Numerical Implementation of Harmonic Polylogarithms to Weight w = 8

Abstract

We present the FORTRAN-code HPOLY.f for the numerical calculation of harmonic polylogarithms up to w = 8 at an absolute accuracy of $\sim 4.9\cdot 10^{-15}$ or better. Using algebraic and argument relations the numerical representation can be limited to the range $x\in [0,\sqrt{2}-1]$. We provide replacement files to map all harmonic polylogarithms to a basis and the usual range of arguments $x\in ]-\infty ,+\infty [$ to the above interval analytically. We also briefly comment on a numerical implementation of real valued cyclotomic harmonic polylogarithms.

Comments: 19 pages LATEX, 3 Figures, ancillary data