Frama-C-discuss mailing list archives

This page gathers the archives of the old Frama-C-discuss archives, that was hosted by Inria's gforge before its demise at the end of 2020. To search for mails newer than September 2020, please visit the page of the new mailing list on Renater.

[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]

[Frama-c-discuss] Integerdivision

  • Subject: [Frama-c-discuss] Integerdivision
  • From: kerstin.hartig at first.fraunhofer.de (Kerstin Hartig)
  • Date: Thu, 23 Jul 2009 10:38:12 +0200
On Christoph Weber's request I forward the following mail:
-----------------------------

Integerdivision

Hello, I am exploring the limitations of divisions and annotations and I
would
like to know, how many VC can be proven with your development tools:
But I pay special attention to the terms connected with the division.

Sincerely

Christoph

//====================================================================
/*@
	lemma division:   \forall integer x; 0 < x ==> 0 <= x/2;
*/

/*@
	requires limit > 0;
	ensures limit == \result;
*/

int integerdivision(int limit)
{
	int b = 1;
	int a = limit;
	int index = 0;
	int old_a=a;
	int old_b=b;
	/*@
		loop invariant a/2 >= 0;
		loop invariant 0 <= a <= limit;
		loop invariant 1 <= b <= limit;
		loop invariant index == 0 ==> b == old_b;
		loop invariant index == 0 ==> a == old_a;
		loop invariant index > 0 ==> b == old_b/2;
		loop invariant index > 0 ==> a == old_a*2;
	*/
	while (0 < a)
	{
		old_a=a;
		old_b=b;
		a = a/2;
		b = b*2;
		index ++;
	}
	return b;
}
//====================================================================