xref: /dragonfly/sys/sys/tree.h (revision ffe53622)
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 /*
4  * Copyright 2002 Niels Provos <provos@citi.umich.edu>
5  * All rights reserved.
6  *
7  * Redistribution and use in source and binary forms, with or without
8  * modification, are permitted provided that the following conditions
9  * are met:
10  * 1. Redistributions of source code must retain the above copyright
11  *    notice, this list of conditions and the following disclaimer.
12  * 2. Redistributions in binary form must reproduce the above copyright
13  *    notice, this list of conditions and the following disclaimer in the
14  *    documentation and/or other materials provided with the distribution.
15  *
16  * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
17  * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
18  * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
19  * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
20  * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
21  * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
22  * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
23  * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
24  * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
25  * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
26  */
27 
28 #ifndef	_SYS_TREE_H_
29 #define	_SYS_TREE_H_
30 
31 #ifndef _SYS_SPINLOCK_H_
32 #include <sys/spinlock.h>
33 #endif
34 
35 void rb_spin_lock(struct spinlock *spin);
36 void rb_spin_unlock(struct spinlock *spin);
37 
38 /*
39  * This file defines data structures for different types of trees:
40  * splay trees and red-black trees.
41  *
42  * A splay tree is a self-organizing data structure.  Every operation
43  * on the tree causes a splay to happen.  The splay moves the requested
44  * node to the root of the tree and partly rebalances it.
45  *
46  * This has the benefit that request locality causes faster lookups as
47  * the requested nodes move to the top of the tree.  On the other hand,
48  * every lookup causes memory writes.
49  *
50  * The Balance Theorem bounds the total access time for m operations
51  * and n inserts on an initially empty tree as O((m + n)lg n).  The
52  * amortized cost for a sequence of m accesses to a splay tree is O(lg n);
53  *
54  * A red-black tree is a binary search tree with the node color as an
55  * extra attribute.  It fulfills a set of conditions:
56  *	- every search path from the root to a leaf consists of the
57  *	  same number of black nodes,
58  *	- each red node (except for the root) has a black parent,
59  *	- each leaf node is black.
60  *
61  * Every operation on a red-black tree is bounded as O(lg n).
62  * The maximum height of a red-black tree is 2lg (n+1).
63  */
64 
65 #define SPLAY_HEAD(name, type)						\
66 struct name {								\
67 	struct type *sph_root; /* root of the tree */			\
68 }
69 
70 #define SPLAY_INITIALIZER(root)						\
71 	{ NULL }
72 
73 #define SPLAY_INIT(root) do {						\
74 	(root)->sph_root = NULL;					\
75 } while (/*CONSTCOND*/ 0)
76 
77 #define SPLAY_ENTRY(type)						\
78 struct {								\
79 	struct type *spe_left; /* left element */			\
80 	struct type *spe_right; /* right element */			\
81 }
82 
83 #define SPLAY_LEFT(elm, field)		(elm)->field.spe_left
84 #define SPLAY_RIGHT(elm, field)		(elm)->field.spe_right
85 #define SPLAY_ROOT(head)		(head)->sph_root
86 #define SPLAY_EMPTY(head)		(SPLAY_ROOT(head) == NULL)
87 
88 /* SPLAY_ROTATE_{LEFT,RIGHT} expect that tmp hold SPLAY_{RIGHT,LEFT} */
89 #define SPLAY_ROTATE_RIGHT(head, tmp, field) do {			\
90 	SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(tmp, field);	\
91 	SPLAY_RIGHT(tmp, field) = (head)->sph_root;			\
92 	(head)->sph_root = tmp;						\
93 } while (/*CONSTCOND*/ 0)
94 
95 #define SPLAY_ROTATE_LEFT(head, tmp, field) do {			\
96 	SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(tmp, field);	\
97 	SPLAY_LEFT(tmp, field) = (head)->sph_root;			\
98 	(head)->sph_root = tmp;						\
99 } while (/*CONSTCOND*/ 0)
100 
101 #define SPLAY_LINKLEFT(head, tmp, field) do {				\
102 	SPLAY_LEFT(tmp, field) = (head)->sph_root;			\
103 	tmp = (head)->sph_root;						\
104 	(head)->sph_root = SPLAY_LEFT((head)->sph_root, field);		\
105 } while (/*CONSTCOND*/ 0)
106 
107 #define SPLAY_LINKRIGHT(head, tmp, field) do {				\
108 	SPLAY_RIGHT(tmp, field) = (head)->sph_root;			\
109 	tmp = (head)->sph_root;						\
110 	(head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);	\
111 } while (/*CONSTCOND*/ 0)
112 
113 #define SPLAY_ASSEMBLE(head, node, left, right, field) do {		\
114 	SPLAY_RIGHT(left, field) = SPLAY_LEFT((head)->sph_root, field);	\
115 	SPLAY_LEFT(right, field) = SPLAY_RIGHT((head)->sph_root, field);\
116 	SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(node, field);	\
117 	SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(node, field);	\
118 } while (/*CONSTCOND*/ 0)
119 
120 /* Generates prototypes and inline functions */
121 
122 #define SPLAY_PROTOTYPE(name, type, field, cmp)				\
123 void name##_SPLAY(struct name *, struct type *);			\
124 void name##_SPLAY_MINMAX(struct name *, int);				\
125 struct type *name##_SPLAY_INSERT(struct name *, struct type *);		\
126 struct type *name##_SPLAY_REMOVE(struct name *, struct type *);		\
127 									\
128 /* Finds the node with the same key as elm */				\
129 static __inline struct type *						\
130 name##_SPLAY_FIND(struct name *head, struct type *elm)			\
131 {									\
132 	if (SPLAY_EMPTY(head))						\
133 		return(NULL);						\
134 	name##_SPLAY(head, elm);					\
135 	if ((cmp)(elm, (head)->sph_root) == 0)				\
136 		return (head->sph_root);				\
137 	return (NULL);							\
138 }									\
139 									\
140 static __inline struct type *						\
141 name##_SPLAY_NEXT(struct name *head, struct type *elm)			\
142 {									\
143 	name##_SPLAY(head, elm);					\
144 	if (SPLAY_RIGHT(elm, field) != NULL) {				\
145 		elm = SPLAY_RIGHT(elm, field);				\
146 		while (SPLAY_LEFT(elm, field) != NULL) {		\
147 			elm = SPLAY_LEFT(elm, field);			\
148 		}							\
149 	} else								\
150 		elm = NULL;						\
151 	return (elm);							\
152 }									\
153 									\
154 static __inline struct type *						\
155 name##_SPLAY_MIN_MAX(struct name *head, int val)			\
156 {									\
157 	name##_SPLAY_MINMAX(head, val);					\
158         return (SPLAY_ROOT(head));					\
159 }
160 
161 /* Main splay operation.
