Polynomial Request Thread - Page 73

Max0526 · 2017-03-29, 02:31

A slightly better CADO poly:

Code:

Y0: -6563265022568774266354892868611644711400
Y1: 14737700014198380373
c0: -195885654413301742021926350959343936846901860317941
c1: 225759882978210651012918348758579232741188
c2: 23787287493217528319014779999797510
c3: -86292463186759936420108
c4: -70345879932722289
c5: 15085800
skew: 587128506.45611
# lognorm 67.05, E 59.17, alpha -7.88 (proj -1.63), 5 real roots
# MurphyE=1.45014533e-15

confirmed by Msieve:

Code:

# norm 2.357623e-020 alpha -7.882749 e 1.451e-015 rroots 5
skew: 590194466.72
c0: -155816516757130071851347426182023045751672788361920
c1: 1954676842875294690924920084664967178519488
c2: 23218698382896016535491833976337972
c3: -10192710744975184308713704
c4: -67582426053083289
c5: 15085800
Y0: 6563265022568234328740961989776894720257
Y1: -14737700014198380373

firejuggler · 2017-03-29, 12:51

For an imput this large, wouldn't a poly of degree 6 work better?

wombatman · 2017-03-29, 13:06

Quote:

Originally Posted by firejuggler

For an imput this large, wouldn't a poly of degree 6 work better?

Based on a post from earlier in the thread (post 742 or so?), probably not. But I'm not opposed to trying the best scoring degree 6 polynomials just in case.

VBCurtis · 2017-03-29, 21:29

C207 is near the deg-6 cutoff. Msieve struggles with root-opt on deg 6, and Frmky found that even at C215 deg 5 and deg 6 were comparable. CADO's default parameters for c205 are deg 5, while c210 is deg 6; I haven't tried a deg 6 CADO search yet.

Here are the best finds from a CADO search from 10M to 11.1M:

Code:

n: 183724913753361567376492453926230323715345031792001208551707422272237266349933302881515963689094609592709968359761386456940894165548045328984901031969851838708505435691913321760214712695688550560374318369687
skew: 838496424.417
c0: 46940669866055547823109313162012850262763741523200
c1: 3236905767184422265163991871076044888757900
c2: -800578443717778675552745489973381
c3: -17574786098948226617271999
c4: 8665969938351911
c5: 10155780
Y0: -7103803724224543650738252214965600685669
Y1: 3627703029879009973753

Code:

n: 183724913753361567376492453926230323715345031792001208551707422272237266349933302881515963689094609592709968359761386456940894165548045328984901031969851838708505435691913321760214712695688550560374318369687
skew: 320908967.954
c0: 50608218075941554941592343353365754461981759507263
c1: 1381441172185986964849824511200946637939843
c2: -1233655127349780859186011448195019
c3: -50450709273026749596417827
c4: 77575300139332788
c5: 133553160
Y0: -7087473485773569538658762369110485778080
Y1: 3494915370090810326597

Code:

n: 183724913753361567376492453926230323715345031792001208551707422272237266349933302881515963689094609592709968359761386456940894165548045328984901031969851838708505435691913321760214712695688550560374318369687
skew: 366230198.92
c0: 813773569588275365261968461425817298866674784690768
c1: 3861383057198851187427587436368696332048911
c2: -61631780767810719575743108271687814
c3: -91573071945657692896492335
c4: 671457495195380950
c5: 154701960
Y0: -6984897769444385728403767460772654452734
Y1: 3258137590889412483491

I don't have scores for these; I was messing with settings in the params file, and my E-scores came out meaningless (like e-12 range).
I'd appreciate it if someone could post scores for these polys, so I can compare CADO performance to msieve on this number.
The first two are from 10-11M run, while the third is from 11-11.1. I can't even compare the E-scores from the third to the first two, but I expect the first one to be the best (best from a run 10x longer than third, while 2nd had a score 6% lower than first).

Max0526 · 2017-03-29, 22:00

Code:

c0: 46940669866055547823109313162012850262763741523200
c1: 3236905767184422265163991871076044888757900
c2: -800578443717778675552745489973381
c3: -17574786098948226617271999
c4: 8665969938351911
c5: 10155780
Y0: -7103803724224543650738252214965600685669
Y1: 3627703029879009973753
skew: 705844749.41479
E: 1.35647549e-15

Code:

c0: 50608218075941554941592343353365754461981759507263
c1: 1381441172185986964849824511200946637939843
c2: -1233655127349780859186011448195019
c3: -50450709273026749596417827
c4: 77575300139332788
c5: 133553160
Y0: -7087473485773569538658762369110485778080
Y1: 3494915370090810326597
skew: 292023526.43429
E: 1.23478058e-15

Code:

c0: 813773569588275365261968461425817298866674784690768
c1: 3861383057198851187427587436368696332048911
c2: -61631780767810719575743108271687814
c3: -91573071945657692896492335
c4: 671457495195380950
c5: 154701960
Y0: -6984897769444385728403767460772654452734
Y1: 3258137590889412483491
skew: 353529344.18221
E: 9.05441400e-16

VBCurtis · 2017-03-30, 03:03

Thanks, Max.
So, 7 thread-days of CADO produces a best poly roughly in the ballpark of 2 GPU-days of msieve (my best from msieve so far is 1.38e-15). Seems, at least for this size of project, that CADO can profitably be run for poly select, particularly for those not GPU-endowed.

Or, for those of us who prefer our familiar tools, msieve hasn't been usurped yet! My CADO install was a fresh git-clone as of Monday.

firejuggler · 2017-03-30, 19:41

Can someone do the root optimistion step of this line on CADO? The stage 2 score is very good but the stage1 score was left at default at the time, so the resulting e-score isn't good.

