xref: /titanic_41/usr/src/cmd/ssh/include/sys-tree.h (revision b9aa66a73c9016cf5c71fe80efe90ce9f2ca5c73)
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 #ifdef __cplusplus
31 extern "C" {
32 #endif
33 
34 /*
35  * This file defines data structures for different types of trees:
36  * splay trees and red-black trees.
37  *
38  * A splay tree is a self-organizing data structure.  Every operation
39  * on the tree causes a splay to happen.  The splay moves the requested
40  * node to the root of the tree and partly rebalances it.
41  *
42  * This has the benefit that request locality causes faster lookups as
43  * the requested nodes move to the top of the tree.  On the other hand,
44  * every lookup causes memory writes.
45  *
46  * The Balance Theorem bounds the total access time for m operations
47  * and n inserts on an initially empty tree as O((m + n)lg n).  The
48  * amortized cost for a sequence of m accesses to a splay tree is O(lg n);
49  *
50  * A red-black tree is a binary search tree with the node color as an
51  * extra attribute.  It fulfills a set of conditions:
52  *	- every search path from the root to a leaf consists of the
53  *	  same number of black nodes,
54  *	- each red node (except for the root) has a black parent,
55  *	- each leaf node is black.
56  *
57  * Every operation on a red-black tree is bounded as O(lg n).
58  * The maximum height of a red-black tree is 2lg (n+1).
59  */
60 
61 #define SPLAY_HEAD(name, type)						\
62 struct name {								\
63 	struct type *sph_root; /* root of the tree */			\
64 }
65 
66 #define SPLAY_INITIALIZER(root)						\
67 	{ NULL }
68 
69 #define SPLAY_INIT(root) do {						\
70 	(root)->sph_root = NULL;					\
71 } while (0)
72 
73 #define SPLAY_ENTRY(type)						\
74 struct {								\
75 	struct type *spe_left; /* left element */			\
76 	struct type *spe_right; /* right element */			\
77 }
78 
79 #define SPLAY_LEFT(elm, field)		(elm)->field.spe_left
80 #define SPLAY_RIGHT(elm, field)		(elm)->field.spe_right
81 #define SPLAY_ROOT(head)		(head)->sph_root
82 #define SPLAY_EMPTY(head)		(SPLAY_ROOT(head) == NULL)
83 
84 /* SPLAY_ROTATE_{LEFT,RIGHT} expect that tmp hold SPLAY_{RIGHT,LEFT} */
85 #define SPLAY_ROTATE_RIGHT(head, tmp, field) do {			\
86 	SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(tmp, field);	\
87 	SPLAY_RIGHT(tmp, field) = (head)->sph_root;			\
88 	(head)->sph_root = tmp;						\
89 } while (0)
90 
91 #define SPLAY_ROTATE_LEFT(head, tmp, field) do {			\
92 	SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(tmp, field);	\
93 	SPLAY_LEFT(tmp, field) = (head)->sph_root;			\
94 	(head)->sph_root = tmp;						\
95 } while (0)
96 
97 #define SPLAY_LINKLEFT(head, tmp, field) do {				\
98 	SPLAY_LEFT(tmp, field) = (head)->sph_root;			\
99 	tmp = (head)->sph_root;						\
100 	(head)->sph_root = SPLAY_LEFT((head)->sph_root, field);		\
101 } while (0)
102 
103 #define SPLAY_LINKRIGHT(head, tmp, field) do {				\
104 	SPLAY_RIGHT(tmp, field) = (head)->sph_root;			\
105 	tmp = (head)->sph_root;						\
106 	(head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);	\
107 } while (0)
108 
109 #define SPLAY_ASSEMBLE(head, node, left, right, field) do {		\
110 	SPLAY_RIGHT(left, field) = SPLAY_LEFT((head)->sph_root, field);	\
111 	SPLAY_LEFT(right, field) = SPLAY_RIGHT((head)->sph_root, field);\
112 	SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(node, field);	\
113 	SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(node, field);	\
