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JSR_FDED • today at 7:02 AM • 3 replies • view on HN

I just read up on interval arithmetic. I understand its desirable properties. Where in practice have you applied it? What’s a real world application for interval arithmetic?

Replies

ngruhn • today at 7:22 AM

It can be used in static analysis or type checking. E.g.

    if (x >= 0) {
      x += 10
      if (x =< 9) {
        // unreachable 
      }
    }
By maintaining an interval of possible values of x, you can detect the unreachable branch, because the interval becomes empty:

    initial: [-oo, oo]
    x >= 0 : [0, oo]
    x += 10: [10, oo]
    x =< 9 : [10, 9] (empty)
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nickcw • today at 8:24 AM

In physics, whenever you make a measurement it has a precision. Usually you represent this as a normal distribution, but for calculations it can be easier to represent this as an interval.

The police measure the distance my car travelled [ 99.9, 100.1 ] m and the time it took [ 3.3, 3.4 ] s - how fast was my car going? [29.38, 30.33] m/s according to the interval calculator.

Physics students learn exactly this method before they move on to more sophisticated analysis with error distributions.

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nicolodev • today at 7:37 AM

It’s astonishing how nobody hasn’t mentioned abstract interpretation yet. Under classical static analysis, if you can “prove” that a variable does not have values in some unsound zones, you can e.g. “prove” soundness or apply further optimizations.

The interval abstract domain works under interval analysis with an algebra that’s the same of this calculator. It’s funny to implement something like that on source/binary level :)