162  * Moves node close to the key of elm to top
163  */
164 #define SPLAY_GENERATE(name, type, field, cmp)				\
165 struct type *								\
166 name##_SPLAY_INSERT(struct name *head, struct type *elm)		\
167 {									\
168     if (SPLAY_EMPTY(head)) {						\
169 	    SPLAY_LEFT(elm, field) = SPLAY_RIGHT(elm, field) = NULL;	\
170     } else {								\
171 	    int __comp;							\
172 	    name##_SPLAY(head, elm);					\
173 	    __comp = (cmp)(elm, (head)->sph_root);			\
174 	    if(__comp < 0) {						\
175 		    SPLAY_LEFT(elm, field) = SPLAY_LEFT((head)->sph_root, field);\
176 		    SPLAY_RIGHT(elm, field) = (head)->sph_root;		\
177 		    SPLAY_LEFT((head)->sph_root, field) = NULL;		\
178 	    } else if (__comp > 0) {					\
179 		    SPLAY_RIGHT(elm, field) = SPLAY_RIGHT((head)->sph_root, field);\
180 		    SPLAY_LEFT(elm, field) = (head)->sph_root;		\
181 		    SPLAY_RIGHT((head)->sph_root, field) = NULL;	\
182 	    } else							\
183 		    return ((head)->sph_root);				\
184     }									\
185     (head)->sph_root = (elm);						\
186     return (NULL);							\
187 }									\
188 									\
189 struct type *								\
190 name##_SPLAY_REMOVE(struct name *head, struct type *elm)		\
191 {									\
192 	struct type *__tmp;						\
193 	if (SPLAY_EMPTY(head))						\
194 		return (NULL);						\
195 	name##_SPLAY(head, elm);					\
196 	if ((cmp)(elm, (head)->sph_root) == 0) {			\
197 		if (SPLAY_LEFT((head)->sph_root, field) == NULL) {	\
198 			(head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);\
199 		} else {						\
200 			__tmp = SPLAY_RIGHT((head)->sph_root, field);	\
201 			(head)->sph_root = SPLAY_LEFT((head)->sph_root, field);\
202 			name##_SPLAY(head, elm);			\
203 			SPLAY_RIGHT((head)->sph_root, field) = __tmp;	\
204 		}							\
205 		return (elm);						\
206 	}								\
207 	return (NULL);							\
208 }									\
209 									\
210 void									\
211 name##_SPLAY(struct name *head, struct type *elm)			\
212 {									\
213 	struct type __node, *__left, *__right, *__tmp;			\
214 	int __comp;							\
215 \
216 	SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
217 	__left = __right = &__node;					\
218 \
219 	while ((__comp = (cmp)(elm, (head)->sph_root)) != 0) {		\
220 		if (__comp < 0) {					\
221 			__tmp = SPLAY_LEFT((head)->sph_root, field);	\
222 			if (__tmp == NULL)				\
223 				break;					\
224 			if ((cmp)(elm, __tmp) < 0){			\
225 				SPLAY_ROTATE_RIGHT(head, __tmp, field);	\
226 				if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
227 					break;				\
228 			}						\
229 			SPLAY_LINKLEFT(head, __right, field);		\
230 		} else if (__comp > 0) {				\
231 			__tmp = SPLAY_RIGHT((head)->sph_root, field);	\
232 			if (__tmp == NULL)				\
233 				break;					\
234 			if ((cmp)(elm, __tmp) > 0){			\
235 				SPLAY_ROTATE_LEFT(head, __tmp, field);	\
236 				if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
237 					break;				\
238 			}						\
239 			SPLAY_LINKRIGHT(head, __left, field);		\
240 		}							\
241 	}								\
242 	SPLAY_ASSEMBLE(head, &__node, __left, __right, field);		\
243 }									\
244 									\
245 /* Splay with either the minimum or the maximum element			\
246  * Used to find minimum or maximum element in tree.			\
247  */									\
248 void name##_SPLAY_MINMAX(struct name *head, int __comp) 		\
249 {									\
250 	struct type __node, *__left, *__right, *__tmp;			\
251 									\
252 	SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
253 	__left = __right = &__node;					\
254 									\
255 	while (1) {							\
256 		if (__comp < 0) {					\
257 			__tmp = SPLAY_LEFT((head)->sph_root, field);	\
258 			if (__tmp == NULL)				\
259 				break;					\
260 			if (__comp < 0){				\
261 				SPLAY_ROTATE_RIGHT(head, __tmp, field);	\
262 				if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
263 					break;				\
264 			}						\
265 			SPLAY_LINKLEFT(head, __right, field);		\
266 		} else if (__comp > 0) {				\
267 			__tmp = SPLAY_RIGHT((head)->sph_root, field);	\
268 			if (__tmp == NULL)				\
269 				break;					\
270 			if (__comp > 0) {				\
271 				SPLAY_ROTATE_LEFT(head, __tmp, field);	\
272 				if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
273 					break;				\
274 			}						\
275 			SPLAY_LINKRIGHT(head, __left, field);		\
276 		}							\
277 	}								\
278 	SPLAY_ASSEMBLE(head, &__node, __left, __right, field);		\
279 }
280 
281 #define SPLAY_NEGINF	-1
282 #define SPLAY_INF	1
283 
284 #define SPLAY_INSERT(name, x, y)	name##_SPLAY_INSERT(x, y)
285 #define SPLAY_REMOVE(name, x, y)	name##_SPLAY_REMOVE(x, y)
286 #define SPLAY_FIND(name, x, y)		name##_SPLAY_FIND(x, y)
287 #define SPLAY_NEXT(name, x, y)		name##_SPLAY_NEXT(x, y)
288 #define SPLAY_MIN(name, x)		(SPLAY_EMPTY(x) ? NULL	\
289 					: name##_SPLAY_MIN_MAX(x, SPLAY_NEGINF))
