[GHC] #8539: Data.Complex shouldn't use default implementation of (**)

[GHC]

#8539: Data.Complex shouldn't use default implementation of (**)
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       Reporter:  jjaredsimpson      |             Owner:
           Type:  bug                |            Status:  new
       Priority:  low                |         Milestone:
      Component:  Prelude            |           Version:  7.6.3
       Keywords:                     |  Operating System:  Unknown/Multiple
   Architecture:  Unknown/Multiple   |   Type of failure:  Incorrect result
     Difficulty:  Easy (less than 1  |  at runtime
  hour)                              |         Test Case:
     Blocked By:                     |          Blocking:
Related Tickets:                     |
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 {{{
 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)

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Ticket URL: <http://ghc.haskell.org/trac/ghc/ticket/8539>
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