Root squaring using level-index arithmetic (Q1263936)

The symmetric level-index (SLI) system is a system for representing numbers, which eases the monitoring of precision while avoiding the problem associated with overflow and underflow. In SLI system any real number X is represented by its mapping in computer x, a sign s(X) and a reciprocation indicator r(X), so that we have \(X=s(X)\phi (x)^{r(X)},\) where the generalized exponential function \(\phi\) is defined by \(\phi (x)=x,\quad x\in [0,1),\) and \(\phi (x)=e^{\phi (x-1)},\quad x\geq 1.\) The authors discuss the essentials of SLI and apply it to Graeffe's root squaring method for finding zeros of polynomials. Numerical results from test examples are given.