xref: /dragonfly/sys/sys/tree.h (revision 40f79625)
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 1.3 2006/03/03 20:25:46 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_MINMAX(struct name *, int);			\
396 RB_SCAN_INFO(name, type)						\
397 
398 #define RB_PROTOTYPE2(name, type, field, cmp, datatype, datacmp)	\
399 RB_PROTOTYPE(name, type, field, cmp);					\
400 struct type *name##_RB_LOOKUP(struct name *, datatype value)		\
401 
402 /* Main rb operation.
403  * Moves node close to the key of elm to top
404  */
405 #define RB_GENERATE(name, type, field, cmp)				\
406 static void								\
407 name##_RB_INSERT_COLOR(struct name *head, struct type *elm)		\
408 {									\
409 	struct type *parent, *gparent, *tmp;				\
410 	while ((parent = RB_PARENT(elm, field)) != NULL &&		\
411 	    RB_COLOR(parent, field) == RB_RED) {			\
412 		gparent = RB_PARENT(parent, field);			\
413 		if (parent == RB_LEFT(gparent, field)) {		\
414 			tmp = RB_RIGHT(gparent, field);			\
415 			if (tmp && RB_COLOR(tmp, field) == RB_RED) {	\
416 				RB_COLOR(tmp, field) = RB_BLACK;	\
417 				RB_SET_BLACKRED(parent, gparent, field);\
418 				elm = gparent;				\
419 				continue;				\
420 			}						\
421 			if (RB_RIGHT(parent, field) == elm) {		\
422 				RB_ROTATE_LEFT(head, parent, tmp, field);\
423 				tmp = parent;				\
424 				parent = elm;				\
425 				elm = tmp;				\
426 			}						\
427 			RB_SET_BLACKRED(parent, gparent, field);	\
428 			RB_ROTATE_RIGHT(head, gparent, tmp, field);	\
429 		} else {						\
430 			tmp = RB_LEFT(gparent, field);			\
431 			if (tmp && RB_COLOR(tmp, field) == RB_RED) {	\
432 				RB_COLOR(tmp, field) = RB_BLACK;	\
433 				RB_SET_BLACKRED(parent, gparent, field);\
434 				elm = gparent;				\
435 				continue;				\
436 			}						\
437 			if (RB_LEFT(parent, field) == elm) {		\
438 				RB_ROTATE_RIGHT(head, parent, tmp, field);\
439 				tmp = parent;				\
440 				parent = elm;				\
441 				elm = tmp;				\
442 			}						\
443 			RB_SET_BLACKRED(parent, gparent, field);	\
444 			RB_ROTATE_LEFT(head, gparent, tmp, field);	\
445 		}							\
446 	}								\
447 	RB_COLOR(head->rbh_root, field) = RB_BLACK;			\
448 }									\
449 									\
450 static void								\
451 name##_RB_REMOVE_COLOR(struct name *head, struct type *parent,		\
452 			struct type *elm) 				\
453 {									\
454 	struct type *tmp;						\
455 	while ((elm == NULL || RB_COLOR(elm, field) == RB_BLACK) &&	\
456 	    elm != RB_ROOT(head)) {					\
457 		if (RB_LEFT(parent, field) == elm) {			\
458 			tmp = RB_RIGHT(parent, field);			\
459 			if (RB_COLOR(tmp, field) == RB_RED) {		\
460 				RB_SET_BLACKRED(tmp, parent, field);	\
461 				RB_ROTATE_LEFT(head, parent, tmp, field);\
462 				tmp = RB_RIGHT(parent, field);		\
463 			}						\
464 			if ((RB_LEFT(tmp, field) == NULL ||		\
465 			    RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
466 			    (RB_RIGHT(tmp, field) == NULL ||		\
467 			    RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
468 				RB_COLOR(tmp, field) = RB_RED;		\
469 				elm = parent;				\
470 				parent = RB_PARENT(elm, field);		\
471 			} else {					\
472 				if (RB_RIGHT(tmp, field) == NULL ||	\
473 				    RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK) {\
474 					struct type *oleft;		\
475 					if ((oleft = RB_LEFT(tmp, field)) \
476 					    != NULL)			\
477 						RB_COLOR(oleft, field) = RB_BLACK;\
478 					RB_COLOR(tmp, field) = RB_RED;	\
479 					RB_ROTATE_RIGHT(head, tmp, oleft, field);\
480 					tmp = RB_RIGHT(parent, field);	\
481 				}					\
482 				RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
483 				RB_COLOR(parent, field) = RB_BLACK;	\
484 				if (RB_RIGHT(tmp, field))		\
485 					RB_COLOR(RB_RIGHT(tmp, field), field) = RB_BLACK;\
486 				RB_ROTATE_LEFT(head, parent, tmp, field);\
487 				elm = RB_ROOT(head);			\
