/**************************************************************************/
/*                                                                        */
/*  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.                  */
/*                                                                        */
/**************************************************************************/

//@+ CheckArithOverflow = yes

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

/* @ lemma mean_property_2 : 
  @   \forall integer x y; x <= y ==> x <= x+(y-x)/2 <= y; 
  @*/

/*@ predicate is_sorted{L}(int[] t) =
  @   t != null && 
  @   \forall integer i j; 
  @     0 <= i && i <= j && j < t.length ==> t[i] <= t[j];
  @*/


class BinarySearch {

    /* binary_search(t,n,v) search for element v in array t 
       between index 0 and n-1
       array t is assumed to be sorted in increasing order
       returns an index i between 0 and n-1 where t[i] equals v, 
       or -1 if no element in t is equal to v  
    */
    
    /*@ requires 
      @   0 <= n <= t.length &&
      @   \forall integer k1 k2; 
      @       0 <= k1 <= k2 <= n-1 ==> t[k1] <= t[k2];
      @ behavior correctness:
      @ ensures
      @   (\result >= 0 && t[\result] == v) ||
      @   (\result == -1 && \forall integer k; 0 <= k < n ==> t[k] != v);
      @*/
    static int binary_search(int t[], int n, int v) {
	int l = 0, u = n-1;
	/*@ loop_invariant 
	  @   0 <= l && u <= n-1 && 
	  @   \forall integer k; 0 <= k < n ==> t[k] == v ==> l <= k <= u;
	  @ loop_variant 
	  @   u-l ;
	  @*/
	while (l <= u ) {
	    int m = l + (u - l) / 2;
	    if (t[m] < v) l = m + 1;
	    else if (t[m] > v) u = m - 1;
	    else return m; 
	}
	return -1;
    }

    /* idiomatic code, using t.length instead of n as argument */

    /*@ requires t != null;
      @ ensures -1 <= \result < t.length; 
      @ behavior success:
      @   ensures \result >= 0 ==> t[\result] == v;
      @ behavior failure:
      @  assumes 
      @    \forall integer k1 k2; 
      @       0 <= k1 <= k2 <= t.length-1 ==> t[k1] <= t[k2];
      @  ensures \result == -1 ==>
      @     \forall integer k; 0 <= k < t.length ==> t[k] != v;
      @*/
    static int binary_search2(int t[], int v) {
	int l = 0, u = t.length - 1;
	/*@ loop_invariant 
	  @   0 <= l && u <= t.length - 1;
	  @ for failure: 
	  @  loop_invariant 
	  @    \forall integer k; 0 <= k < t.length ==> t[k] == v ==> l <= k <= u;
	  @ loop_variant 
	  @   u-l ;
	  @*/
	while (l <= u ) {
	    int m = l + (u - l) / 2;
	    if (t[m] < v) l = m + 1;
	    else if (t[m] > v) u = m - 1;
	    else return m; 
	}
	return -1;
    }

    /* search in a field */

    public int t[];
    // pb with recursive def of type and logic in Jessie
    // @ invariant t_is_sorted: is_sorted(t);
    
    /*@	requires t != null && t.length <= 2147483647 && is_sorted(t);
      @ behavior search_success:
      @   ensures
      @   \result >= 0 ==> t[\result] == v;
      @ behavior search_failure:
      @   ensures \result < 0 ==> (\forall integer k; 
      @     0 <= k < t.length ==> t[k] != v);
      @*/
    public int binary_search3(int v) {
	int l = 0, u = t.length-1;
	/*@ loop_invariant 
	  @   0 <= l && u <= t.length-1 && 
	  @   \forall integer k; 
	  @     0 <= k < t.length && t[k] == v ==> l <= k <= u;
	  @ loop_variant u-l ;
	  @*/
	while (l <= u ) {
	    int m = l + (u-l) / 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 BinarySearch"
End: 
*/
