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tree.h (33898B)


      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 #include <sys/_null.h>
     31 
     32 /*
     33  * This file defines data structures for different types of trees:
     34  * splay trees and red-black trees.
     35  *
     36  * A splay tree is a self-organizing data structure.  Every operation
     37  * on the tree causes a splay to happen.  The splay moves the requested
     38  * node to the root of the tree and partly rebalances it.
     39  *
     40  * This has the benefit that request locality causes faster lookups as
     41  * the requested nodes move to the top of the tree.  On the other hand,
     42  * every lookup causes memory writes.
     43  *
     44  * The Balance Theorem bounds the total access time for m operations
     45  * and n inserts on an initially empty tree as O((m + n)lg n).  The
     46  * amortized cost for a sequence of m accesses to a splay tree is O(lg n);
     47  *
     48  * A red-black tree is a binary search tree with the node color as an
     49  * extra attribute.  It fulfills a set of conditions:
     50  *	- every search path from the root to a leaf consists of the
     51  *	  same number of black nodes,
     52  *	- each red node (except for the root) has a black parent,
     53  *	- each leaf node is black.
     54  *
     55  * Every operation on a red-black tree is bounded as O(lg n).
     56  * The maximum height of a red-black tree is 2lg (n+1).
     57  */
     58 
     59 #define SPLAY_HEAD(name, type)						\
     60 struct name {								\
     61 	struct type *sph_root; /* root of the tree */			\
     62 }
     63 
     64 #define SPLAY_INITIALIZER(root)						\
     65 	{ NULL }
     66 
     67 #define SPLAY_INIT(root) do {						\
     68 	(root)->sph_root = NULL;					\
     69 } while (0)
     70 
     71 #define SPLAY_ENTRY(type)						\
     72 struct {								\
     73 	struct type *spe_left; /* left element */			\
     74 	struct type *spe_right; /* right element */			\
     75 }
     76 
     77 #define SPLAY_LEFT(elm, field)		(elm)->field.spe_left
     78 #define SPLAY_RIGHT(elm, field)		(elm)->field.spe_right
     79 #define SPLAY_ROOT(head)		(head)->sph_root
     80 #define SPLAY_EMPTY(head)		(SPLAY_ROOT(head) == NULL)
     81 
     82 /* SPLAY_ROTATE_{LEFT,RIGHT} expect that tmp hold SPLAY_{RIGHT,LEFT} */
     83 #define SPLAY_ROTATE_RIGHT(head, tmp, field) do {			\
     84 	SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(tmp, field);	\
     85 	SPLAY_RIGHT(tmp, field) = (head)->sph_root;			\
     86 	(head)->sph_root = tmp;						\
     87 } while (0)
     88 
     89 #define SPLAY_ROTATE_LEFT(head, tmp, field) do {			\
     90 	SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(tmp, field);	\
     91 	SPLAY_LEFT(tmp, field) = (head)->sph_root;			\
     92 	(head)->sph_root = tmp;						\
     93 } while (0)
     94 
     95 #define SPLAY_LINKLEFT(head, tmp, field) do {				\
     96 	SPLAY_LEFT(tmp, field) = (head)->sph_root;			\
     97 	tmp = (head)->sph_root;						\
     98 	(head)->sph_root = SPLAY_LEFT((head)->sph_root, field);		\
     99 } while (0)
    100 
    101 #define SPLAY_LINKRIGHT(head, tmp, field) do {				\
    102 	SPLAY_RIGHT(tmp, field) = (head)->sph_root;			\
    103 	tmp = (head)->sph_root;						\
    104 	(head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);	\
    105 } while (0)
    106 
    107 #define SPLAY_ASSEMBLE(head, node, left, right, field) do {		\
    108 	SPLAY_RIGHT(left, field) = SPLAY_LEFT((head)->sph_root, field);	\
    109 	SPLAY_LEFT(right, field) = SPLAY_RIGHT((head)->sph_root, field);\
    110 	SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(node, field);	\
    111 	SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(node, field);	\
    112 } while (0)
    113 
    114 /* Generates prototypes and inline functions */
    115 
    116 #define SPLAY_PROTOTYPE(name, type, field, cmp)				\
    117 void name##_SPLAY(struct name *, struct type *);			\
    118 void name##_SPLAY_MINMAX(struct name *, int);				\
    119 struct type *name##_SPLAY_INSERT(struct name *, struct type *);		\
    120 struct type *name##_SPLAY_REMOVE(struct name *, struct type *);		\
    121 									\
    122 /* Finds the node with the same key as elm */				\
    123 static __unused __inline struct type *					\
    124 name##_SPLAY_FIND(struct name *head, struct type *elm)			\
    125 {									\
    126 	if (SPLAY_EMPTY(head))						\
    127 		return(NULL);						\
    128 	name##_SPLAY(head, elm);					\
    129 	if ((cmp)(elm, (head)->sph_root) == 0)				\
    130 		return (head->sph_root);				\
    131 	return (NULL);							\
    132 }									\
    133 									\
    134 static __unused __inline struct type *					\
    135 name##_SPLAY_NEXT(struct name *head, struct type *elm)			\
    136 {									\
    137 	name##_SPLAY(head, elm);					\
    138 	if (SPLAY_RIGHT(elm, field) != NULL) {				\
    139 		elm = SPLAY_RIGHT(elm, field);				\
    140 		while (SPLAY_LEFT(elm, field) != NULL) {		\
    141 			elm = SPLAY_LEFT(elm, field);			\
    142 		}							\
    143 	} else								\
    144 		elm = NULL;						\
    145 	return (elm);							\
    146 }									\
    147 									\
    148 static __unused __inline struct type *					\
    149 name##_SPLAY_MIN_MAX(struct name *head, int val)			\
    150 {									\
    151 	name##_SPLAY_MINMAX(head, val);					\
    152         return (SPLAY_ROOT(head));					\
    153 }
    154 
    155 /* Main splay operation.
