Comments on fast and exact accumulation of products

Authors:
Gerd Bohlender;Ulrich Kulisch
Affiliations:
Institute for Applied and Numerical Mathematics 2, Karlsruhe Institue of Technology, Karlsruhe, Germany;Institute for Applied and Numerical Mathematics 2, Karlsruhe Institue of Technology, Karlsruhe, Germany
Venue:
PARA'10 Proceedings of the 10th international conference on Applied Parallel and Scientific Computing - Volume 2
Year:
2010

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Abstract

A new IEEE arithmetic standard 1788 is currently being worked out. It will specify interval arithmetic and an exact dot product (EDP). In an EDP, an arbitrary finite number of products is accumulated without rounding errors. These are essential tools for computations with reliable and accurate results. In high performance computing, it is necessary that implementations of interval arithmetic and the EDP must be as efficient as the ordinary floating-point arithmetic. In this paper, fast and accurate solutions for the EDP are presented.