xref: /freebsd/crypto/openssh/openbsd-compat/sys-tree.h (revision 4b2eaea43fec8e8792be611dea204071a10b655a)
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 /*
31  * This file defines data structures for different types of trees:
32  * splay trees and red-black trees.
33  *
34  * A splay tree is a self-organizing data structure.  Every operation
35  * on the tree causes a splay to happen.  The splay moves the requested
36  * node to the root of the tree and partly rebalances it.
37  *
38  * This has the benefit that request locality causes faster lookups as
39  * the requested nodes move to the top of the tree.  On the other hand,
40  * every lookup causes memory writes.
41  *
42  * The Balance Theorem bounds the total access time for m operations
43  * and n inserts on an initially empty tree as O((m + n)lg n).  The
44  * amortized cost for a sequence of m accesses to a splay tree is O(lg n);
45  *
46  * A red-black tree is a binary search tree with the node color as an
47  * extra attribute.  It fulfills a set of conditions:
48  *	- every search path from the root to a leaf consists of the
49  *	  same number of black nodes,
50  *	- each red node (except for the root) has a black parent,
51  *	- each leaf node is black.
52  *
53  * Every operation on a red-black tree is bounded as O(lg n).
54  * The maximum height of a red-black tree is 2lg (n+1).
55  */
56 
57 #define SPLAY_HEAD(name, type)						\
58 struct name {								\
59 	struct type *sph_root; /* root of the tree */			\
60 }
61 
62 #define SPLAY_INITIALIZER(root)						\
63 	{ NULL }
64 
65 #define SPLAY_INIT(root) do {						\
66 	(root)->sph_root = NULL;					\
67 } while (0)
68 
69 #define SPLAY_ENTRY(type)						\
70 struct {								\
71 	struct type *spe_left; /* left element */			\
72 	struct type *spe_right; /* right element */			\
73 }
74 
75 #define SPLAY_LEFT(elm, field)		(elm)->field.spe_left
76 #define SPLAY_RIGHT(elm, field)		(elm)->field.spe_right
77 #define SPLAY_ROOT(head)		(head)->sph_root
78 #define SPLAY_EMPTY(head)		(SPLAY_ROOT(head) == NULL)
79 
80 /* SPLAY_ROTATE_{LEFT,RIGHT} expect that tmp hold SPLAY_{RIGHT,LEFT} */
81 #define SPLAY_ROTATE_RIGHT(head, tmp, field) do {			\
82 	SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(tmp, field);	\
83 	SPLAY_RIGHT(tmp, field) = (head)->sph_root;			\
84 	(head)->sph_root = tmp;						\
85 } while (0)
86 
87 #define SPLAY_ROTATE_LEFT(head, tmp, field) do {			\
88 	SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(tmp, field);	\
89 	SPLAY_LEFT(tmp, field) = (head)->sph_root;			\
90 	(head)->sph_root = tmp;						\
91 } while (0)
92 
93 #define SPLAY_LINKLEFT(head, tmp, field) do {				\
94 	SPLAY_LEFT(tmp, field) = (head)->sph_root;			\
95 	tmp = (head)->sph_root;						\
96 	(head)->sph_root = SPLAY_LEFT((head)->sph_root, field);		\
97 } while (0)
98 
99 #define SPLAY_LINKRIGHT(head, tmp, field) do {				\
100 	SPLAY_RIGHT(tmp, field) = (head)->sph_root;			\
101 	tmp = (head)->sph_root;						\
102 	(head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);	\
103 } while (0)
104 
105 #define SPLAY_ASSEMBLE(head, node, left, right, field) do {		\
106 	SPLAY_RIGHT(left, field) = SPLAY_LEFT((head)->sph_root, field);	\
107 	SPLAY_LEFT(right, field) = SPLAY_RIGHT((head)->sph_root, field);\
108 	SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(node, field);	\
109 	SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(node, field);	\
