xref: /f-stack/freebsd/sys/tree.h (revision 22ce4aff)
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 <[email protected]>
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 rank-balanced 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 rank-balanced tree is a binary search tree with an integer
54  * rank-difference as an attribute of each pointer from parent to child.
55  * The sum of the rank-differences on any path from a node down to null is
56  * the same, and defines the rank of that node. The rank of the null node
57  * is -1.
58  *
59  * Different additional conditions define different sorts of balanced
60  * trees, including "red-black" and "AVL" trees.  The set of conditions
61  * applied here are the "weak-AVL" conditions of Haeupler, Sen and Tarjan:
62  *	- every rank-difference is 1 or 2.
63  *	- the rank of any leaf is 1.
64  *
65  * For historical reasons, rank differences that are even are associated
66  * with the color red (Rank-Even-Difference), and the child that a red edge
67  * points to is called a red child.
68  *
69  * Every operation on a rank-balanced tree is bounded as O(lg n).
70  * The maximum height of a rank-balanced tree is 2lg (n+1).
71  */
72 
73 #define SPLAY_HEAD(name, type)						\
74 struct name {								\
75 	struct type *sph_root; /* root of the tree */			\
76 }
77 
78 #define SPLAY_INITIALIZER(root)						\
79 	{ NULL }
80 
81 #define SPLAY_INIT(root) do {						\
82 	(root)->sph_root = NULL;					\
83 } while (/*CONSTCOND*/ 0)
84 
85 #define SPLAY_ENTRY(type)						\
86 struct {								\
87 	struct type *spe_left; /* left element */			\
88 	struct type *spe_right; /* right element */			\
89 }
90 
91 #define SPLAY_LEFT(elm, field)		(elm)->field.spe_left
92 #define SPLAY_RIGHT(elm, field)		(elm)->field.spe_right
93 #define SPLAY_ROOT(head)		(head)->sph_root
94 #define SPLAY_EMPTY(head)		(SPLAY_ROOT(head) == NULL)
95 
96 /* SPLAY_ROTATE_{LEFT,RIGHT} expect that tmp hold SPLAY_{RIGHT,LEFT} */
97 #define SPLAY_ROTATE_RIGHT(head, tmp, field) do {			\
98 	SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(tmp, field);	\
99 	SPLAY_RIGHT(tmp, field) = (head)->sph_root;			\
100 	(head)->sph_root = tmp;						\
101 } while (/*CONSTCOND*/ 0)
102 
103 #define SPLAY_ROTATE_LEFT(head, tmp, field) do {			\
104 	SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(tmp, field);	\
105 	SPLAY_LEFT(tmp, field) = (head)->sph_root;			\
106 	(head)->sph_root = tmp;						\
107 } while (/*CONSTCOND*/ 0)
108 
109 #define SPLAY_LINKLEFT(head, tmp, field) do {				\
110 	SPLAY_LEFT(tmp, field) = (head)->sph_root;			\
111 	tmp = (head)->sph_root;						\
112 	(head)->sph_root = SPLAY_LEFT((head)->sph_root, field);		\
113 } while (/*CONSTCOND*/ 0)
114 
115 #define SPLAY_LINKRIGHT(head, tmp, field) do {				\
116 	SPLAY_RIGHT(tmp, field) = (head)->sph_root;			\
117 	tmp = (head)->sph_root;						\
118 	(head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);	\
119 } while (/*CONSTCOND*/ 0)
120 
121 #define SPLAY_ASSEMBLE(head, node, left, right, field) do {		\
122 	SPLAY_RIGHT(left, field) = SPLAY_LEFT((head)->sph_root, field);	\
123 	SPLAY_LEFT(right, field) = SPLAY_RIGHT((head)->sph_root, field);\
124 	SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(node, field);	\
125 	SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(node, field);	\
126 } while (/*CONSTCOND*/ 0)
127 
128 /* Generates prototypes and inline functions */
129 
130 #define SPLAY_PROTOTYPE(name, type, field, cmp)				\
131 void name##_SPLAY(struct name *, struct type *);			\
132 void name##_SPLAY_MINMAX(struct name *, int);				\
133 struct type *name##_SPLAY_INSERT(struct name *, struct type *);		\
