Software techniques for perfect elementary functions in floating-point interval arithmetic

A few recent processors allow very efficient double-precision floating point interval arithmetic for the basic operations. In comparison, the elementary functions available in current interval arithmetic packages suffer two major weaknesses. The first is accuracy, as intervals grow more in an elementary function than what is mathematically possible considering only the number format. The second is performance, well below that of scalar elementary function libraries. The difficulty is that the need to prove the containment property for interval functions usually entails sacrifices in accuracy and/or performance. This articles combines several available techniques to obtain implementations of double-precision interval elementary functions that are as accurate as mathematically possible, less than twice slower than their best available scalar counterparts, and fully verified. Implementations of exponential and natural logarithm on an Itanium © 2-based platform support these claims.