Fast algorithm for generating random bit strings and multispin coding for directed percolation

TL;DR

This paper introduces a fast, efficient algorithm for generating random bit strings with arbitrary probabilities, significantly accelerating simulations like multispin coding in directed percolation and benefiting general Monte Carlo methods.

Contribution

The paper presents a hybrid algorithm for rapid random bit string generation and demonstrates its application to multispin coding, achieving substantial speedups over existing methods.

Findings

3.8 times faster for 32-bit random bit generation

6.8 times faster for 64-bit random bit generation

up to 14-fold acceleration in directed percolation simulations

Abstract

We present efficient algorithms to generate a bit string in which each bit is set with arbitrary probability. By adopting a hybrid algorithm, i.e., a finite-bit density approximation with correction techniques, we achieve 3.8 times faster random bit generation than the simple algorithm for the 32-bit case and 6.8 times faster for the 64-bit case. Employing the developed algorithm, we apply the multispin coding technique to one-dimensional bond-directed percolation. The simulations are accelerated by up to a factor of 14 compared with an optimized scalar implementation. The random bit string generation algorithm proposed here is applicable to general Monte Carlo methods.