134 struct type *name##_SPLAY_REMOVE(struct name *, struct type *);		\
135 									\
136 /* Finds the node with the same key as elm */				\
137 static __unused __inline struct type *					\
138 name##_SPLAY_FIND(struct name *head, struct type *elm)			\
139 {									\
140 	if (SPLAY_EMPTY(head))						\
141 		return(NULL);						\
142 	name##_SPLAY(head, elm);					\
143 	if ((cmp)(elm, (head)->sph_root) == 0)				\
144 		return (head->sph_root);				\
145 	return (NULL);							\
146 }									\
147 									\
148 static __unused __inline struct type *					\
149 name##_SPLAY_NEXT(struct name *head, struct type *elm)			\
150 {									\
151 	name##_SPLAY(head, elm);					\
152 	if (SPLAY_RIGHT(elm, field) != NULL) {				\
153 		elm = SPLAY_RIGHT(elm, field);				\
154 		while (SPLAY_LEFT(elm, field) != NULL) {		\
155 			elm = SPLAY_LEFT(elm, field);			\
156 		}							\
157 	} else								\
158 		elm = NULL;						\
159 	return (elm);							\
160 }									\
161 									\
162 static __unused __inline struct type *					\
163 name##_SPLAY_MIN_MAX(struct name *head, int val)			\
164 {									\
165 	name##_SPLAY_MINMAX(head, val);					\
166         return (SPLAY_ROOT(head));					\
167 }
168 
169 /* Main splay operation.
170  * Moves node close to the key of elm to top
171  */
172 #define SPLAY_GENERATE(name, type, field, cmp)				\
173 struct type *								\
174 name##_SPLAY_INSERT(struct name *head, struct type *elm)		\
175 {									\
176     if (SPLAY_EMPTY(head)) {						\
177 	    SPLAY_LEFT(elm, field) = SPLAY_RIGHT(elm, field) = NULL;	\
178     } else {								\
179 	    int __comp;							\
180 	    name##_SPLAY(head, elm);					\
181 	    __comp = (cmp)(elm, (head)->sph_root);			\
182 	    if(__comp < 0) {						\
183 		    SPLAY_LEFT(elm, field) = SPLAY_LEFT((head)->sph_root, field);\
184 		    SPLAY_RIGHT(elm, field) = (head)->sph_root;		\
185 		    SPLAY_LEFT((head)->sph_root, field) = NULL;		\
186 	    } else if (__comp > 0) {					\
187 		    SPLAY_RIGHT(elm, field) = SPLAY_RIGHT((head)->sph_root, field);\
188 		    SPLAY_LEFT(elm, field) = (head)->sph_root;		\
189 		    SPLAY_RIGHT((head)->sph_root, field) = NULL;	\
190 	    } else							\
191 		    return ((head)->sph_root);				\
192     }									\
193     (head)->sph_root = (elm);						\
194     return (NULL);							\
195 }									\
196 									\
197 struct type *								\
198 name##_SPLAY_REMOVE(struct name *head, struct type *elm)		\
199 {									\
200 	struct type *__tmp;						\
201 	if (SPLAY_EMPTY(head))						\
202 		return (NULL);						\
203 	name##_SPLAY(head, elm);					\
204 	if ((cmp)(elm, (head)->sph_root) == 0) {			\
205 		if (SPLAY_LEFT((head)->sph_root, field) == NULL) {	\
206 			(head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);\
207 		} else {						\
208 			__tmp = SPLAY_RIGHT((head)->sph_root, field);	\
209 			(head)->sph_root = SPLAY_LEFT((head)->sph_root, field);\
210 			name##_SPLAY(head, elm);			\
211 			SPLAY_RIGHT((head)->sph_root, field) = __tmp;	\
212 		}							\
213 		return (elm);						\
214 	}								\
215 	return (NULL);							\
216 }									\
217 									\
218 void									\
219 name##_SPLAY(struct name *head, struct type *elm)			\
220 {									\
221 	struct type __node, *__left, *__right, *__tmp;			\
222 	int __comp;							\
223 \
224 	SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
225 	__left = __right = &__node;					\
226 \
227 	while ((__comp = (cmp)(elm, (head)->sph_root)) != 0) {		\
228 		if (__comp < 0) {					\
229 			__tmp = SPLAY_LEFT((head)->sph_root, field);	\
230 			if (__tmp == NULL)				\
231 				break;					\
232 			if ((cmp)(elm, __tmp) < 0){			\
