"Recall that floating point addition is not associative"

Why do we even use floats in the first place

@socks huh. is that something to do with denormal numbers or some other weird edge case?
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@socks oh wait you said not associative, i was thinking of commutativity

associativity is necessarily lost in rounding
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@socks it's basically the same problem as catastrophic cancellation at its root, which i'm pretty sure there have been studies on ways to circumvent that, but it's been a really long time since we took that algorithms class
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