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.Nm RB_FOREACH , .Nm RB_FOREACH ,
.Nm RB_FOREACH_FROM , .Nm RB_FOREACH_FROM ,
.Nm RB_FOREACH_SAFE , .Nm RB_FOREACH_SAFE ,
.Nm RB_FOREACH_REVERSE , .Nm RB_FOREACH_REVERSE ,
.Nm RB_FOREACH_REVERSE_FROM , .Nm RB_FOREACH_REVERSE_FROM ,
.Nm RB_FOREACH_REVERSE_SAFE , .Nm RB_FOREACH_REVERSE_SAFE ,
.Nm RB_INIT , .Nm RB_INIT ,
.Nm RB_INSERT , .Nm RB_INSERT ,
.Nm RB_REMOVE .Nm RB_REMOVE ,
.Nm ARB_PROTOTYPE ,
.Nm ARB_PROTOTYPE_STATIC ,
.Nm ARB_PROTOTYPE_INSERT ,
.Nm ARB_PROTOTYPE_INSERT_COLOR ,
.Nm ARB_PROTOTYPE_REMOVE ,
.Nm ARB_PROTOTYPE_REMOVE_COLOR ,
.Nm ARB_PROTOTYPE_FIND ,
.Nm ARB_PROTOTYPE_NFIND ,
.Nm ARB_PROTOTYPE_NEXT ,
.Nm ARB_PROTOTYPE_PREV ,
.Nm ARB_PROTOTYPE_MINMAX ,
.Nm ARB_GENERATE ,
.Nm ARB_GENERATE_STATIC ,
.Nm ARB_GENERATE_INSERT ,
.Nm ARB_GENERATE_INSERT_COLOR ,
.Nm ARB_GENERATE_REMOVE ,
.Nm ARB_GENERATE_REMOVE_COLOR ,
.Nm ARB_GENERATE_FIND ,
.Nm ARB_GENERATE_NFIND ,
.Nm ARB_GENERATE_NEXT ,
.Nm ARB_GENERATE_PREV ,
.Nm ARB_GENERATE_MINMAX ,
.Nm ARB8_ENTRY ,
.Nm ARB16_ENTRY ,
.Nm ARB32_ENTRY ,
.Nm ARB8_HEAD ,
.Nm ARB16_HEAD ,
.Nm ARB32_HEAD ,
.Nm ARB_INITIALIZER ,
.Nm ARB_ROOT ,
.Nm ARB_EMPTY ,
.Nm ARB_FULL ,
.Nm ARB_CURNODES ,
.Nm ARB_MAXNODES ,
.Nm ARB_NEXT ,
.Nm ARB_PREV ,
.Nm ARB_MIN ,
.Nm ARB_MAX ,
.Nm ARB_FIND ,
.Nm ARB_NFIND ,
.Nm ARB_LEFT ,
.Nm ARB_LEFTIDX ,
.Nm ARB_RIGHT ,
.Nm ARB_RIGHTIDX ,
.Nm ARB_PARENT ,
.Nm ARB_PARENTIDX ,
.Nm ARB_GETFREE ,
.Nm ARB_FREEIDX ,
.Nm ARB_FOREACH ,
.Nm ARB_FOREACH_FROM ,
.Nm ARB_FOREACH_SAFE ,
.Nm ARB_FOREACH_REVERSE ,
.Nm ARB_FOREACH_REVERSE_FROM ,
.Nm ARB_FOREACH_REVERSE_SAFE ,
.Nm ARB_INIT ,
.Nm ARB_INSERT ,
.Nm ARB_REMOVE
.Nd "implementations of splay and red-black trees" .Nd "implementations of splay and red-black trees"
.Sh SYNOPSIS .Sh SYNOPSIS
.In sys/tree.h .In sys/tree.h
.Fn SPLAY_PROTOTYPE NAME TYPE FIELD CMP .Fn SPLAY_PROTOTYPE NAME TYPE FIELD CMP
.Fn SPLAY_GENERATE NAME TYPE FIELD CMP .Fn SPLAY_GENERATE NAME TYPE FIELD CMP
.Fn SPLAY_ENTRY TYPE .Fn SPLAY_ENTRY TYPE
.Fn SPLAY_HEAD HEADNAME TYPE .Fn SPLAY_HEAD HEADNAME TYPE
.Ft "struct TYPE *" .Ft "struct TYPE *"
Show All 15 Lines
