mfaktc: a CUDA program for Mersenne prefactoring

[Batalov]

Originally Posted by James Heinrich

According to my chart based on one benchmark from a while ago, I have the 680 and 470 very close together, with the 680 slightly behind (206 vs 218 GHz-days/day). Should I increase the expected performance of the compute-3.0 cards?

edit: I've just added more 600 series GPUs to my list. What an ugly mess of computer 2.1 / 3.0 chips making up the lineup. And three variants of the GT 640! Performance-per-watt is all over the place, even performance itself: the GT 630 is rated 672 GFLOPS vs 415 GFLOPS for the 40nm version of the GT 640. But thanks to the discrepancy between 2.1 and 3.0 performance, the GT 640 still outperforms at mfaktc.

I suspect that the 640 which is currently in the table is the rebadged 4xx something (I've read that Nvidia and vendors are doing it).

But now the real (GK107) 640s started showing up (Amazon, Newegg, not Tigerdirect yet). Does anyone have one? I wonder how they measure up. I wonder what were they thinking while putting 2Gb of memory in the new entry level cards; probably, the redefinition of "entry" level or in preparation for even more bloated fine textures etc etc etc.

[James Heinrich]

Originally Posted by Batalov

I wonder what were they thinking while putting 2Gb of memory in the new entry level cards; probably, the redefinition of "entry" level or in preparation for even more bloated fine textures etc etc etc.

It's not such a bad thing -- once we have viable GPU-based P-1 software available maybe we can get 16GB videocards to run it on.

[Batalov]

Oh, you now have GK107s in the list. They look awful (even GDDR5)!
Ok, one less choice to think about (that's for the kids' computer upgrade). :-)

[James Heinrich]

Originally Posted by Batalov

Oh, you now have GK107s in the list. They look awful (even GDDR5)!

Based on very limited benchmark data, but should still be ballpark-accurate.

[TheJudger]

Originally Posted by James Heinrich

[...]
mfaktc:
compute 1.3 = 54%
compute 2.0 = 150%
compute 2.1 = 100%
compute 3.0 = 33%

My current feeling about CC 2.1 (e.g. GTX 460, GTX 560): The "performance issue" is not the ILP (instruction level parallism), it is just the 32-bit integer multiply performance of these chips. Take a recent version of the "CUDA C Programming Guide", in version 4.2 of this document there is a interesting table on page 74 (Arithmetic Instructions)... The additional cores per multiprocessor on the CC 2.1 chips (48 vs. 32 cores per multiprocessor) don't increase the throughput. Mfaktc needs alot of 32-bit interger multiplies...

Oliver

[dbaugh]

What is the real lower limit on exponent size?

no factor for M300109 from 2^60 to 2^61 [mfaktc 0.18-bcp-test2 75bit_mul32] by "David Campeau" on 2012-04-22

- David

[LaurV]

Originally Posted by dbaugh

What is the real lower limit on exponent size?

no factor for M300109 from 2^60 to 2^61 [mfaktc 0.18-bcp-test2 75bit_mul32] by "David Campeau" on 2012-04-22

- David

That is a custom, test version, distributed in "closed circles" to the people who can be trusted in reporting "no factor" results for such small exponents. For the respective version, the lowest limit is 2000. Such low exponents had a lot of ECM done, they theoretically have no factors under 40, 45, 50 decimal digits, that is much over 140-150-165 bits (except some unprobable ECM "miss"). So, again theoretically, one can report fake "no factors" results up to 80, 90 bits etc, without doing any tests, and without risking (too much) to be wrong, and getting thousands of GHzDays of TF credit for such reports. That would be childish, but people are tempted by that huge amount of credit.

If you think you qualify, and want to waste your time in TF-ing extremely-low-exponent range (again, it will be a waste of time, according with the amount of ECM done, and it will not help GIMPS, all exponents are doublechecked, but hey, finding factors is cool!), then you can ask Oliver for a copy. It is slower then the normal version, not only because of the higher amount of possible candidates (the amount of possible candidates at the same bit level is larger and larger as the exponent gets smaller and smaller), but also because special precautions needed in the software (see this thread, 4 or 5 pages before this current page). The revers of the coin is that - in spite of the amount of P-1 and ECM done - you still may find missed factors, and be hero. I did not find any factor up to now, and I only reported about 10% of the "no factors" results I got, and only after discussions with Oliver on PM, when he convinced me that "it is normal not to find factors" (I was very little confident in the beginning, after few hundred tests did not produce any factor, and I tried to push Oliver to look into it). After that I reported few results, and moved on to other work types, more useful for the project, tired to come out empty handed every time.

At least, taking "normal" (50M) exponents from gpu-2-72 is easier, you don't have to crawl the PrimeNet pages by yourself to look for unassigned stuff...

Bcp and few others are still doing this "TF-in-the-extremely-low-range" activity. You may directly PM them for news, status, coordination, etc.

[dbaugh]

Now, that's how to answer a question!! Many thanks. -DB

[c10ck3r]

For ze programmers...
How hard would it be to create a program to do TF in the same manner as mfaktc for, say, 3-, 5-, etc?
Just a curiosity, don't shoot the cat!

[Dubslow]

Originally Posted by c10ck3r

For ze programmers...
How hard would it be to create a program to do TF in the same manner as mfaktc for, say, 3-, 5-, etc?
Just a curiosity, don't shoot the cat!

Depends on if they have special forms for factors, like Meresnne numbers, and if so, how similar are those forms. You'll have to ask someone who knows some math to answer that question.

[Batalov]

Originally Posted by c10ck3r

For ze programmers...
How hard would it be to create a program to do TF in the same manner as mfaktc for, say, 3-, 5-, etc?
Just a curiosity, don't shoot the cat!

Not hard. Already exists. It is called mfaktc.

MrRepunit posted the modifications just recently for 10-. Run diff, observe the differences, check the mod classes for your favorite base. (b-1) is always a factor for b>2.

The harder part is not the code but keeping the dataset and making it easy for prospective contributors to contrubute. For 2- and 10-, there are interested people who do that, but what will you do with a small factor of, say, (3^10000019-1)/2 or even be sure that it has not been known for a decade, or that it will be found again tomorrow by someone? And lastly, who would be interested to know that factor?

For (3^10000079-1)/2, there are some very easy factors; for (3^10000103-1)/2, there's 39094722671497...