Abstract
In this paper we describe a single-node, double precision Field Programmable Gate Array (FPGA) implementation of the Conjugate Gradient algorithm in the context of Lattice Quantum Chromodynamics. As a benchmark of our proposal we invert numerically the Dirac–Wilson operator on a 4-dimensional grid on three Xilinx hardware solutions: Zynq Ultrascale+ evaluation board, the Alveo U250 accelerator and the largest device available on the market, the VU13P device. In our implementation we separate software/hardware parts in such a way that the entire multiplication by the Dirac operator is performed in hardware, and the rest of the algorithm runs on the host. We find out that the FPGA implementation can offer a performance comparable with that obtained using current CPU or Intel’s many core Xeon Phi accelerators. A possible multiple node FPGA-based system is discussed and we argue that power-efficient High Performance Computing (HPC) systems can be implemented using FPGA devices only.
Highlights
In the last years Field Programmable Gate Array (FPGA) devices started to pave their way into the realm of High Performance Computing (HPC), for examples see [1, 2, 3]
In order to answer that question we investigate the performance achieved on a FPGA device by the naive solver, the Conjugate Gradient algorithm
We report on the obtained performances in GFLOPs
Summary
In the last years Field Programmable Gate Array (FPGA) devices started to pave their way into the realm of High Performance Computing (HPC), for examples see [1, 2, 3]. A well-known scientific application in this domain are Monte Carlo simulations of Quantum Chromodynamics (QCD), which are performed in the context of theoretical elementary particles physics. In this work we describe our attempt to port the Conjugate Gradient algorithm [4] which is an example of the most naive of such iterative solvers to a single FPGA device and demonstrate that FPGA devices can compete with modern HPC solutions as far as such academic applications are concerned. From an algorithmic point of view Monte Carlo simulations of Quantum Chromodynamics boil down to a numerical estimation of highly dimensional integrals. A set of complex numbers representing the values of basic degrees of freedom: gluon and quark fields, is associated respectively to each edge and point of the space-time lattice. The larger is the set of available configurations the smaller are the statistical uncertainties and the more precise the final physical result is
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