GT PequanRSS

Special functions in the Arb library
Intervenant(s) : Fredrik Johansson (équipe LFANT, Inria / IMB, Bordeaux)
We discuss methods used for rigorous evaluation of special functions in Arb, a C library for arbitrary-precision real and complex ball (interval) arithmetic. We have implemented many of the familiar special functions such as erf, gamma, zeta, polylogarithms, generalized exponential integrals, Bessel functions, theta and elliptic functions. In most cases, we support complex values of all inputs as well as computation of power series expansions (high-order derivatives). Our implementations are competitive with existing non-interval high-precision software, and often significantly faster. One highlight is a new algorithm for elementary functions, giving up to an order of magnitude speedup at "medium" precision (approximately 200-2000 bits).
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