Sort numbers before adding up!

A few years ago my teammate came up with this statement. At first we misunderstood each other. I thought of integer numbers while he meant floating point. I know how the processor represent floats and I’m aware of how/why floating point numbers are normalized or rounded. But to be honest, I never thought the order of adding numbers is relevant. Ok, let see is it important or not. Before starting I have to say, this is all about floating point numbers, integers are not affected.

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