Exemplo n.º 1
0
static int qpolynomial_bound_on_domain_range(__isl_take isl_basic_set *bset,
	__isl_take isl_qpolynomial *poly, struct range_data *data)
{
	unsigned nparam = isl_basic_set_dim(bset, isl_dim_param);
	unsigned nvar = isl_basic_set_dim(bset, isl_dim_set);
	isl_set *set = NULL;

	if (!bset)
		goto error;

	if (nvar == 0)
		return add_guarded_poly(bset, poly, data);

	set = isl_set_from_basic_set(bset);
	set = isl_set_split_dims(set, isl_dim_param, 0, nparam);
	set = isl_set_split_dims(set, isl_dim_set, 0, nvar);

	data->poly = poly;

	data->test_monotonicity = 1;
	if (isl_set_foreach_basic_set(set, &basic_guarded_poly_bound, data) < 0)
		goto error;

	isl_set_free(set);
	isl_qpolynomial_free(poly);

	return 0;
error:
	isl_set_free(set);
	isl_qpolynomial_free(poly);
	return -1;
}
Exemplo n.º 2
0
static isl_stat basic_guarded_poly_bound(__isl_take isl_basic_set *bset,
	void *user)
{
	struct range_data *data = (struct range_data *)user;
	isl_ctx *ctx;
	unsigned nparam = isl_basic_set_dim(bset, isl_dim_param);
	unsigned dim = isl_basic_set_dim(bset, isl_dim_set);
	isl_stat r;

	data->signs = NULL;

	ctx = isl_basic_set_get_ctx(bset);
	data->signs = isl_alloc_array(ctx, int,
					isl_basic_set_dim(bset, isl_dim_all));

	if (isl_basic_set_dims_get_sign(bset, isl_dim_set, 0, dim,
					data->signs + nparam) < 0)
		goto error;
	if (isl_basic_set_dims_get_sign(bset, isl_dim_param, 0, nparam,
					data->signs) < 0)
		goto error;

	r = propagate_on_domain(bset, isl_qpolynomial_copy(data->poly), data);

	free(data->signs);

	return r;
error:
	free(data->signs);
	isl_basic_set_free(bset);
	return isl_stat_error;
}
Exemplo n.º 3
0
/* Given a lower and upper bound on the final variable and constraints
 * on the remaining variables where these bounds are active,
 * eliminate the variable from data->poly based on these bounds.
 * If the polynomial has been determined to be monotonic
 * in the variable, then simply plug in the appropriate bound.
 * If the current polynomial is tight and if this bound is integer,
 * then the result is still tight.  In all other cases, the results
 * may not be tight.
 * Otherwise, plug in the largest bound (in absolute value) in
 * the positive terms (if an upper bound is wanted) or the negative terms
 * (if a lower bounded is wanted) and the other bound in the other terms.
 *
 * If all variables have been eliminated, then record the result.
 * Ohterwise, recurse on the next variable.
 */
static isl_stat propagate_on_bound_pair(__isl_take isl_constraint *lower,
	__isl_take isl_constraint *upper, __isl_take isl_basic_set *bset,
	void *user)
{
	struct range_data *data = (struct range_data *)user;
	int save_tight = data->tight;
	isl_qpolynomial *poly;
	isl_stat r;
	unsigned nvar;

	nvar = isl_basic_set_dim(bset, isl_dim_set);

	if (data->monotonicity) {
		isl_qpolynomial *sub;
		isl_space *dim = isl_qpolynomial_get_domain_space(data->poly);
		if (data->monotonicity * data->sign > 0) {
			if (data->tight)
				data->tight = bound_is_integer(upper, nvar);
			sub = bound2poly(upper, dim, nvar, 1);
			isl_constraint_free(lower);
		} else {
			if (data->tight)
				data->tight = bound_is_integer(lower, nvar);
			sub = bound2poly(lower, dim, nvar, -1);
			isl_constraint_free(upper);
		}
		poly = isl_qpolynomial_copy(data->poly);
		poly = plug_in_at_pos(poly, nvar, sub, data);
		poly = isl_qpolynomial_drop_dims(poly, isl_dim_in, nvar, 1);
	} else {
		isl_qpolynomial *l, *u;
		isl_qpolynomial *pos, *neg;
		isl_space *dim = isl_qpolynomial_get_domain_space(data->poly);
		unsigned nparam = isl_basic_set_dim(bset, isl_dim_param);
		int sign = data->sign * data->signs[nparam + nvar];

