[Cfp-interest 3087] Re: csinh(0 + i NaN)

[Damian McGuckin]

On Mon, 8 Apr 2024, Damian McGuckin wrote:

> G.6.3.5 says
>
> 	csinh(+0 + i NaN) = +/- 0 + i NaN
>
> without a floating point exception.
>
> Taking inverses of both sides says
>
> 	+0 + i NaN = casinh(+/- 0 + i NaN)
> or
> 	 casinh(+/- 0 + i NaN) = +0 + i NaN  ..... (1)
>
> Is this still valid in the presence of a NaN?
>
> I note that, clause G.6.3.2 says
>
> 	casinh(x + i NaN) returns NaN + i NaN
>
> for finite x. A valid finite x of zero, plugged into G 6.3.2, yields
>
> 	casinh(0 + i NaN) = NaN + i NaN  ........ (2)
>
> As Eq(1) != Eq(2), then G.6.3.2 and G.6.3.5 are is disagreement.

Currently,

 	cacos(x + i NaN)
 	cacosh(x + i NaN)
 	catanh(x + i NaN)
 	ccosh(x + i NaN)
 	csinh(x + i NaN)
 	ctanh(x + i NaN)

all return NaN + i NaN for a non-zero finite x. In G.6.3.5, it says
that casinh(x + i NaN) is an outlier only returns that same result
for a finite domain.

If there is agreement with Eq(1), then casinh(x + i NaN) then returns the
same result over exactly the same domain as its peers. So quite apart from
the fact that Eq(1) follows directly from G.6.3.5, this is a further hint
that Eq(1) is correct.

Thanks - Damian