Abstract
This chapter presents the effects of polynomial degrees on the hierarchical segmentation method (HSM) for approximating functions. HSM uses a novel hierarchy of uniform segments and segments with size varying by powers of two. This scheme enables us to approximate non-linear regions of a function particularly well. The degrees of the polynomials play an important role when approximating functions with HSM: the higher the degree, the fewer segments are needed to meet the same error requirement. However, higher degree polynomials require more multipliers and adders, leading to higher circuit complexity and more delay. Hence, there is a tradeoff between table size, circuit complexity and delay. We explore these tradeoffs with four functions: \(\sqrt { - \log (x)} \), x log(x), a high order rational function and cos(πx/2). We present results for polynomials up to the fifth order for various operand sizes between 8 and 24 bits.
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Lee, DU., Luk, W., Villasenor, J.D., Cheung, P.Y. (2005). The Effects of Polynomial Degrees. In: Lysaght, P., Rosenstiel, W. (eds) New Algorithms, Architectures and Applications for Reconfigurable Computing. Springer, Boston, MA. https://doi.org/10.1007/1-4020-3128-9_24
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DOI: https://doi.org/10.1007/1-4020-3128-9_24
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