[Bug libstdc++/50880] __complex_acosh() picks wrong complex branch

[kreckel at ginac dot de]

http://gcc.gnu.org/bugzilla/show_bug.cgi?id=50880

--- Comment #23 from Richard B. Kreckel <kreckel at ginac dot de> 2011-11-03 23:57:55 UTC ---
(In reply to comment #16)
> Well, I guess this would be most of it:
> 
>   template<typename _Tp>
>     std::complex<_Tp>
>     __complex_acosh(const std::complex<_Tp>& __z)
>     {
>       return _Tp(2.0) * std::log(std::sqrt(_Tp(0.5) * (__z + _Tp(1.0)))
>                  + std::sqrt(_Tp(0.5) * (__z - _Tp(1.0))));
>     }

[Sorry for my temporary absence.]

For future reference, some final remarks:
* Yes, that is a good implementation for this "fallback".
  It relies on __z - _Tp(1.0) not "mutating" the sign of __z's imag part.
* If the complex log does not do the right thing, all is lost anyways
  (besides, __complex_asinh relies on it, too).
* My patch BC1 was flawed. It contains code trying to work around a ctor doing
  multiplication (fixed in PR48760)
* My patch BC2 was flawed for the same reason: __z - __one doesn't preserve
  the sign of __z's imag part.

Looks good. Thanks!