Hmm... Well apparently I am the idiot in this situation. This topic has me intrigued but also somewhat concerned. I have quite naively been doing comparisons between floating point values without regard for the possibility that the underlying calculations might actually be inaccurate to a significant degree.
So I guess I need to convert all of my comparisons into a form which accounts for some margin of error?
On second thought though, I am not certain if I have any direct equivalence tests, mostly just range tests. But it is good to know it is something I should be aware of in the future. I'm just making a 2d platformer though.