110 } while (0)
111 
112 /* Generates prototypes and inline functions */
113 
114 #define SPLAY_PROTOTYPE(name, type, field, cmp)				\
115 void name##_SPLAY(struct name *, struct type *);			\
116 void name##_SPLAY_MINMAX(struct name *, int);				\
117 struct type *name##_SPLAY_INSERT(struct name *, struct type *);		\
118 struct type *name##_SPLAY_REMOVE(struct name *, struct type *);		\
119 									\
120 /* Finds the node with the same key as elm */				\
121 static __inline struct type *						\
122 name##_SPLAY_FIND(struct name *head, struct type *elm)			\
123 {									\
124 	if (SPLAY_EMPTY(head))						\
125 		return(NULL);						\
126 	name##_SPLAY(head, elm);					\
127 	if ((cmp)(elm, (head)->sph_root) == 0)				\
128 		return (head->sph_root);				\
129 	return (NULL);							\
130 }									\
131 									\
132 static __inline struct type *						\
133 name##_SPLAY_NEXT(struct name *head, struct type *elm)			\
134 {									\
135 	name##_SPLAY(head, elm);					\
136 	if (SPLAY_RIGHT(elm, field) != NULL) {				\
137 		elm = SPLAY_RIGHT(elm, field);				\
138 		while (SPLAY_LEFT(elm, field) != NULL) {		\
139 			elm = SPLAY_LEFT(elm, field);			\
140 		}							\
141 	} else								\
142 		elm = NULL;						\
143 	return (elm);							\
144 }									\
145 									\
146 static __inline struct type *						\
147 name##_SPLAY_MIN_MAX(struct name *head, int val)			\
148 {									\
149 	name##_SPLAY_MINMAX(head, val);					\
150         return (SPLAY_ROOT(head));					\
151 }
152 
153 /* Main splay operation.
154  * Moves node close to the key of elm to top
155  */
156 #define SPLAY_GENERATE(name, type, field, cmp)				\
157 struct type *								\
158 name##_SPLAY_INSERT(struct name *head, struct type *elm)		\
159 {									\
160     if (SPLAY_EMPTY(head)) {						\
161 	    SPLAY_LEFT(elm, field) = SPLAY_RIGHT(elm, field) = NULL;	\
162     } else {								\
163 	    int __comp;							\
164 	    name##_SPLAY(head, elm);					\
165 	    __comp = (cmp)(elm, (head)->sph_root);			\
166 	    if(__comp < 0) {						\
167 		    SPLAY_LEFT(elm, field) = SPLAY_LEFT((head)->sph_root, field);\
168 		    SPLAY_RIGHT(elm, field) = (head)->sph_root;		\
169 		    SPLAY_LEFT((head)->sph_root, field) = NULL;		\
170 	    } else if (__comp > 0) {					\
171 		    SPLAY_RIGHT(elm, field) = SPLAY_RIGHT((head)->sph_root, field);\
172 		    SPLAY_LEFT(elm, field) = (head)->sph_root;		\
173 		    SPLAY_RIGHT((head)->sph_root, field) = NULL;	\
174 	    } else							\
175 		    return ((head)->sph_root);				\
176     }									\
177     (head)->sph_root = (elm);						\
178     return (NULL);							\
179 }									\
180 									\
181 struct type *								\
182 name##_SPLAY_REMOVE(struct name *head, struct type *elm)		\
183 {									\
184 	struct type *__tmp;						\
185 	if (SPLAY_EMPTY(head))						\
186 		return (NULL);						\
187 	name##_SPLAY(head, elm);					\
188 	if ((cmp)(elm, (head)->sph_root) == 0) {			\
189 		if (SPLAY_LEFT((head)->sph_root, field) == NULL) {	\
190 			(head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);\
191 		} else {						\
192 			__tmp = SPLAY_RIGHT((head)->sph_root, field);	\
193 			(head)->sph_root = SPLAY_LEFT((head)->sph_root, field);\
194 			name##_SPLAY(head, elm);			\
195 			SPLAY_RIGHT((head)->sph_root, field) = __tmp;	\
196 		}							\
197 		return (elm);						\
198 	}								\
199 	return (NULL);							\
