sub readable {
    my $fh = shift;
    (O_RDONLY | O_RDWR) & fcntl( $fh, F_GETFL, my $slush);
}

for (qw/ > < >> +< +> /) {
    open my $fh, $_, 'foo' or warn $! and next;
    print
        "$_\t",
        readable($fh)? 'readable.': 'not readable.',
        $/;
}

__END__
>       not readable.
<       not readable.
>>      not readable.
+<      readable.
+>      readable.