For the sine and cosine functions, absolute error is natural measure. For the exponential function, relative error is a natural measure. Also, in many cases, the functions are tested very strictly, near the extremes of the particular floating point system. Of course, both relative and absolute accuracy could be improved if a higher precision data type were assumed to be available. If the return-values of the elementary functions are within one unit in the last place of the corresponding mathematical values of the function, then considerable simplification and speedup are possible.
Simplifications are possible in various places if IEEE arithmetic is used.
No additional modifications should be necessary in order to provide an interval data type. We have endeavored to make this package easy to use, maintain, and modify. Please contact us with comments, questions, or problems. We would particularly like to receive suggestions for improvement. The easiest way to reach me is by email.