1. Introduction. Methods are developed for computing e x, tanh x, and, as a consequence of the former, sinh x and cosh x using continued fractions. These methods possess three characteristics highly desirable in programming: they are simple; they converge rapidly over wide ranges of x; and they generate almost no round off error. Consequently, it is possible to evaluate these functions using continued fractions in much less time than is required to evaluate their power series truncated to yield comparable accuracy, and, in so doing, to materially reduce generated errors. 2. Some properties of continued tractions. Consider the continued