Re: [musl] catan(z)

[Szabolcs Nagy <nsz@port70.net>]

* Damian McGuckin <damianm@esi.com.au> [2024-08-12 00:01:01 +1000]:
> 
> In this routine, there are 2 lines of code
> 
>     t = 0.5 * atan2(2.0 * x, a);
>     w = _redupi(t);
> 
> The first computes atan2() which returns a number in the range [-pi,+pi]
> which means that t is a number in the range [-pi/2,+pi/2].
> 
> As far as I understand, the routine _redupi(t) accepts a argument and
> reduces it into the range [-pi, +pi]. Am I mistaken?

*reduces into [-pi/2, pi/2]

> 
> If I am not wrong, and 't' is already in the range that _redupi(t) will
> return, then _redupi() just returns its argument (within a rounding error).
> So it seems like a no-op to me.
> 
> Can anybody comment?

it only changes the endpoints (t=+-pi/2 case) otherwise no-op

i dont know if we care about the endpoints but even if we do
there are better ways to fix them up

i think _redupi can be removed, nice catch.

> 
> The routine is originally from Moshier's Cephes library. I have Moshier's
> book but I cannot find any hints there.
> 
> Thanks - Damian