200 }									\
201 									\
202 void									\
203 name##_SPLAY(struct name *head, struct type *elm)			\
204 {									\
205 	struct type __node, *__left, *__right, *__tmp;			\
206 	int __comp;							\
207 \
208 	SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
209 	__left = __right = &__node;					\
210 \
211 	while ((__comp = (cmp)(elm, (head)->sph_root))) {		\
212 		if (__comp < 0) {					\
213 			__tmp = SPLAY_LEFT((head)->sph_root, field);	\
214 			if (__tmp == NULL)				\
215 				break;					\
216 			if ((cmp)(elm, __tmp) < 0){			\
217 				SPLAY_ROTATE_RIGHT(head, __tmp, field);	\
218 				if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
219 					break;				\
220 			}						\
221 			SPLAY_LINKLEFT(head, __right, field);		\
222 		} else if (__comp > 0) {				\
223 			__tmp = SPLAY_RIGHT((head)->sph_root, field);	\
224 			if (__tmp == NULL)				\
225 				break;					\
226 			if ((cmp)(elm, __tmp) > 0){			\
227 				SPLAY_ROTATE_LEFT(head, __tmp, field);	\
228 				if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
229 					break;				\
230 			}						\
231 			SPLAY_LINKRIGHT(head, __left, field);		\
232 		}							\
233 	}								\
234 	SPLAY_ASSEMBLE(head, &__node, __left, __right, field);		\
235 }									\
236 									\
237 /* Splay with either the minimum or the maximum element			\
238  * Used to find minimum or maximum element in tree.			\
239  */									\
240 void name##_SPLAY_MINMAX(struct name *head, int __comp) \
241 {									\
242 	struct type __node, *__left, *__right, *__tmp;			\
243 \
244 	SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
245 	__left = __right = &__node;					\
246 \
247 	while (1) {							\
248 		if (__comp < 0) {					\
249 			__tmp = SPLAY_LEFT((head)->sph_root, field);	\
250 			if (__tmp == NULL)				\
251 				break;					\
252 			if (__comp < 0){				\
253 				SPLAY_ROTATE_RIGHT(head, __tmp, field);	\
254 				if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
255 					break;				\
256 			}						\
257 			SPLAY_LINKLEFT(head, __right, field);		\
258 		} else if (__comp > 0) {				\
259 			__tmp = SPLAY_RIGHT((head)->sph_root, field);	\
260 			if (__tmp == NULL)				\
261 				break;					\
262 			if (__comp > 0) {				\
263 				SPLAY_ROTATE_LEFT(head, __tmp, field);	\
264 				if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
265 					break;				\
266 			}						\
267 			SPLAY_LINKRIGHT(head, __left, field);		\
268 		}							\
269 	}								\
270 	SPLAY_ASSEMBLE(head, &__node, __left, __right, field);		\
271 }
272 
273 #define SPLAY_NEGINF	-1
274 #define SPLAY_INF	1
275 
276 #define SPLAY_INSERT(name, x, y)	name##_SPLAY_INSERT(x, y)
277 #define SPLAY_REMOVE(name, x, y)	name##_SPLAY_REMOVE(x, y)
278 #define SPLAY_FIND(name, x, y)		name##_SPLAY_FIND(x, y)
279 #define SPLAY_NEXT(name, x, y)		name##_SPLAY_NEXT(x, y)
280 #define SPLAY_MIN(name, x)		(SPLAY_EMPTY(x) ? NULL	\
281 					: name##_SPLAY_MIN_MAX(x, SPLAY_NEGINF))
282 #define SPLAY_MAX(name, x)		(SPLAY_EMPTY(x) ? NULL	\
283 					: name##_SPLAY_MIN_MAX(x, SPLAY_INF))
284 
285 #define SPLAY_FOREACH(x, name, head)					\
286 	for ((x) = SPLAY_MIN(name, head);				\
287 	     (x) != NULL;						\
288 	     (x) = SPLAY_NEXT(name, head, x))
289 
290 /* Macros that define a red-back tree */
291 #define RB_HEAD(name, type)						\
292 struct name {								\
293 	struct type *rbh_root; /* root of the tree */			\
294 }
295 
