A development of an accelerator board dedicated for multi-precision arithmetic operations and its application to Feynman loop integrals II

TL;DR

This paper presents a specialized FPGA-based accelerator system designed for multi-precision arithmetic to efficiently evaluate complex multi-loop Feynman integrals, demonstrating promising numerical results.

Contribution

It introduces a novel FPGA accelerator with dedicated logic for high-precision arithmetic tailored for multi-loop Feynman diagram computations.

Findings

Successful implementation of multi-precision arithmetic on FPGA

Effective evaluation of higher-loop Feynman diagrams

Enhanced computational speed for complex integrals

Abstract

Evaluation of a wide variety of Feynman diagrams with multi-loop integrals and physical parameters and its comparison with high energy experiments are expected to investigate new physics beyond the Standard Model. We have been developing a direct computation method of multi-loop integrals of Feynman diagrams. One of features of our method is that we adopt the double exponential rule for numerical integrations which enables us to evaluate loop integrals with boundary singularities. Another feature is that in order to accelerate the numerical integrations with multi-precision calculations, we develop an accelerator system with Field Programmable Gate Array boards on which processing elements with dedicated logic for quadruple/hexuple/octuple precision arithmetic operations are implemented. In addition, we also develop a programming interface designed for easy use of the system. The development is continued for practical use of the system. We present the current development of our system, and the numerical results of higher-loop diagrams performed using our system.