+ isl_mat_free(bounds);
+ isl_mat_free(U);
+ isl_basic_set_free(bset);
+ return NULL;
+}
+
+/* Find a sample integer point, if any, in bset, which is known
+ * to have equalities. If bset contains no integer points, then
+ * return a zero-length vector.
+ * We simply remove the known equalities, compute a sample
+ * in the resulting bset, using the specified recurse function,
+ * and then transform the sample back to the original space.
+ */
+static struct isl_vec *sample_eq(struct isl_basic_set *bset,
+ struct isl_vec *(*recurse)(struct isl_basic_set *))
+{
+ struct isl_mat *T;
+ struct isl_vec *sample;
+
+ if (!bset)
+ return NULL;
+
+ bset = isl_basic_set_remove_equalities(bset, &T, NULL);
+ sample = recurse(bset);
+ if (!sample || sample->size == 0)
+ isl_mat_free(T);
+ else
+ sample = isl_mat_vec_product(T, sample);
+ return sample;
+}
+
+/* Return a matrix containing the equalities of the tableau
+ * in constraint form. The tableau is assumed to have
+ * an associated bset that has been kept up-to-date.
+ */
+static struct isl_mat *tab_equalities(struct isl_tab *tab)
+{
+ int i, j;
+ int n_eq;
+ struct isl_mat *eq;
+ struct isl_basic_set *bset;
+
+ if (!tab)
+ return NULL;
+
+ bset = isl_tab_peek_bset(tab);
+ isl_assert(tab->mat->ctx, bset, return NULL);
+
+ n_eq = tab->n_var - tab->n_col + tab->n_dead;
+ if (tab->empty || n_eq == 0)
+ return isl_mat_alloc(tab->mat->ctx, 0, tab->n_var);
+ if (n_eq == tab->n_var)
+ return isl_mat_identity(tab->mat->ctx, tab->n_var);
+
+ eq = isl_mat_alloc(tab->mat->ctx, n_eq, tab->n_var);
+ if (!eq)
+ return NULL;
+ for (i = 0, j = 0; i < tab->n_con; ++i) {
+ if (tab->con[i].is_row)
+ continue;
+ if (tab->con[i].index >= 0 && tab->con[i].index >= tab->n_dead)
+ continue;
+ if (i < bset->n_eq)
+ isl_seq_cpy(eq->row[j], bset->eq[i] + 1, tab->n_var);
+ else
+ isl_seq_cpy(eq->row[j],
+ bset->ineq[i - bset->n_eq] + 1, tab->n_var);
+ ++j;
+ }
+ isl_assert(bset->ctx, j == n_eq, goto error);
+ return eq;
+error:
+ isl_mat_free(eq);
+ return NULL;
+}
+
+/* Compute and return an initial basis for the bounded tableau "tab".
+ *
+ * If the tableau is either full-dimensional or zero-dimensional,
+ * the we simply return an identity matrix.
+ * Otherwise, we construct a basis whose first directions correspond
+ * to equalities.
+ */
+static struct isl_mat *initial_basis(struct isl_tab *tab)
+{
+ int n_eq;
+ struct isl_mat *eq;
+ struct isl_mat *Q;
+
+ tab->n_unbounded = 0;
+ tab->n_zero = n_eq = tab->n_var - tab->n_col + tab->n_dead;
+ if (tab->empty || n_eq == 0 || n_eq == tab->n_var)
+ return isl_mat_identity(tab->mat->ctx, 1 + tab->n_var);
+
+ eq = tab_equalities(tab);
+ eq = isl_mat_left_hermite(eq, 0, NULL, &Q);
+ if (!eq)
+ return NULL;
+ isl_mat_free(eq);
+
+ Q = isl_mat_lin_to_aff(Q);
+ return Q;
+}
+
+/* Compute the minimum of the current ("level") basis row over "tab"
+ * and store the result in position "level" of "min".
+ */
+static enum isl_lp_result compute_min(isl_ctx *ctx, struct isl_tab *tab,
+ __isl_keep isl_vec *min, int level)
+{
+ return isl_tab_min(tab, tab->basis->row[1 + level],
+ ctx->one, &min->el[level], NULL, 0);
+}
+
+/* Compute the maximum of the current ("level") basis row over "tab"
+ * and store the result in position "level" of "max".