		data->tight = 0;

		u = bound2poly(upper, isl_space_copy(dim), nvar, 1);
		l = bound2poly(lower, dim, nvar, -1);

		pos = isl_qpolynomial_terms_of_sign(data->poly, data->signs, sign);
		neg = isl_qpolynomial_terms_of_sign(data->poly, data->signs, -sign);

		pos = plug_in_at_pos(pos, nvar, u, data);
		neg = plug_in_at_pos(neg, nvar, l, data);

		poly = isl_qpolynomial_add(pos, neg);
		poly = isl_qpolynomial_drop_dims(poly, isl_dim_in, nvar, 1);
	}

	if (isl_basic_set_dim(bset, isl_dim_set) == 0)
		r = add_guarded_poly(bset, poly, data);
	else
		r = propagate_on_domain(bset, poly, data);

	data->tight = save_tight;

	return r;
}
Exemplo n.º 4
0
/* Construct a parameter compression for "bset".
 * We basically just call isl_mat_parameter_compression with the right input
 * and then extend the resulting matrix to include the variables.
 *
 * Let the equalities be given as
 *
 *	B(p) + A x = 0
 *
 * and let [H 0] be the Hermite Normal Form of A, then
 *
 *	H^-1 B(p)
 *
 * needs to be integer, so we impose that each row is divisible by
 * the denominator.
 */
__isl_give isl_morph *isl_basic_set_parameter_compression(
	__isl_keep isl_basic_set *bset)
{
	unsigned nparam;
	unsigned nvar;
	int n_eq;
	isl_mat *H, *B;
	isl_vec *d;
	isl_mat *map, *inv;
	isl_basic_set *dom, *ran;

	if (!bset)
		return NULL;

	if (isl_basic_set_plain_is_empty(bset))
		return isl_morph_empty(bset);
	if (bset->n_eq == 0)
		return isl_morph_identity(bset);

	isl_assert(bset->ctx, bset->n_div == 0, return NULL);

	n_eq = bset->n_eq;
	nparam = isl_basic_set_dim(bset, isl_dim_param);
	nvar = isl_basic_set_dim(bset, isl_dim_set);

	isl_assert(bset->ctx, n_eq <= nvar, return NULL);

	d = isl_vec_alloc(bset->ctx, n_eq);
	B = isl_mat_sub_alloc6(bset->ctx, bset->eq, 0, n_eq, 0, 1 + nparam);
	H = isl_mat_sub_alloc6(bset->ctx, bset->eq, 0, n_eq, 1 + nparam, nvar);
	H = isl_mat_left_hermite(H, 0, NULL, NULL);
	H = isl_mat_drop_cols(H, n_eq, nvar - n_eq);
	H = isl_mat_lin_to_aff(H);
	H = isl_mat_right_inverse(H);
	if (!H || !d)
		goto error;
	isl_seq_set(d->el, H->row[0][0], d->size);
	H = isl_mat_drop_rows(H, 0, 1);
	H = isl_mat_drop_cols(H, 0, 1);
	B = isl_mat_product(H, B);
	inv = isl_mat_parameter_compression(B, d);
	inv = isl_mat_diagonal(inv, isl_mat_identity(bset->ctx, nvar));
	map = isl_mat_right_inverse(isl_mat_copy(inv));

	dom = isl_basic_set_universe(isl_space_copy(bset->dim));
	ran = isl_basic_set_universe(isl_space_copy(bset->dim));

