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How do you compute the midpoint of an interval?

Abstract : The algorithm that computes the midpoint of an interval with floating-point bounds requires some careful devising to correctly handle all possible inputs. We review several implementations from prominent C/C++ interval arithmetic packages and analyze their potential failure to deliver correct results. We then highlight two implementations that avoid common pitfalls. The results presented are also relevant to non-interval arithmetic computation such as the implementation of bisection methods. Enough background on IEEE 754 floating-point arithmetic is provided for this paper to serve as a practical introduction to the analysis of floating-point computation.
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https://hal.archives-ouvertes.fr/hal-00576641
Contributor : Frédéric Goualard Connect in order to contact the contributor
Submitted on : Thursday, April 17, 2014 - 9:19:10 AM
Last modification on : Wednesday, April 27, 2022 - 4:23:06 AM
Long-term archiving on: : Monday, April 10, 2017 - 2:51:59 PM

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Frédéric Goualard. How do you compute the midpoint of an interval?. ACM Transactions on Mathematical Software, 2014, 40 (2), ⟨10.1145/2493882⟩. ⟨hal-00576641v2⟩

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