In this paper we explore aspects of computer arithmetic from the viewpoint of dynamical systems. We demonstrate the effects of finite precision arithmetic in three uniformly hyperbolic chaotic dynamical systems: Bernoulli shifts, cat maps, and pseudorandom number generators. We show that elementary floating-point operations in binary computer arithmetic possess an inherently fractal structure. Each of these dynamical systems allows us to compare the exact results in integer arithmetic with those obtained by using floating-point arithmetic.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Condensed Matter Physics
- Applied Mathematics