Comparing floating-point numbers (2012)

Summary

This post is a more carefully thought out and peer reviewed version of a floating-point comparison article I wrote many years ago. This one gives solid advice and some surprising observations about the tricky subject of comparing floating-point numbers. A compilable source file with license is available. We’ve finally reached the point in this series that I’ve been waiting for. In this post I am going to share the most crucial piece of floating-point math knowledge that I have. Here it is: [Floating-point] math is hard. You just won’t believe how vastly, hugely, mind-bogglingly hard it is. I mean, you may think it’s difficult to calculate when trains from Chicago and Los Angeles will collide, but that’s just peanuts to floating-point math. Seriously. Each time I think that I’ve wrapped my head around the subtleties and implications of floating-point math I find that I’m wrong and that there is some extra confounding factor that I had failed to consider. So, the lesson to remember is that floating-point math is always more complex than you think it is. Keep that in mind through the rest of the post where we talk about the promised topic of comparing floats, and understand that this post gives some suggestions on techniques, but no silver bullets. Previously on this channel… This is the fifth chapter in a long series. The first couple in the series are particularly important for understanding this point. A (mostly) complete list of the other posts includes: Comparing for equality Floating point math is not exact. Simple values like 0.1 cannot be precisely represented using binary floating point numbers, and the limited precision of floating point numbers means that slight changes in the order of operations or the precision of intermediates can change the result. That means that comparing two floats to see if they are equal is usually not what you want. GCC even has a (well intentioned but misguided) warning for this: “warning: comparing floating point with == or != is...