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I've been studying interval arithmetic for the past few weeks and it's a really interesting field because while there is a ton of super interesting research published over the past decades, it has never really gotten the recognition that it deserves, IMO.

One reason for this is that standard interval arithmetic has really poor handling of division by intervals containing zero. If you compute 1 / [-1, 2] in regular interval arithmetic, you get either [-∞, +∞], or you have to say that the operation is undefined. Both solutions are virtually useless. The real answer of course is [-∞, -1] U [0.5, +∞]: i.e. a union of two disjoint intervals.

This is useful because you can confidently exclude a non empty set of the real numbers ([-1, 0.5]) from the set of possible values that you can get by dividing 1 by a number between -1 and 2.

But this definition of interval division yields a value that is not an interval. This is a problem if you want to define a closed arithmetic system, where you can build and evaluate arbitrary expression over interval values.

(This behavior extends to any non continuous function like tan() for example, which is implemented in my project - not without difficulties!)

Well the obvious solution is to define your arithmetic over disjoint unions of intervals. This is the subject of a 2017 paper called "Interval Unions" by by Schichl, H., Domes, F., Montanher, T. and Kofler, K..

This open-source project I made implements interval union arithmetic in TypeScript in the form of a simple interactive calculator, so you can try it out for yourself! The underlying TypeScript library is dependency free and implements interval union arithmetic over IEEE 754 double precision floats (JS native number type) with outward rounding. This guarantees accuracy of interval results in the presence of rounding issue inherent to floating point.

Comments URL: https://news.ycombinator.com/item?id=47812341

Points: 308

# Comments: 51

"cat readme.txt" is not safe if you use iTerm2

arkadiyt — Fri, 17 Apr 2026 18:43:32 +0000

Article URL: https://blog.calif.io/p/mad-bugs-even-cat-readmetxt-is-not

Comments URL: https://news.ycombinator.com/item?id=47809190

Points: 308

# Comments: 183

All 12 moonwalkers had "lunar hay fever" from dust smelling like gunpowder (2018)

cybermango — Fri, 17 Apr 2026 18:17:01 +0000

Article URL: https://www.esa.int/Science_Exploration/Human_and_Robotic_Exploration/The_toxic_side_of_the_Moon

Comments URL: https://news.ycombinator.com/item?id=47808913

Points: 451

# Comments: 264

Show HN: Smol machines – subsecond coldstart, portable virtual machines

binsquare — Fri, 17 Apr 2026 17:18:58 +0000

Article URL: https://github.com/smol-machines/smolvm

Comments URL: https://news.ycombinator.com/item?id=47808268

Points: 481

# Comments: 143

Show HN: PanicLock – Close your MacBook lid disable TouchID –> password unlock

seanieb — Fri, 17 Apr 2026 16:38:44 +0000

I wrote this after the case of a Washington Post reporter, Hannah Natanson, was compelled to unlock her computer with her fingerprint. This resulted in access to her Desktop Signal on her computer, revealing sources and their conversations.

https://www.yahoo.com/news/articles/washington-post-raid-pro...

Edit: I've a lot more details about the legality and precedence on the apps landing page https://paniclock.github.io/

Comments URL: https://news.ycombinator.com/item?id=47807809

Points: 256

# Comments: 113