Polynomial Request Thread

WraithX · 2013-06-26, 15:52

I've been doing polynomial searches for a C210 for 3 months (since Mar 16) on three different video cards (GTX550Ti, GTX570, and GTX580). In the last few weeks I've been really learning how to tweak the command line options to msieve to start getting good results. I started with degree 5 searches and have been doing a lot of degree 6 searches lately. I think the degree 6 searches are probably returning better results due to my better tweaking of the polynomial search options. Here are the best few results I've found so far. Hopefully this can help others know where their best scores for a C210 should be.

Code:

Degree 5
# norm 1.276810e-20 alpha -9.238464 e 9.932e-16 rroots 5 skew: 380780879.24
# norm 1.161363e-20 alpha -9.018629 e 9.234e-16 rroots 5 skew: 609572156.15
# norm 1.358701e-20 alpha -6.910857 e 1.038e-15 rroots 5 skew: 104279094.33
# norm 1.270759e-20 alpha -7.678108 e 9.961e-16 rroots 3 skew: 291528643.68

Degree 6
# norm 2.827871e-015 alpha -10.512910 e 9.028e-016 rroots 2 skew: 1564743.15
# norm 3.242080e-015 alpha -9.429823 e 1.024e-015 rroots 4 skew: 1013932.94
# norm 3.252680e-015 alpha -7.597478 e 1.032e-015 rroots 6 skew: 830332.96
# norm 3.384932e-015 alpha -7.504910 e 1.054e-015 rroots 6 skew: 673235.34
# norm 3.617168e-015 alpha -7.884669 e 1.120e-015 rroots 6 skew: 741885.74
# norm 3.407911e-015 alpha -8.473234 e 1.056e-015 rroots 6 skew: 788144.46
# norm 3.211134e-015 alpha -9.178180 e 1.016e-015 rroots 4 skew: 924161.97

Also, Jason, when was the msieve/CADO E score change/alignment made? All of the above results were with SVN 845 or later.

I see in the degree 6 group that the best E score has a pretty low alpha. There are some with slightly worse E that have much better alpha's. Will those poly's tend to be better than the one with the best E?

Also, when creating a job file for this C210, should I use the parameters referenced by Batalov in post #43 for the RSA-c212:

Code:

rlim: 250000000
alim: 500000000
lpbr: 33
lpba: 33
mfbr: 66
mfba: 96
rlambda: 2.7
alambda: 3.7

Or should I adjust any of those parameters up or down for this C210?

jasonp · 2013-06-26, 16:35

The comparison between polynomials is meant to be using the E-value alone; a better alpha just means that the average polynomial value is reduced by more when small primes are divided out of it, but the E value score accounts for that already. If the E-value is still worse, it means that across the sieving region the average polynomial value is still too large, and sieving is predicted to be slower.

That being said, when the E values are far apart, it doesn't mean that the sieving will be faster by the ratio of the E-values. Also, when the E values are close between two polynomials you don't necessarily know which one will sieve faster. And of course you can't directly compare degree 5 E-values with degree 6.

The change to the E-value computation occurred late last year in SVN838 (link).

lorgix · 2013-06-29, 17:29

Quote:

Originally Posted by VBCurtis

I think we both would benefit from playing with settings and finding polys for a couple of smaller numbers. Perhaps some of the heavy hitters in this forum would like to supply you and I a couple of C155-180s to poly search? We can discuss settings, try to learn what stage1 bound produces the largest rate of useful nps hits per hour of gpu time, etc.

I have a c147 in my own queue; I had just done -np for 5 days for a poly when this thread began. I tried to apply what we learned last week, and restarted the search. 24 hours of -np1 with stage1 set to 2e21 (default is 2.38e22) produced roughly 700MB of hits with a 460M, which will take almost a core-week to size optimize. This makes me wonder how -np manages to do all 3 steps with just one CPU thread without massively stalling the GPU.

So, my first tentative guideline is to set stage 1 norm 10x tighter than default when running -np1 on its own, and even then the cpu has no chance to keep up. Or does the -nps step work with the -t threads command?

