The Accuracy and Efficiency of Posit Arithmetic

TL;DR

This paper evaluates the accuracy and efficiency of posit arithmetic compared to IEEE 754 FP32, demonstrating that 16-bit posits can match FP32 accuracy with significant speedups in neural network tasks.

Contribution

The paper introduces POSAR, a flexible posit arithmetic unit, and provides a comprehensive analysis of posit performance across benchmarks and applications.

Findings

16-bit posit matches FP32 accuracy on Cifar-10 CNN with 18% speedup

Posit arithmetic can outperform IEEE 754 FP32 in certain benchmarks

8-bit posits are unsuitable for ML due to low accuracy

Abstract

Motivated by the increasing interest in the posit numeric format, in this paper we evaluate the accuracy and efficiency of posit arithmetic in contrast to the traditional IEEE 754 32-bit floating-point (FP32) arithmetic. We first design and implement a Posit Arithmetic Unit (PAU), called POSAR, with flexible bit-sized arithmetic suitable for applications that can trade accuracy for savings in chip area. Next, we analyze the accuracy and efficiency of POSAR with a series of benchmarks including mathematical computations, ML kernels, NAS Parallel Benchmarks (NPB), and Cifar-10 CNN. This analysis is done on our implementation of POSAR integrated into a RISC-V Rocket Chip core in comparison with the IEEE 754-based Floting Point Unit (FPU) of Rocket Chip. Our analysis shows that POSAR can outperform the FPU, but the results are not spectacular. For NPB, 32-bit posit achieves better accuracy than FP32 and improves the execution by up to 2%. However, POSAR with 32-bit posit needs 30% more FPGA resources compared to the FPU. For classic ML algorithms, we find that 8-bit posits are not suitable to replace FP32 because they exhibit low accuracy leading to wrong results. Instead, 16-bit posit offers the best option in terms of accuracy and efficiency. For example, 16-bit posit achieves the same Top-1 accuracy as FP32 on a Cifar-10 CNN with a speedup of 18%.