Representations of Elementary Functions Using Binary Moment Diagrams

This paper considers representations for elementary functions such as polynomial, trigonometric, logarithmic, square root, and reciprocal functions. These real valued functions are converted into integer functions by using fixed-point representation, and they are represented by using binary moment diagrams (BMDs). Elementary functions are represented compactly by applying the arithmetic transform to the functions. For polynomial functions, upper bounds on the numbers of nodes in BMDs and multiterminal binary decision diagrams (MTBDDs) are derived. These results show that for polynomial functions, BMDs require fewer nodes than MTBDDs. Experimental result for 16-bit precision sin(x) function shows that the BMD requires only 20% of the nodes for the MTBDD.