xref: /dragonfly/sys/sys/tree.h (revision 0ac6bf9d) 
1 /*	$NetBSD: tree.h,v 1.8 2004/03/28 19:38:30 provos Exp $	*/
2 /*	$OpenBSD: tree.h,v 1.7 2002/10/17 21:51:54 art Exp $	*/
3 /*	$DragonFly: src/sys/sys/tree.h,v 1.5 2006/03/28 22:17:05 dillon Exp $ */
4 /*
5  * Copyright 2002 Niels Provos <provos@citi.umich.edu>
6  * All rights reserved.
7  *
8  * Redistribution and use in source and binary forms, with or without
9  * modification, are permitted provided that the following conditions
10  * are met:
11  * 1. Redistributions of source code must retain the above copyright
12  *    notice, this list of conditions and the following disclaimer.
13  * 2. Redistributions in binary form must reproduce the above copyright
14  *    notice, this list of conditions and the following disclaimer in the
15  *    documentation and/or other materials provided with the distribution.
16  *
17  * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
18  * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
19  * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
20  * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
21  * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
22  * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
23  * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
24  * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
25  * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
26  * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
27  */
28 
29 #ifndef	_SYS_TREE_H_
30 #define	_SYS_TREE_H_
31 
32 /*
33  * This file defines data structures for different types of trees:
34  * splay trees and red-black trees.
35  *
36  * A splay tree is a self-organizing data structure.  Every operation
37  * on the tree causes a splay to happen.  The splay moves the requested
38  * node to the root of the tree and partly rebalances it.
39  *
40  * This has the benefit that request locality causes faster lookups as
41  * the requested nodes move to the top of the tree.  On the other hand,
42  * every lookup causes memory writes.
43  *
44  * The Balance Theorem bounds the total access time for m operations
45  * and n inserts on an initially empty tree as O((m + n)lg n).  The
46  * amortized cost for a sequence of m accesses to a splay tree is O(lg n);
47  *
48  * A red-black tree is a binary search tree with the node color as an
49  * extra attribute.  It fulfills a set of conditions:
50  *	- every search path from the root to a leaf consists of the
51  *	  same number of black nodes,
52  *	- each red node (except for the root) has a black parent,
53  *	- each leaf node is black.
54  *
55  * Every operation on a red-black tree is bounded as O(lg n).
56  * The maximum height of a red-black tree is 2lg (n+1).
57  */
58 
59 #define SPLAY_HEAD(name, type)						\
60 struct name {								\
61 	struct type *sph_root; /* root of the tree */			\
62 }
63 
64 #define SPLAY_INITIALIZER(root)						\
65 	{ NULL }
66 
67 #define SPLAY_INIT(root) do {						\
68 	(root)->sph_root = NULL;					\
69 } while (/*CONSTCOND*/ 0)
70 
71 #define SPLAY_ENTRY(type)						\
72 struct {								\
73 	struct type *spe_left; /* left element */			\
74 	struct type *spe_right; /* right element */			\
75 }
76 
77 #define SPLAY_LEFT(elm, field)		(elm)->field.spe_left
78 #define SPLAY_RIGHT(elm, field)		(elm)->field.spe_right
79 #define SPLAY_ROOT(head)		(head)->sph_root
80 #define SPLAY_EMPTY(head)		(SPLAY_ROOT(head) == NULL)
81 
82 /* SPLAY_ROTATE_{LEFT,RIGHT} expect that tmp hold SPLAY_{RIGHT,LEFT} */
83 #define SPLAY_ROTATE_RIGHT(head, tmp, field) do {			\
84 	SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(tmp, field);	\
85 	SPLAY_RIGHT(tmp, field) = (head)->sph_root;			\
86 	(head)->sph_root = tmp;						\
87 } while (/*CONSTCOND*/ 0)
88 
89 #define SPLAY_ROTATE_LEFT(head, tmp, field) do {			\
90 	SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(tmp, field);	\
91 	SPLAY_LEFT(tmp, field) = (head)->sph_root;			\
92 	(head)->sph_root = tmp;						\
93 } while (/*CONSTCOND*/ 0)
94 
95 #define SPLAY_LINKLEFT(head, tmp, field) do {				\
