Re: Partitions with numbpart()

[Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>]

On Wed, Mar 07, 2018 at 04:48:29PM +0100, Karim Belabas wrote:
> * Paul Underwood [2018-03-07 15:06]:
> > What makes the latest PARI/GP much quicker when calculating partition
> > numbers? Compare versions 2.7.2 and 2.9.1.
> 
> A direct formula due to Selberg replaced the naive sum involving
> Dedekind sums, see Algorithm 1 in
> 
>   http://dx.doi.org/10.1112/S1461157012001088
> 
> (suggested by Fredrik Johansson). Done in
> 
>   commit dd11540e961686b625fd9638f2adc29030008c5c
>   Author: Bill Allombert <Bill.Allombert@math.u-bordeaux1.fr>
>   Date:   Wed Sep 24 19:02:21 2014 +0200
> 
> > To what extent has the latest version been tested?
> 
> To my knowledge, not extensively. (Checked explicitly for all integers
> up to 400.000 and for isolated values up to 10^9.) Feel free to extend
> that range !

On the other hand the new code is much simpler and was checked by
Fredrik, so it is probably also more robust.

Cheers,
Bill.