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

[Jan Bos]

Dear Richard,

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 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. 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.

Best regards

Jan Bos

On Sun, 2007-07-22 at 12:00 +0200, ginac-list-request at ginac.de wrote:
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> Today's Topics:
> 
>    1. atan2(0,-4) = -Pi? (Jan Bos)
>    2. Re: atan2(0,-4) = -Pi? (Richard B. Kreckel)
> 
> 
> ----------------------------------------------------------------------
> 
> Message: 1
> Date: Sat, 21 Jul 2007 21:24:57 +0200
> From: Jan Bos <jb68 at xs4all.nl>
> Subject: [GiNaC-list] atan2(0,-4) = -Pi?
> To: ginac-list at ginac.de
> Message-ID: <1185045897.9600.20.camel at jbos1>
> Content-Type: text/plain
> 
> Dear All,
> 
> Is there a reason for GiNaC (or ginsh) to evaluate 
> atan2(0,-4) as -Pi instead of +Pi the definition used by for instance
> C/C++? Looking at the code, inifcns_trans.cpp last shown case below,
> explicitly states it should. Or can I expect it to be changed in the
> future?
> 
> static ex atan2_eval(const ex & y, const ex & x)
> {
>   if (y.info(info_flags::numeric) && x.info(info_flags::numeric)) {
> 
>     if (y.is_zero()) {
> 
>       // atan(0, 0) -> 0
>       if (x.is_zero())
> 	return _ex0;
> 
>       // atan(0, x), x real and positive -> 0
>       if (x.info(info_flags::positive))
> 	return _ex0;
> 
>       // atan(0, x), x real and negative -> -Pi
>       if (x.info(info_flags::negative))
> 	return _ex_1*Pi;
>     }
> 
> ...
> 
> The code fragment is from version 1.3.7
> 
> best regards
> 
> Jan Bos
> 
> 
> 
> 
> 
> ------------------------------
> 
> Message: 2
> Date: Sun, 22 Jul 2007 01:16:38 +0200
> From: "Richard B. Kreckel" <kreckel at ginac.de>
> Subject: Re: [GiNaC-list] atan2(0,-4) = -Pi?
> To: GiNaC discussion list <ginac-list at ginac.de>
> Message-ID: <46A293D6.9040301 at ginac.de>
> Content-Type: text/plain; charset=ISO-8859-1; format=flowed
> 
> Dear Jan,
> 
> Jan Bos wrote:
> > Is there a reason for GiNaC (or ginsh) to evaluate 
> > atan2(0,-4) as -Pi instead of +Pi the definition used by for instance
> > C/C++? Looking at the code, inifcns_trans.cpp last shown case below,
> > explicitly states it should. Or can I expect it to be changed in the
> > future?
> > 
> > static ex atan2_eval(const ex & y, const ex & x)
> > {
> >   if (y.info(info_flags::numeric) && x.info(info_flags::numeric)) {
> > 
> >     if (y.is_zero()) {
> > 
> >       // atan(0, 0) -> 0
> >       if (x.is_zero())
> > 	return _ex0;
> > 
> >       // atan(0, x), x real and positive -> 0
> >       if (x.info(info_flags::positive))
> > 	return _ex0;
> > 
> >       // atan(0, x), x real and negative -> -Pi
> >       if (x.info(info_flags::negative))
> > 	return _ex_1*Pi;
> >     }
> > 
> 
> I don't suppose anybody lightly intends to change such definitions.  :)
> 
> Well, I looked in my notes and didn't find anything motivating that 
> choice for atan2.
> 
> I recall that back when I wrote this, CLTL 2nd edition provided guidance 
> when choosing branch cuts of single-argument functions in the complex 
> domain. And later at some point I realized that the C99 standard agrees 
> with CLTL for all single-argument functions. (That appeared to be too 
> good to be true, but it is true.) Nobody was aware of LIA-3 at that time 
> but I'm quite sure that all of GiNaC's single-argument functions agree 
> with LIA-3, simply because they agree with C99.
> 
> Our two-argument function atan2, however, may never have been checked 
> against any standard. I just did that with C99 and CLTL, and they both 
> specify atan2(0,-4) to be +Pi, indeed. Maybe, we ought to change this? 
> Before we do so: What does LIA-3 say?
> 
> Our choice may be bad but I frankly admit that I don't know why +Pi is 
> any better than -Pi, or a more symmetric choice a la Mathematica like 
> atan2(0,x>0)=Pi/2, atan2(0,x<0)=-Pi/2, or 0 for all x. Can you explain 
> that choice?
> 
> Cheers
>    -richy.
> 
> PS: In any case, this is a good lesson how not to write comments, sigh.
> -- 
> Richard B. Kreckel
> <http://www.ginac.de/~kreckel/>
> 
> 
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> End of GiNaC-list Digest, Vol 29, Issue 1
> *****************************************
>