96 	SPLAY_LEFT(tmp, field) = (head)->sph_root;			\
97 	tmp = (head)->sph_root;						\
98 	(head)->sph_root = SPLAY_LEFT((head)->sph_root, field);		\
99 } while (/*CONSTCOND*/ 0)
100 
101 #define SPLAY_LINKRIGHT(head, tmp, field) do {				\
102 	SPLAY_RIGHT(tmp, field) = (head)->sph_root;			\
103 	tmp = (head)->sph_root;						\
104 	(head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);	\
105 } while (/*CONSTCOND*/ 0)
106 
107 #define SPLAY_ASSEMBLE(head, node, left, right, field) do {		\
108 	SPLAY_RIGHT(left, field) = SPLAY_LEFT((head)->sph_root, field);	\
109 	SPLAY_LEFT(right, field) = SPLAY_RIGHT((head)->sph_root, field);\
110 	SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(node, field);	\
111 	SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(node, field);	\
112 } while (/*CONSTCOND*/ 0)
113 
114 /* Generates prototypes and inline functions */
115 
116 #define SPLAY_PROTOTYPE(name, type, field, cmp)				\
117 void name##_SPLAY(struct name *, struct type *);			\
118 void name##_SPLAY_MINMAX(struct name *, int);				\
119 struct type *name##_SPLAY_INSERT(struct name *, struct type *);		\
120 struct type *name##_SPLAY_REMOVE(struct name *, struct type *);		\
121 									\
122 /* Finds the node with the same key as elm */				\
123 static __inline struct type *						\
124 name##_SPLAY_FIND(struct name *head, struct type *elm)			\
125 {									\
126 	if (SPLAY_EMPTY(head))						\
127 		return(NULL);						\
128 	name##_SPLAY(head, elm);					\
129 	if ((cmp)(elm, (head)->sph_root) == 0)				\
130 		return (head->sph_root);				\
131 	return (NULL);							\
132 }									\
133 									\
134 static __inline struct type *						\
135 name##_SPLAY_NEXT(struct name *head, struct type *elm)			\
136 {									\
137 	name##_SPLAY(head, elm);					\
138 	if (SPLAY_RIGHT(elm, field) != NULL) {				\
139 		elm = SPLAY_RIGHT(elm, field);				\
140 		while (SPLAY_LEFT(elm, field) != NULL) {		\
141 			elm = SPLAY_LEFT(elm, field);			\
142 		}							\
143 	} else								\
144 		elm = NULL;						\
145 	return (elm);							\
146 }									\
147 									\
148 static __inline struct type *						\
149 name##_SPLAY_MIN_MAX(struct name *head, int val)			\
150 {									\
151 	name##_SPLAY_MINMAX(head, val);					\
152         return (SPLAY_ROOT(head));					\
153 }
154 
155 /* Main splay operation.
156  * Moves node close to the key of elm to top
157  */
158 #define SPLAY_GENERATE(name, type, field, cmp)				\
159 struct type *								\
160 name##_SPLAY_INSERT(struct name *head, struct type *elm)		\
161 {									\
162     if (SPLAY_EMPTY(head)) {						\
163 	    SPLAY_LEFT(elm, field) = SPLAY_RIGHT(elm, field) = NULL;	\
164     } else {								\
165 	    int __comp;							\
166 	    name##_SPLAY(head, elm);					\
167 	    __comp = (cmp)(elm, (head)->sph_root);			\
168 	    if(__comp < 0) {						\
169 		    SPLAY_LEFT(elm, field) = SPLAY_LEFT((head)->sph_root, field);\
170 		    SPLAY_RIGHT(elm, field) = (head)->sph_root;		\
171 		    SPLAY_LEFT((head)->sph_root, field) = NULL;		\
172 	    } else if (__comp > 0) {					\
173 		    SPLAY_RIGHT(elm, field) = SPLAY_RIGHT((head)->sph_root, field);\
174 		    SPLAY_LEFT(elm, field) = (head)->sph_root;		\
175 		    SPLAY_RIGHT((head)->sph_root, field) = NULL;	\
176 	    } else							\
177 		    return ((head)->sph_root);				\
178     }									\
179     (head)->sph_root = (elm);						\
180     return (NULL);							\
181 }									\
182 									\
183 struct type *								\
184 name##_SPLAY_REMOVE(struct name *head, struct type *elm)		\
185 {									\
186 	struct type *__tmp;						\
187 	if (SPLAY_EMPTY(head))						\
188 		return (NULL);						\
189 	name##_SPLAY(head, elm);					\
190 	if ((cmp)(elm, (head)->sph_root) == 0) {			\
191 		if (SPLAY_LEFT((head)->sph_root, field) == NULL) {	\
192 			(head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);\
193 		} else {						\
194 			__tmp = SPLAY_RIGHT((head)->sph_root, field);	\
195 			(head)->sph_root = SPLAY_LEFT((head)->sph_root, field);\
196 			name##_SPLAY(head, elm);			\
197 			SPLAY_RIGHT((head)->sph_root, field) = __tmp;	\
198 		}							\
199 		return (elm);						\
