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Sin/Cos Function Via Approximations Plus Error Compensation

IP.com Disclosure Number: IPCOM000041729D
Original Publication Date: 1984-Mar-01
Included in the Prior Art Database: 2005-Feb-02

Publishing Venue

IBM

Related People

Authors:
Murray, JT [+details]

Abstract

This article describes an approximation technique for generating sin and/or cos functions. The first two terms (linear and cubic) of the McLaurin series are used as simple sinusoidal approximations, and the triple angle formula is used to extend the approximation beyond its region of known accuracy. The accuracy of the approximation technique is further improved by adjusting the value error data stored in a compensation table. Direct computation of sin (x) is done by quadrant for the argument 0 < x < PI/2 and adjusted for other quadrants to complete a circular argument 0 to 2 PI. Cos (x) is computed from sin (PI/2 0 x) using the algorithm and similar quadrant adjustment. The McLaurin series: SIN(X) = X - (X**3)/3!+(X**5)/5!-(X**7)/7!+...