Fast renormalize

[IQuick143]

Objective

• Addresses part of Approximate/Fast normalisation for Dir{2,3} #14302 .

Solution

• Add a fast_remormalize method to Dir2/Dir3/Dir3A and Rot2.

Testing

• Added tests too

[BD103]

Good docs and unit tests check out. I have one non-blocking nit, but beyond that it looks good!

[BD103]

Oops, I accidentally though that @Jondolf's review was an approval. Marking this as S-Needs-Review.

[janhohenheim]

Left some documentation improvement suggestions, but nothing blocking :)

[IQuick143]

@janhohenheim Great suggestions, thanks a bunch.

[janhohenheim]

Looks like they had some syntax errors, sorry about that 😅

[IQuick143]

We gotta keep the CI on its toes somehow, right?

[IQuick143]

ah... are these the infamous doctests I've heard of?

How do I fix this CI failure?

[janhohenheim]

🎉

[Jondolf]

LGTM! Adding a similar method for quaternions would be nice, but we can do that later, either by adding it to Glam directly or by using an extension trait.

[janhohenheim]

Added an issue for this to glam: bitshifter/glam-rs#540
Upstreaming the change to Quat would be nice, if you find the time @IQuick143 :)

[BD103]

I ran benchmarks for this and wrote about them in bitshifter/glam-rs#540 (comment). The speed change, while an improvement, is only in a few picoseconds. This is desirable for hot code, but may not be worth upstreaming.

[Jondolf]

I wonder if the performance improvement would be larger when the libm feature is enabled (used for portable and cross-platform deterministic math), since libm might not be able to leverage hardware intrinsics for sqrt on some platforms depending on how it's implemented

[BD103]

I wonder if the performance improvement would be larger when the libm feature is enabled (used for portable and cross-platform deterministic math), since libm might not be able to leverage hardware intrinsics for sqrt on some platforms depending on how it's implemented

I'm not sure how to do that myself, but feel free to try it! This is the code that I used to benchmark.

[Aceeri]

Neat! Hadn't thought about it like this before, but makes sense.

[alice-i-cecile]

Thank you to everyone involved with the authoring or reviewing of this PR! This work is relatively important and needs release notes! Head over to bevyengine/bevy-website#1664 if you'd like to help out.