Floating-point errors, explained

Back in March, we looked at the reasons behind apparent arithmetic “mistakes” that can occur in software programs like R that use floating-point arithmetic, like this:    

> 1.0 – 0.9 – 0.1
[1] -2.775558e-17

Of course, the answer should be zero, but it’s not, not exactly anyway. That example (which I wish I’d thought of myself at the time) comes from an well-written and informative article published in PC Plus and available online at techradar.com. In simple, non-technical terms, it explains why such floating-point errors occur. It also gives some examples of the consequences of not anticipating such errors, like the Ariane 5 rocket that self-destructed 5 seconds after launch, or the Patriot missile that failed to target an Iraqi Scud missile that killed 28 people. 

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These horror stories explain why good programmers should always be aware of the pitfalls of using floating-point arithmetic and to program defensively to avoid them. (I gave some tips for R in that article from March.) It’s a great article to send next time someone asks you why their code isn’t giving a exactly the right result when they think it should.

TechRadar.com: Why computers suck at maths