[Haskell-cafe] Incorrect behavior in Data.Complex ?

[Ross Paterson]

On Sun, Nov 17, 2013 at 08:20:21PM -0800, jared simpson wrote:
> Prelude Data.Complex> 0**2
> 0.0
> Prelude Data.Complex> 0**2 :: Complex Double
> NaN :+ NaN
> [...]
> 
> So Complex uses the default implementation of **. Then when 2*(-inf :+ 0) is
> evaluated. We do (2 * -inf - 0*0) :+ (2*0 + -inf*0). Which because of -inf*0
> sets the imaginary part to NaN. 
> 
> Then exp (-inf :+ NaN) = exp x cos y :+ exp x sin y which becomes 0 * cos NaN
> :+ 0 * sin NaN. So we end up with NaN :+ NaN.
> 
> So is there a library I should be using, or is this a bug?

I would say the default implementation of (**) is wrong: to match the
Float/Double instances it should be

         x ** y  =  if x == 0 then 0 else exp (log x * y)