[HPGMG Forum] Acceptable rounding errors

Mark Adams mfadams at lbl.gov
Mon Aug 3 17:56:40 UTC 2015

Hi Benson,

On Mon, Aug 3, 2015 at 8:45 AM, Benson Muite <benson.muite at ut.ee> wrote:

> Hi,
> Fixing algorithm seems not such a good idea.

Yes, you are right, but we see it as the least bad idea.  Or at least I see
it that way...

> A level of accuracy for
> final result is a better specification, then encourage people to explain
> or post the implementations they have used.

yes, agreed.  We so specify that the solver is asymptotically exact, that
is the error is proportional, with an independent constant, to the
discretization error.  So "precision" is a constraint in the specification,
but we do not reward a solver that is say 10x more accurate than another.

> This doesn't mean CS people
> need to work on the algorithmic/math part, just that they will likely
> have more choices when choosing what to use to optimize and obtain
> results with.

This is a design decision: what do you want center people running HPGMG to
think about?  What do you want machine architects to think about?  Should
there be two specifications, one for each type of user?

This are complex questions.  Let me just say that we have thought about
it.  We need to write this up at some point, so that we can answer your
question fully.  Our current documents touch on these issues but are not


> It would also mean that they may be better able to advise
> people running applications using multigrid what algorithms work well on
> their systems.

Finally, this allows comparison of FE and FV implementations.
> Benson
> ------------------------------ Message: 2 Date: Mon, 3 Aug 2015 08:04:23
> -0700 From: Mark Adams <mfadams at lbl.gov> To: Brian Van Straalen
> <bvstraalen at lbl.gov> Cc: HPGMG Forum <hpgmg-forum at hpgmg.org> Subject:
> Re: [HPGMG Forum] Acceptable rounding errors Message-ID:
> <CADOhEh4T65zVtPM+aXR4SuCT9h4HA-5Yd05Cf5pywdJBH7poqQ at mail.gmail.com>
> Content-Type: text/plain; charset="utf-8" On Fri, Jul 31, 2015 at 2:01
> PM, Brian Van Straalen <bvstraalen at lbl.gov> wrote:
> >> I?ve been wondering about how to automate some level of correctness
> >> testing in HPGMG.   I?m trying figure out if there are some computable
> >> limits to how much a compliant implementation *could* deviate from other
> >> compliant implementations.
> >>
> >> The concern is not trivial.  I?ve spent some time re-reading
> Precimonious
> >> paper (eecs.berkeley.edu/~rubio/includes/sc13.pdf) and I realize that
> it
> >> would not be hard to make a faster version of FMG using mixed precision.
> >> There have been papers over the last few years using 4-byte AMG as a
> >> preconditioner and that seems to work well for many applications.
> >>
> > I have been thinking that we would legislate double precision everywhere.
> > We need to legislate things like order of prolongation, smoother
> > algorithm.  It is a design decision as to what spaces we allow to be
> > optimized.  HPGMG is so simple that we need to defend against
> optimizations
> > (games if you like) that are not readily available to most apps.  I am
> > thinking that mixing precision is not a space that we want to open up.
> >
> > Also, I have always wanted the math to be precisely defined so that the
> CS
> > people, including center staff that are running and optimizing, do not
> have
> > to think about math and can just think about making stuff run fast. (HPCG
> > does not share this philosophy so perhaps I am in the minority here.)
> >
> >
> >> FPGA computing platforms or accelerators also will want to push this
> >> envelope.
> >>
> >> This is added to the other issues like faster FMAs that might not be
> >> totally standard, or fast division.    Our initial condition is also
> based
> >> on trig functions, which have the Table Maker?s Dilemma. The older x86
> fsin
> >> instruction had a wide variability.   We could try to mitigate these
> >> effects (supply the trig function code expressed as in basic operations
> ie.
> >> Hart and Cheney, replace divisions in the reference code with
> >> multiplications when we know they are correct replace 1/(h*h) with
> >> DIM*DIM).  Or perhaps we do none of these things and see what kind of
> >> results people dare to submit.
> >>
> >> I would guess the TOP500 effort is aware of this with the introduction
> of
> >> mixed-precision LINPACK in the last few years (like GHPL).
> >>
> >> So, thoughts?
> >>
> >> Brian
> >>
> >>
> >> Brian Van Straalen         Lawrence Berkeley Lab
> >> BVStraalen at lbl.gov         Computational Research
> >> (510) 486-4976             Division (crd.lbl.gov)
> >>
> >>
> >>
> >>
> >>
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