xref: /freebsd/sys/sys/tree.h (revision e17f5b1d)
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 /* $FreeBSD$ */
4 
5 /*-
6  * SPDX-License-Identifier: BSD-2-Clause-FreeBSD
7  *
8  * Copyright 2002 Niels Provos <provos@citi.umich.edu>
9  * All rights reserved.
10  *
11  * Redistribution and use in source and binary forms, with or without
12  * modification, are permitted provided that the following conditions
13  * are met:
14  * 1. Redistributions of source code must retain the above copyright
15  *    notice, this list of conditions and the following disclaimer.
16  * 2. Redistributions in binary form must reproduce the above copyright
17  *    notice, this list of conditions and the following disclaimer in the
18  *    documentation and/or other materials provided with the distribution.
19  *
20  * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
21  * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
22  * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
23  * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
24  * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
25  * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
26  * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
27  * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
28  * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
29  * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
30  */
31 
32 #ifndef	_SYS_TREE_H_
33 #define	_SYS_TREE_H_
34 
35 #include <sys/cdefs.h>
36 
37 /*
38  * This file defines data structures for different types of trees:
39  * splay trees and red-black trees.
40  *
41  * A splay tree is a self-organizing data structure.  Every operation
42  * on the tree causes a splay to happen.  The splay moves the requested
43  * node to the root of the tree and partly rebalances it.
44  *
45  * This has the benefit that request locality causes faster lookups as
46  * the requested nodes move to the top of the tree.  On the other hand,
47  * every lookup causes memory writes.
48  *
49  * The Balance Theorem bounds the total access time for m operations
50  * and n inserts on an initially empty tree as O((m + n)lg n).  The
51  * amortized cost for a sequence of m accesses to a splay tree is O(lg n);
52  *
53  * A red-black tree is a binary search tree with the node color as an
54  * extra attribute.  It fulfills a set of conditions:
55  *	- every search path from the root to a leaf consists of the
56  *	  same number of black nodes,
57  *	- each red node (except for the root) has a black parent,
58  *	- each leaf node is black.
59  *
60  * Every operation on a red-black tree is bounded as O(lg n).
61  * The maximum height of a red-black tree is 2lg (n+1).
62  */
63 
64 #define SPLAY_HEAD(name, type)						\
65 struct name {								\
66 	struct type *sph_root; /* root of the tree */			\
67 }
68 
69 #define SPLAY_INITIALIZER(root)						\
70 	{ NULL }
71 
72 #define SPLAY_INIT(root) do {						\
73 	(root)->sph_root = NULL;					\
74 } while (/*CONSTCOND*/ 0)
75 
76 #define SPLAY_ENTRY(type)						\
77 struct {								\
78 	struct type *spe_left; /* left element */			\
79 	struct type *spe_right; /* right element */			\
80 }
81 
82 #define SPLAY_LEFT(elm, field)		(elm)->field.spe_left
83 #define SPLAY_RIGHT(elm, field)		(elm)->field.spe_right
84 #define SPLAY_ROOT(head)		(head)->sph_root
85 #define SPLAY_EMPTY(head)		(SPLAY_ROOT(head) == NULL)
86 
87 /* SPLAY_ROTATE_{LEFT,RIGHT} expect that tmp hold SPLAY_{RIGHT,LEFT} */
88 #define SPLAY_ROTATE_RIGHT(head, tmp, field) do {			\
89 	SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(tmp, field);	\
90 	SPLAY_RIGHT(tmp, field) = (head)->sph_root;			\
91 	(head)->sph_root = tmp;						\
92 } while (/*CONSTCOND*/ 0)
93 
94 #define SPLAY_ROTATE_LEFT(head, tmp, field) do {			\
95 	SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(tmp, field);	\
96 	SPLAY_LEFT(tmp, field) = (head)->sph_root;			\
97 	(head)->sph_root = tmp;						\
98 } while (/*CONSTCOND*/ 0)
99 
100 #define SPLAY_LINKLEFT(head, tmp, field) do {				\
101 	SPLAY_LEFT(tmp, field) = (head)->sph_root;			\
102 	tmp = (head)->sph_root;						\
103 	(head)->sph_root = SPLAY_LEFT((head)->sph_root, field);		\
104 } while (/*CONSTCOND*/ 0)
105 
106 #define SPLAY_LINKRIGHT(head, tmp, field) do {				\
107 	SPLAY_RIGHT(tmp, field) = (head)->sph_root;			\
108 	tmp = (head)->sph_root;						\
109 	(head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);	\