488 				break;					\
489 			}						\
490 		} else {						\
491 			tmp = RB_LEFT(parent, field);			\
492 			if (RB_COLOR(tmp, field) == RB_RED) {		\
493 				RB_SET_BLACKRED(tmp, parent, field);	\
494 				RB_ROTATE_RIGHT(head, parent, tmp, field);\
495 				tmp = RB_LEFT(parent, field);		\
496 			}						\
497 			if ((RB_LEFT(tmp, field) == NULL ||		\
498 			    RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
499 			    (RB_RIGHT(tmp, field) == NULL ||		\
500 			    RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
501 				RB_COLOR(tmp, field) = RB_RED;		\
502 				elm = parent;				\
503 				parent = RB_PARENT(elm, field);		\
504 			} else {					\
505 				if (RB_LEFT(tmp, field) == NULL ||	\
506 				    RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) {\
507 					struct type *oright;		\
508 					if ((oright = RB_RIGHT(tmp, field)) \
509 					    != NULL)			\
510 						RB_COLOR(oright, field) = RB_BLACK;\
511 					RB_COLOR(tmp, field) = RB_RED;	\
512 					RB_ROTATE_LEFT(head, tmp, oright, field);\
513 					tmp = RB_LEFT(parent, field);	\
514 				}					\
515 				RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
516 				RB_COLOR(parent, field) = RB_BLACK;	\
517 				if (RB_LEFT(tmp, field))		\
518 					RB_COLOR(RB_LEFT(tmp, field), field) = RB_BLACK;\
519 				RB_ROTATE_RIGHT(head, parent, tmp, field);\
520 				elm = RB_ROOT(head);			\
521 				break;					\
522 			}						\
523 		}							\
524 	}								\
525 	if (elm)							\
526 		RB_COLOR(elm, field) = RB_BLACK;			\
527 }									\
528 									\
529 struct type *								\
530 name##_RB_REMOVE(struct name *head, struct type *elm)			\
531 {									\
532 	struct type *child, *parent, *old;				\
533 	struct name##_scan_info *inprog;				\
534 	int color;							\
535 									\
536 	for (inprog = RB_INPROG(head); inprog; inprog = inprog->link) { \
537 		if (inprog->node == elm) 				\
538 			inprog->node = RB_NEXT(name, head, elm);	\
539 	}								\
540 									\
541 	old = elm;							\
542 	if (RB_LEFT(elm, field) == NULL)				\
543 		child = RB_RIGHT(elm, field);				\
544 	else if (RB_RIGHT(elm, field) == NULL)				\
545 		child = RB_LEFT(elm, field);				\
546 	else {								\
547 		struct type *left;					\
548 		elm = RB_RIGHT(elm, field);				\
549 		while ((left = RB_LEFT(elm, field)) != NULL)		\
550 			elm = left;					\
551 		child = RB_RIGHT(elm, field);				\
552 		parent = RB_PARENT(elm, field);				\
553 		color = RB_COLOR(elm, field);				\
554 		if (child)						\
555 			RB_PARENT(child, field) = parent;		\
556 		if (parent) {						\
557 			if (RB_LEFT(parent, field) == elm)		\
558 				RB_LEFT(parent, field) = child;		\
559 			else						\
560 				RB_RIGHT(parent, field) = child;	\
561 			RB_AUGMENT(parent);				\
562 		} else							\
563 			RB_ROOT(head) = child;				\
564 		if (RB_PARENT(elm, field) == old)			\
565 			parent = elm;					\
566 		(elm)->field = (old)->field;				\
567 		if (RB_PARENT(old, field)) {				\
568 			if (RB_LEFT(RB_PARENT(old, field), field) == old)\
569 				RB_LEFT(RB_PARENT(old, field), field) = elm;\
570 			else						\
571 				RB_RIGHT(RB_PARENT(old, field), field) = elm;\
572 			RB_AUGMENT(RB_PARENT(old, field));		\
573 		} else							\
574 			RB_ROOT(head) = elm;				\
575 		RB_PARENT(RB_LEFT(old, field), field) = elm;		\
576 		if (RB_RIGHT(old, field))				\
577 			RB_PARENT(RB_RIGHT(old, field), field) = elm;	\
578 		if (parent) {						\
579 			left = parent;					\
580 			do {						\
581 				RB_AUGMENT(left);			\
582 			} while ((left = RB_PARENT(left, field)) != NULL); \
583 		}							\
584 		goto color;						\
585 	}								\
586 	parent = RB_PARENT(elm, field);					\
587 	color = RB_COLOR(elm, field);					\
588 	if (child)							\
589 		RB_PARENT(child, field) = parent;			\
590 	if (parent) {							\
591 		if (RB_LEFT(parent, field) == elm)			\
