How well would this card do?

[davieddy]

Originally Posted by Christenson

I'll concur, as long as Davieddy remembers to take the log base 2 of 128 and gets 7. I hadn't even begun to think in terms of the population of available machines.

I said GPU 64x faster, you said 65x faster and said 8 extra bits.
I would have thought a programmer might know that 2⁸=256,
even if he ate quiche.
You tried to wriggle by changing it to 128x faster, and conveniently
ignoring the fact that 70-78 will take twice as long as 77-78.
I say again, 'fess up: you were "thinking" 64=8² instead of 2⁶.

I worked out that a hot GPU could TF 3 bits over the CPU limit
for 500 exponents in the same time it took a CPU to do an LL test,
eliminating ~20 exponents.
Well worth it surely.

I asked you to agree that this meant using a GPU for
LL testing was crazy. You declined to answer without reason..

There's a *lot* of operations in an LL test. Suppose our exponent is 40M. We have
40M iterations of
2*40M log2(40M) operations in the FFTs

Letting log2(40M) be 25, we have:
N = 40M * 40M * 50 arithmetic ops to do.
With a hot GPU, with 700M ops/sec * 500 CPUs, this will take
40M * 40M * 50 /700M/500 =~ 4 * 40M * /700 =160M/700 =~ 200K secs
=~3 days

So this isn't TOO far off....

Too far off what exactly?

David

P.S.
We have been saying a hot GPU is 100x faster at TF than "a CPU".
What CPU are we all talking about here?

[Christenson]

Davie:
You'll have to trust me, I was thinking 100 =~127 = 2^7.....and smoking something to turn 7 into 8. It has a lot to do with a 20C gradient across a heatsink where there's not supposed to be one at work right now, and a million dollars or more (including my salary) hanging on the answer, and management amazingly uninterested in the data. I really need this vacation!

Now, working out that your hot GPU can eliminate 20 exponents with 3 extra bits in the time it takes a CPU to do 1 LL test (half the total work) says 3 extra bits is too few....theorem: We are at optimum in a continuous-parameter problem when we are indifferent to small adjustments of the parameters.
The hot GPU can do a 4th bit and eliminate approximately 7 exponents while the CPU does the second LL test, and so on....

The actual numbers are a bit more complicated because mfaktc uses 1-2 cores to accomplish its work, and those cores aren't doing LL.

Do I think LL on a GPU is crazy? No way...I am calculating roughly how many arithmetic operations are involved in an attempt to show why LLs are going to be slow....even on GPUs. We have a *lot* of LL tests to do, and one approach is to take all the help we can get. Especially if the GPU firepower gets 5,6,7 bits ahead of the original CPU limit, it makes sense to set those GPUs doing LL tests.

In fact, I intend to be setting half or more of my GT480 card to doing LL tests when I return from vacation.

It is an accident involving the purchase of a GT210 for work that won't run CUDALucas that I am working on mfaktc. I feel a strong need to finish that project before moving on; talk is cheap, working,correct code has real value. I want to be remembered for working code.

P.S. The CPU is the "mythical average" CPU, with 2.2 children, born in the last year or two.... 4GHz days credit per day per core is a good number....

[davieddy]

Originally Posted by Christenson

Davie:
You'll have to trust me, I was thinking 100 =~127 = 2^7.....and smoking something to turn 7 into 8....
I really need this vacation!

After a few Special Brews, all now becomes clear:

127=2⁷ therefore 128=2⁸

Now, working out that your hot GPU can eliminate 20 exponents with 3 extra bits in the time it takes a CPU to do 1 LL test (half the total work) says 3 extra bits is too few....

Especially if the GPU firepower gets 5,6,7 bits ahead of the original CPU limit, it makes sense to set those GPUs doing LL tests.

P.S. The CPU is the "mythical average" CPU, with 2.2 children, born in the last year or two.... 4GHz days credit per day per core is a good number....

I know its a bit too soon to judge, but
http://www.mersenne.info/trial_facto...ta/2/50000000/
suggests that we haven't even reached the CPU limit in some cases,
and 1 extra bit is a rarity.
How many GPUs are actually working on this?

Time for some realistic numbers.
200 LL tests completed per day
Our hot GPU can TF 500 exponents to 3 extra bits in 50 days.
10 per day.
We need 20 hot GPUs on the job 24/7 to cope.

Is this too much to hope for?
We'll see in a month or two!.

David

[Rodrigo]

Originally Posted by Christenson

Indeed the LL on the GPU leaves the CPU core(or cores) largely available for whatever you want to point them at....thus my *dreaming* in the previous post.

This is kinda exciting! In effect the GPU (at ~1.6x, for the GT 430) serves as nearly two additional cores.

You know what I'll be buying this week...

Rodrigo

[davieddy]

Originally Posted by Rodrigo

This is kinda exciting! In effect the GPU (at ~1.6x, for the GT 430) serves as nearly two additional cores.

You know what I'll be buying this week...

Rodrigo

Not sure what you mean here, but have you checked that 1.6 isn't
"off by one" (or three)?


David

[Rodrigo]

Originally Posted by davieddy

Not sure what you mean here, but have you checked that 1.6 isn't
"off by one" (or three)?


David

David,

Check out post #18 in this thread. Also see the first post, where the CPU and GPU specs are given. What is kjaget's cited ~1.6x improvement relative to? I've been taking it to mean, GHz-days/day for the given GPU in CUDALucas relative to the given CPU's Prime95 LL productivity.

Rodrigo

[kjaget]

Originally Posted by Rodrigo

David,

Check out post #18 in this thread. Also see the first post, where the CPU and GPU specs are given. What is kjaget's cited ~1.6x improvement relative to? I've been taking it to mean, GHz-days/day for the given GPU in CUDALucas relative to the given CPU's Prime95 LL productivity.

It was current GPU LL performance on first time LL tests vs. the theoretical improvement if we had code which efficiently used non-power of two FFTs in the GPU code. See e.g. http://www.ece.neu.edu/groups/nucar/...iles/thall.pdf, table 8.

For actual performance of the current implementation, first time tests take ~5 days on a top of the line GPU. That's what, like 4x faster than a single core on an average recent CPU? I'm not sure how other cards scale.

[Rodrigo]

Originally Posted by kjaget

It was current GPU LL performance on first time LL tests vs. the theoretical improvement if we had code which efficiently used non-power of two FFTs in the GPU code. See e.g. http://www.ece.neu.edu/groups/nucar/...iles/thall.pdf, table 8.

For actual performance of the current implementation, first time tests take ~5 days on a top of the line GPU. That's what, like 4x faster than a single core on an average recent CPU? I'm not sure how other cards scale.

Ahh, thanks very much.

A very informative paper, BTW, even if the math is above my pay grade. Table 3 (that must be the one you meant) was particularly interesting.

Rodrigo

[ET_]

Originally Posted by kjaget

It was current GPU LL performance on first time LL tests vs. the theoretical improvement if we had code which efficiently used non-power of two FFTs in the GPU code. See e.g. http://www.ece.neu.edu/groups/nucar/...iles/thall.pdf, table 8.

For actual performance of the current implementation, first time tests take ~5 days on a top of the line GPU. That's what, like 4x faster than a single core on an average recent CPU? I'm not sure how other cards scale.

Any news about the source code?

Luigi

[kjaget]

Originally Posted by ET_

Any news about the source code?

Luigi

Nothing so far, but there's no reason I'd know any quicker than they rest of you. Come to think of if, probably lots of reasons I'd know after many of you. I'm always a bit behind on these things...