    156  * Moves node close to the key of elm to top
    157  */
    158 #define SPLAY_GENERATE(name, type, field, cmp)				\
    159 struct type *								\
    160 name##_SPLAY_INSERT(struct name *head, struct type *elm)		\
    161 {									\
    162     if (SPLAY_EMPTY(head)) {						\
    163 	    SPLAY_LEFT(elm, field) = SPLAY_RIGHT(elm, field) = NULL;	\
    164     } else {								\
    165 	    int __comp;							\
    166 	    name##_SPLAY(head, elm);					\
    167 	    __comp = (cmp)(elm, (head)->sph_root);			\
    168 	    if(__comp < 0) {						\
    169 		    SPLAY_LEFT(elm, field) = SPLAY_LEFT((head)->sph_root, field);\
    170 		    SPLAY_RIGHT(elm, field) = (head)->sph_root;		\
    171 		    SPLAY_LEFT((head)->sph_root, field) = NULL;		\
    172 	    } else if (__comp > 0) {					\
    173 		    SPLAY_RIGHT(elm, field) = SPLAY_RIGHT((head)->sph_root, field);\
    174 		    SPLAY_LEFT(elm, field) = (head)->sph_root;		\
    175 		    SPLAY_RIGHT((head)->sph_root, field) = NULL;	\
    176 	    } else							\
    177 		    return ((head)->sph_root);				\
    178     }									\
    179     (head)->sph_root = (elm);						\
    180     return (NULL);							\
    181 }									\
    182 									\
    183 struct type *								\
    184 name##_SPLAY_REMOVE(struct name *head, struct type *elm)		\
    185 {									\
    186 	struct type *__tmp;						\
    187 	if (SPLAY_EMPTY(head))						\
    188 		return (NULL);						\
    189 	name##_SPLAY(head, elm);					\
    190 	if ((cmp)(elm, (head)->sph_root) == 0) {			\
    191 		if (SPLAY_LEFT((head)->sph_root, field) == NULL) {	\
    192 			(head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);\
    193 		} else {						\
    194 			__tmp = SPLAY_RIGHT((head)->sph_root, field);	\
    195 			(head)->sph_root = SPLAY_LEFT((head)->sph_root, field);\
    196 			name##_SPLAY(head, elm);			\
    197 			SPLAY_RIGHT((head)->sph_root, field) = __tmp;	\
    198 		}							\
    199 		return (elm);						\
    200 	}								\
    201 	return (NULL);							\
    202 }									\
    203 									\
    204 void									\
    205 name##_SPLAY(struct name *head, struct type *elm)			\
    206 {									\
    207 	struct type __node, *__left, *__right, *__tmp;			\
    208 	int __comp;							\
    209 \
    210 	SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
    211 	__left = __right = &__node;					\
    212 \
    213 	while ((__comp = (cmp)(elm, (head)->sph_root))) {		\
    214 		if (__comp < 0) {					\
    215 			__tmp = SPLAY_LEFT((head)->sph_root, field);	\
    216 			if (__tmp == NULL)				\
    217 				break;					\
    218 			if ((cmp)(elm, __tmp) < 0){			\
    219 				SPLAY_ROTATE_RIGHT(head, __tmp, field);	\
    220 				if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
    221 					break;				\
    222 			}						\
    223 			SPLAY_LINKLEFT(head, __right, field);		\
    224 		} else if (__comp > 0) {				\
    225 			__tmp = SPLAY_RIGHT((head)->sph_root, field);	\
    226 			if (__tmp == NULL)				\
    227 				break;					\
    228 			if ((cmp)(elm, __tmp) > 0){			\
    229 				SPLAY_ROTATE_LEFT(head, __tmp, field);	\
    230 				if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
    231 					break;				\
    232 			}						\
    233 			SPLAY_LINKRIGHT(head, __left, field);		\
    234 		}							\
    235 	}								\
    236 	SPLAY_ASSEMBLE(head, &__node, __left, __right, field);		\
    237 }									\
    238 									\
    239 /* Splay with either the minimum or the maximum element			\
    240  * Used to find minimum or maximum element in tree.			\
    241  */									\
    242 void name##_SPLAY_MINMAX(struct name *head, int __comp) \
    243 {									\
    244 	struct type __node, *__left, *__right, *__tmp;			\
    245 \
    246 	SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;\
    247 	__left = __right = &__node;					\
    248 \
    249 	while (1) {							\
    250 		if (__comp < 0) {					\
    251 			__tmp = SPLAY_LEFT((head)->sph_root, field);	\
    252 			if (__tmp == NULL)				\
    253 				break;					\
    254 			if (__comp < 0){				\
    255 				SPLAY_ROTATE_RIGHT(head, __tmp, field);	\
    256 				if (SPLAY_LEFT((head)->sph_root, field) == NULL)\
    257 					break;				\
    258 			}						\
    259 			SPLAY_LINKLEFT(head, __right, field);		\
    260 		} else if (__comp > 0) {				\
    261 			__tmp = SPLAY_RIGHT((head)->sph_root, field);	\
    262 			if (__tmp == NULL)				\
    263 				break;					\
    264 			if (__comp > 0) {				\
    265 				SPLAY_ROTATE_LEFT(head, __tmp, field);	\
    266 				if (SPLAY_RIGHT((head)->sph_root, field) == NULL)\
    267 					break;				\
    268 			}						\
    269 			SPLAY_LINKRIGHT(head, __left, field);		\
    270 		}							\
    271 	}								\
    272 	SPLAY_ASSEMBLE(head, &__node, __left, __right, field);		\
    273 }
    274 
    275 #define SPLAY_NEGINF	-1
    276 #define SPLAY_INF	1
    277 
    278 #define SPLAY_INSERT(name, x, y)	name##_SPLAY_INSERT(x, y)
    279 #define SPLAY_REMOVE(name, x, y)	name##_SPLAY_REMOVE(x, y)
