+
+/* Given two constraints "a" and "b" on the variable at position "abs_pos"
+ * (in "a" and "b"), add a constraint to "bset" that ensures that the
+ * bound implied by "a" is (strictly) larger than the bound implied by "b".
+ *
+ * If both constraints imply lower bounds, then this means that "a" is
+ * active in the result.
+ * If both constraints imply upper bounds, then this means that "b" is
+ * active in the result.
+ */
+static __isl_give isl_basic_set *add_larger_bound_constraint(
+ __isl_take isl_basic_set *bset, isl_int *a, isl_int *b,
+ unsigned abs_pos, int strict)
+{
+ int k;
+ isl_int t;
+ unsigned total;
+
+ k = isl_basic_set_alloc_inequality(bset);
+ if (k < 0)
+ goto error;
+
+ total = isl_basic_set_dim(bset, isl_dim_all);
+
+ isl_int_init(t);
+ isl_int_neg(t, b[1 + abs_pos]);
+
+ isl_seq_combine(bset->ineq[k], t, a, a[1 + abs_pos], b, 1 + abs_pos);
+ isl_seq_combine(bset->ineq[k] + 1 + abs_pos,
+ t, a + 1 + abs_pos + 1, a[1 + abs_pos], b + 1 + abs_pos + 1,
+ total - abs_pos);
+
+ if (strict)
+ isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
+
+ isl_int_clear(t);
+
+ return bset;
+error:
+ isl_basic_set_free(bset);
+ return NULL;
+}
+
+/* Add constraints to "context" that ensure that "u" is the smallest
+ * (and therefore active) upper bound on "abs_pos" in "bset" and return
+ * the resulting basic set.
+ */
+static __isl_give isl_basic_set *set_smallest_upper_bound(
+ __isl_keep isl_basic_set *context,
+ __isl_keep isl_basic_set *bset, unsigned abs_pos, int n_upper, int u)
+{
+ int j;
+
+ context = isl_basic_set_copy(context);
+ context = isl_basic_set_cow(context);
+
+ context = isl_basic_set_extend_constraints(context, 0, n_upper - 1);
+
+ for (j = 0; j < bset->n_ineq; ++j) {
+ if (j == u)
+ continue;
+ if (!isl_int_is_neg(bset->ineq[j][1 + abs_pos]))
+ continue;
+ context = add_larger_bound_constraint(context,
+ bset->ineq[j], bset->ineq[u], abs_pos, j > u);
+ }
+
+ context = isl_basic_set_simplify(context);
+ context = isl_basic_set_finalize(context);
+
+ return context;
+}
+
+/* Add constraints to "context" that ensure that "u" is the largest
+ * (and therefore active) upper bound on "abs_pos" in "bset" and return
+ * the resulting basic set.
+ */
+static __isl_give isl_basic_set *set_largest_lower_bound(
+ __isl_keep isl_basic_set *context,
+ __isl_keep isl_basic_set *bset, unsigned abs_pos, int n_lower, int l)
+{
+ int j;
+
+ context = isl_basic_set_copy(context);
+ context = isl_basic_set_cow(context);
+
+ context = isl_basic_set_extend_constraints(context, 0, n_lower - 1);
+
+ for (j = 0; j < bset->n_ineq; ++j) {
+ if (j == l)
+ continue;
+ if (!isl_int_is_pos(bset->ineq[j][1 + abs_pos]))
+ continue;
+ context = add_larger_bound_constraint(context,
+ bset->ineq[l], bset->ineq[j], abs_pos, j > l);
+ }
+
+ context = isl_basic_set_simplify(context);
+ context = isl_basic_set_finalize(context);
+
+ return context;
+}
+
+static int foreach_upper_bound(__isl_keep isl_basic_set *bset,
+ enum isl_dim_type type, unsigned abs_pos,
+ __isl_take isl_basic_set *context, int n_upper,
+ int (*fn)(__isl_take isl_constraint *lower,
+ __isl_take isl_constraint *upper,
+ __isl_take isl_basic_set *bset, void *user), void *user)
+{
+ isl_basic_set *context_i;
+ isl_constraint *upper = NULL;
+ int i;
+
+ for (i = 0; i < bset->n_ineq; ++i) {
+ if (isl_int_is_zero(bset->ineq[i][1 + abs_pos]))
+ continue;
+
+ context_i = set_smallest_upper_bound(context, bset,
+ abs_pos, n_upper, i);
+ if (isl_basic_set_is_empty(context_i)) {
+ isl_basic_set_free(context_i);
+ continue;
+ }
