Staggered Correction Computations with Enhanced Accuracy and Extremely Wide Exponent Range ∗

In C-XSC a staggered interval arithmetic with precision p is defined as an array of p + 1 components of type double. The disadvantage of this multiple precision arithmetic is the rather small exponent range and particularly the dramatic loss of accuracy, if intermediate results of computations lie near the underflow range. In order to avoid these difficulties a new class lx interval is implemented with objects of the form 2 r · x, r ∈ Z of type double and x of type l interval, the original staggered interval data type. Now the intervals x can be scaled in such a way that the basic arithmetic operations can be performed in a remarkable higher accuracy. Numerical examples demonstrate the ability of the new arithmetic