Cluster-wide overclocking...

[Robert G. Brown]

On Thu, 24 Sep 1998, Kragen wrote:

> On Thu, 24 Sep 1998, Robert G. Brown wrote:
> > floats a day.  At one error per 10^9, that is around 10^5 errors/day.  I
> > cannot even think of a sanity check that would work in this case in
> > Monte Carlo code (my particular problem) -- random errors at this rate
> > undoubtedly have a distribution and undoubtedly the distribution
> > satisfies the Central Limit Theorem, so two daylong runs will both
> > produce the same -- wrong -- answer.  This would be true even if the
> > runs were only ten or twenty minutes long.
> 
> If your errors accumulate linearly -- and they conceivably could for a
> Monte Carlo simulation -- you can have a significant fraction of them
> be wrong without affecting your results significantly.  If they don't
> accumulate linearly, then your reasoning is wrong -- you'll get
> different wrong answers every day.  :)

How can I argue when you're (basically) right?  Let us find a way,
hmmmm.  I picked MC specifically because my statistical error per run is
often quite high and is likely to be comparable to or larger than that
produced on average my a low rate of some kinds of bit-level errors
(those that didn't cause my code to bomb altogether, which is of course
by far the most likely outcome). That is, I already get different wrong
answers every day, they are just distributed according to the CLT about
the correct mean value with the usual statistical blah blah blah.  With
the errors, I'd still get a distribution about some mean value -- how am
I to determine that it is the wrong one?  If the deviation is egregious
(or if, more likely, the system freezes up in mid-calculation) this
isn't a problem.  If it just adds random numerical noise in some bounded
range with some distribution, though, it is a big problem.

> 
> > The same problem exists with many random number
> > generators -- an algorithm with a period that used to be "infinity" ten
> > years ago can cycle once or twice a day today. 
> 
> True.  But there are random number generators that have cycles that are
> large enough that we don't have to worry about that happening in a
> future.  

So true, and one can even convert one of type a to one of type b via
shuffling.  So needless to say, I ALWAYS shuffle.

   rgb

Robert G. Brown	                       http://www.phy.duke.edu/~rgb/
Duke University Dept. of Physics, Box 90305
Durham, N.C. 27708-0305
Phone: 1-919-660-2567  Fax: 919-660-2525     email:rgb@phy.duke.edu