dedup

deduplicating backup program
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tree.h (33874B)


      1 /*	$OpenBSD: tree.h,v 1.29 2017/07/30 19:27:20 deraadt 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 /*
     31  * This file defines data structures for different types of trees:
     32  * splay trees and red-black trees.
     33  *
     34  * A splay tree is a self-organizing data structure.  Every operation
     35  * on the tree causes a splay to happen.  The splay moves the requested
     36  * node to the root of the tree and partly rebalances it.
     37  *
     38  * This has the benefit that request locality causes faster lookups as
     39  * the requested nodes move to the top of the tree.  On the other hand,
     40  * every lookup causes memory writes.
     41  *
     42  * The Balance Theorem bounds the total access time for m operations
     43  * and n inserts on an initially empty tree as O((m + n)lg n).  The
     44  * amortized cost for a sequence of m accesses to a splay tree is O(lg n);
     45  *
     46  * A red-black tree is a binary search tree with the node color as an
     47  * extra attribute.  It fulfills a set of conditions:
     48  *	- every search path from the root to a leaf consists of the
     49  *	  same number of black nodes,
     50  *	- each red node (except for the root) has a black parent,
     51  *	- each leaf node is black.
     52  *
     53  * Every operation on a red-black tree is bounded as O(lg n).
     54  * The maximum height of a red-black tree is 2lg (n+1).
     55  */
     56 
     57 #define SPLAY_HEAD(name, type)						\
     58 struct name {								\
     59 	struct type *sph_root; /* root of the tree */			\
     60 }
     61 
     62 #define SPLAY_INITIALIZER(root)						\
     63 	{ NULL }
     64 
     65 #define SPLAY_INIT(root) do {						\
     66 	(root)->sph_root = NULL;					\
     67 } while (0)
     68 
     69 #define SPLAY_ENTRY(type)						\
     70 struct {								\
     71 	struct type *spe_left; /* left element */			\
     72 	struct type *spe_right; /* right element */			\
     73 }
     74 
     75 #define SPLAY_LEFT(elm, field)		(elm)->field.spe_left
     76 #define SPLAY_RIGHT(elm, field)		(elm)->field.spe_right
     77 #define SPLAY_ROOT(head)		(head)->sph_root
     78 #define SPLAY_EMPTY(head)		(SPLAY_ROOT(head) == NULL)
     79 
     80 /* SPLAY_ROTATE_{LEFT,RIGHT} expect that tmp hold SPLAY_{RIGHT,LEFT} */
     81 #define SPLAY_ROTATE_RIGHT(head, tmp, field) do {			\
     82 	SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(tmp, field);	\
     83 	SPLAY_RIGHT(tmp, field) = (head)->sph_root;			\
     84 	(head)->sph_root = tmp;						\
     85 } while (0)
     86 
     87 #define SPLAY_ROTATE_LEFT(head, tmp, field) do {			\
     88 	SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(tmp, field);	\
     89 	SPLAY_LEFT(tmp, field) = (head)->sph_root;			\
     90 	(head)->sph_root = tmp;						\
     91 } while (0)
     92 
     93 #define SPLAY_LINKLEFT(head, tmp, field) do {				\
     94 	SPLAY_LEFT(tmp, field) = (head)->sph_root;			\
     95 	tmp = (head)->sph_root;						\
     96 	(head)->sph_root = SPLAY_LEFT((head)->sph_root, field);		\
     97 } while (0)
     98 
     99 #define SPLAY_LINKRIGHT(head, tmp, field) do {				\
    100 	SPLAY_RIGHT(tmp, field) = (head)->sph_root;			\
    101 	tmp = (head)->sph_root;						\
    102 	(head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);	\
    103 } while (0)
    104 
    105 #define SPLAY_ASSEMBLE(head, node, left, right, field) do {		\
    106 	SPLAY_RIGHT(left, field) = SPLAY_LEFT((head)->sph_root, field);	\
    107 	SPLAY_LEFT(right, field) = SPLAY_RIGHT((head)->sph_root, field);\
    108 	SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(node, field);	\
    109 	SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(node, field);	\
    110 } while (0)
    111 
    112 /* Generates prototypes and inline functions */
    113 
    114 #define SPLAY_PROTOTYPE(name, type, field, cmp)				\
    115 void name##_SPLAY(struct name *, struct type *);			\
    116 void name##_SPLAY_MINMAX(struct name *, int);				\
    117 struct type *name##_SPLAY_INSERT(struct name *, struct type *);		\
    118 struct type *name##_SPLAY_REMOVE(struct name *, struct type *);		\
    119 									\
    120 /* Finds the node with the same key as elm */				\
    121 static __unused __inline struct type *					\
    122 name##_SPLAY_FIND(struct name *head, struct type *elm)			\
    123 {									\
    124 	if (SPLAY_EMPTY(head))						\
    125 		return(NULL);						\
    126 	name##_SPLAY(head, elm);					\
    127 	if ((cmp)(elm, (head)->sph_root) == 0)				\
    128 		return (head->sph_root);				\
    129 	return (NULL);							\
    130 }									\
    131 									\
    132 static __unused __inline struct type *					\
    133 name##_SPLAY_NEXT(struct name *head, struct type *elm)			\
    134 {									\
    135 	name##_SPLAY(head, elm);					\
    136 	if (SPLAY_RIGHT(elm, field) != NULL) {				\
    137 		elm = SPLAY_RIGHT(elm, field);				\
    138 		while (SPLAY_LEFT(elm, field) != NULL) {		\
    139 			elm = SPLAY_LEFT(elm, field);			\
    140 		}							\
    141 	} else								\
    142 		elm = NULL;						\
    143 	return (elm);							\
    144 }									\
    145 									\
    146 static __unused __inline struct type *					\
    147 name##_SPLAY_MIN_MAX(struct name *head, int val)			\
    148 {									\
    149 	name##_SPLAY_MINMAX(head, val);					\
    150         return (SPLAY_ROOT(head));					\
    151 }
    152 
    153 /* Main splay operation.
