basic operations on continued fractions

CF.hs

  bihom a b _ _ e f _ _ xs [] = hom a b e f xs
  bihom a _ c _ e _ g _ [] ys = hom a c e g ys
  bihom a b c d e f g h xs@(x:xs') ys@(y:ys')
     | e /= 0, f /= 0, g /= 0, h /= 0 
     , q <- quot a e, q == quot b f
     , q == quot c g, q == quot d h
     = q : go e f g h (a-q*e) (b-q*f) (c-q*g) (d-q*h) xs ys
     | e /= 0 || f /= 0
     , (e == 0 && g == 0) || abs (g*e*b - g*a*f) > abs (f*e*c - g*a*f)
       = go (a*x+b) a (c*x+d) c (e*x+f) e (g*x+h) g xs' ys
     | otherwise
       = go (a*y+c) (b*y+d) a b (e*y+g) (f*y+h) e f xs ys'
       
  (+) = bihom 0 1 1 0 0 0 0 1
  (-) = bihom 0 1 (-1) 0 0 0 0 1
  (*) = bihom 1 0 0 0 0 0 0 1
  (/) = bihom 0 1 0 0 0 0 1 0