I discuss some recent algorithms implemented on HARP-2 which should also be suitable for HARP-6. The key features of the new Stumpff KS Hermite formulation (Mikkola and Aarseth, 1998) are presented. This two-body regularization method has proved to be efficient and accurate for studying binaries. The presence of many persistent hierarchical systems is of particular concern. A semi-analytical formula for long-term stability (Mardling and Aarseth, 1999) permits the inner binary to be treated in the centre-of-mass approximation, thereby enabling the outer component to be introduced as a temporary KS solution. Higher-order systems are considered in a similar way.
The present scheme for integrating the centre-of-mass motion of perturbed regularized binaries suffers from considerable overheads by sending zero masses of perturbers and c.m. bodies to HARP at each block-step and restoring them to normal values. A new algorithm is outlined which circumvents this problem by a differential correction procedure, where the force on all particles are first calculated on the HARP. The loss of accuracy due to different precision on HARP and the host does not appear to degrade the accuracy since the force errors (of relative size 2x10^{-7}) are uncorrelated. The speed-up is substantial for a distribution of wide primordial binaries but such binaries still place a high requirement on the host which must also integrate the regularized motion.