Cascaded implementation of an iterative inverse-square-root algorithm, with overflow lookahead

Abstract

We present an unconventional method of computing the inverse of the square root. It implements the equivalent of two iterations of a well-known multiplicative method to obtain 24-bit mantissa accuracy. We implement each "iteration" as a separate logic module and exploit knowledge about the relative error during computation. To reduce the size of the implementation. We use overflow lookahead logic to facilitate the exponent computations. No division is required in the entire process. Examples and error analysis are given.<>