    154  * Moves node close to the key of elm to top
    155  */
    156 #define SPLAY_GENERATE(name, type, field, cmp)				\
    157 struct type *								\
    158 name##_SPLAY_INSERT(struct name *head, struct type *elm)		\
    159 {									\
    160     if (SPLAY_EMPTY(head)) {						\
    161 	    SPLAY_LEFT(elm, field) = SPLAY_RIGHT(elm, field) = NULL;	\
    162     } else {								\
    163 	    int __comp;							\
    164 	    name##_SPLAY(head, elm);					\
    165 	    __comp = (cmp)(elm, (head)->sph_root);			\
    166 	    if(__comp < 0) {						\
    167 		    SPLAY_LEFT(elm, field) = SPLAY_LEFT((head)->sph_root, field);\
    168 		    SPLAY_RIGHT(elm, field) = (head)->sph_root;		\
    169 		    SPLAY_LEFT((head)->sph_root, field) = NULL;		\
    170 	    } else if (__comp > 0) {					\
    171 		    SPLAY_RIGHT(elm, field) = SPLAY_RIGHT((head)->sph_root, field);\
    172 		    SPLAY_LEFT(elm, field) = (head)->sph_root;		\
    173 		    SPLAY_RIGHT((head)->sph_root, field) = NULL;	\
    174 	    } else							\
    175 		    return ((head)->sph_root);				\
    176     }									\
    177     (head)->sph_root = (elm);						\
    178     return (NULL);							\
    179 }									\
    180 									\
    181 struct type *								\
    182 name##_SPLAY_REMOVE(struct name *head, struct type *elm)		\
    183 {									\
    184 	struct type *__tmp;						\
    185 	if (SPLAY_EMPTY(head))						\
    186 		return (NULL);						\
    187 	name##_SPLAY(head, elm);					\
    188 	if ((cmp)(elm, (head)->sph_root) == 0) {			\
    189 		if (SPLAY_LEFT((head)->sph_root, field) == NULL) {	\
    190 			(head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);\
    191 		} else {						\
    192 			__tmp = SPLAY_RIGHT((head)->sph_root, field);	\
    193 			(head)->sph_root = SPLAY_LEFT((head)->sph_root, field);\
    194 			name##_SPLAY(head, elm);			\
    195 			SPLAY_RIGHT((head)->sph_root, field) = __tmp;	\
    196 		}							\
    197 		return (elm);						\
    198 	}								\
    199 	return (NULL);							\
    200 }									\
    201 									\
    202 void									\
    203 name##_SPLAY(struct name *head, struct type *elm)			\
    204 {									\
    205 	struct type __node, *__left, *__right, *__tmp;			\
    206 	int __comp;							\
    207 \
    208 	SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
    209 	__left = __right = &__node;					\
    210 \
    211 	while ((__comp = (cmp)(elm, (head)->sph_root))) {		\
    212 		if (__comp < 0) {					\
    213 			__tmp = SPLAY_LEFT((head)->sph_root, field);	\
    214 			if (__tmp == NULL)				\
    215 				break;					\
    216 			if ((cmp)(elm, __tmp) < 0){			\
    217 				SPLAY_ROTATE_RIGHT(head, __tmp, field);	\
    218 				if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
    219 					break;				\
    220 			}						\
    221 			SPLAY_LINKLEFT(head, __right, field);		\
    222 		} else if (__comp > 0) {				\
    223 			__tmp = SPLAY_RIGHT((head)->sph_root, field);	\
    224 			if (__tmp == NULL)				\
    225 				break;					\
    226 			if ((cmp)(elm, __tmp) > 0){			\
    227 				SPLAY_ROTATE_LEFT(head, __tmp, field);	\
    228 				if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
    229 					break;				\
    230 			}						\
    231 			SPLAY_LINKRIGHT(head, __left, field);		\
    232 		}							\
    233 	}								\
    234 	SPLAY_ASSEMBLE(head, &__node, __left, __right, field);		\
    235 }									\
    236 									\
    237 /* Splay with either the minimum or the maximum element			\
    238  * Used to find minimum or maximum element in tree.			\
    239  */									\
    240 void name##_SPLAY_MINMAX(struct name *head, int __comp) \
    241 {									\
    242 	struct type __node, *__left, *__right, *__tmp;			\
    243 \
    244 	SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
    245 	__left = __right = &__node;					\
    246 \
    247 	while (1) {							\
    248 		if (__comp < 0) {					\
    249 			__tmp = SPLAY_LEFT((head)->sph_root, field);	\
    250 			if (__tmp == NULL)				\
    251 				break;					\
    252 			if (__comp < 0){				\
    253 				SPLAY_ROTATE_RIGHT(head, __tmp, field);	\
    254 				if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
    255 					break;				\
    256 			}						\
    257 			SPLAY_LINKLEFT(head, __right, field);		\
    258 		} else if (__comp > 0) {				\
    259 			__tmp = SPLAY_RIGHT((head)->sph_root, field);	\
    260 			if (__tmp == NULL)				\
    261 				break;					\
    262 			if (__comp > 0) {				\
    263 				SPLAY_ROTATE_LEFT(head, __tmp, field);	\
    264 				if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
    265 					break;				\
    266 			}						\
    267 			SPLAY_LINKRIGHT(head, __left, field);		\
    268 		}							\
    269 	}								\
    270 	SPLAY_ASSEMBLE(head, &__node, __left, __right, field);		\
    271 }
    272 
    273 #define SPLAY_NEGINF	-1
    274 #define SPLAY_INF	1
    275 
    276 #define SPLAY_INSERT(name, x, y)	name##_SPLAY_INSERT(x, y)
    277 #define SPLAY_REMOVE(name, x, y)	name##_SPLAY_REMOVE(x, y)
