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Comment by heresy | Hacker News Reader

My point is, this is elementary stuff that you need to know as a computer scientist or self-taught hacker.

Whether you can convert a decimal number into its binary IEEE-754 equivalent, or not, is besides the point.

You just need to know that it is lossy for certain classes of decimal numbers, and how to avoid or mitigate those effects.

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Sure, if you want to have computer hacking be a big part of your life you should know that numbers are binary on computers, and that that has side effects. But I don't think it betrays a serious lack of education that someone who does know that theoretically has never realized that practically means there's no such thing as 0.1 on a computer.

You theoretically shouldn't even have to be a computer scientist. A standard mathematical education ought to teach you that for any given base, the only numbers that can be represented in that base exactly are numbers where the prime factorization of the denominator contains only prime numbers that are also contained in the prime factorization of the base itself, or is simply 1 for integers. Base 10 has 2 and 5. .2 is 1/5, so it's precise. .5 is 1/2, so it's precise. 1/12 has 2 2s in it, which works, and a 3, which doesn't, so 1/12 is recurring.

But prime factorization seems to be taught for almost superstitious reasons, as some sort of math trick rather than a fundamental aspect of understanding numbers at even the most basic of levels, with neither students nor teachers nor the curriculum writers really understanding why this is in the lesson plan, so, yeah, I suppose you have to be some sort of super expert genius to swiftly realize that 1/3 can't be represented in a base-2 number. But it shouldn't be that way.

I think the connection that "computer numbers are base 2" is what's missing. You input them into the computer in base 10, and they are printed in base 10. The base 10 representation is wrong because information was lost when converting to a fixed-width base 2 number. But that is hidden by the compiler or program, so it confuses programmers and users.

It works in Excel...

Excel does "cosmetic" rounding, that ends up producing some surprising results - in the words of this author, it "confers supernatural powers upon some (not all) parentheses": http://www.cs.berkeley.edu/~wkahan/Mindless.pdf

0.1 is perfectly representable "on a computer", just not in binary floating point.

See e.g. Haskell's Data.Ratio (http://haskell.org/ghc/docs/6.12.1/html/libraries/base-4.2.0...) module for rational numbers.

Or computers with decimal floating point hardware.

Yes, but that's such a special case. I'd rather go with base 11 than decimal.

Well, if you take Java for example, floating point measurements are only IEEE-754 when classes or methods are declared with the strictfp keyword, yet non-strictfp floating point calculations are still imprecise because of the very nature of fractional math. They're just less imprecise by default. I agree with the sentiment others have posted that it is disappointing that this reality isn't more commonly taught in CS education.

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