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> But, assuming my application is doing non-trivial math, it's probably aware of the above edge cases. Thus, dropping in posits might have lots of weird side effects where I had to work around weird side effects of floats.

Yeah, but posits appear to have fewer weird edge-cases. Plus the people trying out posits are constantly trying to find methods to work around the limitations too.

During this years conference on posit maths Florent de Dinechin had a really nice talk bringing up all current issues with posits and ways that floating point maths had found workarounds over the year, as a kind of challenge to make posits catch up[0][1]. The community took it really well, as far as I can see, and Gustafson in particular seemed delighted because he genuinely wants everyone to start using better numerical methods.

[0] https://www.youtube.com/channel/UCOstJ2IVC4Y8mbgN0IsowKw

[1] https://www.youtube.com/watch?v=tcX2nRCdZvs

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