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We present a symbolic perturbation scheme for arbitrary polynomial geometricpredicates which combines the benefits of Emiris and Canny's simple randomizedlinear perturbation scheme with Yap's multiple infinitesimal scheme for generalpredicates. Like the randomized scheme, our method accepts black box polynomialfunctions as input. For nonmaliciously chosen predicates, our method is as fastas the linear scheme, scaling reasonably with the degree of the polynomial evenfor fully degenerate input. Like Yap's scheme, the computed sign isdeterministic, never requiring an algorithmic restart (assuming a high qualitypseudorandom generator), and works for arbitrary predicates with no knowledgeof their structure. We also apply our technique to exactly or nearly exactlyrounded constructions that work correctly for degenerate input, usingl'Hopital's rule to compute the necessary singular limits. We provide an opensource prototype implementation including example algorithms for Delaunaytriangulation and Boolean operations on polygons and circular arcs in theplane.

A deterministic pseudorandom perturbation scheme for arbitrary polynomial predicates