Discussion related to cado-nfs

[Paul Zimmermann <Paul.Zimmermann@inria.fr>]

       Dear Elena,

> Why did not the qmin parameter set to a much smaller value in all parameters
> files?
> It is true that sieving in these intervals takes a longer time but on the
> other hand, it will find much more relations. Is this statement true that 
> the
> found relations in the regions around 0 will be removed in the filtering?

when you decrease qmin, you get more duplicate relations. In previous versions
of cado-nfs, we started at qmin = lim1, where lim1 is the algebraic factor
base bound. Now we start at qmin = lim1/2, which seems better, but might not
be optimal. Please tell us if you find some better value of qmin for some
params.cxxx file.

> One more question, In params.c120, it is mentioned that the BWC is about
> WN+CN^2 where W is weight, N is size of matrix and C is a constant 17.2 It
> seems this relation is a very helpful for finding the best values of
> max_level merging and target_density to have a good tradeoff between W and 
> N.
> The question is whether C is 17.2 for all numbers? If not, how can I
> calculate it for other numbers such as RSA-512bit? 

This "constant" is maybe valid for a fixed size (and for a given machine),
but I'm not sure you can use it for other sizes. For example, for RSA-250
we did three filtering tries, with target densities 200, 225 and 250:

       N          W            WN      CN^2    WN+CN^2
200 435137414 87535677490    3.81e19  3.26e18  4.13e19
225 418993015 94485091257    3.96e19  3.02e18  4.26e19
250 404711409 101961355931   4.13e19  2.82e18  4.41e19

In the end, after some initial testing with bwc (after a few minutes or hours
you can get a precise idea of the total bwc time, extrapolating from the bwc
output), we decided to use the "250" matrix. This would mean C > 142.

In conclusion, the best method is to launch bwc.pl, and to extrapolate the
total time after a few iterations.

Best regards,
Paul