Batched Ranged Random Integer Generation

TL;DR

This paper introduces an efficient algorithm for generating multiple unbiased, uniformly-random integers within a range from a single random binary word, significantly improving speed for array shuffling tasks.

Contribution

The paper presents a novel algorithm that produces multiple independent bounded integers from one random word without bias, optimizing performance over existing methods.

Findings

More than double the speed of unbiased random shuffling for small to medium arrays

Uses one multiplication and no division per generated value in typical cases

Produces multiple independent uniform integers efficiently from a single random word

Abstract

Pseudorandom values are often generated as 64-bit binary words. These random words need to be converted into ranged values without statistical bias. We present an efficient algorithm to generate multiple independent uniformly-random bounded integers from a single uniformly-random binary word, without any bias. In the common case, our method uses one multiplication and no division operations per value produced. In practice, our algorithm can more than double the speed of unbiased random shuffling for small to moderately large arrays.