Support of other real types (`Float32`, auxiliary)

[huiyuxie]

The first extra part of #1909, mainly addressing src/auxiliary.

TODO: https://github.com/trixi-framework/Trixi.jl/pull/1929#discussion_r1590639060

[github-actions[bot]]

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[codecov[bot]]

Codecov Report

Attention: Patch coverage is 0% with 12 lines in your changes are missing coverage. Please review.

Project coverage is 91.13%. Comparing base (c221bca) to head (d7716cb).

Files	Patch %	Lines
src/auxiliary/math.jl	0.00%	12 Missing :warning:

Additional details and impacted files

```diff @@ Coverage Diff @@ ## main #1929 +/- ## ========================================== - Coverage 96.09% 91.13% -4.96% ========================================== Files 453 453 Lines 36481 36489 +8 ========================================== - Hits 35055 33252 -1803 - Misses 1426 3237 +1811 ``` | [Flag](https://app.codecov.io/gh/trixi-framework/Trixi.jl/pull/1929/flags?src=pr&el=flags&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=trixi-framework) | Coverage Δ | | |---|---|---| | [unittests](https://app.codecov.io/gh/trixi-framework/Trixi.jl/pull/1929/flags?src=pr&el=flag&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=trixi-framework) | `91.13% <0.00%> (-4.96%)` | :arrow_down: | Flags with carried forward coverage won't be shown. [Click here](https://docs.codecov.io/docs/carryforward-flags?utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=trixi-framework#carryforward-flags-in-the-pull-request-comment) to find out more.

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[huiyuxie]

Thanks for the review @ranocha ! I am thinking about how to test these PRs. Generally, I would treat these smaller PRs as preliminary improvements (as the general PR is calling some basic functions here). So basically we could test and merge these smaller PRs first then merge and test the general PR. But what if some PRs are cross-referencing each other (for example, some PRs rely on the improvements from each other)?

I am not sure whether the case I mentioned above is going to happen in these improvements.

[ranocha]

Thanks for the review @ranocha ! I am thinking about how to test these PRs. Generally, I would treat these smaller PRs as preliminary improvements (as the general PR is calling some basic functions here). So basically we could test and merge these smaller PRs first then merge and test the general PR. But what if some PRs are cross-referencing each other (for example, some PRs rely on the improvements from each other)?

I am not sure whether the case I mentioned above is going to happen in these improvements.

In this case, the PRs providing functionality required by other changes should be merged first.

[sloede]

This depends on #1909 (or at least similar issues apply), right? If yes, please re-request my review here once changes in #1909 that are also pertinent for this PR here have been applied here as well 🙂

[huiyuxie]

1909 depends on this PR (and possibly more small PRs like this in the future).

[huiyuxie]

Rerun CI please (if you like). I locally ran CI when these were running here - hitting the limit and thus too many CI failures here.