If I understand previous advice, I should not bother to npr more than, say, 500 best nps hits?
-Curtis

Here are a few 157-digit GNFS candidates:

Code:

(181^103-1)/((181-1)*7417*3386023*1622748672647*767015484026387551*1656939272001358583196903067208809)
(877^79-1)/((877-1)*4583*208520387347*96078130292657*103086319456710261705085017633872730943681601)
(5591^61-1)/((5591-1)*16556099215542617537*743213379283195327995487*11686924821525596917649777)
(421^101-1)/((421-1)*3637*52859291287277*15527015834461272375419*384360771211140230121323*3103491858106402597710257788494888754189303)

They are also listed at the OPN composites page. They have each had a t50.

chris2be8 · 2013-07-03, 16:45

And here are a few C155s from the brent tables:

Code:

37^148+1: 53256352248508781310601406937700148401433921469238262986221221969535186719520246104398418441069199796933268854865064708804615169745013643006481466447660961
39^158+1: 57251144267448459013407835983100098695823895728185123234566440360247697204733683280958505357854575913997481470550923347918936942495096589838578570989796317
84^131-1: 41165489682949123266408283036002947056410598293692637659169409441265128442052082335024569998521857926287112862036984560544046563790581362400293870259353717

Decent polynomials would be much appreciated. And used within a few weeks.

Chris

VBCurtis · 2013-07-04, 06:25

Lorgix:
Here is the poly for the first of your C157s. Working on the second one now.

Code:

 # norm 3.949172e-015 alpha -8.210982 e 2.273e-012 rroots 5
skew: 1383524.30
c0: -10405392053173879819844165201642065059
c1: 36925967403223132546442214528403
c2: 58143858551344578567358429
c3: -109070046618529232111
c4: -37237435898622
c5: 7000056
Y0: -931783012256402861904377561482
Y1: 10572282005725577

msieve's "expected" range is 1.99 to 2.29, so this is the best I've found yet compared to the range.

wombatman · 2013-07-04, 20:13

I'm currently visiting my parents for a few days, but I'll take a whack at those C155 when I get back starting on Sunday night.

Edit: And man, Curtis, you're getting good at finding quality polynomials ;)

firejuggler · 2013-07-04, 22:45

for the last C155; i have

Code:

Fri Jul 05 00:42:15 2013  R0: -827616417405609634728088002150
Fri Jul 05 00:42:15 2013  R1: 28187403266123
Fri Jul 05 00:42:15 2013  A0: 5969861234518297522907000759225553806219
Fri Jul 05 00:42:15 2013  A1: -1242828883684993362593839952820816
Fri Jul 05 00:42:15 2013  A2: -314872315331335981141115807
Fri Jul 05 00:42:15 2013  A3: 7334506598186025480
Fri Jul 05 00:42:15 2013  A4: 1345922527272
Fri Jul 05 00:42:15 2013  A5: 106020
Fri Jul 05 00:42:15 2013  skew 10612394.92, size 3.542e-015, alpha -7.552, combined = 2.295e-012 rroots = 3

the skew is horrible, i'll try to get it better.

firejuggler · 2013-07-05, 01:20

another one a tad better

Code:

Fri Jul 05 03:08:35 2013  R0: -623447711050511546995815433789
Fri Jul 05 03:08:35 2013  R1: 8761390491389
Fri Jul 05 03:08:35 2013  A0: 905530941064703484336217099566456480
Fri Jul 05 03:08:35 2013  A1: -861646222655766816418285571222
Fri Jul 05 03:08:35 2013  A2: -3497899057671750440311749
Fri Jul 05 03:08:35 2013  A3: -1030131356148504116
Fri Jul 05 03:08:35 2013  A4: -152229414212
Fri Jul 05 03:08:35 2013  A5: 437052
Fri Jul 05 03:08:35 2013  skew 1472568.84, size 3.533e-015, alpha -4.681, combined = 2.342e-012 rroots = 3

wombatman · 2013-07-08, 04:21

I'm running the 1st C155 on the GPU overnight. I'll do the root optimization tomorrow during the day on the top 200 polynomials and report back what I get.

firejuggler · 2013-07-08, 09:32

I found a few god one, but 2 in particular might be of interest

Code:

