Standard Functions for Real and Complex Point and Interval Arguments with Dynamic Accuracy

Standard Functions for Real and Complex Point and Interval Arguments with Dynamic Accuracy. Algorithms for the high-accuracy evaluation of the real and complex standard functions ex, sin x, cos x, tan x, cot x, sinh x, cosh x, tanh x, coth x, $$ \sqrt x $$ and x2 for point and interval arguments in general floating-point screens are treated. In case of interval functions an inclusion of the exact result is computed. The number of guard digits necessary to obtain this result in general floating-point screens is specified for each function. The error bounds stated in this paper are proved in [3]. The missing inverse standard functions can be found in short in [6] or more detailed in [7].