    280 #define SPLAY_FIND(name, x, y)		name##_SPLAY_FIND(x, y)
    281 #define SPLAY_NEXT(name, x, y)		name##_SPLAY_NEXT(x, y)
    282 #define SPLAY_MIN(name, x)		(SPLAY_EMPTY(x) ? NULL	\
    283 					: name##_SPLAY_MIN_MAX(x, SPLAY_NEGINF))
    284 #define SPLAY_MAX(name, x)		(SPLAY_EMPTY(x) ? NULL	\
    285 					: name##_SPLAY_MIN_MAX(x, SPLAY_INF))
    286 
    287 #define SPLAY_FOREACH(x, name, head)					\
    288 	for ((x) = SPLAY_MIN(name, head);				\
    289 	     (x) != NULL;						\
    290 	     (x) = SPLAY_NEXT(name, head, x))
    291 
    292 /* Macros that define a red-black tree */
    293 #define RB_HEAD(name, type)						\
    294 struct name {								\
    295 	struct type *rbh_root; /* root of the tree */			\
    296 }
    297 
    298 #define RB_INITIALIZER(root)						\
    299 	{ NULL }
    300 
    301 #define RB_INIT(root) do {						\
    302 	(root)->rbh_root = NULL;					\
    303 } while (0)
    304 
    305 #define RB_BLACK	0
    306 #define RB_RED		1
    307 #define RB_ENTRY(type)							\
    308 struct {								\
    309 	struct type *rbe_left;		/* left element */		\
    310 	struct type *rbe_right;		/* right element */		\
    311 	struct type *rbe_parent;	/* parent element */		\
    312 	int rbe_color;			/* node color */		\
    313 }
    314 
    315 #define RB_LEFT(elm, field)		(elm)->field.rbe_left
    316 #define RB_RIGHT(elm, field)		(elm)->field.rbe_right
    317 #define RB_PARENT(elm, field)		(elm)->field.rbe_parent
    318 #define RB_COLOR(elm, field)		(elm)->field.rbe_color
    319 #define RB_ROOT(head)			(head)->rbh_root
    320 #define RB_EMPTY(head)			(RB_ROOT(head) == NULL)
    321 
    322 #define RB_SET(elm, parent, field) do {					\
    323 	RB_PARENT(elm, field) = parent;					\
    324 	RB_LEFT(elm, field) = RB_RIGHT(elm, field) = NULL;		\
    325 	RB_COLOR(elm, field) = RB_RED;					\
    326 } while (0)
    327 
    328 #define RB_SET_BLACKRED(black, red, field) do {				\
    329 	RB_COLOR(black, field) = RB_BLACK;				\
    330 	RB_COLOR(red, field) = RB_RED;					\
    331 } while (0)
    332 
    333 #ifndef RB_AUGMENT
    334 #define RB_AUGMENT(x)	do {} while (0)
    335 #endif
    336 
    337 #define RB_ROTATE_LEFT(head, elm, tmp, field) do {			\
    338 	(tmp) = RB_RIGHT(elm, field);					\
    339 	if ((RB_RIGHT(elm, field) = RB_LEFT(tmp, field))) {		\
    340 		RB_PARENT(RB_LEFT(tmp, field), field) = (elm);		\
    341 	}								\
    342 	RB_AUGMENT(elm);						\
    343 	if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field))) {		\
    344 		if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))	\
    345 			RB_LEFT(RB_PARENT(elm, field), field) = (tmp);	\
    346 		else							\
    347 			RB_RIGHT(RB_PARENT(elm, field), field) = (tmp);	\
    348 	} else								\
    349 		(head)->rbh_root = (tmp);				\
    350 	RB_LEFT(tmp, field) = (elm);					\
    351 	RB_PARENT(elm, field) = (tmp);					\
    352 	RB_AUGMENT(tmp);						\
    353 	if ((RB_PARENT(tmp, field)))					\
    354 		RB_AUGMENT(RB_PARENT(tmp, field));			\
    355 } while (0)
    356 
    357 #define RB_ROTATE_RIGHT(head, elm, tmp, field) do {			\
    358 	(tmp) = RB_LEFT(elm, field);					\
    359 	if ((RB_LEFT(elm, field) = RB_RIGHT(tmp, field))) {		\
    360 		RB_PARENT(RB_RIGHT(tmp, field), field) = (elm);		\
    361 	}								\
    362 	RB_AUGMENT(elm);						\
    363 	if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field))) {		\
    364 		if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))	\
    365 			RB_LEFT(RB_PARENT(elm, field), field) = (tmp);	\
    366 		else							\
    367 			RB_RIGHT(RB_PARENT(elm, field), field) = (tmp);	\
    368 	} else								\
    369 		(head)->rbh_root = (tmp);				\
    370 	RB_RIGHT(tmp, field) = (elm);					\
    371 	RB_PARENT(elm, field) = (tmp);					\
    372 	RB_AUGMENT(tmp);						\
    373 	if ((RB_PARENT(tmp, field)))					\
    374 		RB_AUGMENT(RB_PARENT(tmp, field));			\
    375 } while (0)
    376 
    377 /* Generates prototypes and inline functions */
    378 #define	RB_PROTOTYPE(name, type, field, cmp)				\
    379 	RB_PROTOTYPE_INTERNAL(name, type, field, cmp,)
    380 #define	RB_PROTOTYPE_STATIC(name, type, field, cmp)			\
    381 	RB_PROTOTYPE_INTERNAL(name, type, field, cmp, __attribute__((__unused__)) static)
    382 #define RB_PROTOTYPE_INTERNAL(name, type, field, cmp, attr)		\
    383 attr void name##_RB_INSERT_COLOR(struct name *, struct type *);		\
    384 attr void name##_RB_REMOVE_COLOR(struct name *, struct type *, struct type *);\
    385 attr struct type *name##_RB_REMOVE(struct name *, struct type *);	\
    386 attr struct type *name##_RB_INSERT(struct name *, struct type *);	\
    387 attr struct type *name##_RB_FIND(struct name *, struct type *);		\
    388 attr struct type *name##_RB_NFIND(struct name *, struct type *);	\
    389 attr struct type *name##_RB_NEXT(struct type *);			\
    390 attr struct type *name##_RB_PREV(struct type *);			\
    391 attr struct type *name##_RB_MINMAX(struct name *, int);			\
    392 									\
    393 
    394 /* Main rb operation.
