Fix small amount of Float64 computation

[huiyuxie]

Some amount of Float64 was brought by the initial conditions - see changes.

[github-actions]

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[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 95.42%. Comparing base (1d7b256) to head (9b9b4d6).
Report is 7 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #2099      +/-   ##
==========================================
- Coverage   96.34%   95.42%   -0.92%     
==========================================
  Files         470      470              
  Lines       37514    37599      +85     
==========================================
- Hits        36142    35877     -265     
- Misses       1372     1722     +350     

Flag	Coverage Δ
unittests	95.42% <ø> (-0.92%)	⬇️

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[ranocha]

But it will bring some Float64 computation

If there is a reasonable way to avoid Float64, I would prefer that

[huiyuxie]

I cannot understand why we have to avoid Float64 entirely - GPU has tolerance for mixed precision.

[huiyuxie]

Please do not merge - I don't think it is a good way.

[huiyuxie]

This final version cannot solve my problem trixi-gpu/TrixiCUDA.jl#68 (I will think about another way) but it solves the original problem about small computation of Float64.

I want to confirm these things -

1. I cannot understand why we have to avoid Float64 entirely - GPU has tolerance for mixed precision computation so ensuring type preserving for results is enough
2. I am not sure whether 2^(i - 1) * (1 - 2) * RealT(1.1691) / (1 - 2^ncomponents(equations)) is better than 2^(i - 1) * (1 - 2) / (RealT(1) - 2^ncomponents(equations)) * RealT(1.1691)

Ready for review @ranocha

[ranocha]

There is a huge amount of changes that seem to be unrelated to the original purpose of this PR. Please fix it.

[ranocha]

• I cannot understand why we have to avoid Float64 entirely - GPU has tolerance for mixed precision computation so ensuring type preserving for results is enough

Where do you draw the line between an acceptable amount of Float64 and wasting time/energy? For example, you have insisted quite strictly on pure Float32 computations and maximal speedup in #2042

• I am not sure whether 2^(i - 1) * (1 - 2) * RealT(1.1691) / (1 - 2^ncomponents(equations)) is better than 2^(i - 1) * (1 - 2) / (RealT(1) - 2^ncomponents(equations)) * RealT(1.1691)

I prefer the first version since a * b / c is easier for me to read than a / c * b (which could be confused with a / (c * b)).

[huiyuxie]

👍

[ranocha]

Did you intend to close this PR? I'm asking since you have changed its title after closing it.

[huiyuxie]

Yes - it is more convenient to open a new PR and I don't like to work on my local main branch.