[GiNaC-devel] atan2 throws divide by zero

[G B]

Thanks, All.  I'll look forward to the changes percolating through.

Cheers--
 Greg


On Thu, Mar 25, 2010 at 2:41 PM, Richard B. Kreckel <kreckel at ginac.de>wrote:

> Hi!
>
>
> Jens Vollinga wrote:
>
>> Am 25.03.2010 00:17, schrieb G B:
>>
>>> I stumbled upon this using Sage, but developers there have traced it to
>>> a problem in GiNaC by running the following in ginsh:
>>>
>>>  > atan2(-Pi,0);
>>>
>>> The response is:
>>> power::eval(): division by zero
>>>
>>> atan2 appears to work for other values, including (positive) (Pi,0), but
>>> (-Pi,0) fails.
>>>
>>
>> thanks for the bug report. I fixed that bug in the repository.
>> Finally it is time to make a new release ... :-)
>>
>
> Wait a minute, I think your fix is wrong. It assumes that if y.info(info_flags::real)
> and not y.info(info_flags::positive) and not y.is_zero(), then y must be
> negative. But that's not correct, because info returns true if the predicate
> is known to be true and false if it os known to be false or if it is
> unknown. Consider, for instance, positive symbols a and b and ex x = a-b.
> So, the patch introduces actually a new bug.
>
> What's really wrong is the last part in atan2_eval, where atan(real, real)
> -> atan(y/x) +/- Pi. Ironically, it is suffering from the same mistake as
> your patch. This ought to fix it:
>
> @@ -877,10 +877,13 @@ static ex atan2_eval(const ex & y, const ex & x)
>        if (y.info(info_flags::real) && x.info(info_flags::real)) {
>                if (x.info(info_flags::positive))
>                        return atan(y/x);
> -               else if (y.info(info_flags::positive))
> -                       return atan(y/x)+Pi;
> -               else
> -                       return atan(y/x)-Pi;
> +
> +               if (x.info(info_flags::negative)) {
> +                       if (y.info(info_flags::positive))
> +                               return atan(y/x)+Pi;
> +                       if (y.info(info_flags::negative))
> +                               return atan(y/x)-Pi;
> +               }
>        }
>
>        return atan2(y, x).hold();
>
> It appears that this bug has been latent until Vladimir's patch
> c7299e51d5ecf6. The bad news is that with my patch atan2(-Pi,0) isn't
> simplified at all any more. One could argue that GiNaC should evaluate
> ex(-Pi).info(info_flags::negative) -> true. This would make atan2(-Pi,0)
> evaluate to -Pi/2 again.
>
>  -richy.
> --
> Richard B. Kreckel
> <http://www.ginac.de/~kreckel/>
>
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