Abstract
Arithmetic circuits in general do not exactly match specifications, leading to different implementations within allowed imprecision. Starting from real-valued representation, such as Taylor series, we propose a new technique based on arithmetic transform (AT) to analyze simultaneous selection of multiple word lengths and even the function approximation schemes, and then derive a verification algorithm to check whether an implementation fits the error bound. To find optimized implementations which both satisfy a given error bound and constraints included interface input, delay and area. An optimization algorithm is derived to explore multiple precision parameters and get the optimized implementations by various constraints.
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