/**************************************************************************/
/*                                                                        */
/*  The Why platform for program certification                            */
/*                                                                        */
/*  Copyright (C) 2002-2014                                               */
/*                                                                        */
/*    Jean-Christophe FILLIATRE, CNRS & Univ. Paris-sud                   */
/*    Claude MARCHE, INRIA & Univ. Paris-sud                              */
/*    Yannick MOY, Univ. Paris-sud                                        */
/*    Romain BARDOU, Univ. Paris-sud                                      */
/*                                                                        */
/*  Secondary contributors:                                               */
/*                                                                        */
/*    Thierry HUBERT, Univ. Paris-sud  (former Caduceus front-end)        */
/*    Nicolas ROUSSET, Univ. Paris-sud (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    (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 this tells regtests to run Simplify in this example

//@ lemma mean: \forall integer x, y; x <= y ==> x <= (x+y)/2 <= y;

/*@ predicate sorted{L}(long *t, integer a, integer b) =
  @    \forall integer i,j; a <= i <= j <= b ==> t[i] <= t[j];
  @*/

/*@ requires n >= 0 && \valid(t+(0..n-1));
  @ ensures -1 <= \result < n;
  @ behavior success:
  @   ensures \result >= 0 ==> t[\result] == v;
  @ behavior failure:
  @   assumes sorted(t,0,n-1);
  @   ensures \result == -1 ==>
  @     \forall integer k; 0 <= k < n ==> t[k] != v;
  @*/
int binary_search(long t[], int n, long v) {
  int l = 0, u = n-1;
  /*@ loop invariant
    @   0 <= l && u <= n-1;
    @ for failure:
    @   loop invariant
    @   \forall integer k; 0 <= k < n && t[k] == v ==> l <= k <= u;
    @ loop variant u-l;
    @*/
  while (l <= u ) {
    int m = (l + u) / 2;
    //@ assert l <= m <= u;
    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.why3ide"
End:
*/
