[Haskell-cafe] GHC optimisations
isaacdupree at charter.net
Thu Aug 23 08:05:44 EDT 2007
Hugh Perkins wrote:
> On 8/22/07, Twan van Laarhoven <twanvl at gmail.com> wrote:
>> But Double is already quite badly behaved:
>> > let x = 1e20
>> > Prelude> 1 + (x - x)
>> > 1.0
>> > Prelude> (1 + x) - x
>> > 0.0
> Ewwww. Whilst that's understandable and unavoidable, that kindof
> rings alarm bells for folds of Doubles in an automatic threading
> situation. Ie, if we split our fold between 4 cores, we might get a
> different answer than if we split it between 8 cores?
Yep, Double's (+) isn't associative.
I was trying to come up with ANY common mathematical property that
Double fulfills and this was what I came up with:
--> for all x::Float. not (x > x + 1)
I'm not even sure it's true in the presence of very large numbers,
optimizations and extra precision being added in the CPU. Note that
it's not (x <= x + 1) because of NaN.
Is Double's (+) commutative? I don't know for sure. Its (==) isn't
reflexive (is it transitive? probably, at least if there aren't too many
optimizations, but floating-point transitive equality isn't very useful).
--> Okay... so (+), (*), (==) are probably symmetric too.
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