114 } while (0)
115 
116 /* Generates prototypes and inline functions */
117 
118 #define SPLAY_PROTOTYPE(name, type, field, cmp)				\
119 void name##_SPLAY(struct name *, struct type *);			\
120 void name##_SPLAY_MINMAX(struct name *, int);				\
121 struct type *name##_SPLAY_INSERT(struct name *, struct type *);		\
122 struct type *name##_SPLAY_REMOVE(struct name *, struct type *);		\
123 									\
124 /* Finds the node with the same key as elm */				\
125 static __inline struct type *						\
126 name##_SPLAY_FIND(struct name *head, struct type *elm)			\
127 {									\
128 	if (SPLAY_EMPTY(head))						\
129 		return(NULL);						\
130 	name##_SPLAY(head, elm);					\
131 	if ((cmp)(elm, (head)->sph_root) == 0)				\
132 		return (head->sph_root);				\
133 	return (NULL);							\
134 }									\
135 									\
136 static __inline struct type *						\
137 name##_SPLAY_NEXT(struct name *head, struct type *elm)			\
138 {									\
139 	name##_SPLAY(head, elm);					\
140 	if (SPLAY_RIGHT(elm, field) != NULL) {				\
141 		elm = SPLAY_RIGHT(elm, field);				\
142 		while (SPLAY_LEFT(elm, field) != NULL) {		\
143 			elm = SPLAY_LEFT(elm, field);			\
144 		}							\
145 	} else								\
146 		elm = NULL;						\
147 	return (elm);							\
148 }									\
149 									\
150 static __inline struct type *						\
151 name##_SPLAY_MIN_MAX(struct name *head, int val)			\
152 {									\
153 	name##_SPLAY_MINMAX(head, val);					\
154         return (SPLAY_ROOT(head));					\
155 }
156 
157 /* Main splay operation.
158  * Moves node close to the key of elm to top
159  */
160 #define SPLAY_GENERATE(name, type, field, cmp)				\
161 struct type *								\
162 name##_SPLAY_INSERT(struct name *head, struct type *elm)		\
163 {									\
164     if (SPLAY_EMPTY(head)) {						\
165 	    SPLAY_LEFT(elm, field) = SPLAY_RIGHT(elm, field) = NULL;	\
166     } else {								\
167 	    int __comp;							\
168 	    name##_SPLAY(head, elm);					\
169 	    __comp = (cmp)(elm, (head)->sph_root);			\
170 	    if(__comp < 0) {						\
171 		    SPLAY_LEFT(elm, field) = SPLAY_LEFT((head)->sph_root, field);\
172 		    SPLAY_RIGHT(elm, field) = (head)->sph_root;		\
173 		    SPLAY_LEFT((head)->sph_root, field) = NULL;		\
174 	    } else if (__comp > 0) {					\
175 		    SPLAY_RIGHT(elm, field) = SPLAY_RIGHT((head)->sph_root, field);\
176 		    SPLAY_LEFT(elm, field) = (head)->sph_root;		\
177 		    SPLAY_RIGHT((head)->sph_root, field) = NULL;	\
178 	    } else							\
179 		    return ((head)->sph_root);				\
180     }									\
181     (head)->sph_root = (elm);						\
182     return (NULL);							\
183 }									\
184 									\
185 struct type *								\
186 name##_SPLAY_REMOVE(struct name *head, struct type *elm)		\
187 {									\
188 	struct type *__tmp;						\
189 	if (SPLAY_EMPTY(head))						\
190 		return (NULL);						\
191 	name##_SPLAY(head, elm);					\
192 	if ((cmp)(elm, (head)->sph_root) == 0) {			\
193 		if (SPLAY_LEFT((head)->sph_root, field) == NULL) {	\
194 			(head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);\
195 		} else {						\
196 			__tmp = SPLAY_RIGHT((head)->sph_root, field);	\
197 			(head)->sph_root = SPLAY_LEFT((head)->sph_root, field);\
198 			name##_SPLAY(head, elm);			\
199 			SPLAY_RIGHT((head)->sph_root, field) = __tmp;	\
200 		}							\
201 		return (elm);						\
202 	}								\
203 	return (NULL);							\
204 }									\
205 									\
206 void									\
