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); and one or more data tables corresponding to at least one of the RCP, SQRT, EXP or LOG functions operable to be coupled to the single pipeline according to one or more opcodes; wherein the single pipeline is operable for computing at least one of RCP, SQRT, EXP or LOG functions according to the one or more 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 pipline 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. LOG2(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.

主权项

1. An apparatus for computing mathematical functions, the apparatus comprising:
a first hardware pipeline configured to receive an argument x and an opcode and perform a polynomial approximation of second degree or higher, the first hardware pipeline including a plurality of stages; and a plurality of data tables, each associated with at least one of LOG (logarithm), COS (cosine), DIV (division), and SIN (sine) functions and configured to be coupled to the first hardware pipeline according to the at least one opcode, wherein each of the plurality of data tables includes data associated with implementing the associated function, the first hardware pipeline being configured to calculate a value A(x) by performing the polynomial approximation with respect to data from the data tables of the plurality of data tables corresponding to the opcode and x; a second hardware pipeline configured to calculate an adjustment factor B(x) corresponding to the opcode; and wherein the first hardware pipeline further configured to calculate an output value as B(x)*A(x).