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ARB(3)		       FreeBSD Library Functions Manual			ARB(3)

NAME
     ARB_PROTOTYPE, ARB_PROTOTYPE_STATIC, ARB_PROTOTYPE_INSERT,
     ARB_PROTOTYPE_INSERT_COLOR, ARB_PROTOTYPE_REMOVE,
     ARB_PROTOTYPE_REMOVE_COLOR, ARB_PROTOTYPE_FIND, ARB_PROTOTYPE_NFIND,
     ARB_PROTOTYPE_NEXT, ARB_PROTOTYPE_PREV, ARB_PROTOTYPE_MINMAX,
     ARB_PROTOTYPE_REINSERT, ARB_GENERATE, ARB_GENERATE_STATIC,
     ARB_GENERATE_INSERT, ARB_GENERATE_INSERT_COLOR, ARB_GENERATE_REMOVE,
     ARB_GENERATE_REMOVE_COLOR,	ARB_GENERATE_FIND, ARB_GENERATE_NFIND,
     ARB_GENERATE_NEXT,	ARB_GENERATE_PREV, ARB_GENERATE_MINMAX,
     ARB_GENERATE_REINSERT, ARB8_ENTRY,	ARB16_ENTRY, ARB32_ENTRY, ARB8_HEAD,
     ARB16_HEAD, ARB32_HEAD, ARB_ALLOCSIZE, ARB_INITIALIZER, ARB_ROOT,
     ARB_EMPTY,	ARB_FULL, ARB_CURNODES,	ARB_MAXNODES, ARB_NEXT,	ARB_PREV,
     ARB_MIN, ARB_MAX, ARB_FIND, ARB_NFIND, ARB_LEFT, ARB_LEFTIDX, ARB_RIGHT,
     ARB_RIGHTIDX, ARB_PARENT, ARB_PARENTIDX, ARB_GETFREE, ARB_FREEIDX,
     ARB_FOREACH, ARB_FOREACH_FROM, ARB_FOREACH_SAFE, ARB_FOREACH_REVERSE,
     ARB_FOREACH_REVERSE_FROM, ARB_FOREACH_REVERSE_SAFE, ARB_INIT, ARB_INSERT,
     ARB_REMOVE, ARB_REINSERT, ARB_RESET_TREE -- array-based red-black trees

SYNOPSIS
     #include <sys/arb.h>

     ARB_PROTOTYPE(NAME, TYPE, FIELD, CMP);

     ARB_PROTOTYPE_STATIC(NAME,	TYPE, FIELD, CMP);

     ARB_PROTOTYPE_INSERT(NAME,	TYPE, ATTR);

     ARB_PROTOTYPE_INSERT_COLOR(NAME, TYPE, ATTR);

     ARB_PROTOTYPE_REMOVE(NAME,	TYPE, ATTR);

     ARB_PROTOTYPE_REMOVE_COLOR(NAME, TYPE, ATTR);

     ARB_PROTOTYPE_FIND(NAME, TYPE, ATTR);

     ARB_PROTOTYPE_NFIND(NAME, TYPE, ATTR);

     ARB_PROTOTYPE_NEXT(NAME, TYPE, ATTR);

     ARB_PROTOTYPE_PREV(NAME, TYPE, ATTR);

     ARB_PROTOTYPE_MINMAX(NAME,	TYPE, ATTR);

     ARB_PROTOTYPE_REINSERT(NAME, TYPE,	ATTR);

     ARB_GENERATE(NAME,	TYPE, FIELD, CMP);

     ARB_GENERATE_STATIC(NAME, TYPE, FIELD, CMP);

     ARB_GENERATE_INSERT(NAME, TYPE, FIELD, CMP, ATTR);

     ARB_GENERATE_INSERT_COLOR(NAME, TYPE, FIELD, ATTR);

     ARB_GENERATE_REMOVE(NAME, TYPE, FIELD, ATTR);

     ARB_GENERATE_REMOVE_COLOR(NAME, TYPE, FIELD, ATTR);

     ARB_GENERATE_FIND(NAME, TYPE, FIELD, CMP, ATTR);

