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Comment by jeroenhd | Hacker News Reader

Testing these problems in https://www.cemetech.net/projects/jstified/ seems to indicate that "modern" (as in, late 90s) calculators have these problems well under control.

Android's built in calculator on my phone and tablet (take note, Apple) both seem to get the answer right as well.

Fun problems for people trying to build their own calculators, but not really a problem if you're actually trying to solve equations using existing ones.

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The Android calculator is indeed super amazing. There's a super interesting paper behind the tech (constructive reals): https://cacm.acm.org/magazines/2017/8/219594-small-data-comp... written by Boehm (the same person behind the eponymous garbage collector).

Sometimes they "control" the problem with trickery that occasionally blows up. For example, there was talk some time ago about how some Casio models sometimes invent a factor pi in something that should obviously be a rational number: https://twitter.com/standupmaths/status/1284117779025727494 . (Ok, admittedly this is a much nastier trick than just using a few extra hidden digits for floating point numbers.)

Apple’s calculator seems to get the first set of problems from the pdf right as well. Did you test with it and get something different?

Consider this example from the article where it asks you to calculate the limit of ln(1+h)/h as h tends to zero. Set h to be 10^(-17). The Android calculator reliably succeeds and gives the same answer as Mathematica. The iOS calculator reliably fails; at least it knows its limits and refuses to give even an approximate answer.

and yet today I saw a website calculate 3.3 x 4 to be 13.200000000000003

Calculators don't use floating point for a reason.

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