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Old 2020-05-16, 19:03   #4
VBCurtis's Avatar
Feb 2005
Riverside, CA

22×13×89 Posts

Originally Posted by EdH View Post
- (degree) Is there a "rule-of-thumb" for determining what degree?

- (admin) Other than to eliminate duplication, is there a reason not to start searching at admin = 0?

- (nrkeep) I see 200 for the default number to keep at 190 digit sizes. If there is ranking of polynomials done to determine which 200 to keep, is it really possible that one far down the initial ranking would turn out better than the rest later on?
There is a theoretical property of NFS for determining degree. However, the poly-search capabilities of the software influence this also- deg 6 is simply harder to search than deg 5.
While using CADO, I've found the deg 4/5 cutoff to be just under 100 digits, and deg 5/6 to be around 215.
For SNFS, poly search obviously doesn't matter, so theory predicts optimal degree more accurately. If I recall, 4/5 is around 110 digits, 5/6 205-210, 6/7 340 or 350. Sorry that I'm too lazy to locate the formula for you!

There are two reasons to set admin:
1. As you've discovered quite a few times, CADO sometimes gets "stuck" on a small c5 value, delaying poly select quite a lot.
2. As the size of the input rises, it becomes less and less likely that a very-small c5 value will produce the best poly. Generally, this is because skew gets too high (at least, that's my layman's grasp of what goes on).

For 120-140 digit inputs, #1 has me setting admin in the 2000-10000 range to try to avoid those software hiccups. For 180-210 digits, I set admin higher because of #2.

How many polys to root-opt is a matter of time spent vs chance of reward. CADO has a better size-opt ranking algo than msieve, so it's not necessary to root-opt hundreds of polys in CADO like we used to in msieve. That said, at large inputs like 190 digits the root-opt phase is a tiny fraction of size-opt search time, so may as well root-opt a few hundred in case something unusual happens.
On small inputs, say <130 digits, the root-opt step is a large fraction of size-opt time; I've found I get better results by adding extra size-opt effort and reducing the nrkeep to 48 or lower. The time is better spent generating more candidates than hoping a 50th place poly ends up best after root-opt. You can see this clearly if you mess with the settings on a C100; root-opt takes longer than size-opt with default settings (if you change to deg 5, at least)! Doubling size-opt time and halving nrkeep usually yields a better poly. CADO root-opts in blocks of 6 polys, so I make nrkeep a multiple of 6 nearly always.
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