> which gives excellent results. Pari uses
>
> \[ |B_n| = \frac{2n!}{(2\pi)^n}\zeta(n) \]
>
> with floats but you have to completely control the precision.
I don't know exactly, but I'd bet that Sage builds on flint2 for the
computation of Bernoulli (implemented (if I am not wrong) by Fredrik
http://fredrikj.net/).
http://flintlib.org/benchmarks.html
Since that is free software, it would make sense to think about using
that library.
Ralf
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