+
+static int is_subset_of_identity(__isl_keep isl_map *map)
+{
+ int is_subset;
+ isl_space *dim;
+ isl_map *id;
+
+ if (!map)
+ return -1;
+
+ if (!isl_space_tuple_match(map->dim, isl_dim_in, map->dim, isl_dim_out))
+ return 0;
+
+ dim = isl_map_get_space(map);
+ id = isl_map_identity(dim);
+
+ is_subset = isl_map_is_subset(map, id);
+
+ isl_map_free(id);
+
+ return is_subset;
+}
+
+/* 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_union_map_is_single_valued(__isl_keep isl_union_map *umap)
+{
+ isl_union_map *test;
+ int sv;
+
+ if (isl_union_map_n_map(umap) == 1) {
+ isl_map *map;
+ umap = isl_union_map_copy(umap);
+ map = isl_map_from_union_map(umap);
+ sv = isl_map_is_single_valued(map);
+ isl_map_free(map);
+ return sv;
+ }
+
+ test = isl_union_map_reverse(isl_union_map_copy(umap));
+ test = isl_union_map_apply_range(test, isl_union_map_copy(umap));
+
+ sv = union_map_forall(test, &is_subset_of_identity);
+
+ isl_union_map_free(test);
+
+ return sv;
+}
+
+int isl_union_map_is_injective(__isl_keep isl_union_map *umap)
+{
+ int in;
+
+ umap = isl_union_map_copy(umap);
+ umap = isl_union_map_reverse(umap);
+ in = isl_union_map_is_single_valued(umap);
+ isl_union_map_free(umap);
+
+ return in;
+}
+
+/* Represents a map that has a fixed value (v) for one of its
+ * range dimensions.
+ * The map in this structure is not reference counted, so it
+ * is only valid while the isl_union_map from which it was
+ * obtained is still alive.
+ */
+struct isl_fixed_map {
+ isl_int v;
+ isl_map *map;
+};
+
+static struct isl_fixed_map *alloc_isl_fixed_map_array(isl_ctx *ctx,
+ int n)
+{
+ int i;
+ struct isl_fixed_map *v;
+
+ v = isl_calloc_array(ctx, struct isl_fixed_map, n);
+ if (!v)
+ return NULL;
+ for (i = 0; i < n; ++i)
+ isl_int_init(v[i].v);
+ return v;
+}
+
+static void free_isl_fixed_map_array(struct isl_fixed_map *v, int n)
+{
+ int i;
+
+ if (!v)
+ return;
+ for (i = 0; i < n; ++i)
+ isl_int_clear(v[i].v);
+ free(v);
+}
+
+/* Compare the "v" field of two isl_fixed_map structs.
+ */
+static int qsort_fixed_map_cmp(const void *p1, const void *p2)
+{
+ const struct isl_fixed_map *e1 = (const struct isl_fixed_map *) p1;
+ const struct isl_fixed_map *e2 = (const struct isl_fixed_map *) p2;
+
+ return isl_int_cmp(e1->v, e2->v);
+}
+
+/* Internal data structure used while checking whether all maps
+ * in a union_map have a fixed value for a given output dimension.
+ * v is the list of maps, with the fixed value for the dimension
+ * n is the number of maps considered so far
+ * pos is the output dimension under investigation
+ */
+struct isl_fixed_dim_data {
+ struct isl_fixed_map *v;
+ int n;
+ int pos;
+};
+
+static int fixed_at_pos(__isl_keep isl_map *map, void *user)
+{
+ struct isl_fixed_dim_data *data = user;
+
+ data->v[data->n].map = map;
+ return isl_map_plain_is_fixed(map, isl_dim_out, data->pos,
+ &data->v[data->n++].v);
+}
+
+static int plain_injective_on_range(__isl_take isl_union_map *umap,
+ int first, int n_range);
+
+/* Given a list of the maps, with their fixed values at output dimension "pos",
+ * check whether the ranges of the maps form an obvious partition.
+ *
+ * We first sort the maps according to their fixed values.
