Method and system for performing pipelined reciprocal and reciprocal square root operations

Abstract

A pipelined circuit configured to generate a Taylor's series approximation at least one function, preferably at least one of the reciprocal and the reciprocal square root, of an input value. The circuit is preloaded with or configured to generate a predetermined set of Taylor's series coefficients for each segment of the input value range. Other aspects of the invention are methods for determining preferred parameters for elements of such a circuit, a circuit designed in accordance with such a method, and a system (e.g., a pipelined graphics processor) for and method of pipelined graphics data processing using any embodiment of the circuit. The preferred parameters are determined by minimizing the circuit's size subject to constraints on input and output value format and output accuracy, assuming a specific function to be approximated and a specific degree for the approximation but allowing variation of parameters such as coefficient width and number of input value range segments.