SYSTEMS AND METHODS FOR COMPUTING MATHEMATICAL FUNCTIONS

摘要

Mathematical functions are computed in a single pipeline performing a polynomial approximation (e.g. a quadratic approximation, or the like) using data tables for RCP, SQRT, EXP or LOG using a single pipeline according and opcodes. SIN and COS are also computed using the pipeline according to the approximation ((−1)̂IntX)*Sin(π*Min(FracX, 1.0−FracX)/Min(FracX, 1.0−FracX). A pipeline portion approximates Sin(π*FracX) using tables and interpolation and a subsequent stage multiplies this approximation by FracX. For input arguments of x close 1.0. LOG 2(x−1)/(x−1) is computed using a first pipeline portion using tables and interpolation and subsequently multiplied by (x−1). A DIV operation may also be performed with input arguments scaled up to avoid underflow as needed. Inverse trigonometric functions may be calculated using a pre-processing stage and post processing stage in order to obtain multiple inverse trigonometric functions from a single pipeline.

主权项

1. An apparatus for computing mathematical functions, the apparatus comprising:
a pre-processing hardware stage circuit configured to take as inputs an opcode and one or more input arguments and produce one or more output arguments according to the one or more input arguments and opcode; an inverse function hardware stage configured to calculate a value G(Z), where Z is one of the output arguments where the opcode corresponds to an inverse function other than A cos and one of the one or more input arguments when the opcode corresponds to A cos, and G(Z)=A cos(Z)/Sqrt(1−Z*Z); and a post-processing hardware stage configured to process G(Z) and at least one of the one or more input arguments and the one or more output arguments according to the opcode to obtain a final result.