110 } while (/*CONSTCOND*/ 0)
111 
112 #define SPLAY_ASSEMBLE(head, node, left, right, field) do {		\
113 	SPLAY_RIGHT(left, field) = SPLAY_LEFT((head)->sph_root, field);	\
114 	SPLAY_LEFT(right, field) = SPLAY_RIGHT((head)->sph_root, field);\
115 	SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(node, field);	\
116 	SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(node, field);	\
117 } while (/*CONSTCOND*/ 0)
118 
119 /* Generates prototypes and inline functions */
120 
121 #define SPLAY_PROTOTYPE(name, type, field, cmp)				\
122 void name##_SPLAY(struct name *, struct type *);			\
123 void name##_SPLAY_MINMAX(struct name *, int);				\
124 struct type *name##_SPLAY_INSERT(struct name *, struct type *);		\
125 struct type *name##_SPLAY_REMOVE(struct name *, struct type *);		\
126 									\
127 /* Finds the node with the same key as elm */				\
128 static __unused __inline struct type *					\
129 name##_SPLAY_FIND(struct name *head, struct type *elm)			\
130 {									\
131 	if (SPLAY_EMPTY(head))						\
132 		return(NULL);						\
133 	name##_SPLAY(head, elm);					\
134 	if ((cmp)(elm, (head)->sph_root) == 0)				\
135 		return (head->sph_root);				\
136 	return (NULL);							\
137 }									\
138 									\
139 static __unused __inline struct type *					\
140 name##_SPLAY_NEXT(struct name *head, struct type *elm)			\
141 {									\
142 	name##_SPLAY(head, elm);					\
143 	if (SPLAY_RIGHT(elm, field) != NULL) {				\
144 		elm = SPLAY_RIGHT(elm, field);				\
145 		while (SPLAY_LEFT(elm, field) != NULL) {		\
146 			elm = SPLAY_LEFT(elm, field);			\
147 		}							\
148 	} else								\
149 		elm = NULL;						\
150 	return (elm);							\
151 }									\
152 									\
153 static __unused __inline struct type *					\
154 name##_SPLAY_MIN_MAX(struct name *head, int val)			\
155 {									\
156 	name##_SPLAY_MINMAX(head, val);					\
157         return (SPLAY_ROOT(head));					\
158 }
159 
160 /* Main splay operation.
161  * Moves node close to the key of elm to top
162  */
163 #define SPLAY_GENERATE(name, type, field, cmp)				\
164 struct type *								\
165 name##_SPLAY_INSERT(struct name *head, struct type *elm)		\
166 {									\
167     if (SPLAY_EMPTY(head)) {						\
168 	    SPLAY_LEFT(elm, field) = SPLAY_RIGHT(elm, field) = NULL;	\
169     } else {								\
170 	    int __comp;							\
171 	    name##_SPLAY(head, elm);					\
172 	    __comp = (cmp)(elm, (head)->sph_root);			\
173 	    if(__comp < 0) {						\
174 		    SPLAY_LEFT(elm, field) = SPLAY_LEFT((head)->sph_root, field);\
175 		    SPLAY_RIGHT(elm, field) = (head)->sph_root;		\
176 		    SPLAY_LEFT((head)->sph_root, field) = NULL;		\
177 	    } else if (__comp > 0) {					\
178 		    SPLAY_RIGHT(elm, field) = SPLAY_RIGHT((head)->sph_root, field);\
179 		    SPLAY_LEFT(elm, field) = (head)->sph_root;		\
180 		    SPLAY_RIGHT((head)->sph_root, field) = NULL;	\
181 	    } else							\
182 		    return ((head)->sph_root);				\
183     }									\
184     (head)->sph_root = (elm);						\
185     return (NULL);							\
186 }									\
187 									\
188 struct type *								\
189 name##_SPLAY_REMOVE(struct name *head, struct type *elm)		\
190 {									\
191 	struct type *__tmp;						\
192 	if (SPLAY_EMPTY(head))						\
193 		return (NULL);						\
194 	name##_SPLAY(head, elm);					\
195 	if ((cmp)(elm, (head)->sph_root) == 0) {			\
196 		if (SPLAY_LEFT((head)->sph_root, field) == NULL) {	\
197 			(head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);\
198 		} else {						\
199 			__tmp = SPLAY_RIGHT((head)->sph_root, field);	\
200 			(head)->sph_root = SPLAY_LEFT((head)->sph_root, field);\
201 			name##_SPLAY(head, elm);			\
202 			SPLAY_RIGHT((head)->sph_root, field) = __tmp;	\
203 		}							\
204 		return (elm);						\
205 	}								\
206 	return (NULL);							\
207 }									\
208 									\
209 void									\
210 name##_SPLAY(struct name *head, struct type *elm)			\
211 {									\
212 	struct type __node, *__left, *__right, *__tmp;			\
213 	int __comp;							\
214 \
215 	SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
216 	__left = __right = &__node;					\
217 \
218 	while ((__comp = (cmp)(elm, (head)->sph_root)) != 0) {		\
219 		if (__comp < 0) {					\
220 			__tmp = SPLAY_LEFT((head)->sph_root, field);	\
221 			if (__tmp == NULL)				\
222 				break;					\
223 			if ((cmp)(elm, __tmp) < 0){			\
224 				SPLAY_ROTATE_RIGHT(head, __tmp, field);	\
