The interval logarithmic number system

We introduce the interval logarithmic number system (ILNS), in which the logarithmic number system (LNS) is used as the underlying number system for interval arithmetic. The basic operations in ILNS are introduced and an efficient method for performing ILNS addition and subtraction is presented. We compare ILNS to interval floating point (IFP) for a few sample applications. For applications like the N-body problem, which have a large percentage of multiplies, divides and square roots, ILNS provides much narrower intervals than IFP. In other applications, like the fast Fourier transform, where addition and subtraction dominate, ILNS and IFP produce intervals having similar widths. Based on our analysis, ILNS is an attractive alternative to IFP for application that can tolerate low to moderate precisions.

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