[CogitoCogito]

I hadn't thought about the infinities part. If they had the same behavior in all operations involving other numbers, then I could see how they could nonetheless be the same from a C++ type perspective, but given they behave differently, C++ certainly couldn't consider them the same.

Thanks for clearing that up!

[ncmncm]

If you keep infinities and NaNs out of a subsystem, then float and double are totally ordered within that subsystem. So, it is a choice. I would not hesitate on that basis.

Of more moment is that floating point variables often represent imprecise values, such that e.g. 1.41 could represent a value that should equal another transcribed as 1.39. The type system will not help you there. You are obliged to code in tolerance the hard way.