290 #define SPLAY_MAX(name, x)		(SPLAY_EMPTY(x) ? NULL	\
291 					: name##_SPLAY_MIN_MAX(x, SPLAY_INF))
292 
293 #define SPLAY_FOREACH(x, name, head)					\
294 	for ((x) = SPLAY_MIN(name, head);				\
295 	     (x) != NULL;						\
296 	     (x) = SPLAY_NEXT(name, head, x))
297 
298 /*
299  * Macros that define a red-black tree
300  */
301 
302 #define RB_SCAN_INFO(name, type)					\
303 struct name##_scan_info {						\
304 	struct name##_scan_info *link;					\
305 	struct type	*node;						\
306 }
307 
308 #define RB_HEAD(name, type)						\
309 struct name {								\
310 	struct type *rbh_root; 		     /* root of the tree */	\
311 	struct name##_scan_info *rbh_inprog; /* scans in progress */	\
312 	struct spinlock rbh_spin;					\
313 }
314 
315 #define RB_INITIALIZER(root)						\
316 	{ NULL, NULL, SPINLOCK_INITIALIZER(root.spin, "root.spin") }
317 
318 #define RB_INIT(root) do {						\
319 	(root)->rbh_root = NULL;					\
320 	(root)->rbh_inprog = NULL;					\
321 } while (/*CONSTCOND*/ 0)
322 
323 #ifdef _KERNEL
324 #define RB_SCAN_LOCK(spin)	rb_spin_lock(spin)
325 #define RB_SCAN_UNLOCK(spin)	rb_spin_unlock(spin)
326 #else
327 #define RB_SCAN_LOCK(spin)
328 #define RB_SCAN_UNLOCK(spin)
329 #endif
330 
331 #define RB_BLACK	0
332 #define RB_RED		1
333 #define RB_ENTRY(type)							\
334 struct {								\
335 	struct type *rbe_left;		/* left element */		\
336 	struct type *rbe_right;		/* right element */		\
337 	struct type *rbe_parent;	/* parent element */		\
338 	int rbe_color;			/* node color */		\
339 }
340 
341 #define RB_LEFT(elm, field)		(elm)->field.rbe_left
342 #define RB_RIGHT(elm, field)		(elm)->field.rbe_right
343 #define RB_PARENT(elm, field)		(elm)->field.rbe_parent
344 #define RB_COLOR(elm, field)		(elm)->field.rbe_color
345 #define RB_ROOT(head)			(head)->rbh_root
346 #define RB_INPROG(head)			(head)->rbh_inprog
347 #define RB_EMPTY(head)			(RB_ROOT(head) == NULL)
348 
349 #define RB_SET(elm, parent, field) do {					\
350 	RB_PARENT(elm, field) = parent;					\
351 	RB_LEFT(elm, field) = RB_RIGHT(elm, field) = NULL;		\
352 	RB_COLOR(elm, field) = RB_RED;					\
353 } while (/*CONSTCOND*/ 0)
354 
355 #define RB_SET_BLACKRED(black, red, field) do {				\
356 	RB_COLOR(black, field) = RB_BLACK;				\
357 	RB_COLOR(red, field) = RB_RED;					\
358 } while (/*CONSTCOND*/ 0)
359 
360 #ifndef RB_AUGMENT
361 #define RB_AUGMENT(x)	do {} while (0)
362 #endif
363 
364 #define RB_ROTATE_LEFT(head, elm, tmp, field) do {			\
365 	(tmp) = RB_RIGHT(elm, field);					\
366 	if ((RB_RIGHT(elm, field) = RB_LEFT(tmp, field)) != NULL) {	\
367 		RB_PARENT(RB_LEFT(tmp, field), field) = (elm);		\
368 	}								\
369 	RB_AUGMENT(elm);						\
370 	if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) {	\
371 		if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))	\
372 			RB_LEFT(RB_PARENT(elm, field), field) = (tmp);	\
373 		else							\
374 			RB_RIGHT(RB_PARENT(elm, field), field) = (tmp);	\
375 	} else								\
376 		(head)->rbh_root = (tmp);				\
377 	RB_LEFT(tmp, field) = (elm);					\
378 	RB_PARENT(elm, field) = (tmp);					\
379 	RB_AUGMENT(tmp);						\
380 	if ((RB_PARENT(tmp, field)))					\
381 		RB_AUGMENT(RB_PARENT(tmp, field));			\
382 } while (/*CONSTCOND*/ 0)
383 
384 #define RB_ROTATE_RIGHT(head, elm, tmp, field) do {			\
385 	(tmp) = RB_LEFT(elm, field);					\
386 	if ((RB_LEFT(elm, field) = RB_RIGHT(tmp, field)) != NULL) {	\
387 		RB_PARENT(RB_RIGHT(tmp, field), field) = (elm);		\
388 	}								\
389 	RB_AUGMENT(elm);						\
390 	if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) {	\
391 		if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))	\
392 			RB_LEFT(RB_PARENT(elm, field), field) = (tmp);	\
393 		else							\
394 			RB_RIGHT(RB_PARENT(elm, field), field) = (tmp);	\
395 	} else								\
396 		(head)->rbh_root = (tmp);				\
397 	RB_RIGHT(tmp, field) = (elm);					\
398 	RB_PARENT(elm, field) = (tmp);					\
399 	RB_AUGMENT(tmp);						\
400 	if ((RB_PARENT(tmp, field)))					\
401 		RB_AUGMENT(RB_PARENT(tmp, field));			\
402 } while (/*CONSTCOND*/ 0)
403 
404 /* Generates prototypes and inline functions */
405 #define RB_PROTOTYPE(name, type, field, cmp)				\
406 	_RB_PROTOTYPE(name, type, field, cmp,)
407 #define RB_PROTOTYPE_STATIC(name, type, field, cmp)			\
408 	_RB_PROTOTYPE(name, type, field, cmp, __unused static)
409 
410 #define _RB_PROTOTYPE(name, type, field, cmp, STORQUAL)			\
411 STORQUAL void name##_RB_INSERT_COLOR(struct name *, struct type *);	\
412 STORQUAL void name##_RB_REMOVE_COLOR(struct name *, struct type *, struct type *);\
413 STORQUAL struct type *name##_RB_REMOVE(struct name *, struct type *);	\
414 STORQUAL struct type *name##_RB_INSERT(struct name *, struct type *);	\
415 STORQUAL struct type *name##_RB_FIND(struct name *, struct type *);	\
