Impacts of Range Reduction on Polynomial Approximation Efficiency
The RLibm project provides a collection of elementary functions that return correctly rounded results for all inputs. RLibm accomplishes this goal by generating a polynomial that approximates the correctly rounded results. To boost the efficiency of the polynomial and its generation, RLibm employs range reduction, which transforms all inputs in the original domain to values in a smaller range. Complex range reduction methods that greatly reduce the input range could incur costs in the form of lookup tables. This study examines the impacts of employing simplified range reductions. The range reduction method used in this study for the trigonometric function $sinpi(x)$ significantly reduces the input domain while circumventing the usage of any lookup tables. The resulting polynomial is of a higher degree than the one currently used by RLibm. The observation indicates that strict range reductions may be necessary to achieve efficient polynomial approximations, motivating further investigation into finding the optimal balance between the costs of the two procedures.