    278 #define SPLAY_FIND(name, x, y)		name##_SPLAY_FIND(x, y)
    279 #define SPLAY_NEXT(name, x, y)		name##_SPLAY_NEXT(x, y)
    280 #define SPLAY_MIN(name, x)		(SPLAY_EMPTY(x) ? NULL	\
    281 					: name##_SPLAY_MIN_MAX(x, SPLAY_NEGINF))
    282 #define SPLAY_MAX(name, x)		(SPLAY_EMPTY(x) ? NULL	\
    283 					: name##_SPLAY_MIN_MAX(x, SPLAY_INF))
    284 
    285 #define SPLAY_FOREACH(x, name, head)					\
    286 	for ((x) = SPLAY_MIN(name, head);				\
    287 	     (x) != NULL;						\
    288 	     (x) = SPLAY_NEXT(name, head, x))
    289 
    290 /* Macros that define a red-black tree */
    291 #define RB_HEAD(name, type)						\
    292 struct name {								\
    293 	struct type *rbh_root; /* root of the tree */			\
    294 }
    295 
    296 #define RB_INITIALIZER(root)						\
    297 	{ NULL }
    298 
    299 #define RB_INIT(root) do {						\
    300 	(root)->rbh_root = NULL;					\
    301 } while (0)
    302 
    303 #define RB_BLACK	0
    304 #define RB_RED		1
    305 #define RB_ENTRY(type)							\
    306 struct {								\
    307 	struct type *rbe_left;		/* left element */		\
    308 	struct type *rbe_right;		/* right element */		\
    309 	struct type *rbe_parent;	/* parent element */		\
    310 	int rbe_color;			/* node color */		\
    311 }
    312 
    313 #define RB_LEFT(elm, field)		(elm)->field.rbe_left
    314 #define RB_RIGHT(elm, field)		(elm)->field.rbe_right
    315 #define RB_PARENT(elm, field)		(elm)->field.rbe_parent
    316 #define RB_COLOR(elm, field)		(elm)->field.rbe_color
    317 #define RB_ROOT(head)			(head)->rbh_root
    318 #define RB_EMPTY(head)			(RB_ROOT(head) == NULL)
    319 
    320 #define RB_SET(elm, parent, field) do {					\
    321 	RB_PARENT(elm, field) = parent;					\
    322 	RB_LEFT(elm, field) = RB_RIGHT(elm, field) = NULL;		\
    323 	RB_COLOR(elm, field) = RB_RED;					\
    324 } while (0)
    325 
    326 #define RB_SET_BLACKRED(black, red, field) do {				\
    327 	RB_COLOR(black, field) = RB_BLACK;				\
    328 	RB_COLOR(red, field) = RB_RED;					\
    329 } while (0)
    330 
    331 #ifndef RB_AUGMENT
    332 #define RB_AUGMENT(x)	do {} while (0)
    333 #endif
    334 
    335 #define RB_ROTATE_LEFT(head, elm, tmp, field) do {			\
    336 	(tmp) = RB_RIGHT(elm, field);					\
    337 	if ((RB_RIGHT(elm, field) = RB_LEFT(tmp, field))) {		\
    338 		RB_PARENT(RB_LEFT(tmp, field), field) = (elm);		\
    339 	}								\
    340 	RB_AUGMENT(elm);						\
    341 	if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field))) {		\
    342 		if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))	\
    343 			RB_LEFT(RB_PARENT(elm, field), field) = (tmp);	\
    344 		else							\
    345 			RB_RIGHT(RB_PARENT(elm, field), field) = (tmp);	\
    346 	} else								\
    347 		(head)->rbh_root = (tmp);				\
    348 	RB_LEFT(tmp, field) = (elm);					\
    349 	RB_PARENT(elm, field) = (tmp);					\
    350 	RB_AUGMENT(tmp);						\
    351 	if ((RB_PARENT(tmp, field)))					\
    352 		RB_AUGMENT(RB_PARENT(tmp, field));			\
    353 } while (0)
    354 
    355 #define RB_ROTATE_RIGHT(head, elm, tmp, field) do {			\
    356 	(tmp) = RB_LEFT(elm, field);					\
    357 	if ((RB_LEFT(elm, field) = RB_RIGHT(tmp, field))) {		\
    358 		RB_PARENT(RB_RIGHT(tmp, field), field) = (elm);		\
    359 	}								\
    360 	RB_AUGMENT(elm);						\
    361 	if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field))) {		\
    362 		if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))	\
    363 			RB_LEFT(RB_PARENT(elm, field), field) = (tmp);	\
    364 		else							\
    365 			RB_RIGHT(RB_PARENT(elm, field), field) = (tmp);	\
    366 	} else								\
    367 		(head)->rbh_root = (tmp);				\
    368 	RB_RIGHT(tmp, field) = (elm);					\
    369 	RB_PARENT(elm, field) = (tmp);					\
    370 	RB_AUGMENT(tmp);						\
    371 	if ((RB_PARENT(tmp, field)))					\
    372 		RB_AUGMENT(RB_PARENT(tmp, field));			\
    373 } while (0)
    374 
    375 /* Generates prototypes and inline functions */
    376 #define	RB_PROTOTYPE(name, type, field, cmp)				\
    377 	RB_PROTOTYPE_INTERNAL(name, type, field, cmp,)
    378 #define	RB_PROTOTYPE_STATIC(name, type, field, cmp)			\
    379 	RB_PROTOTYPE_INTERNAL(name, type, field, cmp, __attribute__((__unused__)) static)
    380 #define RB_PROTOTYPE_INTERNAL(name, type, field, cmp, attr)		\
    381 attr void name##_RB_INSERT_COLOR(struct name *, struct type *);		\
    382 attr void name##_RB_REMOVE_COLOR(struct name *, struct type *, struct type *);\
    383 attr struct type *name##_RB_REMOVE(struct name *, struct type *);	\
    384 attr struct type *name##_RB_INSERT(struct name *, struct type *);	\
    385 attr struct type *name##_RB_FIND(struct name *, struct type *);		\
    386 attr struct type *name##_RB_NFIND(struct name *, struct type *);	\
    387 attr struct type *name##_RB_NEXT(struct type *);			\
    388 attr struct type *name##_RB_PREV(struct type *);			\
    389 attr struct type *name##_RB_MINMAX(struct name *, int);			\
    390 									\
    391 
    392 /* Main rb operation.
