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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. */
/* */
/**************************************************************************/
// RUNSIMPLIFY: will ask regtests to run Simplify on this program
#pragma JessieIntegerModel(math)
#include "sorting.h"
/*@ requires \valid(t+i) && \valid(t+j);
@ assigns t[i],t[j];
@ ensures Swap{Old,Here}(t,i,j);
@*/
void swap(int t[], int i, int j) {
int tmp = t[i];
t[i] = t[j];
t[j] = tmp;
}
// quick_rec sorts t[l..r]
/*@ requires \valid_range(t,l,r);
@ decreases r-l;
@ assigns t[l..r];
@ behavior sorted:
@ ensures Sorted(t,l,r+1);
@ behavior permutation:
@ ensures Permut{Old,Here}(t,l,r);
@*/
void quick_rec(int t[], int l, int r) {
int v,m,i;
if (l >= r) return;
v = t[l];
m = l;
/*@ loop invariant
@ \forall integer j; l < j <= m ==> t[j] < v;
@ loop invariant
@ \forall integer j; m < j < i ==> t[j] >= v;
@ loop invariant
@ Permut{Pre,Here}(t,l,r);
@ loop invariant t[l] == v && l <= m < i <= r+1;
@ loop variant r-i;
@*/
for (i = l + 1; i <= r; i++) {
if (t[i] < v) {
L1:
swap(t,i,++m);
//@ assert Permut{L1,Here}(t,l,r);
}
}
//@ assert l <= m <= r;
L: swap(t,l,m);
//@ assert Permut{L,Here}(t,l,r);
quick_rec(t,l,m-1);
quick_rec(t,m+1,r);
}
/*@ requires \valid_range(t,0,n-1);
@ behavior sorted:
@ ensures Sorted(t,0,n);
@ behavior permutation:
@ ensures Permut{Old,Here}(t,0,n-1);
@*/
void quick_sort(int t[], int n) {
quick_rec(t,0,n-1);
}
/*
Local Variables:
compile-command: "make quick_sort.why3ml"
End:
*/
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