alt Hacker NewsIs there any constant more misused in compsci than ieee epsilon? :)
It's defined as the difference between 1.0 and the smallest number larger than 1.0. More usefully, it's the spacing between adjacent representable float numbers in the range 1.0 to 2.0.
Because floats get less precise at every integer power of two, it's impossible for two numbers greater than or equal to 2.0 to be epsilon apart. The spacing between 2.0 and the next larger number is 2*epsilon.
That means `abs(a - b) <= epsilon` is equivalent to `a == b` for any a or b greater than or equal to 2.0. And if you use `<` then the limit will be 1.0 instead.
Epsilon is the wrong tool for the job in 99.9% of cases.
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The term I've seen a lot is https://en.wikipedia.org/wiki/Unit_in_the_last_place
So I'd probably rewrite that code to first find the ulp of the larger of the abs of a and b and then assert that their difference is less than or equal to that.
Edit: Or maybe the smaller of the abs of the two, I haven't totally thought through the consequences. It might not matter, because the ulps will only differ when the numbers are significantly apart and then it doesn't matter which one you pick. Perhaps you can just always pick the first number and get its ULP.
i find the best way to remember it is "it's not the epsilon you think it is."
epsilons are fine in the case that you actually want to put a static error bound on an equality comparison. numpy's relative errors are better for floats at arbitrary scales (https://numpy.org/doc/stable/reference/generated/numpy.isclo...).
edit: ahh i forgot all about ulps. that is what people often confuse ieee eps with. also, good background material in the necronomicon (https://en.wikipedia.org/wiki/Numerical_Recipes).
A (perhaps initially) counterintuitive part of the above more explicitly stated: The doubling/halving also means numbers between 0 and 1 actually have _more_ precision than the epsilon would suggest.