Exact real calculator for everyone

Abstract

Despite its simplicity and versatility, the well-known Floating Point System (FPS) has a serious shortcoming: the finite nature of a computer makes rounding-off inevitable. Because of this, FPS can sometimes lead to serious computational errors, i.e., a small round-off error due to truncation can cause a large deviation in the output in iterations within chaotic systems. This paper bridges the gap between theory and practice of Exact Real Arithmetic (ERA), and reports on the design and implementation of a user-friendly scientific calculator ERCE using HASKELL, capable of ERA. With a functional-programming slant, we use ERCE as a channel for the technology of ERA to reach out to a wider community: even a school student can use it.