267 			}						\
268 			SPLAY_LINKRIGHT(head, __left, field);		\
269 		}							\
270 	}								\
271 	SPLAY_ASSEMBLE(head, &__node, __left, __right, field);		\
272 }
273 
274 #define SPLAY_NEGINF	-1
275 #define SPLAY_INF	1
276 
277 #define SPLAY_INSERT(name, x, y)	name##_SPLAY_INSERT(x, y)
278 #define SPLAY_REMOVE(name, x, y)	name##_SPLAY_REMOVE(x, y)
279 #define SPLAY_FIND(name, x, y)		name##_SPLAY_FIND(x, y)
280 #define SPLAY_NEXT(name, x, y)		name##_SPLAY_NEXT(x, y)
281 #define SPLAY_MIN(name, x)		(SPLAY_EMPTY(x) ? NULL	\
282 					: name##_SPLAY_MIN_MAX(x, SPLAY_NEGINF))
283 #define SPLAY_MAX(name, x)		(SPLAY_EMPTY(x) ? NULL	\
284 					: name##_SPLAY_MIN_MAX(x, SPLAY_INF))
285 
286 #define SPLAY_FOREACH(x, name, head)					\
287 	for ((x) = SPLAY_MIN(name, head);				\
288 	     (x) != NULL;						\
289 	     (x) = SPLAY_NEXT(name, head, x))
290 
291 /* Macros that define a red-back tree */
292 #define RB_HEAD(name, type)						\
293 struct name {								\
294 	struct type *rbh_root; /* root of the tree */			\
295 }
296 
297 #define RB_INITIALIZER(root)						\
298 	{ NULL }
299 
300 #define RB_INIT(root) do {						\
301 	(root)->rbh_root = NULL;					\
302 } while (0)
303 
304 #define RB_BLACK	0
305 #define RB_RED		1
306 #define RB_ENTRY(type)							\
307 struct {								\
308 	struct type *rbe_left;		/* left element */		\
309 	struct type *rbe_right;		/* right element */		\
310 	struct type *rbe_parent;	/* parent element */		\
311 	int rbe_color;			/* node color */		\
312 }
313 
314 #define RB_LEFT(elm, field)		(elm)->field.rbe_left
315 #define RB_RIGHT(elm, field)		(elm)->field.rbe_right
316 #define RB_PARENT(elm, field)		(elm)->field.rbe_parent
317 #define RB_COLOR(elm, field)		(elm)->field.rbe_color
318 #define RB_ROOT(head)			(head)->rbh_root
319 #define RB_EMPTY(head)			(RB_ROOT(head) == NULL)
320 
321 #define RB_SET(elm, parent, field) do {					\
322 	RB_PARENT(elm, field) = parent;					\
323 	RB_LEFT(elm, field) = RB_RIGHT(elm, field) = NULL;		\
324 	RB_COLOR(elm, field) = RB_RED;					\
325 } while (0)
326 
327 #define RB_SET_BLACKRED(black, red, field) do {				\
328 	RB_COLOR(black, field) = RB_BLACK;				\
329 	RB_COLOR(red, field) = RB_RED;					\
330 } while (0)
331 
332 #ifndef RB_AUGMENT
333 #define RB_AUGMENT(x)
334 #endif
335 
336 #define RB_ROTATE_LEFT(head, elm, tmp, field) do {			\
337 	(tmp) = RB_RIGHT(elm, field);					\
338 	if ((RB_RIGHT(elm, field) = RB_LEFT(tmp, field))) {		\
339 		RB_PARENT(RB_LEFT(tmp, field), field) = (elm);		\
340 	}								\
341 	RB_AUGMENT(elm);						\
342 	if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field))) {		\
343 		if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))	\
344 			RB_LEFT(RB_PARENT(elm, field), field) = (tmp);	\
345 		else							\
346 			RB_RIGHT(RB_PARENT(elm, field), field) = (tmp);	\
347 	} else								\
348 		(head)->rbh_root = (tmp);				\
349 	RB_LEFT(tmp, field) = (elm);					\
350 	RB_PARENT(elm, field) = (tmp);					\
351 	RB_AUGMENT(tmp);						\
352 	if ((RB_PARENT(tmp, field)))					\
353 		RB_AUGMENT(RB_PARENT(tmp, field));			\
354 } while (0)
355 
356 #define RB_ROTATE_RIGHT(head, elm, tmp, field) do {			\
357 	(tmp) = RB_LEFT(elm, field);					\
358 	if ((RB_LEFT(elm, field) = RB_RIGHT(tmp, field))) {		\
359 		RB_PARENT(RB_RIGHT(tmp, field), field) = (elm);		\
360 	}								\
361 	RB_AUGMENT(elm);						\
362 	if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field))) {		\
363 		if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))	\
364 			RB_LEFT(RB_PARENT(elm, field), field) = (tmp);	\
365 		else							\
366 			RB_RIGHT(RB_PARENT(elm, field), field) = (tmp);	\
367 	} else								\
368 		(head)->rbh_root = (tmp);				\
369 	RB_RIGHT(tmp, field) = (elm);					\
370 	RB_PARENT(elm, field) = (tmp);					\
371 	RB_AUGMENT(tmp);						\
372 	if ((RB_PARENT(tmp, field)))					\
373 		RB_AUGMENT(RB_PARENT(tmp, field));			\
374 } while (0)
375 
376 /* Generates prototypes and inline functions */
377 #define RB_PROTOTYPE(name, type, field, cmp)				\
378 void name##_RB_INSERT_COLOR(struct name *, struct type *);	\
379 void name##_RB_REMOVE_COLOR(struct name *, struct type *, struct type *);\
380 struct type *name##_RB_REMOVE(struct name *, struct type *);		\
381 struct type *name##_RB_INSERT(struct name *, struct type *);		\
382 struct type *name##_RB_FIND(struct name *, struct type *);		\
383 struct type *name##_RB_NEXT(struct type *);				\
384 struct type *name##_RB_MINMAX(struct name *, int);			\
385 									\
386 
387 /* Main rb operation.
