+
+int isl_basic_map_dim_is_bounded(__isl_keep isl_basic_map *bmap,
+ enum isl_dim_type type, unsigned pos)
+{
+ int i;
+ int lower, upper;
+
+ if (!bmap)
+ return -1;
+
+ isl_assert(bmap->ctx, pos < isl_basic_map_dim(bmap, type), return -1);
+
+ pos += isl_basic_map_offset(bmap, type);
+
+ for (i = 0; i < bmap->n_eq; ++i)
+ if (!isl_int_is_zero(bmap->eq[i][pos]))
+ return 1;
+
+ lower = upper = 0;
+ for (i = 0; i < bmap->n_ineq; ++i) {
+ int sgn = isl_int_sgn(bmap->ineq[i][pos]);
+ if (sgn > 0)
+ lower = 1;
+ if (sgn < 0)
+ upper = 1;
+ }
+
+ return lower && upper;
+}
+
+int isl_map_dim_is_bounded(__isl_keep isl_map *map,
+ enum isl_dim_type type, unsigned pos)
+{
+ int i;
+
+ if (!map)
+ return -1;
+
+ for (i = 0; i < map->n; ++i) {
+ int bounded;
+ bounded = isl_basic_map_dim_is_bounded(map->p[i], type, pos);
+ if (bounded < 0 || !bounded)
+ return bounded;
+ }
+
+ return 1;
+}
+
+/* Return 1 if the specified dim is involved in both an upper bound
+ * and a lower bound.
+ */
+int isl_set_dim_is_bounded(__isl_keep isl_set *set,
+ enum isl_dim_type type, unsigned pos)
+{
+ return isl_map_dim_is_bounded((isl_map *)set, type, pos);
+}
+
+/* For each of the "n" variables starting at "first", determine
+ * the sign of the variable and put the results in the first "n"
+ * elements of the array "signs".
+ * Sign
+ * 1 means that the variable is non-negative
+ * -1 means that the variable is non-positive
+ * 0 means the variable attains both positive and negative values.
+ */
+int isl_basic_set_vars_get_sign(__isl_keep isl_basic_set *bset,
+ unsigned first, unsigned n, int *signs)
+{
+ isl_vec *bound = NULL;
+ struct isl_tab *tab = NULL;
+ struct isl_tab_undo *snap;
+ int i;
+
+ if (!bset || !signs)
+ return -1;
+
+ bound = isl_vec_alloc(bset->ctx, 1 + isl_basic_set_total_dim(bset));
+ tab = isl_tab_from_basic_set(bset);
+ if (!bound || !tab)
+ goto error;
+
+ isl_seq_clr(bound->el, bound->size);
+ isl_int_set_si(bound->el[0], -1);
+
+ snap = isl_tab_snap(tab);
+ for (i = 0; i < n; ++i) {
+ int empty;
+
+ isl_int_set_si(bound->el[1 + first + i], -1);
+ if (isl_tab_add_ineq(tab, bound->el) < 0)
+ goto error;
+ empty = tab->empty;
+ isl_int_set_si(bound->el[1 + first + i], 0);
+ if (isl_tab_rollback(tab, snap) < 0)
+ goto error;
+
+ if (empty) {
+ signs[i] = 1;
+ continue;
+ }
+
+ isl_int_set_si(bound->el[1 + first + i], 1);
+ if (isl_tab_add_ineq(tab, bound->el) < 0)
+ goto error;
+ empty = tab->empty;
+ isl_int_set_si(bound->el[1 + first + i], 0);
+ if (isl_tab_rollback(tab, snap) < 0)
+ goto error;
+
+ signs[i] = empty ? -1 : 0;
+ }
+
+ isl_tab_free(tab);
+ isl_vec_free(bound);
+ return 0;
+error:
+ isl_tab_free(tab);
+ isl_vec_free(bound);
+ return -1;
+}
+
+int isl_basic_set_dims_get_sign(__isl_keep isl_basic_set *bset,
+ enum isl_dim_type type, unsigned first, unsigned n, int *signs)
+{
+ if (!bset || !signs)
+ return -1;
+ isl_assert(bset->ctx, first + n <= isl_basic_set_dim(bset, type),
+ return -1);
+
+ first += pos(bset->dim, type) - 1;
+ return isl_basic_set_vars_get_sign(bset, first, n, signs);
+}
+
+/* Check if the given map is single-valued.
