Add numerical support of other real types (helper)

[huiyuxie]

Extra part of #1909. Better saved as draft as it may take longer time.

Tasks:

• [ ] auxiliary/math - check todo
• [ ] surface_flux_function

[github-actions[bot]]

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Created with :heart: by the Trixi.jl community.

[huiyuxie]

Redo #1929 to keep consistency.

I may start my project soon so the whole type issue here may slow down (but won't stop). Let me know if you consider this urgent, and I may adjust my priority :)

[huiyuxie]

What do you mean by other things happening in real life?

[codecov[bot]]

Codecov Report

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

Project coverage is 96.12%. Comparing base (b98b6f0) to head (d9e0f50).

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

Additional details and impacted files

```diff @@ Coverage Diff @@ ## main #1948 +/- ## ========================================== - Coverage 96.15% 96.12% -0.03% ========================================== Files 454 454 Lines 36509 36521 +12 ========================================== Hits 35103 35103 - Misses 1406 1418 +12 ``` | [Flag](https://app.codecov.io/gh/trixi-framework/Trixi.jl/pull/1948/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/1948/flags?src=pr&el=flag&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=trixi-framework) | `96.12% <0.00%> (-0.03%)` | :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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[ranocha]

I can't spend as much time on this open-source project as I would like since I also have to other things

[huiyuxie]

I thought it means something more abstract and high level, but if you are talking about this, no worries.

Does that mean I have total control over my project? As I was always thinking about making this a totally separate package within the ecosystem, like https://github.com/SciML/DiffEqGPU.jl, instead of integrating it directly into the original package.

At least keep an eye on my project - sometimes it moves fast.

[ranocha]

Does that mean I have total control over my project? As I was always thinking about making this a totally separate package within the ecosystem, like https://github.com/SciML/DiffEqGPU.jl, instead of integrating it directly into the original package.

This is open-source software, so we can not disallow this (as long as you respect the license). We would, of course, be happy if you continued contributing to the main Trixi.jl repo - in particular with fixes for floating point types like in this PR.

[huiyuxie]

I will try my best as I work full time during daytime.

This is open-source software, so we can not disallow this (as long as you respect the license).

Why not say, "This is open-source software, so you are allowed to do so"? You are saying something that seems exclusive to me. I believe everyone comes to open-source out of interest and all kinds of contribution are encouraged. This is just so wired for me, I just don’t get the same feeling from other places...

Sorry for above if you are not feeling well, but I am also not feeling well 🥲

[huiyuxie]

This is also offensive. This implies that you already consider the possibility that I may not respect the license. Would you say something like this to your colleagues? Probably no. I'm feeling a sense of inequality and hierarchy from you. Please mind your words even if you don't mean that way. I need some time to adjust myself - sorry for that

I clearly know that MIT license is somehow the most flexible one - for me, only a copycat would be likely to violate it.

[huiyuxie]

I seldom feel a sense of inclusion here. Decisions are made by people who are not actually doing the work, instead of through an open and transparent vote. I feel like I’m just doing tasks that are assigned to me, and independent thinking and open-mindedness are discouraged. Maybe I chose the wrong place - this is an open-source place but makes me feel like a school, some people (includes me) are even tagged with the label of student

[ranocha]

I'm sorry if my words above sound aggressive to you - that was not my goal. Please do whatever you like to do and work on the open-source projects that you enjoy