A Study of the Floating-Point Tuning Behaviour on the N-body Problem

TL;DR

This paper introduces POP, a novel tool that optimizes floating-point precision in N-body simulations by formulating the problem as an ILP, leading to efficient and accurate numerical computations.

Contribution

The paper presents a new ILP-based methodology and tool, POP, for precision tuning of floating-point computations, demonstrated on the N-body problem.

Findings

POP effectively reduces bit-widths for variables in N-body simulations.

The approach achieves accurate results with reduced precision, improving efficiency.

POP's methodology is applicable to various numerical algorithms.

Abstract

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.