416 STORQUAL int name##_RB_SCAN(struct name *, int (*)(struct type *, void *),\
417 			int (*)(struct type *, void *), void *);	\
418 STORQUAL int name##_RB_SCAN_NOLK(struct name *, int (*)(struct type *, void *),\
419 			int (*)(struct type *, void *), void *);	\
420 STORQUAL struct type *name##_RB_NEXT(struct type *);			\
421 STORQUAL struct type *name##_RB_PREV(struct type *);			\
422 STORQUAL struct type *name##_RB_MINMAX(struct name *, int);		\
423 RB_SCAN_INFO(name, type)						\
424 
425 /*
426  * A version which supplies a fast lookup routine for an exact match
427  * on a numeric field.
428  */
429 #define RB_PROTOTYPE2(name, type, field, cmp, datatype)			\
430 RB_PROTOTYPE(name, type, field, cmp);					\
431 struct type *name##_RB_LOOKUP(struct name *, datatype);			\
432 struct type *name##_RB_LOOKUP_REL(struct name *, datatype, struct type *) \
433 
434 /*
435  * A version which supplies a fast lookup routine for a numeric
436  * field which resides within a ranged object, either using (begin,end),
437  * or using (begin,size).
438  */
439 #define RB_PROTOTYPE3(name, type, field, cmp, datatype)			\
440 RB_PROTOTYPE2(name, type, field, cmp, datatype);			\
441 struct type *name##_RB_RLOOKUP(struct name *, datatype)			\
442 
443 #define RB_PROTOTYPE4(name, type, field, cmp, datatype)			\
444 RB_PROTOTYPE2(name, type, field, cmp, datatype);			\
445 struct type *name##_RB_RLOOKUP(struct name *, datatype)			\
446 
447 #define RB_PROTOTYPEX(name, ext, type, field, cmp, datatype)		\
448 RB_PROTOTYPE(name, type, field, cmp);					\
449 struct type *name##_RB_LOOKUP_##ext (struct name *, datatype)		\
450 
451 /* Main rb operation.
452  * Moves node close to the key of elm to top
453  */
454 #define RB_GENERATE(name, type, field, cmp)				\
455 	_RB_GENERATE(name, type, field, cmp,)
456 
457 #define RB_GENERATE_STATIC(name, type, field, cmp)			\
458 	_RB_GENERATE(name, type, field, cmp, __unused static)
459 
460 #define _RB_GENERATE(name, type, field, cmp, STORQUAL)			\
461 STORQUAL void								\
462 name##_RB_INSERT_COLOR(struct name *head, struct type *elm)		\
463 {									\
464 	struct type *parent, *gparent, *tmp;				\
465 	while ((parent = RB_PARENT(elm, field)) != NULL &&		\
466 	    RB_COLOR(parent, field) == RB_RED) {			\
467 		gparent = RB_PARENT(parent, field);			\
468 		if (parent == RB_LEFT(gparent, field)) {		\
469 			tmp = RB_RIGHT(gparent, field);			\
470 			if (tmp && RB_COLOR(tmp, field) == RB_RED) {	\
471 				RB_COLOR(tmp, field) = RB_BLACK;	\
472 				RB_SET_BLACKRED(parent, gparent, field);\
473 				elm = gparent;				\
474 				continue;				\
475 			}						\
476 			if (RB_RIGHT(parent, field) == elm) {		\
477 				RB_ROTATE_LEFT(head, parent, tmp, field);\
478 				tmp = parent;				\
479 				parent = elm;				\
480 				elm = tmp;				\
481 			}						\
482 			RB_SET_BLACKRED(parent, gparent, field);	\
483 			RB_ROTATE_RIGHT(head, gparent, tmp, field);	\
484 		} else {						\
485 			tmp = RB_LEFT(gparent, field);			\
486 			if (tmp && RB_COLOR(tmp, field) == RB_RED) {	\
487 				RB_COLOR(tmp, field) = RB_BLACK;	\
488 				RB_SET_BLACKRED(parent, gparent, field);\
489 				elm = gparent;				\
490 				continue;				\
491 			}						\
492 			if (RB_LEFT(parent, field) == elm) {		\
493 				RB_ROTATE_RIGHT(head, parent, tmp, field);\
494 				tmp = parent;				\
495 				parent = elm;				\
496 				elm = tmp;				\
497 			}						\
498 			RB_SET_BLACKRED(parent, gparent, field);	\
499 			RB_ROTATE_LEFT(head, gparent, tmp, field);	\
500 		}							\
501 	}								\
502 	RB_COLOR(head->rbh_root, field) = RB_BLACK;			\
503 }									\
504 									\
505 STORQUAL void								\
506 name##_RB_REMOVE_COLOR(struct name *head, struct type *parent,		\
507 			struct type *elm) 				\
508 {									\
509 	struct type *tmp;						\
510 	while ((elm == NULL || RB_COLOR(elm, field) == RB_BLACK) &&	\
511 	    elm != RB_ROOT(head)) {					\
512 		if (RB_LEFT(parent, field) == elm) {			\
513 			tmp = RB_RIGHT(parent, field);			\
514 			if (RB_COLOR(tmp, field) == RB_RED) {		\
515 				RB_SET_BLACKRED(tmp, parent, field);	\
516 				RB_ROTATE_LEFT(head, parent, tmp, field);\
517 				tmp = RB_RIGHT(parent, field);		\
518 			}						\
519 			if ((RB_LEFT(tmp, field) == NULL ||		\
520 			    RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
521 			    (RB_RIGHT(tmp, field) == NULL ||		\
522 			    RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
523 				RB_COLOR(tmp, field) = RB_RED;		\
524 				elm = parent;				\
525 				parent = RB_PARENT(elm, field);		\
526 			} else {					\
527 				if (RB_RIGHT(tmp, field) == NULL ||	\
528 				    RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK) {\
529 					struct type *oleft;		\
530 					if ((oleft = RB_LEFT(tmp, field)) \
531 					    != NULL)			\
532 						RB_COLOR(oleft, field) = RB_BLACK;\