Mon Jul 08 11:37:14 2013  Msieve v. 1.51 (SVN 845)
Mon Jul 08 11:37:14 2013  random seeds: 1b8e2a80 95a5f588
Mon Jul 08 11:37:14 2013  factoring 41165489682949123266408283036002947056410598293692637659169409441265128442052082335024569998521857926287112862036984560544046563790581362400293870259353717 (155 digits)
Mon Jul 08 11:37:15 2013  searching for 15-digit factors
Mon Jul 08 11:37:16 2013  commencing number field sieve (155-digit input)
Mon Jul 08 11:37:16 2013  commencing number field sieve polynomial selection
Mon Jul 08 11:37:16 2013  polynomial degree: 5
Mon Jul 08 11:37:16 2013  max stage 1 norm: 9.18e+023
Mon Jul 08 11:37:16 2013  max stage 2 norm: 5.99e+021
Mon Jul 08 11:37:16 2013  min E-value: 2.15e-012
Mon Jul 08 11:37:16 2013  poly select deadline: 1051656
Mon Jul 08 11:39:50 2013  polynomial selection complete
Mon Jul 08 11:39:50 2013  R0: -1501163178758465311986178676080
Mon Jul 08 11:39:50 2013  R1: 174924457784843
Mon Jul 08 11:39:50 2013  A0: 70988493301319445825160212365935410879
Mon Jul 08 11:39:50 2013  A1: 386946903243104424828373548939059
Mon Jul 08 11:39:50 2013  A2: -334142141498605234086353853
Mon Jul 08 11:39:50 2013  A3: 6353932963613881761
Mon Jul 08 11:39:50 2013  A4: 1028510168554
Mon Jul 08 11:39:50 2013  A5: 5400
Mon Jul 08 11:39:50 2013  skew 16379926.92, size 3.737e-015, alpha -7.395, combined = 2.379e-012 rroots = 5
Mon Jul 08 11:39:50 2013  elapsed time 00:02:36
Mon Jul 08 11:40:48 2013  Msieve v. 1.51 (SVN 845)
Mon Jul 08 11:40:48 2013  random seeds: 7a772be0 46b58b0b
Mon Jul 08 11:40:48 2013  factoring 41165489682949123266408283036002947056410598293692637659169409441265128442052082335024569998521857926287112862036984560544046563790581362400293870259353717 (155 digits)
Mon Jul 08 11:40:49 2013  searching for 15-digit factors
Mon Jul 08 11:40:50 2013  commencing number field sieve (155-digit input)
Mon Jul 08 11:40:50 2013  commencing number field sieve polynomial selection
Mon Jul 08 11:40:50 2013  polynomial degree: 5
Mon Jul 08 11:40:50 2013  max stage 1 norm: 9.18e+023
Mon Jul 08 11:40:50 2013  max stage 2 norm: 5.99e+021
Mon Jul 08 11:40:50 2013  min E-value: 2.15e-012
Mon Jul 08 11:40:50 2013  poly select deadline: 1051656
Mon Jul 08 11:43:11 2013  polynomial selection complete
Mon Jul 08 11:43:11 2013  R0: -407412222417409604224962008770
Mon Jul 08 11:43:11 2013  R1: 50546045697907
Mon Jul 08 11:43:11 2013  A0: -1286847112018991239507506042869013549
Mon Jul 08 11:43:11 2013  A1: -7383152566924000392587309855332
Mon Jul 08 11:43:11 2013  A2: 12227613193775654000123047
Mon Jul 08 11:43:11 2013  A3: 47036571506094985398
Mon Jul 08 11:43:11 2013  A4: -17650020048104
Mon Jul 08 11:43:11 2013  A5: 3667440
Mon Jul 08 11:43:11 2013  skew 864607.51, size 3.631e-015, alpha -6.985, combined = 2.377e-012 rroots = 3
Mon Jul 08 11:43:11 2013  elapsed time 00:02:23

the poly are
5400 174924457784843 1501163185421857259726011744947
3667440 50546045697907 407412222368757771589584073595

firejuggler · 2013-07-08, 17:10

Since my leading coefficient has reached 7e6 I have a dry spell, with very few hit passing the -npr stage between 7 and 20e6
( msieve1.50 has a few more, but because the score is sur-evaluated in 1.50, not in later). Should I widen my stage 1 limits?

