Recursive taylor series-based computation of numerical values for mathematical functions
AssigneeTexas Instruments Incorporated
InventorDavid Patrick Magee
Life of this patent
Estimating the term…
Abstract
A recursive method for computing numerical values for mathematical functions includes providing a recursive Taylor series representation of a mathematical function f(x) of a variable x evaluated around a given operating point a. The recursive Taylor series representation includes a plurality of derivative derived terms that include ratios of derivatives of f(x) evaluated at the operating point a. Coefficient data is determined from ones of the derivative derived terms stored in a tangible memory device evaluated at the operating point a over a predetermined range. An approximation for the mathematical function f(x) is computed using the recursive Taylor series representation evaluated with the coefficient data.
Claims12
A recursive method for computing numerical values for mathematical functions, comprising:
- providing a recursive Taylor series representation of a mathematical function f(x) of a variable x around a given operating point a, wherein said recursive Taylor series representation includes a plurality of derivative derived terms that include ratios of derivatives of said mathematical function evaluated at said operating point a;
- determining coefficient data comprising ones of said plurality of derivative derived terms evaluated at said operating point a over a predetermined range, wherein said plurality of derivative derived terms are stored in a tangible memory device, and
- computing an approximation for said mathematical function f(x) using said recursive Taylor series representation evaluated with said coefficient data.
A digital signal processor (DSP) IC for computing numerical values for mathematical functions, comprising:
- a substrate having a semiconductor surface;
- a memory device including a stored recursive Taylor series representation for a mathematical function f(x) of a variable x around a given operating point a that includes a plurality of derivative derived terms that include ratios of derivatives of said mathematical function evaluated at said operating point a;
- a multiply-accumulate (MAC) unit comprising a plurality of multipliers formed on said semiconductor surface coupled to said memory that is operable to (i) determine coefficient data comprising ones of said plurality of derivative derived terms evaluated at said operating point a over a predetermined range, and to (ii) compute an approximation for said mathematical function f(x) using said recursive Taylor series representation evaluated with said coefficient data.
Dependencies are inferred from the claim text.