Abstract: It has been recently shown in [SasaoNagyama2006], that elementary mathematical functions (as trigonometric, logarithmic, square root, gaussian, sigmoid, etc.) are compactly represented by the Arithmetic transform expressions and related Binary Moment Diagrams (BMDs). The complexity of the representations is estimated through the number of non-zero coefficients in arithmetic expressions and the number of nodes in BMDs.
In this paper, we show that further optimization can be achieved when the method in [SasaoNagyama2006] is combined with Fixed-polarity Arithmetic expressions (FPRAs). In addition, besides complexity measures used in [SasaoNagyama2006], we also compared the number of bits and 1-bits required to represent arithmetic transform coefficients in zero polarity and optimal polarity arithmetic expressions. This is a complexity measure relevant for the alternative implementations of elementary functions suggested in [SasaoNagyama2006]. Experimental results confirm that exploiting of FPARs may provide for considerable reduction in terms of the complexity measures considered.
Keywords: Elementary functions, Arithmetic expressions, Fixed-polarity Arithmetic expressions, decision diagrams,