Evaluating Floating-Point Elementary Functions

The elementary functions are the most common mathematical functions: sine, cosine, tangent and their inverses, exponentials and logarithms of radices e, 2 or 10, etc. They appear everywhere in scientific computing; thus being able to evaluate them quickly and accurately is important for many applications. Various very different methods have been used for evaluating them: polynomial or rational approximations, shift-and-add algorithms, table-based methods, etc. The choice of the method greatly depends on whether the function will be implemented on hardware or software, on the target precision (for instance, table-based methods are very good for low precision, but unrealistic for very high precision), and on the required performance (in terms of speed, accuracy, memory consumption, size of code, etc.). With regard to performance, one will also resort to different methods depending on whether one wishes to optimize average performance or worst-case performance.