	return isl_morph_alloc(dom, ran, map, inv);
error:
	isl_mat_free(H);
	isl_mat_free(B);
	isl_vec_free(d);
	return NULL;
}
Exemplo n.º 5
0
int cloog_constraint_set_contains_level(CloogConstraintSet *constraints,
			int level, int nb_parameters)
{
	isl_basic_set *bset;
	bset = cloog_constraints_set_to_isl(constraints);
	return isl_basic_set_dim(bset, isl_dim_set) >= level;
}
Exemplo n.º 6
0
static __isl_give isl_mat *isl_basic_set_scan_samples(
	__isl_take isl_basic_set *bset)
{
	isl_ctx *ctx;
	isl_size dim;
	struct scan_samples ss;

	ctx = isl_basic_set_get_ctx(bset);
	dim = isl_basic_set_dim(bset, isl_dim_all);
	if (dim < 0)
		goto error;
	ss.callback.add = scan_samples_add_sample;
	ss.samples = isl_mat_alloc(ctx, 0, 1 + dim);
	if (!ss.samples)
		goto error;

	if (isl_basic_set_scan(bset, &ss.callback) < 0) {
		isl_mat_free(ss.samples);
		return NULL;
	}

	return ss.samples;
error:
	isl_basic_set_free(bset);
	return NULL;
}
Exemplo n.º 7
0
/* Return an isl_basic_set representation of the equality stored
 * at position i in the given CloogEqualities.
 */
static __isl_give isl_basic_set *equality_to_basic_set(CloogEqualities *equal,
	int i)
{
	isl_constraint *c;
	isl_basic_set *bset;
	unsigned nparam;
	unsigned nvar;

	c = isl_constraint_copy(equal->constraints[i]);
	bset = isl_basic_set_from_constraint(c);
	nparam = isl_basic_set_dim(bset, isl_dim_param);
	nvar = isl_basic_set_dim(bset, isl_dim_set);
	bset = isl_basic_set_add(bset, isl_dim_set,
				      equal->total_dim - (nparam + nvar));
	return bset;
}
Exemplo n.º 8
0
unsigned isl_morph_dom_dim(__isl_keep isl_morph *morph, enum isl_dim_type type)
{
	if (!morph)
		return 0;

	return isl_basic_set_dim(morph->dom, type);
}
Exemplo n.º 9
0
/* Check whether the polynomial "poly" has sign "sign" over "bset",
 * i.e., if sign == 1, check that the lower bound on the polynomial
 * is non-negative and if sign == -1, check that the upper bound on
 * the polynomial is non-positive.
 */
static int has_sign(__isl_keep isl_basic_set *bset,
	__isl_keep isl_qpolynomial *poly, int sign, int *signs)
{
	struct range_data data_m;
	unsigned nparam;
	isl_space *dim;
	isl_val *opt;
	int r;
	enum isl_fold type;

	nparam = isl_basic_set_dim(bset, isl_dim_param);

	bset = isl_basic_set_copy(bset);
	poly = isl_qpolynomial_copy(poly);

	bset = isl_basic_set_move_dims(bset, isl_dim_set, 0,
					isl_dim_param, 0, nparam);
	poly = isl_qpolynomial_move_dims(poly, isl_dim_in, 0,
					isl_dim_param, 0, nparam);

	dim = isl_qpolynomial_get_space(poly);
	dim = isl_space_params(dim);
	dim = isl_space_from_domain(dim);
	dim = isl_space_add_dims(dim, isl_dim_out, 1);

	data_m.test_monotonicity = 0;
	data_m.signs = signs;
	data_m.sign = -sign;
	type = data_m.sign < 0 ? isl_fold_min : isl_fold_max;
	data_m.pwf = isl_pw_qpolynomial_fold_zero(dim, type);
	data_m.tight = 0;
	data_m.pwf_tight = NULL;

	if (propagate_on_domain(bset, poly, &data_m) < 0)
		goto error;

	if (sign > 0)
		opt = isl_pw_qpolynomial_fold_min(data_m.pwf);
	else
		opt = isl_pw_qpolynomial_fold_max(data_m.pwf);

	if (!opt)
		r = -1;
	else if (isl_val_is_nan(opt) ||
		 isl_val_is_infty(opt) ||
		 isl_val_is_neginfty(opt))
		r = 0;
	else
		r = sign * isl_val_sgn(opt) >= 0;

	isl_val_free(opt);