388  * Moves node close to the key of elm to top
389  */
390 #define RB_GENERATE(name, type, field, cmp)				\
391 void									\
392 name##_RB_INSERT_COLOR(struct name *head, struct type *elm)		\
393 {									\
394 	struct type *parent, *gparent, *tmp;				\
395 	while ((parent = RB_PARENT(elm, field)) &&			\
396 	    RB_COLOR(parent, field) == RB_RED) {			\
397 		gparent = RB_PARENT(parent, field);			\
398 		if (parent == RB_LEFT(gparent, field)) {		\
399 			tmp = RB_RIGHT(gparent, field);			\
400 			if (tmp && RB_COLOR(tmp, field) == RB_RED) {	\
401 				RB_COLOR(tmp, field) = RB_BLACK;	\
402 				RB_SET_BLACKRED(parent, gparent, field);\
403 				elm = gparent;				\
404 				continue;				\
405 			}						\
406 			if (RB_RIGHT(parent, field) == elm) {		\
407 				RB_ROTATE_LEFT(head, parent, tmp, field);\
408 				tmp = parent;				\
409 				parent = elm;				\
410 				elm = tmp;				\
411 			}						\
412 			RB_SET_BLACKRED(parent, gparent, field);	\
413 			RB_ROTATE_RIGHT(head, gparent, tmp, field);	\
414 		} else {						\
415 			tmp = RB_LEFT(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_LEFT(parent, field) == elm) {		\
423 				RB_ROTATE_RIGHT(head, parent, tmp, field);\
424 				tmp = parent;				\
425 				parent = elm;				\
426 				elm = tmp;				\
427 			}						\
428 			RB_SET_BLACKRED(parent, gparent, field);	\
429 			RB_ROTATE_LEFT(head, gparent, tmp, field);	\
430 		}							\
431 	}								\
432 	RB_COLOR(head->rbh_root, field) = RB_BLACK;			\
433 }									\
434 									\
435 void									\
436 name##_RB_REMOVE_COLOR(struct name *head, struct type *parent, struct type *elm) \
437 {									\
438 	struct type *tmp;						\
439 	while ((elm == NULL || RB_COLOR(elm, field) == RB_BLACK) &&	\
440 	    elm != RB_ROOT(head)) {					\
441 		if (RB_LEFT(parent, field) == elm) {			\
442 			tmp = RB_RIGHT(parent, field);			\
443 			if (RB_COLOR(tmp, field) == RB_RED) {		\
444 				RB_SET_BLACKRED(tmp, parent, field);	\
445 				RB_ROTATE_LEFT(head, parent, tmp, field);\
446 				tmp = RB_RIGHT(parent, field);		\
447 			}						\
448 			if ((RB_LEFT(tmp, field) == NULL ||		\
449 			    RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
450 			    (RB_RIGHT(tmp, field) == NULL ||		\
451 			    RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
452 				RB_COLOR(tmp, field) = RB_RED;		\
453 				elm = parent;				\
454 				parent = RB_PARENT(elm, field);		\
455 			} else {					\
456 				if (RB_RIGHT(tmp, field) == NULL ||	\
457 				    RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK) {\
458 					struct type *oleft;		\
459 					if ((oleft = RB_LEFT(tmp, field)))\
460 						RB_COLOR(oleft, field) = RB_BLACK;\
461 					RB_COLOR(tmp, field) = RB_RED;	\
462 					RB_ROTATE_RIGHT(head, tmp, oleft, field);\
463 					tmp = RB_RIGHT(parent, field);	\
464 				}					\
465 				RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
466 				RB_COLOR(parent, field) = RB_BLACK;	\
467 				if (RB_RIGHT(tmp, field))		\
468 					RB_COLOR(RB_RIGHT(tmp, field), field) = RB_BLACK;\
469 				RB_ROTATE_LEFT(head, parent, tmp, field);\
470 				elm = RB_ROOT(head);			\
471 				break;					\
472 			}						\
473 		} else {						\
474 			tmp = RB_LEFT(parent, field);			\
475 			if (RB_COLOR(tmp, field) == RB_RED) {		\
476 				RB_SET_BLACKRED(tmp, parent, field);	\
477 				RB_ROTATE_RIGHT(head, parent, tmp, field);\
478 				tmp = RB_LEFT(parent, field);		\
479 			}						\
480 			if ((RB_LEFT(tmp, field) == NULL ||		\
481 			    RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
482 			    (RB_RIGHT(tmp, field) == NULL ||		\
483 			    RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
484 				RB_COLOR(tmp, field) = RB_RED;		\
485 				elm = parent;				\
486 				parent = RB_PARENT(elm, field);		\
487 			} else {					\
488 				if (RB_LEFT(tmp, field) == NULL ||	\
489 				    RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) {\
490 					struct type *oright;		\
491 					if ((oright = RB_RIGHT(tmp, field)))\
492 						RB_COLOR(oright, field) = RB_BLACK;\
493 					RB_COLOR(tmp, field) = RB_RED;	\
494 					RB_ROTATE_LEFT(head, tmp, oright, field);\
495 					tmp = RB_LEFT(parent, field);	\
496 				}					\
497 				RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
498 				RB_COLOR(parent, field) = RB_BLACK;	\
499 				if (RB_LEFT(tmp, field))		\
500 					RB_COLOR(RB_LEFT(tmp, field), field) = RB_BLACK;\
501 				RB_ROTATE_RIGHT(head, parent, tmp, field);\
502 				elm = RB_ROOT(head);			\
503 				break;					\
504 			}						\
505 		}							\
506 	}								\
507 	if (elm)							\
508 		RB_COLOR(elm, field) = RB_BLACK;			\
509 }									\
510 									\
511 struct type *								\
512 name##_RB_REMOVE(struct name *head, struct type *elm)			\
513 {									\
514 	struct type *child, *parent, *old = elm;			\
515 	int color;							\
516 	if (RB_LEFT(elm, field) == NULL)				\
517 		child = RB_RIGHT(elm, field);				\
518 	else if (RB_RIGHT(elm, field) == NULL)				\
519 		child = RB_LEFT(elm, field);				\
520 	else {								\
521 		struct type *left;					\
522 		elm = RB_RIGHT(elm, field);				\
523 		while ((left = RB_LEFT(elm, field)))			\
524 			elm = left;					\
525 		child = RB_RIGHT(elm, field);				\
