Optimizing FDTD Memory Bandwidth by Using Block Float-Point Arithmetic

Stefan Pijetlovic,Milos Subotic,Nebojsa Pjevalica

doi:10.5755/j01.eie.24.4.21475

Abstract

Finite-difference time-domain is a numerical method used for modelling of computational electrodynamics. The method is resource intensive, especially regarding memory usage. Multiple memory accesses are required per single computation so memory bandwidth acts as a bottleneck limiting the overall performance. Existing solutions use either fixed-point or floating-point arithmetic, depending on the complexity of the target platform, to model the data. Floating-point requires less memory access but the computation is more intensive due to the normalisation. Fixed-point is the opposite – simple computation but with more memory access for the same precision. The novelty of this paper is in the block floating-point realization which is the middle ground between the two. The approach is less compute intensive than the floating-point solutions while using less memory than the fixed-point realization. This makes the solution an alternative for bit-exact platforms, such as field-programmable gate arrays. The results are compared to both floating-point and fixed-point implementations and the memory bandwidth and other resources needed for targeted platform are calculated. DOI: http://dx.doi.org/10.5755/j01.eie.24.4.21475

Highlights

Finite-difference time-domain (FDTD) is a powerful algorithm for the modelling of the electromagnetic field
This is almost the same result as when using 16 bit fixed-point solution but with an error 2-6 times smaller, depending on the size of the tile. This shows that the Block-floating point (BFP) can be used in situations where memory usage needs to be as small as possible but without sacrificing the precision too much
The novelty presented in this paper is using the block floating-point arithmetic in an area where it is not usually applied

Summary

INTRODUCTION

Finite-difference time-domain (FDTD) is a powerful algorithm for the modelling of the electromagnetic field. BFP provides a good trade off between complexity and dynamic range, making it an efficient number representation format in some cases [21] It is most commonly used in algorithms which are suited for fixed-point processors such as DSPs but require or benefit from additional dynamic range in certain areas. Afterwards scaling factors have been introduced so that all the values would fit into the range [-1, 1] This was required in order to avoid any overflows when switching from single precision 32bit floating-point to fixed-point. This made it possible to determine the mutual exponent for the tile which allowed a more aggressive scaling. Temporal locality condition is not achieved because the data will not be reused in a time frame short enough so the applicability of caching is very limited and was discarded

RESULTS

Number of tiles

CONCLUSIONS