HandyG -- rapid numerical evaluation of generalised polylogarithms in Fortran

TL;DR

The work addresses the numerical evaluation of generalised polylogarithms (GPLs) for Monte Carlo integration in high-precision quantum field theory calculations. It introduces handyG, a Fortran 90 library implementing the Vollinga-Weinzierl algorithm to map GPLs to convergent series and efficiently evaluate them, with additional interfaces to Mathematica and optional precision features. The paper presents detailed algorithmic steps (trailing-zero removal, convergence facilitation via pending integrals, pending-integral evaluation, and Hölder-based acceleration) and demonstrates strong validation against GiNaC across numerous GPLs up to weight 5, reporting significant speed advantages. The practical impact is a fast, portable GPL evaluator suitable for integration in Monte Carlo codes, expanding the toolkit for high-energy physics computations.

Abstract

Generalised polylogarithms naturally appear in higher-order calculations of quantum field theories. We present handyG, a Fortran 90 library for the evaluation of such functions, by implementing the algorithm proposed by Vollinga and Weinzierl. This allows fast numerical evaluation of generalised polylogarithms with currently relevant weights, suitable for Monte Carlo integration.

Figures (7)

• Figure 1: An overview of systems under which handyG works as expected. All processors are manufactured by Intel. math indicated the version of Mathematica used. The $*$ indicates that for this version of gcc no optimisation is available.
• Figure 2: The default values of the options of handyG
• Figure 3: The example program example.f90 to calculate the example in \ref{['eq:example']}
• Figure 4: An example of how to use handyG in Mathematica to calculate the functions of \ref{['eq:example']}.
• Figure 5: Histogram of average evaluation time of the GPLs needed in Chen:2018dptMastrolia:2017pfyDiVita:2018nnh using handyG (blue) and GiNaC (yellow)