It's an interesting connection. Any finite collection of real values (represented in floating-point or otherwise) has a definite correct sum. If you're constrained to the floating-point to represent that value, you should ideally round the true value to the closest float and return that. Computing this true sum of a sequence of floating-point values is surprisingly hard though. The state of the art seems to be Radford Neal's paper on superaccumulators from 2015:
Comments
It's an interesting connection. Any finite collection of real values (represented in floating-point or otherwise) has a definite correct sum. If you're constrained to the floating-point to represent that value, you should ideally round the true value to the closest float and return that. Computing this true sum of a sequence of floating-point values is surprisingly hard though. The state of the art seems to be Radford Neal's paper on superaccumulators from 2015:
https://arxiv.org/abs/1505.05571
Fortunately pairwise summation (Julia's default) is fast and fairly hard to trip up, although it certainly is possible to trick it.