Real computation: from computability via efficiency to practice

Abstract

We address three subjects regarding real computation. Firstly, we introduce an abstract data type (ADT) for representing compact subsets in Euclidean space in Exact Real Computation. Given a point, it provides membership check up to the desired precision. Furthermore, the visualization is supported for 2D compact subsets. Secondly, we explain a method to accelerate multiplication of 100-bit precision floating-points via Floating-Point Unit (FPU). The experiment shows that it is at least 2-4 times faster than MPFR to multiply matrices and polynomials, respectively. Lastly, we run a simulation to design an outlet shape and installation height for an air purifier so that the clean air flows to the average human effectively. Our simulation has improved the efficiency of the original prototype so that it successfully forms an area of PM2.5 density less than 50μg/m³ around itself.