Re: [eigen] RFC: making a deterministic and reproducable product codepath with Eigen

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Dar Christoph,
Am 08.09.2016 um 19:06 schrieb Christoph Hertzberg:
On 2016-09-06 16:09, Peter wrote:
It's beyond my knowledge, whether scalar products will always be
scheduled in the same way on the FPUs by the hardware,
especially if the scalar product appears after an if-statement.
I'm just sceptical, but maybe I just got surprised too often.

I would be very surprised, if a CPU would give different results for the very same machine instructions (given the same inputs and FPU-configuration, of course), solely based on internal scheduling.

In case you are interested, there's e.g. HP's Dynamo project, <>,
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.
I'm just not sure how far the processors mess around.

For the given use-case, I guess the simplest solution would be to hand-craft a simple library with naive but stable implementations.

I agree, using a F77 BLAS should be sufficient. Although I still don't understand what one learns from bypassing all optimizations.

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.
BTW, exact scalar products could be an interesting extension to Eigen in some future version,
opening the door to verified computing.

Best regards,

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