    393  * Moves node close to the key of elm to top
    394  */
    395 #define	RB_GENERATE(name, type, field, cmp)				\
    396 	RB_GENERATE_INTERNAL(name, type, field, cmp,)
    397 #define	RB_GENERATE_STATIC(name, type, field, cmp)			\
    398 	RB_GENERATE_INTERNAL(name, type, field, cmp, __attribute__((__unused__)) static)
    399 #define RB_GENERATE_INTERNAL(name, type, field, cmp, attr)		\
    400 attr void								\
    401 name##_RB_INSERT_COLOR(struct name *head, struct type *elm)		\
    402 {									\
    403 	struct type *parent, *gparent, *tmp;				\
    404 	while ((parent = RB_PARENT(elm, field)) &&			\
    405 	    RB_COLOR(parent, field) == RB_RED) {			\
    406 		gparent = RB_PARENT(parent, field);			\
    407 		if (parent == RB_LEFT(gparent, field)) {		\
    408 			tmp = RB_RIGHT(gparent, field);			\
    409 			if (tmp && RB_COLOR(tmp, field) == RB_RED) {	\
    410 				RB_COLOR(tmp, field) = RB_BLACK;	\
    411 				RB_SET_BLACKRED(parent, gparent, field);\
    412 				elm = gparent;				\
    413 				continue;				\
    414 			}						\
    415 			if (RB_RIGHT(parent, field) == elm) {		\
    416 				RB_ROTATE_LEFT(head, parent, tmp, field);\
    417 				tmp = parent;				\
    418 				parent = elm;				\
    419 				elm = tmp;				\
    420 			}						\
    421 			RB_SET_BLACKRED(parent, gparent, field);	\
    422 			RB_ROTATE_RIGHT(head, gparent, tmp, field);	\
    423 		} else {						\
    424 			tmp = RB_LEFT(gparent, field);			\
    425 			if (tmp && RB_COLOR(tmp, field) == RB_RED) {	\
    426 				RB_COLOR(tmp, field) = RB_BLACK;	\
    427 				RB_SET_BLACKRED(parent, gparent, field);\
    428 				elm = gparent;				\
    429 				continue;				\
    430 			}						\
    431 			if (RB_LEFT(parent, field) == elm) {		\
    432 				RB_ROTATE_RIGHT(head, parent, tmp, field);\
    433 				tmp = parent;				\
    434 				parent = elm;				\
    435 				elm = tmp;				\
    436 			}						\
    437 			RB_SET_BLACKRED(parent, gparent, field);	\
    438 			RB_ROTATE_LEFT(head, gparent, tmp, field);	\
    439 		}							\
    440 	}								\
    441 	RB_COLOR(head->rbh_root, field) = RB_BLACK;			\
    442 }									\
    443 									\
    444 attr void								\
    445 name##_RB_REMOVE_COLOR(struct name *head, struct type *parent, struct type *elm) \
    446 {									\
    447 	struct type *tmp;						\
    448 	while ((elm == NULL || RB_COLOR(elm, field) == RB_BLACK) &&	\
    449 	    elm != RB_ROOT(head)) {					\
    450 		if (RB_LEFT(parent, field) == elm) {			\
    451 			tmp = RB_RIGHT(parent, field);			\
    452 			if (RB_COLOR(tmp, field) == RB_RED) {		\
    453 				RB_SET_BLACKRED(tmp, parent, field);	\
    454 				RB_ROTATE_LEFT(head, parent, tmp, field);\
    455 				tmp = RB_RIGHT(parent, field);		\
    456 			}						\
    457 			if ((RB_LEFT(tmp, field) == NULL ||		\
    458 			    RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
    459 			    (RB_RIGHT(tmp, field) == NULL ||		\
    460 			    RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
    461 				RB_COLOR(tmp, field) = RB_RED;		\
    462 				elm = parent;				\
    463 				parent = RB_PARENT(elm, field);		\
    464 			} else {					\
    465 				if (RB_RIGHT(tmp, field) == NULL ||	\
    466 				    RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK) {\
    467 					struct type *oleft;		\
    468 					if ((oleft = RB_LEFT(tmp, field)))\
    469 						RB_COLOR(oleft, field) = RB_BLACK;\
    470 					RB_COLOR(tmp, field) = RB_RED;	\
    471 					RB_ROTATE_RIGHT(head, tmp, oleft, field);\
    472 					tmp = RB_RIGHT(parent, field);	\
    473 				}					\
    474 				RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
    475 				RB_COLOR(parent, field) = RB_BLACK;	\
    476 				if (RB_RIGHT(tmp, field))		\
    477 					RB_COLOR(RB_RIGHT(tmp, field), field) = RB_BLACK;\
    478 				RB_ROTATE_LEFT(head, parent, tmp, field);\
    479 				elm = RB_ROOT(head);			\
    480 				break;					\
    481 			}						\
    482 		} else {						\
    483 			tmp = RB_LEFT(parent, field);			\
    484 			if (RB_COLOR(tmp, field) == RB_RED) {		\
    485 				RB_SET_BLACKRED(tmp, parent, field);	\
    486 				RB_ROTATE_RIGHT(head, parent, tmp, field);\
    487 				tmp = RB_LEFT(parent, field);		\
    488 			}						\
    489 			if ((RB_LEFT(tmp, field) == NULL ||		\
    490 			    RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
    491 			    (RB_RIGHT(tmp, field) == NULL ||		\
    492 			    RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
    493 				RB_COLOR(tmp, field) = RB_RED;		\
    494 				elm = parent;				\
    495 				parent = RB_PARENT(elm, field);		\
    496 			} else {					\
    497 				if (RB_LEFT(tmp, field) == NULL ||	\
    498 				    RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) {\
    499 					struct type *oright;		\
