Dear Jori,

> And reason is of course clear, as Fredrik Johansson wrote "If you cache 
> Bernoulli numbers, - -".

in fact there is another reason: the MPFR code computes the Bernoulli numbers
exactly, as integers B(2n)*(2n+1)!, whereas Pari/GP computes a floating-point
approximation. For 1000-bit precision with input pi^2, and the parameters of
Pari/GP, this requires computing Bernoulli numbers of 3800 bits.

We should compute floating-point approximations of the Bernoulli numbers in
MPFR too, but this will require redoing the error analysis, which is non
trivial.

Paul

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