Estimating number of relations needed

swishzzz · 2020-10-21, 19:07

I am trying to run a 200 digit SNFS job for the first time and after sieving from 7.5M to ~15M I've collected about 33.5M relations vs the estimated minimum of about 28.6M but it isn't getting past the filtering step. It reduces to just 3499 relations and 0 ideals after some number of passes and the number of duplicate relations is about 10% the number of relations which is similar to that of some smaller jobs I've finished.

Anyway, I would have expected the number of relations and ideals after filtering to be much greater than what is indicated here. I'm not sure if the issue can be resolved just with more sieving, but if that is the case is there a way to reliably estimate how many more relations I might need?

Full log is also attached.

Code:

Wed Oct 21 14:44:04 2020  Msieve v. 1.53 (SVN unknown)
Wed Oct 21 14:44:04 2020  random seeds: bd75a574 74f633da
Wed Oct 21 14:44:04 2020  factoring 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001023 (200 digits)
Wed Oct 21 14:44:05 2020  searching for 15-digit factors
Wed Oct 21 14:44:05 2020  commencing number field sieve (200-digit input)
Wed Oct 21 14:44:05 2020  R0: 5000000000000000000000000000000000000000
Wed Oct 21 14:44:05 2020  R1: -1
Wed Oct 21 14:44:05 2020  A0: 5115
Wed Oct 21 14:44:05 2020  A1: 0
Wed Oct 21 14:44:05 2020  A2: 0
Wed Oct 21 14:44:05 2020  A3: 0
Wed Oct 21 14:44:05 2020  A4: 0
Wed Oct 21 14:44:05 2020  A5: 16
Wed Oct 21 14:44:05 2020  skew 3.17, size 3.898e-14, alpha 0.504, combined = 1.155e-11 rroots = 1
Wed Oct 21 14:44:05 2020  
Wed Oct 21 14:44:05 2020  commencing relation filtering
Wed Oct 21 14:44:05 2020  estimated available RAM is 7542.8 MB
Wed Oct 21 14:44:05 2020  commencing duplicate removal, pass 1
Wed Oct 21 14:47:13 2020  error -15 reading relation 30460330
Wed Oct 21 14:47:24 2020  error -15 reading relation 32331885
Wed Oct 21 14:47:25 2020  error -15 reading relation 32392947
Wed Oct 21 14:47:25 2020  error -11 reading relation 32423445
Wed Oct 21 14:47:30 2020  error -9 reading relation 33359915
Wed Oct 21 14:47:31 2020  skipped 5 relations with composite factors
Wed Oct 21 14:47:31 2020  found 3606403 hash collisions in 33483146 relations
Wed Oct 21 14:47:49 2020  added 75 free relations
Wed Oct 21 14:47:49 2020  commencing duplicate removal, pass 2
Wed Oct 21 14:48:00 2020  found 3078858 duplicates and 30404363 unique relations
Wed Oct 21 14:48:00 2020  memory use: 138.6 MB
Wed Oct 21 14:48:00 2020  reading ideals above 720000
Wed Oct 21 14:48:00 2020  commencing singleton removal, initial pass
Wed Oct 21 14:50:59 2020  memory use: 753.0 MB
Wed Oct 21 14:50:59 2020  reading all ideals from disk
Wed Oct 21 14:51:00 2020  memory use: 1037.9 MB
Wed Oct 21 14:51:02 2020  keeping 38289591 ideals with weight <= 200, target excess is 159943
Wed Oct 21 14:51:04 2020  commencing in-memory singleton removal
Wed Oct 21 14:51:06 2020  begin with 30404363 relations and 38289591 unique ideals
Wed Oct 21 14:51:12 2020  reduce to 3499 relations and 0 ideals in 17 passes
Wed Oct 21 14:51:12 2020  max relations containing the same ideal: 0
Wed Oct 21 14:51:12 2020  filtering wants 1000000 more relations

Brownfox · 2020-10-21, 19:35

I think you've just crossed a boundary into needing the 14e siever, which is why it seems to be longer.

It just needs more relations - probably 40-45 million, based on similar numbers that I've factored.

VBCurtis · 2020-10-21, 20:54

If the large-prime bound jumped up 1 from your previous jobs, you'll need about 70% more relations than you did for the previous jobs, but not all that much more overall wall-clock time; more relations are found per unit time with a larger large-prime setting.

That's the lpbr and lpba setting in the .poly file.