225 				if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
226 					break;				\
227 			}						\
228 			SPLAY_LINKLEFT(head, __right, field);		\
229 		} else if (__comp > 0) {				\
230 			__tmp = SPLAY_RIGHT((head)->sph_root, field);	\
231 			if (__tmp == NULL)				\
232 				break;					\
233 			if ((cmp)(elm, __tmp) > 0){			\
234 				SPLAY_ROTATE_LEFT(head, __tmp, field);	\
235 				if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
236 					break;				\
237 			}						\
238 			SPLAY_LINKRIGHT(head, __left, field);		\
239 		}							\
240 	}								\
241 	SPLAY_ASSEMBLE(head, &__node, __left, __right, field);		\
242 }									\
243 									\
244 /* Splay with either the minimum or the maximum element			\
245  * Used to find minimum or maximum element in tree.			\
246  */									\
247 void name##_SPLAY_MINMAX(struct name *head, int __comp) \
248 {									\
249 	struct type __node, *__left, *__right, *__tmp;			\
250 \
251 	SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
252 	__left = __right = &__node;					\
253 \
254 	while (1) {							\
255 		if (__comp < 0) {					\
256 			__tmp = SPLAY_LEFT((head)->sph_root, field);	\
257 			if (__tmp == NULL)				\
258 				break;					\
259 			if (__comp < 0){				\
260 				SPLAY_ROTATE_RIGHT(head, __tmp, field);	\
261 				if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
262 					break;				\
263 			}						\
264 			SPLAY_LINKLEFT(head, __right, field);		\
265 		} else if (__comp > 0) {				\
266 			__tmp = SPLAY_RIGHT((head)->sph_root, field);	\
267 			if (__tmp == NULL)				\
268 				break;					\
269 			if (__comp > 0) {				\
270 				SPLAY_ROTATE_LEFT(head, __tmp, field);	\
271 				if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
272 					break;				\
273 			}						\
274 			SPLAY_LINKRIGHT(head, __left, field);		\
275 		}							\
276 	}								\
277 	SPLAY_ASSEMBLE(head, &__node, __left, __right, field);		\
278 }
279 
280 #define SPLAY_NEGINF	-1
281 #define SPLAY_INF	1
282 
283 #define SPLAY_INSERT(name, x, y)	name##_SPLAY_INSERT(x, y)
284 #define SPLAY_REMOVE(name, x, y)	name##_SPLAY_REMOVE(x, y)
285 #define SPLAY_FIND(name, x, y)		name##_SPLAY_FIND(x, y)
286 #define SPLAY_NEXT(name, x, y)		name##_SPLAY_NEXT(x, y)
287 #define SPLAY_MIN(name, x)		(SPLAY_EMPTY(x) ? NULL	\
288 					: name##_SPLAY_MIN_MAX(x, SPLAY_NEGINF))
289 #define SPLAY_MAX(name, x)		(SPLAY_EMPTY(x) ? NULL	\
290 					: name##_SPLAY_MIN_MAX(x, SPLAY_INF))
291 
292 #define SPLAY_FOREACH(x, name, head)					\
293 	for ((x) = SPLAY_MIN(name, head);				\
294 	     (x) != NULL;						\
295 	     (x) = SPLAY_NEXT(name, head, x))
296 
297 /* Macros that define a red-black tree */
298 #define RB_HEAD(name, type)						\
299 struct name {								\
300 	struct type *rbh_root; /* root of the tree */			\
301 }
302 
303 #define RB_INITIALIZER(root)						\
304 	{ NULL }
305 
306 #define RB_INIT(root) do {						\
307 	(root)->rbh_root = NULL;					\
308 } while (/*CONSTCOND*/ 0)
309 
310 #define RB_ENTRY(type)							\
311 struct {								\
312 	struct type *rbe_left;		/* left element */		\
313 	struct type *rbe_right;		/* right element */		\
314 	struct type *rbe_parent;	/* parent element */		\
315 }
316 
317 #define RB_LEFT(elm, field)		(elm)->field.rbe_left
318 #define RB_RIGHT(elm, field)		(elm)->field.rbe_right
319 
320 /*
321  * With the expectation that any object of struct type has an
322  * address that is a multiple of 4, and that therefore the
323  * 2 least significant bits of a pointer to struct type are
324  * always zero, this implementation sets those bits to indicate
325  * that the left or right child of the tree node is "red".
326  */
327 #define RB_UP(elm, field)		(elm)->field.rbe_parent
328 #define RB_BITS(elm, field)		*(__uintptr_t *)&RB_UP(elm, field)
329 #define RB_RED_L			(__uintptr_t)1
330 #define RB_RED_R			(__uintptr_t)2
331 #define RB_RED_MASK			(__uintptr_t)3
332 #define RB_FLIP_LEFT(elm, field)	(RB_BITS(elm, field) ^= RB_RED_L)
333 #define RB_FLIP_RIGHT(elm, field)	(RB_BITS(elm, field) ^= RB_RED_R)
334 #define RB_RED_LEFT(elm, field)		((RB_BITS(elm, field) & RB_RED_L) != 0)
335 #define RB_RED_RIGHT(elm, field)	((RB_BITS(elm, field) & RB_RED_R) != 0)
336 #define RB_PARENT(elm, field)		((__typeof(RB_UP(elm, field)))	\
337 					 (RB_BITS(elm, field) & ~RB_RED_MASK))
338 
339 /*
340  * This header may appear in user code where 'bool' is not defined,
341  * so it defines its own boolean type to avoid breaking that code.