592 			RB_LEFT(parent, field) = child;			\
593 		else							\
594 			RB_RIGHT(parent, field) = child;		\
595 		RB_AUGMENT(parent);					\
596 	} else								\
597 		RB_ROOT(head) = child;					\
598 color:									\
599 	if (color == RB_BLACK)						\
600 		name##_RB_REMOVE_COLOR(head, parent, child);		\
601 	return (old);							\
602 }									\
603 									\
604 /* Inserts a node into the RB tree */					\
605 struct type *								\
606 name##_RB_INSERT(struct name *head, struct type *elm)			\
607 {									\
608 	struct type *tmp;						\
609 	struct type *parent = NULL;					\
610 	int comp = 0;							\
611 	tmp = RB_ROOT(head);						\
612 	while (tmp) {							\
613 		parent = tmp;						\
614 		comp = (cmp)(elm, parent);				\
615 		if (comp < 0)						\
616 			tmp = RB_LEFT(tmp, field);			\
617 		else if (comp > 0)					\
618 			tmp = RB_RIGHT(tmp, field);			\
619 		else							\
620 			return(tmp);					\
621 	}								\
622 	RB_SET(elm, parent, field);					\
623 	if (parent != NULL) {						\
624 		if (comp < 0)						\
625 			RB_LEFT(parent, field) = elm;			\
626 		else							\
627 			RB_RIGHT(parent, field) = elm;			\
628 		RB_AUGMENT(parent);					\
629 	} else								\
630 		RB_ROOT(head) = elm;					\
631 	name##_RB_INSERT_COLOR(head, elm);				\
632 	return (NULL);							\
633 }									\
634 									\
635 /* Finds the node with the same key as elm */				\
636 struct type *								\
637 name##_RB_FIND(struct name *head, struct type *elm)			\
638 {									\
639 	struct type *tmp = RB_ROOT(head);				\
640 	int comp;							\
641 	while (tmp) {							\
642 		comp = cmp(elm, tmp);					\
643 		if (comp < 0)						\
644 			tmp = RB_LEFT(tmp, field);			\
645 		else if (comp > 0)					\
646 			tmp = RB_RIGHT(tmp, field);			\
647 		else							\
648 			return (tmp);					\
649 	}								\
650 	return (NULL);							\
651 }									\
652 									\
653 /*									\
654  * Issue a callback for all matching items.  The scan function must	\
655  * return < 0 for items below the desired range, 0 for items within	\
656  * the range, and > 0 for items beyond the range.   Any item may be	\
657  * deleted while the scan is in progress.				\
658  */									\
659 static int								\
660 name##_SCANCMP_ALL(struct type *type, void *data)			\
661 {									\
662 	return(0);							\
663 }									\
664 									\
665 int									\
666 name##_RB_SCAN(struct name *head,					\
667 		int (*scancmp)(struct type *, void *),			\
668 		int (*callback)(struct type *, void *),			\
669 		void *data)						\
670 {									\
671 	struct name##_scan_info info;					\
672 	struct name##_scan_info **infopp;				\
673 	struct type *best;						\
674 	struct type *tmp;						\
675 	int count;							\
676 	int comp;							\
677 									\
678 	if (scancmp == NULL)						\
679 		scancmp = name##_SCANCMP_ALL;				\
680 									\
681 	/*								\
682 	 * Locate the first element.					\
683 	 */								\
684 	tmp = RB_ROOT(head);						\
685 	best = NULL;							\
686 	while (tmp) {							\
687 		comp = scancmp(tmp, data);				\
688 		if (comp < 0) {						\
689 			tmp = RB_RIGHT(tmp, field);			\
690 		} else if (comp > 0) {					\
691 			tmp = RB_LEFT(tmp, field);			\
692 		} else {						\
693 			best = tmp;					\
694 			if (RB_LEFT(tmp, field) == NULL)		\
695 				break;					\
696 			tmp = RB_LEFT(tmp, field);			\
697 		}							\
698 	}								\
699 	count = 0;							\
700 	if (best) {							\
701 		info.node = RB_NEXT(name, head, best);			\
702 		info.link = RB_INPROG(head);				\
703 		RB_INPROG(head) = &info;				\
704 		while ((comp = callback(best, data)) >= 0) {		\
705 			count += comp;					\
706 			best = info.node;				\
707 			if (best == NULL || scancmp(best, data) != 0)	\
708 				break;					\
709 			info.node = RB_NEXT(name, head, best);		\
710 		}							\
711 		if (comp < 0)	/* error or termination */		\
712 			count = comp;					\
