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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. Functional consistency is the most important factor that aliows the expansion of a function into a continued fraction. Several cases are discussed; in particular the solution of the quadratic equation is discussed in more detail to demonstrate the convergence of the method.