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How to Compute the Area of a Triangle: a Formal Revisit

Abstract : Mathematical values are usually computed using well-known mathematical formulas without thinking about their accuracy, which may turn awful with particular instances. This is the case for the computation of the area of a triangle. When the triangle is needle-like, the common formula has a very poor accuracy. Kahan proposed in 1986 an algorithm he claimed correct within a few ulps. Goldberg took over this algorithm in 1991 and gave a precise error bound. This article presents a formal proof of this algorithm, an improvement of its error bound and new investigations in case of underflow.
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Contributor : Sylvie Boldo <>
Submitted on : Tuesday, February 19, 2013 - 1:32:49 PM
Last modification on : Monday, December 14, 2020 - 5:00:06 PM
Long-term archiving on: : Monday, May 20, 2013 - 4:01:34 AM


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Sylvie Boldo. How to Compute the Area of a Triangle: a Formal Revisit. 21st IEEE International Symposium on Computer Arithmetic, Apr 2013, Austin, TX, United States. pp.91-98, ⟨10.1109/ARITH.2013.29⟩. ⟨hal-00790071⟩



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