Re: Mersenne: P-1 on PIII or P4?
- Original Message - From: Chris Marble [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Tuesday, March 04, 2003 4:00 PM Subject: Mersenne: P-1 on PIII or P4? I've got a couple of P4s that I can use on weekends. I've been using them to finish off exponents that my PIIIs were working on. Is that the right order? P-1 on the PIII and then the rest on the P4. I want to maximize my output. Hmmm. That's an intriguing question. Based upon what I know of the algorithms involved, it *ought* to be the case that you should do any P-1 work on the machine which can give it the most memory, irrespective of processor type. However, some time ago, I was given some information on the actual P-1 bounds chosen for exponents of various sizes, running on systems of various processor/memory configurations. It turns out that P4s choose *much deeper* P-1 bounds than do other processors. For example: 8233409,63,0,Robreid,done,,4,45,,Athlon,1.0/1.3,90 8234243,63,0,Robreid,done,,4,45,,Celeron,540,80 8234257,63,0,Robreid,done,,45000,742500,,P4,1.4,100 The last figure is the amount of available memory. The differences between 80MB and 100MB, and between 8233409 and 8234257 are too small to account for the near doubling in the B2 bound in the case of a P4. Since I do not understand why this should be the case, I don't know for certain, but it looks like a P4 is better for P-1. Whichever machine you choose for P-1, always give it absolutely as much memory as you can without thrashing. There is an upper limit to how much it will use, but this is probably in the gigabytes for exponents in even the current DC range. Memory is not relevant for factorisation, the actual LL test, or stage 1 of the P-1. It used to be the case that TF should be avoided on a P4, but that part of this processor's code has been improved in recent versions, so I don't know if this is still the case. If you ever get an exponent that requires both P-1 and extra TF, do the P-1 before the last bit of TF. This doesn't alter the likelihood of finding a factor, but if you do find one, on average you will find it earlier, and for less work. There are a number of ranges of exponent sizes where it is better to avoid using P4s. George posted the following table some time ago (Best viewed with a fixed width font.) FFT v21 v22.8v21 SSE2 v22.8 SSE2 262144 5255000 5255000 5185000 5158000 327680 652 6545000 6465000 6421000 393216 776 7779000 769 7651000 458752 904 9071000 897 8908000 524288 1033 1038 1024 1018 655360 1283 1289 1272 1265 786432 1530 1534 1516 1507 917504 1785 1789 1766 1755 1048576 2040 2046 2018 2005 1310720 2535 2539 2509 2493 1572864 3015 3019 2992 2969 1835008 3510 3520 3486 3456 2097152 4025 4030 3978 3950 2621440 5000 5002 4935 4910 3145728 5940 5951 5892 5852 3670016 6910 6936 6865 6813 4194304 7930 7930 7836 7791 If you are testing an exponent which is greater than an entry in the fifth column, but less than the corresponding entry int the third column, then avoid using a P4. This applies to all types of work. Where the considerations discussed above conflict, I don't know what the balance is between them. HTH -- [EMAIL PROTECTED] - HMC UNIX Systems Manager Daran G. _ Unsubscribe list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: P-1 on PIII or P4?
On Thursday 06 March 2003 13:03, Daran wrote: Based upon what I know of the algorithms involved, it *ought* to be the case that you should do any P-1 work on the machine which can give it the most memory, irrespective of processor type. ... assuming the OS allows a single process to grab the amount of memory configured in mprime/Prime95 (this may not always be the case, at any rate under linux, even if adequate physical memory is installed.) However, some time ago, I was given some information on the actual P-1 bounds chosen for exponents of various sizes, running on systems of various processor/memory configurations. It turns out that P4s choose *much deeper* P-1 bounds than do other processors. For example: 8233409,63,0,Robreid,done,,4,45,,Athlon,1.0/1.3,90 8234243,63,0,Robreid,done,,4,45,,Celeron,540,80 8234257,63,0,Robreid,done,,45000,742500,,P4,1.4,100 The last figure is the amount of available memory. The differences between 80MB and 100MB, and between 8233409 and 8234257 are too small to account for the near doubling in the B2 bound in the case of a P4. Yes, that does seem odd. I take it the software version is the same? The only thing that I can think of is that the stage 2 storage space for temporaries is critical for exponents around this size such that having 90 MBytes instead of 100 MBytes results in a reduced number of temporaries, therefore a slower stage 2 iteration time, therefore a significantly lower B2 limit. I note also that the limits being used are typical of DC assignments. For exponents a bit smaller than this, using a P3 with memory configured at 320 MBytes (also no OS restriction plenty of physical memory to support it) but requesting first test limits (Pfactor=exponent,tfbits,0) I'm getting B2 ~ 20 B1 e.g. [Thu Mar 06 12:07:46 2003] UID: beejaybee/Simon1, M7479491 completed P-1, B1=9, B2=1732500, E=4, WY1: C198EE63 The balance between stage 1 and stage 2 should not really depend on the limits chosen since the number of temporaries required is going to be independent of the limit, at any rate above an unrealistically small value. Why am I bothering about this exponent? Well, both LL DC are attributed to the same user... not really a problem, but somehow it feels better to either find a factor or have an independent triple-check when this happens! Regards Brian Beesley _ Unsubscribe list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: P-1 on PIII or P4?
Daran wrote: Whichever machine you choose for P-1, always give it absolutely as much memory as you can without thrashing. There is an upper limit to how much it will use, but this is probably in the gigabytes for exponents in even the current DC range. So I should use the PIII with 1 3/4 GB of RAM to do nothing but P-1. It's an older Xeon with 2MB cache. Will that help too? How would I do this? I see the following in undoc.txt: You can do P-1 factoring by adding lines to worktodo.ini: Pfactor=exponent,how_far_factored,has_been_LL_tested_once For example, Pfactor=1157,64,0 There are a number of ranges of exponent sizes where it is better to avoid using P4s. George posted the following table some time ago (Best viewed with a fixed width font.) FFT v21 v22.8v21 SSE2 v22.8 SSE2 262144 5255000 5255000 5185000 5158000 327680 652 6545000 6465000 6421000 393216 776 7779000 769 7651000 458752 904 9071000 897 8908000 524288 1033 1038 1024 1018 655360 1283 1289 1272 1265 786432 1530 1534 1516 1507 917504 1785 1789 1766 1755 1048576 2040 2046 2018 2005 1310720 2535 2539 2509 2493 1572864 3015 3019 2992 2969 1835008 3510 3520 3486 3456 2097152 4025 4030 3978 3950 2621440 5000 5002 4935 4910 3145728 5940 5951 5892 5852 3670016 6910 6936 6865 6813 4194304 7930 7930 7836 7791 If you are testing an exponent which is greater than an entry in the fifth column, but less than the corresponding entry int the third column, then avoid using a P4. This applies to all types of work. Useful info. I've got 2 DCs in one of the ranges but one computer's a PIII and the other's a Dec Alpha running Mlucas-2.7b-gen-5x. -- [EMAIL PROTECTED] - HMC UNIX Systems Manager _ Unsubscribe list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
