[GiNaC-list] Re: GiNaC-list Digest, Vol 29, Issue 1

[Richard B. Kreckel]

Jan Bos wrote:
> Thanks for the prompt reply. I'm no expert and not aware of LIA-3. Maybe
> you could give me a reference as where to obtain it? 

The links in <http://en.wikipedia.org/wiki/ISO/IEC_10967> appear to be 
as good as it gets regarding downloadable stuff.

> The reason I posted the question is that since GiNaC is embedded in C++
> (beautiful concept by the way) it seems odd to have different
> definitions for the case at hand.

Surely, the intent is to avoid such differing definitions.

>                                   Of course I can't oversee the
> consequences of a change, it would be convenient to code decisions based
> on the argument in a uniform way though.

Let's see. atan2 appears in LIA-2 and LIA-3, though not in LIA-1. It 
isn't defined directly, but one finds for instance the formula in LIA-3: 
ln(z)=ln(|z|)+I*atan2(y,x) for z=x+I*y. This implies to bring the branch 
cut in alignment with the branch cut of ln(x+I*y). The latter is defined 
as continuous with the second quadrant of the x-y plane (c.f. C99, 
7.3.3.2: "[...] implementations shall map a cut so the function is 
continuous as the cut is approached coming around the finite endpoint of 
the cut in a counter clockwise direction. (Brnach cuts for the functions 
specified here have just one finite endpoint.)" As I said, this branch 
cut specification for ln(z) is consistent with the other standards.

IINM this implies that atan2(0,-4) should be +Pi, not -Pi.

Unless somebody is going to hold me back I'm going to fix this in GiNaC 
RSN. I'll also consider some minor other issues like atan2(I*1.1,1.1) 
throws an exception but atan2(I,1)->atan2(I,1) (both arguments of atan2 
must be real, full stop.)

   -richy.
-- 
Richard B. Kreckel
<http://www.ginac.de/~kreckel/>