    395  * Moves node close to the key of elm to top
    396  */
    397 #define	RB_GENERATE(name, type, field, cmp)				\
    398 	RB_GENERATE_INTERNAL(name, type, field, cmp,)
    399 #define	RB_GENERATE_STATIC(name, type, field, cmp)			\
    400 	RB_GENERATE_INTERNAL(name, type, field, cmp, __attribute__((__unused__)) static)
    401 #define RB_GENERATE_INTERNAL(name, type, field, cmp, attr)		\
    402 attr void								\
    403 name##_RB_INSERT_COLOR(struct name *head, struct type *elm)		\
    404 {									\
    405 	struct type *parent, *gparent, *tmp;				\
    406 	while ((parent = RB_PARENT(elm, field)) &&			\
    407 	    RB_COLOR(parent, field) == RB_RED) {			\
    408 		gparent = RB_PARENT(parent, field);			\
    409 		if (parent == RB_LEFT(gparent, field)) {		\
    410 			tmp = RB_RIGHT(gparent, field);			\
    411 			if (tmp && RB_COLOR(tmp, field) == RB_RED) {	\
    412 				RB_COLOR(tmp, field) = RB_BLACK;	\
    413 				RB_SET_BLACKRED(parent, gparent, field);\
    414 				elm = gparent;				\
    415 				continue;				\
    416 			}						\
    417 			if (RB_RIGHT(parent, field) == elm) {		\
    418 				RB_ROTATE_LEFT(head, parent, tmp, field);\
    419 				tmp = parent;				\
    420 				parent = elm;				\
    421 				elm = tmp;				\
    422 			}						\
    423 			RB_SET_BLACKRED(parent, gparent, field);	\
    424 			RB_ROTATE_RIGHT(head, gparent, tmp, field);	\
    425 		} else {						\
    426 			tmp = RB_LEFT(gparent, field);			\
    427 			if (tmp && RB_COLOR(tmp, field) == RB_RED) {	\
    428 				RB_COLOR(tmp, field) = RB_BLACK;	\
    429 				RB_SET_BLACKRED(parent, gparent, field);\
    430 				elm = gparent;				\
    431 				continue;				\
    432 			}						\
    433 			if (RB_LEFT(parent, field) == elm) {		\
    434 				RB_ROTATE_RIGHT(head, parent, tmp, field);\
    435 				tmp = parent;				\
    436 				parent = elm;				\
    437 				elm = tmp;				\
    438 			}						\
    439 			RB_SET_BLACKRED(parent, gparent, field);	\
    440 			RB_ROTATE_LEFT(head, gparent, tmp, field);	\
    441 		}							\
    442 	}								\
    443 	RB_COLOR(head->rbh_root, field) = RB_BLACK;			\
    444 }									\
    445 									\
    446 attr void								\
    447 name##_RB_REMOVE_COLOR(struct name *head, struct type *parent, struct type *elm) \
    448 {									\
    449 	struct type *tmp;						\
    450 	while ((elm == NULL || RB_COLOR(elm, field) == RB_BLACK) &&	\
    451 	    elm != RB_ROOT(head)) {					\
    452 		if (RB_LEFT(parent, field) == elm) {			\
    453 			tmp = RB_RIGHT(parent, field);			\
    454 			if (RB_COLOR(tmp, field) == RB_RED) {		\
    455 				RB_SET_BLACKRED(tmp, parent, field);	\
    456 				RB_ROTATE_LEFT(head, parent, tmp, field);\
    457 				tmp = RB_RIGHT(parent, field);		\
    458 			}						\
    459 			if ((RB_LEFT(tmp, field) == NULL ||		\
    460 			    RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
    461 			    (RB_RIGHT(tmp, field) == NULL ||		\
    462 			    RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
    463 				RB_COLOR(tmp, field) = RB_RED;		\
    464 				elm = parent;				\
    465 				parent = RB_PARENT(elm, field);		\
    466 			} else {					\
    467 				if (RB_RIGHT(tmp, field) == NULL ||	\
    468 				    RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK) {\
    469 					struct type *oleft;		\
    470 					if ((oleft = RB_LEFT(tmp, field)))\
    471 						RB_COLOR(oleft, field) = RB_BLACK;\
    472 					RB_COLOR(tmp, field) = RB_RED;	\
    473 					RB_ROTATE_RIGHT(head, tmp, oleft, field);\
    474 					tmp = RB_RIGHT(parent, field);	\
    475 				}					\
    476 				RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
    477 				RB_COLOR(parent, field) = RB_BLACK;	\
    478 				if (RB_RIGHT(tmp, field))		\
    479 					RB_COLOR(RB_RIGHT(tmp, field), field) = RB_BLACK;\
    480 				RB_ROTATE_LEFT(head, parent, tmp, field);\
    481 				elm = RB_ROOT(head);			\
    482 				break;					\
    483 			}						\
    484 		} else {						\
    485 			tmp = RB_LEFT(parent, field);			\
    486 			if (RB_COLOR(tmp, field) == RB_RED) {		\
    487 				RB_SET_BLACKRED(tmp, parent, field);	\
    488 				RB_ROTATE_RIGHT(head, parent, tmp, field);\
    489 				tmp = RB_LEFT(parent, field);		\
    490 			}						\
    491 			if ((RB_LEFT(tmp, field) == NULL ||		\
    492 			    RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&\
    493 			    (RB_RIGHT(tmp, field) == NULL ||		\
    494 			    RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {\
    495 				RB_COLOR(tmp, field) = RB_RED;		\
    496 				elm = parent;				\
    497 				parent = RB_PARENT(elm, field);		\
    498 			} else {					\
    499 				if (RB_LEFT(tmp, field) == NULL ||	\
    500 				    RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) {\
    501 					struct type *oright;		\
