An algorithm to approximate the real trilogarithm for a real argument

TL;DR

This paper introduces an algorithm to accurately approximate the real trilogarithm function for real inputs, optimized for modern CPUs to leverage instruction-level parallelism, achieving double precision accuracy.

Contribution

The paper presents a novel approximation algorithm for the real trilogarithm that is optimized for instruction-level parallelism and double precision accuracy.

Findings

Achieves IEEE 754-1985 double precision accuracy

Designed for efficient execution on CPUs with instruction-level parallelism

Provides a practical method for computing the trilogarithm in scientific applications

Abstract

We present an algorithm to approximate the real trilogarithm for a real argument with IEEE 754-1985 double precision accuracy. The approximation is structured such that it can make use of instruction-level parallelism when executed on appropriate CPUs.