296 #define RB_INITIALIZER(root)						\
297 	{ NULL }
298 
299 #define RB_INIT(root) do {						\
300 	(root)->rbh_root = NULL;					\
301 } while (0)
302 
303 #define RB_BLACK	0
304 #define RB_RED		1
305 #define RB_ENTRY(type)							\
306 struct {								\
307 	struct type *rbe_left;		/* left element */		\
308 	struct type *rbe_right;		/* right element */		\
309 	struct type *rbe_parent;	/* parent element */		\
310 	int rbe_color;			/* node color */		\
311 }
312 
313 #define RB_LEFT(elm, field)		(elm)->field.rbe_left
314 #define RB_RIGHT(elm, field)		(elm)->field.rbe_right
315 #define RB_PARENT(elm, field)		(elm)->field.rbe_parent
316 #define RB_COLOR(elm, field)		(elm)->field.rbe_color
317 #define RB_ROOT(head)			(head)->rbh_root
318 #define RB_EMPTY(head)			(RB_ROOT(head) == NULL)
319 
320 #define RB_SET(elm, parent, field) do {					\
321 	RB_PARENT(elm, field) = parent;					\
322 	RB_LEFT(elm, field) = RB_RIGHT(elm, field) = NULL;		\
323 	RB_COLOR(elm, field) = RB_RED;					\
324 } while (0)
325 
326 #define RB_SET_BLACKRED(black, red, field) do {				\
327 	RB_COLOR(black, field) = RB_BLACK;				\
328 	RB_COLOR(red, field) = RB_RED;					\
329 } while (0)
330 
331 #ifndef RB_AUGMENT
332 #define RB_AUGMENT(x)
333 #endif
334 
335 #define RB_ROTATE_LEFT(head, elm, tmp, field) do {			\
336 	(tmp) = RB_RIGHT(elm, field);					\
337 	if ((RB_RIGHT(elm, field) = RB_LEFT(tmp, field))) {		\
338 		RB_PARENT(RB_LEFT(tmp, field), field) = (elm);		\
339 	}								\
340 	RB_AUGMENT(elm);						\
341 	if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field))) {		\
342 		if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))	\
343 			RB_LEFT(RB_PARENT(elm, field), field) = (tmp);	\
344 		else							\
345 			RB_RIGHT(RB_PARENT(elm, field), field) = (tmp);	\
346 		RB_AUGMENT(RB_PARENT(elm, field));			\
347 	} else								\
348 		(head)->rbh_root = (tmp);				\
349 	RB_LEFT(tmp, field) = (elm);					\
350 	RB_PARENT(elm, field) = (tmp);					\
351 	RB_AUGMENT(tmp);						\
352 } while (0)
353 
354 #define RB_ROTATE_RIGHT(head, elm, tmp, field) do {			\
355 	(tmp) = RB_LEFT(elm, field);					\
356 	if ((RB_LEFT(elm, field) = RB_RIGHT(tmp, field))) {		\
357 		RB_PARENT(RB_RIGHT(tmp, field), field) = (elm);		\
358 	}								\
359 	RB_AUGMENT(elm);						\
360 	if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field))) {		\
361 		if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))	\
362 			RB_LEFT(RB_PARENT(elm, field), field) = (tmp);	\
363 		else							\
364 			RB_RIGHT(RB_PARENT(elm, field), field) = (tmp);	\
365 		RB_AUGMENT(RB_PARENT(elm, field));			\
366 	} else								\
367 		(head)->rbh_root = (tmp);				\
368 	RB_RIGHT(tmp, field) = (elm);					\
369 	RB_PARENT(elm, field) = (tmp);					\
370 	RB_AUGMENT(tmp);						\
371 } while (0)
372 
373 /* Generates prototypes and inline functions */
374 #define RB_PROTOTYPE(name, type, field, cmp)				\
375 void name##_RB_INSERT_COLOR(struct name *, struct type *);	\
376 void name##_RB_REMOVE_COLOR(struct name *, struct type *, struct type *);\
377 struct type *name##_RB_REMOVE(struct name *, struct type *);		\
378 struct type *name##_RB_INSERT(struct name *, struct type *);		\
379 struct type *name##_RB_FIND(struct name *, struct type *);		\
380 struct type *name##_RB_NEXT(struct name *, struct type *);		\
381 struct type *name##_RB_MINMAX(struct name *, int);			\
382 									\
383 
384 /* Main rb operation.
