Representations of Elementary Functions Using Edge-Valued MDDs

This paper proposes a method to represent elementary functions such as trigonometric, logarithmic, square root, and reciprocal functions using edge-valued multi-valued decision diagrams (EVMDDs). We introduce a new class of integer functions, Mp-monotone increasing functions, and derive an upper bound on the number of nodes in an edge-valued binary decision diagram (EVBDD) for the Mp-monotone increasing function. The upper bound shows that EVBDDs represent Mp-monotone increasing functions more compactly than other decision diagrams when p is small. Experimental results using 16-bit precision elementary functions show that: 1) standard elementary functions can be converted into Mp-monotone increasing functions with p = 1 or p = 2, or their linear transformations. And, they can be compactly represented by EVBDDs. 2) EVMDDs represent elementary functions with, on average, only 11% of the memory size needed for binary moment diagrams (BMDs), and only 69% of the memory size needed for EVBDDs.