[II2II]

> Calculators are deterministically correct

Calculators are deterministic, but they are not necessarily correct. Consider 32-bit integer arithmetic:

  30000000 * 1000 / 1000
  30000000 / 1000 * 1000

Mathematically, they are identical. Computationally, the results are deterministic. On the other hand, the computer will produce different results. There are many other cases where the expected result is different from what a computer calculates.

[wongarsu]

A good calculator will however do this correctly (as in: the way anyone would expect). Small cheap calculators revert to confusing syntax, but if you pay $30 for a decent handheld calculator or use something decent like wolframalpha on your phone/laptop/desktop you won't run into precision issues for reasonable numbers.

[Ifkaluva]

He’s not talking about order of operations, he’s talking about floating point error, which will accumulate in different ways in each case, because floating point is an imperfect representation of real numbers

[II2II]

Yeap, the specific example wasn't important. I choose an example involving the order of operations and an integer overflow simply because it would be easy to discuss. (I have been out of the field for nearly 20 years now.) Your example of floating point errors is another. I also encountered artifacts from approximations for transcendental functions.

Choosing a "better" language was not always an option, at least at the time. I was working with grad students who were managing huge datasets, sometimes for large simulations and sometimes from large surveys. They were using C. Some of the faculty may have used Fortran. C exposes you the vulgarities of the hardware, and I'm fairly certain Fortran does as well. They weren't going to use a calculator for those tasks, nor an interpreted language. Even if they wanted to choose another language, the choice of languages was limited by the machines they used. I've long since forgotten what the high performance cluster was running, but it wasn't Linux and it wasn't on Intel. They may have been able to license something like Mathematica for it, but that wasn't the type of computation they were doing.

[wongarsu]

I didn't consider it an order of operations issue. Order of operations doesn't matter in the above example unless you have bad precision. What I was trying to say is that good calculators have plenty of precision.

[skydhash]

But floating point error manifest in different ways. Most people only care about 2 to 4 decimals which even the cheapest calculators can do well for a good amount of consecutive of usual computations. Anyone who cares about better precision will choose a better calculator. So floating point error is remediable.

[anthk]

Good languages with proper number towers will deal with both cases in equal terms.