Abstract
Interval arithmetic, as it is standardized by the IEEE working group P1788 can be implemented by using floating point arithmetic units with directed rounding modes. The easiest way to represent an interval is by its two bounds. Simple formulas for the arithmetic operations can be applied. Our goal is to perform interval operations as fast as their floating point counterparts. Hence, we provide at least two units per operation. We also specify the operation for reverse multiplication (Neumaier in Vienna proposal for interval standardization, 2008) which can be implemented with the division unit. In this paper we do not care about optimization. Our primary intention is to give an easily understandable specification of hardware for interval arithmetic.
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Intel© advanced vector extensions programming reference (2011). http://software.intel.com/file/35247/
Gupte R, Edmonson WW, Ocloo S, Alexander WE (2006) Pipelined alu for signal processing to implement interval arithmetic. In: SiPS. IEEE, USA, pp 95–100. http://dblp.uni-trier.de/db/conf/sips/sips2006.html#GupteEOA06
IEEE Interval Standard Working Group-P1788. http://grouper.ieee.org/groups/1788/
Kirchner R, Kulisch UW (2006) Hardware support for interval arithmetic. Reliab Comput 12(3): 225–237
Kulisch U (2008) Computer arithmetic and validity: theory, implementation, and applications, De Gruyter studies in mathematics. Walter De Gruyter, New York
Lambov B (2008) Interval arithmetic using SSE-2. Lect Notes Comput Sci 5045: 102–113
Nehmeier M, Wolff von Gudenberg J (2011) Interval comparisons and lattice operations based on the interval overlapping relation. In: Proceedings of the world conference on soft computing 2011 (WConSC’11), San Francisco, CA, USA
Nehmeier M, Siegel S, Wolff von Gudenberg J (2010) Parallel detection of interval overlapping. In: Proceedings of the state of the art in scientific and parallel computing (Para 2010). Reykjavìk, Iceland (to appear)
Neumaier A (2008) Vienna proposal for interval standardization, Version 3.0. In: IEEE Interval Standard Working Group-P1788. http://grouper.ieee.org/groups/1788/
Schulte MJ, Swartzlander EE Jr. (2000) A family of variable-precision interval arithmetic processors. IEEE Trans. Comput. 49: 387–397. doi:10.1109/12.859535
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The authors have presented the results of this paper during the SCAN 2010 conference in Lyon, September 2010.
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Nehmeier, M., Siegel, S. & Wolff von Gudenberg, J. Specification of hardware for interval arithmetic. Computing 94, 243–255 (2012). https://doi.org/10.1007/s00607-012-0185-0
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DOI: https://doi.org/10.1007/s00607-012-0185-0