Re: [musl] catan(z)

[Damian McGuckin <damianm@esi.com.au>]

On Sun, 11 Aug 2024, Szabolcs Nagy wrote:

> * 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]

Yes. Silly me. Why? Because ...

 	atan2() returns a number in [-pi, +pi], 't' is in [-pi/2,+pi/2],

 	hence, at least in this case, _redupi(t) just maps that 't' into
 	that same range.

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.

Thanks - Damian