2013-06-26, 15:52	#1
WraithX Mar 2006 541 Posts	Polynomial Request Thread I've been doing polynomial searches for a C210 for 3 months (since Mar 16) on three different video cards (GTX550Ti, GTX570, and GTX580). In the last few weeks I've been really learning how to tweak the command line options to msieve to start getting good results. I started with degree 5 searches and have been doing a lot of degree 6 searches lately. I think the degree 6 searches are probably returning better results due to my better tweaking of the polynomial search options. Here are the best few results I've found so far. Hopefully this can help others know where their best scores for a C210 should be. Code: Degree 5 # norm 1.276810e-20 alpha -9.238464 e 9.932e-16 rroots 5 skew: 380780879.24 # norm 1.161363e-20 alpha -9.018629 e 9.234e-16 rroots 5 skew: 609572156.15 # norm 1.358701e-20 alpha -6.910857 e 1.038e-15 rroots 5 skew: 104279094.33 # norm 1.270759e-20 alpha -7.678108 e 9.961e-16 rroots 3 skew: 291528643.68 Degree 6 # norm 2.827871e-015 alpha -10.512910 e 9.028e-016 rroots 2 skew: 1564743.15 # norm 3.242080e-015 alpha -9.429823 e 1.024e-015 rroots 4 skew: 1013932.94 # norm 3.252680e-015 alpha -7.597478 e 1.032e-015 rroots 6 skew: 830332.96 # norm 3.384932e-015 alpha -7.504910 e 1.054e-015 rroots 6 skew: 673235.34 # norm 3.617168e-015 alpha -7.884669 e 1.120e-015 rroots 6 skew: 741885.74 # norm 3.407911e-015 alpha -8.473234 e 1.056e-015 rroots 6 skew: 788144.46 # norm 3.211134e-015 alpha -9.178180 e 1.016e-015 rroots 4 skew: 924161.97 Also, Jason, when was the msieve/CADO E score change/alignment made? All of the above results were with SVN 845 or later. I see in the degree 6 group that the best E score has a pretty low alpha. There are some with slightly worse E that have much better alpha's. Will those poly's tend to be better than the one with the best E? Also, when creating a job file for this C210, should I use the parameters referenced by Batalov in post #43 for the RSA-c212: Code: rlim: 250000000 alim: 500000000 lpbr: 33 lpba: 33 mfbr: 66 mfba: 96 rlambda: 2.7 alambda: 3.7 Or should I adjust any of those parameters up or down for this C210?

2013-07-04, 20:13	#6
wombatman I moo ablest echo power! May 2013 73F₁₆ Posts	I'm currently visiting my parents for a few days, but I'll take a whack at those C155 when I get back starting on Sunday night. Edit: And man, Curtis, you're getting good at finding quality polynomials ;) Last fiddled with by wombatman on 2013-07-04 at 20:20

2013-07-08, 17:10	#11
firejuggler "Vincent" Apr 2010 Over the rainbow 2²×7×103 Posts	Since my leading coefficient has reached 7e6 I have a dry spell, with very few hit passing the -npr stage between 7 and 20e6 ( msieve1.50 has a few more, but because the score is sur-evaluated in 1.50, not in later). Should I widen my stage 1 limits? Last fiddled with by firejuggler on 2013-07-08 at 17:10

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2013-06-26, 16:35	#2
jasonp Tribal Bullet Oct 2004 3,559 Posts	The comparison between polynomials is meant to be using the E-value alone; a better alpha just means that the average polynomial value is reduced by more when small primes are divided out of it, but the E value score accounts for that already. If the E-value is still worse, it means that across the sieving region the average polynomial value is still too large, and sieving is predicted to be slower. That being said, when the E values are far apart, it doesn't mean that the sieving will be faster by the ratio of the E-values. Also, when the E values are close between two polynomials you don't necessarily know which one will sieve faster. And of course you can't directly compare degree 5 E-values with degree 6. The change to the E-value computation occurred late last year in SVN838 (link).

2013-07-08, 04:21	#9
wombatman I moo ablest echo power! May 2013 5×7×53 Posts	I'm running the 1st C155 on the GPU overnight. I'll do the root optimization tomorrow during the day on the top 200 polynomials and report back what I get.