233 				SPLAY_ROTATE_RIGHT(head, __tmp, field);	\
234 				if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
235 					break;				\
236 			}						\
237 			SPLAY_LINKLEFT(head, __right, field);		\
238 		} else if (__comp > 0) {				\
239 			__tmp = SPLAY_RIGHT((head)->sph_root, field);	\
240 			if (__tmp == NULL)				\
241 				break;					\
242 			if ((cmp)(elm, __tmp) > 0){			\
243 				SPLAY_ROTATE_LEFT(head, __tmp, field);	\
244 				if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
245 					break;				\
246 			}						\
247 			SPLAY_LINKRIGHT(head, __left, field);		\
248 		}							\
249 	}								\
250 	SPLAY_ASSEMBLE(head, &__node, __left, __right, field);		\
251 }									\
252 									\
253 /* Splay with either the minimum or the maximum element			\
254  * Used to find minimum or maximum element in tree.			\
255  */									\
256 void name##_SPLAY_MINMAX(struct name *head, int __comp) \
257 {									\
258 	struct type __node, *__left, *__right, *__tmp;			\
259 \
260 	SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
261 	__left = __right = &__node;					\
262 \
263 	while (1) {							\
264 		if (__comp < 0) {					\
265 			__tmp = SPLAY_LEFT((head)->sph_root, field);	\
266 			if (__tmp == NULL)				\
267 				break;					\
268 			if (__comp < 0){				\
269 				SPLAY_ROTATE_RIGHT(head, __tmp, field);	\
270 				if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
271 					break;				\
272 			}						\
273 			SPLAY_LINKLEFT(head, __right, field);		\
274 		} else if (__comp > 0) {				\
275 			__tmp = SPLAY_RIGHT((head)->sph_root, field);	\
276 			if (__tmp == NULL)				\
277 				break;					\
278 			if (__comp > 0) {				\
279 				SPLAY_ROTATE_LEFT(head, __tmp, field);	\
280 				if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
281 					break;				\
282 			}						\
283 			SPLAY_LINKRIGHT(head, __left, field);		\
284 		}							\
285 	}								\
286 	SPLAY_ASSEMBLE(head, &__node, __left, __right, field);		\
287 }
288 
289 #define SPLAY_NEGINF	-1
290 #define SPLAY_INF	1
291 
292 #define SPLAY_INSERT(name, x, y)	name##_SPLAY_INSERT(x, y)
293 #define SPLAY_REMOVE(name, x, y)	name##_SPLAY_REMOVE(x, y)
294 #define SPLAY_FIND(name, x, y)		name##_SPLAY_FIND(x, y)
295 #define SPLAY_NEXT(name, x, y)		name##_SPLAY_NEXT(x, y)
296 #define SPLAY_MIN(name, x)		(SPLAY_EMPTY(x) ? NULL	\
297 					: name##_SPLAY_MIN_MAX(x, SPLAY_NEGINF))
298 #define SPLAY_MAX(name, x)		(SPLAY_EMPTY(x) ? NULL	\
299 					: name##_SPLAY_MIN_MAX(x, SPLAY_INF))
300 
301 #define SPLAY_FOREACH(x, name, head)					\
302 	for ((x) = SPLAY_MIN(name, head);				\
303 	     (x) != NULL;						\
304 	     (x) = SPLAY_NEXT(name, head, x))
305 
306 /* Macros that define a rank-balanced tree */
307 #define RB_HEAD(name, type)						\
308 struct name {								\
309 	struct type *rbh_root; /* root of the tree */			\
310 }
311 
312 #define RB_INITIALIZER(root)						\
313 	{ NULL }
314 
315 #define RB_INIT(root) do {						\
316 	(root)->rbh_root = NULL;					\
317 } while (/*CONSTCOND*/ 0)
318 
319 #define RB_ENTRY(type)							\
320 struct {								\
321 	struct type *rbe_left;		/* left element */		\
322 	struct type *rbe_right;		/* right element */		\
323 	struct type *rbe_parent;	/* parent element */		\
324 }
325 
326 #define RB_LEFT(elm, field)		(elm)->field.rbe_left
327 #define RB_RIGHT(elm, field)		(elm)->field.rbe_right
328 
329 /*
330  * With the expectation that any object of struct type has an
331  * address that is a multiple of 4, and that therefore the
332  * 2 least significant bits of a pointer to struct type are
333  * always zero, this implementation sets those bits to indicate
334  * that the left or right child of the tree node is "red".
