On Fri, 2021-07-30 at 11:04 -0700, Jerry Morrison wrote:
On Tue, Jul 27, 2021 at 4:55 PM Sebastian Berg < firstname.lastname@example.org> wrote:
there is a proposal to add some Intel specific fast math routine to NumPy:
part of numerical algorithms is that there is always a speed vs. precision trade-off, giving a more precise result is slower.
I have to make a correction: I linked the SVML, which is distinct from VML (which the PR proposes), the actual table for precision is here:
"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.)
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.
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