Efficient Non-sequential Division for FPGAs

TL;DR

This paper introduces an FPGA-specific method for fast, low-complexity division that approximates the reciprocal with high precision in a single clock cycle, suitable for machine learning accelerators.

Contribution

It presents a novel non-sequential division approach for FPGAs using a low complexity reciprocal approximation and correction, enabling high-speed, low-resource division operations.

Findings

Achieves division in one clock cycle with low hardware cost

Provides arbitrarily low approximation errors

Demonstrates superior speed and resource efficiency compared to existing methods

Abstract

The division operation is important for many areas of data processing. Especially considering today's demand for hardware accelerators for machine learning algorithms, there is a high demand for an efficient calculation of the division function, e.g. for averaging operations or the online calculation of activation functions. For such algorithms, which are often iterative in nature, one would like to have a non-sequential way of calculating the division operation. The work presents such an approach especially tailored to FPGAs as processing platforms. It is based on an efficient way of calculating the reciprocal operation, based on a low complexity approximation combined with a correction function. The described approach allows approximating the division operation (with errors that can be made arbitrarily low), within one clock cycle using only low hardware requirements. These hardware requirements are scaleable depending on the desired precision. We show results obtained by synthesis and hardware simulations demonstrating the low complexity and high clock speeds achievable with the described method compared to other methods described in the literature.