Square-related functions such as square, inverse square, square-root and inverse square-root operations are widely used in digital signal processing and digital communication algorithms, and their efficient realizations are commonly required to reduce the hardware complexity. In the implementation point of view, approximate realizations are often desired if they do not degrade performance signi...

For which functions f does A ∈ G ⇒ f(A) ∈ G when G is the matrix automorphism group associated with a bilinear or sesquilinear form? For example, if A is symplectic when is f(A) symplectic? We show that group structure is preserved precisely when f(A) = f(A) for bilinear forms and when f(A) = f(A) for sesquilinear forms. Meromorphic functions that satisfy each of these conditions are characteri...

The square of a graph G, denoted G, is obtained from G by putting an edge between two distinct vertices whenever their distance is two. Then G is called a square root of G. Deciding whether a given graph has a square root is known to be NP-complete, even if the root is required to be a chordal graph or even a split graph. We present a polynomial time algorithm that decides whether a given graph...

Hardware square-root units require large numbers of gates even for iterative implementations. In this paper, we present four low-cost high-performance fullypipelined n-select implementations (nS-Root) based on a non-restoring-remainder square root algorithm. The nSRoot uses a parallel array of carry-save adders (CSAs). For a square root bit calculation, a CSA is used once. This means that the c...

Let G be a countable Abelian group with Zd as a subgroup so that G/Zd is a locally finite group. (An Abelian group is locally finite if every element has finite order.) We can construct a rank one action of G so that the Z-subaction is 2-simple, 2-mixing and only commutes with the other transformations in the action of G. Applications of this construction include a transformation with square ro...

This paper addresses a fast low-power implementation of a shared division and square-root architecture. Two approaches are considered in this paper; these include the SRT (Sweeney, Robertson and Tocher) approach which does not require prescaling and the GST (generalized Svoboda and Tung) approach which requires prescaling of the operands. This paper makes two important contributions. Although S...

Estimating the distribution of impervious surface, a major component of the vegetation–impervious surface–soil (V–I–S) model, is important in monitoring urban areas and understanding human activities. Besides its applications in physical geography, such as run-off models and urban change studies, maps showing impervious surface distribution are essential for estimating socio-economic factors, s...

Given the popularity of decimal arithmetic, hardware implementation of decimal operations has been a hot topic of research in recent decades. Besides the four basic operations, the square root can be implemented as an instruction directly in the hardware, which improves the performance of the decimal floating-point unit in the processors. Hardware implementation of decimal square rooters is usu...