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Message-ID: <5918d2a7-7b3-932b-2b4-b24390832244@esi.com.au>
Date: Mon, 12 Aug 2024 13:56:18 +1000 (AEST)
From: Damian McGuckin <damianm@....com.au>
To: MUSL <musl@...ts.openwall.com>
Subject: Re: catan(z)

On Mon, 12 Aug 2024, Damian McGuckin wrote:

> There is some argument that if you handle the special cases at infinity 
> separately (which I think MUSL should do but I do not have time at the 
> moment), then one can assume that because pi/2 is irrational, then one 
> should never have to deal with the end points in the chunk of code where 
> those two lines of code seen above should appear. I will have a chat 
> sometime with the guy who wrote that logic in a WG14 paper when I get a 
> really clear head and can line him up.

Consider

 	atan2(y, x)

For any finite y and finite non-zero x floating point number arguments, 
i.e. rational numbers, the result of atan2(y, x) must be rational and so 
is never +/- pi (which is irrational and only occurs when the ration y/x 
is a mathematical infinity, not an overflowing infinity). So, we can 
ignore the endpoints as long as our special case handling takes care of 
the case of zero x.

I think that is correct .... or is my brain still not working properly 
after too many late nights watching the Olympics.

Thanks - Damian

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