[methodOverdrive]

I would argue that unums are a "superior replacement" for doubles in many cases, though: in the case that you support unums that are "wide" enough, you can represent doubles exactly, plus you have additional values, plus some nice rules about when approximation error occurs/is propagated and not as many bits need to be stored or moved around on buses. It'll be a while before there's an implementation anywhere near as fast as existing FPUs, but Gustafson makes a good argument for his format. Personally, I'm more interested in the correctness benefits than the space/power/time savings - even if unums are never faster than 64-bit floats, they present an interesting way to do real-number arithmetic and my brief exposure to them leaves me much more confident that I could write numerical algorithms correctly than with doubles - I do numerical/statistical algorithms with doubles in my work, and it's really a pain to reason about things that the "uncertain" (open-inverval) values of the unum format would greatly simplify.

They're also an inferior replacement in the case that you want to take advantage of highly-optimized hardware, and that getting a correct answer doesn't really matter. I don't see unums replacing floats for, say, video game graphics. But for numerical computation, it seems like the only real flaw with unums compared to doubles is the nonexistence of a hardware implementation, and the existing popularity of doubles.

[dnautics]

Agreed. For neural networks. I would argue the opposite is true, you should just have a 16bit float that casts really large values to infinity silently without throwing errors, with a logistic lookup that maps "inf" to +/- 1... A mathematically incorrect float is operationally superior to the correct one.

[methodOverdrive]

Bonus points if values near 0 are treated as 0 (encourages sparsity!)

[GFK_of_xmaspast]

For hardware without a FPU, you can do floats in software when accuracy is more important than speed (vs fixed point), one can imagine that if this thing actually works then for hardware without a "UPU" one can just do unums in software when needed.