Random Floating-Point Values

Generating Pseudo-random Floating-Point Values

by Allen B. Downey

This is a draft of a paper I think I will probably not publish, but I think it is kind of interesting, so I thought I would put it out there. If nothing else, it contains some pedagogical material about IEEE floating-point representation.

Here is the paper in PDF, Compressed Postscript, and Postscript.

And here is C code that implements several versions of my algorithm:

Abstract

The conventional method for generating a pseudorandom floating-point value is to generate a pseudorandom integer and divide by a constant (using floating-point arithmetic). The problems with this approach are (1) the possible outcomes are a small subset of the representable floating-point values (about $7%$ for a typical implementation) and (2) subsequent transformation of these values may not yield the expected distributions (for example, applying a log transformation to numbers from a uniform distribution does not yield an exponential distribution as it would in real arithmetic). We present a new algorithm with the following properties: (1) it can produce every representable floating-point value in a given range, and (2) it is efficient in both time and use of pseudorandom bits.

Allen Downey is the author of Think Python, Think Stats and Think Bayes, all free to read online. He writes the blog Probably Overthinking It. Home page.