Re: Bug in Jacobi elliptic functions

["Ivan E. Panchenko" <ivan at xray dot sai dot msu dot ru>]

Thank you for your prompt reaction.
I will check out the last version from CVS and
hope then to figure out  if if your fix is sufficient.
I have found the bug simply by plotting the function: it should
have been continuous, but on the graph there were clear periodical
dropouts. So plotting the functions with high resolution can be used 
as a generic testing tool for numeric algorithms.

Regards, 
Ivan



> 
> However, I am worried that the new method may
> fail elsewhere. It would be good to have
> more test cases. Unfortunately, I don't
> know how to generate good test cases for this. 
> Does anybody know where I can find some?
> 
> If you are interested in the technical issue,
> the problem was a loss of precision in a
> difference between angle arguments. I transformed
> to a shifted angle which keeps track of small
> differences better. The only remaining issue is
> whether or not the resulting sin(psi[1]-psi[0])
> will suffer loss of precision if psi[1]-psi[0]
> gets close to Pi/2. I'm not sure when this
> can occur. If this case is precisely
> complementary to the cos(phi[1]-phi[0]) case,
> then the fix will be easy, just switch between
> them when the condition is detected. However,
> before inserting that sort of switch, I would
> like to know if it is really necessary.
> 
> 
> Thanks again Ivan.
> 
> -- 
> G. Jungman
>