[Cfp-interest 3070] Re: casinh(x + iNaN) - Annex G.6.3.2

[Damian McGuckin]

On Wed, 3 Apr 2024, Jim Thomas wrote:

>> 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.

Yes. Something is weird.

The G.7 formula

 	casinh(0 + i y) = i asin(y)

is only valid for |y| <= 1. After that, the G.7 formula will return a NaN 
because no asin() function will ever accept a value outside that range. On 
the other hand, a complex function can expand into complex space.

Purely Imaginary numbers introduce their own set of issues.

Are we sure that

 	asinh(iy) = i asin(y)

is a valid inclusion in the current table in clause 2 of G.7.

Thanks - Damian

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