Single LL Question

[petrw1]

On the less effective end:

Q9550 
20,000,001 (Time... 25 iterations)
Cores  Per Iteration  %Improvement
1  14.51
2  9.46  +53%
3  8.32  +21%
4  6.96  +34%

Yes, odd results between 3 and 4 cores, but I ran the test a few times with similar results.

Over all effectiveness 4 cores just slightly more than twice as fast as 1.

[petrw1]

On the more effective end

i5-750 OC to 3.2
20,000,001 (Time... 25 iterations)
Cores  Per Iteration  %Improvement
1  13.05	
2  6.99	87%
3  4.83	84%
4  4.04	53%

Over all effectiveness 4 cores just about 3.25 times as fast as 1.

[Stef42]

The Q9550 is not really a quad-core CPU, just like every other S775 4core CPU.
Actually, 2 dual-cores on one die, so I suppose this architecture has something to do with the test results.

[bcp19]

Originally Posted by Stef42

The Q9550 is not really a quad-core CPU, just like every other S775 4core CPU.
Actually, 2 dual-cores on one die, so I suppose this architecture has something to do with the test results.

It does, a Q8200 I recently tested ran 18.9, 12.1, 20.7 and 9.2 on a 1024k FFT using 1,2,3,4 cores. The slowdown with 3 cores was a bit of a shock, but I noticed it worked better at higher FFT's: 40.5, 24.7, 21.5, 17.7 at 2048k. The memory I was using also probably had an effect, as I was using P-95 to stress test a motherboard I had been given and only had 3GB of PC2-5300 memory to throw in it. I noticed one interesting item during the testing of that motherboard, which had a GT520 that I was also testing mfaktc on. I ran tests using all possible combinations of P95 and mfaktc.

Single thread total throughput on 27.5M exps:
Workers   %/day
1         11.636
2 (C1&C2) 17.95
2 (C1&C3) 21.30
3         22.89
4         24.17
3+mfak 5kSP - 22.1
3+mfak 200Ksp - 20.3
 
Double thread total throughput on 27.5M exps:
Workers  %/day
1        18.48
2        25.13
 
2 instances of P95, 1 single threads, 1 double threads, total throughput on 27.5M exps:
Workers %/day
1 & 1     26.18
2 & 1     25.11
1 & 1 + mfak 5k - 23.80
1 & 1 + mfak 200K - 21.12
2 & 1 + mfak 5k - 24.01

I hope to be able to get some pc2-6400 and pc2-8500 memory and run the same tests to see how much the memory affects timings.

[zanmato]

So a multi-computer test isn't ruled out as potentially faster than a single processor. But a number of known things limit it, as well as probably loads of unknowns which may rule it out completely. For a start the ram of the controller computer has to be fast enough to feed all processors (as I think the fft and inverse can't be split, and it's the multiplication stage which allows multi-core. So the start and end of an iteration would have to be on a single core?). If ram is already the limiting factor then that's that.

Thank you for the replies.

[R.D. Silverman]

Originally Posted by Unregistered

Could an LL test be split across multiple local computers, the goal being to speed up computation of a single LL test for large exponents?

Seeing this same question come up over and over and over again gets
tiring. And the answer remains the same.

The "goal" you suggest is distinctly sub-optimal.

It is much more efficient, given the availability of multiple cores, to simply run
multiple (separate) LL tests on different exponents. Throughput would be
substantially higher.

[bcp19]

Originally Posted by zanmato

So a multi-computer test isn't ruled out as potentially faster than a single processor. But a number of known things limit it, as well as probably loads of unknowns which may rule it out completely. For a start the ram of the controller computer has to be fast enough to feed all processors (as I think the fft and inverse can't be split, and it's the multiplication stage which allows multi-core. So the start and end of an iteration would have to be on a single core?). If ram is already the limiting factor then that's that.

Thank you for the replies.

I am not sure how you would get multiple computers tied together to work on it. From the Gimps math page:

The Lucas-Lehmer primality test is remarkably simple. It states that for P > 2, 2^P-1 is prime if and only if S_p-2 is zero in this sequence: S₀ = 4, S_N = (S_N-1² - 2) mod (2P-1). For example, to prove 27 - 1 is prime:

S₀ = 4
S₁ = (4 * 4 - 2) mod 127 = 14
S₂ = (14 * 14 - 2) mod 127 = 67
S₃ = (67 * 67 - 2) mod 127 = 42
S₄ = (42 * 42 - 2) mod 127 = 111
S₅ = (111 * 111 - 2) mod 127 = 0

S₂ cannot be calculated before S₁ is known, and likely the time to send the multiplication to multiple computers to calculate and receive it back would probably take longer than for a single computer to complete it.

Originally Posted by R.D. Silverman

It is much more efficient, given the availability of multiple cores, to simply run
multiple (separate) LL tests on different exponents. Throughput would be
substantially higher.

This is true, to an extent. The properties of certain processors make them more efficient under certain circumstances. From the testing I was doing, it shows a Core 2 Quad with 1 double thread and 1 single thread exponent running can outperform 4 single thread exponents. With the slowdown George has come across with the optimization of AVX with 4 cores running, the above example may also prove more efficient.

[Dubslow]

Well, okay, in the "typical" use case, RDS is right, where typical excludes such things as a duo-dual-core and AVX. Even with AVX, it's still more efficient to run one per core.