	return r;
error:
	isl_pw_qpolynomial_fold_free(data_m.pwf);
	return -1;
}
Exemplo n.º 10
0
/* Project range of morph onto its parameter domain.
 */
__isl_give isl_morph *isl_morph_ran_params(__isl_take isl_morph *morph)
{
	unsigned n;

	if (!morph)
		return NULL;
	n = isl_basic_set_dim(morph->ran, isl_dim_set);
	morph = isl_morph_remove_ran_dims(morph, isl_dim_set, 0, n);
	if (!morph)
		return NULL;
	morph->ran = isl_basic_set_params(morph->ran);
	if (morph->ran)
		return morph;

	isl_morph_free(morph);
	return NULL;
}
Exemplo n.º 11
0
/* Recursively perform range propagation on the polynomial "poly"
 * defined over the basic set "bset" and collect the results in "data".
 */
static isl_stat propagate_on_domain(__isl_take isl_basic_set *bset,
	__isl_take isl_qpolynomial *poly, struct range_data *data)
{
	isl_ctx *ctx;
	isl_qpolynomial *save_poly = data->poly;
	int save_monotonicity = data->monotonicity;
	unsigned d;

	if (!bset || !poly)
		goto error;

	ctx = isl_basic_set_get_ctx(bset);
	d = isl_basic_set_dim(bset, isl_dim_set);
	isl_assert(ctx, d >= 1, goto error);

	if (isl_qpolynomial_is_cst(poly, NULL, NULL)) {
		bset = isl_basic_set_project_out(bset, isl_dim_set, 0, d);
		poly = isl_qpolynomial_drop_dims(poly, isl_dim_in, 0, d);
		return add_guarded_poly(bset, poly, data);
	}

	if (data->test_monotonicity)
		data->monotonicity = monotonicity(bset, poly, data);
	else
		data->monotonicity = 0;
	if (data->monotonicity < -1)
		goto error;

	data->poly = poly;
	if (isl_basic_set_foreach_bound_pair(bset, isl_dim_set, d - 1,
					    &propagate_on_bound_pair, data) < 0)
		goto error;

	isl_basic_set_free(bset);
	isl_qpolynomial_free(poly);
	data->monotonicity = save_monotonicity;
	data->poly = save_poly;

	return isl_stat_ok;
error:
	isl_basic_set_free(bset);
	isl_qpolynomial_free(poly);
	data->monotonicity = save_monotonicity;
	data->poly = save_poly;
	return isl_stat_error;
}
Exemplo n.º 12
0
/* Return  1 if poly is monotonically increasing in the last set variable,
 *        -1 if poly is monotonically decreasing in the last set variable,
 *	   0 if no conclusion,
 *	  -2 on error.
 *
 * We simply check the sign of p(x+1)-p(x)
 */
static int monotonicity(__isl_keep isl_basic_set *bset,
	__isl_keep isl_qpolynomial *poly, struct range_data *data)
{
	isl_ctx *ctx;
	isl_space *dim;
	isl_qpolynomial *sub = NULL;
	isl_qpolynomial *diff = NULL;
	int result = 0;
	int s;
	unsigned nvar;

	ctx = isl_qpolynomial_get_ctx(poly);
	dim = isl_qpolynomial_get_domain_space(poly);

	nvar = isl_basic_set_dim(bset, isl_dim_set);

	sub = isl_qpolynomial_var_on_domain(isl_space_copy(dim), isl_dim_set, nvar - 1);
	sub = isl_qpolynomial_add(sub,
		isl_qpolynomial_rat_cst_on_domain(dim, ctx->one, ctx->one));

	diff = isl_qpolynomial_substitute(isl_qpolynomial_copy(poly),
			isl_dim_in, nvar - 1, 1, &sub);
	diff = isl_qpolynomial_sub(diff, isl_qpolynomial_copy(poly));

	s = has_sign(bset, diff, 1, data->signs);
	if (s < 0)
		goto error;
	if (s)
		result = 1;
	else {
		s = has_sign(bset, diff, -1, data->signs);
		if (s < 0)
			goto error;
		if (s)
			result = -1;
	}

	isl_qpolynomial_free(diff);
	isl_qpolynomial_free(sub);

