Esempio n. 1
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;
}
Esempio n. 2
0
/* Create a graft for "node" with no guards and no enforced conditions.
 */
__isl_give isl_ast_graft *isl_ast_graft_alloc(
	__isl_take isl_ast_node *node, __isl_keep isl_ast_build *build)
{
	isl_ctx *ctx;
	isl_space *space;
	isl_ast_graft *graft;

	if (!node)
		return NULL;

	ctx = isl_ast_node_get_ctx(node);
	graft = isl_calloc_type(ctx, isl_ast_graft);
	if (!graft)
		goto error;

	space = isl_ast_build_get_space(build, 1);

	graft->ref = 1;
	graft->node = node;
	graft->guard = isl_set_universe(isl_space_copy(space));
	graft->enforced = isl_basic_set_universe(space);

	if (!graft->guard || !graft->enforced)
		return isl_ast_graft_free(graft);

	return graft;
error:
	isl_ast_node_free(node);
	return NULL;
}
Esempio n. 3
0
__isl_give isl_morph *isl_morph_identity(__isl_keep isl_basic_set *bset)
{
	isl_mat *id;
	isl_basic_set *universe;
	unsigned total;

	if (!bset)
		return NULL;

	total = isl_basic_set_total_dim(bset);
	id = isl_mat_identity(bset->ctx, 1 + total);
	universe = isl_basic_set_universe(isl_space_copy(bset->dim));

	return isl_morph_alloc(universe, isl_basic_set_copy(universe),
		id, isl_mat_copy(id));
}
Esempio n. 4
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;
}