[Cfp-interest 3066] Re: csinh(x + i y) - G.6.3.5 - 5th bullet point of special cases

[Damian McGuckin]

Jim, I am reformatting this email a bit because it is hard to see who said 
what.  I was chasing consistency.

> On Sat, 16 Mar 2024, Damian McGuckin wrote:
> 
> The special case is mentioned:
>
>       csinh(x + i * INFINITY) returns NaN + i * NaN for positive
>       finite x
> 
> is given.
> 
> Given the mathematics, I think the domain in the draft is wrong and
> should have read 'finite non-zero x'

On Tue, 2 Apr 2024, Jim Thomas wrote:

> The domain is implicitly extended to cover finite nonzero x by the
> requirements in the first bullet:
>
>        ?csinh(conj(z)) = conj(csinh(z)) and csinh is odd.

Yes (but no from a consistency perspective)

I agree that:

The 1st item in that line says that whatever is good for +y is good for -y.

The 2nd item in that line says that whatever is good for +x is good for -x.

But exploiting that second fact is an extremely inconsistent extrapolation 
because no other bullet point for any special case in all Annex G exploits 
the odd-ness or even-ness of the function in the description of a domain 
as far as I can see.

I was chasing consistency in this description.

I also said (but I hit the 'x' key twice - sorry)

>       As the special case in
>
>       a) the 6th bullet point says 'finite non-zero x?,

The 6th bullet point does not exploit the odd'ness of the function when it 
describes the doamin, so why should the 5th bullet point.

Also, in G.6.3.6 ctanh(), the 4th and 6th bullet points do not exploit the 
odd'ness of the function when the domain is described either.

The description as it stands in the 5th bullet point is an outlier

For consistency with both bullet point 6 in csinh(), and again in tanh() 
and elsewhere such as ccosh(), we need

 	finite non-zero

in bullet point 5.

Ignore my comment about overlap. Changing to 'finite non-zero' covers it.

I also belated note that ccosh() and csinh() uses the following ordering
for the special cases for the 3rd through 6th special cases"

 	0 + i INF

 	0 + i NAN

 	x + i INF

 	x + i NAN

and yet ctanh() shuffles these cases around and inconsistently uses

 	0 + i INF

 	x + i INF

 	0 + i NAN

 	x + i NAN

which is confusing.  It should be rearranged.

You also noted that:

> (n3219 has an erroneous periodic the middle of the first bullet. That 
> typo has been reported to the C editor.)

Yes. Sorry. I missed that.

Thanks - Damian