  Complex interval arithmetic is a powerful tool for the analysis of
computational errors. The naturally arising rectangular, polar, and circular
(together called primitive) interval types are not closed under simple
arithmetic operations, and their use yields overly relaxed bounds. The later
introduced polygonal type, on the other hand, allows for arbitrarily precise
representation of the above operations for a higher computational cost. We
propose the polyarcular interval type as an effective extension of the previous
types. The polyarcular interval can represent all primitive intervals and most
of their arithmetic combinations precisely and has an approximation capability
competing with that of the polygonal interval. In particular, in antenna
tolerance analysis it can achieve perfect accuracy for lower computational cost
then the polygonal type, which we show in a relevant case study. In this paper,
we present a rigorous analysis of the arithmetic properties of all five
interval types, involving a new algebro-geometric method of boundary analysis.
