think you have misunderstood what I meant, originally, you asked me if I knew the internal low level mechanism for floating point.

No, I didn't ask for the "low level" stuff, since when you're using floating point, you're most likely using a floating point library that comes with a compiler. My question was about knowing some of the subtle pitfalls that can occur if you blindly trust the compiler (or any other piece of software) to "do it right". Using floating point doesn't save you from numerics.

There's not much "magic" about adding two floating point numbers. Adding three or more, however, brings an additional level of complexity if you want to do it accurately.

Here's my original question, for the reference (emphasis mine):

Do you know the algorithm to "accurately" add more than two floating point numbers ?