GIMPS HITS {insert number here} COMPUTERS - Page 3

Peter Nelson · 2005-10-26, 05:11

Quote:

Originally Posted by jinydu

Hmm... Do you think Primenet would ever reach 100 teraflops?

ANSWER: YES, and my prediction is before the end of this decade (ie by 2010).

Why? dualcore, multicore processors, math acceleration processors like clearspeed, faster clock speeds, better memory latency, bigger cache sizes in processors will all help improve GIMPS LL throughput, and many will help with "Flops" rating.

Peter Nelson · 2005-10-26, 05:17

When considering "flops" I think we should remember....

LL testing stats are based on having done a test ie all iterations had to be done with so many operations to do the ibdft in each iteration.

However, in terms of primenet credit, factoring is I think considered equivalent to work it avoids. eg IF (and it's rare) trial factoring finds a factor that work is considered as having saved the work of an LL test (actually having saved the work of one LL test PLUS the second doublecheck test). I think that is how its weighted (maybe times the probability of finding a factor in a trial factoring run).

In FAIR comparison of TOTAL gigaflops I would rather we knew and calculated the ACTUAL flops used in the trial factoring. eg if you find a factor at 60 bits level you don't TF further just say "factor found" and do the next exponent.

Therefore the TRUE aggregate primenet performance is total LL test flops PLUS the real TF flops (which we don't know) PLUS the real (P-1) flops (which we also don't know).

jinydu · 2005-10-26, 06:11

Quote:

Originally Posted by Peter Nelson

However, in terms of primenet credit, factoring is I think considered equivalent to work it avoids. eg IF (and it's rare) trial factoring finds a factor that work is considered as having saved the work of an LL test (actually having saved the work of one LL test PLUS the second doublecheck test). I think that is how its weighted (maybe times the probability of finding a factor in a trial factoring run).

I didn't know that. (Then again, I've thought for some time now that the amount of factoring credit I've received is suspiciously low).

Is it true, Mr. Woltman?

Peter Nelson · 2005-10-26, 08:25

There is a formula I once got to work to indicate what factoring credit I would get for a given TF test.

Maybe I can find it again to be sure.

My main point is that people wanting comparison would not count operations that "we didn't need to do because we found a factor".

fatphil · 2005-10-26, 09:12

Quote:

Originally Posted by ppo

how is it computed ?

What? The sustained/peak throughput?

If so - what was wrong with following the obvious link on the front page of the top 500 supercomputer site?

Peter Nelson · 2005-10-26, 09:27

For the top 500 list the PEAK value is the THEORETICAL most amount of work the cpu could do if fully busy all the time on all FP units.

The main figure quoted is the Rmax value. This is the max sustained ie the ACTUAL work which can be done in practice.

The proportion of actual out of peak varies between machine and type of program.

The reason its less may be interprocessor communications are of limited bandwidth, and problem of actually keeping the FP units busy passing them enough calcs.

All those benchmarks are done using Linpack program which is a standard, although there are others.

To compare with GIMPS, we are measuring actual tests done (ie work done) so should probably compare the GIMPS figure with the Rmax Linpack rather than the Peak Linpack.

markr · 2005-10-26, 11:57

Quote:

Originally Posted by Peter Nelson

However, in terms of primenet credit, factoring is I think considered equivalent to work it avoids. eg IF (and it's rare) trial factoring finds a factor that work is considered as having saved the work of an LL test (actually having saved the work of one LL test PLUS the second doublecheck test). I think that is how its weighted (maybe times the probability of finding a factor in a trial factoring run).

That's not been my experience. My one TF machine (a P-200 - three weeks per exponent!) recently found a factor, and my TF credit went up by much less than it does when it doesn't find a factor. When it's "no factor" I get a little over 0.1, and the factor was worth about a third of that.

axn · 2005-10-26, 12:40

The credit for a TF is much less than the credit for an LL test.

I think a current TF which tests to 2^67 gets about 0.1 CPU yr credit, where as a current primality test gets about 4 (?) CPU yr.

But if you find a factor during TF, you get 2.3 times the normal TF (not LL) credit - there's a catch, though. Suppose the factor was a 66 bit one, then you'll get the 2.3 times credit of that of TF'ing to 2^66. So the actual credit you get is affected by the factor size also.