526 		parent = RB_PARENT(elm, field);				\
527 		color = RB_COLOR(elm, field);				\
528 		if (child)						\
529 			RB_PARENT(child, field) = parent;		\
530 		if (parent) {						\
531 			if (RB_LEFT(parent, field) == elm)		\
532 				RB_LEFT(parent, field) = child;		\
533 			else						\
534 				RB_RIGHT(parent, field) = child;	\
535 			RB_AUGMENT(parent);				\
536 		} else							\
537 			RB_ROOT(head) = child;				\
538 		if (RB_PARENT(elm, field) == old)			\
539 			parent = elm;					\
540 		(elm)->field = (old)->field;				\
541 		if (RB_PARENT(old, field)) {				\
542 			if (RB_LEFT(RB_PARENT(old, field), field) == old)\
543 				RB_LEFT(RB_PARENT(old, field), field) = elm;\
544 			else						\
545 				RB_RIGHT(RB_PARENT(old, field), field) = elm;\
546 			RB_AUGMENT(RB_PARENT(old, field));		\
547 		} else							\
548 			RB_ROOT(head) = elm;				\
549 		RB_PARENT(RB_LEFT(old, field), field) = elm;		\
550 		if (RB_RIGHT(old, field))				\
551 			RB_PARENT(RB_RIGHT(old, field), field) = elm;	\
552 		if (parent) {						\
553 			left = parent;					\
554 			do {						\
555 				RB_AUGMENT(left);			\
556 			} while ((left = RB_PARENT(left, field)));	\
557 		}							\
558 		goto color;						\
559 	}								\
560 	parent = RB_PARENT(elm, field);					\
561 	color = RB_COLOR(elm, field);					\
562 	if (child)							\
563 		RB_PARENT(child, field) = parent;			\
564 	if (parent) {							\
565 		if (RB_LEFT(parent, field) == elm)			\
566 			RB_LEFT(parent, field) = child;			\
567 		else							\
568 			RB_RIGHT(parent, field) = child;		\
569 		RB_AUGMENT(parent);					\
570 	} else								\
571 		RB_ROOT(head) = child;					\
572 color:									\
573 	if (color == RB_BLACK)						\
574 		name##_RB_REMOVE_COLOR(head, parent, child);		\
575 	return (old);							\
576 }									\
577 									\
578 /* Inserts a node into the RB tree */					\
579 struct type *								\
580 name##_RB_INSERT(struct name *head, struct type *elm)			\
581 {									\
582 	struct type *tmp;						\
583 	struct type *parent = NULL;					\
584 	int comp = 0;							\
585 	tmp = RB_ROOT(head);						\
586 	while (tmp) {							\
587 		parent = tmp;						\
588 		comp = (cmp)(elm, parent);				\
589 		if (comp < 0)						\
590 			tmp = RB_LEFT(tmp, field);			\
591 		else if (comp > 0)					\
592 			tmp = RB_RIGHT(tmp, field);			\
593 		else							\
594 			return (tmp);					\
595 	}								\
596 	RB_SET(elm, parent, field);					\
597 	if (parent != NULL) {						\
598 		if (comp < 0)						\
599 			RB_LEFT(parent, field) = elm;			\
600 		else							\
601 			RB_RIGHT(parent, field) = elm;			\
602 		RB_AUGMENT(parent);					\
603 	} else								\
604 		RB_ROOT(head) = elm;					\
605 	name##_RB_INSERT_COLOR(head, elm);				\
606 	return (NULL);							\
607 }									\
608 									\
609 /* Finds the node with the same key as elm */				\
610 struct type *								\
611 name##_RB_FIND(struct name *head, struct type *elm)			\
612 {									\
613 	struct type *tmp = RB_ROOT(head);				\
614 	int comp;							\
615 	while (tmp) {							\
616 		comp = cmp(elm, tmp);					\
617 		if (comp < 0)						\
618 			tmp = RB_LEFT(tmp, field);			\
619 		else if (comp > 0)					\
620 			tmp = RB_RIGHT(tmp, field);			\
621 		else							\
622 			return (tmp);					\
623 	}								\
624 	return (NULL);							\
625 }									\
626 									\
627 struct type *								\
628 name##_RB_NEXT(struct type *elm)					\
629 {									\
630 	if (RB_RIGHT(elm, field)) {					\
631 		elm = RB_RIGHT(elm, field);				\
632 		while (RB_LEFT(elm, field))				\
633 			elm = RB_LEFT(elm, field);			\
634 	} else {							\
635 		if (RB_PARENT(elm, field) &&				\
636 		    (elm == RB_LEFT(RB_PARENT(elm, field), field)))	\
637 			elm = RB_PARENT(elm, field);			\
638 		else {							\
639 			while (RB_PARENT(elm, field) &&			\
640 			    (elm == RB_RIGHT(RB_PARENT(elm, field), field)))\
641 				elm = RB_PARENT(elm, field);		\
642 			elm = RB_PARENT(elm, field);			\
643 		}							\
644 	}								\
645 	return (elm);							\
646 }									\
647 									\
648 struct type *								\
649 name##_RB_MINMAX(struct name *head, int val)				\
650 {									\
651 	struct type *tmp = RB_ROOT(head);				\
652 	struct type *parent = NULL;					\
653 	while (tmp) {							\
654 		parent = tmp;						\
655 		if (val < 0)						\
656 			tmp = RB_LEFT(tmp, field);			\
657 		else							\
658 			tmp = RB_RIGHT(tmp, field);			\
659 	}								\
660 	return (parent);						\
661 }
662 
663 #define RB_NEGINF	-1
664 #define RB_INF	1
665 
666 #define RB_INSERT(name, x, y)	name##_RB_INSERT(x, y)
667 #define RB_REMOVE(name, x, y)	name##_RB_REMOVE(x, y)
668 #define RB_FIND(name, x, y)	name##_RB_FIND(x, y)
669 #define RB_NEXT(name, x, y)	name##_RB_NEXT(y)
670 #define RB_MIN(name, x)		name##_RB_MINMAX(x, RB_NEGINF)
671 #define RB_MAX(name, x)		name##_RB_MINMAX(x, RB_INF)
672 
673 #define RB_FOREACH(x, name, head)					\
674 	for ((x) = RB_MIN(name, head);					\
675 	     (x) != NULL;						\
676 	     (x) = name##_RB_NEXT(x))
677 
678 #endif	/* _SYS_TREE_H_ */
679 /*	$OpenBSD: tree.h,v 1.7 2002/10/17 21:51:54 art Exp $	*/
680 /*
681  * Copyright 2002 Niels Provos <provos@citi.umich.edu>
682  * All rights reserved.
