A unified algorithm for elementary functions

Authors:
J. S. Walther
Affiliations:
Hewlett-Packard Company, Palo Alto, California
Venue:
AFIPS '71 (Spring) Proceedings of the May 18-20, 1971, spring joint computer conference
Year:
1971

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Abstract

This paper describes a single unified algorithm for the calculation of elementary functions including multiplication, division, sin, cos, tan, arctan, sinh, cosh, tanh, arctanh, In, exp and square-root. The basis for the algorithm is coordinate rotation in a linear, circular, or hyperbolic coordinate system depending on which function is to be calculated. The only operations required are shifting, adding, subtracting and the recall of prestored constants. The limited domain of convergence of the algorithm is calculated, leading to a discussion of the modifications required to extend the domain for floating point calculations.