Approximating sine functions using variable-precision Taylor polynomials

Sine is one of the fundamental mathematic functions which are widely used in a number of application fields. In particular, signal processing and telecommunications need to calculate sine and cosine of numerical values for several different purposes. One of the challenges which affected the implementation of sine calculation in digital signal processing (DSP) has been the method used to calculate it by means of rational functions, which would allow the implementation of sine calculation in a digital computer system. One possibility is to exploit the Taylor polynomials, even though their main drawback consists of a relatively high grade (thus computational load) already for relatively low-precision approximations. This paper proposes a variable-precision method that allows approximating sine and cosine functions with Taylor polynomials while significantly reducing the computational load required. Our analysis shows how using our method it is possible to achieve the same accuracy marked by other approximation methods, at a lower computational cost.