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

// the number of bits 1 in x
//@ logic int nbits(int x)

//@ axiom nbits_nonneg : \forall int x; nbits(x) >= 0

//@ axiom nbits_zero : nbits(0) == 0

/*@ axiom lowest_bit_zero :
  @   \forall int x; (x&-x) == 0 <=> x == 0
  @*/

/*@ axiom remove_one_bit :
  @    \forall int x; 
  @       x != 0 => nbits(x - (x&-x)) == nbits(x) - 1
  @*/

/*@ ensures \result == nbits(x) */
int count_bits(int x) {
  int d, c;
  /*@ invariant c + nbits(x) == nbits(\at(x,init))
    @ variant   nbits(x)
    @*/
  for (c = 0; d = x&-x; x -= d) c++;
  return c;
}

/*
Local Variables: 
compile-command: "make count_bits.gui"
End: 
*/
