use warnings;
use strict;
use Math::MPFR;

my $nan = Math::MPFR->new();

if($nan != $nan) {print "\$nan is a nan\n"}
else {die "$nan is not a nan\n"}

if($nan) {print "nans are true\n"}
else {print "nans are false\n"}

__END__
Outputs:
$nan is a nan
nans are false