sub reduce {

    # reduce from rightmost end of argument list.
    # left-pad input arguments with 0s to avoid inaccessible items.

    my ($degs,  # degrees
        $mins,  # minutes
        $secs,  # seconds
        ) = map $_ || 0, (0, 0, 0, @_)[ -3 .. -1 ];  # handles undefs

    use integer;

    $secs = $degs * SECS_PER_DEGREE + $mins * SECS_PER_MINUTE + $secs;

    $degs = $secs / SECS_PER_DEGREE;   $secs %= SECS_PER_DEGREE;
    $mins = $secs / SECS_PER_MINUTE;   $secs %= SECS_PER_MINUTE;

    return $degs, $mins, $secs;

    }