you: i wonder if this problem is NP-complete? me: actually a trivial subproblem of it, which seems easy, is NP-complete on its ownpic.twitter.com/miSLFHswsq
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floating point multiplication is totally associative if you want it to be
Some of us think not-IEEE floats are a sin. :)
you can associate IEEE floats!
Under what conditions? Clearly (2*x)*0.5 is not same as 2*(x*0.5) for x=DBL_MAX.
oh i never said it'd be bit-exact ;-)
I understood the problem of optimal rearrangement in terms of equivalence...
i work on graphics, so "equivalence" means "within some reasonable epsilon on our test shaders"
i'm part of the cabal that tells people to never use == on floats
Exponentiating 2**b is still associative =P
Multiplication by 2 is always exact. Hence, you are free to reassociate product chains.
No, you forgot INF is saturating.
No, I didn't. If the product overflows, any bracketing overflows, because the result is always exact, and the only term is 2.
There is no 0.5 allowed in my example. You're only multiplying 2s. It always gives the right answer no matter how you bracket it.
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