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This reminded me of Posits[1] and Unums[2]. I dabbled with my own implementation some years ago, but nothing serious.

Anyone tried them out? I see there's some FPGA implementations and a RISC-V extension idea[3], would be fun to try it on a softcore.

[1]: https://posithub.org/docs/posit_standard.pdf

[2]: http://johngustafson.net/unums.html

[3]: https://www.posithub.org/khub_doc

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Which version?

With current posits, they're a clever way to give more bits to precision near 1 and more bits to exponent near 0 and infinity, but if you're not overflowing or underflowing then it's a marginal improvement at best. Then Unum glues intervals on top, right? But you could do intervals with normal floats too. And you still won't get the correct answer, you'll just know the error exploded. Is the giant accumulator feature able to help here?

For the other versions I tend to get completely lost.

Unfortunately while Posits (and Unums) are more accurate for some computations, they are still designed around using small numbers of bits to represent numbers, so they have error in computations just like floating point. The argument for posits are mostly that they produce less error on the inputs you care about, and more on the ones you don't, but it really depends on your computation; you really have to know what you're doing to use them safely.

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