	return result;
error:
	isl_qpolynomial_free(diff);
	isl_qpolynomial_free(sub);
	return -2;
}
Exemplo n.º 13
0
static struct cloog_isl_dim basic_set_cloog_dim_to_isl_dim(
	__isl_keep isl_basic_set *bset, int pos)
{
	enum isl_dim_type types[] = { isl_dim_set, isl_dim_div, isl_dim_param };
	int i;
	struct cloog_isl_dim ci_dim;

	for (i = 0; i < 3; ++i) {
		unsigned dim = isl_basic_set_dim(bset, types[i]);
		if (pos < dim) {
			ci_dim.type = types[i];
			ci_dim.pos = pos;
			return ci_dim;
		}
		pos -= dim;
	}
	assert(0);
}
Exemplo n.º 14
0
/* Update "enforced" such that it only involves constraints that are
 * also enforced by "graft".
 */
static __isl_give isl_basic_set *update_enforced(
	__isl_take isl_basic_set *enforced, __isl_keep isl_ast_graft *graft,
	int depth)
{
	isl_basic_set *enforced_g;

	enforced_g = isl_ast_graft_get_enforced(graft);
	if (depth < isl_basic_set_dim(enforced_g, isl_dim_set))
		enforced_g = isl_basic_set_eliminate(enforced_g,
							isl_dim_set, depth, 1);
	enforced_g = isl_basic_set_remove_unknown_divs(enforced_g);
	enforced_g = isl_basic_set_align_params(enforced_g,
				isl_basic_set_get_space(enforced));
	enforced = isl_basic_set_align_params(enforced,
				isl_basic_set_get_space(enforced_g));
	enforced = isl_set_simple_hull(isl_basic_set_union(enforced,
						enforced_g));

	return enforced;
}
Exemplo n.º 15
0
int cloog_constraint_set_n_iterators(CloogConstraintSet *constraints, int n_par)
{
	isl_basic_set *bset;
	bset = cloog_constraints_set_to_isl(constraints);
	return isl_basic_set_dim(bset, isl_dim_set);
}
Exemplo n.º 16
0
/* Given a basic set, exploit the equalties in the a basic set to construct
 * a morphishm that maps the basic set to a lower-dimensional space.
 * Specifically, the morphism reduces the number of dimensions of type "type".
 *
 * This function is a slight generalization of isl_mat_variable_compression
 * in that it allows the input to be parametric and that it allows for the
 * compression of either parameters or set variables.
 *
 * We first select the equalities of interest, that is those that involve
 * variables of type "type" and no later variables.
 * Denote those equalities as
 *
 *		-C(p) + M x = 0
 *
 * where C(p) depends on the parameters if type == isl_dim_set and
 * is a constant if type == isl_dim_param.
 *
 * First compute the (left) Hermite normal form of M,
 *
 *		M [U1 U2] = M U = H = [H1 0]
 * or
 *		              M = H Q = [H1 0] [Q1]
 *                                             [Q2]
 *
 * with U, Q unimodular, Q = U^{-1} (and H lower triangular).
 * Define the transformed variables as
 *
 *		x = [U1 U2] [ x1' ] = [U1 U2] [Q1] x
 *		            [ x2' ]           [Q2]
 *
 * The equalities then become
 *
 *		-C(p) + H1 x1' = 0   or   x1' = H1^{-1} C(p) = C'(p)
 *
 * If the denominator of the constant term does not divide the
 * the common denominator of the parametric terms, then every
 * integer point is mapped to a non-integer point and then the original set has no
 * integer solutions (since the x' are a unimodular transformation
 * of the x).  In this case, an empty morphism is returned.
 * Otherwise, the transformation is given by
 *
 *		x = U1 H1^{-1} C(p) + U2 x2'
 *
 * The inverse transformation is simply
 *
 *		x2' = Q2 x
 *
 * Both matrices are extended to map the full original space to the full
 * compressed space.
 */
__isl_give isl_morph *isl_basic_set_variable_compression(
	__isl_keep isl_basic_set *bset, enum isl_dim_type type)
{
	unsigned otype;
	unsigned ntype;
	unsigned orest;
	unsigned nrest;
	int f_eq, n_eq;
	isl_space *dim;
	isl_mat *H, *U, *Q, *C = NULL, *H1, *U1, *U2;
	isl_basic_set *dom, *ran;

