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/**************************************************************************/
/* */
/* The Why platform for program certification */
/* */
/* Copyright (C) 2002-2011 */
/* */
/* Jean-Christophe FILLIATRE, CNRS & Univ. Paris-sud 11 */
/* Claude MARCHE, INRIA & Univ. Paris-sud 11 */
/* Yannick MOY, Univ. Paris-sud 11 */
/* Romain BARDOU, Univ. Paris-sud 11 */
/* */
/* Secondary contributors: */
/* */
/* Thierry HUBERT, Univ. Paris-sud 11 (former Caduceus front-end) */
/* Nicolas ROUSSET, Univ. Paris-sud 11 (on Jessie & Krakatoa) */
/* Ali AYAD, CNRS & CEA Saclay (floating-point support) */
/* Sylvie BOLDO, INRIA (floating-point support) */
/* Jean-Francois COUCHOT, INRIA (sort encodings, hyps pruning) */
/* Mehdi DOGGUY, Univ. Paris-sud 11 (Why GUI) */
/* */
/* This software is free software; you can redistribute it and/or */
/* modify it under the terms of the GNU Lesser General Public */
/* License version 2.1, with the special exception on linking */
/* described in file LICENSE. */
/* */
/* This software is distributed in the hope that it will be useful, */
/* but WITHOUT ANY WARRANTY; without even the implied warranty of */
/* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. */
/* */
/**************************************************************************/
//@+ CheckArithOverflow = no
/*@ lemma distr_right:
@ \forall integer x y z; x*(y+z) == (x*y)+(x*z);
@*/
/*@ lemma distr_left:
@ \forall integer x y z; (x+y)*z == (x*z)+(y*z);
@*/
/*@ lemma distr_right2:
@ \forall integer x y z; x*(y-z) == (x*y)-(x*z);
@*/
/*@ lemma distr_left2:
@ \forall integer x y z; (x-y)*z == (x*z)-(y*z);
@*/
public class Cube {
/*@ requires x > 0;
@ ensures \result == x * x * x;
@*/
public static int cube(int x) {
int a = 1;
int b = 0;
int c = x;
int z = 0;
/*@ loop_invariant
@ 0 <= c &&
@ a == 3*(x-c) + 1 &&
@ b == 3*(x-c)*(x-c) &&
@ z == (x-c)*(x-c)*(x-c);
@ loop_variant c;
@*/
while (c > 0) {
z += a + b;
b += 2*a + 1;
a += 3;
c--;
}
return z;
}
}
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