.Fn SPLAY_RIGHT "struct TYPE *elm" "SPLAY_ENTRY NAME" .Fn SPLAY_RIGHT "struct TYPE *elm" "SPLAY_ENTRY NAME"
.Fn SPLAY_FOREACH VARNAME NAME "SPLAY_HEAD *head" .Fn SPLAY_FOREACH VARNAME NAME "SPLAY_HEAD *head"
.Ft void .Ft void
.Fn SPLAY_INIT "SPLAY_HEAD *head" .Fn SPLAY_INIT "SPLAY_HEAD *head"
.Ft "struct TYPE *" .Ft "struct TYPE *"
.Fn SPLAY_INSERT NAME "SPLAY_HEAD *head" "struct TYPE *elm" .Fn SPLAY_INSERT NAME "SPLAY_HEAD *head" "struct TYPE *elm"
.Ft "struct TYPE *" .Ft "struct TYPE *"
.Fn SPLAY_REMOVE NAME "SPLAY_HEAD *head" "struct TYPE *elm" .Fn SPLAY_REMOVE NAME "SPLAY_HEAD *head" "struct TYPE *elm"
.Fn RB_PROTOTYPE NAME TYPE FIELD CMP .Fn (A)RB_PROTOTYPE NAME TYPE FIELD CMP
.Fn RB_PROTOTYPE_STATIC NAME TYPE FIELD CMP .Fn (A)RB_PROTOTYPE_STATIC NAME TYPE FIELD CMP
.Fn RB_PROTOTYPE_INSERT NAME TYPE ATTR .Fn (A)RB_PROTOTYPE_INSERT NAME TYPE ATTR
.Fn RB_PROTOTYPE_INSERT_COLOR NAME TYPE ATTR .Fn (A)RB_PROTOTYPE_INSERT_COLOR NAME TYPE ATTR
.Fn RB_PROTOTYPE_REMOVE NAME TYPE ATTR .Fn (A)RB_PROTOTYPE_REMOVE NAME TYPE ATTR
.Fn RB_PROTOTYPE_REMOVE_COLOR NAME TYPE ATTR .Fn (A)RB_PROTOTYPE_REMOVE_COLOR NAME TYPE ATTR
.Fn RB_PROTOTYPE_FIND NAME TYPE ATTR .Fn (A)RB_PROTOTYPE_FIND NAME TYPE ATTR
.Fn RB_PROTOTYPE_NFIND NAME TYPE ATTR .Fn (A)RB_PROTOTYPE_NFIND NAME TYPE ATTR
.Fn RB_PROTOTYPE_NEXT NAME TYPE ATTR .Fn (A)RB_PROTOTYPE_NEXT NAME TYPE ATTR
.Fn RB_PROTOTYPE_PREV NAME TYPE ATTR .Fn (A)RB_PROTOTYPE_PREV NAME TYPE ATTR
.Fn RB_PROTOTYPE_MINMAX NAME TYPE ATTR .Fn (A)RB_PROTOTYPE_MINMAX NAME TYPE ATTR
.Fn RB_GENERATE NAME TYPE FIELD CMP .Fn (A)RB_GENERATE NAME TYPE FIELD CMP
.Fn RB_GENERATE_STATIC NAME TYPE FIELD CMP .Fn (A)RB_GENERATE_STATIC NAME TYPE FIELD CMP
.Fn RB_GENERATE_INSERT NAME TYPE FIELD CMP ATTR .Fn (A)RB_GENERATE_INSERT NAME TYPE FIELD CMP ATTR
.Fn RB_GENERATE_INSERT_COLOR NAME TYPE FIELD ATTR .Fn (A)RB_GENERATE_INSERT_COLOR NAME TYPE FIELD ATTR
.Fn RB_GENERATE_REMOVE NAME TYPE FIELD ATTR .Fn (A)RB_GENERATE_REMOVE NAME TYPE FIELD ATTR
.Fn RB_GENERATE_REMOVE_COLOR NAME TYPE FIELD ATTR .Fn (A)RB_GENERATE_REMOVE_COLOR NAME TYPE FIELD ATTR
.Fn RB_GENERATE_FIND NAME TYPE FIELD CMP ATTR .Fn (A)RB_GENERATE_FIND NAME TYPE FIELD CMP ATTR
