#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 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: | -------------------------------------+------------------------------------- {{{ 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) -- Ticket URL: http://ghc.haskell.org/trac/ghc/ticket/8539 GHC http://www.haskell.org/ghc/ The Glasgow Haskell Compiler