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

pp: 106-119

Shinobu Nagayama , Hiroshima City University, Hiroshima

Tsutomu Sasao , Kyushu Institute of Technology, Iizuka

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

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

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

*IEEE Transactions on Computers*, vol.58, no. 1, pp. 106-119, January 2009, doi:10.1109/TC.2008.134REFERENCES