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Analysis of Error in a CML Diffusion Operation

1 Introduction This report supports the paper [Harris, et al. 2002], which describes the implementation of various CML simulations using computer graphics hardware. Because of the limited precision available for fragment computations in graphics hardware, it is important to understand the effect of roundoff error propagation in these computations. Diffusion is an operation that is often used in Coupled Map Lattice (CML) simulations. For this reason, it is useful to study the error in CML simulations by studying diffusion. 2 Fixed Point Error Analysis We will write a fixed-point number x that is the result of an arithmetic operation in a computer as