[Cfp-interest 3069] Re: casinh(x + iNaN) - Annex G.6.3.2

[Jim Thomas]

> On Mar 16, 2024, at 3:41 AM, Damian McGuckin <damianm at esi.com.au> wrote:
> 
> 
> The 4th item in the Dash List says
> 
> 	casinh(x + i NaN) = NaN + i NaN for finite x
> 
> Now, for x = 0
> 
> 	casinh(x + i NaN) = casinh(i NaN)    .... (1)

Why? Annex G regards casinh(iy) to be a mapping from the imaginary axis to the imaginary axis. casinh(z) is a mapping from the complex plane to the complex plane. Complex function results may differ if x is +0 vs -0. From the third bullet, casinh(+0 + i inf) = +inf + i pi/2 and by the first bullet casinh(-0 + i inf) = -inf + i pi/2.

> 
> For a purely imaginary argument, which is where all this is coming from,

> G.7 says
> 
> 	casinh(i NaN) = i asin(NaN) = i NaN
> 
> So, Eq(1) above is now
> 
> 	casinh(0 + i NaN) = 0 + i NaN        .... (2)

Assuming 0 is +0, (2) would imply that the real part of casinh(+0 + iy) is +0 for any (finite or infinite) number y, contrary to bullet 3.

- Jim Thomas

> 
> So, I believe that G.6.3.2 is wrong and should say
> 
> 	casinh(x + i NaN) = NaN + i NaN for finite x != 0
> 
> and an item to reflect Eq(2) above needs to be added.
> 
> Comments please?
> 
> Thanks - Damian
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