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Created September 13, 2016 02:52
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underflow_overflow.md

Using a 64-bit floating point number (AKA a double), what is the smallest integer n such that?

  • 0.1^n == 0.0
  • 10.0^n == Inf
  • exp(-n) == 0.0
  • exp(n) == Inf

I frequently forget these numbers, so here they are:

  • 0.1^n == 0.0: n = 324
  • 10.0^n == Inf: n = 309
  • exp(-n) == 0.0: n = 746
  • exp(n) == Inf: n = 710
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tanh(n) == 1.0: n = 20 via https://twitter.com/stephentyrone

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  • 1 / (1 + exp(-n)) == 1.0: n = 37
  • 1 / (1 + exp(n)) == 0.0: n = 710

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