683  *
684  * Redistribution and use in source and binary forms, with or without
685  * modification, are permitted provided that the following conditions
686  * are met:
687  * 1. Redistributions of source code must retain the above copyright
688  *    notice, this list of conditions and the following disclaimer.
689  * 2. Redistributions in binary form must reproduce the above copyright
690  *    notice, this list of conditions and the following disclaimer in the
691  *    documentation and/or other materials provided with the distribution.
692  *
693  * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
694  * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
695  * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
696  * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
697  * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
698  * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
699  * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
700  * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
701  * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
702  * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
703  */
704 
705 #ifndef	_SYS_TREE_H_
706 #define	_SYS_TREE_H_
707 
708 /*
709  * This file defines data structures for different types of trees:
710  * splay trees and red-black trees.
711  *
712  * A splay tree is a self-organizing data structure.  Every operation
713  * on the tree causes a splay to happen.  The splay moves the requested
714  * node to the root of the tree and partly rebalances it.
715  *
716  * This has the benefit that request locality causes faster lookups as
717  * the requested nodes move to the top of the tree.  On the other hand,
718  * every lookup causes memory writes.
719  *
720  * The Balance Theorem bounds the total access time for m operations
721  * and n inserts on an initially empty tree as O((m + n)lg n).  The
722  * amortized cost for a sequence of m accesses to a splay tree is O(lg n);
723  *
724  * A red-black tree is a binary search tree with the node color as an
725  * extra attribute.  It fulfills a set of conditions:
726  *	- every search path from the root to a leaf consists of the
727  *	  same number of black nodes,
728  *	- each red node (except for the root) has a black parent,
729  *	- each leaf node is black.
730  *
731  * Every operation on a red-black tree is bounded as O(lg n).
732  * The maximum height of a red-black tree is 2lg (n+1).
733  */
734 
735 #define SPLAY_HEAD(name, type)						\
736 struct name {								\
737 	struct type *sph_root; /* root of the tree */			\
738 }
739 
740 #define SPLAY_INITIALIZER(root)						\
741 	{ NULL }
742 
743 #define SPLAY_INIT(root) do {						\
744 	(root)->sph_root = NULL;					\
745 } while (0)
746 
747 #define SPLAY_ENTRY(type)						\
748 struct {								\
749 	struct type *spe_left; /* left element */			\
750 	struct type *spe_right; /* right element */			\
751 }
752 
753 #define SPLAY_LEFT(elm, field)		(elm)->field.spe_left
754 #define SPLAY_RIGHT(elm, field)		(elm)->field.spe_right
755 #define SPLAY_ROOT(head)		(head)->sph_root
756 #define SPLAY_EMPTY(head)		(SPLAY_ROOT(head) == NULL)
757 
758 /* SPLAY_ROTATE_{LEFT,RIGHT} expect that tmp hold SPLAY_{RIGHT,LEFT} */
759 #define SPLAY_ROTATE_RIGHT(head, tmp, field) do {			\
760 	SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(tmp, field);	\
761 	SPLAY_RIGHT(tmp, field) = (head)->sph_root;			\
762 	(head)->sph_root = tmp;						\
763 } while (0)
764 
765 #define SPLAY_ROTATE_LEFT(head, tmp, field) do {			\
766 	SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(tmp, field);	\
767 	SPLAY_LEFT(tmp, field) = (head)->sph_root;			\
768 	(head)->sph_root = tmp;						\
769 } while (0)
770 
771 #define SPLAY_LINKLEFT(head, tmp, field) do {				\
772 	SPLAY_LEFT(tmp, field) = (head)->sph_root;			\
773 	tmp = (head)->sph_root;						\
774 	(head)->sph_root = SPLAY_LEFT((head)->sph_root, field);		\
775 } while (0)
776 
777 #define SPLAY_LINKRIGHT(head, tmp, field) do {				\
778 	SPLAY_RIGHT(tmp, field) = (head)->sph_root;			\
779 	tmp = (head)->sph_root;						\
780 	(head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);	\
781 } while (0)
782 
783 #define SPLAY_ASSEMBLE(head, node, left, right, field) do {		\
784 	SPLAY_RIGHT(left, field) = SPLAY_LEFT((head)->sph_root, field);	\
785 	SPLAY_LEFT(right, field) = SPLAY_RIGHT((head)->sph_root, field);\
786 	SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(node, field);	\
787 	SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(node, field);	\
788 } while (0)
789 
790 /* Generates prototypes and inline functions */
791 
792 #define SPLAY_PROTOTYPE(name, type, field, cmp)				\
793 void name##_SPLAY(struct name *, struct type *);			\
794 void name##_SPLAY_MINMAX(struct name *, int);				\
795 struct type *name##_SPLAY_INSERT(struct name *, struct type *);		\
796 struct type *name##_SPLAY_REMOVE(struct name *, struct type *);		\
797 									\
798 /* Finds the node with the same key as elm */				\
799 static __inline struct type *						\
800 name##_SPLAY_FIND(struct name *head, struct type *elm)			\
801 {									\
802 	if (SPLAY_EMPTY(head))						\
803 		return(NULL);						\
804 	name##_SPLAY(head, elm);					\
805 	if ((cmp)(elm, (head)->sph_root) == 0)				\
806 		return (head->sph_root);				\
807 	return (NULL);							\
808 }									\
809 									\
810 static __inline struct type *						\
811 name##_SPLAY_NEXT(struct name *head, struct type *elm)			\
812 {									\
813 	name##_SPLAY(head, elm);					\
814 	if (SPLAY_RIGHT(elm, field) != NULL) {				\
815 		elm = SPLAY_RIGHT(elm, field);				\
816 		while (SPLAY_LEFT(elm, field) != NULL) {		\
817 			elm = SPLAY_LEFT(elm, field);			\
818 		}							\
819 	} else								\
820 		elm = NULL;						\
821 	return (elm);							\
822 }									\
823 									\
824 static __inline struct type *						\
825 name##_SPLAY_MIN_MAX(struct name *head, int val)			\
826 {									\
827 	name##_SPLAY_MINMAX(head, val);					\
828 	return (SPLAY_ROOT(head));					\
829 }
830 
831 /* Main splay operation.
