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

At 04:23 PM 4/14/2015, Mike Stay wrote:

Is addition commutative?

Probably not, depending upon which computer you use. Leaving aside issues of NaN's, signaling and exponent issues, some computers have larger mantissas for "accumulation", so that very long iterated sums still "work". E.g., Intel x86 "extended precision" floats with 64-bit mantissa. http://en.wikipedia.org/wiki/Extended_precision Since you're now adding numbers of two different mantissa sizes, they are highly unlikely to be commutative. "satanism" is an anagram for "mantissa"; now do you see why floating point is so hard? http://en.wiktionary.org/wiki/mantissa