+ upper = isl_basic_set_constraint(isl_basic_set_copy(bset),
+ &bset->ineq[i]);
+ if (!upper || !context_i)
+ goto error;
+ if (fn(NULL, upper, context_i, user) < 0)
+ break;
+ }
+
+ isl_basic_set_free(context);
+
+ if (i < bset->n_ineq)
+ return -1;
+
+ return 0;
+error:
+ isl_constraint_free(upper);
+ isl_basic_set_free(context_i);
+ isl_basic_set_free(context);
+ return -1;
+}
+
+static int foreach_lower_bound(__isl_keep isl_basic_set *bset,
+ enum isl_dim_type type, unsigned abs_pos,
+ __isl_take isl_basic_set *context, int n_lower,
+ int (*fn)(__isl_take isl_constraint *lower,
+ __isl_take isl_constraint *upper,
+ __isl_take isl_basic_set *bset, void *user), void *user)
+{
+ isl_basic_set *context_i;
+ isl_constraint *lower = NULL;
+ int i;
+
+ for (i = 0; i < bset->n_ineq; ++i) {
+ if (isl_int_is_zero(bset->ineq[i][1 + abs_pos]))
+ continue;
+
+ context_i = set_largest_lower_bound(context, bset,
+ abs_pos, n_lower, i);
+ if (isl_basic_set_is_empty(context_i)) {
+ isl_basic_set_free(context_i);
+ continue;
+ }
+ lower = isl_basic_set_constraint(isl_basic_set_copy(bset),
+ &bset->ineq[i]);
+ if (!lower || !context_i)
+ goto error;
+ if (fn(lower, NULL, context_i, user) < 0)
+ break;
+ }
+
+ isl_basic_set_free(context);
+
+ if (i < bset->n_ineq)
+ return -1;
+
+ return 0;
+error:
+ isl_constraint_free(lower);
+ isl_basic_set_free(context_i);
+ isl_basic_set_free(context);
+ return -1;
+}
+
+static int foreach_bound_pair(__isl_keep isl_basic_set *bset,
+ enum isl_dim_type type, unsigned abs_pos,
+ __isl_take isl_basic_set *context, int n_lower, int n_upper,
+ int (*fn)(__isl_take isl_constraint *lower,
+ __isl_take isl_constraint *upper,
+ __isl_take isl_basic_set *bset, void *user), void *user)
+{
+ isl_basic_set *context_i, *context_j;
+ isl_constraint *lower = NULL;
+ isl_constraint *upper = NULL;
+ int i, j;
+
+ for (i = 0; i < bset->n_ineq; ++i) {
+ if (!isl_int_is_pos(bset->ineq[i][1 + abs_pos]))
+ continue;
+
+ context_i = set_largest_lower_bound(context, bset,
+ abs_pos, n_lower, i);
+ if (isl_basic_set_is_empty(context_i)) {
+ isl_basic_set_free(context_i);
+ continue;
+ }
+
+ for (j = 0; j < bset->n_ineq; ++j) {
+ if (!isl_int_is_neg(bset->ineq[j][1 + abs_pos]))
+ continue;
+
+ context_j = set_smallest_upper_bound(context_i, bset,
+ abs_pos, n_upper, j);
+ context_j = isl_basic_set_extend_constraints(context_j,
+ 0, 1);
+ context_j = add_larger_bound_constraint(context_j,
+ bset->ineq[i], bset->ineq[j], abs_pos, 0);
+ context_j = isl_basic_set_simplify(context_j);
+ context_j = isl_basic_set_finalize(context_j);
+ if (isl_basic_set_is_empty(context_j)) {
+ isl_basic_set_free(context_j);
+ continue;
+ }
+ lower = isl_basic_set_constraint(isl_basic_set_copy(bset),
+ &bset->ineq[i]);
+ upper = isl_basic_set_constraint(isl_basic_set_copy(bset),
+ &bset->ineq[j]);
+ if (!lower || !upper || !context_j)
+ goto error;
+ if (fn(lower, upper, context_j, user) < 0)
+ break;
+ }
+
+ isl_basic_set_free(context_i);
+
+ if (j < bset->n_ineq)
+ break;
+ }
+
+ isl_basic_set_free(context);
+
+ if (i < bset->n_ineq)
+ return -1;
+
+ return 0;
+error:
+ isl_constraint_free(lower);
+ isl_constraint_free(upper);
+ isl_basic_set_free(context_i);
+ isl_basic_set_free(context_j);
+ isl_basic_set_free(context);
+ return -1;
+}
+
+/* For each pair of lower and upper bounds on the variable "pos"
+ * of type "type", call "fn" with these lower and upper bounds and the
+ * set of constraints on the remaining variables where these bounds
+ * are active, i.e., (stricly) larger/smaller than the other lower/upper bounds.
