Discussion related to cado-nfs

[eric.jeancolas@free.fr]

I got it! I used tasks.I=13 instead of tasks.I=12 and a 
tasks.sieve.allow_largesq=true option.
But it took : "Total cpu/elapsed time for entire factorization: 
2.97337e+06/288428" on my 12-core CPU.
Roughly what it would have taken in a standard GNFS factorization for this 
number. So my SNFS polynomial has not been very efficient compared with 
GNFS...
Thanks to you, I understand better the various parameters.
Best regards, Eric


----- Mail original -----
De: "eric jeancolas" <eric.jeancolas@free.fr>
À: "Emmanuel Thomé" <Emmanuel.Thome@inria.fr>
Cc: cado-nfs-discuss@lists.gforge.inria.fr
Envoyé: Mardi 25 Août 2020 12:35:26
Objet: Re: [Cado-nfs-discuss] Breaking a loop in sieving

Thank you for these explanations. I'll keep you posted on the success or 
failure of the different attempts. As it may take a while, the update of this 
thread may take some time.
Best regards, Eric


----- Mail original -----
De: "Emmanuel Thomé" <Emmanuel.Thome@inria.fr>
À: cado-nfs-discuss@lists.gforge.inria.fr
Envoyé: Mardi 25 Août 2020 12:25:38
Objet: Re: [Cado-nfs-discuss] Breaking a loop in sieving

On Mon, Aug 24, 2020 at 05:46:55PM +0200, eric.jeancolas@free.fr wrote:
> Hi
> 
> I have a number whose candidate SNFS is # f(x) = 13717421*x^5-260630989000, 
> # g(x) = -x+1000000000000000000000000000000000
> 
> I get the following problem. Please look at these entries in the log :
> PID21598 2020-08-18 08:33:51,378 Info:Filtering - Singleton removal: After 
> purge, 9696 relations with 380267 primes remain with excess -370571
> PID21598 2020-08-18 09:14:04,744 Info:Filtering - Singleton removal: After 
> purge, 9698 relations with 380268 primes remain with excess -370570
> PID21598 2020-08-18 09:59:50,666 Info:Filtering - Singleton removal: After 
> purge, 9704 relations with 380271 primes remain with excess -370567
> PID21598 2020-08-18 10:47:40,085 Info:Filtering - Singleton removal: After 
> purge, 9708 relations with 380273 primes remain with excess -370565
> PID21598 2020-08-18 11:36:27,501 Info:Filtering - Singleton removal: After 
> purge, 9708 relations with 380273 primes remain with excess -370565
> You see that there is no progress.
> 
> On this one, it ended up with a this error: The special q (28 bits) is 
> larger than the large prime bound on side 0 (27 bits). If I put 
> tasks.sieve.allow_largesq=true, the loop hereabove seems to never end.
> 
> Indeed, at this occurs after a first 100% relations achievement, is there a 
> mean to tell cado something like:
> "Hey cado, let's consider we have enough relations and let's proceed."

The thing is that you can't proceed, unfortunately. A negative excess
after purge means that you don't have enough relations.

Your parameters are not suited to the number you're trying to factor.
You're exhausting your special-q range with too few relations.

There are various things that you can try to do. All of them,
unfortunately, mean that you're going to start over.

The first suggestion is to use a larger sieve area (tasks.I). This means
more effort per q. (For practical matters, you'll probably want to reduce
your q-range accordingly, so that individual jobs remain manageable.)

You should also make sure that you don't miss too many relations. E.g.
set the tasks.lim0 and tasks.lim1 parameters to something that is in the
whereabouts of 2^(2*I-1) / 4.

The cofactoring parameters deserve some caution as well. Larger lpb
parameters means more relations needed. Smaller means less relations, but
harder to find. The ratio between the mfb and lpb bounds should also be
looked at (a ratio of two is not a bad starting point in general).

The interactions of all that are complex, and your mileage may vary. All
paremeters above are entangled, and there's little sense in attempting to
optimize one without paying attention to the others.

E.

> 
> Best regards. Eric.
> 
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