533 					RB_COLOR(tmp, field) = RB_RED;	\
534 					RB_ROTATE_RIGHT(head, tmp, oleft, field);\
535 					tmp = RB_RIGHT(parent, field);	\
536 				}					\
537 				RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
538 				RB_COLOR(parent, field) = RB_BLACK;	\
539 				if (RB_RIGHT(tmp, field))		\
540 					RB_COLOR(RB_RIGHT(tmp, field), field) = RB_BLACK;\
541 				RB_ROTATE_LEFT(head, parent, tmp, field);\
542 				elm = RB_ROOT(head);			\
543 				break;					\
544 			}						\
545 		} else {						\
546 			tmp = RB_LEFT(parent, field);			\
547 			if (RB_COLOR(tmp, field) == RB_RED) {		\
548 				RB_SET_BLACKRED(tmp, parent, field);	\
549 				RB_ROTATE_RIGHT(head, parent, tmp, field);\
550 				tmp = RB_LEFT(parent, field);		\
551 			}						\
552 			if ((RB_LEFT(tmp, field) == NULL ||		\
553 			    RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
554 			    (RB_RIGHT(tmp, field) == NULL ||		\
555 			    RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
556 				RB_COLOR(tmp, field) = RB_RED;		\
557 				elm = parent;				\
558 				parent = RB_PARENT(elm, field);		\
559 			} else {					\
560 				if (RB_LEFT(tmp, field) == NULL ||	\
561 				    RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) {\
562 					struct type *oright;		\
563 					if ((oright = RB_RIGHT(tmp, field)) \
564 					    != NULL)			\
565 						RB_COLOR(oright, field) = RB_BLACK;\
566 					RB_COLOR(tmp, field) = RB_RED;	\
567 					RB_ROTATE_LEFT(head, tmp, oright, field);\
568 					tmp = RB_LEFT(parent, field);	\
569 				}					\
570 				RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
571 				RB_COLOR(parent, field) = RB_BLACK;	\
572 				if (RB_LEFT(tmp, field))		\
573 					RB_COLOR(RB_LEFT(tmp, field), field) = RB_BLACK;\
574 				RB_ROTATE_RIGHT(head, parent, tmp, field);\
575 				elm = RB_ROOT(head);			\
576 				break;					\
577 			}						\
578 		}							\
579 	}								\
580 	if (elm)							\
581 		RB_COLOR(elm, field) = RB_BLACK;			\
582 }									\
583 									\
584 STORQUAL struct type *							\
585 name##_RB_REMOVE(struct name *head, struct type *elm)			\
586 {									\
587 	struct type *child, *parent, *old;				\
588 	struct name##_scan_info *inprog;				\
589 	int color;							\
590 									\
591 	for (inprog = RB_INPROG(head); inprog; inprog = inprog->link) { \
592 		if (inprog->node == elm) 				\
593 			inprog->node = RB_NEXT(name, head, elm);	\
594 	}								\
595 									\
596 	old = elm;							\
597 	if (RB_LEFT(elm, field) == NULL)				\
598 		child = RB_RIGHT(elm, field);				\
599 	else if (RB_RIGHT(elm, field) == NULL)				\
600 		child = RB_LEFT(elm, field);				\
601 	else {								\
602 		struct type *left;					\
603 		elm = RB_RIGHT(elm, field);				\
604 		while ((left = RB_LEFT(elm, field)) != NULL)		\
605 			elm = left;					\
606 		child = RB_RIGHT(elm, field);				\
607 		parent = RB_PARENT(elm, field);				\
608 		color = RB_COLOR(elm, field);				\
609 		if (child)						\
610 			RB_PARENT(child, field) = parent;		\
611 		if (parent) {						\
612 			if (RB_LEFT(parent, field) == elm)		\
613 				RB_LEFT(parent, field) = child;		\
614 			else						\
615 				RB_RIGHT(parent, field) = child;	\
616 			RB_AUGMENT(parent);				\
617 		} else							\
618 			RB_ROOT(head) = child;				\
619 		if (RB_PARENT(elm, field) == old)			\
620 			parent = elm;					\
621 		(elm)->field = (old)->field;				\
622 		if (RB_PARENT(old, field)) {				\
623 			if (RB_LEFT(RB_PARENT(old, field), field) == old)\
624 				RB_LEFT(RB_PARENT(old, field), field) = elm;\
625 			else						\
626 				RB_RIGHT(RB_PARENT(old, field), field) = elm;\
627 			RB_AUGMENT(RB_PARENT(old, field));		\
628 		} else							\
629 			RB_ROOT(head) = elm;				\
630 		RB_PARENT(RB_LEFT(old, field), field) = elm;		\
631 		if (RB_RIGHT(old, field))				\
632 			RB_PARENT(RB_RIGHT(old, field), field) = elm;	\
633 		if (parent) {						\
634 			left = parent;					\
635 			do {						\
636 				RB_AUGMENT(left);			\
637 			} while ((left = RB_PARENT(left, field)) != NULL); \
638 		}							\
639 		goto color;						\
640 	}								\
641 	parent = RB_PARENT(elm, field);					\
642 	color = RB_COLOR(elm, field);					\
643 	if (child)							\
644 		RB_PARENT(child, field) = parent;			\
645 	if (parent) {							\
646 		if (RB_LEFT(parent, field) == elm)			\
647 			RB_LEFT(parent, field) = child;			\
648 		else							\
649 			RB_RIGHT(parent, field) = child;		\
650 		RB_AUGMENT(parent);					\
651 	} else								\
652 		RB_ROOT(head) = child;					\
653 color:									\
654 	if (color == RB_BLACK)						\
655 		name##_RB_REMOVE_COLOR(head, parent, child);		\
656 	return (old);							\
657 }									\
658 									\
659 /* Inserts a node into the RB tree */					\
660 STORQUAL struct type *							\
661 name##_RB_INSERT(struct name *head, struct type *elm)			\
662 {									\
663 	struct type *tmp;						\