    500 					if ((oright = RB_RIGHT(tmp, field)))\
    501 						RB_COLOR(oright, field) = RB_BLACK;\
    502 					RB_COLOR(tmp, field) = RB_RED;	\
    503 					RB_ROTATE_LEFT(head, tmp, oright, field);\
    504 					tmp = RB_LEFT(parent, field);	\
    505 				}					\
    506 				RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
    507 				RB_COLOR(parent, field) = RB_BLACK;	\
    508 				if (RB_LEFT(tmp, field))		\
    509 					RB_COLOR(RB_LEFT(tmp, field), field) = RB_BLACK;\
    510 				RB_ROTATE_RIGHT(head, parent, tmp, field);\
    511 				elm = RB_ROOT(head);			\
    512 				break;					\
    513 			}						\
    514 		}							\
    515 	}								\
    516 	if (elm)							\
    517 		RB_COLOR(elm, field) = RB_BLACK;			\
    518 }									\
    519 									\
    520 attr struct type *							\
    521 name##_RB_REMOVE(struct name *head, struct type *elm)			\
    522 {									\
    523 	struct type *child, *parent, *old = elm;			\
    524 	int color;							\
    525 	if (RB_LEFT(elm, field) == NULL)				\
    526 		child = RB_RIGHT(elm, field);				\
    527 	else if (RB_RIGHT(elm, field) == NULL)				\
    528 		child = RB_LEFT(elm, field);				\
    529 	else {								\
    530 		struct type *left;					\
    531 		elm = RB_RIGHT(elm, field);				\
    532 		while ((left = RB_LEFT(elm, field)))			\
    533 			elm = left;					\
    534 		child = RB_RIGHT(elm, field);				\
    535 		parent = RB_PARENT(elm, field);				\
    536 		color = RB_COLOR(elm, field);				\
    537 		if (child)						\
    538 			RB_PARENT(child, field) = parent;		\
    539 		if (parent) {						\
    540 			if (RB_LEFT(parent, field) == elm)		\
    541 				RB_LEFT(parent, field) = child;		\
    542 			else						\
    543 				RB_RIGHT(parent, field) = child;	\
    544 			RB_AUGMENT(parent);				\
    545 		} else							\
    546 			RB_ROOT(head) = child;				\
    547 		if (RB_PARENT(elm, field) == old)			\
    548 			parent = elm;					\
    549 		(elm)->field = (old)->field;				\
    550 		if (RB_PARENT(old, field)) {				\
    551 			if (RB_LEFT(RB_PARENT(old, field), field) == old)\
    552 				RB_LEFT(RB_PARENT(old, field), field) = elm;\
    553 			else						\
    554 				RB_RIGHT(RB_PARENT(old, field), field) = elm;\
    555 			RB_AUGMENT(RB_PARENT(old, field));		\
    556 		} else							\
    557 			RB_ROOT(head) = elm;				\
    558 		RB_PARENT(RB_LEFT(old, field), field) = elm;		\
    559 		if (RB_RIGHT(old, field))				\
    560 			RB_PARENT(RB_RIGHT(old, field), field) = elm;	\
    561 		if (parent) {						\
    562 			left = parent;					\
    563 			do {						\
    564 				RB_AUGMENT(left);			\
    565 			} while ((left = RB_PARENT(left, field)));	\
    566 		}							\
    567 		goto color;						\
    568 	}								\
    569 	parent = RB_PARENT(elm, field);					\
    570 	color = RB_COLOR(elm, field);					\
    571 	if (child)							\
    572 		RB_PARENT(child, field) = parent;			\
    573 	if (parent) {							\
    574 		if (RB_LEFT(parent, field) == elm)			\
    575 			RB_LEFT(parent, field) = child;			\
    576 		else							\
    577 			RB_RIGHT(parent, field) = child;		\
    578 		RB_AUGMENT(parent);					\
    579 	} else								\
    580 		RB_ROOT(head) = child;					\
    581 color:									\
    582 	if (color == RB_BLACK)						\
    583 		name##_RB_REMOVE_COLOR(head, parent, child);		\
    584 	return (old);							\
    585 }									\
    586 									\
    587 /* Inserts a node into the RB tree */					\
    588 attr struct type *							\
    589 name##_RB_INSERT(struct name *head, struct type *elm)			\
    590 {									\
    591 	struct type *tmp;						\
    592 	struct type *parent = NULL;					\
    593 	int comp = 0;							\
    594 	tmp = RB_ROOT(head);						\
    595 	while (tmp) {							\
    596 		parent = tmp;						\
    597 		comp = (cmp)(elm, parent);				\
    598 		if (comp < 0)						\
    599 			tmp = RB_LEFT(tmp, field);			\
    600 		else if (comp > 0)					\
    601 			tmp = RB_RIGHT(tmp, field);			\
    602 		else							\
    603 			return (tmp);					\
    604 	}								\
    605 	RB_SET(elm, parent, field);					\
    606 	if (parent != NULL) {						\
    607 		if (comp < 0)						\
    608 			RB_LEFT(parent, field) = elm;			\
    609 		else							\
    610 			RB_RIGHT(parent, field) = elm;			\
    611 		RB_AUGMENT(parent);					\
    612 	} else								\
    613 		RB_ROOT(head) = elm;					\
    614 	name##_RB_INSERT_COLOR(head, elm);				\
    615 	return (NULL);							\
    616 }									\
    617 									\
    618 /* Finds the node with the same key as elm */				\
    619 attr struct type *							\
    620 name##_RB_FIND(struct name *head, struct type *elm)			\
    621 {									\
    622 	struct type *tmp = RB_ROOT(head);				\
    623 	int comp;							\
    624 	while (tmp) {							\
