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 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:

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 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 structure 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
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.