713 		infopp = &RB_INPROG(head);				\
714 		while (*infopp != &info) 				\
715 			infopp = &(*infopp)->link;			\
716 		*infopp = info.link;					\
717 	}								\
718 	return(count);							\
719 }									\
720 									\
721 /* ARGSUSED */								\
722 struct type *								\
723 name##_RB_NEXT(struct type *elm)					\
724 {									\
725 	if (RB_RIGHT(elm, field)) {					\
726 		elm = RB_RIGHT(elm, field);				\
727 		while (RB_LEFT(elm, field))				\
728 			elm = RB_LEFT(elm, field);			\
729 	} else {							\
730 		if (RB_PARENT(elm, field) &&				\
731 		    (elm == RB_LEFT(RB_PARENT(elm, field), field)))	\
732 			elm = RB_PARENT(elm, field);			\
733 		else {							\
734 			while (RB_PARENT(elm, field) &&			\
735 			    (elm == RB_RIGHT(RB_PARENT(elm, field), field)))\
736 				elm = RB_PARENT(elm, field);		\
737 			elm = RB_PARENT(elm, field);			\
738 		}							\
739 	}								\
740 	return (elm);							\
741 }									\
742 									\
743 struct type *								\
744 name##_RB_MINMAX(struct name *head, int val)				\
745 {									\
746 	struct type *tmp = RB_ROOT(head);				\
747 	struct type *parent = NULL;					\
748 	while (tmp) {							\
749 		parent = tmp;						\
750 		if (val < 0)						\
751 			tmp = RB_LEFT(tmp, field);			\
752 		else							\
753 			tmp = RB_RIGHT(tmp, field);			\
754 	}								\
755 	return (parent);						\
756 }
757 
758 /*
759  * This extended version implements a fast LOOKUP function given
760  * a numeric data type.
761  *
762  * The element whos index/offset field is exactly the specified value
763  * will be returned, or NULL.
764  */
765 #define RB_GENERATE2(name, type, field, cmp, datatype, indexfield)	\
766 RB_GENERATE(name, type, field, cmp)					\
767 									\
768 struct type *								\
769 name##_RB_LOOKUP(struct name *head, datatype value)			\
770 {									\
771 	struct type *tmp;						\
772 									\
773 	tmp = RB_ROOT(head);						\
774 	while (tmp) {							\
775 		if (value > tmp->indexfield) 				\
776 			tmp = RB_RIGHT(tmp, field);			\
777 		else if (value < tmp->indexfield) 			\
778 			tmp = RB_LEFT(tmp, field);			\
779 		else 							\
780 			return(tmp);					\
781 	}								\
782 	return(NULL);							\
783 }									\
784 
785 /*
786  * This extended version implements a fast ranged-based LOOKUP function
787  * given a numeric data type, for data types with a beginning and end
788  * (end non-inclusive).
789  *
790  * The element whos range contains the specified value is returned, or NULL
791  */
792 #define RB_GENERATE3(name, type, field, cmp, datatype, begfield, endfield) \
793 RB_GENERATE2(name, type, field, cmp, datatype, begfield)		\
794 									\
795 struct type *								\
796 name##_RB_RANGED_LOOKUP(struct name *head, datatype value)		\
797 {									\
798 	struct type *tmp;						\
799 									\
800 	tmp = RB_ROOT(head);						\
801 	while (tmp) {							\
802 		if (value >= tmp->begfield && value < tmp->endfield) 	\
803 			return(tmp);					\
804 		if (value > tmp->begfield) 				\
805 			tmp = RB_RIGHT(tmp, field);			\
806 		else							\
807 			tmp = RB_LEFT(tmp, field);			\
808 	}								\
809 	return(NULL);							\
810 }									\
811 
812 #define RB_NEGINF	-1
813 #define RB_INF	1
814 
815 #define RB_INSERT(name, x, y)	name##_RB_INSERT(x, y)
816 #define RB_REMOVE(name, x, y)	name##_RB_REMOVE(x, y)
817 #define RB_FIND(name, x, y)	name##_RB_FIND(x, y)
818 #define RB_SCAN(name, root, cmp, callback, data) 		\
819 				name##_RB_SCAN(root, cmp, callback, data)
820 #define RB_NEXT(name, x, y)	name##_RB_NEXT(y)
821 #define RB_MIN(name, x)		name##_RB_MINMAX(x, RB_NEGINF)
822 #define RB_MAX(name, x)		name##_RB_MINMAX(x, RB_INF)
823 
824 #define RB_FOREACH(x, name, head)					\
825 	for ((x) = RB_MIN(name, head);					\
826 	     (x) != NULL;						\
827 	     (x) = name##_RB_NEXT(x))
828 
829 #endif	/* _SYS_TREE_H_ */
830