+ isl_seq_cpy(bset->eq[k] + 1, tab->basis->row[1 + i] + 1,
+ vec->size - 1);
+ isl_seq_inner_product(bset->eq[k] + 1, vec->el +1,
+ vec->size - 1, &bset->eq[k][0]);
+ isl_int_neg(bset->eq[k][0], bset->eq[k][0]);
+ }
+ bset->sample = vec;
+ bset = isl_basic_set_gauss(bset, NULL);
+
+ return bset;
+error:
+ isl_basic_set_free(bset);
+ isl_vec_free(vec);
+ return NULL;
+}
+
+/* Given a tableau of a set and a tableau of the corresponding
+ * recession cone, detect and add all equalities to the tableau.
+ * If the tableau is bounded, then we can simply keep the
+ * tableau in its state after the return from extend_affine_hull.
+ * However, if the tableau is unbounded, then
+ * isl_tab_set_initial_basis_with_cone will add some additional
+ * constraints to the tableau that have to be removed again.
+ * In this case, we therefore rollback to the state before
+ * any constraints were added and then add the equalities back in.
+ */
+struct isl_tab *isl_tab_detect_equalities(struct isl_tab *tab,
+ struct isl_tab *tab_cone)
+{
+ int j;
+ struct isl_vec *sample;
+ struct isl_basic_set *hull = NULL;
+ struct isl_tab_undo *snap;
+
+ if (!tab || !tab_cone)
+ goto error;
+
+ snap = isl_tab_snap(tab);
+
+ isl_mat_free(tab->basis);
+ tab->basis = NULL;
+
+ isl_assert(tab->mat->ctx, tab->bmap, goto error);
+ isl_assert(tab->mat->ctx, tab->samples, goto error);
+ isl_assert(tab->mat->ctx, tab->samples->n_col == 1 + tab->n_var, goto error);
+ isl_assert(tab->mat->ctx, tab->n_sample > tab->n_outside, goto error);
+
+ if (isl_tab_set_initial_basis_with_cone(tab, tab_cone) < 0)
+ goto error;
+
+ sample = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_var);
+ if (!sample)
+ goto error;
+
+ isl_seq_cpy(sample->el, tab->samples->row[tab->n_outside], sample->size);
+
+ isl_vec_free(tab->bmap->sample);
+ tab->bmap->sample = isl_vec_copy(sample);
+
+ if (tab->n_unbounded == 0)
+ hull = isl_basic_set_from_vec(isl_vec_copy(sample));
+ else
+ hull = initial_hull(tab, isl_vec_copy(sample));
+
+ for (j = tab->n_outside + 1; j < tab->n_sample; ++j) {
+ isl_seq_cpy(sample->el, tab->samples->row[j], sample->size);
+ hull = affine_hull(hull,
+ isl_basic_set_from_vec(isl_vec_copy(sample)));
+ }
+
+ isl_vec_free(sample);
+
+ hull = extend_affine_hull(tab, hull, NULL);
+ if (!hull)
+ goto error;
+
+ if (tab->n_unbounded == 0) {
+ isl_basic_set_free(hull);
+ return tab;
+ }
+
+ if (isl_tab_rollback(tab, snap) < 0)
+ goto error;
+
+ if (hull->n_eq > tab->n_zero) {
+ for (j = 0; j < hull->n_eq; ++j) {
+ isl_seq_normalize(tab->mat->ctx, hull->eq[j], 1 + tab->n_var);
+ if (isl_tab_add_eq(tab, hull->eq[j]) < 0)
+ goto error;
+ }
+ }
+
+ isl_basic_set_free(hull);
+
+ return tab;
+error:
+ isl_basic_set_free(hull);
+ isl_tab_free(tab);
+ return NULL;
+}
+
+/* Compute the affine hull of "bset", where "cone" is the recession cone
+ * of "bset".
+ *
+ * We first compute a unimodular transformation that puts the unbounded
+ * directions in the last dimensions. In particular, we take a transformation
+ * that maps all equalities to equalities (in HNF) on the first dimensions.
+ * Let x be the original dimensions and y the transformed, with y_1 bounded
+ * and y_2 unbounded.
