Cache optimized linear sieve

TL;DR

This paper introduces cache-optimized techniques for the linear sieve, combining cyclic data structures and in-place bucket-sort to improve performance and robustness in memory access during the sieve of Eratosthenes.

Contribution

It proposes a novel cache-friendly implementation of the sieve of Eratosthenes using cyclic data structures and in-place bucket-sort, enhancing efficiency and robustness.

Findings

Improved performance over traditional sieving methods

Reduced impact of slow memory on sieve efficiency

More robust sieving process with cache optimization

Abstract

Sieving is essential in different number theoretical algorithms. Sieving with large primes violates locality of memory access, thus degrading performance. Our suggestion on how to tackle this problem is to use cyclic data structures in combination with in-place bucket-sort. We present our results on the implementation of the sieve of Eratosthenes, using these ideas, which show that this approach is more robust and less affected by slow memory.