(feat): elem_mul 64 bit upcast option

[ilan-gold]

• Closes elem_mul in variance calculation should use float64 casting #3127
• Tests included or not required because:

• Release notes not necessary because:

[ilan-gold]

I'm putting this in scanpy2.0 because this setting should be turned on then

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 75.38%. Comparing base (f7acd02) to head (75531f3).

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #3392      +/-   ##
==========================================
+ Coverage   75.36%   75.38%   +0.01%     
==========================================
  Files         112      112              
  Lines       13219    13229      +10     
==========================================
+ Hits         9963     9973      +10     
  Misses       3256     3256              

Files with missing lines	Coverage Δ
src/scanpy/_settings.py	89.10% <100.00%> (+0.35%)	⬆️
src/scanpy/_utils/__init__.py	74.56% <100.00%> (+0.09%)	⬆️

[flying-sheep]

So this will just use 64 bits for computation and downcast again after?

[ilan-gold]

So this will just use 64 bits for computation and downcast again after?

I hadn't considered that. There's no downcasting at the moment, it just uses 64 bits for the multiplication. Maybe it should downcast to the original?

I could see that being beneficial, but then the question is what do we downcast to? The data type of the right or left matrix?

We would have to make this clear in the documentation.

[flying-sheep]

@ivirshup said on Zulip:

I think the intermediary upcast is an implementation detail (in theory we could rewrite the calculation to not upcast, and still be accurate) and should not change the result dtype. For what dtype the result should be, we should use numpy type promotion rules, which should be: f32 * f32 -> f32, f32 * f64 -> f64, f64 * f64 -> f64.