342  */
343 #define RB_BOOL				int
344 #define RB_TRUE				1
345 #define RB_FALSE			0
346 
347 #define RB_ROOT(head)			(head)->rbh_root
348 #define RB_EMPTY(head)			(RB_ROOT(head) == NULL)
349 
350 #define RB_SET_PARENT(dst, src, field) do {				\
351 	RB_BITS(dst, field) &= RB_RED_MASK;				\
352 	RB_BITS(dst, field) |= (__uintptr_t)src;			\
353 } while (/*CONSTCOND*/ 0)
354 
355 #define RB_SET(elm, parent, field) do {					\
356 	RB_UP(elm, field) = parent;					\
357 	RB_LEFT(elm, field) = RB_RIGHT(elm, field) = NULL;		\
358 } while (/*CONSTCOND*/ 0)
359 
360 #define RB_COLOR(elm, field)	(RB_PARENT(elm, field) == NULL ? RB_FALSE : \
361 				RB_LEFT(RB_PARENT(elm, field), field) == elm ? \
362 				RB_RED_LEFT(RB_PARENT(elm, field), field) : \
363 				RB_RED_RIGHT(RB_PARENT(elm, field), field))
364 
365 /*
366  * Something to be invoked in a loop at the root of every modified subtree,
367  * from the bottom up to the root, to update augmented node data.
368  */
369 #ifndef RB_AUGMENT
370 #define RB_AUGMENT(x)	break
371 #endif
372 
373 #define RB_SWAP_CHILD(head, out, in, field) do {			\
374 	if (RB_PARENT(out, field) == NULL)				\
375 		RB_ROOT(head) = (in);					\
376 	else if ((out) == RB_LEFT(RB_PARENT(out, field), field))	\
377 		RB_LEFT(RB_PARENT(out, field), field) = (in);		\
378 	else								\
379 		RB_RIGHT(RB_PARENT(out, field), field) = (in);		\
380 } while (/*CONSTCOND*/ 0)
381 
382 #define RB_ROTATE_LEFT(head, elm, tmp, field) do {			\
383 	(tmp) = RB_RIGHT(elm, field);					\
384 	if ((RB_RIGHT(elm, field) = RB_LEFT(tmp, field)) != NULL) {	\
385 		RB_SET_PARENT(RB_RIGHT(elm, field), elm, field);	\
386 	}								\
387 	RB_SET_PARENT(tmp, RB_PARENT(elm, field), field);		\
388 	RB_SWAP_CHILD(head, elm, tmp, field);				\
389 	RB_LEFT(tmp, field) = (elm);					\
390 	RB_SET_PARENT(elm, tmp, field);					\
391 	RB_AUGMENT(elm);						\
392 } while (/*CONSTCOND*/ 0)
393 
394 #define RB_ROTATE_RIGHT(head, elm, tmp, field) do {			\
395 	(tmp) = RB_LEFT(elm, field);					\
396 	if ((RB_LEFT(elm, field) = RB_RIGHT(tmp, field)) != NULL) {	\
397 		RB_SET_PARENT(RB_LEFT(elm, field), elm, field);		\
398 	}								\
399 	RB_SET_PARENT(tmp, RB_PARENT(elm, field), field);		\
400 	RB_SWAP_CHILD(head, elm, tmp, field);				\
401 	RB_RIGHT(tmp, field) = (elm);					\
402 	RB_SET_PARENT(elm, tmp, field);					\
403 	RB_AUGMENT(elm);						\
404 } while (/*CONSTCOND*/ 0)
405 
406 /* Generates prototypes and inline functions */
407 #define	RB_PROTOTYPE(name, type, field, cmp)				\
408 	RB_PROTOTYPE_INTERNAL(name, type, field, cmp,)
409 #define	RB_PROTOTYPE_STATIC(name, type, field, cmp)			\
410 	RB_PROTOTYPE_INTERNAL(name, type, field, cmp, __unused static)
411 #define RB_PROTOTYPE_INTERNAL(name, type, field, cmp, attr)		\
412 	RB_PROTOTYPE_INSERT_COLOR(name, type, attr);			\
413 	RB_PROTOTYPE_REMOVE_COLOR(name, type, attr);			\
414 	RB_PROTOTYPE_INSERT(name, type, attr);				\
415 	RB_PROTOTYPE_REMOVE(name, type, attr);				\
416 	RB_PROTOTYPE_FIND(name, type, attr);				\
417 	RB_PROTOTYPE_NFIND(name, type, attr);				\
418 	RB_PROTOTYPE_NEXT(name, type, attr);				\
419 	RB_PROTOTYPE_PREV(name, type, attr);				\
420 	RB_PROTOTYPE_MINMAX(name, type, attr);				\
421 	RB_PROTOTYPE_REINSERT(name, type, attr);
422 #define RB_PROTOTYPE_INSERT_COLOR(name, type, attr)			\
423 	attr void name##_RB_INSERT_COLOR(struct name *, struct type *)
424 #define RB_PROTOTYPE_REMOVE_COLOR(name, type, attr)			\
425 	attr void name##_RB_REMOVE_COLOR(struct name *, struct type *)
426 #define RB_PROTOTYPE_REMOVE(name, type, attr)				\
427 	attr struct type *name##_RB_REMOVE(struct name *, struct type *)
428 #define RB_PROTOTYPE_INSERT(name, type, attr)				\