    502 					if ((oright = RB_RIGHT(tmp, field)))\
    503 						RB_COLOR(oright, field) = RB_BLACK;\
    504 					RB_COLOR(tmp, field) = RB_RED;	\
    505 					RB_ROTATE_LEFT(head, tmp, oright, field);\
    506 					tmp = RB_LEFT(parent, field);	\
    507 				}					\
    508 				RB_COLOR(tmp, field) = RB_COLOR(parent, field);\
    509 				RB_COLOR(parent, field) = RB_BLACK;	\
    510 				if (RB_LEFT(tmp, field))		\
    511 					RB_COLOR(RB_LEFT(tmp, field), field) = RB_BLACK;\
    512 				RB_ROTATE_RIGHT(head, parent, tmp, field);\
    513 				elm = RB_ROOT(head);			\
    514 				break;					\
    515 			}						\
    516 		}							\
    517 	}								\
    518 	if (elm)							\
    519 		RB_COLOR(elm, field) = RB_BLACK;			\
    520 }									\
    521 									\
    522 attr struct type *							\
    523 name##_RB_REMOVE(struct name *head, struct type *elm)			\
    524 {									\
    525 	struct type *child, *parent, *old = elm;			\
    526 	int color;							\
    527 	if (RB_LEFT(elm, field) == NULL)				\
    528 		child = RB_RIGHT(elm, field);				\
    529 	else if (RB_RIGHT(elm, field) == NULL)				\
    530 		child = RB_LEFT(elm, field);				\
    531 	else {								\
    532 		struct type *left;					\
    533 		elm = RB_RIGHT(elm, field);				\
    534 		while ((left = RB_LEFT(elm, field)))			\
    535 			elm = left;					\
    536 		child = RB_RIGHT(elm, field);				\
    537 		parent = RB_PARENT(elm, field);				\
    538 		color = RB_COLOR(elm, field);				\
    539 		if (child)						\
    540 			RB_PARENT(child, field) = parent;		\
    541 		if (parent) {						\
    542 			if (RB_LEFT(parent, field) == elm)		\
    543 				RB_LEFT(parent, field) = child;		\
    544 			else						\
    545 				RB_RIGHT(parent, field) = child;	\
    546 			RB_AUGMENT(parent);				\
    547 		} else							\
    548 			RB_ROOT(head) = child;				\
    549 		if (RB_PARENT(elm, field) == old)			\
    550 			parent = elm;					\
    551 		(elm)->field = (old)->field;				\
    552 		if (RB_PARENT(old, field)) {				\
    553 			if (RB_LEFT(RB_PARENT(old, field), field) == old)\
    554 				RB_LEFT(RB_PARENT(old, field), field) = elm;\
    555 			else						\
    556 				RB_RIGHT(RB_PARENT(old, field), field) = elm;\
    557 			RB_AUGMENT(RB_PARENT(old, field));		\
    558 		} else							\
    559 			RB_ROOT(head) = elm;				\
    560 		RB_PARENT(RB_LEFT(old, field), field) = elm;		\
    561 		if (RB_RIGHT(old, field))				\
    562 			RB_PARENT(RB_RIGHT(old, field), field) = elm;	\
    563 		if (parent) {						\
    564 			left = parent;					\
    565 			do {						\
    566 				RB_AUGMENT(left);			\
    567 			} while ((left = RB_PARENT(left, field)));	\
    568 		}							\
    569 		goto color;						\
    570 	}								\
    571 	parent = RB_PARENT(elm, field);					\
    572 	color = RB_COLOR(elm, field);					\
    573 	if (child)							\
    574 		RB_PARENT(child, field) = parent;			\
    575 	if (parent) {							\
    576 		if (RB_LEFT(parent, field) == elm)			\
    577 			RB_LEFT(parent, field) = child;			\
    578 		else							\
    579 			RB_RIGHT(parent, field) = child;		\
    580 		RB_AUGMENT(parent);					\
    581 	} else								\
    582 		RB_ROOT(head) = child;					\
    583 color:									\
    584 	if (color == RB_BLACK)						\
    585 		name##_RB_REMOVE_COLOR(head, parent, child);		\
    586 	return (old);							\
    587 }									\
    588 									\
    589 /* Inserts a node into the RB tree */					\
    590 attr struct type *							\
    591 name##_RB_INSERT(struct name *head, struct type *elm)			\
    592 {									\
    593 	struct type *tmp;						\
    594 	struct type *parent = NULL;					\
    595 	int comp = 0;							\
    596 	tmp = RB_ROOT(head);						\
    597 	while (tmp) {							\
    598 		parent = tmp;						\
    599 		comp = (cmp)(elm, parent);				\
    600 		if (comp < 0)						\
    601 			tmp = RB_LEFT(tmp, field);			\
    602 		else if (comp > 0)					\
    603 			tmp = RB_RIGHT(tmp, field);			\
    604 		else							\
    605 			return (tmp);					\
    606 	}								\
    607 	RB_SET(elm, parent, field);					\
    608 	if (parent != NULL) {						\
    609 		if (comp < 0)						\
    610 			RB_LEFT(parent, field) = elm;			\
    611 		else							\
    612 			RB_RIGHT(parent, field) = elm;			\
    613 		RB_AUGMENT(parent);					\
    614 	} else								\
    615 		RB_ROOT(head) = elm;					\
    616 	name##_RB_INSERT_COLOR(head, elm);				\
    617 	return (NULL);							\
    618 }									\
    619 									\
    620 /* Finds the node with the same key as elm */				\
    621 attr struct type *							\
    622 name##_RB_FIND(struct name *head, struct type *elm)			\
    623 {									\
    624 	struct type *tmp = RB_ROOT(head);				\
    625 	int comp;							\
    626 	while (tmp) {							\