200 	}								\
201 	return (NULL);							\
202 }									\
203 									\
204 void									\
205 name##_SPLAY(struct name *head, struct type *elm)			\
206 {									\
207 	struct type __node, *__left, *__right, *__tmp;			\
208 	int __comp;							\
209 \
210 	SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
211 	__left = __right = &__node;					\
212 \
213 	while ((__comp = (cmp)(elm, (head)->sph_root)) != 0) {		\
214 		if (__comp < 0) {					\
215 			__tmp = SPLAY_LEFT((head)->sph_root, field);	\
216 			if (__tmp == NULL)				\
217 				break;					\
218 			if ((cmp)(elm, __tmp) < 0){			\
219 				SPLAY_ROTATE_RIGHT(head, __tmp, field);	\
220 				if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
221 					break;				\
222 			}						\
223 			SPLAY_LINKLEFT(head, __right, field);		\
224 		} else if (__comp > 0) {				\
225 			__tmp = SPLAY_RIGHT((head)->sph_root, field);	\
226 			if (__tmp == NULL)				\
227 				break;					\
228 			if ((cmp)(elm, __tmp) > 0){			\
229 				SPLAY_ROTATE_LEFT(head, __tmp, field);	\
230 				if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
231 					break;				\
232 			}						\
233 			SPLAY_LINKRIGHT(head, __left, field);		\
234 		}							\
235 	}								\
236 	SPLAY_ASSEMBLE(head, &__node, __left, __right, field);		\
237 }									\
238 									\
239 /* Splay with either the minimum or the maximum element			\
240  * Used to find minimum or maximum element in tree.			\
241  */									\
242 void name##_SPLAY_MINMAX(struct name *head, int __comp) \
243 {									\
244 	struct type __node, *__left, *__right, *__tmp;			\
245 \
246 	SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
247 	__left = __right = &__node;					\
248 \
249 	while (1) {							\
250 		if (__comp < 0) {					\
251 			__tmp = SPLAY_LEFT((head)->sph_root, field);	\
252 			if (__tmp == NULL)				\
253 				break;					\
254 			if (__comp < 0){				\
255 				SPLAY_ROTATE_RIGHT(head, __tmp, field);	\
256 				if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
257 					break;				\
258 			}						\
259 			SPLAY_LINKLEFT(head, __right, field);		\
260 		} else if (__comp > 0) {				\
261 			__tmp = SPLAY_RIGHT((head)->sph_root, field);	\
262 			if (__tmp == NULL)				\
263 				break;					\
264 			if (__comp > 0) {				\
265 				SPLAY_ROTATE_LEFT(head, __tmp, field);	\
266 				if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
267 					break;				\
268 			}						\
269 			SPLAY_LINKRIGHT(head, __left, field);		\
270 		}							\
271 	}								\
272 	SPLAY_ASSEMBLE(head, &__node, __left, __right, field);		\
273 }
274 
275 #define SPLAY_NEGINF	-1
276 #define SPLAY_INF	1
277 
278 #define SPLAY_INSERT(name, x, y)	name##_SPLAY_INSERT(x, y)
279 #define SPLAY_REMOVE(name, x, y)	name##_SPLAY_REMOVE(x, y)
280 #define SPLAY_FIND(name, x, y)		name##_SPLAY_FIND(x, y)
281 #define SPLAY_NEXT(name, x, y)		name##_SPLAY_NEXT(x, y)
282 #define SPLAY_MIN(name, x)		(SPLAY_EMPTY(x) ? NULL	\
283 					: name##_SPLAY_MIN_MAX(x, SPLAY_NEGINF))
284 #define SPLAY_MAX(name, x)		(SPLAY_EMPTY(x) ? NULL	\
285 					: name##_SPLAY_MIN_MAX(x, SPLAY_INF))
286 
287 #define SPLAY_FOREACH(x, name, head)					\
288 	for ((x) = SPLAY_MIN(name, head);				\
289 	     (x) != NULL;						\
290 	     (x) = SPLAY_NEXT(name, head, x))
291 
292 /* Macros that define a red-black tree */
293 
294 #define RB_SCAN_INFO(name, type)					\
295 struct name##_scan_info {						\
296 	struct name##_scan_info *link;					\
297 	struct type	*node;						\
298 }
299 
300 #define RB_HEAD(name, type)						\
301 struct name {								\
302 	struct type *rbh_root; 		     /* root of the tree */	\
303 	struct name##_scan_info *rbh_inprog; /* scans in progress */	\
304 }
305 
306 #define RB_INITIALIZER(root)						\
307 	{ NULL, NULL }
308 
309 #define RB_INIT(root) do {						\
310 	(root)->rbh_root = NULL;					\
311 	(root)->rbh_inprog = NULL;					\
312 } while (/*CONSTCOND*/ 0)
313 
314 #define RB_BLACK	0
315 #define RB_RED		1
316 #define RB_ENTRY(type)							\
317 struct {								\
318 	struct type *rbe_left;		/* left element */		\
319 	struct type *rbe_right;		/* right element */		\
