gistfile1.hs

instance  (RealFloat a) => Fractional (Complex a)  where
    {-# SPECIALISE instance Fractional (Complex Float) #-}
    {-# SPECIALISE instance Fractional (Complex Double) #-}
    (x:+y) / (x':+y')   =  (x*x''+y*y'') / d :+ (y*x''-x*y'') / d
                           where x'' = scaleFloat k x'
                                 y'' = scaleFloat k y'
                                 k   = - max (exponent x') (exponent y')
                                 d   = x'*x'' + y'*y''

2 Naive and non-naive algorithms
6
Fig. 3:
Smith’s algorithm for the complex division.
function z = compdiv_smith ( x , y )
a = real(x); b = imag(x);
c = real(y); d = imag(y);
if ( abs(d) <= abs(c) ) then
r = d/c
den = c + d * r
e = (a + b * r) / den
f = (b - a * r) / den
else
r = c/d
den = c * r + d
e = (a * r + b) / den
f = (b * r - a) / den