	if (!bset)
		return NULL;

	if (isl_basic_set_plain_is_empty(bset))
		return isl_morph_empty(bset);

	isl_assert(bset->ctx, bset->n_div == 0, return NULL);

	otype = 1 + isl_space_offset(bset->dim, type);
	ntype = isl_basic_set_dim(bset, type);
	orest = otype + ntype;
	nrest = isl_basic_set_total_dim(bset) - (orest - 1);

	for (f_eq = 0; f_eq < bset->n_eq; ++f_eq)
		if (isl_seq_first_non_zero(bset->eq[f_eq] + orest, nrest) == -1)
			break;
	for (n_eq = 0; f_eq + n_eq < bset->n_eq; ++n_eq)
		if (isl_seq_first_non_zero(bset->eq[f_eq + n_eq] + otype, ntype) == -1)
			break;
	if (n_eq == 0)
		return isl_morph_identity(bset);

	H = isl_mat_sub_alloc6(bset->ctx, bset->eq, f_eq, n_eq, otype, ntype);
	H = isl_mat_left_hermite(H, 0, &U, &Q);
	if (!H || !U || !Q)
		goto error;
	Q = isl_mat_drop_rows(Q, 0, n_eq);
	Q = isl_mat_diagonal(isl_mat_identity(bset->ctx, otype), Q);
	Q = isl_mat_diagonal(Q, isl_mat_identity(bset->ctx, nrest));
	C = isl_mat_alloc(bset->ctx, 1 + n_eq, otype);
	if (!C)
		goto error;
	isl_int_set_si(C->row[0][0], 1);
	isl_seq_clr(C->row[0] + 1, otype - 1);
	isl_mat_sub_neg(C->ctx, C->row + 1, bset->eq + f_eq, n_eq, 0, 0, otype);
	H1 = isl_mat_sub_alloc(H, 0, H->n_row, 0, H->n_row);
	H1 = isl_mat_lin_to_aff(H1);
	C = isl_mat_inverse_product(H1, C);
	if (!C)
		goto error;
	isl_mat_free(H);

	if (!isl_int_is_one(C->row[0][0])) {
		int i;
		isl_int g;

		isl_int_init(g);
		for (i = 0; i < n_eq; ++i) {
			isl_seq_gcd(C->row[1 + i] + 1, otype - 1, &g);
			isl_int_gcd(g, g, C->row[0][0]);
			if (!isl_int_is_divisible_by(C->row[1 + i][0], g))
				break;
		}
		isl_int_clear(g);

		if (i < n_eq) {
			isl_mat_free(C);
			isl_mat_free(U);
			isl_mat_free(Q);
			return isl_morph_empty(bset);
		}

		C = isl_mat_normalize(C);
	}

	U1 = isl_mat_sub_alloc(U, 0, U->n_row, 0, n_eq);
	U1 = isl_mat_lin_to_aff(U1);
	U2 = isl_mat_sub_alloc(U, 0, U->n_row, n_eq, U->n_row - n_eq);
	U2 = isl_mat_lin_to_aff(U2);
	isl_mat_free(U);

	C = isl_mat_product(U1, C);
	C = isl_mat_aff_direct_sum(C, U2);
	C = insert_parameter_rows(C, otype - 1);
	C = isl_mat_diagonal(C, isl_mat_identity(bset->ctx, nrest));

	dim = isl_space_copy(bset->dim);
	dim = isl_space_drop_dims(dim, type, 0, ntype);
	dim = isl_space_add_dims(dim, type, ntype - n_eq);
	ran = isl_basic_set_universe(dim);
	dom = copy_equalities(bset, f_eq, n_eq);

