Relatedly, there's a relatively new julia package called MultiFloats.jl [1] for doing arithmetic with numbers of the form a_1 + a_2 + ... + a_n where a_{i+1} is of the order of the round off of a_i. So it's fixed precision, but the cool thing is you can easily generate code for arbitrary `n`. The package itself is just a few hundred lines of code. I've tried it on an NVIDIA GPU with fast double precision, and it seems to "just work" for basic linear algebra.