+ * If all maps have a different value, then we know the ranges form
+ * a partition.
+ * Otherwise, we collect the maps with the same fixed value and
+ * check whether each such collection is obviously injective
+ * based on later dimensions.
+ */
+static int separates(struct isl_fixed_map *v, int n,
+ __isl_take isl_space *dim, int pos, int n_range)
+{
+ int i;
+
+ if (!v)
+ goto error;
+
+ qsort(v, n, sizeof(*v), &qsort_fixed_map_cmp);
+
+ for (i = 0; i + 1 < n; ++i) {
+ int j, k;
+ isl_union_map *part;
+ int injective;
+
+ for (j = i + 1; j < n; ++j)
+ if (isl_int_ne(v[i].v, v[j].v))
+ break;
+
+ if (j == i + 1)
+ continue;
+
+ part = isl_union_map_alloc(isl_space_copy(dim), j - i);
+ for (k = i; k < j; ++k)
+ part = isl_union_map_add_map(part,
+ isl_map_copy(v[k].map));
+
+ injective = plain_injective_on_range(part, pos + 1, n_range);
+ if (injective < 0)
+ goto error;
+ if (!injective)
+ break;
+
+ i = j - 1;
+ }
+
+ isl_space_free(dim);
+ free_isl_fixed_map_array(v, n);
+ return i + 1 >= n;
+error:
+ isl_space_free(dim);
+ free_isl_fixed_map_array(v, n);
+ return -1;
+}
+
+/* Check whether the maps in umap have obviously distinct ranges.
+ * In particular, check for an output dimension in the range
+ * [first,n_range) for which all maps have a fixed value
+ * and then check if these values, possibly along with fixed values
+ * at later dimensions, entail distinct ranges.
+ */
+static int plain_injective_on_range(__isl_take isl_union_map *umap,
+ int first, int n_range)
+{
+ isl_ctx *ctx;
+ int n;
+ struct isl_fixed_dim_data data = { NULL };
+
+ ctx = isl_union_map_get_ctx(umap);
+
+ n = isl_union_map_n_map(umap);
+ if (!umap)
+ goto error;
+
+ if (n <= 1) {
+ isl_union_map_free(umap);
+ return 1;
+ }
+
+ if (first >= n_range) {
+ isl_union_map_free(umap);
+ return 0;
+ }
+
+ data.v = alloc_isl_fixed_map_array(ctx, n);
+ if (!data.v)
+ goto error;
+
+ for (data.pos = first; data.pos < n_range; ++data.pos) {
+ int fixed;
+ int injective;
+ isl_space *dim;
+
+ data.n = 0;
+ fixed = union_map_forall_user(umap, &fixed_at_pos, &data);
+ if (fixed < 0)
+ goto error;
+ if (!fixed)
+ continue;
+ dim = isl_union_map_get_space(umap);
+ injective = separates(data.v, n, dim, data.pos, n_range);
+ isl_union_map_free(umap);
+ return injective;
+ }
+
+ free_isl_fixed_map_array(data.v, n);
+ isl_union_map_free(umap);
+
+ return 0;
+error:
+ free_isl_fixed_map_array(data.v, n);
+ isl_union_map_free(umap);
+ return -1;
+}
+
+/* Check whether the maps in umap that map to subsets of "ran"
+ * have obviously distinct ranges.
+ */
+static int plain_injective_on_range_wrap(__isl_keep isl_set *ran, void *user)
+{
+ isl_union_map *umap = user;
+
+ umap = isl_union_map_copy(umap);
+ umap = isl_union_map_intersect_range(umap,
+ isl_union_set_from_set(isl_set_copy(ran)));
+ return plain_injective_on_range(umap, 0, isl_set_dim(ran, isl_dim_set));
+}
+
+/* Check if the given union_map is obviously injective.
+ *
+ * In particular, we first check if all individual maps are obviously
+ * injective and then check if all the ranges of these maps are
+ * obviously disjoint.
