Closing the Gap Between Float and Posit Hardware Efficiency

Abstract

The b-posit, or bounded posit, is a variation of the posit format designed for high performance computing (HPC) and AI applications. Unlike traditional floating-point formats (floats), posits use variable-length fields for exponent scaling and significand, providing better efficiency for the same bit width. However, this flexibility introduces high worst-case overhead in decode-encode logic, exceeding the cost of handling subnormals for floats. To address this, the b-posit restricts the regime field to a 6-bit limit, reducing variability in regime and fraction sizes. With an exponent size eS of 5 bits, the dynamic range is $2^{-192}$ to $2^{192}$ (about $10^{-58}$ to $10^{58}$) and the quire size is 800 bits, for any precision $n>12$. This constraint improves numerical properties and simplifies hardware implementation by allowing decode-encode operations with basic multiplexers. Our 32-bit b-posit decoder circuits achieve significant improvements: 79 percent less power consumption, 71 percent smaller area, and 60 percent reduced latency compared to standard posit decoders. The 32-bit b-posit encoder shows 68 percent lower power usage, 46 percent less area, and 44 percent shorter delay. The proposed b-posit hardware exhibits superior scalability with increasing bit widths, outperforming standard posit hardware at higher precisions, with even greater advantages at 64-bit. Notably, the b-posit decode-encode hardware matches or exceeds IEEE compliant 32-bit floating-point performance, offering faster and smaller area implementation, with slight increase in worst-case power due to higher speed. The b-posit hardware design provides the clean mathematical behavior and higher accuracy of posits versus IEEE floats without the power, area, or latency costs observed for the Posit Standard (2022). We believe the b-posit should influence future standard revisions.