335  */
336 #define RB_UP(elm, field)		(elm)->field.rbe_parent
337 #define RB_BITS(elm, field)		(*(__uintptr_t *)&RB_UP(elm, field))
338 #define RB_RED_L			((__uintptr_t)1)
339 #define RB_RED_R			((__uintptr_t)2)
340 #define RB_RED_MASK			((__uintptr_t)3)
341 #define RB_FLIP_LEFT(elm, field)	(RB_BITS(elm, field) ^= RB_RED_L)
342 #define RB_FLIP_RIGHT(elm, field)	(RB_BITS(elm, field) ^= RB_RED_R)
343 #define RB_RED_LEFT(elm, field)		((RB_BITS(elm, field) & RB_RED_L) != 0)
344 #define RB_RED_RIGHT(elm, field)	((RB_BITS(elm, field) & RB_RED_R) != 0)
345 #define RB_PARENT(elm, field)		((__typeof(RB_UP(elm, field)))	\
346 					 (RB_BITS(elm, field) & ~RB_RED_MASK))
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 ? 0 :	\
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 *,			\
426 	    struct type *, struct type *)
427 #define RB_PROTOTYPE_REMOVE(name, type, attr)				\
428 	attr struct type *name##_RB_REMOVE(struct name *, struct type *)
429 #define RB_PROTOTYPE_INSERT(name, type, attr)				\
430 	attr struct type *name##_RB_INSERT(struct name *, struct type *)
431 #define RB_PROTOTYPE_FIND(name, type, attr)				\
432 	attr struct type *name##_RB_FIND(struct name *, struct type *)
433 #define RB_PROTOTYPE_NFIND(name, type, attr)				\
434 	attr struct type *name##_RB_NFIND(struct name *, struct type *)
435 #define RB_PROTOTYPE_NEXT(name, type, attr)				\
436 	attr struct type *name##_RB_NEXT(struct type *)
437 #define RB_PROTOTYPE_PREV(name, type, attr)				\
438 	attr struct type *name##_RB_PREV(struct type *)
439 #define RB_PROTOTYPE_MINMAX(name, type, attr)				\
440 	attr struct type *name##_RB_MINMAX(struct name *, int)
441 #define RB_PROTOTYPE_REINSERT(name, type, attr)			\
442 	attr struct type *name##_RB_REINSERT(struct name *, struct type *)
443 
444 /* Main rb operation.
445  * Moves node close to the key of elm to top
446  */
447 #define	RB_GENERATE(name, type, field, cmp)				\
448 	RB_GENERATE_INTERNAL(name, type, field, cmp,)
449 #define	RB_GENERATE_STATIC(name, type, field, cmp)			\
450 	RB_GENERATE_INTERNAL(name, type, field, cmp, __unused static)
451 #define RB_GENERATE_INTERNAL(name, type, field, cmp, attr)		\
452 	RB_GENERATE_INSERT_COLOR(name, type, field, attr)		\
453 	RB_GENERATE_REMOVE_COLOR(name, type, field, attr)		\
454 	RB_GENERATE_INSERT(name, type, field, cmp, attr)		\
455 	RB_GENERATE_REMOVE(name, type, field, attr)			\
456 	RB_GENERATE_FIND(name, type, field, cmp, attr)			\
457 	RB_GENERATE_NFIND(name, type, field, cmp, attr)			\
458 	RB_GENERATE_NEXT(name, type, field, attr)			\
459 	RB_GENERATE_PREV(name, type, field, attr)			\
460 	RB_GENERATE_MINMAX(name, type, field, attr)			\
461 	RB_GENERATE_REINSERT(name, type, field, cmp, attr)
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 *child, *parent;					\
468 	while ((parent = RB_PARENT(elm, field)) != NULL) {		\
469 		if (RB_LEFT(parent, field) == elm) {			\
470 			if (RB_RED_LEFT(parent, field)) {		\
471 				RB_FLIP_LEFT(parent, field);		\
472 				return;					\
473 			}						\
474 			RB_FLIP_RIGHT(parent, field);			\