207 name##_SPLAY(struct name *head, struct type *elm)			\
208 {									\
209 	struct type __node, *__left, *__right, *__tmp;			\
210 	int __comp;							\
211 \
212 	SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
213 	__left = __right = &__node;					\
214 \
215 	while ((__comp = (cmp)(elm, (head)->sph_root))) {		\
216 		if (__comp < 0) {					\
217 			__tmp = SPLAY_LEFT((head)->sph_root, field);	\
218 			if (__tmp == NULL)				\
219 				break;					\
220 			if ((cmp)(elm, __tmp) < 0){			\
221 				SPLAY_ROTATE_RIGHT(head, __tmp, field);	\
222 				if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
223 					break;				\
224 			}						\
225 			SPLAY_LINKLEFT(head, __right, field);		\
226 		} else if (__comp > 0) {				\
227 			__tmp = SPLAY_RIGHT((head)->sph_root, field);	\
228 			if (__tmp == NULL)				\
229 				break;					\
230 			if ((cmp)(elm, __tmp) > 0){			\
231 				SPLAY_ROTATE_LEFT(head, __tmp, field);	\
232 				if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
233 					break;				\
234 			}						\
235 			SPLAY_LINKRIGHT(head, __left, field);		\
236 		}							\
237 	}								\
238 	SPLAY_ASSEMBLE(head, &__node, __left, __right, field);		\
239 }									\
240 									\
241 /* Splay with either the minimum or the maximum element			\
242  * Used to find minimum or maximum element in tree.			\
243  */									\
244 void name##_SPLAY_MINMAX(struct name *head, int __comp) \
245 {									\
246 	struct type __node, *__left, *__right, *__tmp;			\
247 \
248 	SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
249 	__left = __right = &__node;					\
250 \
251 	while (1) {							\
252 		if (__comp < 0) {					\
253 			__tmp = SPLAY_LEFT((head)->sph_root, field);	\
254 			if (__tmp == NULL)				\
255 				break;					\
256 			if (__comp < 0){				\
257 				SPLAY_ROTATE_RIGHT(head, __tmp, field);	\
258 				if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
259 					break;				\
260 			}						\
261 			SPLAY_LINKLEFT(head, __right, field);		\
262 		} else if (__comp > 0) {				\
263 			__tmp = SPLAY_RIGHT((head)->sph_root, field);	\
264 			if (__tmp == NULL)				\
265 				break;					\
266 			if (__comp > 0) {				\
267 				SPLAY_ROTATE_LEFT(head, __tmp, field);	\
268 				if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
269 					break;				\
270 			}						\
271 			SPLAY_LINKRIGHT(head, __left, field);		\
272 		}							\
273 	}								\
274 	SPLAY_ASSEMBLE(head, &__node, __left, __right, field);		\
275 }
276 
277 #define SPLAY_NEGINF	-1
278 #define SPLAY_INF	1
279 
280 #define SPLAY_INSERT(name, x, y)	name##_SPLAY_INSERT(x, y)
281 #define SPLAY_REMOVE(name, x, y)	name##_SPLAY_REMOVE(x, y)
282 #define SPLAY_FIND(name, x, y)		name##_SPLAY_FIND(x, y)
283 #define SPLAY_NEXT(name, x, y)		name##_SPLAY_NEXT(x, y)
284 #define SPLAY_MIN(name, x)		(SPLAY_EMPTY(x) ? NULL	\
285 					: name##_SPLAY_MIN_MAX(x, SPLAY_NEGINF))
286 #define SPLAY_MAX(name, x)		(SPLAY_EMPTY(x) ? NULL	\
287 					: name##_SPLAY_MIN_MAX(x, SPLAY_INF))
288 
289 #define SPLAY_FOREACH(x, name, head)					\
290 	for ((x) = SPLAY_MIN(name, head);				\
291 	     (x) != NULL;						\
292 	     (x) = SPLAY_NEXT(name, head, x))
293 
294 /* Macros that define a red-back tree */
295 #define RB_HEAD(name, type)						\
296 struct name {								\
297 	struct type *rbh_root; /* root of the tree */			\
298 }
299 
300 #define RB_INITIALIZER(root)						\
301 	{ NULL }
302 
303 #define RB_INIT(root) do {						\
304 	(root)->rbh_root = NULL;					\
305 } while (0)
306 
