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# [Frama-c-discuss] an example involving floats

• Subject: [Frama-c-discuss] an example involving floats
• From: Claude.Marche at inria.fr (Claude Marché)
• Date: Fri, 06 Mar 2009 17:32:47 +0100
• References: <1236278646.26616.13.camel@ossiriand>

```
David DELMAS wrote:
> Hello,
>
> here is an apparently simple example :
>
> /*@
> assigns \nothing;
> ensures E < A ==> \result == B;
> */
> float F(float E, float A, float B)
> {
>     if (E < A) return B;
>     else return 0.;
> }
>
> The postcondition is proved by Z3, Yices and CVC3, but neither by Alt-
> Ergo, nor by Simplify.
> (of course it is proved by all if I change the float type to int)
>
> I would appreciate some intuition on the reason why it is so.

First thing: by default, the jessie plugin interprets floats by
mathematical real numbers. This might change later, but for the moment
the default is such because true floating-point support is not fully
operational.

So we have to think of E, A, B as real numbers. The VC for the "else"
branch has the form

E >= A  (* for the negation of the test *)
implies the post-condition which is of the form E < A ==> some P

in principle, this seems trivial because P must be proved under
contradictory hypotheses E >= A and E < A. The point is that here
>= and < denote comparisons of real numbers, and for Simplify and
Alt-Ergo, the support for reals numbers is void or very weak, in the
sense that they do not even know that >= is the negation of <.

The authors of Alt-Ergo are certainly willing to improve their tool. We
can hope for a better Alt-Ergo in the future (I forward this example to
their dev team!).

On the other hand, Simplify will not evolve anymore so it will never
support real numbers.

- Claude

--
Claude March?                          | tel: +33 1 72 92 59 69
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```