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I am running some experiments which require use of the following function:

import math

def sigmoid(x):
    return 1.0 / (1.0 + math.exp(-x))

The function returns a number from 0.0 to 1.0 (see https://en.wikipedia.org/wiki/Sigmoid_function). If I give it small values for input x, then the result is as expected, e.g. 

>>> sigmoid(1)
0.7310585786300049
>>> sigmoid(5)
0.9933071490757153
>>> sigmoid(7)
0.9990889488055994
>>> sigmoid(10)
0.9999546021312976
>>> sigmoid(20)
0.9999999979388463
>>> sigmoid(30)
0.9999999999999065

However, when the x gets larger, then the function always returns 1.0.

>>> sigmoid(40)
1.0
>>> sigmoid(45)
1.0
>>> sigmoid(50)

I suspect this has to do with the part of the function that adds 1.0 with a potentially very small number (1.0 + math.exp(-x)). e.g.

>>> 1.0 + math.exp(-30)
1.0000000000000935
>>> 1.0 + math.exp(-40)
1.0
>>> 1.0 + math.exp(-50)
1.0
>>> 1.0 + math.exp(-60)
1.0

How do I prevent Python from making such errors? I think it's an overflow (or underflow??) issue. Any tips? Thanks in advance.

Siato
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    The issue is, how floating point values are stored - you have only a limited space to work with, and the rest gets cut off. You could use `fractions.Fraction`. – CodenameLambda Jul 06 '16 at 09:52
  • ... and probably such small errors won't matter in your application. – Adam Sosnowski Jul 06 '16 at 10:04
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    A better duplicate target would be http://stackoverflow.com/questions/11522933/python-floating-point-arbitrary-precision-available – tripleee Jul 06 '16 at 10:10

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