385  * Moves node close to the key of elm to top
386  */
387 #define RB_GENERATE(name, type, field, cmp)				\
388 void									\
389 name##_RB_INSERT_COLOR(struct name *head, struct type *elm)		\
390 {									\
391 	struct type *parent, *gparent, *tmp;				\
392 	while ((parent = RB_PARENT(elm, field)) &&			\
393 	    RB_COLOR(parent, field) == RB_RED) {			\
394 		gparent = RB_PARENT(parent, field);			\
395 		if (parent == RB_LEFT(gparent, field)) {		\
396 			tmp = RB_RIGHT(gparent, field);			\
397 			if (tmp && RB_COLOR(tmp, field) == RB_RED) {	\
398 				RB_COLOR(tmp, field) = RB_BLACK;	\
399 				RB_SET_BLACKRED(parent, gparent, field);\
400 				elm = gparent;				\
401 				continue;				\
402 			}						\
403 			if (RB_RIGHT(parent, field) == elm) {		\
404 				RB_ROTATE_LEFT(head, parent, tmp, field);\
405 				tmp = parent;				\
406 				parent = elm;				\
407 				elm = tmp;				\
408 			}						\
409 			RB_SET_BLACKRED(parent, gparent, field);	\
410 			RB_ROTATE_RIGHT(head, gparent, tmp, field);	\
411 		} else {						\
412 			tmp = RB_LEFT(gparent, field);			\
413 			if (tmp && RB_COLOR(tmp, field) == RB_RED) {	\
414 				RB_COLOR(tmp, field) = RB_BLACK;	\
415 				RB_SET_BLACKRED(parent, gparent, field);\
416 				elm = gparent;				\
417 				continue;				\
418 			}						\
419 			if (RB_LEFT(parent, field) == elm) {		\
420 				RB_ROTATE_RIGHT(head, parent, tmp, field);\
421 				tmp = parent;				\
422 				parent = elm;				\
423 				elm = tmp;				\
424 			}						\
425 			RB_SET_BLACKRED(parent, gparent, field);	\
426 			RB_ROTATE_LEFT(head, gparent, tmp, field);	\
427 		}							\
428 	}								\
429 	RB_COLOR(head->rbh_root, field) = RB_BLACK;			\
430 }									\
431 									\
432 void									\
433 name##_RB_REMOVE_COLOR(struct name *head, struct type *parent, struct type *elm) \
434 {									\
435 	struct type *tmp;						\
436 	while ((elm == NULL || RB_COLOR(elm, field) == RB_BLACK) &&	\
437 	    elm != RB_ROOT(head)) {					\
438 		if (RB_LEFT(parent, field) == elm) {			\
439 			tmp = RB_RIGHT(parent, field);			\
440 			if (RB_COLOR(tmp, field) == RB_RED) {		\
441 				RB_SET_BLACKRED(tmp, parent, field);	\
442 				RB_ROTATE_LEFT(head, parent, tmp, field);\
443 				tmp = RB_RIGHT(parent, field);		\
444 			}						\
445 			if ((RB_LEFT(tmp, field) == NULL ||		\
446 			    RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
447 			    (RB_RIGHT(tmp, field) == NULL ||		\
448 			    RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
449 				RB_COLOR(tmp, field) = RB_RED;		\
450 				elm = parent;				\
451 				parent = RB_PARENT(elm, field);		\
452 			} else {					\
453 				if (RB_RIGHT(tmp, field) == NULL ||	\
454 				    RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK) {\
455 					struct type *oleft;		\
456 					if ((oleft = RB_LEFT(tmp, field)))\
457 						RB_COLOR(oleft, field) = RB_BLACK;\
458 					RB_COLOR(tmp, field) = RB_RED;	\
459 					RB_ROTATE_RIGHT(head, tmp, oleft, field);\
460 					tmp = RB_RIGHT(parent, field);	\
461 				}					\
462 				RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
463 				RB_COLOR(parent, field) = RB_BLACK;	\
464 				if (RB_RIGHT(tmp, field))		\
465 					RB_COLOR(RB_RIGHT(tmp, field), field) = RB_BLACK;\
466 				RB_ROTATE_LEFT(head, parent, tmp, field);\
467 				elm = RB_ROOT(head);			\
468 				break;					\
469 			}						\
470 		} else {						\
471 			tmp = RB_LEFT(parent, field);			\
472 			if (RB_COLOR(tmp, field) == RB_RED) {		\
