Logarithmic and Exponential Function Evaluation in a Variable Structure Digital Computer

Sequential table look-up algorithms are proposed for the evaluation of ln x and exp x. Tables of pre-computed constants are utilized in transforming the argument into a range where the function may be approximated by a simpler polynomial. In the case of ln x, x is transformed so that it falls into a close neighborhood of 1; in the case of exp x, x is transformed to a close neighborhood of 0. These algorithms are particularly effective when mechanized so as to carry out the predetermined sequence of operations without waste manipulation. Such special purpose organization is reasonable within the variable structure part of UCLA's proposed Fixed-Plus-Variable structure computer, as the same equipment may be reorganized for use in other special purpose configurations at other times. In this paper the sequential table look-up algorithms and their speed advantages over existing subroutine approximation procedures are described. The design of special purpose configurations which leads to another factor of speed increase as compared to a stored program implementation of the algorithms is presented. The properties of the supervisory control which integrate the operation of the ``fixed structure'' general purpose computer and the ``variable structure'' special purpose configurations are specified and the over-all computational gains evaluated. An order-of-magnitude increase in speed compared to existing subroutines is predicted in both cases.