429 	attr struct type *name##_RB_INSERT(struct name *, struct type *)
430 #define RB_PROTOTYPE_FIND(name, type, attr)				\
431 	attr struct type *name##_RB_FIND(struct name *, struct type *)
432 #define RB_PROTOTYPE_NFIND(name, type, attr)				\
433 	attr struct type *name##_RB_NFIND(struct name *, struct type *)
434 #define RB_PROTOTYPE_NEXT(name, type, attr)				\
435 	attr struct type *name##_RB_NEXT(struct type *)
436 #define RB_PROTOTYPE_PREV(name, type, attr)				\
437 	attr struct type *name##_RB_PREV(struct type *)
438 #define RB_PROTOTYPE_MINMAX(name, type, attr)				\
439 	attr struct type *name##_RB_MINMAX(struct name *, int)
440 #define RB_PROTOTYPE_REINSERT(name, type, attr)			\
441 	attr struct type *name##_RB_REINSERT(struct name *, struct type *)
442 
443 /* Main rb operation.
444  * Moves node close to the key of elm to top
445  */
446 #define	RB_GENERATE(name, type, field, cmp)				\
447 	RB_GENERATE_INTERNAL(name, type, field, cmp,)
448 #define	RB_GENERATE_STATIC(name, type, field, cmp)			\
449 	RB_GENERATE_INTERNAL(name, type, field, cmp, __unused static)
450 #define RB_GENERATE_INTERNAL(name, type, field, cmp, attr)		\
451 	RB_GENERATE_INSERT_COLOR(name, type, field, attr)		\
452 	RB_GENERATE_REMOVE_COLOR(name, type, field, attr)		\
453 	RB_GENERATE_INSERT(name, type, field, cmp, attr)		\
454 	RB_GENERATE_REMOVE(name, type, field, attr)			\
455 	RB_GENERATE_FIND(name, type, field, cmp, attr)			\
456 	RB_GENERATE_NFIND(name, type, field, cmp, attr)			\
457 	RB_GENERATE_NEXT(name, type, field, attr)			\
458 	RB_GENERATE_PREV(name, type, field, attr)			\
459 	RB_GENERATE_MINMAX(name, type, field, attr)			\
460 	RB_GENERATE_REINSERT(name, type, field, cmp, attr)
461 
462 
463 #define RB_GENERATE_INSERT_COLOR(name, type, field, attr)		\
464 attr void								\
465 name##_RB_INSERT_COLOR(struct name *head, struct type *elm)		\
466 {									\
467 	struct type *gparent, *parent;					\
468 	while ((parent = RB_PARENT(elm, field)) != NULL) {		\
469 		if (RB_LEFT(parent, field) == elm)			\
470 			RB_FLIP_LEFT(parent, field);			\
471 		else							\
472 			RB_FLIP_RIGHT(parent, field);			\
473 		if ((gparent = RB_PARENT(parent, field)) == NULL)	\
474 			break;						\
475 		if (RB_RED_LEFT(gparent, field) &&			\
476 		    RB_RED_RIGHT(gparent, field)) {			\
477 			RB_FLIP_LEFT(gparent, field);			\
478 			RB_FLIP_RIGHT(gparent, field);			\
479 			elm = gparent;					\
480 			continue;					\
481 		}							\
482 		if (RB_RED_LEFT(gparent, field) &&			\
483 		    parent == RB_LEFT(gparent, field)) { 		\
484 			if (RB_RIGHT(parent, field) == elm) {		\
485 				RB_ROTATE_LEFT(head, parent, elm, field);\
486 				RB_FLIP_RIGHT(parent, field);		\
487 				RB_FLIP_LEFT(elm, field);		\
488 				parent = elm;				\
489 			}						\
490 			RB_ROTATE_RIGHT(head, gparent, parent, field);	\
491 			RB_FLIP_LEFT(gparent, field);			\
492 			RB_FLIP_RIGHT(parent, field);			\
493 		} else if (RB_RED_RIGHT(gparent, field) &&		\
494 		    parent == RB_RIGHT(gparent, field)) {		\
495 			if (RB_LEFT(parent, field) == elm) {		\
496 				RB_ROTATE_RIGHT(head, parent, elm, field);\
497 				RB_FLIP_LEFT(parent, field);		\
498 				RB_FLIP_RIGHT(elm, field);		\
499 				parent = elm;				\
500 			}						\
501 			RB_ROTATE_LEFT(head, gparent, parent, field);	\
502 			RB_FLIP_RIGHT(gparent, field);			\
503 			RB_FLIP_LEFT(parent, field);			\
504 		}							\
505 		break;							\
506 	}								\
507 }
508 
509 #define RB_GENERATE_REMOVE_COLOR(name, type, field, attr)		\
510 attr void								\
511 name##_RB_REMOVE_COLOR(struct name *head, struct type *par)		\
512 {									\
513 	struct type *gpr, *sib, *nec;					\
