Geoff, you are correct. Exression template technique does not give you much
when you multiply or invert matrices (any operation mixing several indices
instead of one, like in summation). You will need to apply tiling technique
to deal with the cashe issues.
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Svetlana G. Shasharina
Vice President of Networking Technology
Tech-X Corporation
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----- Original Message -----
From: Geoffrey Furnish <furnish@actel.com>
To: <oon-list@oonumerics.org>
Cc: <Peter.Murray@gs.com>
Sent: Thursday, February 15, 2001 10:14 AM
Subject: Re: OON: RE: alpha release of MET, C++ matrix with expression
templates
> Masakatsu ITO writes:
> > I had always wanted to simplify the fortran codes for linear algebraic
> > expressions. Consider u = M*v + w, where u,v and w are vectors and
> > M is matrix. Fortran requires multiple loops or subroutine calls with
> > complicated argument list. But it was said until recently,
> > C++ abstraction was the enemy of performance. A naive implementation
> > of overloaded operators introduces temporary and copies of objects.
> >
> > [...]
> >
> > Expression template is a way to eliminate that overhead but keep
> > the advantage of OOP. Using MET, you can simply write u = m*v + w
> > in your source without any temporaries or copies.
>
> While it is true that notational convenience and the elimination of
> superfluous temporaries are key benefits of expression templates, it
> seems to me that perhaps there is an additional factor that
> significantly impacts performance in cases like this. I think a naive
> implementation of the double loop that ranges over the m*v product
> term will thrash the cache if m is of any significant size. Perhaps
> someone could correct me if I've got this wrong, but I am under the
> impression that there exist techniques for clever reorderings of these
> computational kernels that produce 3 to 10 x perfromance improvements
> on scalar cache-based architectures, compared to the naive
> implementation.
>
> Do the evaluation kernels that are under the hood of your ET machinery
> for matrix math take advantage of such opportunities to produce this
> sort of blazing throughput?
>
> --
> Geoffrey Furnish Actel Corporation furnish@actel.com
> Senior Staff Engineer 955 East Arques Ave voice: 408-522-7528
> Placement & Routing Sunnyvale, CA 94086-4533 fax: 408-522-8041
>
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