method and apparatus for generating trigonometric functions and other functions

摘要

A method of solving a function for values of a variable when values of an independent variable are given, the method being especially valuable for use in or with a computer, an advantage being minimization of storage requirements. The method is an extension of the branch of mathematics known as numerical analysis, and specifically of the division of that branch known as approximation. An expression is developed for a locus of points which approach points on the given function, i.e., a polynomial expression having a high degree of convergence. The method includes finding solutions to the terms of the polynomial expression by reiterated interpolation. Only a relatively small number of factors need be stored. The method can be employed to calculate values to predetermined accuracy, and is suitable for many functions although it is especially well suited for many transcendental functions. Embodiments of apparatus suitable for performing the method are also disclosed. The apparatus includes elements of electronic data processing such as shift registers, adders, and the like to perform the interpolation involving addition, subtraction and division by 2. The algorithm developed as a manifestation of this method is describable as an add-shift algorithm.