import Data.Fixed

toDeg, toRad :: Floating a => a -> a
toDeg d = d * 180 / pi
toRad d = d * pi / 180

navigate1 :: Float -> Float -> Float -> Float -> Float -> [Int]
navigate1 d gt wn ws as = map round [gs, a, th, ft] where
    b  = toRad $ gt - wn + 180
    a  = toDeg $ asin (ws * sin b / as)
    th = mod' (gt + a) 360
    gs = (cos . toRad $ th - gt) * as + ws * cos b
    ft = d / gs * 60

navigate2 :: Float -> Float -> Float -> Float -> Float -> [Int]
navigate2 d gt wn ws as = if det < 0 || gs < 0 then error "strange"
                          else map round [gs, a, th, ft] where
    b   = mod' (gt - wn + 180) 360
    x   = ws * cos (toRad b)
    det = x^2 - ws^2 + as^2
    gs  = x + sqrt det
    a   = (if b < 180 then id else negate) . toDeg . acos $
          (as^2 + gs^2 - ws^2) / (2 * gs * as)
    th  = gt + a
    ft  = d / gs * 60