.Fn RB_GENERATE_NFIND NAME TYPE FIELD CMP ATTR .Fn (A)RB_GENERATE_NFIND NAME TYPE FIELD CMP ATTR
.Fn RB_GENERATE_NEXT NAME TYPE FIELD ATTR .Fn (A)RB_GENERATE_NEXT NAME TYPE FIELD ATTR
.Fn RB_GENERATE_PREV NAME TYPE FIELD ATTR .Fn (A)RB_GENERATE_PREV NAME TYPE FIELD ATTR
.Fn RB_GENERATE_MINMAX NAME TYPE FIELD ATTR .Fn (A)RB_GENERATE_MINMAX NAME TYPE FIELD ATTR
.Fn RB_ENTRY TYPE .Fn RB_ENTRY TYPE
.Fn RB_HEAD HEADNAME TYPE .Fn RB_HEAD HEADNAME TYPE
.Fn RB_INITIALIZER "RB_HEAD *head" .Fn RB_INITIALIZER "RB_HEAD *head"
.Fn ARB<8|16|32>_ENTRY
.Fn ARB<8|16|32>_HEAD HEADNAME TYPE
.Fn ARB_INITIALIZER "ARB_HEAD *head" "int<8|16|32>_t maxnodes"
.Ft "struct TYPE *" .Ft "struct TYPE *"
.Fn RB_ROOT "RB_HEAD *head" .Fn (A)RB_ROOT "(A)RB_HEAD *head"
.Ft "bool" .Ft "bool"
.Fn RB_EMPTY "RB_HEAD *head" .Fn (A)RB_EMPTY "(A)RB_HEAD *head"
.Ft "bool"
.Fn ARB_FULL "ARB_HEAD *head"
.Ft "int<8|16|32>_t"
.Fn ARB_CURNODES "ARB_HEAD *head"
.Ft "int<8|16|32>_t"
.Fn ARB_MAXNODES "ARB_HEAD *head"
.Ft "struct TYPE *" .Ft "struct TYPE *"
.Fn RB_NEXT NAME "RB_HEAD *head" "struct TYPE *elm" .Fn (A)RB_NEXT NAME "(A)RB_HEAD *head" "struct TYPE *elm"
.Ft "struct TYPE *" .Ft "struct TYPE *"
.Fn RB_PREV NAME "RB_HEAD *head" "struct TYPE *elm" .Fn (A)RB_PREV NAME "(A)RB_HEAD *head" "struct TYPE *elm"
.Ft "struct TYPE *" .Ft "struct TYPE *"
.Fn RB_MIN NAME "RB_HEAD *head" .Fn (A)RB_MIN NAME "(A)RB_HEAD *head"
.Ft "struct TYPE *" .Ft "struct TYPE *"
.Fn RB_MAX NAME "RB_HEAD *head" .Fn (A)RB_MAX NAME "(A)RB_HEAD *head"
.Ft "struct TYPE *" .Ft "struct TYPE *"
.Fn RB_FIND NAME "RB_HEAD *head" "struct TYPE *elm" .Fn (A)RB_FIND NAME "(A)RB_HEAD *head" "struct TYPE *elm"
.Ft "struct TYPE *" .Ft "struct TYPE *"
.Fn RB_NFIND NAME "RB_HEAD *head" "struct TYPE *elm" .Fn (A)RB_NFIND NAME "(A)RB_HEAD *head" "struct TYPE *elm"
.Ft "struct TYPE *" .Ft "struct TYPE *"
.Fn RB_LEFT "struct TYPE *elm" "RB_ENTRY NAME" .Fn (A)RB_LEFT "struct TYPE *elm" "(A)RB_ENTRY NAME"
.Ft "int<8|16|32>_t"
.Fn ARB_LEFTIDX "struct TYPE *elm" "ARB_ENTRY NAME"
.Ft "struct TYPE *" .Ft "struct TYPE *"
