A Study of the Floating-Point Tuning Behaviour on the N-body Problem
This work addresses precision optimization for numerical computations in domains like mathematical libraries and IoT, but it is incremental as it applies an existing methodology to a specific problem.
The authors tackled the problem of optimizing floating-point precision in the N-body problem using a tool called POP, which reduces precision tuning to an Integer Linear Problem (ILP) and achieves efficient mixed-precision tuning for a five-body gravitational simulation.
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.