[threeducks]

What exactly do you say is not commutative? This Wikipedia article claims that at least floating-point addition and multiplication are both commutative:

https://en.wikipedia.org/wiki/Floating-point_arithmetic#Accu...

[adgjlsfhk1]

it is for finite values, but because IEEE did some dumb things it isn't specified to be for NaN values (and on several architectures, isn't).