320 	struct type *rbe_parent;	/* parent element */		\
321 	int rbe_color;			/* node color */		\
322 }
323 
324 #define RB_LEFT(elm, field)		(elm)->field.rbe_left
325 #define RB_RIGHT(elm, field)		(elm)->field.rbe_right
326 #define RB_PARENT(elm, field)		(elm)->field.rbe_parent
327 #define RB_COLOR(elm, field)		(elm)->field.rbe_color
328 #define RB_ROOT(head)			(head)->rbh_root
329 #define RB_INPROG(head)			(head)->rbh_inprog
330 #define RB_EMPTY(head)			(RB_ROOT(head) == NULL)
331 
332 #define RB_SET(elm, parent, field) do {					\
333 	RB_PARENT(elm, field) = parent;					\
334 	RB_LEFT(elm, field) = RB_RIGHT(elm, field) = NULL;		\
335 	RB_COLOR(elm, field) = RB_RED;					\
336 } while (/*CONSTCOND*/ 0)
337 
338 #define RB_SET_BLACKRED(black, red, field) do {				\
339 	RB_COLOR(black, field) = RB_BLACK;				\
340 	RB_COLOR(red, field) = RB_RED;					\
341 } while (/*CONSTCOND*/ 0)
342 
343 #ifndef RB_AUGMENT
344 #define RB_AUGMENT(x)
345 #endif
346 
347 #define RB_ROTATE_LEFT(head, elm, tmp, field) do {			\
348 	(tmp) = RB_RIGHT(elm, field);					\
349 	if ((RB_RIGHT(elm, field) = RB_LEFT(tmp, field)) != NULL) {	\
350 		RB_PARENT(RB_LEFT(tmp, field), field) = (elm);		\
351 	}								\
352 	RB_AUGMENT(elm);						\
353 	if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) {	\
354 		if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))	\
355 			RB_LEFT(RB_PARENT(elm, field), field) = (tmp);	\
356 		else							\
357 			RB_RIGHT(RB_PARENT(elm, field), field) = (tmp);	\
358 	} else								\
359 		(head)->rbh_root = (tmp);				\
360 	RB_LEFT(tmp, field) = (elm);					\
361 	RB_PARENT(elm, field) = (tmp);					\
362 	RB_AUGMENT(tmp);						\
363 	if ((RB_PARENT(tmp, field)))					\
364 		RB_AUGMENT(RB_PARENT(tmp, field));			\
365 } while (/*CONSTCOND*/ 0)
366 
367 #define RB_ROTATE_RIGHT(head, elm, tmp, field) do {			\
368 	(tmp) = RB_LEFT(elm, field);					\
369 	if ((RB_LEFT(elm, field) = RB_RIGHT(tmp, field)) != NULL) {	\
370 		RB_PARENT(RB_RIGHT(tmp, field), field) = (elm);		\
371 	}								\
372 	RB_AUGMENT(elm);						\
373 	if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) {	\
374 		if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))	\
375 			RB_LEFT(RB_PARENT(elm, field), field) = (tmp);	\
376 		else							\
377 			RB_RIGHT(RB_PARENT(elm, field), field) = (tmp);	\
378 	} else								\
379 		(head)->rbh_root = (tmp);				\
380 	RB_RIGHT(tmp, field) = (elm);					\
381 	RB_PARENT(elm, field) = (tmp);					\
382 	RB_AUGMENT(tmp);						\
383 	if ((RB_PARENT(tmp, field)))					\
384 		RB_AUGMENT(RB_PARENT(tmp, field));			\
385 } while (/*CONSTCOND*/ 0)
386 
387 /* Generates prototypes and inline functions */
388 #define RB_PROTOTYPE(name, type, field, cmp)				\
389 struct type *name##_RB_REMOVE(struct name *, struct type *);		\
390 struct type *name##_RB_INSERT(struct name *, struct type *);		\
391 struct type *name##_RB_FIND(struct name *, struct type *);		\
392 int name##_RB_SCAN(struct name *, int (*)(struct type *, void *),	\
393 			int (*)(struct type *, void *), void *);	\
394 struct type *name##_RB_NEXT(struct type *);				\
395 struct type *name##_RB_PREV(struct type *);				\
396 struct type *name##_RB_MINMAX(struct name *, int);			\
397 RB_SCAN_INFO(name, type)						\
398 
399 /*
400  * A version which supplies a fast lookup routine for an exact match
401  * on a numeric field.
402  */
403 #define RB_PROTOTYPE2(name, type, field, cmp, datatype)			\
404 RB_PROTOTYPE(name, type, field, cmp);					\
405 struct type *name##_RB_LOOKUP(struct name *, datatype)			\
406 
407 /*
408  * A version which supplies a fast lookup routine for a numeric
409  * field which resides within a ranged object, either using (begin,end),
410  * or using (begin,size).
411  */
412 #define RB_PROTOTYPE3(name, type, field, cmp, datatype)			\
413 RB_PROTOTYPE2(name, type, field, cmp, datatype);			\
414 struct type *name##_RB_RLOOKUP(struct name *, datatype)			\
415 
416 #define RB_PROTOTYPE4(name, type, field, cmp, datatype)			\
417 RB_PROTOTYPE2(name, type, field, cmp, datatype);			\
418 struct type *name##_RB_RLOOKUP(struct name *, datatype)			\
419 
420 /* Main rb operation.
