{
enum isl_ineq_type type = isl_tab_ineq_type(tab, ineq);
switch (type) {
+ default:
case isl_ineq_error: return STATUS_ERROR;
case isl_ineq_redundant: return STATUS_VALID;
case isl_ineq_separate: return STATUS_SEPARATE;
for (k = 0; k < map->p[i]->n_eq; ++k) {
if (eq_i && (eq_i[2 * k] != STATUS_VALID ||
eq_i[2 * k + 1] != STATUS_VALID))
+ continue;
l = isl_basic_map_alloc_equality(fused);
if (l < 0)
goto error;
isl_seq_cpy(fused->ineq[l], map->p[j]->ineq[k], 1 + total);
}
+ for (k = 0; k < map->p[i]->n_div; ++k) {
+ int l = isl_basic_map_alloc_div(fused);
+ if (l < 0)
+ goto error;
+ isl_seq_cpy(fused->div[l], map->p[i]->div[k], 1 + 1 + total);
+ }
+
for (k = 0; k < extra_rows; ++k) {
l = isl_basic_map_alloc_inequality(fused);
if (l < 0)
for (k = 0; k < map->p[i]->n_ineq; ++k) {
if (ineq_i[k] != STATUS_CUT)
continue;
- tabs[i] = isl_tab_select_facet(tabs[i], n_eq + k);
+ if (isl_tab_select_facet(tabs[i], n_eq + k) < 0)
+ return -1;
for (l = 0; l < map->p[j]->n_ineq; ++l) {
int stat;
if (ineq_j[l] != STATUS_CUT)
snap = isl_tab_snap(tabs[i]);
tabs[i] = isl_tab_relax(tabs[i], n_eq + k);
snap2 = isl_tab_snap(tabs[i]);
- tabs[i] = isl_tab_select_facet(tabs[i], n_eq + k);
+ if (isl_tab_select_facet(tabs[i], n_eq + k) < 0)
+ return -1;
super = contains(map, j, ineq_j, tabs[i]);
if (super) {
if (isl_tab_rollback(tabs[i], snap2) < 0)
return 0;
}
+/* Check if the constraints in "wraps" from "first" until the last
+ * are all valid for the basic set represented by "tab".
+ * If not, wraps->n_row is set to zero.
+ */
+static int check_wraps(__isl_keep isl_mat *wraps, int first,
+ struct isl_tab *tab)
+{
+ int i;
+
+ for (i = first; i < wraps->n_row; ++i) {
+ enum isl_ineq_type type;
+ type = isl_tab_ineq_type(tab, wraps->row[i]);
+ if (type == isl_ineq_error)
+ return -1;
+ if (type == isl_ineq_redundant)
+ continue;
+ wraps->n_row = 0;
+ return 0;
+ }
+
+ return 0;
+}
+
+/* Return a set that corresponds to the non-redudant constraints
+ * (as recorded in tab) of bmap.
+ *
+ * It's important to remove the redundant constraints as some
+ * of the other constraints may have been modified after the
+ * constraints were marked redundant.
+ * In particular, a constraint may have been relaxed.
+ * Redundant constraints are ignored when a constraint is relaxed
+ * and should therefore continue to be ignored ever after.
+ * Otherwise, the relaxation might be thwarted by some of
+ * these constraints.
+ */
+static __isl_give isl_set *set_from_updated_bmap(__isl_keep isl_basic_map *bmap,
+ struct isl_tab *tab)
+{
+ bmap = isl_basic_map_copy(bmap);
+ bmap = isl_basic_map_cow(bmap);
+ bmap = isl_basic_map_update_from_tab(bmap, tab);
+ return isl_set_from_basic_set(isl_basic_map_underlying_set(bmap));
+}
+
/* Given a basic set i with a constraint k that is adjacent to either the
* whole of basic set j or a facet of basic set j, check if we can wrap
* both the facet corresponding to k and the facet of j (or the whole of j)
*
* All constraints of i (except k) are assumed to be valid for j.
*
+ * However, the constraints of j may not be valid for i and so
+ * we have to check that the wrapping constraints for j are valid for i.
+ *
* In the case where j has a facet adjacent to i, tab[j] is assumed
* to have been restricted to this facet, so that the non-redundant
* constraints in tab[j] are the ridges of the facet.
* Note that for the purpose of wrapping, it does not matter whether
- * we wrap the ridges of i aronud the whole of j or just around
+ * we wrap the ridges of i around the whole of j or just around
* the facet since all the other constraints are assumed to be valid for j.
* In practice, we wrap to include the whole of j.
