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This paper presents a method for evaluating functions based on piecewise polynomial approximations (splines) with a hierarchical segmentation scheme targeting hardware implementation. The methodology provides significant reduction in table size compared to traditional uniform segmentation approaches. The use of hierarchies involving uniform splines and splines with size varying by powers of two is particularly well suited for the coverage of nonlinear regions. The segmentation step is automated and supports user-supplied precision requirements and approximation method. Bit-widths of the coefficients and arithmetic operators are optimized to minimize circuit area and enable a guarantee of 1 unit in the last place (ulp) accuracy at the output.
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