Bill Allombert on Tue, 03 Feb 2009 14:02:43 +0100

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Re: APRCL e(t) table

On Mon, Feb 02, 2009 at 04:32:27PM +0000, wrote:
> I am very impressed with the speed of the pari APRCL implementation -
> it beats by a long way the best public ECPP implementations, and looks

Really ? I find that rather unexpected and vaguely alarming. 

> as if the asymptotics will be significantly better up well into the
> range where the computations take too long.
> However for N>10^2000 or so it takes an awfully long time to compute a
> usable e(t), because it's calculating them to full precision (without
> using product trees in a product-of-600-ints situation -- is there a
> multiply-ints-with-product-tree function in the pari library?)

Yes, divide_conquer_prod.

> and comparing rather than comparing logarithms - and if I have debug
> set to 3 to get lots of APRCL logging, I get impossibly-many log
> messages from the isprime() calls in e(). I've computed e(t) (with my
> own code checked against pari's results) for t<10^9 and am doing it
> for t<10^11 with 5040|t; would you be interested in an improved e(t)
> table capable of handling at least N<10^5512.7 and probably well
> beyond ? I should have it ready by the end of the week.

Well, it would certainly be interesting!