     ARB_GENERATE_NFIND(NAME, TYPE, FIELD, CMP,	ATTR);

     ARB_GENERATE_NEXT(NAME, TYPE, FIELD, ATTR);

     ARB_GENERATE_PREV(NAME, TYPE, FIELD, ATTR);

     ARB_GENERATE_MINMAX(NAME, TYPE, FIELD, ATTR);

     ARB_GENERATE_REINSERT(NAME, TYPE, FIELD, CMP, ATTR);

     ARB<8|16|32>_ENTRY();

     ARB<8|16|32>_HEAD(HEADNAME, TYPE);

     size_t
     ARB_ALLOCSIZE(ARB_HEAD *head, int_8|16|32__t maxnodes, struct TYPE	*elm);

     ARB_INITIALIZER(ARB_HEAD *head, int_8|16|32__t maxnodes);

     struct TYPE *
     ARB_ROOT(ARB_HEAD *head);

     bool
     ARB_EMPTY(ARB_HEAD	*head);

     bool
     ARB_FULL(ARB_HEAD *head);

     int_8|16|32__t
     ARB_CURNODES(ARB_HEAD *head);

     int_8|16|32__t
     ARB_MAXNODES(ARB_HEAD *head);

     struct TYPE *
     ARB_NEXT(NAME, ARB_HEAD *head, struct TYPE	*elm);

     struct TYPE *
     ARB_PREV(NAME, ARB_HEAD *head, struct TYPE	*elm);

     struct TYPE *
     ARB_MIN(NAME, ARB_HEAD *head);

     struct TYPE *
     ARB_MAX(NAME, ARB_HEAD *head);

     struct TYPE *
     ARB_FIND(NAME, ARB_HEAD *head, struct TYPE	*elm);

     struct TYPE *
     ARB_NFIND(NAME, ARB_HEAD *head, struct TYPE *elm);

     struct TYPE *
     ARB_LEFT(struct TYPE *elm,	ARB_ENTRY NAME);

     int_8|16|32__t
     ARB_LEFTIDX(struct	TYPE *elm, ARB_ENTRY NAME);

     struct TYPE *
     ARB_RIGHT(struct TYPE *elm, ARB_ENTRY NAME);

     int_8|16|32__t
     ARB_RIGHTIDX(struct TYPE *elm, ARB_ENTRY NAME);

     struct TYPE *
     ARB_PARENT(struct TYPE *elm, ARB_ENTRY NAME);

     int_8|16|32__t
     ARB_PARENTIDX(struct TYPE *elm, ARB_ENTRY NAME);

     struct TYPE *
     ARB_GETFREE(ARB_HEAD *head, FIELD);

     int_8|16|32__t
     ARB_FREEIDX(ARB_HEAD *head);

     ARB_FOREACH(VARNAME, NAME,	ARB_HEAD *head);

     ARB_FOREACH_FROM(VARNAME, NAME, POS_VARNAME);

     ARB_FOREACH_SAFE(VARNAME, NAME, ARB_HEAD *head, TEMP_VARNAME);

     ARB_FOREACH_REVERSE(VARNAME, NAME,	ARB_HEAD *head);

     ARB_FOREACH_REVERSE_FROM(VARNAME, NAME, POS_VARNAME);

     ARB_FOREACH_REVERSE_SAFE(VARNAME, NAME, ARB_HEAD *head, TEMP_VARNAME);

     void
     ARB_INIT(struct TYPE *elm,	FIELD, ARB_HEAD	*head,
	 int_8|16|32__t	maxnodes);

     struct TYPE *
     ARB_INSERT(NAME, ARB_HEAD *head, struct TYPE *elm);

     struct TYPE *
     ARB_REMOVE(NAME, ARB_HEAD *head, struct TYPE *elm);

     struct TYPE *
     ARB_REINSERT(NAME,	ARB_HEAD *head,	struct TYPE *elm);

     void
     ARB_RESET_TREE(ARB_HEAD *head, NAME, int_8|16|32__t maxnodes);

DESCRIPTION
     These macros define data structures for and array-based red-black trees.
     They use a	single,	continuous chunk of memory, and	are useful e.g., when
     the tree needs to be transferred between userspace	and kernel.

