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Old 2019-05-16, 20:06   #11
bsquared
 
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"Ben"
Feb 2007

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Quote:
Originally Posted by henryzz View Post
The aim with SIQS is to make switching polynomial very fast such that many more polynomials can be used than MPQS. However, I believe that my implementation still spends 10% of its time switching A.
Is that time spent just building new A polys or does it also include setup time for the new poly (e.g., computing A^-1 mod p for all factor base p)? 10% seems high either way but if that's just for building new A polys then it seems *really* high. In contrast I usually spend < 3% total for building new A's and all of the setup for new A's.

Quote:
Originally Posted by henryzz View Post
At 50 digits I use about 11 As. This increases rapidly from here as numbers get bigger. Unless you are spending all your time generating them I wouldn't worry about having a few As. Each A had 6 factors allowing for 64 Bs per A .
Seems reasonable given your other parameters. I typically see anywhere from 50 to 150 A's at 50 digits, using 6 factors per A, but I use a far smaller factor base and sieve interval. It is all a tradeoff.

Quote:
Originally Posted by tabidots View Post

So my basic question is, what kind of gotchas should I look for with the polynomials to make sure they can capture as many smooth relations as possible? I have already verified that b^2 or (a - b)^2 is congruent to N mod a for each b.
I would ask, how are you determining smoothness exactly? In other words, the sieve value above (or below) which you try to find a relation. If your polynomials and roots are good then maybe it is as simple as tweaking your smoothness bound so as to generate more potential relation reports.

The value I use is obtained from a bunch of empirically determined magic numbers, loosely related to Contini's suggestion along the lines of:
"compute the number of bits in M/2*sqrt(N/2), then subtract some slack". M is the size of your sieve interval.
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