664 	struct type *parent = NULL;					\
665 	int comp = 0;							\
666 	tmp = RB_ROOT(head);						\
667 	while (tmp) {							\
668 		parent = tmp;						\
669 		comp = (cmp)(elm, parent);				\
670 		if (comp < 0)						\
671 			tmp = RB_LEFT(tmp, field);			\
672 		else if (comp > 0)					\
673 			tmp = RB_RIGHT(tmp, field);			\
674 		else							\
675 			return(tmp);					\
676 	}								\
677 	RB_SET(elm, parent, field);					\
678 	if (parent != NULL) {						\
679 		if (comp < 0)						\
680 			RB_LEFT(parent, field) = elm;			\
681 		else							\
682 			RB_RIGHT(parent, field) = elm;			\
683 		RB_AUGMENT(parent);					\
684 	} else								\
685 		RB_ROOT(head) = elm;					\
686 	name##_RB_INSERT_COLOR(head, elm);				\
687 	return (NULL);							\
688 }									\
689 									\
690 /* Finds the node with the same key as elm */				\
691 STORQUAL struct type *							\
692 name##_RB_FIND(struct name *head, struct type *elm)			\
693 {									\
694 	struct type *tmp = RB_ROOT(head);				\
695 	int comp;							\
696 	while (tmp) {							\
697 		comp = cmp(elm, tmp);					\
698 		if (comp < 0)						\
699 			tmp = RB_LEFT(tmp, field);			\
700 		else if (comp > 0)					\
701 			tmp = RB_RIGHT(tmp, field);			\
702 		else							\
703 			return (tmp);					\
704 	}								\
705 	return (NULL);							\
706 }									\
707 									\
708 /*									\
709  * Issue a callback for all matching items.  The scan function must	\
710  * return < 0 for items below the desired range, 0 for items within	\
711  * the range, and > 0 for items beyond the range.   Any item may be	\
712  * deleted while the scan is in progress.				\
713  */									\
714 static int								\
715 name##_SCANCMP_ALL(struct type *type __unused, void *data __unused)	\
716 {									\
717 	return(0);							\
718 }									\
719 									\
720 static __inline void							\
721 name##_scan_info_link(struct name##_scan_info *scan, struct name *head)	\
722 {									\
723 	RB_SCAN_LOCK(&head->rbh_spin);					\
724 	scan->link = RB_INPROG(head);					\
725 	RB_INPROG(head) = scan;						\
726 	RB_SCAN_UNLOCK(&head->rbh_spin);				\
727 }									\
728 									\
729 static __inline void							\
730 name##_scan_info_done(struct name##_scan_info *scan, struct name *head)	\
731 {									\
732 	struct name##_scan_info **infopp;				\
733 									\
734 	RB_SCAN_LOCK(&head->rbh_spin);					\
735 	infopp = &RB_INPROG(head);					\
736 	while (*infopp != scan) 					\
737 		infopp = &(*infopp)->link;				\
738 	*infopp = scan->link;						\
739 	RB_SCAN_UNLOCK(&head->rbh_spin);				\
740 }									\
741 									\
742 static __inline int							\
743 _##name##_RB_SCAN(struct name *head,					\
744 		int (*scancmp)(struct type *, void *),			\
745 		int (*callback)(struct type *, void *),			\
746 		void *data, int uselock)				\
747 {									\
748 	struct name##_scan_info info;					\
749 	struct type *best;						\
750 	struct type *tmp;						\
751 	int count;							\
752 	int comp;							\
753 									\
754 	if (scancmp == NULL)						\
755 		scancmp = name##_SCANCMP_ALL;				\
756 									\
757 	/*								\
758 	 * Locate the first element.					\
759 	 */								\
760 	tmp = RB_ROOT(head);						\
761 	best = NULL;							\
762 	while (tmp) {							\
763 		comp = scancmp(tmp, data);				\
764 		if (comp < 0) {						\
765 			tmp = RB_RIGHT(tmp, field);			\
766 		} else if (comp > 0) {					\
767 			tmp = RB_LEFT(tmp, field);			\
768 		} else {						\
769 			best = tmp;					\
770 			if (RB_LEFT(tmp, field) == NULL)		\
771 				break;					\
772 			tmp = RB_LEFT(tmp, field);			\
773 		}							\
774 	}								\
775 	count = 0;							\
776 	if (best) {							\
777 		info.node = RB_NEXT(name, head, best);			\
778 		if (uselock)						\
779 			name##_scan_info_link(&info, head);		\
780 		while ((comp = callback(best, data)) >= 0) {		\
781 			count += comp;					\
782 			best = info.node;				\
783 			if (best == NULL || scancmp(best, data) != 0)	\
784 				break;					\
785 			info.node = RB_NEXT(name, head, best);		\
786 		}							\
787 		if (uselock)						\
788 			name##_scan_info_done(&info, head);		\
789 		if (comp < 0)	/* error or termination */		\
790 			count = comp;					\
791 	}								\
792 	return(count);							\
793 }									\
794 									\
795 STORQUAL int								\
796 name##_RB_SCAN(struct name *head,					\
797 		int (*scancmp)(struct type *, void *),			\
798 		int (*callback)(struct type *, void *),			\
799 		void *data)						\
800 {									\
801 	return _##name##_RB_SCAN(head, scancmp, callback, data, 1);	\
802 }									\
803 									\
804 STORQUAL int								\
805 name##_RB_SCAN_NOLK(struct name *head,					\
806 		int (*scancmp)(struct type *, void *),			\
807 		int (*callback)(struct type *, void *),			\
808 		void *data)						\
809 {									\
810 	return _##name##_RB_SCAN(head, scancmp, callback, data, 0);	\