.Fn RB_RIGHT "struct TYPE *elm" "RB_ENTRY NAME" .Fn (A)RB_RIGHT "struct TYPE *elm" "(A)RB_ENTRY NAME"
.Ft "int<8|16|32>_t"
.Fn ARB_RIGHTIDX "struct TYPE *elm" "ARB_ENTRY NAME"
.Ft "struct TYPE *" .Ft "struct TYPE *"
.Fn RB_PARENT "struct TYPE *elm" "RB_ENTRY NAME" .Fn (A)RB_PARENT "struct TYPE *elm" "(A)RB_ENTRY NAME"
.Fn RB_FOREACH VARNAME NAME "RB_HEAD *head" .Ft "int<8|16|32>_t"
.Fn RB_FOREACH_FROM "VARNAME" "NAME" "POS_VARNAME" .Fn ARB_PARENTIDX "struct TYPE *elm" "ARB_ENTRY NAME"
.Fn RB_FOREACH_SAFE "VARNAME" "NAME" "RB_HEAD *head" "TEMP_VARNAME" .Ft "struct TYPE *"
.Fn RB_FOREACH_REVERSE VARNAME NAME "RB_HEAD *head" .Fn ARB_GETFREE "ARB_HEAD *head"
.Fn RB_FOREACH_REVERSE_FROM "VARNAME" "NAME" "POS_VARNAME" .Ft "int<8|16|32>_t"
.Fn RB_FOREACH_REVERSE_SAFE "VARNAME" "NAME" "RB_HEAD *head" "TEMP_VARNAME" .Fn ARB_FREEIDX "ARB_HEAD *head"
.Fn (A)RB_FOREACH VARNAME NAME "(A)RB_HEAD *head"
.Fn (A)RB_FOREACH_FROM "VARNAME" "NAME" "POS_VARNAME"
.Fn (A)RB_FOREACH_SAFE "VARNAME" "NAME" "(A)RB_HEAD *head" "TEMP_VARNAME"
.Fn (A)RB_FOREACH_REVERSE VARNAME NAME "(A)RB_HEAD *head"
.Fn (A)RB_FOREACH_REVERSE_FROM "VARNAME" "NAME" "POS_VARNAME"
.Fn (A)RB_FOREACH_REVERSE_SAFE "VARNAME" "NAME" "(A)RB_HEAD *head" "TEMP_VARNAME"
.Ft void .Ft void
.Fn RB_INIT "RB_HEAD *head" .Fn RB_INIT "RB_HEAD *head"
.Ft void
.Fn ARB_INIT "ARB_HEAD *head" "int<8|16|32>_t maxnodes"
.Ft "struct TYPE *" .Ft "struct TYPE *"
.Fn RB_INSERT NAME "RB_HEAD *head" "struct TYPE *elm" .Fn (A)RB_INSERT NAME "(A)RB_HEAD *head" "struct TYPE *elm"
.Ft "struct TYPE *" .Ft "struct TYPE *"
.Fn RB_REMOVE NAME "RB_HEAD *head" "struct TYPE *elm" .Fn (A)RB_REMOVE NAME "(A)RB_HEAD *head" "struct TYPE *elm"
.Sh DESCRIPTION .Sh DESCRIPTION
These macros define data structures for different types of trees: These macros define data structures for three different types of trees:
splay trees and red-black trees. splay trees (macros with the
.Dv SPLAY_
prefix), red-black trees (the
.Dv RB_
prefix), and array-based red-black trees (the
.Dv ARB_
prefix).
The last one use a single, continuous chunk of memory, and are useful
e.g., when the tree needs to be trasferred between userspace and kernel.
