function prog(x1, y1, x2, y2, x3, y3, x4, y4)
    """
    (x1,y1)と(x2,y2)を通る直線と，(x3,y3)と(x4,y4)を通る直線の交点の座標を求める
    戻り値は交点の x, y 座標。交点がない場合は (NaN, NaN) を返す。
    """
    if x1 == x2 && x3 == x4
        x = y = NaN
    elseif x1 == x2
        x = x1
        y = (y4 - y3)/(x4 - x3)*(x1 - x3) + y3
    elseif x3 == x4
        x = x3
        y = (y2 - y1)/(x2 - x1)*(x3 - x1) + y1
    else
        a1 = (y2 - y1)/(x2 - x1)
        a3 = (y4 - y3)/(x4 - x3)
        if (a1 == a3)
            x = y = NaN
        else
            x = (a1*x1 - y1 - a3*x3 + y3)/(a1 - a3)
            y = (y2 - y1)/(x2 - x1)*(x - x1) + y1
        end
    end
    return (x, y)
end;

prog(4, 8, 8, 0, 2, 2, 12, 7) |> println
prog(4, 1, 4, 5, -1, -1, 6, 3) |> println
prog(-1, -1, 6, 3, 4, 1, 4, 5) |> println
prog(-1, -1, 6, 3, 4, 1, 4+1e-3, 5) |> println
prog(1, 2, 5, 2, 0, 3, 8, 3) |> println
prog(1, 1, 5, 5, -1, 0, 6, 7) |> println
prog(-5, 2, -5, 8, 2, 3, 2, 7) |> println

(6.0, 4.0)
(4, 1.8571428571428568)
(4, 1.8571428571428568)
(4.000214316330904, 1.8572653236176593)
(NaN, NaN)
(NaN, NaN)
(NaN, NaN)