421  * Moves node close to the key of elm to top
422  */
423 #define RB_GENERATE(name, type, field, cmp)				\
424 static void								\
425 name##_RB_INSERT_COLOR(struct name *head, struct type *elm)		\
426 {									\
427 	struct type *parent, *gparent, *tmp;				\
428 	while ((parent = RB_PARENT(elm, field)) != NULL &&		\
429 	    RB_COLOR(parent, field) == RB_RED) {			\
430 		gparent = RB_PARENT(parent, field);			\
431 		if (parent == RB_LEFT(gparent, field)) {		\
432 			tmp = RB_RIGHT(gparent, field);			\
433 			if (tmp && RB_COLOR(tmp, field) == RB_RED) {	\
434 				RB_COLOR(tmp, field) = RB_BLACK;	\
435 				RB_SET_BLACKRED(parent, gparent, field);\
436 				elm = gparent;				\
437 				continue;				\
438 			}						\
439 			if (RB_RIGHT(parent, field) == elm) {		\
440 				RB_ROTATE_LEFT(head, parent, tmp, field);\
441 				tmp = parent;				\
442 				parent = elm;				\
443 				elm = tmp;				\
444 			}						\
445 			RB_SET_BLACKRED(parent, gparent, field);	\
446 			RB_ROTATE_RIGHT(head, gparent, tmp, field);	\
447 		} else {						\
448 			tmp = RB_LEFT(gparent, field);			\
449 			if (tmp && RB_COLOR(tmp, field) == RB_RED) {	\
450 				RB_COLOR(tmp, field) = RB_BLACK;	\
451 				RB_SET_BLACKRED(parent, gparent, field);\
452 				elm = gparent;				\
453 				continue;				\
454 			}						\
455 			if (RB_LEFT(parent, field) == elm) {		\
456 				RB_ROTATE_RIGHT(head, parent, tmp, field);\
457 				tmp = parent;				\
458 				parent = elm;				\
459 				elm = tmp;				\
460 			}						\
461 			RB_SET_BLACKRED(parent, gparent, field);	\
462 			RB_ROTATE_LEFT(head, gparent, tmp, field);	\
463 		}							\
464 	}								\
465 	RB_COLOR(head->rbh_root, field) = RB_BLACK;			\
466 }									\
467 									\
468 static void								\
469 name##_RB_REMOVE_COLOR(struct name *head, struct type *parent,		\
470 			struct type *elm) 				\
471 {									\
472 	struct type *tmp;						\
473 	while ((elm == NULL || RB_COLOR(elm, field) == RB_BLACK) &&	\
474 	    elm != RB_ROOT(head)) {					\
475 		if (RB_LEFT(parent, field) == elm) {			\
476 			tmp = RB_RIGHT(parent, field);			\
477 			if (RB_COLOR(tmp, field) == RB_RED) {		\
478 				RB_SET_BLACKRED(tmp, parent, field);	\
479 				RB_ROTATE_LEFT(head, parent, tmp, field);\
480 				tmp = RB_RIGHT(parent, field);		\
481 			}						\
482 			if ((RB_LEFT(tmp, field) == NULL ||		\
483 			    RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
484 			    (RB_RIGHT(tmp, field) == NULL ||		\
485 			    RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
486 				RB_COLOR(tmp, field) = RB_RED;		\
487 				elm = parent;				\
488 				parent = RB_PARENT(elm, field);		\
489 			} else {					\
490 				if (RB_RIGHT(tmp, field) == NULL ||	\
491 				    RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK) {\
492 					struct type *oleft;		\
493 					if ((oleft = RB_LEFT(tmp, field)) \
494 					    != NULL)			\
495 						RB_COLOR(oleft, field) = RB_BLACK;\
496 					RB_COLOR(tmp, field) = RB_RED;	\
497 					RB_ROTATE_RIGHT(head, tmp, oleft, field);\
498 					tmp = RB_RIGHT(parent, field);	\
499 				}					\
500 				RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
501 				RB_COLOR(parent, field) = RB_BLACK;	\
502 				if (RB_RIGHT(tmp, field))		\
503 					RB_COLOR(RB_RIGHT(tmp, field), field) = RB_BLACK;\
504 				RB_ROTATE_LEFT(head, parent, tmp, field);\
505 				elm = RB_ROOT(head);			\
506 				break;					\
507 			}						\
508 		} else {						\
509 			tmp = RB_LEFT(parent, field);			\
510 			if (RB_COLOR(tmp, field) == RB_RED) {		\
511 				RB_SET_BLACKRED(tmp, parent, field);	\
512 				RB_ROTATE_RIGHT(head, parent, tmp, field);\
513 				tmp = RB_LEFT(parent, field);		\
514 			}						\
515 			if ((RB_LEFT(tmp, field) == NULL ||		\
516 			    RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
517 			    (RB_RIGHT(tmp, field) == NULL ||		\
518 			    RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
519 				RB_COLOR(tmp, field) = RB_RED;		\
520 				elm = parent;				\
521 				parent = RB_PARENT(elm, field);		\
522 			} else {					\
523 				if (RB_LEFT(tmp, field) == NULL ||	\
524 				    RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) {\
525 					struct type *oright;		\
526 					if ((oright = RB_RIGHT(tmp, field)) \
527 					    != NULL)			\
528 						RB_COLOR(oright, field) = RB_BLACK;\
529 					RB_COLOR(tmp, field) = RB_RED;	\
530 					RB_ROTATE_LEFT(head, tmp, oright, field);\
531 					tmp = RB_LEFT(parent, field);	\