+ *
+ * If the designated variable is equal to an affine combination of the
+ * other variables then fn is called with both lower and upper
+ * set to the corresponding equality.
+ *
+ * If there is no lower (or upper) bound, then NULL is passed
+ * as the corresponding bound.
+ *
+ * We first check if the variable is involved in any equality.
+ * If not, we count the number of lower and upper bounds and
+ * act accordingly.
+ */
+int isl_basic_set_foreach_bound_pair(__isl_keep isl_basic_set *bset,
+ enum isl_dim_type type, unsigned pos,
+ int (*fn)(__isl_take isl_constraint *lower,
+ __isl_take isl_constraint *upper,
+ __isl_take isl_basic_set *bset, void *user), void *user)
+{
+ int i;
+ isl_constraint *lower = NULL;
+ isl_constraint *upper = NULL;
+ isl_basic_set *context = NULL;
+ unsigned abs_pos;
+ int n_lower, n_upper;
+
+ if (!bset)
+ return -1;
+ isl_assert(bset->ctx, pos < isl_basic_set_dim(bset, type), return -1);
+ isl_assert(bset->ctx, type == isl_dim_param || type == isl_dim_set,
+ return -1);
+
+ abs_pos = pos;
+ if (type == isl_dim_set)
+ abs_pos += isl_basic_set_dim(bset, isl_dim_param);
+
+ for (i = 0; i < bset->n_eq; ++i) {
+ if (isl_int_is_zero(bset->eq[i][1 + abs_pos]))
+ continue;
+
+ lower = isl_basic_set_constraint(isl_basic_set_copy(bset),
+ &bset->eq[i]);
+ upper = isl_constraint_copy(lower);
+ context = isl_basic_set_remove_dims(isl_basic_set_copy(bset),
+ type, pos, 1);
+ if (!lower || !upper || !context)
+ goto error;
+ return fn(lower, upper, context, user);
+ }
+
+ n_lower = 0;
+ n_upper = 0;
+ for (i = 0; i < bset->n_ineq; ++i) {
+ if (isl_int_is_pos(bset->ineq[i][1 + abs_pos]))
+ n_lower++;
+ else if (isl_int_is_neg(bset->ineq[i][1 + abs_pos]))
+ n_upper++;
+ }
+
+ context = isl_basic_set_copy(bset);
+ context = isl_basic_set_cow(context);
+ if (!context)
+ goto error;
+ for (i = context->n_ineq - 1; i >= 0; --i)
+ if (!isl_int_is_zero(context->ineq[i][1 + abs_pos]))
+ isl_basic_set_drop_inequality(context, i);
+
+ context = isl_basic_set_drop(context, type, pos, 1);
+ if (!n_lower && !n_upper)
+ return fn(NULL, NULL, context, user);
+ if (!n_lower)
+ return foreach_upper_bound(bset, type, abs_pos, context, n_upper,
+ fn, user);
+ if (!n_upper)
+ return foreach_lower_bound(bset, type, abs_pos, context, n_lower,
+ fn, user);
+ return foreach_bound_pair(bset, type, abs_pos, context, n_lower, n_upper,
+ fn, user);
+error:
+ isl_constraint_free(lower);
+ isl_constraint_free(upper);
+ isl_basic_set_free(context);
+ return -1;
+}
+
+__isl_give isl_aff *isl_constraint_get_bound(
+ __isl_keep isl_constraint *constraint, enum isl_dim_type type, int pos)
+{
+ isl_aff *aff;
+ isl_ctx *ctx;
+
+ if (!constraint)
+ return NULL;
+ ctx = isl_constraint_get_ctx(constraint);
