Sum of float64 vector gives slightly incorrect answer

[mbauman]

I know this has been a long and wide-ranging discussion, but I feel like it’s incomplete without linking to Stefan’s post about the ability to sum a list of 2046 elements to any floating point value you so choose just based upon its ordering. Because sometimes it’s helpful to see the absolute worst case while you’re chasing the best.

Array ordering and naive summation

One of the first things you learn in numerical analysis is that floating-point operations are not associative. A classic example is this: julia> (0.1 + 0.2) + 0.3 0.6000000000000001 julia> 0.1 + (0.2 + 0.3) 0.6 I was thinking of ways to make floating-point summation independent of the order of the summands without making the performance much worse (this is a hobby of mine). Julia currently uses a pairwise summation algorithm, which is much better than naive left-to-right reduction while havin…