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

[GHC]

#8539: Data.Complex shouldn't use default implementation of (**)
-------------------------------------+-------------------------------------
        Reporter:  jjaredsimpson     |            Owner:
            Type:  bug               |           Status:  patch
        Priority:  low               |        Milestone:
       Component:  Prelude           |          Version:  7.6.3
      Resolution:                    |         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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Comment (by yalas):

 I think x raised to 0 must always be equal 1. Even for NaN:
 {{{
 Prelude> (1/0*0) :: Double
 NaN
 Prelude> (1/0*0) ** 0 :: Double
 1.0
 }}}
 New complex power implementation:
 {{{
 _ ** (0:+0)    =  1 :+ 0
 x ** (1:+0)    =  x
 (x:+0) ** (y:+0)
   | x >= 0     =  (x ** y) :+ 0
 x ** y         =  exp (log x * y)
 }}}
 But what about raising zero to complex power?
 Current implementation gets NaN:
 {{{
 Prelude Data.Complex> exp $ log 0 * (1:+1) :: Complex Double
 NaN :+ NaN
 }}}
 Python throws an exception:
 {{{
 >>> 0**(1+1j)
 Traceback (most recent call last):
   File "<stdin>", line 1, in <module>
 ZeroDivisionError: 0.0 to a negative or complex power
 }}}
 But wolphramalpha gets
 [https://www.wolframalpha.com/input/?i=0%5E%281%2B1i%29 0],
 [https://www.wolframalpha.com/input/?i=0%5E%28-1%2B1i%29 infinity] or
 [https://www.wolframalpha.com/input/?i=0%5E%281i%29 indeterminate].

--
Ticket URL: <http://ghc.haskell.org/trac/ghc/ticket/8539#comment:8>
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