I'd like to present my result on variance arithmetic, which is an interval arithmetic with statistical bounding rather than absolute bounding. It shows that from statistics, a bounding interval is a necessity. On the other hand, the statistical bounding seems better than the absolute bounding because:
- The statistical bounding can obtain Taylor expansion easily;
- It rejects calculations such as inverting an interval containing 0.
- It has no dependency problem.
The source code and the theory is presented as an open source project:
Chengpu0707/VarianceArithmetic: A floating-point arithmetic with value and uncertainty (variance) pair (github.com)
In the discussion, the paper calls:
- a unsigned floating-point representation to hold variance.
- recalculating all numerical libraries with uncertainty for each value.
The predecessor of this arithmetic has been published (C.P. Wang. A New Uncertainty-Bearing Floating-Point Arithmetic.Reliable Computing, 16:308-361, 2012), but I have been unsatisfied with that result. Now its theory starts to become satisfactory, and there are plenty of tests to verify its correctness. Many thanks to these in this list who participated in reviewing my previous paper and gave me good feedbacks.
Please take time to read the paper, which I have attached to this email. It is a little bit long (87 pages) because it contains a lot of verification.
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