832  * Moves node close to the key of elm to top
833  */
834 #define SPLAY_GENERATE(name, type, field, cmp)				\
835 struct type *								\
836 name##_SPLAY_INSERT(struct name *head, struct type *elm)		\
837 {									\
838     if (SPLAY_EMPTY(head)) {						\
839 	    SPLAY_LEFT(elm, field) = SPLAY_RIGHT(elm, field) = NULL;	\
840     } else {								\
841 	    int __comp;							\
842 	    name##_SPLAY(head, elm);					\
843 	    __comp = (cmp)(elm, (head)->sph_root);			\
844 	    if(__comp < 0) {						\
845 		    SPLAY_LEFT(elm, field) = SPLAY_LEFT((head)->sph_root, field);\
846 		    SPLAY_RIGHT(elm, field) = (head)->sph_root;		\
847 		    SPLAY_LEFT((head)->sph_root, field) = NULL;		\
848 	    } else if (__comp > 0) {					\
849 		    SPLAY_RIGHT(elm, field) = SPLAY_RIGHT((head)->sph_root, field);\
850 		    SPLAY_LEFT(elm, field) = (head)->sph_root;		\
851 		    SPLAY_RIGHT((head)->sph_root, field) = NULL;	\
852 	    } else							\
853 		    return ((head)->sph_root);				\
854     }									\
855     (head)->sph_root = (elm);						\
856     return (NULL);							\
857 }									\
858 									\
859 struct type *								\
860 name##_SPLAY_REMOVE(struct name *head, struct type *elm)		\
861 {									\
862 	struct type *__tmp;						\
863 	if (SPLAY_EMPTY(head))						\
864 		return (NULL);						\
865 	name##_SPLAY(head, elm);					\
866 	if ((cmp)(elm, (head)->sph_root) == 0) {			\
867 		if (SPLAY_LEFT((head)->sph_root, field) == NULL) {	\
868 			(head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);\
869 		} else {						\
870 			__tmp = SPLAY_RIGHT((head)->sph_root, field);	\
871 			(head)->sph_root = SPLAY_LEFT((head)->sph_root, field);\
872 			name##_SPLAY(head, elm);			\
873 			SPLAY_RIGHT((head)->sph_root, field) = __tmp;	\
874 		}							\
875 		return (elm);						\
876 	}								\
877 	return (NULL);							\
878 }									\
879 									\
880 void									\
881 name##_SPLAY(struct name *head, struct type *elm)			\
882 {									\
883 	struct type __node, *__left, *__right, *__tmp;			\
884 	int __comp;							\
885 \
886 	SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
887 	__left = __right = &__node;					\
888 \
889 	while ((__comp = (cmp)(elm, (head)->sph_root))) {		\
890 		if (__comp < 0) {					\
891 			__tmp = SPLAY_LEFT((head)->sph_root, field);	\
892 			if (__tmp == NULL)				\
893 				break;					\
894 			if ((cmp)(elm, __tmp) < 0){			\
895 				SPLAY_ROTATE_RIGHT(head, __tmp, field);	\
896 				if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
897 					break;				\
898 			}						\
899 			SPLAY_LINKLEFT(head, __right, field);		\
900 		} else if (__comp > 0) {				\
901 			__tmp = SPLAY_RIGHT((head)->sph_root, field);	\
902 			if (__tmp == NULL)				\
903 				break;					\
904 			if ((cmp)(elm, __tmp) > 0){			\
905 				SPLAY_ROTATE_LEFT(head, __tmp, field);	\
906 				if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
907 					break;				\
908 			}						\
909 			SPLAY_LINKRIGHT(head, __left, field);		\
910 		}							\
911 	}								\
912 	SPLAY_ASSEMBLE(head, &__node, __left, __right, field);		\
913 }									\
914 									\
915 /* Splay with either the minimum or the maximum element			\
916  * Used to find minimum or maximum element in tree.			\
917  */									\
918 void name##_SPLAY_MINMAX(struct name *head, int __comp) \
919 {									\
920 	struct type __node, *__left, *__right, *__tmp;			\
921 \
922 	SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
923 	__left = __right = &__node;					\
924 \
925 	while (1) {							\
926 		if (__comp < 0) {					\
927 			__tmp = SPLAY_LEFT((head)->sph_root, field);	\
928 			if (__tmp == NULL)				\
929 				break;					\
930 			if (__comp < 0){				\
931 				SPLAY_ROTATE_RIGHT(head, __tmp, field);	\
932 				if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
933 					break;				\
934 			}						\
935 			SPLAY_LINKLEFT(head, __right, field);		\
936 		} else if (__comp > 0) {				\
937 			__tmp = SPLAY_RIGHT((head)->sph_root, field);	\
938 			if (__tmp == NULL)				\
939 				break;					\
940 			if (__comp > 0) {				\
941 				SPLAY_ROTATE_LEFT(head, __tmp, field);	\
942 				if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
943 					break;				\
944 			}						\
945 			SPLAY_LINKRIGHT(head, __left, field);		\
946 		}							\
947 	}								\
948 	SPLAY_ASSEMBLE(head, &__node, __left, __right, field);		\
949 }
950 
951 #define SPLAY_NEGINF	-1