532 				}					\
533 				RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
534 				RB_COLOR(parent, field) = RB_BLACK;	\
535 				if (RB_LEFT(tmp, field))		\
536 					RB_COLOR(RB_LEFT(tmp, field), field) = RB_BLACK;\
537 				RB_ROTATE_RIGHT(head, parent, tmp, field);\
538 				elm = RB_ROOT(head);			\
539 				break;					\
540 			}						\
541 		}							\
542 	}								\
543 	if (elm)							\
544 		RB_COLOR(elm, field) = RB_BLACK;			\
545 }									\
546 									\
547 struct type *								\
548 name##_RB_REMOVE(struct name *head, struct type *elm)			\
549 {									\
550 	struct type *child, *parent, *old;				\
551 	struct name##_scan_info *inprog;				\
552 	int color;							\
553 									\
554 	for (inprog = RB_INPROG(head); inprog; inprog = inprog->link) { \
555 		if (inprog->node == elm) 				\
556 			inprog->node = RB_NEXT(name, head, elm);	\
557 	}								\
558 									\
559 	old = elm;							\
560 	if (RB_LEFT(elm, field) == NULL)				\
561 		child = RB_RIGHT(elm, field);				\
562 	else if (RB_RIGHT(elm, field) == NULL)				\
563 		child = RB_LEFT(elm, field);				\
564 	else {								\
565 		struct type *left;					\
566 		elm = RB_RIGHT(elm, field);				\
567 		while ((left = RB_LEFT(elm, field)) != NULL)		\
568 			elm = left;					\
569 		child = RB_RIGHT(elm, field);				\
570 		parent = RB_PARENT(elm, field);				\
571 		color = RB_COLOR(elm, field);				\
572 		if (child)						\
573 			RB_PARENT(child, field) = parent;		\
574 		if (parent) {						\
575 			if (RB_LEFT(parent, field) == elm)		\
576 				RB_LEFT(parent, field) = child;		\
577 			else						\
578 				RB_RIGHT(parent, field) = child;	\
579 			RB_AUGMENT(parent);				\
580 		} else							\
581 			RB_ROOT(head) = child;				\
582 		if (RB_PARENT(elm, field) == old)			\
583 			parent = elm;					\
584 		(elm)->field = (old)->field;				\
585 		if (RB_PARENT(old, field)) {				\
586 			if (RB_LEFT(RB_PARENT(old, field), field) == old)\
587 				RB_LEFT(RB_PARENT(old, field), field) = elm;\
588 			else						\
589 				RB_RIGHT(RB_PARENT(old, field), field) = elm;\
590 			RB_AUGMENT(RB_PARENT(old, field));		\
591 		} else							\
592 			RB_ROOT(head) = elm;				\
593 		RB_PARENT(RB_LEFT(old, field), field) = elm;		\
594 		if (RB_RIGHT(old, field))				\
595 			RB_PARENT(RB_RIGHT(old, field), field) = elm;	\
596 		if (parent) {						\
597 			left = parent;					\
598 			do {						\
599 				RB_AUGMENT(left);			\
600 			} while ((left = RB_PARENT(left, field)) != NULL); \
601 		}							\
602 		goto color;						\
603 	}								\
604 	parent = RB_PARENT(elm, field);					\
605 	color = RB_COLOR(elm, field);					\
606 	if (child)							\
607 		RB_PARENT(child, field) = parent;			\
608 	if (parent) {							\
609 		if (RB_LEFT(parent, field) == elm)			\
610 			RB_LEFT(parent, field) = child;			\
611 		else							\
612 			RB_RIGHT(parent, field) = child;		\
613 		RB_AUGMENT(parent);					\
614 	} else								\
615 		RB_ROOT(head) = child;					\
616 color:									\
617 	if (color == RB_BLACK)						\
618 		name##_RB_REMOVE_COLOR(head, parent, child);		\
619 	return (old);							\
620 }									\
621 									\
622 /* Inserts a node into the RB tree */					\
623 struct type *								\
624 name##_RB_INSERT(struct name *head, struct type *elm)			\
625 {									\
626 	struct type *tmp;						\
627 	struct type *parent = NULL;					\
628 	int comp = 0;							\
629 	tmp = RB_ROOT(head);						\
630 	while (tmp) {							\
631 		parent = tmp;						\
632 		comp = (cmp)(elm, parent);				\
633 		if (comp < 0)						\
634 			tmp = RB_LEFT(tmp, field);			\
635 		else if (comp > 0)					\
636 			tmp = RB_RIGHT(tmp, field);			\
637 		else							\
638 			return(tmp);					\
639 	}								\
640 	RB_SET(elm, parent, field);					\
641 	if (parent != NULL) {						\
642 		if (comp < 0)						\
643 			RB_LEFT(parent, field) = elm;			\
644 		else							\
645 			RB_RIGHT(parent, field) = elm;			\
646 		RB_AUGMENT(parent);					\
647 	} else								\
648 		RB_ROOT(head) = elm;					\
649 	name##_RB_INSERT_COLOR(head, elm);				\
650 	return (NULL);							\
651 }									\
652 									\
653 /* Finds the node with the same key as elm */				\
654 struct type *								\
655 name##_RB_FIND(struct name *head, struct type *elm)			\
656 {									\
657 	struct type *tmp = RB_ROOT(head);				\
658 	int comp;							\
659 	while (tmp) {							\
660 		comp = cmp(elm, tmp);					\
661 		if (comp < 0)						\
