Re: non trivial constant folding

Hans-Bernhard Broeker <broeker@physik.rwth-aachen.de>
5 Jan 2001 14:45:28 -0500

          From comp.compilers

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non trivial constant folding mpointie@eden-studios.fr (MickaŽl Pointier) (2001-01-05)
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Re: non trivial constant folding mihai@cs.wisc.edu (Mihai Christodorescu) (2001-01-06)
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[15 later articles]
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From: Hans-Bernhard Broeker <broeker@physik.rwth-aachen.de>
Newsgroups: comp.compilers
Date: 5 Jan 2001 14:45:28 -0500
Organization: Aachen University of Technology (RWTH)
References: 01-01-015
Keywords: arithmetic, optimize, comment
Posted-Date: 05 Jan 2001 14:45:28 EST
Originator: broeker@

"MickaŽl Pointier" <mpointie@eden-studios.fr> wrote:
[...]
> My problem is that I do not manage to find a clean solution
> to optimise this:


> eval(1+var+1)


Just a warning, even though there's not much compiler theory behind
it: you're operating in floating point numbers, where neither additive
nor multiplicative operations are truly associative. In that
environment, optimizing this into '2+var' would introduce subtle or
even catastrophic changes in results.


Example, assuming 3 decimal digits of accuracy for illustrative
purpose:


5 + var + (-10), with var happening to be 5.01:


        +(+(5, 5.01), -10)
    = +(10.0, -10)
    = 0


        +(5, +(5.01, -10))
    = +(5, -4.99)
    = 0.01


100% error, just by changing associativity of the opeators. Your
proposed change would have the same kind of effect. It's up to you to
decide whether optimization gains warrant such a potentially
devastating change of result.
--
Hans-Bernhard Broeker (broeker@physik.rwth-aachen.de)
[It depends on the definition of the language. Fortran explicitly
says that any optimzation that's mathematically equivalent is fair
game, so if you want to force an order of computation, you have to use
parentheses. But anyway, in practice I've found that this is much
more common with integers, particularly in subscript calculations
where one of the constants is the lower bound of the array. -John]


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