.Pp .Pp
In the macro definitions, In the macro definitions,
.Fa TYPE .Fa TYPE
is the name tag of a user defined structure that must contain a field of type is the name tag of a user defined structure that must contain a field of type
.Vt SPLAY_ENTRY , .Vt SPLAY_ENTRY ,
or or
.Vt RB_ENTRY , .Vt Po A Pc Ns RB_ENTRY ,
named named
.Fa ENTRYNAME . .Fa ENTRYNAME .
The argument The argument
.Fa HEADNAME .Fa HEADNAME
is the name tag of a user defined structure that must be declared is the name tag of a user defined structure that must be declared
using the macros using the macros
.Fn SPLAY_HEAD , .Fn SPLAY_HEAD ,
or or
.Fn RB_HEAD . .Fn (A)RB_HEAD .
The argument The argument
.Fa NAME .Fa NAME
has to be a unique name prefix for every tree that is defined. has to be a unique name prefix for every tree that is defined.
.Pp .Pp
The function prototypes are declared with The function prototypes are declared with
.Fn SPLAY_PROTOTYPE , .Fn SPLAY_PROTOTYPE ,
.Fn RB_PROTOTYPE , .Fn (A)RB_PROTOTYPE ,
or or
.Fn RB_PROTOTYPE_STATIC . .Fn (A)RB_PROTOTYPE_STATIC .
The function bodies are generated with The function bodies are generated with
.Fn SPLAY_GENERATE , .Fn SPLAY_GENERATE ,
.Fn RB_GENERATE , .Fn (A)RB_GENERATE ,
or or
.Fn RB_GENERATE_STATIC . .Fn (A)RB_GENERATE_STATIC .
See the examples below for further explanation of how these macros are used. See the examples below for further explanation of how these macros are used.
.Sh SPLAY TREES .Sh SPLAY TREES
A splay tree is a self-organizing data structure. A splay tree is a self-organizing data structure.
Every operation on the tree causes a splay to happen. Every operation on the tree causes a splay to happen.
The splay moves the requested The splay moves the requested
node to the root of the tree and partly rebalances it. node to the root of the tree and partly rebalances it.
.Pp .Pp
This has the benefit that request locality causes faster lookups as This has the benefit that request locality causes faster lookups as
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Each leaf node is black. Each leaf node is black.
.El .El
.Pp .Pp
Every operation on a red-black tree is bounded as Every operation on a red-black tree is bounded as
.Fn O "lg n" . .Fn O "lg n" .
The maximum height of a red-black tree is The maximum height of a red-black tree is
.Fn 2lg "n + 1" . .Fn 2lg "n + 1" .
.Pp .Pp
.Fn RB_*
variant trees link an arbitrary number of individually allocated entries
together using memory pointers.
.Fn ARB_*
variant trees require entries to be allocated as an array, and uses array
indices to link entries together.
The maximum number of
.Fn ARB_*
tree entries is therefore constrained by the minimum of array size and choice of
signed integer data type used to store array indices.
.Pp
A red-black tree is headed by a structure defined by the A red-black tree is headed by a structure defined by the
.Fn RB_HEAD .Fn (A)RB_HEAD
macro. macro.
A A
structure is declared as follows: structure is declared with either of the following:
.Bd -ragged -offset indent .Bd -ragged -offset indent
.Fn RB_HEAD HEADNAME TYPE .Fn RB_HEAD HEADNAME TYPE
.Va head ; .Va head ;
.Ed .Ed
.Bd -ragged -offset indent
.Fn ARB<8|16|32>_HEAD HEADNAME TYPE
.Va head ;
.Ed
.Pp .Pp
where where
.Fa HEADNAME .Fa HEADNAME
is the name of the structure to be defined, and struct is the name of the structure to be defined, and struct
.Fa TYPE .Fa TYPE
is the type of the elements to be inserted into the tree. is the type of the elements to be inserted into the tree.
.Pp .Pp
The The
.Fn RB_ENTRY .Fn ARB_HEAD
variant includes a suffix denoting the signed integer data type size
.Pq in bits
used to store array indices.
For example,
.Fn ARB_HEAD8
creates a red-black tree head strucutre with 8-bit signed array indices capable
of indexing up to 128 entries.
.Pp
The
.Fn (A)RB_ENTRY
macro declares a structure that allows elements to be connected in the tree. macro declares a structure that allows elements to be connected in the tree.
