Data.Complex shouldn't use default implementation of (**)

Prelude Data.Complex> 0**2
0.0
Prelude Data.Complex> 0**2 :: Complex Double
NaN :+ NaN
Prelude Data.Complex> exp $ 2 * log 0 :: Complex Double
NaN :+ NaN
Prelude Data.Complex> log 0 :: Complex Double
(-Infinity) :+ 0.0
Prelude Data.Complex> 2 * it :: Complex Double
(-Infinity) :+ NaN
Prelude Data.Complex> exp it :: 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.

Ross Paterson suggested:

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)

Trac metadata

Trac field	Value
Version	7.6.3
Type	Bug
TypeOfFailure	OtherFailure
Priority	low
Resolution	Unresolved
Component	Prelude
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