+ *
+ * [ y_1 ] [ y_1 ] [ Q_1 ]
+ * x = U [ y_2 ] [ y_2 ] = [ Q_2 ] x
+ *
+ * Let's call the input basic set S. We compute S' = preimage(S, U)
+ * and drop the final dimensions including any constraints involving them.
+ * This results in set S''.
+ * Then we compute the affine hull A'' of S''.
+ * Let F y_1 >= g be the constraint system of A''. In the transformed
+ * space the y_2 are unbounded, so we can add them back without any constraints,
+ * resulting in
+ *
+ * [ y_1 ]
+ * [ F 0 ] [ y_2 ] >= g
+ * or
+ * [ Q_1 ]
+ * [ F 0 ] [ Q_2 ] x >= g
+ * or
+ * F Q_1 x >= g
+ *
+ * The affine hull in the original space is then obtained as
+ * A = preimage(A'', Q_1).
+ */
+static struct isl_basic_set *affine_hull_with_cone(struct isl_basic_set *bset,
+ struct isl_basic_set *cone)
+{
+ unsigned total;
+ unsigned cone_dim;
+ struct isl_basic_set *hull;
+ struct isl_mat *M, *U, *Q;
+
+ if (!bset || !cone)
+ goto error;
+
+ total = isl_basic_set_total_dim(cone);
+ cone_dim = total - cone->n_eq;
+
+ M = isl_mat_sub_alloc6(bset->ctx, cone->eq, 0, cone->n_eq, 1, total);
+ M = isl_mat_left_hermite(M, 0, &U, &Q);
+ if (!M)
+ goto error;
+ isl_mat_free(M);
+
+ U = isl_mat_lin_to_aff(U);
+ bset = isl_basic_set_preimage(bset, isl_mat_copy(U));
+
+ bset = isl_basic_set_drop_constraints_involving(bset, total - cone_dim,
+ cone_dim);
+ bset = isl_basic_set_drop_dims(bset, total - cone_dim, cone_dim);
+
+ Q = isl_mat_lin_to_aff(Q);
+ Q = isl_mat_drop_rows(Q, 1 + total - cone_dim, cone_dim);
+
+ if (bset && bset->sample && bset->sample->size == 1 + total)
+ bset->sample = isl_mat_vec_product(isl_mat_copy(Q), bset->sample);
+
+ hull = uset_affine_hull_bounded(bset);
+
+ if (!hull) {
+ isl_mat_free(Q);
+ isl_mat_free(U);
+ } else {
+ struct isl_vec *sample = isl_vec_copy(hull->sample);
+ U = isl_mat_drop_cols(U, 1 + total - cone_dim, cone_dim);
+ if (sample && sample->size > 0)
+ sample = isl_mat_vec_product(U, sample);
+ else
+ isl_mat_free(U);
+ hull = isl_basic_set_preimage(hull, Q);
+ if (hull) {
+ isl_vec_free(hull->sample);
+ hull->sample = sample;
+ } else
+ isl_vec_free(sample);
+ }
+
+ isl_basic_set_free(cone);
+
+ return hull;
+error:
+ isl_basic_set_free(bset);
+ isl_basic_set_free(cone);
+ return NULL;
+}
+
+/* Look for all equalities satisfied by the integer points in bset,
+ * which is assumed not to have any explicit equalities.
+ *
+ * The equalities are obtained by successively looking for
+ * a point that is affinely independent of the points found so far.
+ * In particular, for each equality satisfied by the points so far,
+ * we check if there is any point on a hyperplane parallel to the
+ * corresponding hyperplane shifted by at least one (in either direction).
+ *
+ * Before looking for any outside points, we first compute the recession
+ * cone. The directions of this recession cone will always be part
+ * of the affine hull, so there is no need for looking for any points
+ * in these directions.
+ * In particular, if the recession cone is full-dimensional, then
+ * the affine hull is simply the whole universe.
