Parallel random variates generator for GPUs based on normal numbers

TL;DR

This paper presents a GPU-based parallel pseudorandom number generator leveraging the normal number α_{2,3}, achieving faster performance than existing methods by optimizing modular reduction and memory operations.

Contribution

The paper introduces a GPU implementation of a linear congruential generator based on the normal number α_{2,3}, with improved modular reduction techniques for enhanced speed.

Findings

Faster generation rate than existing methods

Most operations performed in 64-bit integer arithmetic

Generation rate close to GPU global memory write limit

Abstract

Pseudorandom number generators are required for many computational tasks, such as stochastic modelling and simulation. This paper investigates the serial CPU and parallel GPU implementation of a Linear Congruential Generator based on the binary representation of the normal number $\alpha_{2,3}$. We adapted two methods of modular reduction which allowed us to perform most operations in 64-bit integer arithmetic, improving on the original implementation based on 106-bit double-double operations. We found that our implementation is faster than existing methods in literature, and our generation rate is close to the limiting rate imposed by the efficiency of writing to a GPU's global memory.