Honestly, I think IEEE 754 floating point numbers are a pretty bad way of dealing with real numbers and just cause tons of headaches that every math library has to deal with. Even high level programmers aren't shielded from the NaN nonsense. It would be great if we had an underlying implementation we could ignore and that allowed us to think at a more mathematical level.
I actually found something recently on this topic while googling for any alternatives, its called Unum and looks very interesting: https://en.wikipedia.org/wiki/Unum_(number_format)
Does anyone know more about this? Are there any chips out there that support it?