475 			if (RB_RED_RIGHT(parent, field)) {		\
476 				elm = parent;				\
477 				continue;				\
478 			}						\
479 			if (!RB_RED_RIGHT(elm, field)) {		\
480 				RB_FLIP_LEFT(elm, field);		\
481 				RB_ROTATE_LEFT(head, elm, child, field);\
482 				if (RB_RED_LEFT(child, field))		\
483 					RB_FLIP_RIGHT(elm, field);	\
484 				else if (RB_RED_RIGHT(child, field))	\
485 					RB_FLIP_LEFT(parent, field);	\
486 				elm = child;				\
487 			}						\
488 			RB_ROTATE_RIGHT(head, parent, elm, field);	\
489 		} else {						\
490 			if (RB_RED_RIGHT(parent, field)) {		\
491 				RB_FLIP_RIGHT(parent, field);		\
492 				return;					\
493 			}						\
494 			RB_FLIP_LEFT(parent, field);			\
495 			if (RB_RED_LEFT(parent, field)) {		\
496 				elm = parent;				\
497 				continue;				\
498 			}						\
499 			if (!RB_RED_LEFT(elm, field)) {			\
500 				RB_FLIP_RIGHT(elm, field);		\
501 				RB_ROTATE_RIGHT(head, elm, child, field);\
502 				if (RB_RED_RIGHT(child, field))		\
503 					RB_FLIP_LEFT(elm, field);	\
504 				else if (RB_RED_LEFT(child, field))	\
505 					RB_FLIP_RIGHT(parent, field);	\
506 				elm = child;				\
507 			}						\
508 			RB_ROTATE_LEFT(head, parent, elm, field);	\
509 		}							\
510 		RB_BITS(elm, field) &= ~RB_RED_MASK;			\
511 		break;							\
512 	}								\
513 }
514 
515 #define RB_GENERATE_REMOVE_COLOR(name, type, field, attr)		\
516 attr void								\
517 name##_RB_REMOVE_COLOR(struct name *head,				\
518     struct type *parent, struct type *elm)				\
519 {									\
520 	struct type *sib;						\
521 	if (RB_LEFT(parent, field) == elm &&				\
522 	    RB_RIGHT(parent, field) == elm) {				\
523 		RB_BITS(parent, field) &= ~RB_RED_MASK;			\
524 		elm = parent;						\
525 		parent = RB_PARENT(elm, field);				\
526 		if (parent == NULL)					\
527 			return;						\
528 	}								\
529 	do  {								\
530 		if (RB_LEFT(parent, field) == elm) {			\
531 			if (!RB_RED_LEFT(parent, field)) {		\
532 				RB_FLIP_LEFT(parent, field);		\
533 				return;					\
534 			}						\
535 			if (RB_RED_RIGHT(parent, field)) {		\
536 				RB_FLIP_RIGHT(parent, field);		\
537 				elm = parent;				\
538 				continue;				\
539 			}						\
540 			sib = RB_RIGHT(parent, field);			\
541 			if ((~RB_BITS(sib, field) & RB_RED_MASK) == 0) {\
542 				RB_BITS(sib, field) &= ~RB_RED_MASK;	\
543 				elm = parent;				\
544 				continue;				\
545 			}						\
546 			RB_FLIP_RIGHT(sib, field);			\
547 			if (RB_RED_LEFT(sib, field))			\
548 				RB_FLIP_LEFT(parent, field);		\
549 			else if (!RB_RED_RIGHT(sib, field)) {		\
550 				RB_FLIP_LEFT(parent, field);		\
551 				RB_ROTATE_RIGHT(head, sib, elm, field);	\
552 				if (RB_RED_RIGHT(elm, field))		\
553 					RB_FLIP_LEFT(sib, field);	\
554 				if (RB_RED_LEFT(elm, field))		\
555 					RB_FLIP_RIGHT(parent, field);	\
556 				RB_BITS(elm, field) |= RB_RED_MASK;	\
557 				sib = elm;				\
558 			}						\
559 			RB_ROTATE_LEFT(head, parent, sib, field);	\
560 		} else {						\
561 			if (!RB_RED_RIGHT(parent, field)) {		\
562 				RB_FLIP_RIGHT(parent, field);		\
563 				return;					\
