/* poly-eq(C, X, y) == min(y) <= sum(C . X) <= max(y) */

static int fd_poly_eq_filter(fd_constraint this)
{

  int ub, lb;
  int min, max;
  int terms = this->nconstants;
  int *mins, *maxs;
  int i;
#ifdef CONSTRAINT_TEMPS
  int *base;

  assert(!fd__constraint_data_valid(this));

  if (!constraint_memory[this->index])
    constraint_memory[this->index] = malloc((2 * terms + 4) * sizeof(int));

  base = constraint_memory[this->index];

  mins = base + 4;
  maxs = mins + terms;
#else
  mins = alloca(terms * sizeof(*mins));
  maxs = alloca(terms * sizeof(*maxs));
#endif

  lb = _fd_var_min(VAR(this, this->nvariables - 1));	// lower bound
  ub = _fd_var_max(VAR(this, this->nvariables - 1));	// upper bound

  // sum the minima and the maxima of the terms
  min = max = 0;

  for (i = 0; i < terms; ++i)
    {
      int vl, vh;

      if (this->constants[i] > 0)
	{
	  vl = mins[i] = _fd_var_min(VAR(this, i));
	  vh = maxs[i] = _fd_var_max(VAR(this, i));
	}
      else
	{
	  vl = maxs[i] = _fd_var_max(VAR(this, i));
	  vh = mins[i] = _fd_var_min(VAR(this, i));
	}

      min += this->constants[i] * vl;
      max += this->constants[i] * vh;
    }

  if (min > ub || max < lb)
    return FD_NOSOLUTION;

  if ((min > lb && _fd_var_del_lt(min, VAR(this, this->nvariables - 1))) |
      (max < ub && _fd_var_del_gt(max, VAR(this, this->nvariables - 1))))
    {

      if (fd_domain_empty(VAR(this, this->nvariables - 1)))

	return FD_NOSOLUTION;

      _fd_revise_connected(this, VAR(this, this->nvariables - 1));
    }

  if (min == max)
    return FD_OK;

  // XXX: poor man's propagation

  if (min == ub)

    for (i = 0; i < terms; ++i)

      {
	int c = this->constants[i];

	if (c && mins[i] != maxs[i])
	  {
	    if (c > 0)
	      {
		_fd_var_del_gt(mins[i], VAR(this, i));

		// check needed for when variables occur twice and

		// with opposite signs

		if (fd_domain_empty(VAR(this, i)))

		  return FD_NOSOLUTION;

		_fd_revise_connected(this, VAR(this, i));
	      }
	    else
	      {

		_fd_var_del_lt(maxs[i], VAR(this, i));

		if (fd_domain_empty(VAR(this, i)))

		  return FD_NOSOLUTION;

		_fd_revise_connected(this, VAR(this, i));

	      }

	  }

      }

  else if (max == lb)
    for (i = 0; i < terms; ++i)
      {

	int c = this->constants[i];

	if (c && mins[i] != maxs[i])
	  {
	    if (c > 0)

	      {

		_fd_var_del_lt(maxs[i], VAR(this, i));

		if (fd_domain_empty(VAR(this, i)))

		  return FD_NOSOLUTION;

		_fd_revise_connected(this, VAR(this, i));
	      }
	    else
	      {
		_fd_var_del_gt(mins[i], VAR(this, i));

		if (fd_domain_empty(VAR(this, i)))
		  return FD_NOSOLUTION;

		_fd_revise_connected(this, VAR(this, i));
	      }
	  }

      }

  else

    {

      if (max > ub)
	for (i = 0; i < terms; ++i)
	  {

	    int c = this->constants[i];

	    int xmin = mins[i];
	    int xmax = maxs[i];

	    if (c > 0)

	      {

		if ((xmax - xmin) * c > ub - min)
		  {
		    // xmax = floor((ub - min) / c) + xmin

		    xmax = (ub - min) / c + xmin;

		    _fd_var_del_gt(xmax, VAR(this, i));

		    if (fd_domain_empty(VAR(this, i)))
		      return FD_NOSOLUTION;

		    _fd_revise_connected(this, VAR(this, i));

		  }

	      }
	    else if (c < 0)
	      {
		if ((xmin - xmax) * c > ub - min)
		  {
		    // xmin = ceil((ub - min) / c) + xmax

		    xmin = (ub - min) / c + xmax;

		    _fd_var_del_lt(xmin, VAR(this, i));

		    if (fd_domain_empty(VAR(this, i)))

		      return FD_NOSOLUTION;

