BLD, TST: Build and test Pyodide wheels for `pandas` in CI
- [x] closes #57891 
- [ ] [Tests added and passed](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#writing-tests) if fixing a bug or adding a new feature
- [x] All [code checks passed](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#pre-commit).
- [ ] Added [type annotations](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#type-hints) to new arguments/methods/functions.
- [ ] Added an entry in the latest `doc/source/whatsnew/vX.X.X.rst` file if fixing a bug or adding a new feature.

## Description

This PR adds a workflow, `emscripten.yml`, to the GitHub Actions CI activities where WebAssembly wheels for `pandas` using Pyodide/Emscripten are built and then tested. I have fixed up a few of the tests, but most of them are skipped for now and these differences _probably_ do not affect major functionality.
Here is one of the latest workflow runs on my fork: https://github.com/agriyakhetarpal/pandas/actions/runs/8331354944/job/22798065116

The associated failures right now are mostly coming from a singular test that (which is associated with a hypothesis generator that brings additional test cases?)

For example, there is a floating point inaccuracy, here – which could be corrected by setting the relative and absolute tolerances differently:

```
E           AssertionError: DataFrame.iloc[:, 2] (column name="dt_as_dt") are different
E           
E           DataFrame.iloc[:, 2] (column name="dt_as_dt") values are different (100.0 %)
E           [index]: [0, 1]
E           [left]:  [253402127999999, 1564703999999]
E           [right]: [253402127999998, 1564703999998]
```

and some `tzlocal` tests, which seem to bring overflow errors. Note: this output is truncated, please see the entirety of them in the workflow logs:

```
_______________ test_apply_out_of_range[tzlocal()-BusinessHour] ________________
[XPASS(strict)] OverflowError inside tzlocal past 2038
_____________ test_apply_out_of_range[tzlocal()-BusinessMonthEnd] ______________
[XPASS(strict)] OverflowError inside tzlocal past 2038
____________ test_apply_out_of_range[tzlocal()-BusinessMonthBegin] _____________
[XPASS(strict)] OverflowError inside tzlocal past 2038
```

I am not completely sure how to fix these tests – I don't get why these aren't skipped completely? I would appreciate another pair of eyes on this; happy to receive pointers from someone experienced with the codebase :) > I am not completely sure how to fix these tests – I don't get why these aren't skipped completely? I would appreciate another pair of eyes on this; happy to receive pointers from someone experienced with the codebase :)

At least for the second test it looks like it is imperatively skipping for platforms that are not 64 bit. I take it the platform these are running on is still 64 bit but we are cross compiling to a 32 bit WASM target?

https://github.com/pandas-dev/pandas/blob/495f80896852e450badc8866ee7ebe8c434fa228/pandas/tests/indexes/datetimes/methods/test_resolution.py#L25
 > At least for the second test it looks like it is imperatively skipping for platforms that are not 64 bit. I take it the platform these are running on is still 64 bit but we are cross compiling to a 32 bit WASM target?

Hi, @WillAyd, yes – cross-compilation is indeed what is happening here and the platform is 64-bit, but the Python interpreter that runs the test suite is 32-bit (so it should, in theory, skip this, but it doesn't). I disabled the check in https://github.com/pandas-dev/pandas/pull/57896/commits/d54d198a3824a6c13150a494b7f4b2af247737aa which I hope should fix it. Pyodide had a new release recently to fix an error in the `pyodide build` command. I have just merged `main` and pushed a944f5287dce1439778f32525ebf5d973e75b817 to fix that. The next step from my end would be to fix some of the failing tests (which I did not have much progress on the last time and I don't want them to xfail them yet), but also to wait here until #53007 lands – I suppose that it would make running the tests against a built wheel a bit more difficult, but without the PR getting merged, I'm not sure how that will be navigated here. The good thing is that `pandas-tests` will be a pure Python package and will have a few APIs to collect and pass data files around, and installation for pure Python wheels is supported out-of-the-box in Pyodide.

If there's something else here that I should do in the meantime, I'm happy to do that – open to suggestions about resolving the two failing tests. This pull request is stale because it has been open for thirty days with no activity. Please [update](https://pandas.pydata.org/pandas-docs/stable/development/contributing.html#updating-your-pull-request) and respond to this comment if you're still interested in working on this. Putting up my response to the above comment that I am still interested in working on this. @agriyakhetarpal it seems reasonable to either skip the `tzlocal` test under WASM or lower the test tolerance specifically when running under WASM. If that is all that is needed to get the test suite to pass, I suggest doing that and then marking this as ready for review. It's easier for reviewers to give feedback when something works already. Just merged the `main` branch, which re-triggered CI – would be good to see if some new tests or features have been added that will fail, before I resolve everything. Thanks for sticking with this. It's looking close to merge With most of the tests skipped where it is not possible or relevant to fix them, we are down to zero failures, and all other tests pass or xpass (or are xfailed for other reasons). The logs from the workflow run are here: https://github.com/pandas-dev/pandas/actions/runs/8945452670/job/24574452414. The doc build failures at the time of writing look to be unrelated to the changes made in this PR.

Some of the tests that have been skipped can be, perhaps, adapted to use a 32-bit version of them; I am happy to add a few of those where necessary. I'm marking this PR ready for review so that it can get the attention of more maintainers. Great work here @agriyakhetarpal  Thanks for the merge, @mroeschke! I wish to ask if I can write a PR directly for pushing these wheels [nightly](https://pandas.pydata.org/docs/dev/getting_started/install.html#installing-the-development-version-of-pandas) to the `scientific-python` Anaconda.org index, or is it preferred to open an issue first and then link a PR to it?

For context, this is a part of the greater goal as highlighted in https://github.com/pandas-dev/pandas/issues/57891#issue-2192853050, in order to push towards interactive Sphinx-based documentation via JupyterLite. Doing this will be a much more trivial change in comparison; I am happy to contribute further. An example that highlights some interactive documentation is available for the API reference for PyWavelets: https://pywavelets.readthedocs.io/en/latest/ref/dwt-discrete-wavelet-transform.html (work on the Usage Examples section is underway) Feel free just to open a PR directly to add the wheels configurations to `.github/workflows/wheels.yml` and `pyproject.toml`