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Representations of elementary functions using edgevalued MDDs
 37th International Symposium on MultipleValued Logic
"... This paper proposes a method to represent elementary functions such as trigonometric, logarithmic, square root, and reciprocal functions using edgevalued multivalued decision diagrams (EVMDDs). We introduce a new class of integer functions, Mpmonotone increasing functions, and derive an upper bou ..."
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This paper proposes a method to represent elementary functions such as trigonometric, logarithmic, square root, and reciprocal functions using edgevalued multivalued decision diagrams (EVMDDs). We introduce a new class of integer functions, Mpmonotone increasing functions, and derive an upper bound on the number of nodes in an edgevalued binary decision diagram (EVBDD) for the Mpmonotone increasing function. The upper bound shows that EVBDDs represent Mpmonotone increasing functions more compactly than other decision diagrams when p is small. Experimental results using 16bit precision elementary functions show that: 1) standard elementary functions can be converted into Mpmonotone 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. 1.
Remarks on Applications of Arithmetic Expressions for Efficient Implementation of Elementary Functions
, 2007
"... Abstract: It has been recently shown in [1], 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 ..."
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Abstract: It has been recently shown in [1], 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 nonzero 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 [1] is combined with Fixedpolarity Arithmetic expressions (FPRAs). In addition, besides complexity measures used in [1], we also compared the number of bits and 1bits 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 [1]. Experimental results confirm that exploiting of FPARs may provide for considerable reduction in terms of the complexity measures considered.
Representations of TwoVariable Elementary Functions Using EVMDDs and Their Applications to Function Generators
"... This paper proposes a method to represent twovariable elementary functions using edgevalued multivalued decision diagrams (EVMDDs), and presents a design method and an architecture for function generators using EVMDDs. To show the compactness of EVMDDs, this paper introduces a new class of inte ..."
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This paper proposes a method to represent twovariable elementary functions using edgevalued multivalued decision diagrams (EVMDDs), and presents a design method and an architecture for function generators using EVMDDs. To show the compactness of EVMDDs, this paper introduces a new class of integervalued functions, lrestricted Mpmonotone increasing functions, and derives an upper bound on the number of nodes in an edgevalued binary decision diagram (EVBDD) for the lrestricted Mpmonotone increasing function. EVBDDs represent lrestricted Mpmonotone increasing functions more compactly than MTBDDs and BMDs when p is small. Experimental results show that all the twovariable elementary functions considered in this paper can be converted into lrestricted Mpmonotone increasing functions with p 1 or p 3, and can be compactly represented by EVBDDs. Since EVMDDs have shorter paths and smaller memory size than EVBDDs, EVMDDs can produce fast and compact elementary function generators. 1.