Application of continued fractions for fast evaluation of certain functions on a digital computer

Abstract

The purpose of this paper is to develop a method for evaluation of certain elementary functions on a digital computer by the use of continued fractions. The time required for this evaluation is drastically reduced by using “short” operations like shift and add, instead of multiplications. Consistency is the most important factor that allows the expansion of a function into a continued fraction. Several cases are discussed and in particular the solution of the quadratic equation is discussed in more detail to demonstrate the convergence of the method.