+ if (pos >= isl_constraint_dim(constraint, type))
+ isl_die(ctx, isl_error_invalid,
+ "index out of bounds", return NULL);
+ if (isl_constraint_dim(constraint, isl_dim_in) != 0)
+ isl_die(ctx, isl_error_invalid,
+ "not a set constraint", return NULL);
+
+ pos += offset(constraint, type);
+ if (isl_int_is_zero(constraint->v->el[pos]))
+ isl_die(ctx, isl_error_invalid,
+ "constraint does not define a bound on given dimension",
+ return NULL);
+
+ aff = isl_aff_alloc(isl_local_space_copy(constraint->ls));
+ if (!aff)
+ return NULL;
+
+ if (isl_int_is_neg(constraint->v->el[pos]))
+ isl_seq_cpy(aff->v->el + 1, constraint->v->el, aff->v->size - 1);
+ else
+ isl_seq_neg(aff->v->el + 1, constraint->v->el, aff->v->size - 1);
+ isl_int_set_si(aff->v->el[1 + pos], 0);
+ isl_int_abs(aff->v->el[0], constraint->v->el[pos]);
+
+ return aff;
+}
+
+/* For an inequality constraint
+ *
+ * f >= 0
+ *
+ * or an equality constraint
+ *
+ * f = 0
+ *
+ * return the affine expression f.
+ */
+__isl_give isl_aff *isl_constraint_get_aff(
+ __isl_keep isl_constraint *constraint)
+{
+ isl_aff *aff;
+
+ if (!constraint)
+ return NULL;
+
+ aff = isl_aff_alloc(isl_local_space_copy(constraint->ls));
+ if (!aff)
+ return NULL;
+
+ isl_seq_cpy(aff->v->el + 1, constraint->v->el, aff->v->size - 1);
+ isl_int_set_si(aff->v->el[0], 1);
+
+ return aff;
+}
+
+/* Construct an equality constraint equating the given affine expression
+ * to zero.
+ */
+__isl_give isl_constraint *isl_equality_from_aff(__isl_take isl_aff *aff)
+{
+ int k;
+ isl_local_space *ls;
+ isl_basic_set *bset;
+
+ if (!aff)
+ return NULL;
+
+ ls = isl_aff_get_domain_local_space(aff);
+ bset = isl_basic_set_from_local_space(ls);
+ bset = isl_basic_set_extend_constraints(bset, 1, 0);
+ k = isl_basic_set_alloc_equality(bset);
+ if (k < 0)
+ goto error;
+
+ isl_seq_cpy(bset->eq[k], aff->v->el + 1, aff->v->size - 1);
+ isl_aff_free(aff);
+
+ return isl_basic_set_constraint(bset, &bset->eq[k]);
+error:
+ isl_aff_free(aff);
+ isl_basic_set_free(bset);
+ return NULL;
+}
+
+/* Construct an inequality constraint enforcing the given affine expression
+ * to be non-negative.
+ */
+__isl_give isl_constraint *isl_inequality_from_aff(__isl_take isl_aff *aff)
+{
+ int k;
+ isl_local_space *ls;
+ isl_basic_set *bset;
+
+ if (!aff)
+ return NULL;
+
+ ls = isl_aff_get_domain_local_space(aff);
+ bset = isl_basic_set_from_local_space(ls);
+ bset = isl_basic_set_extend_constraints(bset, 0, 1);
+ k = isl_basic_set_alloc_inequality(bset);
+ if (k < 0)
+ goto error;
+
+ isl_seq_cpy(bset->ineq[k], aff->v->el + 1, aff->v->size - 1);
+ isl_aff_free(aff);
+
+ return isl_basic_set_constraint(bset, &bset->ineq[k]);
+error:
+ isl_aff_free(aff);
+ isl_basic_set_free(bset);
+ return NULL;
+}