| Re: [eigen] RFC: making a deterministic and reproducable product codepath with Eigen |
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On 08.09.2016 at 21:45, Peter wrote:
In case you are interested, there's e.g. HP's Dynamo project,
<http://www.hpl.hp.com/techreports/1999/HPL-1999-77.html>,
which messes around with binaries. And for scalar products, it's
sufficient to change the order of evaluation,
to loose bit-wise accuracy, eg. the scalar product of ( 1, 1e-50, 1)
with ( 1, 1, -1 ) is a simple example.
Sure, I'm aware that IEEE math is non-associative ...
I'm just not sure how far the processors mess around.
By design they should only execute things out of order, if the
instructions (or the generated micro-instructions) are independent.
Everything beyond that would be insane, IMO. I'm not a CPU expert, but
I'm pretty sure a lot of people would have complaining about it, if CPUs
would do that.
I agree, using a F77 BLAS should be sufficient. Although I still don't
understand what one learns from bypassing all optimizations.
If you have a BLAS implementation that does exactly the same on every
target architecture, you should be fine as well, of course. I don't know
what the status of F77->GPU compilers is.
If correctness is important one should switch to exact scalar product,
like in C-XSC,
which removes the dependence on the order of evaluation and just _has_
to provide the same result everywhere.
The original RFC was just on reproducibility not on exactness, I think.
BTW, exact scalar products could be an interesting extension to Eigen in
some future version,
opening the door to verified computing.
Sure, that would be interesting. I'm not sure how complicated this will
be to integrate though. And it will certainly be significantly slower.
Christoph
--
Dipl. Inf., Dipl. Math. Christoph Hertzberg
Universität Bremen
FB 3 - Mathematik und Informatik
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