Spectral Transform Decision Diagrams

Abstract-This paper proposes new architectures for numeric function generators (NFGs) using piecewise arithmetic expressions. The proposed architectures are programmable, and they realize a wide range of numeric functions. To design an NFG for a given function, we partition the domain of the function into uniform segments, and transform a subfunction in each segment into an arithmetic spectrum. From this arithmetic spectrum, we derive an arithmetic expression, and realize the arithmetic expression with hardware. Since the arithmetic spectrum has many zero coefficients and repeated coefficients, by storing only distinct nonzero coefficients in a

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“…This subsection introduces the arithmetic transform, the arithmetic spectrum, and the arithmetic expression [18].…”

Section: B Arithmetic Transformmentioning

confidence: 99%

Numeric Function Generators Using Piecewise Arithmetic Expressions

Nagayama

Sasao

Butler

2011

2011 41st IEEE International Symposium on Multiple-Valued Logic

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“…In this part, we define the Reed-Muller spectrum and the Reed-Muller transformation matrix [21]. For an eigenfunction, the canonical sum-of-products expression and the PPRM are isomorphic, and have the same number of products.…”

Section: Reed-muller Transformationmentioning

confidence: 99%

The Eigenfunction of the Reed-Muller Transformation

Sasao

Bulter²

2007

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“…Polynomial expressions for binary functions and their generalizations to MVB and MV functions are defined in terms of different expansion rules with respect to their variables [28], which can be alternatively interpreted as choosing different sets of basis functions [29]. Within some of these classes of expressions, a further optimization can be performed by using literals of different polarity for variables, which leads to a variety of fixed-and mixed-polarity expressions [6,7,8].…”

Section: Introductionmentioning

confidence: 99%

Optimization of Polynomial Expressions by Using the Extended Dual Polarity

Janković

Stanković

Moraga

2009

IEEE Trans. Comput.

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-A method for optimization of polynomial expressions in terms of fixed polarities for discrete functions is presented. The method is based on the principle of extended dual polarity, which provides a simple way of ordering polarities to obtain an effective way of finding the optimal polarity. The method still implies exhaustive search, but it is an optimized search, which may be expressed in very simple rules. Experimental results illustrate the effectivity of the proposed method.

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Spectral Transform Decision Diagrams

Cited by 54 publications

References 7 publications

Numeric Function Generators Using Piecewise Arithmetic Expressions

Numeric Function Generators Using Piecewise Arithmetic Expressions

The Eigenfunction of the Reed-Muller Transformation

Optimization of Polynomial Expressions by Using the Extended Dual Polarity

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