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/**************************************************************************/
/* */
/* The Why platform for program certification */
/* Copyright (C) 2002-2008 */
/* Romain BARDOU */
/* Jean-Franois COUCHOT */
/* Mehdi DOGGUY */
/* Jean-Christophe FILLITRE */
/* Thierry HUBERT */
/* Claude MARCH */
/* Yannick MOY */
/* Christine PAULIN */
/* Yann RGIS-GIANAS */
/* Nicolas ROUSSET */
/* Xavier URBAIN */
/* */
/* This software is free software; you can redistribute it and/or */
/* modify it under the terms of the GNU General Public */
/* License version 2, as published by the Free Software Foundation. */
/* */
/* 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. */
/* */
/* See the GNU General Public License version 2 for more details */
/* (enclosed in the file GPL). */
/* */
/**************************************************************************/
/*@ axiom mean_1 : \forall int x, int y; x <= y => x <= (x+y)/2 <= y */
/* binary_search(t,n,v) search for element v in array t
between index 0 and n-1
array t is assumed sorted in increasing order
returns an index i between 0 and n-1 where t[i] equals v,
or -1 if no element of t is equal to v
*/
/*@ requires
@ n >= 0 && \valid_range(t,0,n-1) &&
@ \forall int k1, int k2; 0 <= k1 <= k2 <= n-1 => t[k1] <= t[k2]
@ ensures
@ (\result >= 0 && t[\result] == v) ||
@ (\result == -1 && \forall int k; 0 <= k < n => t[k] != v)
@*/
int binary_search(int* t, int n, int v) {
int l = 0, u = n-1;
/*@ invariant
@ 0 <= l && u <= n-1 &&
@ \forall int k; 0 <= k < n => t[k] == v => l <= k <= u
@ variant u-l
@*/
while (l <= u ) {
int m = (l + u) / 2;
if (t[m] < v) l = m + 1;
else if (t[m] > v) u = m - 1;
else return m;
}
return -1;
}
/*
Local Variables:
compile-command: "make binary_search.overflows"
End:
*/
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