+ */
+int isl_union_map_plain_is_injective(__isl_keep isl_union_map *umap)
+{
+ int in;
+ isl_union_map *univ;
+ isl_union_set *ran;
+
+ in = union_map_forall(umap, &isl_map_plain_is_injective);
+ if (in < 0)
+ return -1;
+ if (!in)
+ return 0;
+
+ univ = isl_union_map_universe(isl_union_map_copy(umap));
+ ran = isl_union_map_range(univ);
+
+ in = union_map_forall_user(ran, &plain_injective_on_range_wrap, umap);
+
+ isl_union_set_free(ran);
+
+ return in;
+}
+
+int isl_union_map_is_bijective(__isl_keep isl_union_map *umap)
+{
+ int sv;
+
+ sv = isl_union_map_is_single_valued(umap);
+ if (sv < 0 || !sv)
+ return sv;
+
+ return isl_union_map_is_injective(umap);
+}
+
+static int zip_entry(void **entry, void *user)
+{
+ isl_map *map = *entry;
+ isl_union_map **res = user;
+
+ if (!isl_map_can_zip(map))
+ return 0;
+
+ *res = isl_union_map_add_map(*res, isl_map_zip(isl_map_copy(map)));
+
+ return 0;
+}
+
+__isl_give isl_union_map *isl_union_map_zip(__isl_take isl_union_map *umap)
+{
+ return cond_un_op(umap, &zip_entry);
+}
+
+static int uncurry_entry(void **entry, void *user)
+{
+ isl_map *map = *entry;
+ isl_union_map **res = user;
+
+ if (!isl_map_can_uncurry(map))
+ return 0;
+
+ *res = isl_union_map_add_map(*res, isl_map_uncurry(isl_map_copy(map)));
+
+ return 0;
+}
+
+/* Given a union map, take the maps of the form A -> (B -> C) and
+ * return the union of the corresponding maps (A -> B) -> C.
+ */
+__isl_give isl_union_map *isl_union_map_uncurry(__isl_take isl_union_map *umap)
+{
+ return cond_un_op(umap, &uncurry_entry);
+}
+
+static int curry_entry(void **entry, void *user)
+{
+ isl_map *map = *entry;
+ isl_union_map **res = user;
+
+ if (!isl_map_can_curry(map))
+ return 0;
+
+ *res = isl_union_map_add_map(*res, isl_map_curry(isl_map_copy(map)));
+
+ return 0;
+}
+
+/* Given a union map, take the maps of the form (A -> B) -> C and
+ * return the union of the corresponding maps A -> (B -> C).
+ */
+__isl_give isl_union_map *isl_union_map_curry(__isl_take isl_union_map *umap)
+{
+ return cond_un_op(umap, &curry_entry);
+}
+
+static int lift_entry(void **entry, void *user)
+{
+ isl_set *set = *entry;
+ isl_union_set **res = user;
+
+ *res = isl_union_set_add_set(*res, isl_set_lift(isl_set_copy(set)));
+
+ return 0;
+}
+
+__isl_give isl_union_set *isl_union_set_lift(__isl_take isl_union_set *uset)
+{
+ return cond_un_op(uset, &lift_entry);
+}
+
+static int coefficients_entry(void **entry, void *user)
+{
+ isl_set *set = *entry;
+ isl_union_set **res = user;
+
+ set = isl_set_copy(set);
+ set = isl_set_from_basic_set(isl_set_coefficients(set));
+ *res = isl_union_set_add_set(*res, set);
+
+ return 0;
+}
+
+__isl_give isl_union_set *isl_union_set_coefficients(
+ __isl_take isl_union_set *uset)
+{
+ isl_ctx *ctx;
+ isl_space *dim;
+ isl_union_set *res;
+
+ if (!uset)
+ return NULL;
+
+ ctx = isl_union_set_get_ctx(uset);
+ dim = isl_space_set_alloc(ctx, 0, 0);
+ res = isl_union_map_alloc(dim, uset->table.n);
+ if (isl_hash_table_foreach(uset->dim->ctx, &uset->table,
+ &coefficients_entry, &res) < 0)
+ goto error;
+
+ isl_union_set_free(uset);
+ return res;
+error:
+ isl_union_set_free(uset);
+ isl_union_set_free(res);
