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A comment on The Fundamental Axiom of Floating Point Arithmetic. Parent comment

Re:The Fundamental Axiom of Floating Point Arithmetic by hpcjoe on Wednesday August 05, 2020 @10:59AM (#24061529)
This is due to the non-associative nature of FP. (a+b) + c != a + (b+c).

I disagree that the "axiom" as stated is fundamental. My main argument with it is that I don't see an easy way to go from the axiom to usable theorems about FP.

Happy to be wrong on this, but I am missing this at this time.

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Re:The Fundamental Axiom of Floating Point Arithmetic by augustt on Wednesday August 05, 2020 @03:37PM (#24064680)
I'd say not only is fundamental, it's pretty much the only tool you have to start the analysis of an FP algorithm. If you want to analyze a naive sum algorithm for instance you do that by recursively applying the a ⊕ b = (a + b)(1 + ε) rule and figure out how the epsilons bubble up - the result being that the error is linear with the sum length.
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