Analysis of the Basic Implementation Aspects of Hardware-Accelerated Density Functional Theory Calculations

Abstract

This paper presents a Field Programmable Gate Array (FPGA) implementation of a calculation module for exponential part of Gaussian Type Orbital (GTO). The module is composed of several specially crafted floating-point modules which are fully pipelined and optimized for high performance. The hardware implementation revealed significant speed-up for the finite sum of the exponential products calculation ranging from 2.5x to 20x in comparison to a general-purpose Central Processing Unit (CPU) version. Calculating values of GTOs is one of computationally critical parts of the Kohn-Sham algorithm. The approach proposed in the paper aims to increase the performance of a part of the quantum chemistry computational system by employing FPGA-based accelerator. Several issues are addressed, such as identification of code fragments which benefit most from hardware acceleration, porting a part of the Kohn-Sham algorithm to FPGA, data precision adjustment and data transfer overhead. The authors' intention was also to make hardware implementation of calculating the orbital function universal and easily attachable to different quantum-chemistry software packages.