Fixed-Posit: A Floating-Point Representation for Error-Resilient Applications

Abstract:

IEEE-754 floating point is the standard used today to represent real numbers in practically all computer systems. Recently, posit—which offers superior accuracy and a wider dynamic range—was suggested as a substitute for IEEE-754 floating point. Posit may be customized to have a different amount of regime and exponent bits, which has prevented widespread use. We suggest a fixed-posit format to address this flaw and show the construction of a fixed-posit multiplier. In this representation, the number of regime and exponent bits are fixed. Using the AxBench, OpenBLAS, and neural network benchmarks as well as error-tolerant applications, we assess the fixed-posit multiplier. When compared to posit multipliers, the proposed fixed-posit multiplier saves 47%, 38.5%, 22%, and up to 70%, 66%, 26% of the power, area, and latency of the 32-bit IEEE-754 multiplier, respectively. For workloads using OpenBLAS and AxBench, these savings come with a negligible output quality reduction (1.2% average relative error). Additionally, we see a tiny accuracy reduction (0.12%) when using the fixed-posit multiplier for neural networks like ResNet-18 on ImageNet.

Keywords: IEEE-754 floating point, Posit, Multipliers, Intel Pin, Power and Error analysis