811 }									\
812 									\
813 /* ARGSUSED */								\
814 STORQUAL struct type *							\
815 name##_RB_NEXT(struct type *elm)					\
816 {									\
817 	if (RB_RIGHT(elm, field)) {					\
818 		elm = RB_RIGHT(elm, field);				\
819 		while (RB_LEFT(elm, field))				\
820 			elm = RB_LEFT(elm, field);			\
821 	} else {							\
822 		if (RB_PARENT(elm, field) &&				\
823 		    (elm == RB_LEFT(RB_PARENT(elm, field), field)))	\
824 			elm = RB_PARENT(elm, field);			\
825 		else {							\
826 			while (RB_PARENT(elm, field) &&			\
827 			    (elm == RB_RIGHT(RB_PARENT(elm, field), field)))\
828 				elm = RB_PARENT(elm, field);		\
829 			elm = RB_PARENT(elm, field);			\
830 		}							\
831 	}								\
832 	return (elm);							\
833 }									\
834 									\
835 /* ARGSUSED */								\
836 STORQUAL struct type *							\
837 name##_RB_PREV(struct type *elm)					\
838 {									\
839 	if (RB_LEFT(elm, field)) {					\
840 		elm = RB_LEFT(elm, field);				\
841 		while (RB_RIGHT(elm, field))				\
842 			elm = RB_RIGHT(elm, field);			\
843 	} else {							\
844 		if (RB_PARENT(elm, field) &&				\
845 		    (elm == RB_RIGHT(RB_PARENT(elm, field), field)))	\
846 			elm = RB_PARENT(elm, field);			\
847 		else {							\
848 			while (RB_PARENT(elm, field) &&			\
849 			    (elm == RB_LEFT(RB_PARENT(elm, field), field)))\
850 				elm = RB_PARENT(elm, field);		\
851 			elm = RB_PARENT(elm, field);			\
852 		}							\
853 	}								\
854 	return (elm);							\
855 }									\
856 									\
857 STORQUAL struct type *							\
858 name##_RB_MINMAX(struct name *head, int val)				\
859 {									\
860 	struct type *tmp = RB_ROOT(head);				\
861 	struct type *parent = NULL;					\
862 	while (tmp) {							\
863 		parent = tmp;						\
864 		if (val < 0)						\
865 			tmp = RB_LEFT(tmp, field);			\
866 		else							\
867 			tmp = RB_RIGHT(tmp, field);			\
868 	}								\
869 	return (parent);						\
870 }
871 
872 /*
873  * This extended version implements a fast LOOKUP function given
874  * a numeric data type.
875  *
876  * The element whos index/offset field is exactly the specified value
877  * will be returned, or NULL.
878  */
879 #define RB_GENERATE2(name, type, field, cmp, datatype, indexfield)	\
880 RB_GENERATE(name, type, field, cmp)					\
881 									\
882 struct type *								\
883 name##_RB_LOOKUP(struct name *head, datatype value)			\
884 {									\
885 	struct type *tmp;						\
886 									\
887 	tmp = RB_ROOT(head);						\
888 	while (tmp) {							\
889 		if (value > tmp->indexfield) 				\
890 			tmp = RB_RIGHT(tmp, field);			\
891 		else if (value < tmp->indexfield) 			\
892 			tmp = RB_LEFT(tmp, field);			\
893 		else 							\
894 			return(tmp);					\
895 	}								\
896 	return(NULL);							\
897 }									\
898 									\
899 struct type *								\
900 name##_RB_LOOKUP_REL(struct name *head, datatype value, struct type *rel)\
901 {									\
902 	struct type *tmp;						\
903 									\
904 	if (value == rel->indexfield - 1) {				\
905 		tmp = name##_RB_PREV(rel);				\
906 		if (tmp && value != tmp->indexfield)			\
907 			tmp = NULL;					\
908 		return tmp;						\
909 	}								\
910 	if (value == rel->indexfield + 1) {				\
911 		tmp = name##_RB_NEXT(rel);				\
912 		if (tmp && value != tmp->indexfield)			\
913 			tmp = NULL;					\
914 		return tmp;						\
915 	}								\
916 									\
917 	tmp = RB_ROOT(head);						\
918 	while (tmp) {							\
919 		if (value > tmp->indexfield) 				\
920 			tmp = RB_RIGHT(tmp, field);			\
921 		else if (value < tmp->indexfield) 			\
922 			tmp = RB_LEFT(tmp, field);			\
923 		else 							\
924 			return(tmp);					\
925 	}								\
926 	return(NULL);							\
927 }									\
928 
929 /*
930  * This extended version implements a fast ranged-based LOOKUP function
931  * given a numeric data type, for data types with a beginning and end
932  * (end is inclusive).
933  *
934  * The element whos range contains the specified value is returned, or NULL
935  */
936 #define RB_GENERATE3(name, type, field, cmp, datatype, begfield, endfield) \
937 RB_GENERATE2(name, type, field, cmp, datatype, begfield)		\
938 									\
939 struct type *								\
940 name##_RB_RLOOKUP(struct name *head, datatype value)			\
941 {									\
942 	struct type *tmp;						\
943 									\
944 	tmp = RB_ROOT(head);						\
945 	while (tmp) {							\
946 		if (value >= tmp->begfield && value <= tmp->endfield) 	\
947 			return(tmp);					\
948 		if (value > tmp->begfield) 				\
949 			tmp = RB_RIGHT(tmp, field);			\
950 		else							\
951 			tmp = RB_LEFT(tmp, field);			\
952 	}								\
953 	return(NULL);							\
954 }									\
955 
956 /*
957  * This extended version implements a fast ranged-based LOOKUP function
958  * given a numeric data type, for data types with a beginning and size.
