+ 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)