ENH: testing: make assertion functions public

[lucascolley]

Towards gh-17.

[lucascolley]

@ev-br @mdhaber @paddyroddy could I perhaps interest anyone in running pixi run open-docs on this branch and reviewing the documentation of this new public API?

[lundybernard]

@ev-br @mdhaber @paddyroddy could I perhaps interest anyone in running pixi run open-docs on this branch and reviewing the documentation of this new public API?

assert_close rtol and atol parameters

Docs are unclear, both params say only "Relative tolerance" / "Absolute tolerance" with no explanation of how they combine in the comparison. Since these are core to the function, additional details in the NOTES section or doc-string would be helpful.
The NumPy docs are similarly sparse.

rtol default value

The Notes section mentions sqrt(eps) as the default rtol basis, but doesn't explain why. That came from SciPy PR #20625 (scipy/scipy#20625) and a Scientific Python Discourse thread about float32 vs float64 strictness. The rationale (float32 tolerance ~1e-3 vs float64 ~6e-8) is not obvious and worth a sentence in the Notes.

xp param

At first glance this name is perplexing, there's a good explanation on the first page of the docs. A link to the full explanation may be helpful, but its easy enough to dig up.

[lundybernard]

spotted a few minor issues

[lucascolley]

gonna click this in so that feedback on the new docs is easier once they are deployed. The API is still subject to change until the next release. But this will at least unblock work on gh-755