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Even sqrt(x * x + y * y) is wrong. I'm slightly ashamed to say that I learned of the C hypot function only a few days ago. I've been doing this wrong for decades.

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Indeed, overflow is also an issue that easily comes sneaking. Nice post on calculating the hypotenuse here[1].

[1]: https://www.johndcook.com/blog/2010/06/02/whats-so-hard-abou...

I would think overflow is a very rare problem for floats; I don't think any code I have ever written would need to handle the overflow case. The more significant problem should be precision loss.

Is the algorithm in [1] significantly more precise for inputs that don't result in overflow?

Edit: I made a small program to check a few values. It is seems like the algorithm in [1] is better in terms on precision, but only by a small margin (on the small set of values I checked).

sqrt(x*x + y*y) loses a lot of precision if x and y differ greatly in magnitude.

Do you have an example where this is true? I have not seen an example with > 2 ulp difference from the true value or > 1 ulp difference between the two algorithms.

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