+ */
+static enum isl_lp_result compute_max(isl_ctx *ctx, struct isl_tab *tab,
+ __isl_keep isl_vec *max, int level)
+{
+ enum isl_lp_result res;
+ unsigned dim = tab->n_var;
+
+ isl_seq_neg(tab->basis->row[1 + level] + 1,
+ tab->basis->row[1 + level] + 1, dim);
+ res = isl_tab_min(tab, tab->basis->row[1 + level],
+ ctx->one, &max->el[level], NULL, 0);
+ isl_seq_neg(tab->basis->row[1 + level] + 1,
+ tab->basis->row[1 + level] + 1, dim);
+ isl_int_neg(max->el[level], max->el[level]);
+
+ return res;
+}
+
+/* Perform a greedy search for an integer point in the set represented
+ * by "tab", given that the minimal rational value (rounded up to the
+ * nearest integer) at "level" is smaller than the maximal rational
+ * value (rounded down to the nearest integer).
+ *
+ * Return 1 if we have found an integer point (if tab->n_unbounded > 0
+ * then we may have only found integer values for the bounded dimensions
+ * and it is the responsibility of the caller to extend this solution
+ * to the unbounded dimensions).
+ * Return 0 if greedy search did not result in a solution.
+ * Return -1 if some error occurred.
+ *
+ * We assign a value half-way between the minimum and the maximum
+ * to the current dimension and check if the minimal value of the
+ * next dimension is still smaller than (or equal) to the maximal value.
+ * We continue this process until either
+ * - the minimal value (rounded up) is greater than the maximal value
+ * (rounded down). In this case, greedy search has failed.
+ * - we have exhausted all bounded dimensions, meaning that we have
+ * found a solution.
+ * - the sample value of the tableau is integral.
+ * - some error has occurred.
+ */
+static int greedy_search(isl_ctx *ctx, struct isl_tab *tab,
+ __isl_keep isl_vec *min, __isl_keep isl_vec *max, int level)
+{
+ struct isl_tab_undo *snap;
+ enum isl_lp_result res;
+
+ snap = isl_tab_snap(tab);
+
+ do {
+ isl_int_add(tab->basis->row[1 + level][0],
+ min->el[level], max->el[level]);
+ isl_int_fdiv_q_ui(tab->basis->row[1 + level][0],
+ tab->basis->row[1 + level][0], 2);
+ isl_int_neg(tab->basis->row[1 + level][0],
+ tab->basis->row[1 + level][0]);
+ if (isl_tab_add_valid_eq(tab, tab->basis->row[1 + level]) < 0)
+ return -1;
+ isl_int_set_si(tab->basis->row[1 + level][0], 0);
+
+ if (++level >= tab->n_var - tab->n_unbounded)
+ return 1;
+ if (isl_tab_sample_is_integer(tab))
+ return 1;
+
+ res = compute_min(ctx, tab, min, level);
+ if (res == isl_lp_error)
+ return -1;
+ if (res != isl_lp_ok)
+ isl_die(ctx, isl_error_internal,
+ "expecting bounded rational solution",
+ return -1);
+ res = compute_max(ctx, tab, max, level);
+ if (res == isl_lp_error)
+ return -1;
+ if (res != isl_lp_ok)
+ isl_die(ctx, isl_error_internal,
+ "expecting bounded rational solution",
+ return -1);
+ } while (isl_int_le(min->el[level], max->el[level]));
+
+ if (isl_tab_rollback(tab, snap) < 0)
+ return -1;
+
+ return 0;
+}
+
+/* Given a tableau representing a set, find and return
+ * an integer point in the set, if there is any.
+ *
+ * We perform a depth first search
+ * for an integer point, by scanning all possible values in the range
+ * attained by a basis vector, where an initial basis may have been set
+ * by the calling function. Otherwise an initial basis that exploits
+ * the equalities in the tableau is created.
+ * tab->n_zero is currently ignored and is clobbered by this function.
+ *
+ * The tableau is allowed to have unbounded direction, but then
+ * the calling function needs to set an initial basis, with the
+ * unbounded directions last and with tab->n_unbounded set
+ * to the number of unbounded directions.
+ * Furthermore, the calling functions needs to add shifted copies
+ * of all constraints involving unbounded directions to ensure
+ * that any feasible rational value in these directions can be rounded
+ * up to yield a feasible integer value.
+ * In particular, let B define the given basis x' = B x
+ * and let T be the inverse of B, i.e., X = T x'.
+ * Let a x + c >= 0 be a constraint of the set represented by the tableau,
+ * or a T x' + c >= 0 in terms of the given basis. Assume that
+ * the bounded directions have an integer value, then we can safely
+ * round up the values for the unbounded directions if we make sure
+ * that x' not only satisfies the original constraint, but also
+ * the constraint "a T x' + c + s >= 0" with s the sum of all
+ * negative values in the last n_unbounded entries of "a T".
