[math-fun] What kind of structure are IEEE 754 doubles?

Addition isn't even associative in floating point: http://en.wikipedia.org/wiki/Associative_property#Nonassociativity_of_floati... so floating point numbers don't even form a monoid under addition. Is addition commutative? Is there some concise characterization of what kind of structure they do form, like "Addition and multiplication are magmas with an absorbing element NaN such that ..."? -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com