     In	the macro definitions, TYPE is the name	tag of a user defined struc-
     ture that must contain a field of type ARB_ENTRY, named ENTRYNAME.	 The
     argument HEADNAME is the name tag of a user defined structure that	must
     be	declared using the ARB_HEAD() macro.  The argument NAME	has to be a
     unique name prefix	for every tree that is defined.

     The function prototypes are declared with ARB_PROTOTYPE(),	or
     ARB_PROTOTYPE_STATIC().  The function bodies are generated	with
     ARB_GENERATE(), or	ARB_GENERATE_STATIC().	See the	examples below for
     further explanation of how	these macros are used.

     A red-black tree is a binary search tree with the node color as an	extra
     attribute.	 It fulfills a set of conditions:

	   1.	Every search path from the root	to a leaf consists of the same
		number of black	nodes.

	   2.	Each red node (except for the root) has	a black	parent.

	   3.	Each leaf node is black.

     Every operation on	a red-black tree is bounded as O(lg n).	 The maximum
     height of a red-black tree	is 2lg(n + 1).

     ARB_*() trees require entries to be allocated as an array,	and uses array
     indices to	link entries together.	The maximum number of ARB_*() tree en-
     tries is therefore	constrained by the minimum of array size and choice of
     signed integer data type used to store array indices.  Use
     ARB_ALLOCSIZE() to	compute	the size of memory chunk to allocate.

     A red-black tree is headed	by a structure defined by the ARB_HEAD()
     macro.  A structure is declared with either of the	following:

	   ARB<8|16|32>_HEAD(HEADNAME, TYPE) head;

     where HEADNAME is the name	of the structure to be defined,	and struct
     TYPE is the type of the elements to be inserted into the tree.

     The ARB_HEAD() variant includes a suffix denoting the signed integer data
     type size (in bits) used to store array indices.  For example,
     ARB_HEAD8() creates a red-black tree head strucutre with 8-bit signed ar-
     ray indices capable of indexing up	to 128 entries.

     The ARB_ENTRY() macro declares a structure	that allows elements to	be
     connected in the tree.  Similarly to the ARB<8|16|32>_HEAD() macro, the
     ARB_ENTRY() variant includes a suffix denoting the	signed integer data
     type size (in bits) used to store array indices.  Entries should use the
     same number of bits as the	tree head structure they will be linked	into.

     In	order to use the functions that	manipulate the tree structure, their
     prototypes	need to	be declared with the ARB_PROTOTYPE() or
     ARB_PROTOTYPE_STATIC() macro, where NAME is a unique identifier for this
     particular	tree.  The TYPE	argument is the	type of	the structure that is
     being managed by the tree.	 The FIELD argument is the name	of the element
     defined by	ARB_ENTRY().  Individual prototypes can	be declared with
     ARB_PROTOTYPE_INSERT(), ARB_PROTOTYPE_INSERT_COLOR(),
     ARB_PROTOTYPE_REMOVE(), ARB_PROTOTYPE_REMOVE_COLOR(),
     ARB_PROTOTYPE_FIND(), ARB_PROTOTYPE_NFIND(), ARB_PROTOTYPE_NEXT(),
     ARB_PROTOTYPE_PREV(), ARB_PROTOTYPE_MINMAX(), and
     ARB_PROTOTYPE_REINSERT() in case not all functions	are required.  The in-
     dividual prototype	macros expect NAME, TYPE, and ATTR arguments.  The
     ATTR argument must	be empty for global functions or static	for static
     functions.

     The function bodies are generated with the	ARB_GENERATE() or
     ARB_GENERATE_STATIC() macro.  These macros	take the same arguments	as the
     ARB_PROTOTYPE() and ARB_PROTOTYPE_STATIC()	macros,	but should be used
     only once.	 As an alternative individual function bodies are generated
     with the ARB_GENERATE_INSERT(), ARB_GENERATE_INSERT_COLOR(),
     ARB_GENERATE_REMOVE(), ARB_GENERATE_REMOVE_COLOR(), ARB_GENERATE_FIND(),
     ARB_GENERATE_NFIND(), ARB_GENERATE_NEXT(),	ARB_GENERATE_PREV(),
     ARB_GENERATE_MINMAX(), and	ARB_GENERATE_REINSERT()	macros.

