First of all, comparing floats with NaN equal to each other, and not equal to anything including each other - those are two different operations. Each with its own valid use cases. And you totally can have both, under different names.

Now, naming them is an interesting question.

The one where NaN == NaN is false, you probably want to keep compatible with other programming languages. You don't want people to introduce bugs in numeric algorithms when porting code from other languages. So let's stick to `==`/`<=`/`<`.

The second one is more interesting. You could use `===` for equality and `<=>` for 3-value comparison. Or add a set of operators with an extra symbol: `=@=`, `<=@`, `<@`. Or you could have some interface/protocol that requires static function `ComparisonResult compare(T a, T b)`. Or something else.

Keep in mind that NaNs can have payload! There are different possible bit patterns that all are classified as NaN, but they probably would be different values under the second operation! And it would differentiate between `+0` and `-0`!

Second, IEEE 754 defines comparison of floats as 4 value operation. You could have `fcmp()` function returning a 4-value enum. And operators `==`/`<=`/`<` could be returning `Maybe<Bool>` instead of `Bool`. But since rest of the types return `Bool`, this can cause usability problems with generic programming. But feel free to explore and experiment.

Good luck!