DocumentCode
610859
Title
How to Compute the Area of a Triangle: A Formal Revisit
Author
Boldo, S.
fYear
2013
fDate
7-10 April 2013
Firstpage
91
Lastpage
98
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.
Keywords
algorithm theory; floating point arithmetic; theorem proving; Kahan algorithm; algorithm proof; floating-point arithmetic; mathematical value; triangle area; Accuracy; Algorithm design and analysis; Digital arithmetic; Electronic mail; Error analysis; Libraries; Standards; Coq; floating-point arithmetic; formal proof; triangle; underflow;
fLanguage
English
Publisher
ieee
Conference_Titel
Computer Arithmetic (ARITH), 2013 21st IEEE Symposium on
Conference_Location
Austin, TX
ISSN
1063-6889
Print_ISBN
978-1-4673-5644-2
Type
conf
DOI
10.1109/ARITH.2013.29
Filename
6545896
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