random() in python

Question

In python the function random() generates a random float uniformly in the semi-open range [0.0, 1.0). In principle can it ever generate 0.0 (i.e. zero) and 1.0 (i.e. unity)? What is the scenario in practicality?

Answer 1

0.0 can be generated; 1.0 cannot (since it isn't within the range, hence the ) as opposed to [).

The probability of generating 0.0 is equal to the probability of generating any other number within that range, namely, 1/X where X is the number of different possible results. For a standard unsigned double-precision floating point, this usually means 53 bits of fractional component, for 2^53 possible combinations, leading to a 1/(2^53) chance of generating exactly 0.0.

So while it's possible for it to return exactly 0.0, it's unlikely that you'll see it any time soon - but it's just as unlikely that you'd see exactly any other particular value you might choose in advance.

Answer 2

The [ indicates that 0.0 is included in the range of valid outputs. The ) indicates 1.0 is not in the range of valid outputs.