    627 		comp = cmp(elm, tmp);					\
    628 		if (comp < 0)						\
    629 			tmp = RB_LEFT(tmp, field);			\
    630 		else if (comp > 0)					\
    631 			tmp = RB_RIGHT(tmp, field);			\
    632 		else							\
    633 			return (tmp);					\
    634 	}								\
    635 	return (NULL);							\
    636 }									\
    637 									\
    638 /* Finds the first node greater than or equal to the search key */	\
    639 attr struct type *							\
    640 name##_RB_NFIND(struct name *head, struct type *elm)			\
    641 {									\
    642 	struct type *tmp = RB_ROOT(head);				\
    643 	struct type *res = NULL;					\
    644 	int comp;							\
    645 	while (tmp) {							\
    646 		comp = cmp(elm, tmp);					\
    647 		if (comp < 0) {						\
    648 			res = tmp;					\
    649 			tmp = RB_LEFT(tmp, field);			\
    650 		}							\
    651 		else if (comp > 0)					\
    652 			tmp = RB_RIGHT(tmp, field);			\
    653 		else							\
    654 			return (tmp);					\
    655 	}								\
    656 	return (res);							\
    657 }									\
    658 									\
    659 /* ARGSUSED */								\
    660 attr struct type *							\
    661 name##_RB_NEXT(struct type *elm)					\
    662 {									\
    663 	if (RB_RIGHT(elm, field)) {					\
    664 		elm = RB_RIGHT(elm, field);				\
    665 		while (RB_LEFT(elm, field))				\
    666 			elm = RB_LEFT(elm, field);			\
    667 	} else {							\
    668 		if (RB_PARENT(elm, field) &&				\
    669 		    (elm == RB_LEFT(RB_PARENT(elm, field), field)))	\
    670 			elm = RB_PARENT(elm, field);			\
    671 		else {							\
    672 			while (RB_PARENT(elm, field) &&			\
    673 			    (elm == RB_RIGHT(RB_PARENT(elm, field), field)))\
    674 				elm = RB_PARENT(elm, field);		\
    675 			elm = RB_PARENT(elm, field);			\
    676 		}							\
    677 	}								\
    678 	return (elm);							\
    679 }									\
    680 									\
    681 /* ARGSUSED */								\
    682 attr struct type *							\
    683 name##_RB_PREV(struct type *elm)					\
    684 {									\
    685 	if (RB_LEFT(elm, field)) {					\
    686 		elm = RB_LEFT(elm, field);				\
    687 		while (RB_RIGHT(elm, field))				\
    688 			elm = RB_RIGHT(elm, field);			\
    689 	} else {							\
    690 		if (RB_PARENT(elm, field) &&				\
    691 		    (elm == RB_RIGHT(RB_PARENT(elm, field), field)))	\
    692 			elm = RB_PARENT(elm, field);			\
    693 		else {							\
    694 			while (RB_PARENT(elm, field) &&			\
    695 			    (elm == RB_LEFT(RB_PARENT(elm, field), field)))\
    696 				elm = RB_PARENT(elm, field);		\
    697 			elm = RB_PARENT(elm, field);			\
    698 		}							\
    699 	}								\
    700 	return (elm);							\
    701 }									\
    702 									\
    703 attr struct type *							\
    704 name##_RB_MINMAX(struct name *head, int val)				\
    705 {									\
    706 	struct type *tmp = RB_ROOT(head);				\
    707 	struct type *parent = NULL;					\
    708 	while (tmp) {							\
    709 		parent = tmp;						\
    710 		if (val < 0)						\
    711 			tmp = RB_LEFT(tmp, field);			\
    712 		else							\
    713 			tmp = RB_RIGHT(tmp, field);			\
    714 	}								\
    715 	return (parent);						\
    716 }
    717 
    718 #define RB_NEGINF	-1
    719 #define RB_INF	1
    720 
    721 #define RB_INSERT(name, x, y)	name##_RB_INSERT(x, y)
    722 #define RB_REMOVE(name, x, y)	name##_RB_REMOVE(x, y)
    723 #define RB_FIND(name, x, y)	name##_RB_FIND(x, y)
    724 #define RB_NFIND(name, x, y)	name##_RB_NFIND(x, y)
    725 #define RB_NEXT(name, x, y)	name##_RB_NEXT(y)
    726 #define RB_PREV(name, x, y)	name##_RB_PREV(y)
    727 #define RB_MIN(name, x)		name##_RB_MINMAX(x, RB_NEGINF)
    728 #define RB_MAX(name, x)		name##_RB_MINMAX(x, RB_INF)
    729 
    730 #define RB_FOREACH(x, name, head)					\
    731 	for ((x) = RB_MIN(name, head);					\
    732 	     (x) != NULL;						\
    733 	     (x) = name##_RB_NEXT(x))
    734 
    735 #define RB_FOREACH_SAFE(x, name, head, y)				\
    736 	for ((x) = RB_MIN(name, head);					\
    737 	    ((x) != NULL) && ((y) = name##_RB_NEXT(x), 1);		\
    738 	     (x) = (y))
    739 
    740 #define RB_FOREACH_REVERSE(x, name, head)				\
    741 	for ((x) = RB_MAX(name, head);					\
    742 	     (x) != NULL;						\
    743 	     (x) = name##_RB_PREV(x))
    744 
    745 #define RB_FOREACH_REVERSE_SAFE(x, name, head, y)			\
    746 	for ((x) = RB_MAX(name, head);					\
    747 	    ((x) != NULL) && ((y) = name##_RB_PREV(x), 1);		\
    748 	     (x) = (y))
    749 
    750 
    751 /*
    752  * Copyright (c) 2016 David Gwynne <dlg@openbsd.org>
    753  *
    754  * Permission to use, copy, modify, and distribute this software for any
    755  * purpose with or without fee is hereby granted, provided that the above
    756  * copyright notice and this permission notice appear in all copies.