662 			tmp = RB_LEFT(tmp, field);			\
663 		else if (comp > 0)					\
664 			tmp = RB_RIGHT(tmp, field);			\
665 		else							\
666 			return (tmp);					\
667 	}								\
668 	return (NULL);							\
669 }									\
670 									\
671 /*									\
672  * Issue a callback for all matching items.  The scan function must	\
673  * return < 0 for items below the desired range, 0 for items within	\
674  * the range, and > 0 for items beyond the range.   Any item may be	\
675  * deleted while the scan is in progress.				\
676  */									\
677 static int								\
678 name##_SCANCMP_ALL(struct type *type, void *data)			\
679 {									\
680 	return(0);							\
681 }									\
682 									\
683 int									\
684 name##_RB_SCAN(struct name *head,					\
685 		int (*scancmp)(struct type *, void *),			\
686 		int (*callback)(struct type *, void *),			\
687 		void *data)						\
688 {									\
689 	struct name##_scan_info info;					\
690 	struct name##_scan_info **infopp;				\
691 	struct type *best;						\
692 	struct type *tmp;						\
693 	int count;							\
694 	int comp;							\
695 									\
696 	if (scancmp == NULL)						\
697 		scancmp = name##_SCANCMP_ALL;				\
698 									\
699 	/*								\
700 	 * Locate the first element.					\
701 	 */								\
702 	tmp = RB_ROOT(head);						\
703 	best = NULL;							\
704 	while (tmp) {							\
705 		comp = scancmp(tmp, data);				\
706 		if (comp < 0) {						\
707 			tmp = RB_RIGHT(tmp, field);			\
708 		} else if (comp > 0) {					\
709 			tmp = RB_LEFT(tmp, field);			\
710 		} else {						\
711 			best = tmp;					\
712 			if (RB_LEFT(tmp, field) == NULL)		\
713 				break;					\
714 			tmp = RB_LEFT(tmp, field);			\
715 		}							\
716 	}								\
717 	count = 0;							\
718 	if (best) {							\
719 		info.node = RB_NEXT(name, head, best);			\
720 		info.link = RB_INPROG(head);				\
721 		RB_INPROG(head) = &info;				\
722 		while ((comp = callback(best, data)) >= 0) {		\
723 			count += comp;					\
724 			best = info.node;				\
725 			if (best == NULL || scancmp(best, data) != 0)	\
726 				break;					\
727 			info.node = RB_NEXT(name, head, best);		\
728 		}							\
729 		if (comp < 0)	/* error or termination */		\
730 			count = comp;					\
731 		infopp = &RB_INPROG(head);				\
732 		while (*infopp != &info) 				\
733 			infopp = &(*infopp)->link;			\
734 		*infopp = info.link;					\
735 	}								\
736 	return(count);							\
737 }									\
738 									\
739 /* ARGSUSED */								\
740 struct type *								\
741 name##_RB_NEXT(struct type *elm)					\
742 {									\
743 	if (RB_RIGHT(elm, field)) {					\
744 		elm = RB_RIGHT(elm, field);				\
745 		while (RB_LEFT(elm, field))				\
746 			elm = RB_LEFT(elm, field);			\
747 	} else {							\
748 		if (RB_PARENT(elm, field) &&				\
749 		    (elm == RB_LEFT(RB_PARENT(elm, field), field)))	\
750 			elm = RB_PARENT(elm, field);			\
751 		else {							\
752 			while (RB_PARENT(elm, field) &&			\
753 			    (elm == RB_RIGHT(RB_PARENT(elm, field), field)))\
754 				elm = RB_PARENT(elm, field);		\
755 			elm = RB_PARENT(elm, field);			\
756 		}							\
757 	}								\
758 	return (elm);							\
759 }									\
760 									\
761 /* ARGSUSED */								\
762 struct type *								\
763 name##_RB_PREV(struct type *elm)					\
764 {									\
765 	if (RB_LEFT(elm, field)) {					\
766 		elm = RB_LEFT(elm, field);				\
767 		while (RB_RIGHT(elm, field))				\
768 			elm = RB_RIGHT(elm, field);			\
769 	} else {							\
770 		if (RB_PARENT(elm, field) &&				\
771 		    (elm == RB_RIGHT(RB_PARENT(elm, field), field)))	\
772 			elm = RB_PARENT(elm, field);			\
773 		else {							\
774 			while (RB_PARENT(elm, field) &&			\
775 			    (elm == RB_LEFT(RB_PARENT(elm, field), field)))\
776 				elm = RB_PARENT(elm, field);		\
777 			elm = RB_PARENT(elm, field);			\
778 		}							\
779 	}								\
780 	return (elm);							\
781 }									\
782 									\
783 struct type *								\
784 name##_RB_MINMAX(struct name *head, int val)				\
785 {									\
786 	struct type *tmp = RB_ROOT(head);				\
787 	struct type *parent = NULL;					\
788 	while (tmp) {							\
789 		parent = tmp;						\
790 		if (val < 0)						\
791 			tmp = RB_LEFT(tmp, field);			\
792 		else							\
793 			tmp = RB_RIGHT(tmp, field);			\
794 	}								\
795 	return (parent);						\
796 }
797 
798 /*
799  * This extended version implements a fast LOOKUP function given
800  * a numeric data type.