		    _fd_revise_connected(this, VAR(this, i));

		  }

	      }

	  }

      if (min < lb)
	for (i = 0; i < terms; ++i)
	  {
	    int c = this->constants[i];

	    int xmin = mins[i];

	    int xmax = maxs[i];

	    if (c > 0)

	      {

		if ((xmax - xmin) * c > max - lb)
		  {

		    // xmin = ceil((lb - max) / c) + xmax
		    xmin = (lb - max) / c + xmax;

		    _fd_var_del_lt(xmin, VAR(this, i));

		    if (fd_domain_empty(VAR(this, i))) // domains may have holes
		      return FD_NOSOLUTION;

		    _fd_revise_connected(this, VAR(this, i));

		  }
	      }

	    else if (c < 0)

	      {

		if ((xmax - xmin) * c < lb - max)

		  {
		    // xmax = floor((lb - max) / c) + xmin

		    xmax = (lb - max) / c + xmin;

		    _fd_var_del_gt(xmax, VAR(this, i));

		    if (fd_domain_empty(VAR(this, i))) // domains may have holes

		      return FD_NOSOLUTION;

		    _fd_revise_connected(this, VAR(this, i));

		  }
	      }

	  }

    }

#ifdef CONSTRAINT_TEMPS
  // save values

  *base = lb;
  *(base + 1) = ub;
  *(base + 2) = min;
  *(base + 3) = max;

  fd__constraint_remember(this);
#endif

  return FD_OK;
}

static int fd_poly_eq_propagate2(fd_constraint this, fd_int culprit)
{
#ifdef CONSTRAINT_TEMPS
  int ub, lb;
  int min, max;
  int terms = this->nconstants;
  int *mins, *maxs;
  int i;
  int *base;
  int x, c;
  int nmin, nmin_x, nmax, nmax_x;

  if (!fd__constraint_data_valid(this))
    return fd_poly_eq_filter(this);	// ignores culprit

  // bounds filtering

  base = constraint_memory[this->index];

  mins = base + 4;
  maxs = mins + terms;

  lb = *base;
  ub = *(base + 1);

  min = *(base + 2);
  max = *(base + 3);

  if (culprit == VAR(this, this->nvariables - 1))

    {

      // the culprit is the sum variable
      int nlb, nub;

      nlb = _fd_var_min(culprit);
      nub = _fd_var_max(culprit);

      if (nlb == lb && nub == ub)
	return FD_OK;

      if (nlb != lb)
	{
	  if (max < nlb)
	    return FD_NOSOLUTION;

	  if (max == nlb)
	    for (i = 0; i < terms; ++i)
	      {
		if (this->constants[i] > 0)
		  {
		    if (_fd_var_del_lt(maxs[i], VAR(this, i)))
		      {

			if (fd_domain_empty(VAR(this, i)))

			  return FD_NOSOLUTION;

			_fd_revise_connected(this, VAR(this, i));

		      }
		  }

		else if (this->constants[i] < 0)

		  {
		    if (_fd_var_del_gt(mins[i], VAR(this, i)))
		      {
			if (fd_domain_empty(VAR(this, i)))
			  return FD_NOSOLUTION;

			_fd_revise_connected(this, VAR(this, i));
		      }
		  }
	      }

      if (min < nlb)
	for (i = 0; i < terms; ++i)
	  {
	    int c = this->constants[i];
	    int xmin = mins[i];
	    int xmax = maxs[i];

	    if (c > 0)
	      {

		if ((xmax - xmin) * c > max - nlb)

		  {
		    // xmin = ceil((nlb - max) / c) + xmax
		    xmin = (nlb - max) / c + xmax;

		    _fd_var_del_lt(xmin, VAR(this, i));

		    if (fd_domain_empty(VAR(this, i))) // domains may have holes

		      return FD_NOSOLUTION;

		    _fd_revise_connected(this, VAR(this, i));
		  }

	      }

	    else if (c < 0)
	      {

		if ((xmax - xmin) * c < nlb - max)

		  {
		    // xmax = floor((nlb - max) / c) + xmin
		    xmax = (nlb - max) / c + xmin;

		    _fd_var_del_gt(xmax, VAR(this, i));

		    if (fd_domain_empty(VAR(this, i))) // domains may have holes

		      return FD_NOSOLUTION;

		    _fd_revise_connected(this, VAR(this, i));

		  }
	      }
	  }

	  *base = nlb;
	}

      if (nub != ub)

