A fast floating-point square-rooting routine for the 8080/8085 microprocessors

Square-root is a function for which numerous numerical methods have been developed. In most math packages for microprocessors, simple iterative methods have been used, as no special demands for speed — nor even for accuracy in some cases are expected: e.g. in [ l ] and [2] the execution time of square-rooting is approx. 2-5 times longer than that of multiplication, and in [3] a quintuple error limit compared with other operations is accepted. Some floating-point packages do not support this function at all leaving its evaluation to user defined programs (e.g. W). In the floating-point subroutine package for the Intel 8080/8085 microprocessors [6] developed in the Institute of Information Theory and Automation in Prague, the speed of operation has been strongly emphasized; and as a fiequent use in software for self-tuning controllers with square-root filters has been expected, there was a special demand for a fast square-rooting subroutine with the same accuracy ( + 1 LSB) as with all the other operations. It took a considerable effort to match this condition, and every promising method of accelerating the calculation was tested — even empirical or intuitive; special testing programs were developed for this purpose, checking the real deviation of the square-root returned by the subroutine under test for all the 32 k significantly different input values and printing those values yielding results with an error exceeding a preset limit of 0-5, 0-75 or 1 LSB only.