    757  *
    758  * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
    759  * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
    760  * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
    761  * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
    762  * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
    763  * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
    764  * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
    765  */
    766 
    767 struct rb_type {
    768 	int		(*t_compare)(const void *, const void *);
    769 	void		(*t_augment)(void *);
    770 	unsigned int	  t_offset;	/* offset of rb_entry in type */
    771 };
    772 
    773 struct rb_tree {
    774 	struct rb_entry	*rbt_root;
    775 };
    776 
    777 struct rb_entry {
    778 	struct rb_entry	 *rbt_parent;
    779 	struct rb_entry	 *rbt_left;
    780 	struct rb_entry	 *rbt_right;
    781 	unsigned int	  rbt_color;
    782 };
    783 
    784 #define RBT_HEAD(_name, _type)						\
    785 struct _name {								\
    786 	struct rb_tree rbh_root;					\
    787 }
    788 
    789 #define RBT_ENTRY(_type)	struct rb_entry
    790 
    791 static inline void
    792 _rb_init(struct rb_tree *rbt)
    793 {
    794 	rbt->rbt_root = NULL;
    795 }
    796 
    797 static inline int
    798 _rb_empty(struct rb_tree *rbt)
    799 {
    800 	return (rbt->rbt_root == NULL);
    801 }
    802 
    803 void	*_rb_insert(const struct rb_type *, struct rb_tree *, void *);
    804 void	*_rb_remove(const struct rb_type *, struct rb_tree *, void *);
    805 void	*_rb_find(const struct rb_type *, struct rb_tree *, const void *);
    806 void	*_rb_nfind(const struct rb_type *, struct rb_tree *, const void *);
    807 void	*_rb_root(const struct rb_type *, struct rb_tree *);
    808 void	*_rb_min(const struct rb_type *, struct rb_tree *);
    809 void	*_rb_max(const struct rb_type *, struct rb_tree *);
    810 void	*_rb_next(const struct rb_type *, void *);
    811 void	*_rb_prev(const struct rb_type *, void *);
    812 void	*_rb_left(const struct rb_type *, void *);
    813 void	*_rb_right(const struct rb_type *, void *);
    814 void	*_rb_parent(const struct rb_type *, void *);
    815 void	 _rb_set_left(const struct rb_type *, void *, void *);
    816 void	 _rb_set_right(const struct rb_type *, void *, void *);
    817 void	 _rb_set_parent(const struct rb_type *, void *, void *);
    818 void	 _rb_poison(const struct rb_type *, void *, unsigned long);
    819 int	 _rb_check(const struct rb_type *, void *, unsigned long);
    820 
    821 #define RBT_INITIALIZER(_head)	{ { NULL } }
    822 
    823 #define RBT_PROTOTYPE(_name, _type, _field, _cmp)			\
    824 extern const struct rb_type *const _name##_RBT_TYPE;			\
    825 									\
    826 __unused static inline void						\
    827 _name##_RBT_INIT(struct _name *head)					\
    828 {									\
    829 	_rb_init(&head->rbh_root);					\
    830 }									\
    831 									\
    832 __unused static inline struct _type *					\
    833 _name##_RBT_INSERT(struct _name *head, struct _type *elm)		\
    834 {									\
    835 	return _rb_insert(_name##_RBT_TYPE, &head->rbh_root, elm);	\
    836 }									\
    837 									\
    838 __unused static inline struct _type *					\
    839 _name##_RBT_REMOVE(struct _name *head, struct _type *elm)		\
    840 {									\
    841 	return _rb_remove(_name##_RBT_TYPE, &head->rbh_root, elm);	\
    842 }									\
    843 									\
    844 __unused static inline struct _type *					\
    845 _name##_RBT_FIND(struct _name *head, const struct _type *key)		\
    846 {									\
    847 	return _rb_find(_name##_RBT_TYPE, &head->rbh_root, key);	\
    848 }									\
    849 									\
    850 __unused static inline struct _type *					\
    851 _name##_RBT_NFIND(struct _name *head, const struct _type *key)		\
    852 {									\
    853 	return _rb_nfind(_name##_RBT_TYPE, &head->rbh_root, key);	\
    854 }									\
    855 									\
    856 __unused static inline struct _type *					\
    857 _name##_RBT_ROOT(struct _name *head)					\
    858 {									\
    859 	return _rb_root(_name##_RBT_TYPE, &head->rbh_root);		\
    860 }									\
    861 									\
    862 __unused static inline int						\
    863 _name##_RBT_EMPTY(struct _name *head)					\
    864 {									\
    865 	return _rb_empty(&head->rbh_root);				\
    866 }									\
    867 									\
    868 __unused static inline struct _type *					\
    869 _name##_RBT_MIN(struct _name *head)					\
    870 {									\
    871 	return _rb_min(_name##_RBT_TYPE, &head->rbh_root);		\
    872 }									\
    873 									\
    874 __unused static inline struct _type *					\
    875 _name##_RBT_MAX(struct _name *head)					\
    876 {									\
    877 	return _rb_max(_name##_RBT_TYPE, &head->rbh_root);		\
    878 }									\
    879 									\
    880 __unused static inline struct _type *					\
    881 _name##_RBT_NEXT(struct _type *elm)					\
    882 {									\
    883 	return _rb_next(_name##_RBT_TYPE, elm);				\
    884 }									\
    885 									\
    886 __unused static inline struct _type *					\
    887 _name##_RBT_PREV(struct _type *elm)					\