P-1 is a whole different ball game - you get 0.001 or 0.0023 CPU yr depending on whether you found a factor or not - irrespective of the actual B1, B2 bounds.

garo · 2005-10-26, 13:00

Quote:

Originally Posted by Peter Nelson

There is a formula I once got to work to indicate what factoring credit I would get for a given TF test.

Maybe I can find it again to be sure.

My main point is that people wanting comparison would not count operations that "we didn't need to do because we found a factor".

No this is incorrect. The current formula is biased against factoring credit. That is on almost all machines running factoring gets you significantly less (say from 30-70% less) CPU years than LL testing. The ratio varies from machine to machine with the new P4 Celerons and AMD 64s being among the least penalized and Northwoods among the most penalized.

Moreover, there is no correlation between "work saved" and credit awarded. A 62 bit factor for the same number will receive 1/4th as much credit as a 64 bit factor for the same number. However, finding a factor does give you some additional credit as opposed to not finding a factor.

EDIT: axn1 has got it right. In addition a 62 bit factor will indeed score significantly less than factoring to 66 bits and not finding a factor.

jinydu · 2005-10-26, 15:05

So why the bias against trial factoring?

garo · 2005-10-26, 16:28

I guess this was a design decision with the v4 server that was never rectified. George is probably the best person to answer though I think it had something to do with making sure that only about 10% of processing computers chose factoring.

2005-10-26, 12:40	#30
axn Jun 2003 5,051 Posts	Credit for a TF The credit for a TF is much less than the credit for an LL test. I think a current TF which tests to 2^67 gets about 0.1 CPU yr credit, where as a current primality test gets about 4 (?) CPU yr. But if you find a factor during TF, you get 2.3 times the normal TF (not LL) credit - there's a catch, though. Suppose the factor was a 66 bit one, then you'll get the 2.3 times credit of that of TF'ing to 2^66. So the actual credit you get is affected by the factor size also. P-1 is a whole different ball game - you get 0.001 or 0.0023 CPU yr depending on whether you found a factor or not - irrespective of the actual B1, B2 bounds. Last fiddled with by axn on 2005-10-26 at 12:42 Reason: Grammar!

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2005-10-26, 05:17	#24
Peter Nelson Oct 2004 1021₈ Posts	When considering "flops" I think we should remember.... LL testing stats are based on having done a test ie all iterations had to be done with so many operations to do the ibdft in each iteration. However, in terms of primenet credit, factoring is I think considered equivalent to work it avoids. eg IF (and it's rare) trial factoring finds a factor that work is considered as having saved the work of an LL test (actually having saved the work of one LL test PLUS the second doublecheck test). I think that is how its weighted (maybe times the probability of finding a factor in a trial factoring run). In FAIR comparison of TOTAL gigaflops I would rather we knew and calculated the ACTUAL flops used in the trial factoring. eg if you find a factor at 60 bits level you don't TF further just say "factor found" and do the next exponent. Therefore the TRUE aggregate primenet performance is total LL test flops PLUS the real TF flops (which we don't know) PLUS the real (P-1) flops (which we also don't know).

2005-10-26, 08:25	#26
Peter Nelson Oct 2004 1021₈ Posts	There is a formula I once got to work to indicate what factoring credit I would get for a given TF test. Maybe I can find it again to be sure. My main point is that people wanting comparison would not count operations that "we didn't need to do because we found a factor".

2005-10-26, 09:27	#28
Peter Nelson Oct 2004 1021₈ Posts	For the top 500 list the PEAK value is the THEORETICAL most amount of work the cpu could do if fully busy all the time on all FP units. The main figure quoted is the Rmax value. This is the max sustained ie the ACTUAL work which can be done in practice. The proportion of actual out of peak varies between machine and type of program. The reason its less may be interprocessor communications are of limited bandwidth, and problem of actually keeping the FP units busy passing them enough calcs. All those benchmarks are done using Linpack program which is a standard, although there are others. To compare with GIMPS, we are measuring actual tests done (ie work done) so should probably compare the GIMPS figure with the Rmax Linpack rather than the Peak Linpack.

2005-10-26, 15:05	#32
jinydu Dec 2003 Hopefully Near M48 2·3·293 Posts	So why the bias against trial factoring?

2005-10-26, 16:28	#33
garo Aug 2002 Termonfeckin, IE ACC₁₆ Posts	I guess this was a design decision with the v4 server that was never rectified. George is probably the best person to answer though I think it had something to do with making sure that only about 10% of processing computers chose factoring.