Re: Floating point optimizations

[John Fine <johnsfine at verizon dot net>]

The general concept of optimizations is to preserve the answer while 
reducing the time needed to compute the answer.  There are some cases in 
which an optimization fails to preserve the answer, but those usually 
occur in complex situations where the designer of the optimization had 
no practical way to avoid the difference.

As you noted c-(c-a) is routinely different from a.  Anyone designing 
optimizations would understand that.  So making that optimization would 
violate the general principle of optimization.

I don't know of any gcc option that might turn on that questionable 
"optimization".  I doubt that there is one, but I'm not certain there isn't.


Christian Keil wrote:

> Hi,
>
> we are currently investigating some numerical algorithms and the claim
> appeared that a C statement like
>  x = c - (c - a);
> would be easily transformed into
>  x = a;
> by the compiler. Now investigating this with a vanilla GCC 4.1.2 failed
> to support the claim. Compiling the below program with -O3 -ffast-math
> keeps the computation of x. The output shows x is different from a. The
> question is, is there some compiler switch or the like to get GCC to
> make the above transformation? I searched the docs but had the
> impression that all relevant flags should be included in the above two
> (especially ffast-math).
>
> Please let me know if you need any additional information or if this is
> the wrong list for this kind of question.
>
> Cheers,
> Christian
>
> ------8<--------
> #include <stdio.h>
> #include <stdlib.h>
>
> int
> main(void)
> {
>  double a, x;
>  double c;
>
>  scanf("%lf", &a);
>  c = ((1 << 27) + 1) * a;
>  x = c - (c - a);
>
>  printf("a = %e(%a)\n", a, a);
>  printf("x = %e(%a)\n", x, x);
> }
> ------8<--------
>
>