引力透镜建模的高性能计算：GPU和CPU上的单精度与双精度
High Performance Computing for gravitational lens modeling: single vs double precision on GPUs and CPUs
摘要：
强引力透镜是研究宇宙学和暗物质分布的有力工具。高效的透镜软件已经成为充分发挥其潜力的必要条件，并且性能需求只会随着下一代望远镜的出现而增加。在本文中，我们研究了高性能计算技术对广泛使用的镜头建模软件LENSTOOL的性能关键部分的可能影响。我们实现的算法一次作为一个高度优化的CPU版本，一次与图形卡加速一个简单的参数化镜头模型。此外，我们研究了有限的机器精度对透镜算法的影响。虽然双精度是科学应用的默认选择，但我们发现单精度对于我们的目的来说足够准确，并导致很大的加速。因此，我们开发和提出了一种混合精度算法，只使用双精度时，必要的。我们测量了不同实现的性能，发现使用高性能计算技术大大提高了CPU和GPU上的代码性能。与目前在12个CPU内核上实现的LENSTOOL相比，我们获得了高达170的加速因子。我们通过在现代超级计算机中常见的高端GPU上使用我们的混合精度算法来实现这种最佳性能。我们还表明，这些技术降低了高达98%的能源消耗。此外，我们证明了一个极具竞争力的加速可以达到与消费者GPU。虽然它们比高端显卡便宜一个数量级，但由于其低双精度性能，它们很少用于科学计算。我们的混合精度算法释放了它们的全部潜力。消费级GPU提供的加速比仅比高端GPU实现的最佳加速比低四倍。
英文摘要：
Strong gravitational lensing is a powerful probe of cosmology and the dark matter distribution. Efficient lensing software is already a necessity to fully use its potential and the performance demands will only increase with the upcoming generation of telescopes. In this paper, we study the possible impact of High Performance Computing techniques on a performance-critical part of the widely used lens modeling software LENSTOOL. We implement the algorithm once as a highly optimized CPU version and once with graphics card acceleration for a simple parametric lens model. In addition, we study the impact of finite machine precision on the lensing algorithm. While double precision is the default choice for scientific applications, we find that single precision can be sufficiently accurate for our purposes and lead to a big speedup. Therefore we develop and present a mixed precision algorithm which only uses double precision when necessary. We measure the performance of the different implementations and find that the use of High Performance Computing Techniques dramatically improves the code performance both on CPUs and GPUs. Compared to the current LENSTOOL implementation on 12 CPU cores, we obtain speedup factors of up to 170. We achieve this optimal performance by using our mixed precision algorithm on a high-end GPU which is common in modern supercomputers. We also show that these techniques reduce the energy consumption by up to 98%. Furthermore, we demonstrate that a highly competitive speedup can be reached with consumer GPUs. While they are an order of magnitude cheaper than the high-end graphics cards, they are rarely used for scientific computations due to their low double precision performance. Our mixed precision algorithm unlocks their full potential. The consumer GPU delivers a speedup which is only a factor of four lower than the best speedup achieved by a high-end GPU.
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