# A revision of the subtract-with-borrow random number generators

## TL;DR

This paper reimplements the popular subtract-with-borrow random number generator RANLUX as a large-integer linear congruential generator, achieving faster performance and improved seeding capabilities on modern computers.

## Contribution

It introduces a novel, efficient modular multiplication method for RANLUX, enabling faster random number generation and unique sequence seeding.

## Key findings

- Significant speed improvement over traditional RANLUX
- Comparable performance to other high-quality generators
- Fast state skipping for unique sequence seeding

## Abstract

The most popular and widely used subtract-with-borrow generator, also known as RANLUX, is reimplemented as a linear congruential generator using large integer arithmetic with the modulus size of 576 bits. Modern computers, as well as the specific structure of the modulus inferred from RANLUX, allow for the development of a fast modular multiplication -- the core of the procedure. This was previously believed to be slow and have too high cost in terms of computing resources. Our tests show a significant gain in generation speed which is comparable with other fast, high quality random number generators. An additional feature is the fast skipping of generator states leading to a seeding scheme which guarantees the uniqueness of random number sequences.