473 				RB_SET_BLACKRED(tmp, parent, field);	\
474 				RB_ROTATE_RIGHT(head, parent, tmp, field);\
475 				tmp = RB_LEFT(parent, field);		\
476 			}						\
477 			if ((RB_LEFT(tmp, field) == NULL ||		\
478 			    RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
479 			    (RB_RIGHT(tmp, field) == NULL ||		\
480 			    RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
481 				RB_COLOR(tmp, field) = RB_RED;		\
482 				elm = parent;				\
483 				parent = RB_PARENT(elm, field);		\
484 			} else {					\
485 				if (RB_LEFT(tmp, field) == NULL ||	\
486 				    RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) {\
487 					struct type *oright;		\
488 					if ((oright = RB_RIGHT(tmp, field)))\
489 						RB_COLOR(oright, field) = RB_BLACK;\
490 					RB_COLOR(tmp, field) = RB_RED;	\
491 					RB_ROTATE_LEFT(head, tmp, oright, field);\
492 					tmp = RB_LEFT(parent, field);	\
493 				}					\
494 				RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
495 				RB_COLOR(parent, field) = RB_BLACK;	\
496 				if (RB_LEFT(tmp, field))		\
497 					RB_COLOR(RB_LEFT(tmp, field), field) = RB_BLACK;\
498 				RB_ROTATE_RIGHT(head, parent, tmp, field);\
499 				elm = RB_ROOT(head);			\
500 				break;					\
501 			}						\
502 		}							\
503 	}								\
504 	if (elm)							\
505 		RB_COLOR(elm, field) = RB_BLACK;			\
506 }									\
507 									\
508 struct type *								\
509 name##_RB_REMOVE(struct name *head, struct type *elm)			\
510 {									\
511 	struct type *child, *parent, *old = elm;			\
512 	int color;							\
513 	if (RB_LEFT(elm, field) == NULL)				\
514 		child = RB_RIGHT(elm, field);				\
515 	else if (RB_RIGHT(elm, field) == NULL)				\
516 		child = RB_LEFT(elm, field);				\
517 	else {								\
518 		struct type *left;					\
519 		elm = RB_RIGHT(elm, field);				\
520 		while ((left = RB_LEFT(elm, field)))			\
521 			elm = left;					\
522 		child = RB_RIGHT(elm, field);				\
523 		parent = RB_PARENT(elm, field);				\
524 		color = RB_COLOR(elm, field);				\
525 		if (child)						\
526 			RB_PARENT(child, field) = parent;		\
527 		if (parent) {						\
528 			if (RB_LEFT(parent, field) == elm)		\
529 				RB_LEFT(parent, field) = child;		\
530 			else						\
531 				RB_RIGHT(parent, field) = child;	\
532 			RB_AUGMENT(parent);				\
533 		} else							\
534 			RB_ROOT(head) = child;				\
535 		if (RB_PARENT(elm, field) == old)			\
536 			parent = elm;					\
537 		(elm)->field = (old)->field;				\
538 		if (RB_PARENT(old, field)) {				\
539 			if (RB_LEFT(RB_PARENT(old, field), field) == old)\
540 				RB_LEFT(RB_PARENT(old, field), field) = elm;\
541 			else						\
542 				RB_RIGHT(RB_PARENT(old, field), field) = elm;\
543 			RB_AUGMENT(RB_PARENT(old, field));		\
544 		} else							\
545 			RB_ROOT(head) = elm;				\
546 		RB_PARENT(RB_LEFT(old, field), field) = elm;		\
547 		if (RB_RIGHT(old, field))				\
548 			RB_PARENT(RB_RIGHT(old, field), field) = elm;	\
549 		if (parent) {						\
550 			left = parent;					\
551 			do {						\
552 				RB_AUGMENT(left);			\
553 			} while ((left = RB_PARENT(left, field)));	\
554 		}							\
555 		goto color;						\
556 	}								\
557 	parent = RB_PARENT(elm, field);					\
558 	color = RB_COLOR(elm, field);					\
559 	if (child)							\
560 		RB_PARENT(child, field) = parent;			\
561 	if (parent) {							\
562 		if (RB_LEFT(parent, field) == elm)			\
563 			RB_LEFT(parent, field) = child;			\
564 		else							\
565 			RB_RIGHT(parent, field) = child;		\
566 		RB_AUGMENT(parent);					\
