Hain and Freire have proposed different floating point square root algorithms that can be efficiently implemented in hardware. The algorithms are compared and evaluated on both performance and precision.

Digital computers are built out of circuits that have definite, discrete states: on or off, zero or one, high voltage or low voltage. Engineers go to great lengths to make sure these circuits never settle into some intermediate condition. Quantum-mechanical systems, as it happens, offer a guarantee of discreteness without any engineering effort at all. When you measure the spin orientation of a...

We prove regularity (i.e., smoothness) of measures on R d satisfying the equation L = 0 where L is an operator of type Lu = tr(Au 00) + B ru. Here A is a Lipschitz continuous, uniformly elliptic matrix-valued map and B is merely-square integrable. We also treat a class of corresponding innnite dimensional cases where IR d is replaced by a locally convex topological vector space X. In this cases...

Consider the problem: given a real number x and an error bound ε, find an interval such that it contains √ x and its width is less than ε. One way to solve the problem is to start with an initial interval and repeatedly to update it by applying an interval refinement map on it until it becomes narrow enough. In this paper, we prove that the well known Secant-Newton map is the optimal among a ce...

We suggest an approach to grid optimization for a second order finite-difference scheme for elliptic equations. A model problem corresponding to the three-point finite-difference semidiscretization of the Laplace equation on a semi-infinite strip is considered. We relate the approximate boundary Neumann-to-Dirichlet map to a rational function and calculate steps of our finite-difference grid us...

soil texture is an important soil physical property that governs most physical, chemical, biological, and hydrological processes in soils. detailed information on soil texture variability is crucial for proper crop and land management and environmental studies. therefore, at present research, 103 soil profiles were dogged and then sampled in order to prepare digital map of soil texture in bijar...

Many low-cost platforms that support floating-point arithmetic, such as microcontrollers and field-programmable gate arrays, do not include fast hardware or software methods for calculating the square root and/or reciprocal root. Typically, functions are implemented using direct lookup tables polynomial approximations, with a subsequent application of Newton–Raphson method. Other, more complex ...