952 #define SPLAY_INF	1
953 
954 #define SPLAY_INSERT(name, x, y)	name##_SPLAY_INSERT(x, y)
955 #define SPLAY_REMOVE(name, x, y)	name##_SPLAY_REMOVE(x, y)
956 #define SPLAY_FIND(name, x, y)		name##_SPLAY_FIND(x, y)
957 #define SPLAY_NEXT(name, x, y)		name##_SPLAY_NEXT(x, y)
958 #define SPLAY_MIN(name, x)		(SPLAY_EMPTY(x) ? NULL	\
959 					: name##_SPLAY_MIN_MAX(x, SPLAY_NEGINF))
960 #define SPLAY_MAX(name, x)		(SPLAY_EMPTY(x) ? NULL	\
961 					: name##_SPLAY_MIN_MAX(x, SPLAY_INF))
962 
963 #define SPLAY_FOREACH(x, name, head)					\
964 	for ((x) = SPLAY_MIN(name, head);				\
965 	     (x) != NULL;						\
966 	     (x) = SPLAY_NEXT(name, head, x))
967 
968 /* Macros that define a red-back tree */
969 #define RB_HEAD(name, type)						\
970 struct name {								\
971 	struct type *rbh_root; /* root of the tree */			\
972 }
973 
974 #define RB_INITIALIZER(root)						\
975 	{ NULL }
976 
977 #define RB_INIT(root) do {						\
978 	(root)->rbh_root = NULL;					\
979 } while (0)
980 
981 #define RB_BLACK	0
982 #define RB_RED		1
983 #define RB_ENTRY(type)							\
984 struct {								\
985 	struct type *rbe_left;		/* left element */		\
986 	struct type *rbe_right;		/* right element */		\
987 	struct type *rbe_parent;	/* parent element */		\
988 	int rbe_color;			/* node color */		\
989 }
990 
991 #define RB_LEFT(elm, field)		(elm)->field.rbe_left
992 #define RB_RIGHT(elm, field)		(elm)->field.rbe_right
993 #define RB_PARENT(elm, field)		(elm)->field.rbe_parent
994 #define RB_COLOR(elm, field)		(elm)->field.rbe_color
995 #define RB_ROOT(head)			(head)->rbh_root
996 #define RB_EMPTY(head)			(RB_ROOT(head) == NULL)
997 
998 #define RB_SET(elm, parent, field) do {					\
999 	RB_PARENT(elm, field) = parent;					\
1000 	RB_LEFT(elm, field) = RB_RIGHT(elm, field) = NULL;		\
1001 	RB_COLOR(elm, field) = RB_RED;					\
1002 } while (0)
1003 
1004 #define RB_SET_BLACKRED(black, red, field) do {				\
1005 	RB_COLOR(black, field) = RB_BLACK;				\
1006 	RB_COLOR(red, field) = RB_RED;					\
1007 } while (0)
1008 
1009 #ifndef RB_AUGMENT
1010 #define RB_AUGMENT(x)
1011 #endif
1012 
1013 #define RB_ROTATE_LEFT(head, elm, tmp, field) do {			\
1014 	(tmp) = RB_RIGHT(elm, field);					\
1015 	if ((RB_RIGHT(elm, field) = RB_LEFT(tmp, field))) {		\
1016 		RB_PARENT(RB_LEFT(tmp, field), field) = (elm);		\
1017 	}								\
1018 	RB_AUGMENT(elm);						\
1019 	if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field))) {		\
1020 		if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))	\
1021 			RB_LEFT(RB_PARENT(elm, field), field) = (tmp);	\
1022 		else							\
1023 			RB_RIGHT(RB_PARENT(elm, field), field) = (tmp);	\
1024 	} else								\
1025 		(head)->rbh_root = (tmp);				\
1026 	RB_LEFT(tmp, field) = (elm);					\
1027 	RB_PARENT(elm, field) = (tmp);					\
1028 	RB_AUGMENT(tmp);						\
1029 	if ((RB_PARENT(tmp, field)))					\
1030 		RB_AUGMENT(RB_PARENT(tmp, field));			\
1031 } while (0)
1032 
1033 #define RB_ROTATE_RIGHT(head, elm, tmp, field) do {			\
1034 	(tmp) = RB_LEFT(elm, field);					\
1035 	if ((RB_LEFT(elm, field) = RB_RIGHT(tmp, field))) {		\
1036 		RB_PARENT(RB_RIGHT(tmp, field), field) = (elm);		\
1037 	}								\
1038 	RB_AUGMENT(elm);						\
1039 	if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field))) {		\
1040 		if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))	\
1041 			RB_LEFT(RB_PARENT(elm, field), field) = (tmp);	\
1042 		else							\
1043 			RB_RIGHT(RB_PARENT(elm, field), field) = (tmp);	\
1044 	} else								\
1045 		(head)->rbh_root = (tmp);				\
1046 	RB_RIGHT(tmp, field) = (elm);					\
1047 	RB_PARENT(elm, field) = (tmp);					\
1048 	RB_AUGMENT(tmp);						\
1049 	if ((RB_PARENT(tmp, field)))					\
1050 		RB_AUGMENT(RB_PARENT(tmp, field));			\
1051 } while (0)
1052 
1053 /* Generates prototypes and inline functions */
1054 #define RB_PROTOTYPE(name, type, field, cmp)				\
1055 void name##_RB_INSERT_COLOR(struct name *, struct type *);	\
1056 void name##_RB_REMOVE_COLOR(struct name *, struct type *, struct type *);\
1057 struct type *name##_RB_REMOVE(struct name *, struct type *);		\
1058 struct type *name##_RB_INSERT(struct name *, struct type *);		\
1059 struct type *name##_RB_FIND(struct name *, struct type *);		\
1060 struct type *name##_RB_NEXT(struct type *);				\
1061 struct type *name##_RB_MINMAX(struct name *, int);			\
1062 									\
1063 
1064 /* Main rb operation.
