Customizing fixed-point and floating-point arithmetic — A case study in K-means clustering

Abstract

This paper presents a comparison between custom fixed-point (FxP) and floating-point (FlP) arithmetic, applied to bidimensional K-means clustering algorithm. After a discussion on the K-means clustering algorithm and arithmetic characteristics, hardware implementations of FxP and FlP arithmetic operators are compared in terms of area, delay and energy, for different bitwidth, using the ApxPerf2.0 framework. Finally, both are compared in the context of K-means clustering. The direct comparison shows the large difference between 8-to-16-bit FxP and FlP operators, FlP adders consuming 5–12 χ more energy than FxP adders, and multipliers 2–10χ more. However, when applied to K-means clustering algorithm, the gap between FxP and FlP tightens. Indeed, the accuracy improvements brought by FlP make the computation more accurate and lead to an accuracy equivalent to FxP with less iterations of the algorithm, proportionally reducing the global energy spent. The 8-bit version of the algorithm becomes more profitable using FlP, which is 80% more accurate with only 1.6 χ more energy. This paper finally discusses the stake of custom FlP for low-energy general-purpose computation, thanks to its ease of use, supported by an energy overhead lower than what could have been expected.