> This has, however, recently come up for Nx (numerical elixir) which had to implement and standardize ways to shim these IEEE concepts back into the VM for interop purposes.

This would have been an excellent place to use Ada. The package "Interfaces" has types exactly for IEEE Floats: `Interfaces.IEEE_Float_64`.

You could then get rid of non-numeric representations (raising `Constraint_Error` instead) via the following subtype-definition:

    subtype Float is Interfaces.IEEE_Float_64 range Interfaces.IEEE_Float_64'Range;

(I've thought about writing an Erlang in Ada, hoping to tie together Erlang's actors w/ Ada's Task where possible [ie focus on interop], but haven't found any Erlang language definition that's anywhere near recent.)

Is there any language that treats the zeros as unequal? That would seem like the real "screw IEEE".

in the specific case of erlang, and the erlang beam vms,

0 !== 0.0

Of course 0 == 0.0

I imagine if they had chosen to follow IEEE, it would have been that 0.0 !== -0.0 and 0.0 == 0.0.

I don't know erlang, but it looks to me like that's a difference between types. (integer vs float)

Is there a language that treats different float values of zero as unequal? That would be surprising to me. And possibly silly.

What a guess! I guessed "Julia" and that is correct: https://stackoverflow.com/questions/38601141/what-is-the-dif...

In Julia 0.0 == -0.0 but 0.0 === -0.0 evaluates to false.

Note that -0.0 and 0.0 are different at the binary representation level, which is what === checks for.