+ * The calling function therefore needs to add the constraint
+ * a x + c + s >= 0. The current function then scans the first
+ * directions for an integer value and once those have been found,
+ * it can compute "T ceil(B x)" to yield an integer point in the set.
+ * Note that during the search, the first rows of B may be changed
+ * by a basis reduction, but the last n_unbounded rows of B remain
+ * unaltered and are also not mixed into the first rows.
+ *
+ * The search is implemented iteratively. "level" identifies the current
+ * basis vector. "init" is true if we want the first value at the current
+ * level and false if we want the next value.
+ *
+ * At the start of each level, we first check if we can find a solution
+ * using greedy search. If not, we continue with the exhaustive search.
+ *
+ * The initial basis is the identity matrix. If the range in some direction
+ * contains more than one integer value, we perform basis reduction based
+ * on the value of ctx->opt->gbr
+ * - ISL_GBR_NEVER: never perform basis reduction
+ * - ISL_GBR_ONCE: only perform basis reduction the first
+ * time such a range is encountered
+ * - ISL_GBR_ALWAYS: always perform basis reduction when
+ * such a range is encountered
+ *
+ * When ctx->opt->gbr is set to ISL_GBR_ALWAYS, then we allow the basis
+ * reduction computation to return early. That is, as soon as it
+ * finds a reasonable first direction.
+ */
+struct isl_vec *isl_tab_sample(struct isl_tab *tab)
+{
+ unsigned dim;
+ unsigned gbr;
+ struct isl_ctx *ctx;
+ struct isl_vec *sample;
+ struct isl_vec *min;
+ struct isl_vec *max;
+ enum isl_lp_result res;
+ int level;
+ int init;
+ int reduced;
+ struct isl_tab_undo **snap;
+
+ if (!tab)
+ return NULL;
+ if (tab->empty)
+ return isl_vec_alloc(tab->mat->ctx, 0);
+
+ if (!tab->basis)
+ tab->basis = initial_basis(tab);
+ if (!tab->basis)
+ return NULL;
+ isl_assert(tab->mat->ctx, tab->basis->n_row == tab->n_var + 1,
+ return NULL);
+ isl_assert(tab->mat->ctx, tab->basis->n_col == tab->n_var + 1,
+ return NULL);
+
+ ctx = tab->mat->ctx;
+ dim = tab->n_var;
+ gbr = ctx->opt->gbr;
+
+ if (tab->n_unbounded == tab->n_var) {
+ sample = isl_tab_get_sample_value(tab);
+ sample = isl_mat_vec_product(isl_mat_copy(tab->basis), sample);
+ sample = isl_vec_ceil(sample);
+ sample = isl_mat_vec_inverse_product(isl_mat_copy(tab->basis),
+ sample);
+ return sample;
+ }
+
+ if (isl_tab_extend_cons(tab, dim + 1) < 0)
+ return NULL;
+
+ min = isl_vec_alloc(ctx, dim);
+ max = isl_vec_alloc(ctx, dim);
+ snap = isl_alloc_array(ctx, struct isl_tab_undo *, dim);
+
+ if (!min || !max || !snap)
+ goto error;
+
+ level = 0;
+ init = 1;
+ reduced = 0;
+
+ while (level >= 0) {
+ if (init) {
+ int choice;
+
+ res = compute_min(ctx, tab, min, level);
+ if (res == isl_lp_error)
+ goto error;
+ if (res != isl_lp_ok)
+ isl_die(ctx, isl_error_internal,
+ "expecting bounded rational solution",
+ goto error);
+ if (isl_tab_sample_is_integer(tab))
+ break;
+ res = compute_max(ctx, tab, max, level);
+ if (res == isl_lp_error)
+ goto error;
+ if (res != isl_lp_ok)
+ isl_die(ctx, isl_error_internal,
+ "expecting bounded rational solution",
+ goto error);
+ if (isl_tab_sample_is_integer(tab))
+ break;
+ choice = isl_int_lt(min->el[level], max->el[level]);
+ if (choice) {
+ int g;
+ g = greedy_search(ctx, tab, min, max, level);
+ if (g < 0)
