isl_map_convex_hull((struct isl_map *)set);
}
+struct sh_data_entry {
+ struct isl_hash_table *table;
+ struct isl_tab *tab;
+};
+
+/* Holds the data needed during the simple hull computation.
+ * In particular,
+ * n the number of basic sets in the original set
+ * hull_table a hash table of already computed constraints
+ * in the simple hull
+ * p for each basic set,
+ * table a hash table of the constraints
+ * tab the tableau corresponding to the basic set
+ */
+struct sh_data {
+ struct isl_ctx *ctx;
+ unsigned n;
+ struct isl_hash_table *hull_table;
+ struct sh_data_entry p[0];
+};
+
+static void sh_data_free(struct sh_data *data)
+{
+ int i;
+
+ if (!data)
+ return;
+ isl_hash_table_free(data->ctx, data->hull_table);
+ for (i = 0; i < data->n; ++i) {
+ isl_hash_table_free(data->ctx, data->p[i].table);
+ isl_tab_free(data->ctx, data->p[i].tab);
+ }
+ free(data);
+}
+
+struct ineq_cmp_data {
+ unsigned len;
+ isl_int *p;
+};
+
+static int has_ineq(const void *entry, const void *val)
+{
+ isl_int *row = (isl_int *)entry;
+ struct ineq_cmp_data *v = (struct ineq_cmp_data *)val;
+
+ return isl_seq_eq(row + 1, v->p + 1, v->len) ||
+ isl_seq_is_neg(row + 1, v->p + 1, v->len);
+}
+
+static int hash_ineq(struct isl_ctx *ctx, struct isl_hash_table *table,
+ isl_int *ineq, unsigned len)
+{
+ uint32_t c_hash;
+ struct ineq_cmp_data v;
+ struct isl_hash_table_entry *entry;
+
+ v.len = len;
+ v.p = ineq;
+ c_hash = isl_seq_hash(ineq + 1, len, isl_hash_init());
+ entry = isl_hash_table_find(ctx, table, c_hash, has_ineq, &v, 1);
+ if (!entry)
+ return - 1;
+ entry->data = ineq;
+ return 0;
+}
+
+/* Fill hash table "table" with the constraints of "bset".
+ * Equalities are added as two inequalities.
+ * The value in the hash table is a pointer to the (in)equality of "bset".
+ */
+static int hash_basic_set(struct isl_hash_table *table,
+ struct isl_basic_set *bset)
+{
+ int i, j;
+ unsigned dim = isl_basic_set_total_dim(bset);
+
+ for (i = 0; i < bset->n_eq; ++i) {
+ for (j = 0; j < 2; ++j) {
+ isl_seq_neg(bset->eq[i], bset->eq[i], 1 + dim);
+ if (hash_ineq(bset->ctx, table, bset->eq[i], dim) < 0)
+ return -1;
+ }
+ }
+ for (i = 0; i < bset->n_ineq; ++i) {
+ if (hash_ineq(bset->ctx, table, bset->ineq[i], dim) < 0)
+ return -1;
+ }
+ return 0;
+}
+
+static struct sh_data *sh_data_alloc(struct isl_set *set, unsigned n_ineq)
+{
+ struct sh_data *data;
+ int i;
+
+ data = isl_calloc(set->ctx, struct sh_data,
+ sizeof(struct sh_data) + set->n * sizeof(struct sh_data_entry));
+ if (!data)
+ return NULL;
+ data->ctx = set->ctx;
+ data->n = set->n;
+ data->hull_table = isl_hash_table_alloc(set->ctx, n_ineq);
+ if (!data->hull_table)
+ goto error;
+ for (i = 0; i < set->n; ++i) {
+ data->p[i].table = isl_hash_table_alloc(set->ctx,
+ 2 * set->p[i]->n_eq + set->p[i]->n_ineq);
+ if (!data->p[i].table)
+ goto error;
+ if (hash_basic_set(data->p[i].table, set->p[i]) < 0)
+ goto error;
+ }
+ return data;
+error:
+ sh_data_free(data);
+ return NULL;
+}
+
+/* Check if inequality "ineq" is a bound for basic set "j" or if
+ * it can be relaxed (by increasing the constant term) to become
+ * a bound for that basic set. In the latter case, the constant
+ * term is updated.
