Floating point arithmetic teaching for computational science

Abstract

Computational science is based upon numerical computing and, consequently, requires excellent knowledge of floating point computer arithmetic. In general, the average computational science student has a relatively limited understanding of the implications of floating point computation. This paper presents an initiative to teach floating point number representation and arithmetic in undergraduate courses in computational science. The approach is based on carefully designed practical exercises which highlight the main properties and computational issues of finite length number representation and arithmetic. In conjunction to the exercises, an auxiliary educational tool constitutes a valuable support for students to learn and understand the concepts involved. Simpler formats are used as an introduction to the IEEE 754 standard, with the aim of presenting the fundamentals of the floating point computation and emphasizing its limitations. This approach could be included in courses related to computer organization, programming, discrete mathematics, numerical methods or scientific computing in computational science curricula.