----- 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,,40000,450000,,Athlon,1.0/1.3,90 8234243,63,0,Robreid,done,,40000,450000,,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 v22.8 v21 SSE2 v22.8 SSE2 262144 5255000 5255000 5185000 5158000 327680 6520000 6545000 6465000 6421000 393216 7760000 7779000 7690000 7651000 458752 9040000 9071000 8970000 8908000 524288 10330000 10380000 10240000 10180000 655360 12830000 12890000 12720000 12650000 786432 15300000 15340000 15160000 15070000 917504 17850000 17890000 17660000 17550000 1048576 20400000 20460000 20180000 20050000 1310720 25350000 25390000 25090000 24930000 1572864 30150000 30190000 29920000 29690000 1835008 35100000 35200000 34860000 34560000 2097152 40250000 40300000 39780000 39500000 2621440 50000000 50020000 49350000 49100000 3145728 59400000 59510000 58920000 58520000 3670016 69100000 69360000 68650000 68130000 4194304 79300000 79300000 78360000 77910000 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
