/* X = Y * Z */

// XXX: assuming non-negative values 

static int fd_var_eq_times_filter(fd_constraint this)
{
  fd_int x, y, z;
  int min_x, max_x, min_y, max_y, min_z, max_z;
  int changed_x, changed_y, changed_z;

  x = VAR(this, 0);
  y = VAR(this, 1);
  z = VAR(this, 2);

  // XXX: just do (a kind of) bounds consistency, for now

  min_x = _fd_var_min(x);
  max_x = _fd_var_max(x);

  min_z = _fd_var_min(z);
  max_z = _fd_var_max(z);

  if (max_z > 0)
    changed_y =  _fd_var_del_lt(min_x / max_z, y);
  if (min_z > 0)
    changed_y |= _fd_var_del_gt(max_x / min_z, y);

  if (changed_y && fd_domain_empty(y))
    {
      return FD_NOSOLUTION;

      _fd_revise_connected(NULL, y);
    }

  min_y = _fd_var_min(y);
  max_y = _fd_var_max(y);

  if (max_y > 0)
    changed_z =  _fd_var_del_lt(min_x / max_y, z);
  if (min_y > 0)
    changed_z |= _fd_var_del_gt(max_x / min_y, z);

  if (changed_z && fd_domain_empty(z))
    {
      return FD_NOSOLUTION;

      _fd_revise_connected(NULL, z);

      min_z = _fd_var_min(z);
      max_z = _fd_var_max(z);
    }

  changed_x =  _fd_var_del_lt(min_y * min_z, x);
  changed_x |= _fd_var_del_gt(max_y * max_z, x);

  if (changed_x && fd_domain_empty(x))
    {
      return FD_NOSOLUTION;

      _fd_revise_connected(NULL, x);
    }

#if CONSTRAINT_TEMPS > 3
  if (fd_var_single(x, 0) && fd_var_single(y, 0) && fd_var_single(z, 0))
    fd__constraint_set_entailed(this);
#endif

  return FD_OK;
}

int fd_var_eq_times_propagate2(fd_constraint this, fd_int culprit)
{
  fd_int x, y, z;
  int min_x, max_x, min_y, max_y, min_z, max_z;
  int changed_x = 0, changed_y = 0, changed_z = 0;

  x = VAR(this, 0);
  y = VAR(this, 1);
  z = VAR(this, 2);

  // XXX: just do bounds consistency, for now

  if (culprit == x)
    {
      min_x = _fd_var_min(x);
      max_x = _fd_var_max(x);

      min_z = _fd_var_min(z);
      max_z = _fd_var_max(z);

      if (max_z > 0)
	changed_y =  _fd_var_del_lt(min_x / max_z, y);
      if (min_z > 0)
	changed_y |= _fd_var_del_gt(max_x / min_z, y);

      if (changed_y && fd_domain_empty(y))
	return FD_NOSOLUTION;

      min_y = _fd_var_min(y);
      max_y = _fd_var_max(y);

      if (max_y > 0)
	changed_z =  _fd_var_del_lt(min_x / max_y, z);
      if (min_y > 0)
	changed_z |= _fd_var_del_gt(max_x / min_y, z);

      if (changed_z && fd_domain_empty(z))
	return FD_NOSOLUTION;
    }
  else if (culprit == y) // culprit == y || culprit == z
    {
      min_y = _fd_var_min(y);
      max_y = _fd_var_max(y);

      min_z = _fd_var_min(z);
      max_z = _fd_var_max(z);

      changed_x =  _fd_var_del_lt(min_y * min_z, x);
      changed_x |= _fd_var_del_gt(max_y * max_z, x);

      if (changed_x && fd_domain_empty(x))
	return FD_NOSOLUTION;

      min_x = _fd_var_min(x);
      max_x = _fd_var_max(x);

      if (max_y > 0)
	changed_z =  _fd_var_del_lt(min_x / max_y, z);
      if (min_y > 0)
	changed_z |= _fd_var_del_gt(max_x / min_y, z);

      if (changed_z && fd_domain_empty(z))
	return FD_NOSOLUTION;
    }
  else // culprit == z
    {
      min_y = _fd_var_min(y);
      max_y = _fd_var_max(y);

      min_z = _fd_var_min(z);
      max_z = _fd_var_max(z);

      changed_x =  _fd_var_del_lt(min_y * min_z, x);
      changed_x |= _fd_var_del_gt(max_y * max_z, x);

      if (changed_x && fd_domain_empty(x))
	return FD_NOSOLUTION;

      min_x = _fd_var_min(x);
      max_x = _fd_var_max(x);

      if (max_z > 0)
	changed_y =  _fd_var_del_lt(min_x / max_z, y);
      if (min_z > 0)
	changed_y |= _fd_var_del_gt(max_x / min_z, y);

      if (changed_y && fd_domain_empty(y))
	return FD_NOSOLUTION;
    }

  if (changed_x)
    _fd_revise_connected(NULL, x);	// XXX: NULL or this?

  if (changed_y)
    _fd_revise_connected(NULL, y);	// XXX: NULL or this?

  if (changed_z)
    _fd_revise_connected(NULL, z);	// XXX: NULL or this?

#if CONSTRAINT_TEMPS > 3
  if (fd_var_single(x, 0) && fd_var_single(y, 0) && fd_var_single(z, 0))
    fd__constraint_set_entailed(this);
#endif

  return FD_OK;
}

fd_constraint fd_var_eq_times(fd_int x, fd_int y, fd_int z)
{
  fd_constraint c = _fd_constraint_new(3, 0);

  if (c)
    {
      c->variables[0] = FD_INT2C_VAR(x);
      c->variables[1] = FD_INT2C_VAR(y);
      c->variables[2] = FD_INT2C_VAR(z);
#ifdef CONSTRAINT_CLASS
      c->kind = FD_CONSTR_VAR_EQ_TIMES;
#else /* CONSTRAINT_CLASS */
      c->propagator2 = fd_var_eq_times_propagate2;
#endif /* CONSTRAINT_CLASS */

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

      _fd_add_constraint(c);
    }

  return c;
}