A Very Fast Symplectic Integrator for Planetary Systems: WHFast512 in x86 Assembly

Long-term integrations of planetary systems are used in a variety of astrophysical applications, for example to determine a system's stability. In this paper, we describe significant speed and accuracy improvements to the WHFast512 integrator. By completely rewriting WHFast512 in x86 assembly, we gain fine-grained control over CPU instructions and are able to keep the entire simulation state in CPU registers, only writing to memory when an output is required. We also reduce the number of branches in the code, improve the Kepler solver's speed and accuracy with a convergence check, switch the Hamiltonian splitting to Jacobi coordinates, implement symplectic correctors, and add support for ejection and collision detection. As a benchmark we run simulations of the Solar System with all eight planets and general relativistic corrections for 5 Gyr. With our improvements, we can integrate this system in 9 hours, more than 8x faster than the standard version of WHFast. This makes WHFast512 by far the fastest N-body integrator for this kind of simulation. We run extensive tests to verify the integrator's accuracy, with a particular focus on removing any long-term bias, and show that the accuracy is now five orders of magnitude better for typical setups compared to the earlier version of WHFast512. The new WHFast512 integrator is freely available in the REBOUND integrator package.