+ */
+static struct isl_basic_set *uset_affine_hull(struct isl_basic_set *bset)
+{
+ struct isl_basic_set *cone;
+
+ if (isl_basic_set_plain_is_empty(bset))
+ return bset;
+
+ cone = isl_basic_set_recession_cone(isl_basic_set_copy(bset));
+ if (!cone)
+ goto error;
+ if (cone->n_eq == 0) {
+ struct isl_basic_set *hull;
+ isl_basic_set_free(cone);
+ hull = isl_basic_set_universe_like(bset);
+ isl_basic_set_free(bset);
+ return hull;
+ }
+
+ if (cone->n_eq < isl_basic_set_total_dim(cone))
+ return affine_hull_with_cone(bset, cone);
+
+ isl_basic_set_free(cone);
+ return uset_affine_hull_bounded(bset);
+error:
+ isl_basic_set_free(bset);
+ return NULL;
+}
+
+/* Look for all equalities satisfied by the integer points in bmap
+ * that are independent of the equalities already explicitly available
+ * in bmap.
+ *
+ * We first remove all equalities already explicitly available,
+ * then look for additional equalities in the reduced space
+ * and then transform the result to the original space.
+ * The original equalities are _not_ added to this set. This is
+ * the responsibility of the calling function.
+ * The resulting basic set has all meaning about the dimensions removed.
+ * In particular, dimensions that correspond to existential variables
+ * in bmap and that are found to be fixed are not removed.
+ */
+static struct isl_basic_set *equalities_in_underlying_set(
+ struct isl_basic_map *bmap)
+{
+ struct isl_mat *T1 = NULL;
+ struct isl_mat *T2 = NULL;
+ struct isl_basic_set *bset = NULL;
+ struct isl_basic_set *hull = NULL;
+
+ bset = isl_basic_map_underlying_set(bmap);
+ if (!bset)
+ return NULL;
+ if (bset->n_eq)
+ bset = isl_basic_set_remove_equalities(bset, &T1, &T2);
+ if (!bset)
+ goto error;
+
+ hull = uset_affine_hull(bset);
+ if (!T2)
+ return hull;
+
+ if (!hull) {
+ isl_mat_free(T1);
+ isl_mat_free(T2);
+ } else {
+ struct isl_vec *sample = isl_vec_copy(hull->sample);
+ if (sample && sample->size > 0)
+ sample = isl_mat_vec_product(T1, sample);
+ else
+ isl_mat_free(T1);
+ hull = isl_basic_set_preimage(hull, T2);
+ if (hull) {
+ isl_vec_free(hull->sample);
+ hull->sample = sample;
+ } else
+ isl_vec_free(sample);
+ }
+
+ return hull;
+error:
+ isl_mat_free(T1);
+ isl_mat_free(T2);
+ isl_basic_set_free(bset);
+ isl_basic_set_free(hull);
+ return NULL;
+}
+
+/* Detect and make explicit all equalities satisfied by the (integer)
+ * points in bmap.
+ */
+struct isl_basic_map *isl_basic_map_detect_equalities(
+ struct isl_basic_map *bmap)
+{
+ int i, j;
+ struct isl_basic_set *hull = NULL;
+
+ if (!bmap)
+ return NULL;
+ if (bmap->n_ineq == 0)
+ return bmap;
+ if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
+ return bmap;
+ if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_ALL_EQUALITIES))
+ return bmap;
+ if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
+ return isl_basic_map_implicit_equalities(bmap);
+
+ hull = equalities_in_underlying_set(isl_basic_map_copy(bmap));
+ if (!hull)
+ goto error;
+ if (ISL_F_ISSET(hull, ISL_BASIC_SET_EMPTY)) {
+ isl_basic_set_free(hull);
+ return isl_basic_map_set_to_empty(bmap);
+ }
+ bmap = isl_basic_map_extend_space(bmap, isl_space_copy(bmap->dim), 0,
+ hull->n_eq, 0);
+ for (i = 0; i < hull->n_eq; ++i) {