959  *
960  * WARNING: The full range of the data type is not supported due to a
961  * boundary condition at the end, where (beginning + size) might overflow.
962  *
963  * The element whos range contains the specified value is returned, or NULL
964  */
965 #define RB_GENERATE4(name, type, field, cmp, datatype, begfield, sizefield) \
966 RB_GENERATE2(name, type, field, cmp, datatype, begfield)		\
967 									\
968 struct type *								\
969 name##_RB_RLOOKUP(struct name *head, datatype value)			\
970 {									\
971 	struct type *tmp;						\
972 									\
973 	tmp = RB_ROOT(head);						\
974 	while (tmp) {							\
975 		if (value >= tmp->begfield &&				\
976 		    value < tmp->begfield + tmp->sizefield) { 		\
977 			return(tmp);					\
978 		}							\
979 		if (value > tmp->begfield) 				\
980 			tmp = RB_RIGHT(tmp, field);			\
981 		else							\
982 			tmp = RB_LEFT(tmp, field);			\
983 	}								\
984 	return(NULL);							\
985 }									\
986 
987 /*
988  * This generates a custom lookup function for a red-black tree.
989  * Note that the macro may be used with a storage qualifier.
990  */
991 
992 #define RB_GENERATE_XLOOKUP(name, ext, type, field, xcmp, datatype)	   \
993 	_RB_GENERATE_XLOOKUP(name, ext, type, field, xcmp, datatype,)
994 #define RB_GENERATE_XLOOKUP_STATIC(name, ext, type, field, xcmp, datatype) \
995 	_RB_GENERATE_XLOOKUP(name, ext, type, field, xcmp, datatype, __unused static)
996 
997 #define _RB_GENERATE_XLOOKUP(name, ext, type, field, xcmp, datatype, STORQUAL)\
998 									\
999 STORQUAL struct type *							\
1000 name##_RB_LOOKUP_##ext (struct name *head, datatype value)		\
1001 {									\
1002 	struct type *tmp;						\
1003 	int r;								\
1004 									\
1005 	tmp = RB_ROOT(head);						\
1006 	while (tmp) {							\
1007 		r = xcmp(value, tmp);					\
1008 		if (r == 0)						\
1009 			return(tmp);					\
1010 		if (r > 0) 						\
1011 			tmp = RB_RIGHT(tmp, field);			\
1012 		else							\
1013 			tmp = RB_LEFT(tmp, field);			\
1014 	}								\
1015 	return(NULL);							\
1016 }									\
1017 
1018 
1019 #define RB_NEGINF	-1
1020 #define RB_INF	1
1021 
1022 #define RB_INSERT(name, root, elm)	name##_RB_INSERT(root, elm)
1023 #define RB_REMOVE(name, root, elm)	name##_RB_REMOVE(root, elm)
1024 #define RB_FIND(name, root, elm)	name##_RB_FIND(root, elm)
1025 #define RB_LOOKUP(name, root, value)	name##_RB_LOOKUP(root, value)
1026 #define RB_RLOOKUP(name, root, value)	name##_RB_RLOOKUP(root, value)
1027 #define RB_SCAN(name, root, cmp, callback, data) 			\
1028 				name##_RB_SCAN(root, cmp, callback, data)
1029 #define RB_SCAN_NOLK(name, root, cmp, callback, data) 			\
1030 				name##_RB_SCAN_NOLK(root, cmp, callback, data)
1031 #define RB_FIRST(name, root)		name##_RB_MINMAX(root, RB_NEGINF)
1032 #define RB_NEXT(name, root, elm)	name##_RB_NEXT(elm)
1033 #define RB_PREV(name, root, elm)	name##_RB_PREV(elm)
1034 #define RB_MIN(name, root)		name##_RB_MINMAX(root, RB_NEGINF)
1035 #define RB_MAX(name, root)		name##_RB_MINMAX(root, RB_INF)
1036 
1037 #define RB_FOREACH(x, name, head)					\
1038 	for ((x) = RB_MIN(name, head);					\
1039 	     (x) != NULL;						\
1040 	     (x) = name##_RB_NEXT(x))
1041 
1042 #define RB_FOREACH_FROM(x, name, y)					\
1043 	for ((x) = (y);							\
1044 	    ((x) != NULL) && ((y) = name##_RB_NEXT(x), (x) != NULL);	\
1045 	     (x) = (y))
1046 
1047 #define RB_FOREACH_SAFE(x, name, head, y)				\
1048 	for ((x) = RB_MIN(name, head);					\
1049 	    ((x) != NULL) && ((y) = name##_RB_NEXT(x), (x) != NULL);	\
1050 	     (x) = (y))
1051 
1052 #define RB_FOREACH_REVERSE(x, name, head)				\
1053 	for ((x) = RB_MAX(name, head);					\
1054 	     (x) != NULL;						\
1055 	     (x) = name##_RB_PREV(x))
1056 
1057 #define RB_FOREACH_REVERSE_FROM(x, name, y)				\
1058 	for ((x) = (y);							\
1059 	    ((x) != NULL) && ((y) = name##_RB_PREV(x), (x) != NULL);	\
1060 	     (x) = (y))
1061 
1062 #define RB_FOREACH_REVERSE_SAFE(x, name, head, y)			\
1063 	for ((x) = RB_MAX(name, head);					\
1064 	    ((x) != NULL) && ((y) = name##_RB_PREV(x), (x) != NULL);	\
1065 	     (x) = (y))
1066 
1067 #endif	/* _SYS_TREE_H_ */
1068