Truncated Logarithmic Approximation

Abstract

The speed and levels of integration of modern devices have risen to the point that arithmetic can be performed very fast and with high precision. Precise arithmetic comes at a hidden cost-by computing results past the precision they require, systems inefficiently utilize their resources. Numerous designs over the past fifty years have demonstrated scalable efficiency by utilizing approximate logarithms. Many such designs are based off of a linear approximation algorithm developed by Mitchell. This paper evaluates a truncated form of binary logarithm as a replacement for Mitchell's algorithm. The truncated approximate logarithm simultaneously improves the efficiency and precision of Mitchell's approximation while remaining simple to implement.