In floating-point numbers, the NaN value is weirdly special. It's never equal to any NaN, even itself. It's possible for x != x to be true because of NaN.
Because of such weird values, Rust has two levels of equality: PartialEq and Eq, and two levels of ordering PartialOrd and Ord. Floating point numbers (f32, f64) implement only PartialEq and PartialOrd.
Floats can't be sorted using the regular .sort() method that requires Ord. There is a total_cmp helper method that does give ordering to NaN values, which makes sorting work:
floats.sort_by;
Similarly, floats can't be keys in a HashMap due to lack of Eq. That's for the best, because exact comparison of floats is tricky anyway.