Similarly to the
.Fn ARB<8|16|32>_HEAD
macro, the
.Fn ARB_ENTRY
variant includes a suffix denoting the signed integer data type size
.Pq 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.
.Pp .Pp
In order to use the functions that manipulate the tree structure, In order to use the functions that manipulate the tree structure,
their prototypes need to be declared with the their prototypes need to be declared with the
.Fn RB_PROTOTYPE .Fn (A)RB_PROTOTYPE
or or
.Fn RB_PROTOTYPE_STATIC .Fn (A)RB_PROTOTYPE_STATIC
macro, macro,
where where
.Fa NAME .Fa NAME
is a unique identifier for this particular tree. is a unique identifier for this particular tree.
The The
.Fa TYPE .Fa TYPE
argument is the type of the structure that is being managed argument is the type of the structure that is being managed
by the tree. by the tree.
The The
.Fa FIELD .Fa FIELD
argument is the name of the element defined by argument is the name of the element defined by
.Fn RB_ENTRY . .Fn (A)RB_ENTRY .
Individual prototypes can be declared with Individual prototypes can be declared with
.Fn RB_PROTOTYPE_INSERT , .Fn (A)RB_PROTOTYPE_INSERT ,
.Fn RB_PROTOTYPE_INSERT_COLOR , .Fn (A)RB_PROTOTYPE_INSERT_COLOR ,
.Fn RB_PROTOTYPE_REMOVE , .Fn (A)RB_PROTOTYPE_REMOVE ,
.Fn RB_PROTOTYPE_REMOVE_COLOR , .Fn (A)RB_PROTOTYPE_REMOVE_COLOR ,
.Fn RB_PROTOTYPE_FIND , .Fn (A)RB_PROTOTYPE_FIND ,
.Fn RB_PROTOTYPE_NFIND , .Fn (A)RB_PROTOTYPE_NFIND ,
.Fn RB_PROTOTYPE_NEXT , .Fn (A)RB_PROTOTYPE_NEXT ,
.Fn RB_PROTOTYPE_PREV , .Fn (A)RB_PROTOTYPE_PREV ,
and and
.Fn RB_PROTOTYPE_MINMAX .Fn (A)RB_PROTOTYPE_MINMAX
in case not all functions are required. in case not all functions are required.
The individual prototype macros expect The individual prototype macros expect
.Fa NAME , .Fa NAME ,
.Fa TYPE , .Fa TYPE ,
and and
.Fa ATTR .Fa ATTR
arguments. arguments.
The The
.Fa ATTR .Fa ATTR
argument must be empty for global functions or argument must be empty for global functions or
.Fa static .Fa static
for static functions. for static functions.
.Pp .Pp
The function bodies are generated with the The function bodies are generated with the
.Fn RB_GENERATE .Fn (A)RB_GENERATE
or or
.Fn RB_GENERATE_STATIC .Fn (A)RB_GENERATE_STATIC
macro. macro.
These macros take the same arguments as the These macros take the same arguments as the
.Fn RB_PROTOTYPE .Fn (A)RB_PROTOTYPE
and and
.Fn RB_PROTOTYPE_STATIC .Fn (A)RB_PROTOTYPE_STATIC
macros, but should be used only once. macros, but should be used only once.
As an alternative individual function bodies are generated with the As an alternative individual function bodies are generated with the
.Fn RB_GENERATE_INSERT , .Fn (A)RB_GENERATE_INSERT ,
.Fn RB_GENERATE_INSERT_COLOR , .Fn (A)RB_GENERATE_INSERT_COLOR ,
.Fn RB_GENERATE_REMOVE , .Fn (A)RB_GENERATE_REMOVE ,
.Fn RB_GENERATE_REMOVE_COLOR , .Fn (A)RB_GENERATE_REMOVE_COLOR ,
.Fn RB_GENERATE_FIND , .Fn (A)RB_GENERATE_FIND ,
.Fn RB_GENERATE_NFIND , .Fn (A)RB_GENERATE_NFIND ,
.Fn RB_GENERATE_NEXT , .Fn (A)RB_GENERATE_NEXT ,
.Fn RB_GENERATE_PREV , .Fn (A)RB_GENERATE_PREV ,
and and
.Fn RB_GENERATE_MINMAX .Fn (A)RB_GENERATE_MINMAX
macros. macros.
