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Subnormal floating-point numbers are expensive on Intel processors

69 points · 54 comments · zdw

gwbas1c · 1789737860 · focus · HN ↗
I'm still trying to understand what a subnormal number is; IE, I'm looking for the TLDR so I know just enough to know if I'm using them and need to learn more.
Unfortunately, the Wikipedia article, while probably being accurate, doesn't give a clear and concise answer.
IE, is 0.0001 a subnormal? Or is it 0.000000000000000000001?
1. ant6n · 1789738864 · focus · HN ↗
  Usually IEEE floats have an implied 1 in the front. So for the standard represented numbers, there's some minimum number 1.bbbbbb.. * 2^-N. This allows 1bit more precision than is actually stored.
  between any two numbers, there's basically the same epsilon difference, but from the smallest number to zero it's bigger.
  A subnormal number breaks that convention, it just becomes 0.bbbbb... * 2^-N. As the numbers get smaller, the relative difference between the numbers gets larger. That also means their precision is smaller than the normal floats.

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