+ j = isl_basic_map_alloc_equality(bmap);
+ if (j < 0)
+ goto error;
+ isl_seq_cpy(bmap->eq[j], hull->eq[i],
+ 1 + isl_basic_set_total_dim(hull));
+ }
+ isl_vec_free(bmap->sample);
+ bmap->sample = isl_vec_copy(hull->sample);
+ isl_basic_set_free(hull);
+ ISL_F_SET(bmap, ISL_BASIC_MAP_NO_IMPLICIT | ISL_BASIC_MAP_ALL_EQUALITIES);
+ bmap = isl_basic_map_simplify(bmap);
+ return isl_basic_map_finalize(bmap);
+error:
+ isl_basic_set_free(hull);
+ isl_basic_map_free(bmap);
+ return NULL;
+}
+
+__isl_give isl_basic_set *isl_basic_set_detect_equalities(
+ __isl_take isl_basic_set *bset)
+{
+ return (isl_basic_set *)
+ isl_basic_map_detect_equalities((isl_basic_map *)bset);
+}
+
+__isl_give isl_map *isl_map_inline_foreach_basic_map(__isl_take isl_map *map,
+ __isl_give isl_basic_map *(*fn)(__isl_take isl_basic_map *bmap))
+{
+ struct isl_basic_map *bmap;
+ int i;
+
+ if (!map)
+ return NULL;
+
+ for (i = 0; i < map->n; ++i) {
+ bmap = isl_basic_map_copy(map->p[i]);
+ bmap = fn(bmap);
+ if (!bmap)
+ goto error;
+ isl_basic_map_free(map->p[i]);
+ map->p[i] = bmap;
+ }
+
+ return map;
+error:
+ isl_map_free(map);
+ return NULL;
+}
+
+__isl_give isl_map *isl_map_detect_equalities(__isl_take isl_map *map)
+{
+ return isl_map_inline_foreach_basic_map(map,
+ &isl_basic_map_detect_equalities);
+}
+
+__isl_give isl_set *isl_set_detect_equalities(__isl_take isl_set *set)
+{
+ return (isl_set *)isl_map_detect_equalities((isl_map *)set);
+}
+
+/* After computing the rational affine hull (by detecting the implicit
+ * equalities), we compute the additional equalities satisfied by
+ * the integer points (if any) and add the original equalities back in.
+ */
+struct isl_basic_map *isl_basic_map_affine_hull(struct isl_basic_map *bmap)
+{
+ bmap = isl_basic_map_detect_equalities(bmap);
+ bmap = isl_basic_map_cow(bmap);
+ if (bmap)
+ isl_basic_map_free_inequality(bmap, bmap->n_ineq);
+ bmap = isl_basic_map_finalize(bmap);
+ return bmap;
+}
+
+struct isl_basic_set *isl_basic_set_affine_hull(struct isl_basic_set *bset)
+{
+ return (struct isl_basic_set *)
+ isl_basic_map_affine_hull((struct isl_basic_map *)bset);
+}
+
+struct isl_basic_map *isl_map_affine_hull(struct isl_map *map)
+{
+ int i;
+ struct isl_basic_map *model = NULL;
+ struct isl_basic_map *hull = NULL;
+ struct isl_set *set;
+
+ map = isl_map_detect_equalities(map);
+ map = isl_map_align_divs(map);
+
+ if (!map)
+ return NULL;
+
+ if (map->n == 0) {
+ hull = isl_basic_map_empty_like_map(map);
+ isl_map_free(map);
+ return hull;
+ }
+
+ model = isl_basic_map_copy(map->p[0]);
+ set = isl_map_underlying_set(map);
+ set = isl_set_cow(set);
+ if (!set)
+ goto error;
+
+ for (i = 0; i < set->n; ++i) {
+ set->p[i] = isl_basic_set_cow(set->p[i]);
+ set->p[i] = isl_basic_set_affine_hull(set->p[i]);
+ set->p[i] = isl_basic_set_gauss(set->p[i], NULL);
+ if (!set->p[i])
+ goto error;
+ }
+ set = isl_set_remove_empty_parts(set);
+ if (set->n == 0) {
+ hull = isl_basic_map_empty_like(model);
+ isl_basic_map_free(model);
+ } else {
+ struct isl_basic_set *bset;
+ while (set->n > 1) {
+ set->p[0] = affine_hull(set->p[0], set->p[--set->n]);
+ if (!set->p[0])
+ goto error;
+ }
+ bset = isl_basic_set_copy(set->p[0]);
+ hull = isl_basic_map_overlying_set(bset, model);