801  *
802  * The element whos index/offset field is exactly the specified value
803  * will be returned, or NULL.
804  */
805 #define RB_GENERATE2(name, type, field, cmp, datatype, indexfield)	\
806 RB_GENERATE(name, type, field, cmp)					\
807 									\
808 struct type *								\
809 name##_RB_LOOKUP(struct name *head, datatype value)			\
810 {									\
811 	struct type *tmp;						\
812 									\
813 	tmp = RB_ROOT(head);						\
814 	while (tmp) {							\
815 		if (value > tmp->indexfield) 				\
816 			tmp = RB_RIGHT(tmp, field);			\
817 		else if (value < tmp->indexfield) 			\
818 			tmp = RB_LEFT(tmp, field);			\
819 		else 							\
820 			return(tmp);					\
821 	}								\
822 	return(NULL);							\
823 }									\
824 
825 /*
826  * This extended version implements a fast ranged-based LOOKUP function
827  * given a numeric data type, for data types with a beginning and end
828  * (end is inclusive).
829  *
830  * The element whos range contains the specified value is returned, or NULL
831  */
832 #define RB_GENERATE3(name, type, field, cmp, datatype, begfield, endfield) \
833 RB_GENERATE2(name, type, field, cmp, datatype, begfield)		\
834 									\
835 struct type *								\
836 name##_RB_RLOOKUP(struct name *head, datatype value)			\
837 {									\
838 	struct type *tmp;						\
839 									\
840 	tmp = RB_ROOT(head);						\
841 	while (tmp) {							\
842 		if (value >= tmp->begfield && value <= tmp->endfield) 	\
843 			return(tmp);					\
844 		if (value > tmp->begfield) 				\
845 			tmp = RB_RIGHT(tmp, field);			\
846 		else							\
847 			tmp = RB_LEFT(tmp, field);			\
848 	}								\
849 	return(NULL);							\
850 }									\
851 
852 /*
853  * This extended version implements a fast ranged-based LOOKUP function
854  * given a numeric data type, for data types with a beginning and size.
855  *
856  * WARNING: The full range of the data type is not supported due to a
857  * boundary condition at the end, where (beginning + size) might overflow.
858  *
859  * The element whos range contains the specified value is returned, or NULL
860  */
861 #define RB_GENERATE4(name, type, field, cmp, datatype, begfield, sizefield) \
862 RB_GENERATE2(name, type, field, cmp, datatype, begfield)		\
863 									\
864 struct type *								\
865 name##_RB_RLOOKUP(struct name *head, datatype value)			\
866 {									\
867 	struct type *tmp;						\
868 									\
869 	tmp = RB_ROOT(head);						\
870 	while (tmp) {							\
871 		if (value >= tmp->begfield &&				\
872 		    value < tmp->begfield + tmp->sizefield) { 		\
873 			return(tmp);					\
874 		}							\
875 		if (value > tmp->begfield) 				\
876 			tmp = RB_RIGHT(tmp, field);			\
877 		else							\
878 			tmp = RB_LEFT(tmp, field);			\
879 	}								\
880 	return(NULL);							\
881 }									\
882 
883 
884 #define RB_NEGINF	-1
885 #define RB_INF	1
886 
887 #define RB_INSERT(name, root, elm)	name##_RB_INSERT(root, elm)
888 #define RB_REMOVE(name, root, elm)	name##_RB_REMOVE(root, elm)
889 #define RB_FIND(name, root, elm)	name##_RB_FIND(root, elm)
890 #define RB_LOOKUP(name, root, value)	name##_RB_LOOKUP(root, value)
891 #define RB_RLOOKUP(name, root, value)	name##_RB_RLOOKUP(root, value)
892 #define RB_SCAN(name, root, cmp, callback, data) 			\
893 				name##_RB_SCAN(root, cmp, callback, data)
894 #define RB_NEXT(name, root, elm)	name##_RB_NEXT(elm)
895 #define RB_PREV(name, root, elm)	name##_RB_PREV(elm)
896 #define RB_MIN(name, root)		name##_RB_MINMAX(root, RB_NEGINF)
897 #define RB_MAX(name, root)		name##_RB_MINMAX(root, RB_INF)
898 
899 #define RB_FOREACH(x, name, head)					\
900 	for ((x) = RB_MIN(name, head);					\
901 	     (x) != NULL;						\
902 	     (x) = name##_RB_NEXT(x))
903 
904 #endif	/* _SYS_TREE_H_ */
905