On Dec 29, 2019, at 15:19, David Mertz <me...@gnosis.cx> wrote: > > > On Sun, Dec 29, 2019, 5:20 PM Andrew Barnert via Python-ideas >> But it is, out of all of the possible magma-over-magma structures on those >> values, the one that most closely approximates—in a well-defined and useful, >> if very complicated, way—the rationals. > > > I'm sort of convinced that Posits better approximate the behavior of > rationals than do IEEE-754 floats: > > > https://en.m.wikipedia.org/wiki/Unum_(number_format)
I played with whatever previous version of the concept is available in Julia, and it seemed cool. But I’m pretty sure they’re still not a field, and they don’t approximate the rationals (or any other field) more closely than IEEE floats do in the same well-defined way; rather, they’re the closest approximation in an equally well-defined but very different way, one that’s hopefully usually more useful in practice, but apparently even harder to define.
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