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Re: Re: Non-deterministic numerical inaccuracies in

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  • Subject: [mg95727] Re: [mg95698] Re: Non-deterministic numerical inaccuracies in
  • From: danl at
  • Date: Sun, 25 Jan 2009 21:48:40 -0500 (EST)
  • References: <gjcuio$cnf$> <gjkvd4$92g$>

> Daniel Lichtblau wrote:
>>> The bad news is that it is a consequence of the M.K.L. which can't
>>> be avoided. The good news is that you should not care about it.
>>> If the difference seems important then you are doing something
>>> wrong.

First I should point out that the above remark was not mine. It was in a
note I had at least in part quoted. That said, I neither fully agree nor
disagree with it. If small machine arithmetic fuzz is bedeviling your
code, you almost certainly are doing something a bit unsafe.

> I think we should care about it! Lots of programs have different
> behaviours depending on a real number threshold, and this behaviour
> means that there is the possibility of a test flipping different ways on
> different runs of a program!

One has to be careful about choosing the threshold, etc. A few bits for
BLAS machine arithmetic tolerance seems not unreasonable to me.

> This could be a debugging nightmare, and will be in the back of people's
> minds whenever anything 'strange' happens.
> Would it not be possible to revert to the previous, slightly less
> optimal, library until (presumably) the library is fixed?
> David Bailey

My understranding is that the library vendors do not regard it as broken,
so I am not optimistic that the library itself will change. We have made
some effort to align machine floats to 16 bits so this particular behavior
should stabilize in a future release.

I am not really competent to discuss the issues involved in going to a
different library. Maybe others can address that. I can only voice my
suspicion that it would be difficult, and offer dubious gain.

Daniel Lichtblau
Wolfram Research

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