Issue No. 01 - January (2009 vol. 58)

ISSN: 0018-9340

pp: 106-119

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TC.2008.134

Tsutomu Sasao , Kyushu Institute of Technology, Iizuka

Shinobu Nagayama , Hiroshima City University, Hiroshima

ABSTRACT

This paper analyzes complexities of decision diagrams for elementary functions such as polynomial, trigonometric, logarithmic, square root, and reciprocal functions. These real functions are converted into integer-valued functions by using fixed-point representation. This paper presents the numbers of nodes in decision diagrams representing the integer-valued functions. First, complexities of decision diagrams for polynomial functions are analyzed, since elementary functions can be approximated by polynomial functions. A theoretical analysis shows that binary moment diagrams (BMDs) have low complexity for polynomial functions. Second, this paper analyzes complexity of edge-valued binary decision diagrams (EVBDDs) for monotone functions, since many common elementary functions are monotone. It introduces a new class of integer functions, Mp-monotone increasing function, and derives an upper bound on the number of nodes in an EVBDD for the Mp-monotone increasing function. A theoretical analysis shows that EVBDDs have low complexity for Mp-monotone increasing functions. This paper also presents the exact number of nodes in the smallest EVBDD for the n-bit multiplier function, and a variable order for the smallest EVBDD.

INDEX TERMS

Decision Diagrams, General, Trees, Elementary function approximation, Representations

CITATION

Tsutomu Sasao, Shinobu Nagayama, "Complexities of Graph-Based Representations for Elementary Functions",

*IEEE Transactions on Computers*, vol. 58, no. , pp. 106-119, January 2009, doi:10.1109/TC.2008.134