    625 		comp = cmp(elm, tmp);					\
    626 		if (comp < 0)						\
    627 			tmp = RB_LEFT(tmp, field);			\
    628 		else if (comp > 0)					\
    629 			tmp = RB_RIGHT(tmp, field);			\
    630 		else							\
    631 			return (tmp);					\
    632 	}								\
    633 	return (NULL);							\
    634 }									\
    635 									\
    636 /* Finds the first node greater than or equal to the search key */	\
    637 attr struct type *							\
    638 name##_RB_NFIND(struct name *head, struct type *elm)			\
    639 {									\
    640 	struct type *tmp = RB_ROOT(head);				\
    641 	struct type *res = NULL;					\
    642 	int comp;							\
    643 	while (tmp) {							\
    644 		comp = cmp(elm, tmp);					\
    645 		if (comp < 0) {						\
    646 			res = tmp;					\
    647 			tmp = RB_LEFT(tmp, field);			\
    648 		}							\
    649 		else if (comp > 0)					\
    650 			tmp = RB_RIGHT(tmp, field);			\
    651 		else							\
    652 			return (tmp);					\
    653 	}								\
    654 	return (res);							\
    655 }									\
    656 									\
    657 /* ARGSUSED */								\
    658 attr struct type *							\
    659 name##_RB_NEXT(struct type *elm)					\
    660 {									\
    661 	if (RB_RIGHT(elm, field)) {					\
    662 		elm = RB_RIGHT(elm, field);				\
    663 		while (RB_LEFT(elm, field))				\
    664 			elm = RB_LEFT(elm, field);			\
    665 	} else {							\
    666 		if (RB_PARENT(elm, field) &&				\
    667 		    (elm == RB_LEFT(RB_PARENT(elm, field), field)))	\
    668 			elm = RB_PARENT(elm, field);			\
    669 		else {							\
    670 			while (RB_PARENT(elm, field) &&			\
    671 			    (elm == RB_RIGHT(RB_PARENT(elm, field), field)))\
    672 				elm = RB_PARENT(elm, field);		\
    673 			elm = RB_PARENT(elm, field);			\
    674 		}							\
    675 	}								\
    676 	return (elm);							\
    677 }									\
    678 									\
    679 /* ARGSUSED */								\
    680 attr struct type *							\
    681 name##_RB_PREV(struct type *elm)					\
    682 {									\
    683 	if (RB_LEFT(elm, field)) {					\
    684 		elm = RB_LEFT(elm, field);				\
    685 		while (RB_RIGHT(elm, field))				\
    686 			elm = RB_RIGHT(elm, field);			\
    687 	} else {							\
    688 		if (RB_PARENT(elm, field) &&				\
    689 		    (elm == RB_RIGHT(RB_PARENT(elm, field), field)))	\
    690 			elm = RB_PARENT(elm, field);			\
    691 		else {							\
    692 			while (RB_PARENT(elm, field) &&			\
    693 			    (elm == RB_LEFT(RB_PARENT(elm, field), field)))\
    694 				elm = RB_PARENT(elm, field);		\
    695 			elm = RB_PARENT(elm, field);			\
    696 		}							\
    697 	}								\
    698 	return (elm);							\
    699 }									\
    700 									\
    701 attr struct type *							\
    702 name##_RB_MINMAX(struct name *head, int val)				\
    703 {									\
    704 	struct type *tmp = RB_ROOT(head);				\
    705 	struct type *parent = NULL;					\
    706 	while (tmp) {							\
    707 		parent = tmp;						\
    708 		if (val < 0)						\
    709 			tmp = RB_LEFT(tmp, field);			\
    710 		else							\
    711 			tmp = RB_RIGHT(tmp, field);			\
    712 	}								\
    713 	return (parent);						\
    714 }
    715 
    716 #define RB_NEGINF	-1
    717 #define RB_INF	1
    718 
    719 #define RB_INSERT(name, x, y)	name##_RB_INSERT(x, y)
    720 #define RB_REMOVE(name, x, y)	name##_RB_REMOVE(x, y)
    721 #define RB_FIND(name, x, y)	name##_RB_FIND(x, y)
    722 #define RB_NFIND(name, x, y)	name##_RB_NFIND(x, y)
    723 #define RB_NEXT(name, x, y)	name##_RB_NEXT(y)
    724 #define RB_PREV(name, x, y)	name##_RB_PREV(y)
    725 #define RB_MIN(name, x)		name##_RB_MINMAX(x, RB_NEGINF)
    726 #define RB_MAX(name, x)		name##_RB_MINMAX(x, RB_INF)
    727 
    728 #define RB_FOREACH(x, name, head)					\
    729 	for ((x) = RB_MIN(name, head);					\
    730 	     (x) != NULL;						\
    731 	     (x) = name##_RB_NEXT(x))
    732 
    733 #define RB_FOREACH_SAFE(x, name, head, y)				\
    734 	for ((x) = RB_MIN(name, head);					\
    735 	    ((x) != NULL) && ((y) = name##_RB_NEXT(x), 1);		\
    736 	     (x) = (y))
    737 
    738 #define RB_FOREACH_REVERSE(x, name, head)				\
    739 	for ((x) = RB_MAX(name, head);					\
    740 	     (x) != NULL;						\
    741 	     (x) = name##_RB_PREV(x))
    742 
    743 #define RB_FOREACH_REVERSE_SAFE(x, name, head, y)			\
    744 	for ((x) = RB_MAX(name, head);					\
    745 	    ((x) != NULL) && ((y) = name##_RB_PREV(x), 1);		\
    746 	     (x) = (y))
    747 
    748 
    749 /*
    750  * Copyright (c) 2016 David Gwynne <dlg@openbsd.org>
    751  *
    752  * Permission to use, copy, modify, and distribute this software for any
    753  * purpose with or without fee is hereby granted, provided that the above
    754  * copyright notice and this permission notice appear in all copies.
