用于行星系统的极快辛积分器：x86 汇编中的 WHFast512
A Very Fast Symplectic Integrator for Planetary Systems: WHFast512 in x86 Assembly
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中文总结 AI 辅助
本文通过 x86 汇编重写 WHFast512 积分器，实现太阳系 5 Gyr 模拟仅需 9 小时，速度提升 8 倍以上，精度提高五个数量级，并支持抛射与碰撞检测。
中文摘要 AI 辅助
行星系统的长期积分被用于多种天体物理应用，例如确定系统的稳定性。在本文中，我们描述了 WHFast512 积分器在速度和精度上的显著改进。通过用 x86 汇编完全重写 WHFast512，我们获得了对 CPU 指令的细粒度控制，并能将整个模拟状态保存在 CPU 寄存器中，仅在需要输出时才写入内存。我们还减少了代码中的分支数量，通过收敛检查提高了开普勒求解器的速度和精度，将哈密顿量分裂切换为雅可比坐标，实现了辛校正器，并增加了对抛射和碰撞检测的支持。作为基准，我们运行了包含所有八颗行星和广义相对论修正的太阳系模拟，时长 5 Gyr。通过我们的改进，我们可以在 9 小时内积分该系统，比标准版 WHFast 快 8 倍以上。这使得 WHFast512 成为此类模拟中迄今为止最快的 N 体积分器。我们进行了大量测试以验证积分器的精度，特别关注消除任何长期偏差，并表明对于典型设置，其精度现在比早期版本的 WHFast512 提高了五个数量级。新的 WHFast512 积分器可在 REBOUND 积分器包中免费获取。
英文摘要
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.
发表机构
- University of Toronto（多伦多大学）
- University of Toronto at Scarborough（多伦多大学士嘉堡校区）
机构由 AI 辅助整理，请以论文原文为准。