564 			}						\
565 			if (RB_RED_LEFT(parent, field)) {		\
566 				RB_FLIP_LEFT(parent, field);		\
567 				elm = parent;				\
568 				continue;				\
569 			}						\
570 			sib = RB_LEFT(parent, field);			\
571 			if ((~RB_BITS(sib, field) & RB_RED_MASK) == 0) {\
572 				RB_BITS(sib, field) &= ~RB_RED_MASK;	\
573 				elm = parent;				\
574 				continue;				\
575 			}						\
576 			RB_FLIP_LEFT(sib, field);			\
577 			if (RB_RED_RIGHT(sib, field))			\
578 				RB_FLIP_RIGHT(parent, field);		\
579 			else if (!RB_RED_LEFT(sib, field)) {		\
580 				RB_FLIP_RIGHT(parent, field);		\
581 				RB_ROTATE_LEFT(head, sib, elm, field);	\
582 				if (RB_RED_LEFT(elm, field))		\
583 					RB_FLIP_RIGHT(sib, field);	\
584 				if (RB_RED_RIGHT(elm, field))		\
585 					RB_FLIP_LEFT(parent, field);	\
586 				RB_BITS(elm, field) |= RB_RED_MASK;	\
587 				sib = elm;				\
588 			}						\
589 			RB_ROTATE_RIGHT(head, parent, sib, field);	\
590 		}							\
591 		break;							\
592 	} while ((parent = RB_PARENT(elm, field)) != NULL);		\
593 }
594 
595 #define RB_GENERATE_REMOVE(name, type, field, attr)			\
596 attr struct type *							\
597 name##_RB_REMOVE(struct name *head, struct type *elm)			\
598 {									\
599 	struct type *child, *old, *parent, *right;			\
600 									\
601 	old = elm;							\
602 	parent = RB_PARENT(elm, field);					\
603 	right = RB_RIGHT(elm, field);					\
604 	if (RB_LEFT(elm, field) == NULL)				\
605 		elm = child = right;					\
606 	else if (right == NULL)						\
607 		elm = child = RB_LEFT(elm, field);			\
608 	else {								\
609 		if ((child = RB_LEFT(right, field)) == NULL) {		\
610 			child = RB_RIGHT(right, field);			\
611 			RB_RIGHT(old, field) = child;			\
612 			parent = elm = right;				\
613 		} else {						\
614 			do						\
615 				elm = child;				\
616 			while ((child = RB_LEFT(elm, field)) != NULL);	\
617 			child = RB_RIGHT(elm, field);			\
618 			parent = RB_PARENT(elm, field);			\
619 			RB_LEFT(parent, field) = child;			\
620 			RB_SET_PARENT(RB_RIGHT(old, field), elm, field);\
621 		}							\
622 		RB_SET_PARENT(RB_LEFT(old, field), elm, field);		\
623 		elm->field = old->field;				\
624 	}								\
625 	RB_SWAP_CHILD(head, old, elm, field);				\
626 	if (child != NULL)						\
627 		RB_SET_PARENT(child, parent, field);			\
628 	if (parent != NULL)						\
629 		name##_RB_REMOVE_COLOR(head, parent, child);		\
630 	while (parent != NULL) {					\
631 		RB_AUGMENT(parent);					\
632 		parent = RB_PARENT(parent, field);			\
633 	}								\
634 	return (old);							\
635 }
636 
637 #define RB_GENERATE_INSERT(name, type, field, cmp, attr)		\
638 /* Inserts a node into the RB tree */					\
639 attr struct type *							\
640 name##_RB_INSERT(struct name *head, struct type *elm)			\
641 {									\
642 	struct type *tmp;						\
643 	struct type *parent = NULL;					\
644 	int comp = 0;							\
645 	tmp = RB_ROOT(head);						\
646 	while (tmp) {							\
647 		parent = tmp;						\
648 		comp = (cmp)(elm, parent);				\
649 		if (comp < 0)						\
650 			tmp = RB_LEFT(tmp, field);			\
