Implementation of Zeta functions in libstdc++

[Ed Smith-Rowland]

On 08/03/2014 08:28 PM, Florian Goth wrote:
> Hi!
> Thanks Ed for the kind reception of this idea.
> To show what I have done so far I have set up a git repository here:
> https://github.com/CaptainSifff/zeta
> Obviously it is not yet in a state where it looks like sth. from the standard library; it still uses my conventions right now.
> This commit
> https://github.com/CaptainSifff/zeta/commit/6f4d70975f0a064a1d551fd5319f5ac3391f4234
> gives an example where the old implementation failed and which essentially led me to recode all this.
> So, what do you think,
> What it be nice to have that functionality in gcc and is it worthwhile to patch it up for the std library?
> I would be willing to do the work and get a copyright assignment.
>   
> Another thing:
> I fiddled with the code for the evaluation of the Riemann Zeta function.
> By removing a lot of calls to special functions in the innermost loop I
> could speed it up by about a factor of 3 on my machines(core2 + core-i7).
> The commits are
> https://github.com/CaptainSifff/zeta/commit/d1d32f2ac2422d9c5408e1b850984dcb3cd2aeb6
> and to clean things up:
> https://github.com/CaptainSifff/zeta/commit/e48ba770a0591af8d56150401a50807218c00026
> The basic idea is to replace the evaluation of the binomial coefficient via exp(log(gamma(x)))
> by a recursive relation of the binomial coefficient. This does not worsen the numerical stability since
> all intermediate results are perfectly representable. Of course that hard boundary where the result of the binomial coefficient is not
> representable anymore is still present.
>   
>
> Florian.
>
Florian,

Great work!  Please continue your work.  The polylog function would also 
make a nice extension to the function library in it's own right.
Please begin you copyright assignment quickly - that can take a long 
time to get through.

Finally, this is a C++ library issue so we should move our conversation 
there.

Thank you,
Ed