    755  *
    756  * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
    757  * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
    758  * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
    759  * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
    760  * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
    761  * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
    762  * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
    763  */
    764 
    765 struct rb_type {
    766 	int		(*t_compare)(const void *, const void *);
    767 	void		(*t_augment)(void *);
    768 	unsigned int	  t_offset;	/* offset of rb_entry in type */
    769 };
    770 
    771 struct rb_tree {
    772 	struct rb_entry	*rbt_root;
    773 };
    774 
    775 struct rb_entry {
    776 	struct rb_entry	 *rbt_parent;
    777 	struct rb_entry	 *rbt_left;
    778 	struct rb_entry	 *rbt_right;
    779 	unsigned int	  rbt_color;
    780 };
    781 
    782 #define RBT_HEAD(_name, _type)						\
    783 struct _name {								\
    784 	struct rb_tree rbh_root;					\
    785 }
    786 
    787 #define RBT_ENTRY(_type)	struct rb_entry
    788 
    789 static inline void
    790 _rb_init(struct rb_tree *rbt)
    791 {
    792 	rbt->rbt_root = NULL;
    793 }
    794 
    795 static inline int
    796 _rb_empty(struct rb_tree *rbt)
    797 {
    798 	return (rbt->rbt_root == NULL);
    799 }
    800 
    801 void	*_rb_insert(const struct rb_type *, struct rb_tree *, void *);
    802 void	*_rb_remove(const struct rb_type *, struct rb_tree *, void *);
    803 void	*_rb_find(const struct rb_type *, struct rb_tree *, const void *);
    804 void	*_rb_nfind(const struct rb_type *, struct rb_tree *, const void *);
    805 void	*_rb_root(const struct rb_type *, struct rb_tree *);
    806 void	*_rb_min(const struct rb_type *, struct rb_tree *);
    807 void	*_rb_max(const struct rb_type *, struct rb_tree *);
    808 void	*_rb_next(const struct rb_type *, void *);
    809 void	*_rb_prev(const struct rb_type *, void *);
    810 void	*_rb_left(const struct rb_type *, void *);
    811 void	*_rb_right(const struct rb_type *, void *);
    812 void	*_rb_parent(const struct rb_type *, void *);
    813 void	 _rb_set_left(const struct rb_type *, void *, void *);
    814 void	 _rb_set_right(const struct rb_type *, void *, void *);
    815 void	 _rb_set_parent(const struct rb_type *, void *, void *);
    816 void	 _rb_poison(const struct rb_type *, void *, unsigned long);
    817 int	 _rb_check(const struct rb_type *, void *, unsigned long);
    818 
    819 #define RBT_INITIALIZER(_head)	{ { NULL } }
    820 
    821 #define RBT_PROTOTYPE(_name, _type, _field, _cmp)			\
    822 extern const struct rb_type *const _name##_RBT_TYPE;			\
    823 									\
    824 __unused static inline void						\
    825 _name##_RBT_INIT(struct _name *head)					\
    826 {									\
    827 	_rb_init(&head->rbh_root);					\
    828 }									\
    829 									\
    830 __unused static inline struct _type *					\
    831 _name##_RBT_INSERT(struct _name *head, struct _type *elm)		\
    832 {									\
    833 	return _rb_insert(_name##_RBT_TYPE, &head->rbh_root, elm);	\
    834 }									\
    835 									\
    836 __unused static inline struct _type *					\
    837 _name##_RBT_REMOVE(struct _name *head, struct _type *elm)		\
    838 {									\
    839 	return _rb_remove(_name##_RBT_TYPE, &head->rbh_root, elm);	\
    840 }									\
    841 									\
    842 __unused static inline struct _type *					\
    843 _name##_RBT_FIND(struct _name *head, const struct _type *key)		\
    844 {									\
    845 	return _rb_find(_name##_RBT_TYPE, &head->rbh_root, key);	\
    846 }									\
    847 									\
    848 __unused static inline struct _type *					\
    849 _name##_RBT_NFIND(struct _name *head, const struct _type *key)		\
    850 {									\
    851 	return _rb_nfind(_name##_RBT_TYPE, &head->rbh_root, key);	\
    852 }									\
    853 									\
    854 __unused static inline struct _type *					\
    855 _name##_RBT_ROOT(struct _name *head)					\
    856 {									\
    857 	return _rb_root(_name##_RBT_TYPE, &head->rbh_root);		\
    858 }									\
    859 									\
    860 __unused static inline int						\
    861 _name##_RBT_EMPTY(struct _name *head)					\
    862 {									\
    863 	return _rb_empty(&head->rbh_root);				\
    864 }									\
    865 									\
    866 __unused static inline struct _type *					\
    867 _name##_RBT_MIN(struct _name *head)					\
    868 {									\
    869 	return _rb_min(_name##_RBT_TYPE, &head->rbh_root);		\
    870 }									\
    871 									\
    872 __unused static inline struct _type *					\
    873 _name##_RBT_MAX(struct _name *head)					\
    874 {									\
    875 	return _rb_max(_name##_RBT_TYPE, &head->rbh_root);		\
    876 }									\
    877 									\
    878 __unused static inline struct _type *					\
    879 _name##_RBT_NEXT(struct _type *elm)					\
    880 {									\
    881 	return _rb_next(_name##_RBT_TYPE, elm);				\
    882 }									\
    883 									\
    884 __unused static inline struct _type *					\
    885 _name##_RBT_PREV(struct _type *elm)					\