    888 {									\
    889 	return _rb_prev(_name##_RBT_TYPE, elm);				\
    890 }									\
    891 									\
    892 __unused static inline struct _type *					\
    893 _name##_RBT_LEFT(struct _type *elm)					\
    894 {									\
    895 	return _rb_left(_name##_RBT_TYPE, elm);				\
    896 }									\
    897 									\
    898 __unused static inline struct _type *					\
    899 _name##_RBT_RIGHT(struct _type *elm)					\
    900 {									\
    901 	return _rb_right(_name##_RBT_TYPE, elm);			\
    902 }									\
    903 									\
    904 __unused static inline struct _type *					\
    905 _name##_RBT_PARENT(struct _type *elm)					\
    906 {									\
    907 	return _rb_parent(_name##_RBT_TYPE, elm);			\
    908 }									\
    909 									\
    910 __unused static inline void						\
    911 _name##_RBT_SET_LEFT(struct _type *elm, struct _type *left)		\
    912 {									\
    913 	return _rb_set_left(_name##_RBT_TYPE, elm, left);		\
    914 }									\
    915 									\
    916 __unused static inline void						\
    917 _name##_RBT_SET_RIGHT(struct _type *elm, struct _type *right)		\
    918 {									\
    919 	return _rb_set_right(_name##_RBT_TYPE, elm, right);		\
    920 }									\
    921 									\
    922 __unused static inline void						\
    923 _name##_RBT_SET_PARENT(struct _type *elm, struct _type *parent)		\
    924 {									\
    925 	return _rb_set_parent(_name##_RBT_TYPE, elm, parent);		\
    926 }									\
    927 									\
    928 __unused static inline void						\
    929 _name##_RBT_POISON(struct _type *elm, unsigned long poison)		\
    930 {									\
    931 	return _rb_poison(_name##_RBT_TYPE, elm, poison);		\
    932 }									\
    933 									\
    934 __unused static inline int						\
    935 _name##_RBT_CHECK(struct _type *elm, unsigned long poison)		\
    936 {									\
    937 	return _rb_check(_name##_RBT_TYPE, elm, poison);		\
    938 }
    939 
    940 #define RBT_GENERATE_INTERNAL(_name, _type, _field, _cmp, _aug)		\
    941 static int								\
    942 _name##_RBT_COMPARE(const void *lptr, const void *rptr)			\
    943 {									\
    944 	const struct _type *l = lptr, *r = rptr;			\
    945 	return _cmp(l, r);						\
    946 }									\
    947 static const struct rb_type _name##_RBT_INFO = {			\
    948 	_name##_RBT_COMPARE,						\
    949 	_aug,								\
    950 	offsetof(struct _type, _field),					\
    951 };									\
    952 const struct rb_type *const _name##_RBT_TYPE = &_name##_RBT_INFO
    953 
    954 #define RBT_GENERATE_AUGMENT(_name, _type, _field, _cmp, _aug)		\
    955 static void								\
    956 _name##_RBT_AUGMENT(void *ptr)						\
    957 {									\
    958 	struct _type *p = ptr;						\
    959 	return _aug(p);							\
    960 }									\
    961 RBT_GENERATE_INTERNAL(_name, _type, _field, _cmp, _name##_RBT_AUGMENT)
    962 
    963 #define RBT_GENERATE(_name, _type, _field, _cmp)			\
    964     RBT_GENERATE_INTERNAL(_name, _type, _field, _cmp, NULL)
    965 
    966 #define RBT_INIT(_name, _head)		_name##_RBT_INIT(_head)
    967 #define RBT_INSERT(_name, _head, _elm)	_name##_RBT_INSERT(_head, _elm)
    968 #define RBT_REMOVE(_name, _head, _elm)	_name##_RBT_REMOVE(_head, _elm)
    969 #define RBT_FIND(_name, _head, _key)	_name##_RBT_FIND(_head, _key)
    970 #define RBT_NFIND(_name, _head, _key)	_name##_RBT_NFIND(_head, _key)
    971 #define RBT_ROOT(_name, _head)		_name##_RBT_ROOT(_head)
    972 #define RBT_EMPTY(_name, _head)		_name##_RBT_EMPTY(_head)
    973 #define RBT_MIN(_name, _head)		_name##_RBT_MIN(_head)
    974 #define RBT_MAX(_name, _head)		_name##_RBT_MAX(_head)
    975 #define RBT_NEXT(_name, _elm)		_name##_RBT_NEXT(_elm)
    976 #define RBT_PREV(_name, _elm)		_name##_RBT_PREV(_elm)
    977 #define RBT_LEFT(_name, _elm)		_name##_RBT_LEFT(_elm)
    978 #define RBT_RIGHT(_name, _elm)		_name##_RBT_RIGHT(_elm)
    979 #define RBT_PARENT(_name, _elm)		_name##_RBT_PARENT(_elm)
    980 #define RBT_SET_LEFT(_name, _elm, _l)	_name##_RBT_SET_LEFT(_elm, _l)
    981 #define RBT_SET_RIGHT(_name, _elm, _r)	_name##_RBT_SET_RIGHT(_elm, _r)
    982 #define RBT_SET_PARENT(_name, _elm, _p)	_name##_RBT_SET_PARENT(_elm, _p)
    983 #define RBT_POISON(_name, _elm, _p)	_name##_RBT_POISON(_elm, _p)
    984 #define RBT_CHECK(_name, _elm, _p)	_name##_RBT_CHECK(_elm, _p)
    985 
    986 #define RBT_FOREACH(_e, _name, _head)					\
    987 	for ((_e) = RBT_MIN(_name, (_head));				\
    988 	     (_e) != NULL;						\
    989 	     (_e) = RBT_NEXT(_name, (_e)))
    990 
    991 #define RBT_FOREACH_SAFE(_e, _name, _head, _n)				\
    992 	for ((_e) = RBT_MIN(_name, (_head));				\
    993 	     (_e) != NULL && ((_n) = RBT_NEXT(_name, (_e)), 1);	\
    994 	     (_e) = (_n))
    995 
    996 #define RBT_FOREACH_REVERSE(_e, _name, _head)				\
    997 	for ((_e) = RBT_MAX(_name, (_head));				\
    998 	     (_e) != NULL;						\
    999 	     (_e) = RBT_PREV(_name, (_e)))
   1000 
   1001 #define RBT_FOREACH_REVERSE_SAFE(_e, _name, _head, _n)			\
   1002 	for ((_e) = RBT_MAX(_name, (_head));				\
   1003 	     (_e) != NULL && ((_n) = RBT_PREV(_name, (_e)), 1);	\
   1004 	     (_e) = (_n))
   1005 
   1006 #endif	/* _SYS_TREE_H_ */