+ * Return 1 if "ineq" is a bound
+ * 0 if "ineq" may attain arbitrarily small values on basic set "j"
+ * -1 if some error occurred
+ */
+static int is_bound(struct sh_data *data, struct isl_set *set, int j,
+ isl_int *ineq)
+{
+ enum isl_lp_result res;
+ isl_int opt;
+
+ if (!data->p[j].tab) {
+ data->p[j].tab = isl_tab_from_basic_set(set->p[j]);
+ if (!data->p[j].tab)
+ return -1;
+ }
+
+ isl_int_init(opt);
+
+ res = isl_tab_min(data->ctx, data->p[j].tab, ineq, data->ctx->one,
+ &opt, NULL);
+ if (res == isl_lp_ok && isl_int_is_neg(opt))
+ isl_int_sub(ineq[0], ineq[0], opt);
+
+ isl_int_clear(opt);
+
+ return res == isl_lp_ok ? 1 :
+ res == isl_lp_unbounded ? 0 : -1;
+}
+
+/* Check if inequality "ineq" from basic set "i" can be relaxed to
+ * become a bound on the whole set. If so, add the (relaxed) inequality
+ * to "hull".
+ *
+ * We first check if "hull" already contains a translate of the inequality.
+ * If so, we are done.
+ * Then, we check if any of the previous basic sets contains a translate
+ * of the inequality. If so, then we have already considered this
+ * inequality and we are done.
+ * Otherwise, for each basic set other than "i", we check if the inequality
+ * is a bound on the basic set.
+ * For previous basic sets, we know that they do not contain a translate
+ * of the inequality, so we directly call is_bound.
+ * For following basic sets, we first check if a translate of the
+ * inequality appears in its description and if so directly update
+ * the inequality accordingly.
+ */
+static struct isl_basic_set *add_bound(struct isl_basic_set *hull,
+ struct sh_data *data, struct isl_set *set, int i, isl_int *ineq)
+{
+ uint32_t c_hash;
+ struct ineq_cmp_data v;
+ struct isl_hash_table_entry *entry;
+ int j, k;
+
+ if (!hull)
+ return NULL;
+
+ v.len = isl_basic_set_total_dim(hull);
+ v.p = ineq;
+ c_hash = isl_seq_hash(ineq + 1, v.len, isl_hash_init());
+
+ entry = isl_hash_table_find(hull->ctx, data->hull_table, c_hash,
+ has_ineq, &v, 0);
+ if (entry)
+ return hull;
+
+ for (j = 0; j < i; ++j) {
+ entry = isl_hash_table_find(hull->ctx, data->p[j].table,
+ c_hash, has_ineq, &v, 0);
+ if (entry)
+ break;
+ }
+ if (j < i)
+ return hull;
+
+ k = isl_basic_set_alloc_inequality(hull);
+ isl_seq_cpy(hull->ineq[k], ineq, 1 + v.len);
+ if (k < 0)
+ goto error;
+
+ for (j = 0; j < i; ++j) {
+ int bound;
+ bound = is_bound(data, set, j, hull->ineq[k]);
+ if (bound < 0)
+ goto error;
+ if (!bound)
+ break;
+ }
+ if (j < i) {
+ isl_basic_set_free_inequality(hull, 1);
+ return hull;
+ }
+
+ for (j = i + 1; j < set->n; ++j) {
+ int bound, neg;
+ isl_int *ineq_j;
+ entry = isl_hash_table_find(hull->ctx, data->p[j].table,
+ c_hash, has_ineq, &v, 0);
+ if (entry) {
+ ineq_j = entry->data;
+ neg = isl_seq_is_neg(ineq_j + 1,
+ hull->ineq[k] + 1, v.len);
+ if (neg)
+ isl_int_neg(ineq_j[0], ineq_j[0]);
+ if (isl_int_gt(ineq_j[0], hull->ineq[k][0]))
+ isl_int_set(hull->ineq[k][0], ineq_j[0]);
+ if (neg)
+ isl_int_neg(ineq_j[0], ineq_j[0]);
+ continue;
+ }
+ bound = is_bound(data, set, j, hull->ineq[k]);
+ if (bound < 0)
+ goto error;
+ if (!bound)
+ break;
+ }
+ if (j < set->n) {
+ isl_basic_set_free_inequality(hull, 1);
+ return hull;
+ }
+
+ entry = isl_hash_table_find(hull->ctx, data->hull_table, c_hash,
+ has_ineq, &v, 1);
+ if (!entry)
+ goto error;
+ entry->data = hull->ineq[k];
+
+ return hull;
+error:
+ isl_basic_set_free(hull);
+ return NULL;
+}
+
+/* Check if any inequality from basic set "i" can be relaxed to
+ * become a bound on the whole set. If so, add the (relaxed) inequality
+ * to "hull".
