Re: [eigen] Slow matrix-matrix multiply

[Christoph Hertzberg <chtz@xxxxxxxxxxxxxxxxxxxxxxxx>]

On 02.04.2013 03:21, Sameer Agarwal wrote:
> We replaced one of the more frequently called eigen expressions with a
> simple three loop GEMM implementation (with some template sizing tricks)
> and it instantly gives us >10% speedups. Doing the same to two other GEMM
> expressions givs us an overall 30% speedup. The sizes of the matrices
> involved is fairly small; in our benchmark, our matrices are of sizes 6x3,
> 3x3, 3x6, and are sized at compile time.

Yes, small matrices have very much room for optimization, see this bug:

http://eigen.tuxfamily.org/bz/show_bug.cgi?id=404
For small fixed sizes it should be possible to solve this with template 
specializations (i.e. fall back to text-book GEMM, if 
vectorization/blocking gives no benefit).


Another thing that bugs me are that dynamic matrices (even if only one 
dimension is dynamic and the other fixed and small) always fall back to 
the generic matrix multiplication which is mostly optimized for very 
large products.

Maybe it would be possible to fall back to a very simple "three loop 
GEMM" if the sizes are small. This could be checked at runtime or 
indicated by the user somehow (maybe configurable by a compile flag). If 
a program only uses small matrix products this might also reduce the 
binary size noticeably.


Christoph

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Dipl.-Inf., Dipl.-Math. Christoph Hertzberg
Cartesium 0.049
Universität Bremen
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