In this article, we apply a new methodology for precision tuning to the N-body problem. Our technique, implemented in a tool named POP, makes it possible to optimize the numerical data types of a program performing floating-point computations by taking into account the requested accuracy on the results. POP reduces the problem of finding the minimal number of bits needed for each variable of the program to an Integer Linear Problem (ILP) which can be optimally solved in one shot by a classical linear programming solver. The POP tool has been successfully tested on programs implementing several numerical algorithms coming from mathematical libraries and other applicative domains such as IoT. In this work, we demonstrate the efficiency of POP to tune the classical gravitational N-body problem by considering five bodies that interact under gravitational force from one another, subject to Newton's laws of motion. Results on the effect of POP in term of mixed-precision tuning of the N-body example are discussed.

翻译：在本篇文章中,我们应用了一种新的方法来精确调整N-body问题。我们用一个名为POP的工具应用了我们的技术,通过考虑对结果要求的准确性,优化了一个进行浮动点计算的程序的数字数据类型。POP减少了找到程序每个变量所需的最小比特数的问题,以找到一个整数线性问题(ILP),这种比特数可以通过经典线性编程解答器的一个镜头来最佳地解决。POP工具已经成功地测试了实施数种数字算法的方案,这些算法来自数学图书馆和其他辅助领域,如IoT。在这项工作中,我们通过考虑五个在引力下相互作用的机构,在牛顿运动法下相互作用,展示了POP在混精调N-body实例方面的效果。会上讨论了关于POP效果的结果。