|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, email@example.com 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! Cheers, Bill.