[Cfp-interest 3072] Re: casinh(x + iNaN) - Annex G.6.3.2

[Damian McGuckin]

Jim,

On Thu, 4 Apr 2024, Jim Thomas wrote:

> 	casinh(iy) = 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.
>
> The formula is defining a function on imaginary numbers, not complex ones.

Got it.

I treat Imaginary numbers as Complex numbers with no real component and 
some functions of imaginary numbers return a real, some an imaginary, and 
some a complex.

I missed the point in what Annex G is doing as far as Imaginary numbers 
go. It is only working along the imaginary axis.

Its useful, but how useful is another question. But that has nothing to do 
with the review of the document for errors.

>> 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.
>
> There might be a more general issue with whether the type-generic macros 
> should ever introduce functions on imaginary types, because of 
> portability problems between implementations that have imaginary types 
> and those that don?t. Maybe this issue can be viewed as part of the 
> bigger one of what to do with imaginary types.

Yes.

In that case, ignore my earlier ramblings.

Thanks - Damian

Pacific Engineering Systems International ..... 20D Grose St, Glebe NSW 2037
Ph:+61-2-8571-0847 .. Fx:+61-2-9692-9623 | unsolicited email not wanted here
Views & opinions here are mine and not those of any past or present employer