[Beowulf] Re: Matrix Multiply

Dan Kidger daniel.kidger at quadrics.com
Sat Feb 11 06:13:52 PST 2006

Tom Elken wrote:

>> mathematician but im trying to understand how the benchmark operates.
>> I would like to test my system by seeing how many FLOPS are achieved
>> using only the Matrix Multiply.
> You could probably download the HPC Challenge benchmark (from 
> http://icl.cs.utk.edu/hpcc/software/index.html )  and cut-paste some 
> code from it's DGEMM (Double-precision, GEneral Matrix-Multiply) 
> sub-benchmark as a relatively easy way to get a test program for 
> matrix-multiply.
> DGEMM is typically ~90% or more of the HPL benchmark's profile.

Indeed I have been doing that for the last couple of years since hpcc appeared. It is trivial to slightly modify one file of the hpcc source such that you can run just one or two or the seven contained benchmarks via setting a shell variable - for example just to run dgemm in your case, or say ptrans or gups in my case. It is also very easy to pipe the hpcc output though a couple of lines of perl or sed so as to get just the summary output lines for the subset of tests that you ran.

As for the flops, this can depend on the lower bits of the matrix size - it is common to see dgemm implimentations oscilate due to cache line hits and the like.  rather than speak in terms of actual flops, it usuely make more sense to quote the percentage of theoretical peak you get. The theoretical peak is well defined - simply the cpu's clock speed mulitplied up by favious factors like:
  - times number of cpus per Motherboard
  - times number of cores per cpu
  - times number of floating point instructions issues per cycle (2 for itanium and alpha, 1 for xeon/opteron)
  - times width of any SIMD unit (2 for the 2*64-bit wide SSE2)
  - times two if your FPUs can do chained muladd (like itanium)
  - times 75% reduction factor if you can't issue floating point loads fast enough (was this G5?)

Some cpu architectures come out better than others but you should expect to get say >85% even on the worst (thank you Mr Goto :-) )


Dr. Dan Kidger, Quadrics Ltd.      daniel.kidger at quadrics.com
One Bridewell St., Bristol, BS1 2AA, UK         0117 915 5505
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