On Fri, Jul 30, 2021 at 12:22 PM Sebastian Berg <sebastian@sipsolutions.net> wrote:
On Fri, 2021-07-30 at 11:04 -0700, Jerry Morrison wrote:
> On Tue, Jul 27, 2021 at 4:55 PM Sebastian Berg <
> sebastian@sipsolutions.net>
> wrote:
> > Hi all,
> >
> > there is a proposal to add some Intel specific fast math routine to
> > NumPy:
> >
> >     https://github.com/numpy/numpy/pull/19478
> >
> > part of numerical algorithms is that there is always a speed vs.
> > precision trade-off, giving a more precise result is slower.
> >

> "Close enough" depends on the application but non-linear models can
> get the
> "butterfly effect" where the results diverge if they aren't
> identical.

Right, so my hope was to gauge what the general expectation is.  I take
it you expect a high accuracy.

The error for the computations itself is seems low on first sight, but
of course they can explode quickly in non-linear settings...
(In the chaotic systems I worked with, the shadowing theorem would
usually alleviate such worries. And testing the integration would be
more important.  But I am sure for certain questions things may be far
more tricky.)

I'll put forth an expectation that after installing a specific set of libraries, the floating point results would be identical across platforms and into the future. Ideally developers could install library updates (for hardware compatibility, security fixes, or other reasons) and still get identical results.

That expectation is for reproducibility, not high accuracy. So it'd be fine to install different libraries [or maybe use those pip package options in brackets, whatever they do?] to trade accuracy for speed. Could any particular choice of accuracy still provide reproducible results across platforms and time?

> For a certain class of scientific programming applications,
> reproducibility
> is paramount.
> Development teams may use a variety of development laptops,
> workstations,
> scientific computing clusters, and cloud computing platforms. If the
> tests
> pass on your machine but fail in CI, you have a debugging problem.
> If your published scientific article links to source code that
> replicates
> your computation, scientists will expect to be able to run that code,
> now
> or in a couple decades, and replicate the same outputs. They'll be
> using
> different OS releases and maybe different CPU + accelerator
> architectures.
> Reproducible Science is good. Replicated Science is better.
> <http://rescience.github.io/>
> Clearly there are other applications where it's easy to trade
> reproducibility and some precision for speed.

Agreed, although there are so many factors, often out of our control,
that I am not sure that true replicability is achievable without
containers :(.

It would be amazing if NumPy could have a "replicable" mode, but I am
not sure how that could be done, or if the "ground work" in the math
and linear algebra libraries even exists.

However, even if it is practically impossible to make things
replicable, there is an argument for improving reproducibility and
replicability, e.g. by choosing the high-accuracy version here.  Even
if it is impossible to actually ensure.

Yes! Let's at least have reproducibility in mind and work on improving it, e.g. by removing failure modes.
(Ditto for security :-)