[Cfp-interest 3081] Re: casinh(x + iNaN) - Annex G.6.3.2

[Damian McGuckin]

On Fri, 5 Apr 2024, Damian McGuckin wrote:

> 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.

Yes. But nowhere does it say that a function or macro which takes an 
imaginary argumnt must return an imaginary result. In fact, at the end of 
clause 1, G.7 refers to other macros which return complex results. It does 
not define them. I assume they are acos, acosh, log and sqrt,

The only functions in that table which cause a problem are

 	asinh(iy)
and
 	atan(iy)

If you define either in terms of a real function, there are problems when

 	|y} > 1

because those real functions return NaN for that case. I think I have 
captured all the problem cases.

If they got moved into the last batch of undefined macros which can return 
a complex number, then for any of those macros in that table (or the 
missing ones) say 'name', then

 	name(iy) = cname(0 + iy)

There are no outliers and all the previous special cases still hold.

What do you think - Damian