+ return NULL;
+}
+
+static int solutions_entry(void **entry, void *user)
+{
+ isl_set *set = *entry;
+ isl_union_set **res = user;
+
+ set = isl_set_copy(set);
+ set = isl_set_from_basic_set(isl_set_solutions(set));
+ if (!*res)
+ *res = isl_union_set_from_set(set);
+ else
+ *res = isl_union_set_add_set(*res, set);
+
+ if (!*res)
+ return -1;
+
+ return 0;
+}
+
+__isl_give isl_union_set *isl_union_set_solutions(
+ __isl_take isl_union_set *uset)
+{
+ isl_union_set *res = NULL;
+
+ if (!uset)
+ return NULL;
+
+ if (uset->table.n == 0) {
+ res = isl_union_set_empty(isl_union_set_get_space(uset));
+ isl_union_set_free(uset);
+ return res;
+ }
+
+ if (isl_hash_table_foreach(uset->dim->ctx, &uset->table,
+ &solutions_entry, &res) < 0)
+ goto error;
+
+ isl_union_set_free(uset);
+ return res;
+error:
+ isl_union_set_free(uset);
+ isl_union_set_free(res);
+ return NULL;
+}
+
+/* Internal data structure for isl_union_map_preimage_domain_multi_aff.
+ *
+ * "ma" is the function under which the preimage should be taken.
+ * "space" is the space of "ma".
+ * "res" collects the results.
+ */
+struct isl_union_map_preimage_domain_data {
+ isl_space *space;
+ isl_multi_aff *ma;
+ isl_union_map *res;
+};
+
+/* Compute the preimage of the domain of *entry under the function
+ * represented by data->ma, provided the domain space of *entry
+ * match the target space of data->ma, and add the result to data->res.
+ */
+static int preimage_domain_entry(void **entry, void *user)
+{
+ int m;
+ isl_map *map = *entry;
+ struct isl_union_map_preimage_domain_data *data = user;
+ int empty;
+
+ m = isl_space_tuple_match(map->dim, isl_dim_in,
+ data->space, isl_dim_out);
+ if (m < 0)
+ return -1;
+ if (!m)
+ return 0;
+
+ map = isl_map_copy(map);
+ map = isl_map_preimage_domain_multi_aff(map,
+ isl_multi_aff_copy(data->ma));
+
+ empty = isl_map_is_empty(map);
+ if (empty < 0 || empty) {
+ isl_map_free(map);
+ return empty < 0 ? -1 : 0;
+ }
+
+ data->res = isl_union_map_add_map(data->res, map);
+
+ return 0;
+}
+
+/* Compute the preimage of the domain of "umap" under the function
+ * represented by "ma".
+ * In other words, plug in "ma" in the domain of "umap".
+ * The result contains maps that live in the same spaces as the maps of "umap"
+ * with domain space equal to the target space of "ma",
+ * except that the domain has been replaced by the domain space of "ma".
+ */
+__isl_give isl_union_map *isl_union_map_preimage_domain_multi_aff(
+ __isl_take isl_union_map *umap, __isl_take isl_multi_aff *ma)
+{
+ isl_ctx *ctx;
+ isl_space *space;
+ struct isl_union_map_preimage_domain_data data;
+
+ if (!umap || !ma)
+ goto error;
+
+ ctx = isl_union_map_get_ctx(umap);
+ space = isl_union_map_get_space(umap);
+ data.space = isl_multi_aff_get_space(ma);
+ data.ma = ma;
+ data.res = isl_union_map_alloc(space, umap->table.n);
+ if (isl_hash_table_foreach(ctx, &umap->table, &preimage_domain_entry,
+ &data) < 0)
+ data.res = isl_union_map_free(data.res);
+
+ isl_space_free(data.space);
+ isl_union_map_free(umap);
+ isl_multi_aff_free(ma);
+ return data.res;
+error:
+ isl_union_map_free(umap);
+ isl_multi_aff_free(ma);
+ return NULL;
+}