514 	RB_BOOL left_elm, left_par, red_gpr;				\
515 	left_par = (RB_LEFT(par, field) == NULL);			\
516 	do {								\
517 		left_elm = left_par;					\
518 		if (left_elm ?						\
519 		    !RB_RED_RIGHT(par, field) :				\
520 		    !RB_RED_LEFT(par, field)) {				\
521 			gpr = RB_PARENT(par, field);			\
522 			left_par = gpr != NULL &&			\
523 			    RB_LEFT(gpr, field) == par;			\
524 			red_gpr = gpr == NULL ?				\
525 				RB_TRUE: RB_COLOR(par, field);		\
526 		}							\
527 		if (left_elm) {						\
528 			if (RB_RED_RIGHT(par, field)) {			\
529 				red_gpr = RB_TRUE;			\
530 				RB_ROTATE_LEFT(head, par, gpr, field);	\
531 				RB_FLIP_RIGHT(par, field);		\
532 				RB_FLIP_LEFT(gpr, field);		\
533 			}						\
534 			sib = RB_RIGHT(par, field);			\
535 			if (RB_RED_RIGHT(sib, field)) {			\
536 				if (RB_RED_LEFT(sib, field)) {		\
537 					RB_FLIP_LEFT(sib, field);	\
538 					RB_FLIP_RIGHT(par, field);	\
539 				}					\
540 				RB_FLIP_RIGHT(sib, field);		\
541 			} else if (RB_RED_LEFT(sib, field)) {		\
542 				RB_ROTATE_RIGHT(head, sib, nec, field);	\
543 				RB_FLIP_LEFT(sib, field);		\
544 				sib = nec;				\
545 			} else {					\
546 				RB_FLIP_RIGHT(par, field);		\
547 				par = gpr;				\
548 				continue;				\
549 			}						\
550 			RB_ROTATE_LEFT(head, par, sib, field);		\
551 			return;						\
552 		} else {						\
553 			if (RB_RED_LEFT(par, field)) {			\
554 				red_gpr = RB_TRUE;			\
555 				RB_ROTATE_RIGHT(head, par, gpr, field); \
556 				RB_FLIP_LEFT(par, field);		\
557 				RB_FLIP_RIGHT(gpr, field);		\
558 			}						\
559 			sib = RB_LEFT(par, field);			\
560 			if (RB_RED_LEFT(sib, field)) {			\
561 				if (RB_RED_RIGHT(sib, field)) {		\
562 					RB_FLIP_RIGHT(sib, field);	\
563 					RB_FLIP_LEFT(par, field);	\
564 				}					\
565 				RB_FLIP_LEFT(sib, field);		\
566 			} else if (RB_RED_RIGHT(sib, field)) {		\
567 				RB_ROTATE_LEFT(head, sib, nec, field);	\
568 				RB_FLIP_RIGHT(sib, field);		\
569 				sib = nec;				\
570 			} else {					\
571 				RB_FLIP_LEFT(par, field);		\
572 				par = gpr;				\
573 				continue;				\
574 			}						\
575 			RB_ROTATE_RIGHT(head, par, sib, field);		\
576 			return;						\
577 		}							\
578 	} while (!red_gpr);						\
579 	if (gpr == NULL);						\
580 	else if (left_par)						\
581 		RB_FLIP_LEFT(gpr, field);				\
582 	else								\
583 		RB_FLIP_RIGHT(gpr, field);				\
584 }
585 
586 #define RB_GENERATE_REMOVE(name, type, field, attr)			\
587 attr struct type *							\
588 name##_RB_REMOVE(struct name *head, struct type *elm)			\
589 {									\
590 	struct type *child, *old, *parent, *right;			\
591 	RB_BOOL red;							\
592 									\
593 	old = elm;							\
594 	parent = RB_PARENT(elm, field);					\
595 	right = RB_RIGHT(elm, field);					\
596 	if (RB_LEFT(elm, field) == NULL)				\
597 		elm = child = right;					\
598 	else if (right == NULL)						\
599 		elm = child = RB_LEFT(elm, field);			\
600 	else {								\
601 		if ((child = RB_LEFT(right, field)) == NULL) {		\
602 			child = RB_RIGHT(right, field);			\
603 			red = RB_RED_RIGHT(old, field);			\
604 			if (red)					\
605 				RB_FLIP_RIGHT(old, field);		\
606 			RB_RIGHT(old, field) = child;			\
607 			parent = elm = right;				\
608 		} else {						\
609 			do						\
610 				elm = child;				\
611 			while ((child = RB_LEFT(elm, field)) != NULL);	\
612 			child = RB_RIGHT(elm, field);			\
613 			parent = RB_PARENT(elm, field);			\
614 			red = RB_RED_LEFT(parent, field);		\
615 			if (red)					\
616 				RB_FLIP_LEFT(parent, field);		\
617 			RB_LEFT(parent, field) = child;			\
618 			RB_SET_PARENT(RB_RIGHT(old, field), elm, field); \
619 		}							\
620 		RB_SET_PARENT(RB_LEFT(old, field), elm, field);		\