Code:

15371820 199603181376851496 -464061867426405603721855 -536423470663592338542591101952400 3139561114446069455952657370671068118688 190076853681281304214128837345996420962798447979 72539914394644909709 -6538656944145978618245663846995823201854 -2.17 5.814211e+026

For my est score, see a few post earlier, 1.425 e-15, and it has a second stage value of 3.975482e+027 compared to the 5.8xxxxxe+026 above.

Max0526 · 2017-03-31, 00:35

@firejuggler
Is your E score for this poly also 4.81160629e-16? (skew: 61396319.59660 or so?)
If so, CADO will not do the magic optimizing it to > 1.425 e-15. Too big of a stretch.

Max0526 · 2017-03-31, 00:47

@firejuggler
Oops! Ignore my previous post. I guess you are asking to optimize

Code:

R0: -6538656944147030901974729281399477396702
R1: 72539914394644909709
A0: -41444190994060695382448148406658444357662062124275
A1: 754844027559316401567668757262830610578795
A2: -264679992220691908321444752075053
A3: -12013706814805249129944703
A4: 198488242366576296
A5: 15371820
skew 282712296.24, size 1.468e-020, alpha -7.436, combined = 1.186e-015 rroots = 3

The jump from 1.186e-15 to > 1.425e-15 (or a CADO optimized 1.451e-15 -- see my March 28th post) seems not very likely.
For the fun of it though, I'll try and let you know.

wombatman · 2017-03-31, 01:22

Just as an update, I've taken the polynomials provided thus far and re-run them with my best found one. A number of the provided ones were better, and the best (shown below) decreased the expected run time by ~1/3.

Code:

Y0: -6563265022568774266354892868611644711400
Y1: 14737700014198380373
c0: -195885654413301742021926350959343936846901860317941
c1: 225759882978210651012918348758579232741188
c2: 23787287493217528319014779999797510
c3: -86292463186759936420108
c4: -70345879932722289
c5: 15085800
skew: 587128506.45611
type: gnfs

firejuggler · 2017-03-31, 02:03

thank you Max.

2017-03-30, 19:41	#799
firejuggler Apr 2010 Over the rainbow 2·1,303 Posts	Can someone do the root optimistion step of this line on CADO? The stage 2 score is very good but the stage1 score was left at default at the time, so the resulting e-score isn't good. Code: 15371820 199603181376851496 -464061867426405603721855 -536423470663592338542591101952400 3139561114446069455952657370671068118688 190076853681281304214128837345996420962798447979 72539914394644909709 -6538656944145978618245663846995823201854 -2.17 5.814211e+026 For my est score, see a few post earlier, 1.425 e-15, and it has a second stage value of 3.975482e+027 compared to the 5.8xxxxxe+026 above. Last fiddled with by firejuggler on 2017-03-30 at 19:47

2017-03-31, 00:35	#800
Max0526 "Max" Jun 2016 Toronto 19×47 Posts	root optimization in CADO @firejuggler Is your E score for this poly also 4.81160629e-16? (skew: 61396319.59660 or so?) If so, CADO will not do the magic optimizing it to > 1.425 e-15. Too big of a stretch.

2017-03-31, 00:47	#801
Max0526 "Max" Jun 2016 Toronto 19×47 Posts	root optimization in CADO @firejuggler Oops! Ignore my previous post. I guess you are asking to optimize Code: R0: -6538656944147030901974729281399477396702 R1: 72539914394644909709 A0: -41444190994060695382448148406658444357662062124275 A1: 754844027559316401567668757262830610578795 A2: -264679992220691908321444752075053 A3: -12013706814805249129944703 A4: 198488242366576296 A5: 15371820 skew 282712296.24, size 1.468e-020, alpha -7.436, combined = 1.186e-015 rroots = 3 The jump from 1.186e-15 to > 1.425e-15 (or a CADO optimized 1.451e-15 -- see my March 28th post) seems not very likely. For the fun of it though, I'll try and let you know.

2017-03-31, 01:22	#802
wombatman I moo ablest echo power! May 2013 6F5₁₆ Posts	Just as an update, I've taken the polynomials provided thus far and re-run them with my best found one. A number of the provided ones were better, and the best (shown below) decreased the expected run time by ~1/3. Code: Y0: -6563265022568774266354892868611644711400 Y1: 14737700014198380373 c0: -195885654413301742021926350959343936846901860317941 c1: 225759882978210651012918348758579232741188 c2: 23787287493217528319014779999797510 c3: -86292463186759936420108 c4: -70345879932722289 c5: 15085800 skew: 587128506.45611 type: gnfs

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2017-03-29, 12:51	#794
firejuggler Apr 2010 Over the rainbow 2×1,303 Posts	For an imput this large, wouldn't a poly of degree 6 work better?

2017-03-30, 03:03	#798
VBCurtis "Curtis" Feb 2005 Riverside, CA 4873₁₀ Posts	Thanks, Max. So, 7 thread-days of CADO produces a best poly roughly in the ballpark of 2 GPU-days of msieve (my best from msieve so far is 1.38e-15). Seems, at least for this size of project, that CADO can profitably be run for poly select, particularly for those not GPU-endowed. Or, for those of us who prefer our familiar tools, msieve hasn't been usurped yet! My CADO install was a fresh git-clone as of Monday.

2017-03-31, 02:03	#803
firejuggler Apr 2010 Over the rainbow 2606₁₀ Posts	thank you Max.