P-1 on OBD candidates

[lavalamp]

Does anyone know of some utility that can handle P-1 on these monsters?

v29.8 of prime95 says it only accepts exponents up to 595,800,000, which I assume corresponds to its maximum FFT size.

A few years ago LaurV made a post about potentially implementing P-1 in CUDA which sounds encouraging, but I don't know if he or anyone else got much further.
https://www.mersenneforum.org/showpo...3&postcount=11

At least Prime95 can give optimal bounds for P-1. If I put in a candidate TF'd to 86 bits, it recommends B1=B2=44,680,000, no stage 2 due to RAM limitations I believe. This doesn't sound completely unreasonable, and offers a 3.53% chance of a factor, this is slightly higher than the chance of a factor from continuing TF up to 89 bits (3/89 ~ 3.37%).

If I say the candidate has been TF'd to 91 bits instead (which seems to be vaguely where GPU TFing should probably stop), then Prime95 offers the bounds B1=B2=30,920,000 with a 2.07% chance of a factor. Seems a bit odd to me that the bounds are LOWER when TF has progressed more, but alright.

[kriesel]

On an FMA3-capable system prime95 should be capable of going to 920M (50M fft since V29.2). I'm running 701M now on 29.7b1 x64.
https://www.mersenneforum.org/showpo...&postcount=218
CUDAPm1 has been around for years but doesn't reach that high, due to various issues, although it nominally supports sufficiently large fft lengths, on gpus with sufficient ram. https://www.mersenneforum.org/showthread.php?t=23389

Originally Posted by lavalamp

If I say the candidate has been TF'd to 91 bits instead (which seems to be vaguely where GPU TFing should probably stop), then Prime95 offers the bounds B1=B2=30,920,000 with a 2.07% chance of a factor. Seems a bit odd to me that the bounds are LOWER when TF has progressed more, but alright.

Total odds of finding a factor, are odds from TF, plus odds from P-1. It's not worth going as deep in P-1, if a great deal of effort has been expended in TF. Prime95 and CUDAPm1 contain code that computes many different bounds combinations' chances of finding P-1 factors, and selects bounds for the optimal probable compute time savings.

[lavalamp]

Originally Posted by kriesel

On an FMA3-capable system prime95 should be capable of going to 920M. I'm running 701M now.

That'd be why then, I'm not. Still rocking an i5 3570K, the generation before Haswell and FMA.

Even so, 920M is still not high enough for OBD, that needs 3320M+.

[kriesel]

Originally Posted by lavalamp

That'd be why then, I'm not. Still rocking an i5 3570K, the generation before Haswell and FMA.

Even so, 920M is still not high enough for OBD, that needs 3320M+.

Right, 920M<gigabit<gigadigit. Highest stage 1 I've been able to get through CUDAPm1 is 735M-740M; stage 2, 432M. CUDAPm1 would need some alteration and debugging to get there. https://www.mersenneforum.org/showpo...65&postcount=7

[lavalamp]

Perhaps in time the limits will be raised such that stage 1 for these numbers will be possible. Though I completely understand why enabling such functionality is not exactly top priority.

For the memory usage, is there any possibility that it could be lowered if the second stage was broken down into multiple chunks, similar to stage 2 of ECM?

[kriesel]

Originally Posted by lavalamp

Perhaps in time the limits will be raised such that stage 1 for these numbers will be possible. Though I completely understand why enabling such functionality is not exactly top priority.

For the memory usage, is there any possibility that it could be lowered if the second stage was broken down into multiple chunks, similar to stage 2 of ECM?

Stage 1 takes of order 2 bytes/bit in CUDAPm1, so an 8GB or larger gpu should be ok in stage 1. Existing software already does stage 2 in chunks, when possible and necessary, by varying the number of relative primes to fit within available memory. In my experience one of the walls CUDAPm1 hits, on smaller-gpu-ram cards, is the exponent at which even nrp=1 requires more ram than the gpu has; p~177-178M for 1GB on the Quadro 2000 for example; ~290M on the 1.5GB GTX480; ~340M on the 2GB Quadro 4000, etc. Fitting through the 1 and 1.5GB data, and extrapolating widely, suggests ~15GB could be enough, and a few high end gpus currently offer 16GB. On prime95, I suppose one could resort to virtual memory with a solid state disk if lacking enough ram. A recent prime95 run was 701M in 8192MB allowed (half of actual system ram), giving nrp=25 as I recall. CUDAPm1 is limited by gpu ram a bit, but by other issues (bugs in this alpha software) to a much greater extent, and already nominally supports fft lengths up to 256M. That fft length would be more than sufficient for gigadigit primes, if the variable for p was unsigned 32-bit, but currently it is signed, capping exponent at 2³¹-1. In practice, CUDAPm1 is limited to much lower p. For prime95, the current limitation is maximum fft length available; as I recall, the largest implemented is 50M, but gigadigit processing requires around 192M. Gpuowl may be a possibility, although the very few tests I've tried have failed.

Of course, they are all going to be impacted by the roughly p^2.2 run time scaling also. The 701M P-1 run on my i7-8750H (all cores one worker) took 32.3 days at NRP~25, while a recent 430M P-1 on a 3GB GTX1060 took ~5. days at NRP=5 (for both stages, no factor found). Those would scale to ~989. days and ~449. days respectively, per P-1 on a gigadigit candidate. Note that run time also lengthens when NRP goes toward 1 due to memory size limitations. (CUDAPm1 reference info https://www.mersenneforum.org/showthread.php?t=23389
re prime95 see https://www.mersenneforum.org/showthread.php?t=23900)