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Comment by phkahler | Hacker News Reader

My enthusiasm for posits was never about the precision. It was due to not having signed zero, and not having NaN. Just give me the nearest representable value please. Operations on numbers should never yield results that are not numbers.

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IEEE does define x/0 to be infinity and -x/0 as -infinity. But what about 0/0? Or sqrt(-1)?

What should happen if you divide 1 by 0?

inf

That's not really a number either. But what about 0/0?

It seems that posits have a value called NaR ("not a real") which serves the purpose of all the special values (including both infinities) in IEEE floats. There are some key differences though:

  NaR (posits)                 NaN (floats)
  ------------                 ------------
  one bit pattern              many different bit patterns
  always equal to itself       never equals itself
  less than all other values   falsifies all orderings

It's a mode you can turn on that substitutes inf for NaR.

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