The Ghost in the Model (and Other Effects of Floating Point Arithmetic)

This paper will explore the effects of errors in floating point arithmetic in two published agent-based models: the first a model of land use change (Polhill et al. 2001; Gotts et al. 2003), the second a model of the stock market (LeBaron et al. 1999). The first example demonstrates how branching statements with floating point operands of comparison operators create a high degree of nonlinearity, leading in this case to the creation of 'ghost' agents -- visible to some parts of the program but not to others. A potential solution to this problem is proposed. The second example shows how mathematical descriptions of models in the literature are insufficient to enable exact replication of work since mathematically equivalent implementations in terms of real number arithmetic are not equivalent in terms of floating point arithmetic.