+ goto error;
+ if (g)
+ break;
+ }
+ if (!reduced && choice &&
+ ctx->opt->gbr != ISL_GBR_NEVER) {
+ unsigned gbr_only_first;
+ if (ctx->opt->gbr == ISL_GBR_ONCE)
+ ctx->opt->gbr = ISL_GBR_NEVER;
+ tab->n_zero = level;
+ gbr_only_first = ctx->opt->gbr_only_first;
+ ctx->opt->gbr_only_first =
+ ctx->opt->gbr == ISL_GBR_ALWAYS;
+ tab = isl_tab_compute_reduced_basis(tab);
+ ctx->opt->gbr_only_first = gbr_only_first;
+ if (!tab || !tab->basis)
+ goto error;
+ reduced = 1;
+ continue;
+ }
+ reduced = 0;
+ snap[level] = isl_tab_snap(tab);
+ } else
+ isl_int_add_ui(min->el[level], min->el[level], 1);
+
+ if (isl_int_gt(min->el[level], max->el[level])) {
+ level--;
+ init = 0;
+ if (level >= 0)
+ if (isl_tab_rollback(tab, snap[level]) < 0)
+ goto error;
+ continue;
+ }
+ isl_int_neg(tab->basis->row[1 + level][0], min->el[level]);
+ if (isl_tab_add_valid_eq(tab, tab->basis->row[1 + level]) < 0)
+ goto error;
+ isl_int_set_si(tab->basis->row[1 + level][0], 0);
+ if (level + tab->n_unbounded < dim - 1) {
+ ++level;
+ init = 1;
+ continue;
+ }
+ break;
+ }
+
+ if (level >= 0) {
+ sample = isl_tab_get_sample_value(tab);
+ if (!sample)
+ goto error;
+ if (tab->n_unbounded && !isl_int_is_one(sample->el[0])) {
+ sample = isl_mat_vec_product(isl_mat_copy(tab->basis),
+ sample);
+ sample = isl_vec_ceil(sample);
+ sample = isl_mat_vec_inverse_product(
+ isl_mat_copy(tab->basis), sample);
+ }
+ } else
+ sample = isl_vec_alloc(ctx, 0);
+
+ ctx->opt->gbr = gbr;
+ isl_vec_free(min);
+ isl_vec_free(max);
+ free(snap);
+ return sample;
+error:
+ ctx->opt->gbr = gbr;
+ isl_vec_free(min);
+ isl_vec_free(max);
+ free(snap);
+ return NULL;
+}
+
+static struct isl_vec *sample_bounded(struct isl_basic_set *bset);
+
+/* Compute a sample point of the given basic set, based on the given,
+ * non-trivial factorization.
+ */
+static __isl_give isl_vec *factored_sample(__isl_take isl_basic_set *bset,
+ __isl_take isl_factorizer *f)
+{
+ int i, n;
+ isl_vec *sample = NULL;
+ isl_ctx *ctx;
+ unsigned nparam;
+ unsigned nvar;
+
+ ctx = isl_basic_set_get_ctx(bset);
+ if (!ctx)
+ goto error;
+
+ nparam = isl_basic_set_dim(bset, isl_dim_param);
+ nvar = isl_basic_set_dim(bset, isl_dim_set);
+
+ sample = isl_vec_alloc(ctx, 1 + isl_basic_set_total_dim(bset));
+ if (!sample)
+ goto error;
+ isl_int_set_si(sample->el[0], 1);
+
+ bset = isl_morph_basic_set(isl_morph_copy(f->morph), bset);
+
+ for (i = 0, n = 0; i < f->n_group; ++i) {
+ isl_basic_set *bset_i;
+ isl_vec *sample_i;
+
+ bset_i = isl_basic_set_copy(bset);
+ bset_i = isl_basic_set_drop_constraints_involving(bset_i,
+ nparam + n + f->len[i], nvar - n - f->len[i]);
+ bset_i = isl_basic_set_drop_constraints_involving(bset_i,
+ nparam, n);
+ bset_i = isl_basic_set_drop(bset_i, isl_dim_set,
+ n + f->len[i], nvar - n - f->len[i]);
+ bset_i = isl_basic_set_drop(bset_i, isl_dim_set, 0, n);
+
+ sample_i = sample_bounded(bset_i);
+ if (!sample_i)
+ goto error;
+ if (sample_i->size == 0) {
+ isl_basic_set_free(bset);
+ isl_factorizer_free(f);
+ isl_vec_free(sample);
+ return sample_i;
+ }
+ isl_seq_cpy(sample->el + 1 + nparam + n,
+ sample_i->el + 1, f->len[i]);
+ isl_vec_free(sample_i);
+
+ n += f->len[i];
+ }
+
+ f->morph = isl_morph_inverse(f->morph);
+ sample = isl_morph_vec(isl_morph_copy(f->morph), sample);
+
+ isl_basic_set_free(bset);
+ isl_factorizer_free(f);
+ return sample;
+error: