1 /*	$OpenBSD: tree.h,v 1.30 2020/10/10 18:03:41 otto Exp $	*/
2 /*
3  * Copyright 2002 Niels Provos <provos@citi.umich.edu>
4  * All rights reserved.
5  *
6  * Redistribution and use in source and binary forms, with or without
7  * modification, are permitted provided that the following conditions
8  * are met:
9  * 1. Redistributions of source code must retain the above copyright
10  *    notice, this list of conditions and the following disclaimer.
11  * 2. Redistributions in binary form must reproduce the above copyright
12  *    notice, this list of conditions and the following disclaimer in the
13  *    documentation and/or other materials provided with the distribution.
14  *
15  * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
16  * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
17  * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
18  * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
19  * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
20  * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
21  * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
22  * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
23  * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
24  * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
25  */
26 
27 #ifndef	_SYS_TREE_H_
28 #define	_SYS_TREE_H_
29 
30 #include <stddef.h>
31 
32 /*
33  * Local modifications:
34  *  - dropped __unused
35  *  - __inline -> inline
36  */
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 (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 (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 (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 (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 (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 (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))) {		\
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 /* Macros that define a red-black tree */
299 #define RB_HEAD(name, type)						\
300 struct name {								\
301 	struct type *rbh_root; /* root of the tree */			\
302 }
303 
304 #define RB_INITIALIZER(root)						\
305 	{ NULL }
306 
307 #define RB_INIT(root) do {						\
308 	(root)->rbh_root = NULL;					\
309 } while (0)
310 
311 #define RB_BLACK	0
312 #define RB_RED		1
313 #define RB_ENTRY(type)							\
314 struct {								\
315 	struct type *rbe_left;		/* left element */		\
316 	struct type *rbe_right;		/* right element */		\
317 	struct type *rbe_parent;	/* parent element */		\
318 	int rbe_color;			/* node color */		\
319 }
320 
321 #define RB_LEFT(elm, field)		(elm)->field.rbe_left
322 #define RB_RIGHT(elm, field)		(elm)->field.rbe_right
323 #define RB_PARENT(elm, field)		(elm)->field.rbe_parent
324 #define RB_COLOR(elm, field)		(elm)->field.rbe_color
325 #define RB_ROOT(head)			(head)->rbh_root
326 #define RB_EMPTY(head)			(RB_ROOT(head) == NULL)
327 
328 #define RB_SET(elm, parent, field) do {					\
329 	RB_PARENT(elm, field) = parent;					\
330 	RB_LEFT(elm, field) = RB_RIGHT(elm, field) = NULL;		\
331 	RB_COLOR(elm, field) = RB_RED;					\
332 } while (0)
333 
334 #define RB_SET_BLACKRED(black, red, field) do {				\
335 	RB_COLOR(black, field) = RB_BLACK;				\
336 	RB_COLOR(red, field) = RB_RED;					\
337 } while (0)
338 
339 #ifndef RB_AUGMENT
340 #define RB_AUGMENT(x)	do {} while (0)
341 #endif
342 
343 #define RB_ROTATE_LEFT(head, elm, tmp, field) do {			\
344 	(tmp) = RB_RIGHT(elm, field);					\
345 	if ((RB_RIGHT(elm, field) = RB_LEFT(tmp, field))) {		\
346 		RB_PARENT(RB_LEFT(tmp, field), field) = (elm);		\
347 	}								\
348 	RB_AUGMENT(elm);						\
349 	if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field))) {		\
350 		if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))	\
351 			RB_LEFT(RB_PARENT(elm, field), field) = (tmp);	\
352 		else							\
353 			RB_RIGHT(RB_PARENT(elm, field), field) = (tmp);	\
354 	} else								\
355 		(head)->rbh_root = (tmp);				\
356 	RB_LEFT(tmp, field) = (elm);					\
357 	RB_PARENT(elm, field) = (tmp);					\
358 	RB_AUGMENT(tmp);						\
359 	if ((RB_PARENT(tmp, field)))					\
360 		RB_AUGMENT(RB_PARENT(tmp, field));			\
361 } while (0)
362 
363 #define RB_ROTATE_RIGHT(head, elm, tmp, field) do {			\
364 	(tmp) = RB_LEFT(elm, field);					\
365 	if ((RB_LEFT(elm, field) = RB_RIGHT(tmp, field))) {		\
366 		RB_PARENT(RB_RIGHT(tmp, field), field) = (elm);		\
367 	}								\
368 	RB_AUGMENT(elm);						\
369 	if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field))) {		\
370 		if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))	\
371 			RB_LEFT(RB_PARENT(elm, field), field) = (tmp);	\
372 		else							\
373 			RB_RIGHT(RB_PARENT(elm, field), field) = (tmp);	\
374 	} else								\
375 		(head)->rbh_root = (tmp);				\
376 	RB_RIGHT(tmp, field) = (elm);					\
377 	RB_PARENT(elm, field) = (tmp);					\
378 	RB_AUGMENT(tmp);						\
379 	if ((RB_PARENT(tmp, field)))					\
380 		RB_AUGMENT(RB_PARENT(tmp, field));			\
381 } while (0)
382 
383 /* Generates prototypes and inline functions */
384 #define	RB_PROTOTYPE(name, type, field, cmp)				\
385 	RB_PROTOTYPE_INTERNAL(name, type, field, cmp,)
386 #define	RB_PROTOTYPE_STATIC(name, type, field, cmp)			\
387 	RB_PROTOTYPE_INTERNAL(name, type, field, cmp, __attribute__((__unused__)) static)
388 #define RB_PROTOTYPE_INTERNAL(name, type, field, cmp, attr)		\
389 attr void name##_RB_INSERT_COLOR(struct name *, struct type *);		\
390 attr void name##_RB_REMOVE_COLOR(struct name *, struct type *, struct type *);\
391 attr struct type *name##_RB_REMOVE(struct name *, struct type *);	\
392 attr struct type *name##_RB_INSERT(struct name *, struct type *);	\
393 attr struct type *name##_RB_FIND(struct name *, struct type *);		\
394 attr struct type *name##_RB_NFIND(struct name *, struct type *);	\
395 attr struct type *name##_RB_NEXT(struct type *);			\
396 attr struct type *name##_RB_PREV(struct type *);			\
397 attr struct type *name##_RB_MINMAX(struct name *, int);			\
398 									\
399 
400 /* Main rb operation.
401  * Moves node close to the key of elm to top
402  */
403 #define	RB_GENERATE(name, type, field, cmp)				\
404 	RB_GENERATE_INTERNAL(name, type, field, cmp,)
405 #define	RB_GENERATE_STATIC(name, type, field, cmp)			\
406 	RB_GENERATE_INTERNAL(name, type, field, cmp, __attribute__((__unused__)) static)
407 #define RB_GENERATE_INTERNAL(name, type, field, cmp, attr)		\
408 attr void								\
409 name##_RB_INSERT_COLOR(struct name *head, struct type *elm)		\
410 {									\
411 	struct type *parent, *gparent, *tmp;				\
412 	while ((parent = RB_PARENT(elm, field)) &&			\
413 	    RB_COLOR(parent, field) == RB_RED) {			\
414 		gparent = RB_PARENT(parent, field);			\
415 		if (parent == RB_LEFT(gparent, field)) {		\
416 			tmp = RB_RIGHT(gparent, field);			\
417 			if (tmp && RB_COLOR(tmp, field) == RB_RED) {	\
418 				RB_COLOR(tmp, field) = RB_BLACK;	\
419 				RB_SET_BLACKRED(parent, gparent, field);\
420 				elm = gparent;				\
421 				continue;				\
422 			}						\
423 			if (RB_RIGHT(parent, field) == elm) {		\
424 				RB_ROTATE_LEFT(head, parent, tmp, field);\
425 				tmp = parent;				\
426 				parent = elm;				\
427 				elm = tmp;				\
428 			}						\
429 			RB_SET_BLACKRED(parent, gparent, field);	\
430 			RB_ROTATE_RIGHT(head, gparent, tmp, field);	\
431 		} else {						\
432 			tmp = RB_LEFT(gparent, field);			\
433 			if (tmp && RB_COLOR(tmp, field) == RB_RED) {	\
434 				RB_COLOR(tmp, field) = RB_BLACK;	\
435 				RB_SET_BLACKRED(parent, gparent, field);\
436 				elm = gparent;				\
437 				continue;				\
438 			}						\
439 			if (RB_LEFT(parent, field) == elm) {		\
440 				RB_ROTATE_RIGHT(head, parent, tmp, field);\
441 				tmp = parent;				\
442 				parent = elm;				\
443 				elm = tmp;				\
444 			}						\
445 			RB_SET_BLACKRED(parent, gparent, field);	\
446 			RB_ROTATE_LEFT(head, gparent, tmp, field);	\
447 		}							\
448 	}								\
449 	RB_COLOR(head->rbh_root, field) = RB_BLACK;			\
450 }									\
451 									\
452 attr void								\
453 name##_RB_REMOVE_COLOR(struct name *head, struct type *parent, struct type *elm) \
454 {									\
455 	struct type *tmp;						\
456 	while ((elm == NULL || RB_COLOR(elm, field) == RB_BLACK) &&	\
457 	    elm != RB_ROOT(head)) {					\
458 		if (RB_LEFT(parent, field) == elm) {			\
459 			tmp = RB_RIGHT(parent, field);			\
460 			if (RB_COLOR(tmp, field) == RB_RED) {		\
461 				RB_SET_BLACKRED(tmp, parent, field);	\
462 				RB_ROTATE_LEFT(head, parent, tmp, field);\
463 				tmp = RB_RIGHT(parent, field);		\
464 			}						\
465 			if ((RB_LEFT(tmp, field) == NULL ||		\
466 			    RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
467 			    (RB_RIGHT(tmp, field) == NULL ||		\
468 			    RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
469 				RB_COLOR(tmp, field) = RB_RED;		\
470 				elm = parent;				\
471 				parent = RB_PARENT(elm, field);		\
472 			} else {					\
473 				if (RB_RIGHT(tmp, field) == NULL ||	\
474 				    RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK) {\
475 					struct type *oleft;		\
476 					if ((oleft = RB_LEFT(tmp, field)))\
477 						RB_COLOR(oleft, field) = RB_BLACK;\
478 					RB_COLOR(tmp, field) = RB_RED;	\
479 					RB_ROTATE_RIGHT(head, tmp, oleft, field);\
480 					tmp = RB_RIGHT(parent, field);	\
481 				}					\
482 				RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
483 				RB_COLOR(parent, field) = RB_BLACK;	\
484 				if (RB_RIGHT(tmp, field))		\
485 					RB_COLOR(RB_RIGHT(tmp, field), field) = RB_BLACK;\
486 				RB_ROTATE_LEFT(head, parent, tmp, field);\
487 				elm = RB_ROOT(head);			\
488 				break;					\
489 			}						\
490 		} else {						\
491 			tmp = RB_LEFT(parent, field);			\
492 			if (RB_COLOR(tmp, field) == RB_RED) {		\
493 				RB_SET_BLACKRED(tmp, parent, field);	\
494 				RB_ROTATE_RIGHT(head, parent, tmp, field);\
495 				tmp = RB_LEFT(parent, field);		\
496 			}						\
497 			if ((RB_LEFT(tmp, field) == NULL ||		\
498 			    RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
499 			    (RB_RIGHT(tmp, field) == NULL ||		\
500 			    RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
501 				RB_COLOR(tmp, field) = RB_RED;		\
502 				elm = parent;				\
503 				parent = RB_PARENT(elm, field);		\
504 			} else {					\
505 				if (RB_LEFT(tmp, field) == NULL ||	\
506 				    RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) {\
507 					struct type *oright;		\
508 					if ((oright = RB_RIGHT(tmp, field)))\
509 						RB_COLOR(oright, field) = RB_BLACK;\
510 					RB_COLOR(tmp, field) = RB_RED;	\
511 					RB_ROTATE_LEFT(head, tmp, oright, field);\
512 					tmp = RB_LEFT(parent, field);	\
513 				}					\
514 				RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
515 				RB_COLOR(parent, field) = RB_BLACK;	\
516 				if (RB_LEFT(tmp, field))		\
517 					RB_COLOR(RB_LEFT(tmp, field), field) = RB_BLACK;\
518 				RB_ROTATE_RIGHT(head, parent, tmp, field);\
519 				elm = RB_ROOT(head);			\
520 				break;					\
521 			}						\
522 		}							\
523 	}								\
524 	if (elm)							\
525 		RB_COLOR(elm, field) = RB_BLACK;			\
526 }									\
527 									\
528 attr struct type *							\
529 name##_RB_REMOVE(struct name *head, struct type *elm)			\
530 {									\
531 	struct type *child, *parent, *old = elm;			\
532 	int color;							\
533 	if (RB_LEFT(elm, field) == NULL)				\
534 		child = RB_RIGHT(elm, field);				\
535 	else if (RB_RIGHT(elm, field) == NULL)				\
536 		child = RB_LEFT(elm, field);				\
537 	else {								\
538 		struct type *left;					\
539 		elm = RB_RIGHT(elm, field);				\
540 		while ((left = RB_LEFT(elm, field)))			\
541 			elm = left;					\
542 		child = RB_RIGHT(elm, field);				\
543 		parent = RB_PARENT(elm, field);				\
544 		color = RB_COLOR(elm, field);				\
545 		if (child)						\
546 			RB_PARENT(child, field) = parent;		\
547 		if (parent) {						\
548 			if (RB_LEFT(parent, field) == elm)		\
549 				RB_LEFT(parent, field) = child;		\
550 			else						\
551 				RB_RIGHT(parent, field) = child;	\
552 			RB_AUGMENT(parent);				\
553 		} else							\
554 			RB_ROOT(head) = child;				\
555 		if (RB_PARENT(elm, field) == old)			\
556 			parent = elm;					\
557 		(elm)->field = (old)->field;				\
558 		if (RB_PARENT(old, field)) {				\
559 			if (RB_LEFT(RB_PARENT(old, field), field) == old)\
560 				RB_LEFT(RB_PARENT(old, field), field) = elm;\
561 			else						\
562 				RB_RIGHT(RB_PARENT(old, field), field) = elm;\
563 			RB_AUGMENT(RB_PARENT(old, field));		\
564 		} else							\
565 			RB_ROOT(head) = elm;				\
566 		RB_PARENT(RB_LEFT(old, field), field) = elm;		\
567 		if (RB_RIGHT(old, field))				\
568 			RB_PARENT(RB_RIGHT(old, field), field) = elm;	\
569 		if (parent) {						\
570 			left = parent;					\
571 			do {						\
572 				RB_AUGMENT(left);			\
573 			} while ((left = RB_PARENT(left, field)));	\
574 		}							\
575 		goto color;						\
576 	}								\
577 	parent = RB_PARENT(elm, field);					\
578 	color = RB_COLOR(elm, field);					\
579 	if (child)							\
580 		RB_PARENT(child, field) = parent;			\
581 	if (parent) {							\
582 		if (RB_LEFT(parent, field) == elm)			\
583 			RB_LEFT(parent, field) = child;			\
584 		else							\
585 			RB_RIGHT(parent, field) = child;		\
586 		RB_AUGMENT(parent);					\
587 	} else								\
588 		RB_ROOT(head) = child;					\
589 color:									\
590 	if (color == RB_BLACK)						\
591 		name##_RB_REMOVE_COLOR(head, parent, child);		\
592 	return (old);							\
593 }									\
594 									\
595 /* Inserts a node into the RB tree */					\
596 attr struct type *							\
597 name##_RB_INSERT(struct name *head, struct type *elm)			\
598 {									\
599 	struct type *tmp;						\
600 	struct type *parent = NULL;					\
601 	int comp = 0;							\
602 	tmp = RB_ROOT(head);						\
603 	while (tmp) {							\
604 		parent = tmp;						\
605 		comp = (cmp)(elm, parent);				\
606 		if (comp < 0)						\
607 			tmp = RB_LEFT(tmp, field);			\
608 		else if (comp > 0)					\
609 			tmp = RB_RIGHT(tmp, field);			\
610 		else							\
611 			return (tmp);					\
612 	}								\
613 	RB_SET(elm, parent, field);					\
614 	if (parent != NULL) {						\
615 		if (comp < 0)						\
616 			RB_LEFT(parent, field) = elm;			\
617 		else							\
618 			RB_RIGHT(parent, field) = elm;			\
619 		RB_AUGMENT(parent);					\
620 	} else								\
621 		RB_ROOT(head) = elm;					\
622 	name##_RB_INSERT_COLOR(head, elm);				\
623 	return (NULL);							\
624 }									\
625 									\
626 /* Finds the node with the same key as elm */				\
627 attr struct type *							\
628 name##_RB_FIND(struct name *head, struct type *elm)			\
629 {									\
630 	struct type *tmp = RB_ROOT(head);				\
631 	int comp;							\
632 	while (tmp) {							\
633 		comp = cmp(elm, tmp);					\
634 		if (comp < 0)						\
635 			tmp = RB_LEFT(tmp, field);			\
636 		else if (comp > 0)					\
637 			tmp = RB_RIGHT(tmp, field);			\
638 		else							\
639 			return (tmp);					\
640 	}								\
641 	return (NULL);							\
642 }									\
643 									\
644 /* Finds the first node greater than or equal to the search key */	\
645 attr struct type *							\
646 name##_RB_NFIND(struct name *head, struct type *elm)			\
647 {									\
648 	struct type *tmp = RB_ROOT(head);				\
649 	struct type *res = NULL;					\
650 	int comp;							\
651 	while (tmp) {							\
652 		comp = cmp(elm, tmp);					\
653 		if (comp < 0) {						\
654 			res = tmp;					\
655 			tmp = RB_LEFT(tmp, field);			\
656 		}							\
657 		else if (comp > 0)					\
658 			tmp = RB_RIGHT(tmp, field);			\
659 		else							\
660 			return (tmp);					\
661 	}								\
662 	return (res);							\
663 }									\
664 									\
665 /* ARGSUSED */								\
666 attr struct type *							\
667 name##_RB_NEXT(struct type *elm)					\
668 {									\
669 	if (RB_RIGHT(elm, field)) {					\
670 		elm = RB_RIGHT(elm, field);				\
671 		while (RB_LEFT(elm, field))				\
672 			elm = RB_LEFT(elm, field);			\
673 	} else {							\
674 		if (RB_PARENT(elm, field) &&				\
675 		    (elm == RB_LEFT(RB_PARENT(elm, field), field)))	\
676 			elm = RB_PARENT(elm, field);			\
677 		else {							\
678 			while (RB_PARENT(elm, field) &&			\
679 			    (elm == RB_RIGHT(RB_PARENT(elm, field), field)))\
680 				elm = RB_PARENT(elm, field);		\
681 			elm = RB_PARENT(elm, field);			\
682 		}							\
683 	}								\
684 	return (elm);							\
685 }									\
686 									\
687 /* ARGSUSED */								\
688 attr struct type *							\
689 name##_RB_PREV(struct type *elm)					\
690 {									\
691 	if (RB_LEFT(elm, field)) {					\
692 		elm = RB_LEFT(elm, field);				\
693 		while (RB_RIGHT(elm, field))				\
694 			elm = RB_RIGHT(elm, field);			\
695 	} else {							\
696 		if (RB_PARENT(elm, field) &&				\
697 		    (elm == RB_RIGHT(RB_PARENT(elm, field), field)))	\
698 			elm = RB_PARENT(elm, field);			\
699 		else {							\
700 			while (RB_PARENT(elm, field) &&			\
701 			    (elm == RB_LEFT(RB_PARENT(elm, field), field)))\
702 				elm = RB_PARENT(elm, field);		\
703 			elm = RB_PARENT(elm, field);			\
704 		}							\
705 	}								\
706 	return (elm);							\
707 }									\
708 									\
709 attr struct type *							\
710 name##_RB_MINMAX(struct name *head, int val)				\
711 {									\
712 	struct type *tmp = RB_ROOT(head);				\
713 	struct type *parent = NULL;					\
714 	while (tmp) {							\
715 		parent = tmp;						\
716 		if (val < 0)						\
717 			tmp = RB_LEFT(tmp, field);			\
718 		else							\
719 			tmp = RB_RIGHT(tmp, field);			\
720 	}								\
721 	return (parent);						\
722 }
723 
724 #define RB_NEGINF	-1
725 #define RB_INF	1
726 
727 #define RB_INSERT(name, x, y)	name##_RB_INSERT(x, y)
728 #define RB_REMOVE(name, x, y)	name##_RB_REMOVE(x, y)
729 #define RB_FIND(name, x, y)	name##_RB_FIND(x, y)
730 #define RB_NFIND(name, x, y)	name##_RB_NFIND(x, y)
731 #define RB_NEXT(name, x, y)	name##_RB_NEXT(y)
732 #define RB_PREV(name, x, y)	name##_RB_PREV(y)
733 #define RB_MIN(name, x)		name##_RB_MINMAX(x, RB_NEGINF)
734 #define RB_MAX(name, x)		name##_RB_MINMAX(x, RB_INF)
735 
736 #define RB_FOREACH(x, name, head)					\
737 	for ((x) = RB_MIN(name, head);					\
738 	     (x) != NULL;						\
739 	     (x) = name##_RB_NEXT(x))
740 
741 #define RB_FOREACH_SAFE(x, name, head, y)				\
742 	for ((x) = RB_MIN(name, head);					\
743 	    ((x) != NULL) && ((y) = name##_RB_NEXT(x), 1);		\
744 	     (x) = (y))
745 
746 #define RB_FOREACH_REVERSE(x, name, head)				\
747 	for ((x) = RB_MAX(name, head);					\
748 	     (x) != NULL;						\
749 	     (x) = name##_RB_PREV(x))
750 
751 #define RB_FOREACH_REVERSE_SAFE(x, name, head, y)			\
752 	for ((x) = RB_MAX(name, head);					\
753 	    ((x) != NULL) && ((y) = name##_RB_PREV(x), 1);		\
754 	     (x) = (y))
755 
756 
757 /*
758  * Copyright (c) 2016 David Gwynne <dlg@openbsd.org>
759  *
760  * Permission to use, copy, modify, and distribute this software for any
761  * purpose with or without fee is hereby granted, provided that the above
762  * copyright notice and this permission notice appear in all copies.
763  *
764  * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
765  * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
766  * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
767  * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
768  * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
769  * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
770  * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
771  */
772 
773 struct rb_type {
774 	int		(*t_compare)(const void *, const void *);
775 	void		(*t_augment)(void *);
776 	unsigned int	  t_offset;	/* offset of rb_entry in type */
777 };
778 
779 struct rb_tree {
780 	struct rb_entry	*rbt_root;
781 };
782 
783 struct rb_entry {
784 	struct rb_entry	 *rbt_parent;
785 	struct rb_entry	 *rbt_left;
786 	struct rb_entry	 *rbt_right;
787 	unsigned int	  rbt_color;
788 };
789 
790 #define RBT_HEAD(_name, _type)						\
791 struct _name {								\
792 	struct rb_tree rbh_root;					\
793 }
794 
795 #define RBT_ENTRY(_type)	struct rb_entry
796 
797 static inline void
798 _rb_init(struct rb_tree *rbt)
799 {
800 	rbt->rbt_root = NULL;
801 }
802 
803 static inline int
804 _rb_empty(struct rb_tree *rbt)
805 {
806 	return (rbt->rbt_root == NULL);
807 }
808 
809 void	*_rb_insert(const struct rb_type *, struct rb_tree *, void *);
810 void	*_rb_remove(const struct rb_type *, struct rb_tree *, void *);
811 void	*_rb_find(const struct rb_type *, struct rb_tree *, const void *);
812 void	*_rb_nfind(const struct rb_type *, struct rb_tree *, const void *);
813 void	*_rb_root(const struct rb_type *, struct rb_tree *);
814 void	*_rb_min(const struct rb_type *, struct rb_tree *);
815 void	*_rb_max(const struct rb_type *, struct rb_tree *);
816 void	*_rb_next(const struct rb_type *, void *);
817 void	*_rb_prev(const struct rb_type *, void *);
818 void	*_rb_left(const struct rb_type *, void *);
819 void	*_rb_right(const struct rb_type *, void *);
820 void	*_rb_parent(const struct rb_type *, void *);
821 void	 _rb_set_left(const struct rb_type *, void *, void *);
822 void	 _rb_set_right(const struct rb_type *, void *, void *);
823 void	 _rb_set_parent(const struct rb_type *, void *, void *);
824 void	 _rb_poison(const struct rb_type *, void *, unsigned long);
825 int	 _rb_check(const struct rb_type *, void *, unsigned long);
826 
827 #define RBT_INITIALIZER(_head)	{ { NULL } }
828 
829 #define RBT_PROTOTYPE(_name, _type, _field, _cmp)			\
830 extern const struct rb_type *const _name##_RBT_TYPE;			\
831 									\
832 static inline void							\
833 _name##_RBT_INIT(struct _name *head)					\
834 {									\
835 	_rb_init(&head->rbh_root);					\
836 }									\
837 									\
838 static inline struct _type *						\
839 _name##_RBT_INSERT(struct _name *head, struct _type *elm)		\
840 {									\
841 	return _rb_insert(_name##_RBT_TYPE, &head->rbh_root, elm);	\
842 }									\
843 									\
844 static inline struct _type *						\
845 _name##_RBT_REMOVE(struct _name *head, struct _type *elm)		\
846 {									\
847 	return _rb_remove(_name##_RBT_TYPE, &head->rbh_root, elm);	\
848 }									\
849 									\
850 static inline struct _type *						\
851 _name##_RBT_FIND(struct _name *head, const struct _type *key)		\
852 {									\
853 	return _rb_find(_name##_RBT_TYPE, &head->rbh_root, key);	\
854 }									\
855 									\
856 static inline struct _type *						\
857 _name##_RBT_NFIND(struct _name *head, const struct _type *key)		\
858 {									\
859 	return _rb_nfind(_name##_RBT_TYPE, &head->rbh_root, key);	\
860 }									\
861 									\
862 static inline struct _type *						\
863 _name##_RBT_ROOT(struct _name *head)					\
864 {									\
865 	return _rb_root(_name##_RBT_TYPE, &head->rbh_root);		\
866 }									\
867 									\
868 static inline int							\
869 _name##_RBT_EMPTY(struct _name *head)					\
870 {									\
871 	return _rb_empty(&head->rbh_root);				\
872 }									\
873 									\
874 static inline struct _type *						\
875 _name##_RBT_MIN(struct _name *head)					\
876 {									\
877 	return _rb_min(_name##_RBT_TYPE, &head->rbh_root);		\
878 }									\
879 									\
880 static inline struct _type *						\
881 _name##_RBT_MAX(struct _name *head)					\
882 {									\
883 	return _rb_max(_name##_RBT_TYPE, &head->rbh_root);		\
884 }									\
885 									\
886 static inline struct _type *						\
887 _name##_RBT_NEXT(struct _type *elm)					\
888 {									\
889 	return _rb_next(_name##_RBT_TYPE, elm);				\
890 }									\
891 									\
892 static inline struct _type *						\
893 _name##_RBT_PREV(struct _type *elm)					\
894 {									\
895 	return _rb_prev(_name##_RBT_TYPE, elm);				\
896 }									\
897 									\
898 static inline struct _type *						\
899 _name##_RBT_LEFT(struct _type *elm)					\
900 {									\
901 	return _rb_left(_name##_RBT_TYPE, elm);				\
902 }									\
903 									\
904 static inline struct _type *						\
905 _name##_RBT_RIGHT(struct _type *elm)					\
906 {									\
907 	return _rb_right(_name##_RBT_TYPE, elm);			\
908 }									\
909 									\
910 static inline struct _type *						\
911 _name##_RBT_PARENT(struct _type *elm)					\
912 {									\
913 	return _rb_parent(_name##_RBT_TYPE, elm);			\
914 }									\
915 									\
916 static inline void							\
917 _name##_RBT_SET_LEFT(struct _type *elm, struct _type *left)		\
918 {									\
919 	_rb_set_left(_name##_RBT_TYPE, elm, left);			\
920 }									\
921 									\
922 static inline void							\
923 _name##_RBT_SET_RIGHT(struct _type *elm, struct _type *right)		\
924 {									\
925 	_rb_set_right(_name##_RBT_TYPE, elm, right);			\
926 }									\
927 									\
928 static inline void							\
929 _name##_RBT_SET_PARENT(struct _type *elm, struct _type *parent)		\
930 {									\
931 	_rb_set_parent(_name##_RBT_TYPE, elm, parent);			\
932 }									\
933 									\
934 static inline void							\
935 _name##_RBT_POISON(struct _type *elm, unsigned long poison)		\
936 {									\
937 	_rb_poison(_name##_RBT_TYPE, elm, poison);			\
938 }									\
939 									\
940 static inline int							\
941 _name##_RBT_CHECK(struct _type *elm, unsigned long poison)		\
942 {									\
943 	return _rb_check(_name##_RBT_TYPE, elm, poison);		\
944 }
945 
946 #define RBT_GENERATE_INTERNAL(_name, _type, _field, _cmp, _aug)		\
947 static int								\
948 _name##_RBT_COMPARE(const void *lptr, const void *rptr)			\
949 {									\
950 	const struct _type *l = lptr, *r = rptr;			\
951 	return _cmp(l, r);						\
952 }									\
953 static const struct rb_type _name##_RBT_INFO = {			\
954 	_name##_RBT_COMPARE,						\
955 	_aug,								\
956 	offsetof(struct _type, _field),					\
957 };									\
958 const struct rb_type *const _name##_RBT_TYPE = &_name##_RBT_INFO
959 
960 #define RBT_GENERATE_AUGMENT(_name, _type, _field, _cmp, _aug)		\
961 static void								\
962 _name##_RBT_AUGMENT(void *ptr)						\
963 {									\
964 	struct _type *p = ptr;						\
965 	return _aug(p);							\
966 }									\
967 RBT_GENERATE_INTERNAL(_name, _type, _field, _cmp, _name##_RBT_AUGMENT)
968 
969 #define RBT_GENERATE(_name, _type, _field, _cmp)			\
970     RBT_GENERATE_INTERNAL(_name, _type, _field, _cmp, NULL)
971 
972 #define RBT_INIT(_name, _head)		_name##_RBT_INIT(_head)
973 #define RBT_INSERT(_name, _head, _elm)	_name##_RBT_INSERT(_head, _elm)
974 #define RBT_REMOVE(_name, _head, _elm)	_name##_RBT_REMOVE(_head, _elm)
975 #define RBT_FIND(_name, _head, _key)	_name##_RBT_FIND(_head, _key)
976 #define RBT_NFIND(_name, _head, _key)	_name##_RBT_NFIND(_head, _key)
977 #define RBT_ROOT(_name, _head)		_name##_RBT_ROOT(_head)
978 #define RBT_EMPTY(_name, _head)		_name##_RBT_EMPTY(_head)
979 #define RBT_MIN(_name, _head)		_name##_RBT_MIN(_head)
980 #define RBT_MAX(_name, _head)		_name##_RBT_MAX(_head)
981 #define RBT_NEXT(_name, _elm)		_name##_RBT_NEXT(_elm)
982 #define RBT_PREV(_name, _elm)		_name##_RBT_PREV(_elm)
983 #define RBT_LEFT(_name, _elm)		_name##_RBT_LEFT(_elm)
984 #define RBT_RIGHT(_name, _elm)		_name##_RBT_RIGHT(_elm)
985 #define RBT_PARENT(_name, _elm)		_name##_RBT_PARENT(_elm)
986 #define RBT_SET_LEFT(_name, _elm, _l)	_name##_RBT_SET_LEFT(_elm, _l)
987 #define RBT_SET_RIGHT(_name, _elm, _r)	_name##_RBT_SET_RIGHT(_elm, _r)
988 #define RBT_SET_PARENT(_name, _elm, _p)	_name##_RBT_SET_PARENT(_elm, _p)
989 #define RBT_POISON(_name, _elm, _p)	_name##_RBT_POISON(_elm, _p)
990 #define RBT_CHECK(_name, _elm, _p)	_name##_RBT_CHECK(_elm, _p)
991 
992 #define RBT_FOREACH(_e, _name, _head)					\
993 	for ((_e) = RBT_MIN(_name, (_head));				\
994 	     (_e) != NULL;						\
995 	     (_e) = RBT_NEXT(_name, (_e)))
996 
997 #define RBT_FOREACH_SAFE(_e, _name, _head, _n)				\
998 	for ((_e) = RBT_MIN(_name, (_head));				\
999 	     (_e) != NULL && ((_n) = RBT_NEXT(_name, (_e)), 1);	\
1000 	     (_e) = (_n))
1001 
1002 #define RBT_FOREACH_REVERSE(_e, _name, _head)				\
1003 	for ((_e) = RBT_MAX(_name, (_head));				\
1004 	     (_e) != NULL;						\
1005 	     (_e) = RBT_PREV(_name, (_e)))
1006 
1007 #define RBT_FOREACH_REVERSE_SAFE(_e, _name, _head, _n)			\
1008 	for ((_e) = RBT_MAX(_name, (_head));				\
1009 	     (_e) != NULL && ((_n) = RBT_PREV(_name, (_e)), 1);	\
1010 	     (_e) = (_n))
1011 
1012 #endif	/* _SYS_TREE_H_ */