ok, so the docstring reaveals (1) that the pari version is "by far the
fastest" as I suspected, but also that for n>50000 that we use a gp
interface rather than the pari library " since the C-library interface
to PARI
is limited in memory for individual operations" -- whatever that means!
That might explain David's timing observations.
I tihnk the pari implementation is actually quite simple (and there is
a huge amount about Berouilli nos in Henri Cohen's latest book too)
which suggests that doing a cython implementation would not be hard.
Maybe this is time for a repeat performance of the partitions
competition with M**ca!
John
2008/5/2 John Cremona <[EMAIL PROTECTED]>:
> I might take a look at this, as there are some ways fo computing B nos
> which are very much faster tha others, and not everyone knows them.
> Pari has something respectable, certainly.
>
> John
>
> 2008/5/2 mhampton <[EMAIL PROTECTED]>:
>
>
> >
> > It takes about 30 seconds on my machine to get the 10^5 Bernoulli
> > number. The mathematica blog says it took a "development" version of
> > mathematica 6 days to do the 10^7 calc. So it would probably take
> > some work, but we are not that badly off as is.
> >
> > -M. Hampton
> >
> > On May 2, 12:34 pm, Fredrik Johansson <[EMAIL PROTECTED]>
> > wrote:
> >
> > > Oleksandr Pavlyk reports on the Wolfram Blog that he has computed the
> > > 10 millionth Bernoulli number using
> Mathematica:http://blog.wolfram.com/2008/04/29/today-we-broke-the-bernoulli-recor...
> >
> >
> > >
> > > How does sage's Bernoulli number implementation compare? I'd like to
> > > see bernoulli(10^7) in sage beating Mathematica's time. And then
> > > computing the 20 millionth Bernoulli number...
> > >
> > > Fredrik
> > > >
> >
>
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