.Pp .Pp
Finally, Finally,
the the
.Fa CMP .Fa CMP
argument is the name of a function used to compare tree nodes argument is the name of a function used to compare tree nodes
with each other. with each other.
The function takes two arguments of type The function takes two arguments of type
.Vt "struct TYPE *" . .Vt "struct TYPE *" .
If the first argument is smaller than the second, the function returns a If the first argument is smaller than the second, the function returns a
value smaller than zero. value smaller than zero.
If they are equal, the function returns zero. If they are equal, the function returns zero.
Otherwise, it should return a value greater than zero. Otherwise, it should return a value greater than zero.
The compare The compare
function defines the order of the tree elements. function defines the order of the tree elements.
.Pp .Pp
The The
.Fn RB_INIT .Fn (A)RB_INIT
macro initializes the tree referenced by macro initializes the tree referenced by
.Fa head . .Fa head ,
with the
.Fn ARB_INIT
variant also taking the array length
.Fa maxnodes .
.Pp .Pp
The red-black tree can also be initialized statically by using the The red-black tree can also be initialized statically by using the
.Fn RB_INITIALIZER .Fn (A)RB_INITIALIZER
macro like this: macro like either:
.Bd -ragged -offset indent .Bd -ragged -offset indent
.Fn RB_HEAD HEADNAME TYPE .Fn RB_HEAD HEADNAME TYPE
.Va head .Va head
= =
.Fn RB_INITIALIZER &head ; .Fn RB_INITIALIZER &head ;
.Ed .Ed
.Bd -ragged -offset indent
.Fn ARB<8|16|32>_HEAD HEADNAME TYPE
.Va head
=
.Fn ARB_INITIALIZER &head maxnodes ;
.Ed
.Pp .Pp
The The
.Fn RB_INSERT .Fn (A)RB_INSERT
macro inserts the new element macro inserts the new element
.Fa elm .Fa elm
into the tree. into the tree.
.Pp .Pp
The The
.Fn RB_REMOVE .Fn (A)RB_REMOVE
macro removes the element macro removes the element
.Fa elm .Fa elm
from the tree pointed by from the tree pointed by
.Fa head . .Fa head .
.Pp .Pp
The The
.Fn RB_FIND .Fn (A)RB_FIND
and and
.Fn RB_NFIND .Fn (A)RB_NFIND
macros can be used to find a particular element in the tree. macros can be used to find a particular element in the tree.
.Bd -literal -offset indent .Bd -literal -offset indent
struct TYPE find, *res; struct TYPE find, *res;
find.key = 30; find.key = 30;
res = RB_FIND(NAME, head, &find); res = RB_FIND(NAME, head, &find);
.Ed .Ed
.Pp .Pp
The The
.Fn RB_ROOT , .Fn (A)RB_ROOT ,
.Fn RB_MIN , .Fn (A)RB_MIN ,
.Fn RB_MAX , .Fn (A)RB_MAX ,
.Fn RB_NEXT , .Fn (A)RB_NEXT ,
and and
.Fn RB_PREV .Fn (A)RB_PREV
macros can be used to traverse the tree: macros can be used to traverse the tree:
.Pp .Pp
.Dl "for (np = RB_MIN(NAME, &head); np != NULL; np = RB_NEXT(NAME, &head, np))" .Dl "for (np = RB_MIN(NAME, &head); np != NULL; np = RB_NEXT(NAME, &head, np))"
.Pp .Pp
Or, for simplicity, one can use the Or, for simplicity, one can use the
.Fn RB_FOREACH .Fn (A)RB_FOREACH
or or
.Fn RB_FOREACH_REVERSE .Fn (A)RB_FOREACH_REVERSE
macro: macro:
.Bd -ragged -offset indent .Bd -ragged -offset indent
.Fn RB_FOREACH np NAME head .Fn RB_FOREACH np NAME head
.Ed .Ed
.Pp .Pp
The macros The macros
.Fn RB_FOREACH_SAFE .Fn (A)RB_FOREACH_SAFE
and and
.Fn RB_FOREACH_REVERSE_SAFE .Fn (A)RB_FOREACH_REVERSE_SAFE
traverse the tree referenced by head traverse the tree referenced by head
in a forward or reverse direction respectively, in a forward or reverse direction respectively,
assigning each element in turn to np. assigning each element in turn to np.