651 		else if (comp > 0)					\
652 			tmp = RB_RIGHT(tmp, field);			\
653 		else							\
654 			return (tmp);					\
655 	}								\
656 	RB_SET(elm, parent, field);					\
657 	if (parent == NULL)						\
658 		RB_ROOT(head) = elm;					\
659 	else if (comp < 0)						\
660 		RB_LEFT(parent, field) = elm;				\
661 	else								\
662 		RB_RIGHT(parent, field) = elm;				\
663 	name##_RB_INSERT_COLOR(head, elm);				\
664 	while (elm != NULL) {						\
665 		RB_AUGMENT(elm);					\
666 		elm = RB_PARENT(elm, field);				\
667 	}								\
668 	return (NULL);							\
669 }
670 
671 #define RB_GENERATE_FIND(name, type, field, cmp, attr)			\
672 /* Finds the node with the same key as elm */				\
673 attr struct type *							\
674 name##_RB_FIND(struct name *head, struct type *elm)			\
675 {									\
676 	struct type *tmp = RB_ROOT(head);				\
677 	int comp;							\
678 	while (tmp) {							\
679 		comp = cmp(elm, tmp);					\
680 		if (comp < 0)						\
681 			tmp = RB_LEFT(tmp, field);			\
682 		else if (comp > 0)					\
683 			tmp = RB_RIGHT(tmp, field);			\
684 		else							\
685 			return (tmp);					\
686 	}								\
687 	return (NULL);							\
688 }
689 
690 #define RB_GENERATE_NFIND(name, type, field, cmp, attr)			\
691 /* Finds the first node greater than or equal to the search key */	\
692 attr struct type *							\
693 name##_RB_NFIND(struct name *head, struct type *elm)			\
694 {									\
695 	struct type *tmp = RB_ROOT(head);				\
696 	struct type *res = NULL;					\
697 	int comp;							\
698 	while (tmp) {							\
699 		comp = cmp(elm, tmp);					\
700 		if (comp < 0) {						\
701 			res = tmp;					\
702 			tmp = RB_LEFT(tmp, field);			\
703 		}							\
704 		else if (comp > 0)					\
705 			tmp = RB_RIGHT(tmp, field);			\
706 		else							\
707 			return (tmp);					\
708 	}								\
709 	return (res);							\
710 }
711 
712 #define RB_GENERATE_NEXT(name, type, field, attr)			\
713 /* ARGSUSED */								\
714 attr struct type *							\
715 name##_RB_NEXT(struct type *elm)					\
716 {									\
717 	if (RB_RIGHT(elm, field)) {					\
718 		elm = RB_RIGHT(elm, field);				\
719 		while (RB_LEFT(elm, field))				\
720 			elm = RB_LEFT(elm, field);			\
721 	} else {							\
722 		if (RB_PARENT(elm, field) &&				\
723 		    (elm == RB_LEFT(RB_PARENT(elm, field), field)))	\
724 			elm = RB_PARENT(elm, field);			\
725 		else {							\
726 			while (RB_PARENT(elm, field) &&			\
727 			    (elm == RB_RIGHT(RB_PARENT(elm, field), field)))\
728 				elm = RB_PARENT(elm, field);		\
729 			elm = RB_PARENT(elm, field);			\
730 		}							\
731 	}								\
732 	return (elm);							\
733 }
734 
735 #define RB_GENERATE_PREV(name, type, field, attr)			\
736 /* ARGSUSED */								\
737 attr struct type *							\
738 name##_RB_PREV(struct type *elm)					\
739 {									\
740 	if (RB_LEFT(elm, field)) {					\
741 		elm = RB_LEFT(elm, field);				\
742 		while (RB_RIGHT(elm, field))				\
743 			elm = RB_RIGHT(elm, field);			\
744 	} else {							\
745 		if (RB_PARENT(elm, field) &&				\
746 		    (elm == RB_RIGHT(RB_PARENT(elm, field), field)))	\
