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YalAA: Yet Another Library for Affine Arithmetic

In this paper, we present YalAA, a new library for affine arithmetic. Recently, affine arithmetic has been given increased attention even from outside the traditional verified computing community, for example, in the areas of circuit design, GPU based rendering of implicit objects and global optimization. Furthermore, several improvements to the original affine model were proposed. However, a fully verified, object-oriented implementation supporting at least some of the extensions is currently not available. The goal of YalAA is to provide a wide range of elementary functions and to allow the user to incorporate improvements for the original affine model easily. In contrast to other available libraries, YalAA also provides verified implementations of non-convex or non-concave elementary functions. Our library has a policy based design. That is, the user can alter different aspects in the library’s behavior to reflect variations of the original model while relying on the same code base. Because affine arithmetic is often used in combination with interval arithmetic, we followed the principles of the upcoming P1788 interval standard during the design process. Therefore, YalAA can be integrated seamlessly into an existing interval arithmetic environment.