Comparing floating-point and logarithmic number representations for reconfigurable acceleration

Abstract

The paper investigates floating-point and logarithmic number representations for computing with FPGAs. The key issue is to select the best number format for an application to improve performance and accuracy. Using A Stream Compiler, ASC as the hardware design and compilation tool, a convenient scheme to compare the designs of both floating-point and logarithmic numbers and select the solution with the best performance and accuracy, was developed. Its contributions are: (1) optimized function evaluations for conversions between logarithmic and floating-point numbers; (2) design and implementation of logarithmic arithmetic, with optimized segmentation and polynomial degree; (3) a practical comparison case study of Monte Carlo radiative heat transfer simulation. Compared to prior work, our design supports two to six times more LNS conversion and LNS arithmetic units on one FPGA. For Monte Carlo simulation, our designs of both number systems produce 39-80% higher throughput with either a smaller area or a higher accuracy