307 #define RB_BLACK	0
308 #define RB_RED		1
309 #define RB_ENTRY(type)							\
310 struct {								\
311 	struct type *rbe_left;		/* left element */		\
312 	struct type *rbe_right;		/* right element */		\
313 	struct type *rbe_parent;	/* parent element */		\
314 	int rbe_color;			/* node color */		\
315 }
316 
317 #define RB_LEFT(elm, field)		(elm)->field.rbe_left
318 #define RB_RIGHT(elm, field)		(elm)->field.rbe_right
319 #define RB_PARENT(elm, field)		(elm)->field.rbe_parent
320 #define RB_COLOR(elm, field)		(elm)->field.rbe_color
321 #define RB_ROOT(head)			(head)->rbh_root
322 #define RB_EMPTY(head)			(RB_ROOT(head) == NULL)
323 
324 #define RB_SET(elm, parent, field) do {					\
325 	RB_PARENT(elm, field) = parent;					\
326 	RB_LEFT(elm, field) = RB_RIGHT(elm, field) = NULL;		\
327 	RB_COLOR(elm, field) = RB_RED;					\
328 } while (0)
329 
330 #define RB_SET_BLACKRED(black, red, field) do {				\
331 	RB_COLOR(black, field) = RB_BLACK;				\
332 	RB_COLOR(red, field) = RB_RED;					\
333 } while (0)
334 
335 #ifndef RB_AUGMENT
336 #define RB_AUGMENT(x)
337 #endif
338 
339 #define RB_ROTATE_LEFT(head, elm, tmp, field) do {			\
340 	(tmp) = RB_RIGHT(elm, field);					\
341 	if ((RB_RIGHT(elm, field) = RB_LEFT(tmp, field))) {		\
342 		RB_PARENT(RB_LEFT(tmp, field), field) = (elm);		\
343 	}								\
344 	RB_AUGMENT(elm);						\
345 	if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field))) {		\
346 		if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))	\
347 			RB_LEFT(RB_PARENT(elm, field), field) = (tmp);	\
348 		else							\
349 			RB_RIGHT(RB_PARENT(elm, field), field) = (tmp);	\
350 		RB_AUGMENT(RB_PARENT(elm, field));			\
351 	} else								\
352 		(head)->rbh_root = (tmp);				\
353 	RB_LEFT(tmp, field) = (elm);					\
354 	RB_PARENT(elm, field) = (tmp);					\
355 	RB_AUGMENT(tmp);						\
356 } while (0)
357 
358 #define RB_ROTATE_RIGHT(head, elm, tmp, field) do {			\
359 	(tmp) = RB_LEFT(elm, field);					\
360 	if ((RB_LEFT(elm, field) = RB_RIGHT(tmp, field))) {		\
361 		RB_PARENT(RB_RIGHT(tmp, field), field) = (elm);		\
362 	}								\
363 	RB_AUGMENT(elm);						\
364 	if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field))) {		\
365 		if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))	\
366 			RB_LEFT(RB_PARENT(elm, field), field) = (tmp);	\
367 		else							\
368 			RB_RIGHT(RB_PARENT(elm, field), field) = (tmp);	\
369 		RB_AUGMENT(RB_PARENT(elm, field));			\
370 	} else								\
371 		(head)->rbh_root = (tmp);				\
372 	RB_RIGHT(tmp, field) = (elm);					\
373 	RB_PARENT(elm, field) = (tmp);					\
374 	RB_AUGMENT(tmp);						\
375 } while (0)
376 
377 /* Generates prototypes and inline functions */
378 #define RB_PROTOTYPE(name, type, field, cmp)				\
379 void name##_RB_INSERT_COLOR(struct name *, struct type *);	\
380 void name##_RB_REMOVE_COLOR(struct name *, struct type *, struct type *);\
381 struct type *name##_RB_REMOVE(struct name *, struct type *);		\
382 struct type *name##_RB_INSERT(struct name *, struct type *);		\
383 struct type *name##_RB_FIND(struct name *, struct type *);		\
384 struct type *name##_RB_NEXT(struct name *, struct type *);		\
385 struct type *name##_RB_MINMAX(struct name *, int);
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 name *head, 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(x, 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(head, x))
677 
678 #ifdef __cplusplus
679 }
680 #endif
681 
682 #endif /* _SYS_TREE_H */
683