Interval Union Calculator: Handling Disjoint Interval Arithmetic
The author has developed an open-source project that implements interval union arithmetic in TypeScript, allowing for accurate calculations over disjoint sets of intervals, including handling division by intervals containing zero.
Why it matters
This project addresses a key limitation in standard interval arithmetic, enabling more robust and accurate calculations over disjoint sets of intervals, which has applications in various scientific and engineering domains.
Key Points
- 1Standard interval arithmetic has poor handling of division by intervals containing zero
- 2The real solution is to define arithmetic over disjoint unions of intervals
- 3The project implements interval union arithmetic in TypeScript with outward rounding for accuracy
- 4Handles non-continuous functions like trigonometry that regular interval arithmetic struggles with
Details
The author has been studying interval arithmetic and found that while there is a lot of interesting research in this field, it has not received the recognition it deserves. One key issue with standard interval arithmetic is the poor handling of division by intervals containing zero, which can result in useless solutions like [-∞, +∞]. The author explains that the real solution is to define arithmetic over disjoint unions of intervals, as described in a 2017 paper. The open-source project implements this interval union arithmetic in TypeScript, allowing for accurate calculations even with non-continuous functions like trigonometry. The underlying library is dependency-free and uses IEEE 754 double precision floats with outward rounding to guarantee accuracy in the presence of floating-point rounding issues.
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