Complex arg-trig functions

[Stephen Montgomery-Smith]

On 09/06/2012 06:42 AM, Bruce Evans wrote:
> I'm back from a holiday.
>
> On Sun, 26 Aug 2012, Stephen Montgomery-Smith wrote:

> I tested your latest version and found regressions for NaNs.  (Also,
> the float version is less accurate now that it doesn't call double
> functions, but that is a progression.)
> 1. casin*() abuses x and y for |x| and |y| and thus loses the sign of
>     NaNs.  The quick fix is to reload the original values.  The correct
>     fix is to use separate variables for the absolute values, as is
>     done for cacosh*() and catanh*().

I now uniformly use ax and ay for |x| and |y| throughout.

> 2. NaNs are now filtered out early

It is not correct to filter out the NaNs early.  This is because of the 
way expressions like cacosh(NaN + I*INF) are defined in C99.  The INFs 
must be filtered out first.


> % @@ -289,7 +284,16 @@
> %           * the arguments is not NaN, so we opt not to raise it.
> %           */
> % -        return (cpack(x+y, x+y));
> % +        return (cpack(x+0.0L+(y+0), x+0.0L+(y+0)));
> %      }

Why does the second way work, and the first way doesn't?