PLAUs: Posit Logarithmic Approximate Units to Implement Low-Cost Operations with Real Numbers

The posit numeric format is getting more and more attention in recent years. Its tapered precision makes it especially suitable in many applications including machine learning computation. However, due to its dynamic component bit-width, the cost of implementing posit arithmetic in hardware is more expensive than its floating-point counterpart. To solve this cost problem, in this paper, approximate logarithmic designs for posit multiplication, division, and square root are proposed. It is found that approximate logarithmic units are more suitable for applications that tolerate large errors, such as machine learning algorithms, but require less power consumption.