We present an r-th root extraction algorithm over a finite field Fq. Our algorithm precomputes a primitive r-th root of unity ξ where s is the largest positive integer satisfying r|q − 1, and is applicable for the cases when s is small. The proposed algorithm requires one exponentiation for the r-th root computation and is favorably compared to the existing algorithms.

In this study, qualitative land suitability evaluation was made for research station of East Azarbaijan, for tomato, potato, onion and bean. The study was done using Simple Limitation Method (SLM), Limitation Method regarding Number and Intensity (LMNI) and Parametric Methods (PM) such as the square root and the Storie methods. The results from different methods indicated that the most importan...

The construction of new explicit Runge–Kutta methods taking into account, not only their accuracy, but also the preservation of Quadratic Invariants (QIs) is studied. An expression of the error of conservation of a QI by a Runge–Kutta method is given, and a new six–stage formula with classical order four and seventh order of QI–conservation is obtained by choosing their coefficients so that the...

ÐThe aim of this paper is to accelerate division, square root, and square root reciprocal computations when the Goldschmidt method is used on a pipelined multiplier. This is done by replacing the last iteration by the addition of a correcting term that can be looked up during the early iterations. We describe several variants of the Goldschmidt algorithm, assuming 4-cycle pipelined multiplier, ...

We present a square root algorithm in Fq which generalizes Atkins’s square root algorithm [6] for q ≡ 5 (mod 8) and Kong et al.’s algorithm [8] for q ≡ 9 (mod 16). Our algorithm precomputes a primitive 2-th root of unity ξ where s is the largest positive integer satisfying 2|q − 1, and is applicable for the cases when s is small. The proposed algorithm requires one exponentiation for square roo...

A new method for the high-speed computation of double-precision floating-point reciprocal, division, square root, and inverse square root operations is presented in this paper. This method employs a second-degree minimax polynomial approximation to obtain an accurate initial estimate of the reciprocal and the inverse square root values, and then performs a modified Goldschmidt iteration. The hi...