1065  * Moves node close to the key of elm to top
1066  */
1067 #define RB_GENERATE(name, type, field, cmp)				\
1068 void									\
1069 name##_RB_INSERT_COLOR(struct name *head, struct type *elm)		\
1070 {									\
1071 	struct type *parent, *gparent, *tmp;				\
1072 	while ((parent = RB_PARENT(elm, field)) &&			\
1073 	    RB_COLOR(parent, field) == RB_RED) {			\
1074 		gparent = RB_PARENT(parent, field);			\
1075 		if (parent == RB_LEFT(gparent, field)) {		\
1076 			tmp = RB_RIGHT(gparent, field);			\
1077 			if (tmp && RB_COLOR(tmp, field) == RB_RED) {	\
1078 				RB_COLOR(tmp, field) = RB_BLACK;	\
1079 				RB_SET_BLACKRED(parent, gparent, field);\
1080 				elm = gparent;				\
1081 				continue;				\
1082 			}						\
1083 			if (RB_RIGHT(parent, field) == elm) {		\
1084 				RB_ROTATE_LEFT(head, parent, tmp, field);\
1085 				tmp = parent;				\
1086 				parent = elm;				\
1087 				elm = tmp;				\
1088 			}						\
1089 			RB_SET_BLACKRED(parent, gparent, field);	\
1090 			RB_ROTATE_RIGHT(head, gparent, tmp, field);	\
1091 		} else {						\
1092 			tmp = RB_LEFT(gparent, field);			\
1093 			if (tmp && RB_COLOR(tmp, field) == RB_RED) {	\
1094 				RB_COLOR(tmp, field) = RB_BLACK;	\
1095 				RB_SET_BLACKRED(parent, gparent, field);\
1096 				elm = gparent;				\
1097 				continue;				\
1098 			}						\
1099 			if (RB_LEFT(parent, field) == elm) {		\
1100 				RB_ROTATE_RIGHT(head, parent, tmp, field);\
1101 				tmp = parent;				\
1102 				parent = elm;				\
1103 				elm = tmp;				\
1104 			}						\
1105 			RB_SET_BLACKRED(parent, gparent, field);	\
1106 			RB_ROTATE_LEFT(head, gparent, tmp, field);	\
1107 		}							\
1108 	}								\
1109 	RB_COLOR(head->rbh_root, field) = RB_BLACK;			\
1110 }									\
1111 									\
1112 void									\
1113 name##_RB_REMOVE_COLOR(struct name *head, struct type *parent, struct type *elm) \
1114 {									\
1115 	struct type *tmp;						\
1116 	while ((elm == NULL || RB_COLOR(elm, field) == RB_BLACK) &&	\
1117 	    elm != RB_ROOT(head)) {					\
1118 		if (RB_LEFT(parent, field) == elm) {			\
1119 			tmp = RB_RIGHT(parent, field);			\
1120 			if (RB_COLOR(tmp, field) == RB_RED) {		\
1121 				RB_SET_BLACKRED(tmp, parent, field);	\
1122 				RB_ROTATE_LEFT(head, parent, tmp, field);\
1123 				tmp = RB_RIGHT(parent, field);		\
1124 			}						\
1125 			if ((RB_LEFT(tmp, field) == NULL ||		\
1126 			    RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
1127 			    (RB_RIGHT(tmp, field) == NULL ||		\
1128 			    RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
1129 				RB_COLOR(tmp, field) = RB_RED;		\
1130 				elm = parent;				\
1131 				parent = RB_PARENT(elm, field);		\
1132 			} else {					\
1133 				if (RB_RIGHT(tmp, field) == NULL ||	\
1134 				    RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK) {\
1135 					struct type *oleft;		\
1136 					if ((oleft = RB_LEFT(tmp, field)))\
1137 						RB_COLOR(oleft, field) = RB_BLACK;\
1138 					RB_COLOR(tmp, field) = RB_RED;	\
1139 					RB_ROTATE_RIGHT(head, tmp, oleft, field);\
1140 					tmp = RB_RIGHT(parent, field);	\
1141 				}					\
1142 				RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
1143 				RB_COLOR(parent, field) = RB_BLACK;	\
1144 				if (RB_RIGHT(tmp, field))		\
1145 					RB_COLOR(RB_RIGHT(tmp, field), field) = RB_BLACK;\
1146 				RB_ROTATE_LEFT(head, parent, tmp, field);\
1147 				elm = RB_ROOT(head);			\
1148 				break;					\
1149 			}						\
1150 		} else {						\
1151 			tmp = RB_LEFT(parent, field);			\
1152 			if (RB_COLOR(tmp, field) == RB_RED) {		\
1153 				RB_SET_BLACKRED(tmp, parent, field);	\
1154 				RB_ROTATE_RIGHT(head, parent, tmp, field);\
1155 				tmp = RB_LEFT(parent, field);		\
1156 			}						\
1157 			if ((RB_LEFT(tmp, field) == NULL ||		\
1158 			    RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
1159 			    (RB_RIGHT(tmp, field) == NULL ||		\
1160 			    RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
1161 				RB_COLOR(tmp, field) = RB_RED;		\
1162 				elm = parent;				\
1163 				parent = RB_PARENT(elm, field);		\
1164 			} else {					\
1165 				if (RB_LEFT(tmp, field) == NULL ||	\
1166 				    RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) {\
1167 					struct type *oright;		\
1168 					if ((oright = RB_RIGHT(tmp, field)))\
1169 						RB_COLOR(oright, field) = RB_BLACK;\
1170 					RB_COLOR(tmp, field) = RB_RED;	\
1171 					RB_ROTATE_LEFT(head, tmp, oright, field);\
1172 					tmp = RB_LEFT(parent, field);	\
1173 				}					\
1174 				RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
1175 				RB_COLOR(parent, field) = RB_BLACK;	\
1176 				if (RB_LEFT(tmp, field))		\
1177 					RB_COLOR(RB_LEFT(tmp, field), field) = RB_BLACK;\
1178 				RB_ROTATE_RIGHT(head, parent, tmp, field);\
1179 				elm = RB_ROOT(head);			\
1180 				break;					\
1181 			}						\
1182 		}							\
1183 	}								\
1184 	if (elm)							\
1185 		RB_COLOR(elm, field) = RB_BLACK;			\
1186 }									\
1187 									\
1188 struct type *								\
1189 name##_RB_REMOVE(struct name *head, struct type *elm)			\
1190 {									\
1191 	struct type *child, *parent, *old = elm;			\
1192 	int color;							\
1193 	if (RB_LEFT(elm, field) == NULL)				\
1194 		child = RB_RIGHT(elm, field);				\
1195 	else if (RB_RIGHT(elm, field) == NULL)				\
1196 		child = RB_LEFT(elm, field);				\
1197 	else {								\