However, unlike their unsafe counterparts, However, unlike their unsafe counterparts,
they permit both the removal of np they permit both the removal of np
as well as freeing it from within the loop safely as well as freeing it from within the loop safely
without interfering with the traversal. without interfering with the traversal.
.Pp .Pp
Both Both
.Fn RB_FOREACH_FROM .Fn (A)RB_FOREACH_FROM
and and
.Fn RB_FOREACH_REVERSE_FROM .Fn (A)RB_FOREACH_REVERSE_FROM
may be used to continue an interrupted traversal may be used to continue an interrupted traversal
in a forward or reverse direction respectively. in a forward or reverse direction respectively.
The head pointer is not required. The head pointer is not required.
The pointer to the node from where to resume the traversal The pointer to the node from where to resume the traversal
should be passed as their last argument, should be passed as their last argument,
and will be overwritten to provide safe traversal. and will be overwritten to provide safe traversal.
.Pp .Pp
The The
.Fn RB_EMPTY .Fn (A)RB_EMPTY
macro should be used to check whether a red-black tree is empty. macro should be used to check whether a red-black tree is empty.
.Pp
Given that ARB trees have an intrinsic upper bound on the number of entries,
some ARB-specific additional macros are defined.
The
.Fn ARB_FULL
macro returns a boolean indicating whether the current number of tree entries
equals the tree's maximum.
The
.Fn ARB_CURNODES
and
.Fn ARB_MAXNODES
macros return the current and maximum number of entries respectively.
The
.Fn ARB_GETFREE
macro returns a pointer to the next free entry in the array of entries, ready to
be linked into the tree.
.Sh EXAMPLES .Sh EXAMPLES
The following example demonstrates how to declare a red-black tree The following example demonstrates how to declare a red-black tree
holding integers. holding integers.
Values are inserted into it and the contents of the tree are printed Values are inserted into it and the contents of the tree are printed
in order. in order.
Lastly, the internal structure of the tree is printed. Lastly, the internal structure of the tree is printed.
.Bd -literal -offset 3n .Bd -literal -offset 3n
#include <sys/tree.h> #include <sys/tree.h>
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for (var = SPLAY_MIN(NAME, head); var != NULL; var = nxt) { for (var = SPLAY_MIN(NAME, head); var != NULL; var = nxt) {
nxt = SPLAY_NEXT(NAME, head, var); nxt = SPLAY_NEXT(NAME, head, var);
SPLAY_REMOVE(NAME, head, var); SPLAY_REMOVE(NAME, head, var);
free(var); free(var);
} }
.Ed .Ed
.Pp .Pp
Both Both
.Fn RB_INSERT .Fn (A)RB_INSERT
and and
.Fn SPLAY_INSERT .Fn SPLAY_INSERT
return return
.Dv NULL .Dv NULL
if the element was inserted in the tree successfully, otherwise they if the element was inserted in the tree successfully, otherwise they
return a pointer to the element with the colliding key. return a pointer to the element with the colliding key.
.Pp .Pp
Accordingly, Accordingly,
.Fn RB_REMOVE .Fn (A)RB_REMOVE
and and
.Fn SPLAY_REMOVE .Fn SPLAY_REMOVE
return the pointer to the removed element otherwise they return return the pointer to the removed element otherwise they return
.Dv NULL .Dv NULL
to indicate an error. to indicate an error.
.Sh SEE ALSO .Sh SEE ALSO
.Xr queue 3 .Xr queue 3
.Sh AUTHORS .Sh AUTHORS
The author of the tree macros is The author of the tree macros is
.An Niels Provos . .An Niels Provos .