	{

	  if (min > nub)

	    return FD_NOSOLUTION;

	  if (min == nub)
	    for (i = 0; i < terms; ++i)
	      {
		if (this->constants[i] > 0)
		  {

		    if (_fd_var_del_gt(mins[i], VAR(this, i)))
		      {

			if (fd_domain_empty(VAR(this, i)))
			  return FD_NOSOLUTION;

			_fd_revise_connected(this, VAR(this, i));
		      }
		  }
		else if (this->constants[i] < 0)

		  {

		    if (_fd_var_del_lt(maxs[i], VAR(this, i)))
		      {
			if (fd_domain_empty(VAR(this, i)))

			  return FD_NOSOLUTION;

			_fd_revise_connected(this, VAR(this, i));
		      }
		  }
	      }

      if (max > nub)

	for (i = 0; i < terms; ++i)

	  {
	    int c = this->constants[i];

	    int xmin = mins[i];

	    int xmax = maxs[i];

	    if (c > 0)
	      {

		if ((xmax - xmin) * c > nub - min)

		  {
		    // xmax = floor((nub - min) / c) + xmin
		    xmax = (nub - min) / c + xmin;

		    if (_fd_var_del_gt(xmax, VAR(this, i)))

		      {
			if (fd_domain_empty(VAR(this, i)))
			  return FD_NOSOLUTION;

			_fd_revise_connected(this, VAR(this, i));
		      }
		  }

	      }
	    else if (c < 0)
	      {

		if ((xmin - xmax) * c > nub - min)

		  {
		    // xmin = ceil((nub - min) / c) + xmax
		    xmin = (nub - min) / c + xmax;

		    if (_fd_var_del_lt(xmin, VAR(this, i)))
		      {
			if (fd_domain_empty(VAR(this, i)))
			  return FD_NOSOLUTION;

			_fd_revise_connected(this, VAR(this, i));
		      }

		  }

	      }

	  }

	  *(base + 1) = nub;

	}

      return FD_OK;

    }

  // the culprit appears in one of the terms, find out which one(s)
  for (x = 0; culprit != VAR(this, x); ++x)
    ;

  nmin_x = _fd_var_min(VAR(this, x));

  nmax_x = _fd_var_max(VAR(this, x));

  if (nmin_x == mins[x] && nmax_x == maxs[x])

    return FD_OK;

  nmin = min;

  nmax = max;

  do
    {

      c = this->constants[x];

      if (c > 0)
	{

	  nmin = nmin + (nmin_x - mins[x]) * c;
	  nmax = nmax - (maxs[x] - nmax_x) * c;
	}

      else if (c < 0)

	{
	  nmin = nmin - (maxs[x] - nmax_x) * c;
	  nmax = nmax + (nmin_x - mins[x]) * c;

	}

      if (nmin > ub || nmax < lb)
	return FD_NOSOLUTION;

      mins[x] = nmin_x;

      maxs[x] = nmax_x;

      while (++x < terms && culprit != VAR(this, x))
	;

    }

  while (x < terms);

  if ((nmin > lb && _fd_var_del_lt(nmin, VAR(this, this->nvariables - 1))) |
      (nmax < ub && _fd_var_del_gt(nmax, VAR(this, this->nvariables - 1))))

    {

      if (fd_domain_empty(VAR(this, this->nvariables - 1)))

	return FD_NOSOLUTION;

      _fd_revise_connected(this, VAR(this, this->nvariables - 1));
    }

  *(base + 2) = nmin;
  *(base + 3) = nmax;

  return FD_OK;

#else /* CONSTRAINT_TEMPS */
  return fd_poly_eq_filter(this);	// ignores culprit

#endif /* CONSTRAINT_TEMPS */
}

fd_constraint fd_poly_eq(int cs[], fd_int xs[], int nterms, fd_int y)
{
  fd_constraint c = _fd_constraint_new(nterms + 1, nterms);
  int i;

  if (c)
    {
      for (i = 0; i < nterms; ++i)

	c->variables[i] = FD_INT2C_VAR(xs[i]);
      c->variables[nterms] = FD_INT2C_VAR(y);
      for (i = 0; i < nterms; ++i)
	c->constants[i] = cs[i];
#ifdef CONSTRAINT_CLASS
      c->kind = FD_CONSTR_POLY_EQ;
#else /* CONSTRAINT_CLASS */
      c->propagator2 = fd_poly_eq_propagate2;
#endif /* CONSTRAINT_CLASS */

      for (i = 0; i < c->nvariables; ++i)
	_fd_var_add_constraint(VAR(c, i), c);

      _fd_add_constraint(c);
    }

  return c;

}