[HPGMG Forum] Acceptable rounding errors

Jed Brown jed at jedbrown.org
Mon Aug 3 20:28:40 UTC 2015

Benson Muite <benson.muite at ut.ee> writes:

> Jed and Mark,
> Thanks for your answers.  My hope would be a specification that gets
> machine architects, algorithm designers and computational scientists
> talking to each other - none of them on their own is likely to enable
> efficient problem solution which is what the benchmark should be a very
> rough indicator of. This may be too much to ask though.

In some sense, we want the HPGMG specification to be a proxy for the
external and functional requirements that a class of production
applications would be subject to.  But we don't want realistic
complexity because it would be difficult for someone outside the
community to understand it and it would look like a special-purpose
benchmark.  The reality is that different applications can end up
needing to use similar algorithms for quite different reasons, so let's
specify just enough about the algorithm that it would be useful the real
environments.  (We chose the target class of algorithms to balance
concerns so that it can be relevant to applications that use very
different algorithms.)  HPGMG's algorithm is very efficient at what it
does and it's unlikely that any amount of innovation outside the rules
will beat what can be accomplished within the rules without significant
tradeoffs.  (This hasn't changed in 40 years.)

I encourage people to try, but please recognize that it's very difficult
to define a synthetic problem for which there are not shortcuts that
turn out to be useless in practice.  Consequently, I would recommend
picking a real application that people care about as the platform to
stage your competition.  There you can compare integral and differential
methods, any order of accuracy, non-PDE models, etc.  Go forth and
innovate with complete freedom.

> If you fix the algorithm too much, how do you make HPGMG more
> representative then a combination of simpler computer system benchmarks
> such as stream and MPI benchmarks?

Operator application/smoothing is different from simpler benchmarks and
there are no "MPI benchmarks" (MPI itself being an overspecification for
our purposes) that test the communication structure of multigrid.  You
could in principle split out the pieces (though "start" and "end" are
delicate to define in a useful manner) and take some kind of weighted
combination, but then all the details and weights are subject to
bikeshedding and require micro-specification.  A single coherent
benchmark that solves a problem is less subject to gaming and
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