1198 		struct type *left;					\
1199 		elm = RB_RIGHT(elm, field);				\
1200 		while ((left = RB_LEFT(elm, field)))			\
1201 			elm = left;					\
1202 		child = RB_RIGHT(elm, field);				\
1203 		parent = RB_PARENT(elm, field);				\
1204 		color = RB_COLOR(elm, field);				\
1205 		if (child)						\
1206 			RB_PARENT(child, field) = parent;		\
1207 		if (parent) {						\
1208 			if (RB_LEFT(parent, field) == elm)		\
1209 				RB_LEFT(parent, field) = child;		\
1210 			else						\
1211 				RB_RIGHT(parent, field) = child;	\
1212 			RB_AUGMENT(parent);				\
1213 		} else							\
1214 			RB_ROOT(head) = child;				\
1215 		if (RB_PARENT(elm, field) == old)			\
1216 			parent = elm;					\
1217 		(elm)->field = (old)->field;				\
1218 		if (RB_PARENT(old, field)) {				\
1219 			if (RB_LEFT(RB_PARENT(old, field), field) == old)\
1220 				RB_LEFT(RB_PARENT(old, field), field) = elm;\
1221 			else						\
1222 				RB_RIGHT(RB_PARENT(old, field), field) = elm;\
1223 			RB_AUGMENT(RB_PARENT(old, field));		\
1224 		} else							\
1225 			RB_ROOT(head) = elm;				\
1226 		RB_PARENT(RB_LEFT(old, field), field) = elm;		\
1227 		if (RB_RIGHT(old, field))				\
1228 			RB_PARENT(RB_RIGHT(old, field), field) = elm;	\
1229 		if (parent) {						\
1230 			left = parent;					\
1231 			do {						\
1232 				RB_AUGMENT(left);			\
1233 			} while ((left = RB_PARENT(left, field)));	\
1234 		}							\
1235 		goto color;						\
1236 	}								\
1237 	parent = RB_PARENT(elm, field);					\
1238 	color = RB_COLOR(elm, field);					\
1239 	if (child)							\
1240 		RB_PARENT(child, field) = parent;			\
1241 	if (parent) {							\
1242 		if (RB_LEFT(parent, field) == elm)			\
1243 			RB_LEFT(parent, field) = child;			\
1244 		else							\
1245 			RB_RIGHT(parent, field) = child;		\
1246 		RB_AUGMENT(parent);					\
1247 	} else								\
1248 		RB_ROOT(head) = child;					\
1249 color:									\
1250 	if (color == RB_BLACK)						\
1251 		name##_RB_REMOVE_COLOR(head, parent, child);		\
1252 	return (old);							\
1253 }									\
1254 									\
1255 /* Inserts a node into the RB tree */					\
1256 struct type *								\
1257 name##_RB_INSERT(struct name *head, struct type *elm)			\
1258 {									\
1259 	struct type *tmp;						\
1260 	struct type *parent = NULL;					\
1261 	int comp = 0;							\
1262 	tmp = RB_ROOT(head);						\
1263 	while (tmp) {							\
1264 		parent = tmp;						\
1265 		comp = (cmp)(elm, parent);				\
1266 		if (comp < 0)						\
1267 			tmp = RB_LEFT(tmp, field);			\
1268 		else if (comp > 0)					\
1269 			tmp = RB_RIGHT(tmp, field);			\
1270 		else							\
1271 			return (tmp);					\
1272 	}								\
1273 	RB_SET(elm, parent, field);					\
1274 	if (parent != NULL) {						\
1275 		if (comp < 0)						\
1276 			RB_LEFT(parent, field) = elm;			\
1277 		else							\
1278 			RB_RIGHT(parent, field) = elm;			\
1279 		RB_AUGMENT(parent);					\
1280 	} else								\
1281 		RB_ROOT(head) = elm;					\
1282 	name##_RB_INSERT_COLOR(head, elm);				\
1283 	return (NULL);							\
1284 }									\
1285 									\
1286 /* Finds the node with the same key as elm */				\
1287 struct type *								\
1288 name##_RB_FIND(struct name *head, struct type *elm)			\
1289 {									\
1290 	struct type *tmp = RB_ROOT(head);				\
1291 	int comp;							\
1292 	while (tmp) {							\
1293 		comp = cmp(elm, tmp);					\
1294 		if (comp < 0)						\
1295 			tmp = RB_LEFT(tmp, field);			\
1296 		else if (comp > 0)					\
1297 			tmp = RB_RIGHT(tmp, field);			\
1298 		else							\
1299 			return (tmp);					\
1300 	}								\
1301 	return (NULL);							\
1302 }									\
1303 									\
1304 struct type *								\
1305 name##_RB_NEXT(struct type *elm)					\
1306 {									\
1307 	if (RB_RIGHT(elm, field)) {					\
1308 		elm = RB_RIGHT(elm, field);				\
1309 		while (RB_LEFT(elm, field))				\
1310 			elm = RB_LEFT(elm, field);			\
1311 	} else {							\
1312 		if (RB_PARENT(elm, field) &&				\
1313 		    (elm == RB_LEFT(RB_PARENT(elm, field), field)))	\
1314 			elm = RB_PARENT(elm, field);			\
1315 		else {							\
1316 			while (RB_PARENT(elm, field) &&			\
1317 			    (elm == RB_RIGHT(RB_PARENT(elm, field), field)))\
1318 				elm = RB_PARENT(elm, field);		\
1319 			elm = RB_PARENT(elm, field);			\
1320 		}							\
1321 	}								\
1322 	return (elm);							\
1323 }									\
1324 									\
1325 struct type *								\
1326 name##_RB_MINMAX(struct name *head, int val)				\
1327 {									\
1328 	struct type *tmp = RB_ROOT(head);				\
1329 	struct type *parent = NULL;					\
1330 	while (tmp) {							\
1331 		parent = tmp;						\
1332 		if (val < 0)						\
1333 			tmp = RB_LEFT(tmp, field);			\
1334 		else							\
1335 			tmp = RB_RIGHT(tmp, field);			\
1336 	}								\
1337 	return (parent);						\
1338 }
1339 
1340 #define RB_NEGINF	-1
1341 #define RB_INF	1
1342 
1343 #define RB_INSERT(name, x, y)	name##_RB_INSERT(x, y)
1344 #define RB_REMOVE(name, x, y)	name##_RB_REMOVE(x, y)
1345 #define RB_FIND(name, x, y)	name##_RB_FIND(x, y)
1346 #define RB_NEXT(name, x, y)	name##_RB_NEXT(y)
1347 #define RB_MIN(name, x)		name##_RB_MINMAX(x, RB_NEGINF)
1348 #define RB_MAX(name, x)		name##_RB_MINMAX(x, RB_INF)
1349 
1350 #define RB_FOREACH(x, name, head)					\
1351 	for ((x) = RB_MIN(name, head);					\
1352 	     (x) != NULL;						\
1353 	     (x) = name##_RB_NEXT(x))
1354 
1355 #endif	/* _SYS_TREE_H_ */
1356