Efficient Non-sequential Division for FPGAs

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.