/* x <= y */

static int fd_le_filter(fd_constraint this)
{
  fd_int x, y;

  x = VAR(this, 0);
  y = VAR(this, 1);

#ifndef DISABLE_ENTAILED
  if (_fd_var_max(x) <= _fd_var_min(y))
    {
      fd__constraint_set_entailed(this);

      return FD_OK;
    }
#endif

  if (_fd_var_del_lt(_fd_var_min(x), y))
    {
      if (fd_domain_empty(y))
	return FD_NOSOLUTION;

      _fd_revise_connected(this, y);
    }

  if (_fd_var_del_gt(_fd_var_max(y), x))
    {
      if (fd_domain_empty(x))
	return FD_NOSOLUTION;

      _fd_revise_connected(this, x);
    }

#ifndef DISABLE_ENTAILED
  if (_fd_var_max(x) <= _fd_var_min(y))
    fd__constraint_set_entailed(this);
#endif

  return FD_OK;
}

static int fd_le_propagate2(fd_constraint this, fd_int culprit)
{
  fd_int x, y;
  int vmax, vmin;
  fd_int revise;
  int changed = 0;

  x = VAR(this, 0);
  y = VAR(this, 1);

#ifndef DISABLE_ENTAILED
  vmax = _fd_var_max(x);
  vmin = _fd_var_min(y);

  if (vmax <= vmin)
    {
      fd__constraint_set_entailed(this);

      return FD_OK;
    }
#endif

  if (culprit == x)
    {
      revise = y;

      vmin = _fd_var_min(x);

      changed = _fd_var_del_lt(vmin, y);
    }
  else
    {
      revise = x;

      vmax = _fd_var_max(y);

      changed = _fd_var_del_gt(vmax, x);
    }

  if (changed)
    {
      if (fd_domain_empty(revise))
	return FD_NOSOLUTION;

      _fd_revise_connected(this, revise);

#ifndef DISABLE_ENTAILED
      // see if the culprit's domain is a singleton
      if (vmin == vmax)
	fd__constraint_set_entailed(this);
#endif
    }

  return FD_OK;
}

static int fd_le_propagate(fd_constraint this, fd_int revise)
{
  int changed = 0;

  if (revise == VAR(this, 0))
    changed = _fd_var_del_gt(_fd_var_max(VAR(this, 1)), revise);
  else
    changed = _fd_var_del_lt(_fd_var_min(VAR(this, 0)), revise);

  if (changed && fd_domain_empty(revise))
    return FD_NOSOLUTION;

#ifdef USE_ENTAILED
  if (_fd_var_max(VAR(this, 0)) <= _fd_var_min(VAR(this, 1)))
    fd__constraint_set_entailed(this);
#endif

  // XXX: enqueue further updates here?
  if (changed)
    _fd_revise_connected(this, revise);

  return FD_OK;
}

fd_constraint fd_le(fd_int x, fd_int y)
{
  fd_constraint c = fd__constraint_new(2, 0);

  if (c)
    {
      c->variables[0] = FD_INT2C_VAR(x); c->variables[1] = FD_INT2C_VAR(y);

      c->kind = FD_CONSTR_LE;

      _fd_var_add_constraint(x, c);
      _fd_var_add_constraint(y, c);

      _fd_add_constraint(c);
    }

  return c;
}