[GHC] #8532: Hyperbolic arc cosine fails on (-1) :: Complex r.

[GHC]

#8532: Hyperbolic arc cosine fails on (-1) :: Complex r.
-------------------------------------+-------------------------------------
       Reporter:  leftaroundabout    |             Owner:
           Type:  bug                |            Status:  new
       Priority:  low                |         Milestone:
      Component:  libraries/base     |           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:  acosh(-1) ::
     Blocked By:                     |  Complex Double
Related Tickets:                     |          Blocking:
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 When allowing for complex results, the hyperbolic arc cosine is
 continuously defined on all ℝ.

 In the {{{(x < (-1))}}} real ray of the complex plane, {{{acosh}}} equals
 {{{\z -> i * pi + acosh(abs z)}}}, which works fine for almost all
 arguments. Thus, {{{acosh (-1)}}} should equal {{{i * pi}}}; however due
 to the implementation as
 {{{
 acosh z = log (z + (z+1) * sqrt ((z-1)/(z+1)))
 }}}
 where the denominator in the root becomes zero at {{{z = -1}}}, this comes
 out as {{{NaN :+ NaN}}}.

 Could be fixed trivially by adding a special case
 {{{
 acosh ((-1):+0) = 0:+pi
 }}}
 to the {{{instance  (RealFloat a) => Floating (Complex a)}}} in
 {{{Data.Complex}}}.

--
Ticket URL: <http://ghc.haskell.org/trac/ghc/ticket/8532>
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