.TH LIBNORMALFORM_XNOR 3 LIBNORMALFORM
.SH NAME
libnormalform_xnor \- Logical equivalence

.SH SYNOPSIS
.nf
#include <libnormalform.h>

LIBNORMALFORM_SENTENCE *libnormalform_xnor(LIBNORMALFORM_SENTENCE **\fIxs\fP);
LIBNORMALFORM_SENTENCE *libnormalform_xnorl(LIBNORMALFORM_SENTENCE *\fIa\fP, ... /*, NULL */);
LIBNORMALFORM_SENTENCE *libnormalform_vxnor(LIBNORMALFORM_SENTENCE *\fIa\fP, va_list \fPargs\fP);
LIBNORMALFORM_SENTENCE *libnormalform_xnor_checked(size_t \fIn\fP, LIBNORMALFORM_SENTENCE **\fIxs\fP);
LIBNORMALFORM_SENTENCE *libnormalform_xnorl_checked(size_t \fIn\fP, LIBNORMALFORM_SENTENCE *\fIa\fP, ... /*, NULL */);
LIBNORMALFORM_SENTENCE *libnormalform_vxnor_checked(size_t \fIn\fP, LIBNORMALFORM_SENTENCE *\fIa\fP, va_list \fPargs\fP);
LIBNORMALFORM_SENTENCE *libnormalform_xnor2(LIBNORMALFORM_SENTENCE *\fIp\fP, LIBNORMALFORM_SENTENCE *\fIq\fP);
#define LIBNORMALFORM_XNOR(...) /* ... */
.fi
.PP
Link with
.IR -lnormalform .

.SH DESCRIPTION
The
.BR libnormalform_xnor ()
function creates a sentence that is logically
equivalent to the logical equivalecne of the
arguments, that is, a sentence that is true
exactly when the parity of the subsentences
equal to whether the number of subsentences is odd.
.PP
The value of the
.I xs
parameter shall be a null-pointer terminated list
of subsentences.
.PP
The
.BR libnormalform_xnorl ()
function is a variant of
.BR libnormalform_xnor ()
which uses variadic arguments instead of an array.
.PP
The
.BR libnormalform_vxnor ()
function is a variant of
.BR libnormalform_xnorl ()
which takes an
.I va_list
in place of variadic arguments.
.PP
The
.BR libnormalform_xnor_checked (),
.BR libnormalform_xnorl_checked (),
and
.BR libnormalform_vxnor_checked ()
functions are variants of the
.BR libnormalform_xnor (),
.BR libnormalform_xnorl (),
and
.BR libnormalform_vxnor ()
functions respectively which assumes
that it is given
.I n
subsentances, and checks that all are
.RI non- NULL .
However, these functions still require
the list of subsentences to be terminated
using a null-pointer.
.PP
.I "libnormalform_xnor2(p, q)"
is equivalent to
.IR "libnormalform_xnorl_checked(2, p, q, NULL)" .
.PP
The
.BR LIBNORMALFORM_XNOR
macro is a wrapper for the
.BR libnormalform_xnor_checked ()
but is more similar to
.BR libnormalform_xnorl ().
Unlike
.BR libnormalform_xnorl (),
the argument list
.I must not
be terminated by a null-pointer, instead
the macro automatically as the null-pointer.
The macro will count the number of arguments
it is given, therefore it will fail it the
argument list is has an extra null-pointer.
.PP
The returned pointer shall either be
deallocated with the
.BR libnormalform_free (3)
function or be relinquished by being
used as part of another sentence.
.PP
These functions adopt the ownership of any
.I LIBNORMALFORM_SENTENCE *
passed into it. Therefore, the user shall
not attempt to deallocate input sentences.
This holds even on failure: if the function
fails, input sentences are deallocated.

.SH RETURN VALUE
Upon successful completion, the
.BR libnormalform_xnor ()
function and its variants return an object
representing  the sentence; otherwise, the
functions return
.I NULL
and set
.I errno
to indicate the error.

.SH ERRORS
These functions fails if:
.TP
.I ENOMEM
Insufficient memory was available to
create the sentence object.
.PP
The
.BR libnormalform_xnor_checked (),
.BR libnormalform_xnorl_checked (),
and
.BR libnormalform_vxnor_checked ()
functions will also fail without setting
.I errno
if any of the first
.I n
.IR "LIBNORMALFORM_SENTENCE *" 's
are
.IR NULL .
Likewise, the
.BR libnormalform_xnor2 ()
function will fail without setting
.I errno
if
.I p
or
.I q
is
.IR NULL .

.SH ATTRIBUTES
For an explanation of the terms used in this
section, see
.BR attributes (7)
and
.IR "info \(dq(libc)POSIX Safety Concepts\(dq" .
.TS
allbox;
lb lb lb
l l l.
Interface	Attribute	Value
T{
.BR libnormalform_xnor (),
.br
.BR libnormalform_xnor_checked ()
T}	Thread safety	MT-Safe race:\fIxs\fP and elements in \fIxs\fP
T{
.BR libnormalform_xnorl (),
.br
.BR libnormalform_xnorl_checked (),
.br
.BR libnormalform_xnor2 (),
.br
.BR LIBNORMALFORM_XNOR ()
T}	Thread safety	MT-Safe race:parameters
T{
.BR libnormalform_vxnor (),
.br
.BR libnormalform_vxnor_checked ()
T}	Thread safety	MT-Safe race:parameters and arguments in \fIargs\fP
T{
.BR libnormalform_xnor (),
.br
.BR libnormalform_xnorl (),
.br
.BR libnormalform_vxnor (),
.br
.BR libnormalform_xnor_checked (),
.br
.BR libnormalform_xnorl_checked (),
.br
.BR libnormalform_vxnor_checked (),
.br
.BR libnormalform_vxnor2 (),
.br
.BR LIBNORMALFORM_XNOR ()
T}	Async-signal safety	AS-Unsafe heap
T{
.BR libnormalform_xnor (),
.br
.BR libnormalform_xnorl (),
.br
.BR libnormalform_vxnor (),
.br
.BR libnormalform_xnor_checked (),
.br
.BR libnormalform_xnorl_checked (),
.br
.BR libnormalform_vxnor_checked (),
.br
.BR libnormalform_vxnor2 (),
.br
.BR LIBNORMALFORM_XNOR ()
T}	Async-cancel safety	AC-Safe mem, AC-Unsafe heap
.TE

.SH NOTES
If there are no subsentences, the resulting sentence is a tautology.
.PP
The connective is commutative and associative. It's truthtable is (1001).
.PP
The
.BR LIBNORMALFORM_XNOR ()
macro requires ISO C23 support.
.PP
Using
.BR libnormalform_xnor2 (),
has greatest performance, however
.BR libnormalform_xnor ()
is better at simplifying the sentence.
The other functions are just wrappers for the
.BR libnormalform_xnor ()
function.
.PP
These functions creates a clause where each term
is connected with the XNOR connective. Unlike what
the name Logical equivalence, this does
.I not
create a sentence that is true when all subsentences
have the same value (this is only the case when there
are 2 or 0 subsentences). Rather, when the number
of terms is odd, it is equivalent to the parity (XOR)
of the terms, but when the number of terms is odd, it
is the inverse of the parity.
.PP
Side-effects in the arguments of the macro
.BR LIBNORMALFORM_XNOR ()
are guaranteed to be applied exactly once.
The side-effects in each macro are applied
in no particular order.

.SH SEE ALSO
.BR libnormalform (7)