在 fortran90/95 或 Python 中的两个大整数之间生成均匀随机数

Question

I want to generate some uniform random numbers between [2E16, 5E20] in fortran90/95 or Python. I know that if "R" is a random number between zero and one (0<R<1), we can transform R to [A, B] as:

R = (ba)*r + a.

But when I use this algorithm to generate some random numbers between [2E16, 5E20], most of generated random numbers are very close to 5E20. I know why this is occurred, it is because of that, the term BA is approximately equal to B (because B is so bigger than A), and most of the generated random numbers are placed within the magnitude of B or B/10 (I mean it was very close to B).

How can I solve this problem?

One solution that I tried to apply is that, I split the [2E16, 5E20] interval into smaller intervals, such as:

[2e16, 2e17], [2e17, 2e18], [2e18, 2e19], [2e19, 2e20], [2e20, 5e20].

And I generated some random numbers between each of the above intervals.

Is there any other solutions? Is my solution correct?

Answer 1

This is less of a programming problem, and more of a maths problem.

You need to think about which distribution you are drawing your random numbers from. Any uniform distribution which spans several orders of magnitude will always produce more numbers with larger exponents than with smaller exponents.

If you want a distribution which produces the same number of numbers with each exponent, you should consider the log uniform distribution , which can be sampled using eg scipy.stats.loguniform .