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Comment by addaon | Hacker News Reader

I'm a huge fan of this system, but it's worth pointing out that it doesn't have a single NaN, it has a single infinity with an undefined sign, modeling the projectively extended real numbers. NaN is a bit of an abomination; projective infinity is an uncommon beast, but one that can be worked with consistently. And yes, by pairing zero with infinity on opposite sides of the number ring, you get a symmetric system with no undefined or redundant encodings.

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Signed infinity is useful for limits, and also for initial values of some algorithms, so missing them seems like a disadvantage.

Also, it still has no total order, so keeps another messy part of IEEE floats

There's an easy alternative: just use the MAX and MIN values. That's what you would do with integers anyway, in case of initial values. As for limits, if you need to express limits in a datatype for expressing a small subset of rational numbers, you've got the wrong tool for the job.

> Also, it still has no total order

This is not true. It is defined to have the exact same ordering, bitwise, as two's complement integers. That means it has total order: the NaN is the most negative, then comes the negative numbers, then zero, and then positive numbers.

They used to call it "infinity with an undefined sign", then "NaR" for "Not a Real" but in the latest papers I've seen they just call it NaN. But that's just a name, it's the projective infinity as you say. I agree that the IEEE NaN is an abomination.

It still seems to be NaR here https://posithub.org/posit_standard4.12.pdf

NaN is a feature of dynamically typed languages; otherwise they would not be able to represent all outcomes of implicit coercion.

And here I thought NaN was a definition from IEEE-754.

Yes, I'm not sure what parent means. Even java double has NaN.

NaN is a feature of IEEE floats to ensure that all arithmetic operations can always create a correct result. For example 0/0 has to evaluate to NaN, no other result would be mathematically correct. If there was no NaN the CPU would have to trigger a fault or return an incorrect result, both are undesirable.

So, today I learned something: the JavaScript critics are wrong at yet another thing.

It crops up more in JavaScript since it doesn't have integers, and if you try to convert non-numeric string to a number you get a NaN

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