621 		elm->field = old->field;				\
622 	}								\
623 	if (elm == child) {						\
624 		red = RB_COLOR(old, field);				\
625 		if (!red);						\
626 		else if (RB_LEFT(parent, field) == old)			\
627 			RB_FLIP_LEFT(parent, field);			\
628 		else							\
629 			RB_FLIP_RIGHT(parent, field);			\
630 	}								\
631 	RB_SWAP_CHILD(head, old, elm, field);				\
632 	if (child != NULL)						\
633 		RB_SET_PARENT(child, parent, field);			\
634 	else if (!red && parent != NULL)				\
635 		name##_RB_REMOVE_COLOR(head, parent);			\
636 	while (parent != NULL) {					\
637 		RB_AUGMENT(parent);					\
638 		parent = RB_PARENT(parent, field);			\
639 	}								\
640 	return (old);							\
641 }
642 
643 #define RB_GENERATE_INSERT(name, type, field, cmp, attr)		\
644 /* Inserts a node into the RB tree */					\
645 attr struct type *							\
646 name##_RB_INSERT(struct name *head, struct type *elm)			\
647 {									\
648 	struct type *tmp;						\
649 	struct type *parent = NULL;					\
650 	int comp = 0;							\
651 	tmp = RB_ROOT(head);						\
652 	while (tmp) {							\
653 		parent = tmp;						\
654 		comp = (cmp)(elm, parent);				\
655 		if (comp < 0)						\
656 			tmp = RB_LEFT(tmp, field);			\
657 		else if (comp > 0)					\
658 			tmp = RB_RIGHT(tmp, field);			\
659 		else							\
660 			return (tmp);					\
661 	}								\
662 	RB_SET(elm, parent, field);					\
663 	if (parent == NULL)						\
664 		RB_ROOT(head) = elm;					\
665 	else if (comp < 0)						\
666 		RB_LEFT(parent, field) = elm;				\
667 	else								\
668 		RB_RIGHT(parent, field) = elm;				\
669 	name##_RB_INSERT_COLOR(head, elm);				\
670 	while (elm != NULL) {						\
671 		RB_AUGMENT(elm);					\
672 		elm = RB_PARENT(elm, field);				\
673 	}								\
674 	return (NULL);							\
675 }
676 
677 #define RB_GENERATE_FIND(name, type, field, cmp, attr)			\
678 /* Finds the node with the same key as elm */				\
679 attr struct type *							\
680 name##_RB_FIND(struct name *head, struct type *elm)			\
681 {									\
682 	struct type *tmp = RB_ROOT(head);				\
683 	int comp;							\
684 	while (tmp) {							\
685 		comp = cmp(elm, tmp);					\
686 		if (comp < 0)						\
687 			tmp = RB_LEFT(tmp, field);			\
688 		else if (comp > 0)					\
689 			tmp = RB_RIGHT(tmp, field);			\
690 		else							\
691 			return (tmp);					\
692 	}								\
693 	return (NULL);							\
694 }
695 
696 #define RB_GENERATE_NFIND(name, type, field, cmp, attr)			\
697 /* Finds the first node greater than or equal to the search key */	\
698 attr struct type *							\
699 name##_RB_NFIND(struct name *head, struct type *elm)			\
700 {									\
701 	struct type *tmp = RB_ROOT(head);				\
702 	struct type *res = NULL;					\
703 	int comp;							\
704 	while (tmp) {							\
705 		comp = cmp(elm, tmp);					\
706 		if (comp < 0) {						\
707 			res = tmp;					\
708 			tmp = RB_LEFT(tmp, field);			\
709 		}							\
710 		else if (comp > 0)					\
711 			tmp = RB_RIGHT(tmp, field);			\
712 		else							\
713 			return (tmp);					\
714 	}								\
715 	return (res);							\
716 }
717 
718 #define RB_GENERATE_NEXT(name, type, field, attr)			\
719 /* ARGSUSED */								\
720 attr struct type *							\
721 name##_RB_NEXT(struct type *elm)					\
722 {									\
723 	if (RB_RIGHT(elm, field)) {					\
724 		elm = RB_RIGHT(elm, field);				\
725 		while (RB_LEFT(elm, field))				\
726 			elm = RB_LEFT(elm, field);			\
727 	} else {							\
728 		if (RB_PARENT(elm, field) &&				\
729 		    (elm == RB_LEFT(RB_PARENT(elm, field), field)))	\
730 			elm = RB_PARENT(elm, field);			\
731 		else {							\
732 			while (RB_PARENT(elm, field) &&			\
733 			    (elm == RB_RIGHT(RB_PARENT(elm, field), field)))\