    886 {									\
    887 	return _rb_prev(_name##_RBT_TYPE, elm);				\
    888 }									\
    889 									\
    890 __unused static inline struct _type *					\
    891 _name##_RBT_LEFT(struct _type *elm)					\
    892 {									\
    893 	return _rb_left(_name##_RBT_TYPE, elm);				\
    894 }									\
    895 									\
    896 __unused static inline struct _type *					\
    897 _name##_RBT_RIGHT(struct _type *elm)					\
    898 {									\
    899 	return _rb_right(_name##_RBT_TYPE, elm);			\
    900 }									\
    901 									\
    902 __unused static inline struct _type *					\
    903 _name##_RBT_PARENT(struct _type *elm)					\
    904 {									\
    905 	return _rb_parent(_name##_RBT_TYPE, elm);			\
    906 }									\
    907 									\
    908 __unused static inline void						\
    909 _name##_RBT_SET_LEFT(struct _type *elm, struct _type *left)		\
    910 {									\
    911 	return _rb_set_left(_name##_RBT_TYPE, elm, left);		\
    912 }									\
    913 									\
    914 __unused static inline void						\
    915 _name##_RBT_SET_RIGHT(struct _type *elm, struct _type *right)		\
    916 {									\
    917 	return _rb_set_right(_name##_RBT_TYPE, elm, right);		\
    918 }									\
    919 									\
    920 __unused static inline void						\
    921 _name##_RBT_SET_PARENT(struct _type *elm, struct _type *parent)		\
    922 {									\
    923 	return _rb_set_parent(_name##_RBT_TYPE, elm, parent);		\
    924 }									\
    925 									\
    926 __unused static inline void						\
    927 _name##_RBT_POISON(struct _type *elm, unsigned long poison)		\
    928 {									\
    929 	return _rb_poison(_name##_RBT_TYPE, elm, poison);		\
    930 }									\
    931 									\
    932 __unused static inline int						\
    933 _name##_RBT_CHECK(struct _type *elm, unsigned long poison)		\
    934 {									\
    935 	return _rb_check(_name##_RBT_TYPE, elm, poison);		\
    936 }
    937 
    938 #define RBT_GENERATE_INTERNAL(_name, _type, _field, _cmp, _aug)		\
    939 static int								\
    940 _name##_RBT_COMPARE(const void *lptr, const void *rptr)			\
    941 {									\
    942 	const struct _type *l = lptr, *r = rptr;			\
    943 	return _cmp(l, r);						\
    944 }									\
    945 static const struct rb_type _name##_RBT_INFO = {			\
    946 	_name##_RBT_COMPARE,						\
    947 	_aug,								\
    948 	offsetof(struct _type, _field),					\
    949 };									\
    950 const struct rb_type *const _name##_RBT_TYPE = &_name##_RBT_INFO
    951 
    952 #define RBT_GENERATE_AUGMENT(_name, _type, _field, _cmp, _aug)		\
    953 static void								\
    954 _name##_RBT_AUGMENT(void *ptr)						\
    955 {									\
    956 	struct _type *p = ptr;						\
    957 	return _aug(p);							\
    958 }									\
    959 RBT_GENERATE_INTERNAL(_name, _type, _field, _cmp, _name##_RBT_AUGMENT)
    960 
    961 #define RBT_GENERATE(_name, _type, _field, _cmp)			\
    962     RBT_GENERATE_INTERNAL(_name, _type, _field, _cmp, NULL)
    963 
    964 #define RBT_INIT(_name, _head)		_name##_RBT_INIT(_head)
    965 #define RBT_INSERT(_name, _head, _elm)	_name##_RBT_INSERT(_head, _elm)
    966 #define RBT_REMOVE(_name, _head, _elm)	_name##_RBT_REMOVE(_head, _elm)
    967 #define RBT_FIND(_name, _head, _key)	_name##_RBT_FIND(_head, _key)
    968 #define RBT_NFIND(_name, _head, _key)	_name##_RBT_NFIND(_head, _key)
    969 #define RBT_ROOT(_name, _head)		_name##_RBT_ROOT(_head)
    970 #define RBT_EMPTY(_name, _head)		_name##_RBT_EMPTY(_head)
    971 #define RBT_MIN(_name, _head)		_name##_RBT_MIN(_head)
    972 #define RBT_MAX(_name, _head)		_name##_RBT_MAX(_head)
    973 #define RBT_NEXT(_name, _elm)		_name##_RBT_NEXT(_elm)
    974 #define RBT_PREV(_name, _elm)		_name##_RBT_PREV(_elm)
    975 #define RBT_LEFT(_name, _elm)		_name##_RBT_LEFT(_elm)
    976 #define RBT_RIGHT(_name, _elm)		_name##_RBT_RIGHT(_elm)
    977 #define RBT_PARENT(_name, _elm)		_name##_RBT_PARENT(_elm)
    978 #define RBT_SET_LEFT(_name, _elm, _l)	_name##_RBT_SET_LEFT(_elm, _l)
    979 #define RBT_SET_RIGHT(_name, _elm, _r)	_name##_RBT_SET_RIGHT(_elm, _r)
    980 #define RBT_SET_PARENT(_name, _elm, _p)	_name##_RBT_SET_PARENT(_elm, _p)
    981 #define RBT_POISON(_name, _elm, _p)	_name##_RBT_POISON(_elm, _p)
    982 #define RBT_CHECK(_name, _elm, _p)	_name##_RBT_CHECK(_elm, _p)
    983 
    984 #define RBT_FOREACH(_e, _name, _head)					\
    985 	for ((_e) = RBT_MIN(_name, (_head));				\
    986 	     (_e) != NULL;						\
    987 	     (_e) = RBT_NEXT(_name, (_e)))
    988 
    989 #define RBT_FOREACH_SAFE(_e, _name, _head, _n)				\
    990 	for ((_e) = RBT_MIN(_name, (_head));				\
    991 	     (_e) != NULL && ((_n) = RBT_NEXT(_name, (_e)), 1);	\
    992 	     (_e) = (_n))
    993 
    994 #define RBT_FOREACH_REVERSE(_e, _name, _head)				\
    995 	for ((_e) = RBT_MAX(_name, (_head));				\
    996 	     (_e) != NULL;						\
    997 	     (_e) = RBT_PREV(_name, (_e)))
    998 
    999 #define RBT_FOREACH_REVERSE_SAFE(_e, _name, _head, _n)			\
   1000 	for ((_e) = RBT_MAX(_name, (_head));				\
   1001 	     (_e) != NULL && ((_n) = RBT_PREV(_name, (_e)), 1);	\
   1002 	     (_e) = (_n))
   1003 
   1004 #endif	/* _SYS_TREE_H_ */