Dual CPU usage (was: Re: Mersenne: Best chance to make a real contribution?)
On 22 Jan 00, at 15:44, St. Dee wrote: This brings up something I've been wondering about. I have a dual Celeron setup running 2 instances of mprime under Linux. With both processors crunching on LL tests, I get iteration times for each processor of around .263 for exponents around 899 (where they are presently cranking). However, if one of them factors while the other does LL testing, the processor doing the LL testing takes about .220 seconds per iteration, while the one factoring also shows a factoring speed more consistent with the speed I would expect for the processor speed. The "problem" here is that the two processors are sharing access to the memory bus. Trial factoring actually uses very little memory access (actually it runs more or less from the L1 cache!) whereas LL testing really does thrash the memory subsystem (unless you have a Xeon with 2MB L2 cache, and even then only if you're testing an exponent less than 10,320,000). I presume you have BX chipset and PC100 memory. Even so, asking for twice the 66 MHz bandwidth of each Celeron CPU is going to congest the memory subsystem, which explains the slowdown. However, the problem is not unique to dual Celeron systems. Unless you have a multi-processor system with a seperate memory bus for each processor - and some means of intercommunication e.g. multiporting - the same problem is going to strike. To the best of my knowledge, only very expensive server motherboards use this technology. (Compaq did have a dual CPU workstation MB based on this technology but they seem to have dropped it when 100 MHz systems came in.) For systems using large clock multipliers, increasing the throughput of the memory bus will help mprime/Prime95 performance substantially - even for uniprocessor systems. In my experience, systems running the VIA chipset using PC133 memory are very disappointing - my PIII- 533 is turning in times very similar to the PII-400 benchmarks. I get the impression that there is a 100 MHz bottleneck inside the chipset, even when CPU and memory buses are both set to 133 MHz. Or it's actually driving the CPU at 100 MHz irrespective of the board jumpers and setup. Intel's Rambus technology looks interesting from this point of view - and boards which use it are starting to filter on to the market. A practical problem is that Rambus memory is extortionately expensive - at least 4 times the price of SDRAM, and you can't even get modules smaller than 64 MB. Intel recently released a version of some boards using the 820 chipset (designed for Rambus) which can take 133 MHz SDRAM, but there is a "gearbox" between the SDRAM and the chipset which reduces the memory bus throughput compared with the native Rambus version - though whether it's any worse than you'd expect projecting from the benchmarks based on a 100 MHz BX chipset is unknown. My question is: Do I get more "work" done by having both doing LL testing, or would this box contribute more to the effort by having one CPU performing factoring while the other does LL testing? Personally I think you get better value by running 1 LL test 1 "something else" which doesn't make big claims on the memory bus. ECM factoring is quite light on the memory bus (though "larger" exponents i.e. above about 2,000 might have difficulty fitting well into the Celeron L2 cache, which is only 128K) and might make an interesting alternative to trial factoring. There are a considerable number of exponents which have been double- checked but have not been trial-factored to the full depth suggested by v19, running some of these would find a number of "first factors", though I don't think PrimeNet would credit you with the CPU time. Factoring (of any kind) will not find primes; trial factoring larger exponents which will be LL tested later will eliminate some candidates, and be credited by PrimeNet (if you use the "automatic" method of reporting assignment results); other types of factoring would be done out of pure interest, to find new or first factors only. Also, the PrimeNet rankings for LL testing factoring are seperate rather than cumulative. If you split your work, your LL testing effort will be reduced compared with what it would be if you ran LL tests on both CPUs. As a compensation, you would zoom up the factoring rankings! Regards Brian Beesley _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Best chance to make a real contribution?
On 22 Jan 00, at 11:35, Gerry Snyder wrote: But finding a factor (or another factor) of a Mersenne number would seem more real. Is there any significant probability that two 500 MHz Celerons and one 333 MHz Celeron could accomplish such a feat in a couple of years? Depends where you look - last summer I found tens of thousands of smallish factors of Mersenne numbers in the 10 million digit range in a few minutes on a PII-350. On the other hand, many, many CPU years have been spent by various people trying to find any factor of the relatively small composite Mersenne number 2^727-1 without success. You get kudos in proportion to the "difficulty" of the task you achieve (essentially this depends on luck, though you can help it along by supplying as much "horsepower" as possible). However, so far as I'm concerned, the main idea is to have fun. Regards Brian Beesley _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: Best chance to make a real contribution?
Hello, Mersenners; First of all, let me say that it is a thrill to be helping in the GIMPS. Getting more computing power for the search is the main reason my new linux system is a dual Celeron rather than a single. If all I ever do is LL tests of non-primes, that will be fine. That helps the cause, and I have no expectation of finding a prime. But finding a factor (or another factor) of a Mersenne number would seem more real. Is there any significant probability that two 500 MHz Celerons and one 333 MHz Celeron could accomplish such a feat in a couple of years? Just thought I'd ask. Thanks for any help, Gerry -- mailto:[EMAIL PROTECTED] Gerry Snyder, AIS Symposium Chair Region 15 Ass't RVP, JT Chair Member San Fernando Valley, Southern California Iris Societies in warm, winterless Los Angeles _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Best chance to make a real contribution?
Hi Gerry, At 11:35 AM 1/22/00 -0800, Gerry Snyder wrote: First of all, let me say that it is a thrill to be helping in the GIMPS. Welcome aboard! Getting more computing power for the search is the main reason my new linux system is a dual Celeron rather than a single. The second processor is a cheap way to add horsepower. It will help on many other computing tasks. An excellent decision. But finding a factor (or another factor) of a Mersenne number would seem more real. Finding new factors isn't hard. Over half of the candidates are eliminated by finding a factor rather than the expensive LL test. GIMPS by default assigns slower machines to do the factoring work. Thus, it is not uncommon for powerful machines to always get LL assignments and never find a factor. If you want the thrill of finding a factor, ask one of your CPUs to get factoring work only (the Test/Primenet dialog box). You can change this setting back at a later time. Finding new factors of small Mersennes, so called Cunningham factors, is getting more difficult. ECMNet and GIMPS have picked off most of the "easy" factors. I have two CPUs running ECM full-time. The last Cunningham factor I found was last summer. I do occasionally find new factors of medium-sized (1200 to 10) Mersenne numbers. In any event, choose the type of work you find most interesting. The goal here is to have fun while contributing to math research. Best regards, George _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Best chance to make a real contribution?
At 15:14 01/22/2000 -0500, George Woltman wrote: Finding new factors isn't hard. Over half of the candidates are eliminated by finding a factor rather than the expensive LL test. GIMPS by default assigns slower machines to do the factoring work. Thus, it is not uncommon for powerful machines to always get LL assignments and never find a factor. This brings up something I've been wondering about. I have a dual Celeron setup running 2 instances of mprime under Linux. With both processors crunching on LL tests, I get iteration times for each processor of around .263 for exponents around 899 (where they are presently cranking). However, if one of them factors while the other does LL testing, the processor doing the LL testing takes about .220 seconds per iteration, while the one factoring also shows a factoring speed more consistent with the speed I would expect for the processor speed. My question is: Do I get more "work" done by having both doing LL testing, or would this box contribute more to the effort by having one CPU performing factoring while the other does LL testing? Thanks! Kel, coming up on 4 years of hunting for Mersenne primes _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
