An algorithm for parallel calculation of trigonometric functions

摘要

The task of computing trigonometric functions is frequently encountered in mathematical software. As a result, there is a substantial interest in fast and efficient algorithms for this task. The authors of this paper recall the classic and often-used coordinate rotation digital computer (CORDIC) approach, and then present their new parallel scheme, PARROT. The latter is based on a blend of Euler's well-known formula relating the sine and cosine functions, and the complex exponential. Using this identity and de Moivre's formula for computing powers of complex exponentials, the authors develop a general framework for a class of algorithms for the evaluation of trigonometric functions. Depending on the precise choice of the values of the parameters intrinsic to this class of algorithms, users can design their own special cases optimized for runtime, memory requirements, and so on. In particular, it is possible to adapt the scheme to the hardware at hand, or even to use it in a joint hardware/software development process, that is, to develop a chip with user-defined on-board memory and number of cores, and to simultaneously optimize the algorithm for this chip.