function JulianDay( theyear, themonth, theday)
{
    # See Meeus page 60
    Y= theyear;
    M= themonth;
    D= theday;
    if ( M < 3 ) {
	Y= Y - 1;
	M= M +12;
    }
    A= int( Y / 100 );
    B= 2 - A + int( A / 4);
    return( int(365.25*(Y+4716)) + int(30.6001*(M+1)) + D + B - 1524.5);
}

function CarringtonRotation( thejulianday)
{
    # See Meeus 29.1, page 191
    # Meeus says this can be off by 0.16 days
    # there is a corrective formula (29.2) in the book, if this turns out to be a problem.
    return int((thejulianday - 2398140.227 ) / 27.2752316);
}

function cr2J( thecr)
{
    return 2398140.2270 + 27.2752316 * thecr;
}

function J2cr( thejul)
{
    return CarringtonRotation( thejul);
}

function J2date( thejul)
{
    Z= int( thejul + 0.5 );
    F= ( thejul + 0.5 ) - Z;
    if ( Z < 2299161 ) 
	A= Z;
    else {
	alpha= int( ( Z - 1867216.25 ) / 36524.25 );
	A= Z + 1 + alpha - int( alpha / 4);
    }
    B= A + 1524;
    C= int( ( B - 122.1 ) / 365.25 );
    D= int( 365.25 * C );
    E= int( ( B - D ) / 30.6001 );
    theday= B - D - int(30.6001 * E ) + F;
    if ( E < 14 )
	themonth= E - 1;
    else
	themonth= E - 13;
    if ( themonth > 2 )
	theyear= C - 4716;
    else
	theyear= C - 4715;

    return sprintf( "%04d%02d%02d", theyear, themonth, theday);
}

{
    print CarringtonRotation( JulianDay( $1, $2, $3)) " " $1 " " $2 " " $3
}