+ */
+static struct isl_basic_set *add_bounds(struct isl_basic_set *bset,
+ struct sh_data *data, struct isl_set *set, int i)
+{
+ int j, k;
+ unsigned dim = isl_basic_set_total_dim(bset);
+
+ for (j = 0; j < set->p[i]->n_eq; ++j) {
+ for (k = 0; k < 2; ++k) {
+ isl_seq_neg(set->p[i]->eq[j], set->p[i]->eq[j], 1+dim);
+ add_bound(bset, data, set, i, set->p[i]->eq[j]);
+ }
+ }
+ for (j = 0; j < set->p[i]->n_ineq; ++j)
+ add_bound(bset, data, set, i, set->p[i]->ineq[j]);
+ return bset;
+}
+
+/* Compute a superset of the convex hull of set that is described
+ * by only translates of the constraints in the constituents of set.
+ */
static struct isl_basic_set *uset_simple_hull(struct isl_set *set)
{
- struct isl_basic_set *bset = NULL;
+ struct sh_data *data = NULL;
+ struct isl_basic_set *hull = NULL;
unsigned n_ineq;
- unsigned dim;
int i, j;
if (!set)
for (i = 0; i < set->n; ++i) {
if (!set->p[i])
goto error;
- n_ineq += set->p[i]->n_ineq;
+ n_ineq += 2 * set->p[i]->n_eq + set->p[i]->n_ineq;
}
- bset = isl_set_affine_hull(isl_set_copy(set));
- if (!bset)
+ hull = isl_set_affine_hull(isl_set_copy(set));
+ if (!hull)
goto error;
- dim = isl_basic_set_n_dim(bset);
- bset = isl_basic_set_extend_dim(bset, isl_dim_copy(bset->dim),
+ hull = isl_basic_set_extend_dim(hull, isl_dim_copy(hull->dim),
0, 0, n_ineq);
- if (!bset)
+ if (!hull)
goto error;
- for (i = 0; i < set->n; ++i) {
- for (j = 0; j < set->p[i]->n_ineq; ++j) {
- int k;
- int is_bound;
+ data = sh_data_alloc(set, n_ineq);
+ if (!data)
+ goto error;
+ if (hash_basic_set(data->hull_table, hull) < 0)
+ goto error;
- k = isl_basic_set_alloc_inequality(bset);
- if (k < 0)
- goto error;
- isl_seq_cpy(bset->ineq[k], set->p[i]->ineq[j], 1 + dim);
- is_bound = uset_is_bound(set->ctx, set, bset->ineq[k],
- 1 + dim);
- if (is_bound < 0)
- goto error;
- if (!is_bound)
- isl_basic_set_free_inequality(bset, 1);
- }
- }
+ for (i = 0; i < set->n; ++i)
+ hull = add_bounds(hull, data, set, i);
- bset = isl_basic_set_simplify(bset);
- bset = isl_basic_set_finalize(bset);
- bset = isl_basic_set_convex_hull(bset);
+ hull = isl_basic_set_convex_hull(hull);
+ sh_data_free(data);
isl_set_free(set);
- return bset;
+ return hull;
error:
- isl_basic_set_free(bset);
+ sh_data_free(data);
+ isl_basic_set_free(hull);
isl_set_free(set);
return NULL;
}
/* Compute a superset of the convex hull of map that is described
* by only translates of the constraints in the constituents of map.
- *
- * The implementation is not very efficient. In particular, if
- * constraints with the same normal appear in more than one
- * basic map, they will be (re)examined each time.
*/
struct isl_basic_map *isl_map_simple_hull(struct isl_map *map)
{
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