734 				elm = RB_PARENT(elm, field);		\
735 			elm = RB_PARENT(elm, field);			\
736 		}							\
737 	}								\
738 	return (elm);							\
739 }
740 
741 #define RB_GENERATE_PREV(name, type, field, attr)			\
742 /* ARGSUSED */								\
743 attr struct type *							\
744 name##_RB_PREV(struct type *elm)					\
745 {									\
746 	if (RB_LEFT(elm, field)) {					\
747 		elm = RB_LEFT(elm, field);				\
748 		while (RB_RIGHT(elm, field))				\
749 			elm = RB_RIGHT(elm, field);			\
750 	} else {							\
751 		if (RB_PARENT(elm, field) &&				\
752 		    (elm == RB_RIGHT(RB_PARENT(elm, field), field)))	\
753 			elm = RB_PARENT(elm, field);			\
754 		else {							\
755 			while (RB_PARENT(elm, field) &&			\
756 			    (elm == RB_LEFT(RB_PARENT(elm, field), field)))\
757 				elm = RB_PARENT(elm, field);		\
758 			elm = RB_PARENT(elm, field);			\
759 		}							\
760 	}								\
761 	return (elm);							\
762 }
763 
764 #define RB_GENERATE_MINMAX(name, type, field, attr)			\
765 attr struct type *							\
766 name##_RB_MINMAX(struct name *head, int val)				\
767 {									\
768 	struct type *tmp = RB_ROOT(head);				\
769 	struct type *parent = NULL;					\
770 	while (tmp) {							\
771 		parent = tmp;						\
772 		if (val < 0)						\
773 			tmp = RB_LEFT(tmp, field);			\
774 		else							\
775 			tmp = RB_RIGHT(tmp, field);			\
776 	}								\
777 	return (parent);						\
778 }
779 
780 #define	RB_GENERATE_REINSERT(name, type, field, cmp, attr)		\
781 attr struct type *							\
782 name##_RB_REINSERT(struct name *head, struct type *elm)			\
783 {									\
784 	struct type *cmpelm;						\
785 	if (((cmpelm = RB_PREV(name, head, elm)) != NULL &&		\
786 	    cmp(cmpelm, elm) >= 0) ||					\
787 	    ((cmpelm = RB_NEXT(name, head, elm)) != NULL &&		\
788 	    cmp(elm, cmpelm) >= 0)) {					\
789 		/* XXXLAS: Remove/insert is heavy handed. */		\
790 		RB_REMOVE(name, head, elm);				\
791 		return (RB_INSERT(name, head, elm));			\
792 	}								\
793 	return (NULL);							\
794 }									\
795 
796 #define RB_NEGINF	-1
797 #define RB_INF	1
798 
799 #define RB_INSERT(name, x, y)	name##_RB_INSERT(x, y)
800 #define RB_REMOVE(name, x, y)	name##_RB_REMOVE(x, y)
801 #define RB_FIND(name, x, y)	name##_RB_FIND(x, y)
802 #define RB_NFIND(name, x, y)	name##_RB_NFIND(x, y)
803 #define RB_NEXT(name, x, y)	name##_RB_NEXT(y)
804 #define RB_PREV(name, x, y)	name##_RB_PREV(y)
805 #define RB_MIN(name, x)		name##_RB_MINMAX(x, RB_NEGINF)
806 #define RB_MAX(name, x)		name##_RB_MINMAX(x, RB_INF)
807 #define RB_REINSERT(name, x, y)	name##_RB_REINSERT(x, y)
808 
809 #define RB_FOREACH(x, name, head)					\
810 	for ((x) = RB_MIN(name, head);					\
811 	     (x) != NULL;						\
812 	     (x) = name##_RB_NEXT(x))
813 
814 #define RB_FOREACH_FROM(x, name, y)					\
815 	for ((x) = (y);							\
816 	    ((x) != NULL) && ((y) = name##_RB_NEXT(x), (x) != NULL);	\
817 	     (x) = (y))
818 
819 #define RB_FOREACH_SAFE(x, name, head, y)				\
820 	for ((x) = RB_MIN(name, head);					\
821 	    ((x) != NULL) && ((y) = name##_RB_NEXT(x), (x) != NULL);	\
822 	     (x) = (y))
823 
824 #define RB_FOREACH_REVERSE(x, name, head)				\
825 	for ((x) = RB_MAX(name, head);					\
826 	     (x) != NULL;						\
827 	     (x) = name##_RB_PREV(x))
828 
829 #define RB_FOREACH_REVERSE_FROM(x, name, y)				\
830 	for ((x) = (y);							\
831 	    ((x) != NULL) && ((y) = name##_RB_PREV(x), (x) != NULL);	\
832 	     (x) = (y))
833 
834 #define RB_FOREACH_REVERSE_SAFE(x, name, head, y)			\
835 	for ((x) = RB_MAX(name, head);					\
836 	    ((x) != NULL) && ((y) = name##_RB_PREV(x), (x) != NULL);	\
837 	     (x) = (y))
838 
839 #endif	/* _SYS_TREE_H_ */
840