CHAPLIN—Complex Harmonic Polylogarithms in Fortran

We present a new Fortran library to evaluate all harmonic polylogarithms up to weight four numerically for any complex argument. The algorithm is based on a reduction of harmonic polylogarithms up to weight four to a minimal set of basis functions that are computed numerically using series expansions allowing for fast and reliable numerical results.Program summaryProgram title: ChaplinCatalogue identifier: AETC_v1_0Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AETC_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 101 192No. of bytes in distributed program, including test data, etc.: 729 234Distribution format: tar.gzProgramming language: Fortran 77.Computer: Computing systems on which Fortran 77 compilers are available.Operating system: Operating systems on which Fortran 77 compilers are available.Classification: 11.1.Nature of problem:Numerical evaluation of harmonic polylogarithms.Solution method:Inside the unit circle: series expansion. Outside the unit circle: inversion relations.Restrictions:Only harmonic polylogarithms up to weight four are supported.Unusual features:Allows the evaluation of HPL’s numerically for any point in the complex plane.Running time:Depending on the weight vector and argument of the HPL, between 0.2 and 400 μs.