Ternary arithmetic polynomial expansions based on new transforms
نویسندگان
چکیده
New classes of Linearly Independent Ternary Arithmetic (LITA) transforms being the bases of ternary arithmetic polynomial expansions are introduced here. Recursive equations defining the LITA transforms and the corresponding butterfly diagrams are shown. Various properties and relations between introduced classes of new transforms are discussed. Computational costs to calculate LITA transforms and applications of corresponding polynomial expansions in logic design are also discussed.
منابع مشابه
Fast Polynomial Transforms Based on Toeplitz and Hankel Matrices
Many standard conversion matrices between coefficients in classical orthogonal polynomial expansions can be decomposed using diagonally-scaled Hadamard products involving Toeplitz and Hankel matrices. This allows us to derive O(N(logN)) algorithms, based on the fast Fourier transform, for converting coefficients of a degree N polynomial in one polynomial basis to coefficients in another. Numeri...
متن کاملHigh-Speed Ternary Half adder based on GNRFET
Superior electronic properties of graphene make it a substitute candidate for beyond-CMOSnanoelectronics in electronic devices such as the field-effect transistors (FETs), tunnel barriers, andquantum dots. The armchair-edge graphene nanoribbons (AGNRs), which have semiconductor behavior,are used to design the digital circuits. This paper presents a new design of ternary half a...
متن کاملArithmetic of Supersingular Koblitz Curves in Characteristic Three
We consider digital expansions of scalars for supersingular Koblitz curves in characteristic three. These are positional representations of integers to the base of τ , where τ is a zero of the characteristic polynomial T 2 ± 3T + 3 of a Frobenius endomorphism. They are then applied to the improvement of scalar multiplication on the Koblitz curves. A simple connection between τ -adic expansions ...
متن کاملBounding Quantification in Parametric Expansions of Presburger Arithmetic
Generalizing Cooper’s method of quantifier elimination for Presburger arithmetic, we give a new proof that all parametric Presburger families {St : t ∈ N} (as defined by Woods in [8]) are definable by formulas with polynomially bounded quantifiers in an expanded language with predicates for divisibility by f(t) for every polynomial f ∈ Z[t]. In fact, this quantifier bounding method works more g...
متن کاملOn the Efficient Parallel Computation of Legendre Transforms
In this article, we discuss a parallel implementation of efficient algorithms for computation of Legendre polynomial transforms and other orthogonal polynomial transforms. We develop an approach to the Driscoll–Healy algorithm using polynomial arithmetic and present experimental results on the accuracy, efficiency, and scalability of our implementation. The algorithms were implemented in ANSI C...
متن کامل