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 structure 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:
- Every search path from the root to a leaf consists of the same number of black nodes.
- Each red node (except for the root) has a black parent.
- 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 entries 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 array 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 individual 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 returns 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 counterparts, 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 respectively. The head pointer is not required. The pointer to the
node from where to resume the traversal should be passed as their last
argument, 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 entries, some ARB-specific additional macros are defined.
The
ARB_FULL
()
macro returns a boolean indicating whether the current number of tree
entries 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
()
returns NULL
if the element was inserted in the tree
successfully, otherwise they return a pointer to the element with the
colliding key.
Accordingly,
ARB_REMOVE
()
returns the pointer to the removed element otherwise 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 modify embedded object values
or the free list.
SEE ALSO
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.