	return isl_morph_alloc(dom, ran, Q, C);
error:
	isl_mat_free(C);
	isl_mat_free(H);
	isl_mat_free(U);
	isl_mat_free(Q);
	return NULL;
}
Exemplo n.º 17
0
/**
 * Reduce the modulo guard expressed by "constraints" using equalities
 * found in outer nesting levels (stored in "equal").
 * The modulo guard may be an equality or a pair of inequalities.
 * In case of a pair of inequalities, *bound contains the bound on the
 * corresponding modulo expression.  If any reduction is performed
 * then this bound is recomputed.
 *
 * "level" may not correspond to an existentially quantified variable.
 *
 * We first check if there are any equalities we can use.  If not,
 * there is again nothing to reduce.
 * For the actual reduction, we use isl_basic_set_gist, but this
 * function will only perform the reduction we want here if the
 * the variable that imposes the modulo constraint has been projected
 * out (i.e., turned into an existentially quantified variable).
 * After the call to isl_basic_set_gist, we need to move the
 * existential variable back into the position where the calling
 * function expects it (assuming there are any constraints left).
 * We do this by adding an equality between the given dimension and
 * the existentially quantified variable.
 *
 * If there are no existentially quantified variables left, then
 * we don't need to add this equality.
 * If, on the other hand, the resulting basic set involves more
 * than one existentially quantified variable, then the caller
 * will not be able to handle the result, so we just return the
 * original input instead.
 */
CloogConstraintSet *cloog_constraint_set_reduce(CloogConstraintSet *constraints,
	int level, CloogEqualities *equal, int nb_par, cloog_int_t *bound)
{
	int j;
	isl_space *idim;
	struct isl_basic_set *eq;
	struct isl_basic_map *id;
	struct cloog_isl_dim dim;
	struct isl_constraint *c;
	unsigned constraints_dim;
	unsigned n_div;
	isl_basic_set *bset, *orig;

	bset = cloog_constraints_set_to_isl(constraints);
	orig = isl_basic_set_copy(bset);
	dim = set_cloog_dim_to_isl_dim(constraints, level - 1);
	assert(dim.type == isl_dim_set);

	eq = NULL;
	for (j = 0; j < level - 1; ++j) {
		isl_basic_set *bset_j;
		if (equal->types[j] != EQTYPE_EXAFFINE)
			continue;
		bset_j = equality_to_basic_set(equal, j);
		if (!eq)
			eq = bset_j;
		else
			eq = isl_basic_set_intersect(eq, bset_j);
	}
	if (!eq) {
		isl_basic_set_free(orig);
		return cloog_constraint_set_from_isl_basic_set(bset);
	}

	idim = isl_space_map_from_set(isl_basic_set_get_space(bset));
	id = isl_basic_map_identity(idim);
	id = isl_basic_map_remove_dims(id, isl_dim_out, dim.pos, 1);
	bset = isl_basic_set_apply(bset, isl_basic_map_copy(id));
	bset = isl_basic_set_apply(bset, isl_basic_map_reverse(id));

	constraints_dim = isl_basic_set_dim(bset, isl_dim_set);
	eq = isl_basic_set_remove_dims(eq, isl_dim_set, constraints_dim,
			isl_basic_set_dim(eq, isl_dim_set) - constraints_dim);
	bset = isl_basic_set_gist(bset, eq);
	n_div = isl_basic_set_dim(bset, isl_dim_div);
	if (n_div > 1) {
		isl_basic_set_free(bset);
		return cloog_constraint_set_from_isl_basic_set(orig);
	}
	if (n_div < 1) {
		isl_basic_set_free(orig);
		return cloog_constraint_set_from_isl_basic_set(bset);
	}

	c = isl_equality_alloc(isl_basic_set_get_local_space(bset));
	c = isl_constraint_set_coefficient_si(c, isl_dim_div, 0, 1);
	c = isl_constraint_set_coefficient_si(c, isl_dim_set, dim.pos, -1);
	bset = isl_basic_set_add_constraint(bset, c);

	isl_int_set_si(*bound, 0);
	constraints = cloog_constraint_set_from_isl_basic_set(bset);
	cloog_constraint_set_foreach_constraint(constraints,
						add_constant_term, bound);

	isl_basic_set_free(orig);
	return cloog_constraint_set_from_isl_basic_set(bset);
}