Re: [musl] catan(z)

[Morten Welinder <mwelinder@gmail.com>]

atan2 definitely isn't supposed to always output rational numbers on
rational input.

atan2(+0,-1) is Pi.
atan2(-0,-1) is -Pi
atan2(1,1) is Pi/4 -- clearly not a rational number.

These aren't exactly rational results (unless you mean their
floating-point approximations).

M.

On Sun, Aug 11, 2024 at 11:56 PM Damian McGuckin <damianm@esi.com.au> wrote:
>
> 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