Implementation of Taylor Model Arithmetic

In the following, we describe in detail the current implementation of Taylor model arithmetic in version 8.1 of the code COSY INFINITY. Since in the Taylor model approach, the coefficients are floating point (FP) numbers, care must be taken that the inaccuracies of conventional FP arithmetic are properly accounted for. Algorithmically the methods are rather straightforward; however for practical use of the methods, the more important question is that of the soundness of the actual implementation. To assure the latter, besides the tests performed by ourselves in the development of the methods, we have decided to ask an outside group to perform extensive and hopefully sufficiently exhaustive independent testing using various test suites.