[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:  new
        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 Scott Turner):

 Agree with isaacdupree that
 0{{{**}}}0 == 1.0

 The above
 {{{
 x ** y = if x == 0 then 0 else exp (log x * y)
 }}}
 is incorrect for negative y. Consider
 {{{
 $ ghci
 GHCi, version 7.6.3: http://www.haskell.org/ghc/  :? for help
 Prelude> 0.0**(-2.0)
 Infinity
 }}}
 There are other interesting cases. If the real part of y is positive, then
 the result should be 0. If the real part is negative, then the result
 should be Infinity. If y is imaginary, the result should be NaN.

 For the most part,
 {{{
 Infinity ** y = 0 ** (negate y)
 }}}
 I won't address -0 and 0:+(-0) because they deserve more controversy than
 I can handle.

--
Ticket URL: <http://ghc.haskell.org/trac/ghc/ticket/8539#comment:2>
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