SNFS has a bunch of moving parts; experience will show you the way. If you're using the factmsieve.py script, the target relations numbers are not very accurate. You can edit the script as you gain experience, to have it not bother trying to filter until it's in the ballpark of your previous jobs of that size. There is quite a bit of speed to be found in tweaking the settings in that script; YAFU has incorporated lots of such tweaks, and if you're in Linux then CADO is faster still but takes some experience to run for SNFS jobs.

swishzzz · 2020-10-21, 21:43

Thanks for the explanations everyone. This job did switch from the 13e to the 14e siever compared to the last one (156 digits) and the large prime bounds actually jumped twice from 2^27 to 2^29. I think I will just manually modify the relations estimate in the factmsieve.py script for now.

LaurV · 2020-10-22, 07:53

I edited the OP, see there the reason. Please mind for the future.

chris2be8 · 2020-10-22, 16:17

Quote:

Originally Posted by swishzzz

Code:

Wed Oct 21 14:51:12 2020  reduce to 3499 relations and 0 ideals in 17 passes

That line implies you need at least 30% more relations. You might need a lot more but won't need significantly less than that.

If the number of relations, X, and the number of ideals, Y, are both reasonably large (at least 4 digits) and X < Y then add 10%+(Y-X)*4 else add 5%.

That's an empirical relationship (ie I don't know why it works). But it's useful.

Chris

swishzzz · 2020-10-23, 01:30

Quote:

Originally Posted by chris2be8

That line implies you need at least 30% more relations. You might need a lot more but won't need significantly less than that.

If the number of relations, X, and the number of ideals, Y, are both reasonably large (at least 4 digits) and X < Y then add 10%+(Y-X)*4 else add 5%.

That's an empirical relationship (ie I don't know why it works). But it's useful.

Chris

Interesting. I've just completed this factorization and my numbers were a little less than what your formula would have suggested. Ended up needing 42.2M raw relations (about 26% more than in my first post); 35.9M was where it first filtered down to a non-trivial number of relations with 4.5M relations and 5.6M ideals, which would have meant 8M relations or ~44M total.

chris2be8 · 2020-10-23, 16:10

I worked out my guidelines doing rather smaller SNFS jobs than your job. So I'm not too surprised you managed with fewer relations. A better guess would take the duplicate rate into account as well. It's only a rough guide but a lot better than repeatedly trying to build a matrix until we have enough relations.

Chris

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2020-10-21, 19:35	#2
Brownfox Dec 2017 3F₁₆ Posts	I think you've just crossed a boundary into needing the 14e siever, which is why it seems to be longer. It just needs more relations - probably 40-45 million, based on similar numbers that I've factored.

2020-10-21, 20:54	#3
VBCurtis "Curtis" Feb 2005 Riverside, CA 2·2,339 Posts	If the large-prime bound jumped up 1 from your previous jobs, you'll need about 70% more relations than you did for the previous jobs, but not all that much more overall wall-clock time; more relations are found per unit time with a larger large-prime setting. That's the lpbr and lpba setting in the .poly file. SNFS has a bunch of moving parts; experience will show you the way. If you're using the factmsieve.py script, the target relations numbers are not very accurate. You can edit the script as you gain experience, to have it not bother trying to filter until it's in the ballpark of your previous jobs of that size. There is quite a bit of speed to be found in tweaking the settings in that script; YAFU has incorporated lots of such tweaks, and if you're in Linux then CADO is faster still but takes some experience to run for SNFS jobs.

2020-10-21, 21:43	#4
swishzzz Jan 2012 Toronto, Canada 2×3³ Posts	Thanks for the explanations everyone. This job did switch from the 13e to the 14e siever compared to the last one (156 digits) and the large prime bounds actually jumped twice from 2^27 to 2^29. I think I will just manually modify the relations estimate in the factmsieve.py script for now.

2020-10-22, 07:53	#5
LaurV Romulan Interpreter Jun 2011 Thailand 10010000111011₂ Posts	I edited the OP, see there the reason. Please mind for the future.

2020-10-23, 16:10	#8
chris2be8 Sep 2009 2·17·59 Posts	I worked out my guidelines doing rather smaller SNFS jobs than your job. So I'm not too surprised you managed with fewer relations. A better guess would take the duplicate rate into account as well. It's only a rough guide but a lot better than repeatedly trying to build a matrix until we have enough relations. Chris