+ * We simply compute
+ *
+ * M \circ M^-1
+ *
+ * and check if the result is a subset of the identity mapping.
+ */
+int isl_map_is_single_valued(__isl_keep isl_map *map)
+{
+ isl_map *test;
+ isl_map *id;
+ int sv;
+
+ test = isl_map_reverse(isl_map_copy(map));
+ test = isl_map_apply_range(test, isl_map_copy(map));
+
+ id = isl_map_identity(isl_dim_range(isl_map_get_dim(map)));
+
+ sv = isl_map_is_subset(test, id);
+
+ isl_map_free(test);
+ isl_map_free(id);
+
+ return sv;
+}
+
+int isl_map_is_bijective(__isl_keep isl_map *map)
+{
+ int sv;
+
+ sv = isl_map_is_single_valued(map);
+ if (sv < 0 || !sv)
+ return sv;
+
+ map = isl_map_copy(map);
+ map = isl_map_reverse(map);
+ sv = isl_map_is_single_valued(map);
+ isl_map_free(map);
+
+ return sv;
+}
+
+int isl_set_is_singleton(__isl_keep isl_set *set)
+{
+ return isl_map_is_single_valued((isl_map *)set);
+}
+
+int isl_map_is_translation(__isl_keep isl_map *map)
+{
+ int ok;
+ isl_set *delta;
+
+ delta = isl_map_deltas(isl_map_copy(map));
+ ok = isl_set_is_singleton(delta);
+ isl_set_free(delta);
+
+ return ok;
+}
+
+static int unique(isl_int *p, unsigned pos, unsigned len)
+{
+ if (isl_seq_first_non_zero(p, pos) != -1)
+ return 0;
+ if (isl_seq_first_non_zero(p + pos + 1, len - pos - 1) != -1)
+ return 0;
+ return 1;
+}
+
+int isl_basic_set_is_box(__isl_keep isl_basic_set *bset)
+{
+ int i, j;
+ unsigned nvar;
+ unsigned ovar;
+
+ if (!bset)
+ return -1;
+
+ if (isl_basic_set_dim(bset, isl_dim_div) != 0)
+ return 0;
+
+ nvar = isl_basic_set_dim(bset, isl_dim_set);
+ ovar = isl_dim_offset(bset->dim, isl_dim_set);
+ for (j = 0; j < nvar; ++j) {
+ int lower = 0, upper = 0;
+ for (i = 0; i < bset->n_eq; ++i) {
+ if (isl_int_is_zero(bset->eq[i][1 + ovar + j]))
+ continue;
+ if (!unique(bset->eq[i] + 1 + ovar, j, nvar))
+ return 0;
+ break;
+ }
+ if (i < bset->n_eq)
+ continue;
+ for (i = 0; i < bset->n_ineq; ++i) {
+ if (isl_int_is_zero(bset->ineq[i][1 + ovar + j]))
+ continue;
+ if (!unique(bset->ineq[i] + 1 + ovar, j, nvar))
+ return 0;
+ if (isl_int_is_pos(bset->ineq[i][1 + ovar + j]))
+ lower = 1;
+ else
+ upper = 1;
+ }
+ if (!lower || !upper)
+ return 0;
+ }
+
+ return 1;
+}
+
+int isl_set_is_box(__isl_keep isl_set *set)
+{
+ if (!set)
+ return -1;
+ if (set->n != 1)
+ return 0;
+
+ return isl_basic_set_is_box(set->p[0]);
+}