Brightening the Optical Flow through Posit Arithmetic

Abstract

As new technologies are invented, their commercial viability needs to be carefully examined along with their technical merits and demerits. The posit TM data format, proposed as a drop-in replacement for IEEE 754 TM float format, is one such invention that requires extensive theoretical and experimental study to identify products that can benefit from the advantages of posits for specific market segments. In this paper, we present an extensive empirical study of posit-based arithmetic vis-à-vis IEEE 754 compliant arithmetic for the optical flow estimation method called Lucas-Kanade (LuKa). First, we use SoftPosit and SoftFloat format emulators to perform an empirical error analysis of the LuKa method. Our study shows that the average error in LuKa with SoftPosit is an order of magnitude lower than LuKa with SoftFloat. We then present the integration of the hardware implementation of a posit adder and multiplier in a RISC-V open-source platform. We make several recommendations, along with the analysis of LuKa in the RISC-V context, for future generation platforms incorporating posit arithmetic units.

An Investigation on Inherent Robustness of Posit Data Representation

“…In general, m-bit posit has a higher dynamic range and better numerical accuracy properties compared to n-bit IEEE 754 compliant number where m = n. It is shown in the literature that for computing systems, n-bit IEEE 754 compliant numbers can be replaced by m-bit posit numbers where m < n since the posit number system exhibits a trade-off between accuracy and dynamic range [4] [5]. These trade-offs allow the selection of the desired posit format that is suitable for computing systems without compromising accuracy and performance [6] [7]. Further details of the number system and the formats are discussed in Section II-A.…”