Does this truely generate a random foating point number? (Python)

Question

For an introduction to Python course, I'm looking at generating a random floating point number in Python, and I have seen a standard recommended code of

import random

lower = 5
upper = 10
range_width = upper - lower
x = random.random() * range_width + lower

for a random floating point from 5 up to but not including 10.

It seems to me that the same effect could be achieved by:

import random

x = random.randrange(5, 10) + random.random()

Since that would give an integer of 5, 6, 7, 8, or 9, and then tack on a decimal to it.

The question I have is would this second code still give a fully even probability distribution, or would it not keep the full randomness of the first version?

Answer 1

According to the documentation then yes random() is indeed a uniform distribution.

random(), which generates a random float uniformly in the semi-open range [0.0, 1.0). Python uses the Mersenne Twister as the core generator.

So both code examples should be fine. To shorten your code, you can equally do:

random.uniform(5, 10)

Note that uniform(a, b) is simply a + (b - a) * random() so the same as your first example.

The second example depends on the version of Python you're using. Prior to 3.2 randrange() could produce a slightly uneven distributions.

Answer 2

There is a difference. Your second method is theoretically superior, although in practice it only matters for large ranges. Indeed, both methods will give you a uniform distribution. But only the second method can return all values in the range that are representable as a floating point number.

Since your range is so small, there is no appreciable difference. But still there is a difference, which you can see by considering a larger range. If you take a random real number between 0 and 1, you get a floating-point representation with a given number of bits. Now suppose your range is, say, in the order of 2**32. By multiplying the original random number by this range, you lose 32 bits of precision in the result. Put differently, there will be gaps between the values that this method can return. The gaps are still there when you multiply by 4: You have lost the two least significant bits of the original random number.