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How to Compute the Area of a Triangle: a Formal Revisit with a Tighter Error Bound

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, investigations in case of underflow and a new improvement of its error bound.
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https://hal.inria.fr/hal-00862653
Contributor : Sylvie Boldo <>
Submitted on : Tuesday, September 17, 2013 - 11:17:26 AM
Last modification on : Monday, December 14, 2020 - 5:00:06 PM
Long-term archiving on: : Friday, December 20, 2013 - 2:20:32 PM

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Sylvie Boldo. How to Compute the Area of a Triangle: a Formal Revisit with a Tighter Error Bound. 2013. ⟨hal-00862653⟩

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