  Electron-ion Bremsstrahlung (free-free) emission and absorption occur in many
astrophysical plasmas for a wide range of physical conditions. This classical
problem has been studied multiple times, and many analytical and numerical
approximations exist. However, accurate calculations of the transition from the
non-relativistic to the relativistic regime remain sparse. Here we provide a
comprehensive study of the free-free Gaunt factors for ions with low charge
(Z<=10). We compute the Gaunt factor using the expressions for the differential
cross section given by Elwert & Haug (EH) and compare to various limiting
cases. We develop a new software package, BRpack, for direct numerical
applications. This package uses a combination of pre-computed tables and
analytical approximations to efficiently cover a wide range of electron and
photon energies, providing a representation of the EH Gaunt factor to better
than 0.03% precision for Z<=2. Our results are compared to those of previous
studies highlighting the improvements achieved here. BRpack should be useful in
computations of spectral distortions of the cosmic microwave background,
radiative transfer problems during reionization or inside galaxy clusters, and
the modeling of galactic free-free foregrounds. The developed computational
methods can furthermore be extended to higher energies and ion charge.