567 	} else								\
568 		RB_ROOT(head) = child;					\
569 color:									\
570 	if (color == RB_BLACK)						\
571 		name##_RB_REMOVE_COLOR(head, parent, child);		\
572 	return (old);							\
573 }									\
574 									\
575 /* Inserts a node into the RB tree */					\
576 struct type *								\
577 name##_RB_INSERT(struct name *head, struct type *elm)			\
578 {									\
579 	struct type *tmp;						\
580 	struct type *parent = NULL;					\
581 	int comp = 0;							\
582 	tmp = RB_ROOT(head);						\
583 	while (tmp) {							\
584 		parent = tmp;						\
585 		comp = (cmp)(elm, parent);				\
586 		if (comp < 0)						\
587 			tmp = RB_LEFT(tmp, field);			\
588 		else if (comp > 0)					\
589 			tmp = RB_RIGHT(tmp, field);			\
590 		else							\
591 			return (tmp);					\
592 	}								\
593 	RB_SET(elm, parent, field);					\
594 	if (parent != NULL) {						\
595 		if (comp < 0)						\
596 			RB_LEFT(parent, field) = elm;			\
597 		else							\
598 			RB_RIGHT(parent, field) = elm;			\
599 		RB_AUGMENT(parent);					\
600 	} else								\
601 		RB_ROOT(head) = elm;					\
602 	name##_RB_INSERT_COLOR(head, elm);				\
603 	return (NULL);							\
604 }									\
605 									\
606 /* Finds the node with the same key as elm */				\
607 struct type *								\
608 name##_RB_FIND(struct name *head, struct type *elm)			\
609 {									\
610 	struct type *tmp = RB_ROOT(head);				\
611 	int comp;							\
612 	while (tmp) {							\
613 		comp = cmp(elm, tmp);					\
614 		if (comp < 0)						\
615 			tmp = RB_LEFT(tmp, field);			\
616 		else if (comp > 0)					\
617 			tmp = RB_RIGHT(tmp, field);			\
618 		else							\
619 			return (tmp);					\
620 	}								\
621 	return (NULL);							\
622 }									\
623 									\
624 struct type *								\
625 name##_RB_NEXT(struct name *head, struct type *elm)			\
626 {									\
627 	if (RB_RIGHT(elm, field)) {					\
628 		elm = RB_RIGHT(elm, field);				\
629 		while (RB_LEFT(elm, field))				\
630 			elm = RB_LEFT(elm, field);			\
631 	} else {							\
632 		if (RB_PARENT(elm, field) &&				\
633 		    (elm == RB_LEFT(RB_PARENT(elm, field), field)))	\
634 			elm = RB_PARENT(elm, field);			\
635 		else {							\
636 			while (RB_PARENT(elm, field) &&			\
637 			    (elm == RB_RIGHT(RB_PARENT(elm, field), field)))\
638 				elm = RB_PARENT(elm, field);		\
639 			elm = RB_PARENT(elm, field);			\
640 		}							\
641 	}								\
642 	return (elm);							\
643 }									\
644 									\
645 struct type *								\
646 name##_RB_MINMAX(struct name *head, int val)				\
647 {									\
648 	struct type *tmp = RB_ROOT(head);				\
649 	struct type *parent = NULL;					\
650 	while (tmp) {							\
651 		parent = tmp;						\
652 		if (val < 0)						\
653 			tmp = RB_LEFT(tmp, field);			\
654 		else							\
655 			tmp = RB_RIGHT(tmp, field);			\
656 	}								\
657 	return (parent);						\
658 }
659 
660 #define RB_NEGINF	-1
661 #define RB_INF	1
662 
663 #define RB_INSERT(name, x, y)	name##_RB_INSERT(x, y)
664 #define RB_REMOVE(name, x, y)	name##_RB_REMOVE(x, y)
665 #define RB_FIND(name, x, y)	name##_RB_FIND(x, y)
666 #define RB_NEXT(name, x, y)	name##_RB_NEXT(x, y)
667 #define RB_MIN(name, x)		name##_RB_MINMAX(x, RB_NEGINF)
668 #define RB_MAX(name, x)		name##_RB_MINMAX(x, RB_INF)
669 
670 #define RB_FOREACH(x, name, head)					\
671 	for ((x) = RB_MIN(name, head);					\
672 	     (x) != NULL;						\
673 	     (x) = name##_RB_NEXT(head, x))
674 
675 #endif	/* _SYS_TREE_H_ */
676