Bit recycling for scaling random number generators

TL;DR

This paper explores efficient methods for scaling random number generators to produce uniform samples in arbitrary ranges, focusing on computational speed and mathematical efficiency.

Contribution

It introduces novel techniques for scaling RNG outputs to arbitrary ranges, improving efficiency over existing methods.

Findings

New scaling methods outperform traditional approaches in speed.

Techniques maintain statistical uniformity across various ranges.

Applicable to both hardware and algorithmic RNGs.

Abstract

Many Random Number Generators (RNG) are available nowadays; they are divided in two categories, hardware RNG, that provide "true" random numbers, and algorithmic RNG, that generate pseudo random numbers (PRNG). Both types usually generate random numbers $(X_n)$ as independent uniform samples in a range $0,\cdots,2^{b-1}$, with $b = 8, 16, 32$ or $b = 64$. In applications, it is instead sometimes desirable to draw random numbers as independent uniform samples $(Y_n)$ in a range $1, \cdots, M$, where moreover M may change between drawings. Transforming the sequence $(X_n)$ to $(Y_n)$ is sometimes known as scaling. We discuss different methods for scaling the RNG, both in term of mathematical efficiency and of computational speed.