747 			elm = RB_PARENT(elm, field);			\
748 		else {							\
749 			while (RB_PARENT(elm, field) &&			\
750 			    (elm == RB_LEFT(RB_PARENT(elm, field), field)))\
751 				elm = RB_PARENT(elm, field);		\
752 			elm = RB_PARENT(elm, field);			\
753 		}							\
754 	}								\
755 	return (elm);							\
756 }
757 
758 #define RB_GENERATE_MINMAX(name, type, field, attr)			\
759 attr struct type *							\
760 name##_RB_MINMAX(struct name *head, int val)				\
761 {									\
762 	struct type *tmp = RB_ROOT(head);				\
763 	struct type *parent = NULL;					\
764 	while (tmp) {							\
765 		parent = tmp;						\
766 		if (val < 0)						\
767 			tmp = RB_LEFT(tmp, field);			\
768 		else							\
769 			tmp = RB_RIGHT(tmp, field);			\
770 	}								\
771 	return (parent);						\
772 }
773 
774 #define	RB_GENERATE_REINSERT(name, type, field, cmp, attr)		\
775 attr struct type *							\
776 name##_RB_REINSERT(struct name *head, struct type *elm)			\
777 {									\
778 	struct type *cmpelm;						\
779 	if (((cmpelm = RB_PREV(name, head, elm)) != NULL &&		\
780 	    cmp(cmpelm, elm) >= 0) ||					\
781 	    ((cmpelm = RB_NEXT(name, head, elm)) != NULL &&		\
782 	    cmp(elm, cmpelm) >= 0)) {					\
783 		/* XXXLAS: Remove/insert is heavy handed. */		\
784 		RB_REMOVE(name, head, elm);				\
785 		return (RB_INSERT(name, head, elm));			\
786 	}								\
787 	return (NULL);							\
788 }									\
789 
790 #define RB_NEGINF	-1
791 #define RB_INF	1
792 
793 #define RB_INSERT(name, x, y)	name##_RB_INSERT(x, y)
794 #define RB_REMOVE(name, x, y)	name##_RB_REMOVE(x, y)
795 #define RB_FIND(name, x, y)	name##_RB_FIND(x, y)
796 #define RB_NFIND(name, x, y)	name##_RB_NFIND(x, y)
797 #define RB_NEXT(name, x, y)	name##_RB_NEXT(y)
798 #define RB_PREV(name, x, y)	name##_RB_PREV(y)
799 #define RB_MIN(name, x)		name##_RB_MINMAX(x, RB_NEGINF)
800 #define RB_MAX(name, x)		name##_RB_MINMAX(x, RB_INF)
801 #define RB_REINSERT(name, x, y)	name##_RB_REINSERT(x, y)
802 
803 #define RB_FOREACH(x, name, head)					\
804 	for ((x) = RB_MIN(name, head);					\
805 	     (x) != NULL;						\
806 	     (x) = name##_RB_NEXT(x))
807 
808 #define RB_FOREACH_FROM(x, name, y)					\
809 	for ((x) = (y);							\
810 	    ((x) != NULL) && ((y) = name##_RB_NEXT(x), (x) != NULL);	\
811 	     (x) = (y))
812 
813 #define RB_FOREACH_SAFE(x, name, head, y)				\
814 	for ((x) = RB_MIN(name, head);					\
815 	    ((x) != NULL) && ((y) = name##_RB_NEXT(x), (x) != NULL);	\
816 	     (x) = (y))
817 
818 #define RB_FOREACH_REVERSE(x, name, head)				\
819 	for ((x) = RB_MAX(name, head);					\
820 	     (x) != NULL;						\
821 	     (x) = name##_RB_PREV(x))
822 
823 #define RB_FOREACH_REVERSE_FROM(x, name, y)				\
824 	for ((x) = (y);							\
825 	    ((x) != NULL) && ((y) = name##_RB_PREV(x), (x) != NULL);	\
826 	     (x) = (y))
827 
828 #define RB_FOREACH_REVERSE_SAFE(x, name, head, y)			\
829 	for ((x) = RB_MAX(name, head);					\
830 	    ((x) != NULL) && ((y) = name##_RB_PREV(x), (x) != NULL);	\
831 	     (x) = (y))
832 
833 #endif	/* _SYS_TREE_H_ */
834