     Finally, the CMP argument is the name of a	function used to compare tree
     nodes with	each other.  The function takes	two arguments of type struct
     TYPE *.  If the first argument is smaller than the	second,	the function
     returns a value smaller than zero.	 If they are equal, the	function re-
     turns zero.  Otherwise, it	should return a	value greater than zero.  The
     compare function defines the order	of the tree elements.

     The ARB_INIT() macro initializes the tree referenced by head, with	the
     array length of maxnodes.

     The red-black tree	can also be initialized	statically by using the
     ARB_INITIALIZER() macro:

	   ARB<8|16|32>_HEAD(HEADNAME, TYPE) head = ARB_INITIALIZER(_head,
	   maxnodes);

     The ARB_INSERT() macro inserts the	new element elm	into the tree.

     The ARB_REMOVE() macro removes the	element	elm from the tree pointed by
     head.

     The ARB_FIND() and	ARB_NFIND() macros can be used to find a particular
     element in	the tree.

	   struct TYPE find, *res;
	   find.key = 30;
	   res = ARB_FIND(NAME,	head, &find);

     The ARB_ROOT(), ARB_MIN(),	ARB_MAX(), ARB_NEXT(), and ARB_PREV() macros
     can be used to traverse the tree:

	   for (np = ARB_MIN(NAME, &head); np != NULL; np = ARB_NEXT(NAME,
	   &head, np))

     Or, for simplicity, one can use the ARB_FOREACH() or
     ARB_FOREACH_REVERSE() macro:

	   ARB_FOREACH(np, NAME, head)

     The macros	ARB_FOREACH_SAFE() and ARB_FOREACH_REVERSE_SAFE() traverse the
     tree referenced by	head in	a forward or reverse direction respectively,
     assigning each element in turn to np.  However, unlike their unsafe coun-
     terparts, they permit both	the removal of np as well as freeing it	from
     within the	loop safely without interfering	with the traversal.

     Both ARB_FOREACH_FROM() and ARB_FOREACH_REVERSE_FROM() may	be used	to
     continue an interrupted traversal in a forward or reverse direction re-
     spectively.  The head pointer is not required.  The pointer to the	node
     from where	to resume the traversal	should be passed as their last argu-
     ment, and will be overwritten to provide safe traversal.

     The ARB_EMPTY() macro should be used to check whether a red-black tree is
     empty.

     Given that	ARB trees have an intrinsic upper bound	on the number of en-
     tries, some ARB-specific additional macros	are defined.  The ARB_FULL()
     macro returns a boolean indicating	whether	the current number of tree en-
     tries equals the tree's maximum.  The ARB_CURNODES() and ARB_MAXNODES()
     macros return the current and maximum number of entries respectively.
     The ARB_GETFREE() macro returns a pointer to the next free	entry in the
     array of entries, ready to	be linked into the tree.  The ARB_INSERT() re-
     turns NULL	if the element was inserted in the tree	successfully, other-
     wise they return a	pointer	to the element with the	colliding key.

     Accordingly, ARB_REMOVE() returns the pointer to the removed element oth-
     erwise they return	NULL to	indicate an error.

     The ARB_REINSERT()	macro updates the position of the element elm in the
     tree.  This must be called	if a member of a tree is modified in a way
     that affects comparison, such as by modifying a node's key.  This is a
     lower overhead alternative	to removing the	element	and reinserting	it
     again.

     The ARB_RESET_TREE() macro	discards the tree topology.  It	does not mod-
     ify embedded object values	or the free list.

SEE ALSO
     queue(3), tree(3)

HISTORY
     The ARB macros first appeared in FreeBSD 13.0.

AUTHORS
     The ARB macros were implemented by	Lawrence Stewart
     <lstewart@FreeBSD.org>, based on tree(3) macros written by
     Niels Provos.

FreeBSD	13.0		       October 14, 2019			  FreeBSD 13.0

NAME | SYNOPSIS | DESCRIPTION | SEE ALSO | HISTORY | AUTHORS

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