#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: -------------------------------------+------------------------------------- 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 GHC http://www.haskell.org/ghc/ The Glasgow Haskell Compiler