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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
/*@ predicate Sorted{L}(long a[], integer l, integer h) =
@ \forall integer i; l <= i < h ==> a[i] <= a[i+1] ;
@*/
/*@ predicate Swap{L1,L2}(long a[], integer i, integer j) =
@ \at(a[i],L1) == \at(a[j],L2) &&
@ \at(a[j],L1) == \at(a[i],L2) &&
@ \forall integer k; k != i && k != j ==> \at(a[k],L1) == \at(a[k],L2);
@*/
/*@ axiomatic Permut {
@ predicate Permut{L1,L2}(long a[], integer l, integer h);
@ axiom Permut_refl{L}:
@ \forall long a[], integer l h; Permut{L,L}(a, l, h) ;
@ axiom Permut_sym{L1,L2}:
@ \forall long a[], integer l h;
@ Permut{L1,L2}(a, l, h) ==> Permut{L2,L1}(a, l, h) ;
@ axiom Permut_trans{L1,L2,L3}:
@ \forall long a[], integer l h;
@ Permut{L1,L2}(a, l, h) && Permut{L2,L3}(a, l, h) ==>
@ Permut{L1,L3}(a, l, h) ;
@ axiom Permut_swap{L1,L2}:
@ \forall long a[], integer l h i j;
@ l <= i <= h && l <= j <= h && Swap{L1,L2}(a, i, j) ==>
@ Permut{L1,L2}(a, l, h) ;
@ }
@*/
class Sorting {
/*@ requires t != null &&
@ 0 <= i < t.length && 0 <= j < t.length;
@ assigns t[i],t[j];
@ ensures Swap{Old,Here}(t,i,j);
@*/
static void swap(long t[], int i, int j) {
int tmp = t[i];
t[i] = t[j];
t[j] = tmp;
}
/*@ requires t != null;
@ behavior sorted:
@ ensures Sorted(t,0,t.length-1);
@ behavior permutation:
@ ensures Permut{Old,Here}(t,0,t.length-1);
@*/
static void min_sort(long t[]) {
int i,j, mi;
long mv;
/*@ loop_invariant 0 <= i;
@ for sorted:
@ loop_invariant Sorted(t,0,i) &&
@ (\forall integer k1 k2 ;
@ 0 <= k1 < i <= k2 < t.length ==> t[k1] <= t[k2]) ;
@ for permutation:
@ loop_invariant Permut{Pre,Here}(t,0,t.length-1);
@*/
for (i=0; i<t.length-1; i++) {
// look for minimum value among t[i..n-1]
mv = t[i]; mi = i;
/*@ loop_invariant i < j && i <= mi < t.length;
@ for sorted:
@ loop_invariant mv == t[mi] &&
@ (\forall integer k; i <= k < j ==> t[k] >= mv);
@ for permutation:
@ loop_invariant Permut{Pre,Here}(t,0,t.length-1);
@*/
for (j=i+1; j < t.length; j++) {
if (t[j] < mv) {
mi = j ; mv = t[j];
}
}
swap(t,i,mi);
}
}
/*@ requires t != null;
@ behavior sorted:
@ ensures Sorted(t,0,t.length-1);
@ behavior permutation:
@ ensures Permut{Old,Here}(t,0,t.length-1);
@*/
static void insert_sort(long t[]) {
/* main loop:
* for i from 1 to t.length-1: sorts t[0..i]
*/
/*@ loop_invariant 1 <= i <= t.length;
@ for sorted:
@ loop_invariant Sorted(t,0,i-1);
@ for permutation:
@ loop_invariant Permut{Pre,Here}(t,0,t.length-1);
@*/
for (int i=1; i < t.length; i++) {
// find the right index mi to insert t[i] into t[0..i-1]
int mi = i;
for (int j=i-1; j >= 0; j--) {
if (t[j] < t[i]) mi=j;
}
// we shift the block t[mi..i-1] to the right
long tmp = t[i];
shift_right(t,mi,i);
// and put t[i] at the right index
t[mi] = tmp;
}
}
/* shift_right(t,a,b) moves the block t[a..b-1] to t[a+1..b]
* beware: the old value of t[b] is lost!
*/
/*@ requires t!=null && 0 <= a && b < t.length ;
@ assigns t[a+1..b];
@ ensures \forall integer k;
@ a+1 <= k <= b ==> t[k] == \old(t[k-1]);
@*/
static void shift_right(long t[], int a, int b);
}
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