* ____ _____
struct isl_vec *bound = NULL;
unsigned total = isl_basic_map_total_dim(map->p[i]);
struct isl_tab_undo *snap;
+ int n;
- snap = isl_tab_snap(tabs[i]);
-
- set_i = isl_set_from_basic_set(
- isl_basic_map_underlying_set(isl_basic_map_copy(map->p[i])));
- set_j = isl_set_from_basic_set(
- isl_basic_map_underlying_set(isl_basic_map_copy(map->p[j])));
+ set_i = set_from_updated_bmap(map->p[i], tabs[i]);
+ set_j = set_from_updated_bmap(map->p[j], tabs[j]);
wraps = isl_mat_alloc(map->ctx, 2 * (map->p[i]->n_eq + map->p[j]->n_eq) +
map->p[i]->n_ineq + map->p[j]->n_ineq,
1 + total);
if (!wraps->n_row)
goto unbounded;
- tabs[i] = isl_tab_select_facet(tabs[i], map->p[i]->n_eq + k);
+ snap = isl_tab_snap(tabs[i]);
+
+ if (isl_tab_select_facet(tabs[i], map->p[i]->n_eq + k) < 0)
+ goto error;
if (isl_tab_detect_redundant(tabs[i]) < 0)
goto error;
isl_seq_neg(bound->el, map->p[i]->ineq[k], 1 + total);
+ n = wraps->n_row;
if (add_wraps(wraps, map->p[i], tabs[i], bound->el, set_j) < 0)
goto error;
+
+ if (isl_tab_rollback(tabs[i], snap) < 0)
+ goto error;
+ if (check_wraps(wraps, n, tabs[i]) < 0)
+ goto error;
if (!wraps->n_row)
goto unbounded;
changed = fuse(map, i, j, tabs, eq_i, ineq_i, eq_j, ineq_j, wraps);
- if (!changed) {
unbounded:
- if (isl_tab_rollback(tabs[i], snap) < 0)
- goto error;
- }
-
isl_mat_free(wraps);
isl_set_free(set_i);
return -1;
}
-/* Given two basic sets i and j such that i has exactly one cut constraint,
- * check if we can wrap the corresponding facet around its ridges to include
- * the other basic set (and nothing else).
+/* Set the is_redundant property of the "n" constraints in "cuts",
+ * except "k" to "v".
+ * This is a fairly tricky operation as it bypasses isl_tab.c.
+ * The reason we want to temporarily mark some constraints redundant
+ * is that we want to ignore them in add_wraps.
+ *
+ * Initially all cut constraints are non-redundant, but the
+ * selection of a facet right before the call to this function
+ * may have made some of them redundant.
+ * Likewise, the same constraints are marked non-redundant
+ * in the second call to this function, before they are officially
+ * made non-redundant again in the subsequent rollback.
+ */
+static void set_is_redundant(struct isl_tab *tab, unsigned n_eq,
+ int *cuts, int n, int k, int v)
+{
+ int l;
+
+ for (l = 0; l < n; ++l) {
+ if (l == k)
+ continue;
+ tab->con[n_eq + cuts[l]].is_redundant = v;
+ }
+}
+
+/* Given a pair of basic maps i and j such that j stick out
+ * of i at n cut constraints, each time by at most one,
+ * try to compute wrapping constraints and replace the two
+ * basic maps by a single basic map.
+ * The other constraints of i are assumed to be valid for j.
+ *
+ * The facets of i corresponding to the cut constraints are
+ * wrapped around their ridges, except those ridges determined
+ * by any of the other cut constraints.
+ * The intersections of cut constraints need to be ignored
+ * as the result of wrapping on cur constraint around another
+ * would result in a constraint cutting the union.
+ * In each case, the facets are wrapped to include the union
+ * of the two basic maps.
+ *
+ * The pieces of j that lie at an offset of exactly one from
+ * one of the cut constraints of i are wrapped around their edges.
+ * Here, there is no need to ignore intersections because we
+ * are wrapping around the union of the two basic maps.
+ *
+ * If any wrapping fails, i.e., if we cannot wrap to touch
+ * the union, then we give up.
+ * Otherwise, the pair of basic maps is replaced by their union.
+ */
+static int wrap_in_facets(struct isl_map *map, int i, int j,
+ int *cuts, int n, struct isl_tab **tabs,
+ int *eq_i, int *ineq_i, int *eq_j, int *ineq_j)
+{
+ int changed = 0;
+ isl_mat *wraps = NULL;
+ isl_set *set = NULL;
+ isl_vec *bound = NULL;
+ unsigned total = isl_basic_map_total_dim(map->p[i]);
+ int max_wrap;
+ int k;
+ struct isl_tab_undo *snap_i, *snap_j;
+
+ if (isl_tab_extend_cons(tabs[j], 1) < 0)
+ goto error;
+
+ max_wrap = 2 * (map->p[i]->n_eq + map->p[j]->n_eq) +
+ map->p[i]->n_ineq + map->p[j]->n_ineq;
+ max_wrap *= n;
+
+ set = isl_set_union(set_from_updated_bmap(map->p[i], tabs[i]),
+ set_from_updated_bmap(map->p[j], tabs[j]));
+ wraps = isl_mat_alloc(map->ctx, max_wrap, 1 + total);
+ bound = isl_vec_alloc(map->ctx, 1 + total);
+ if (!set || !wraps || !bound)
+ goto error;
+
+ snap_i = isl_tab_snap(tabs[i]);
+ snap_j = isl_tab_snap(tabs[j]);
+
+ wraps->n_row = 0;
+
+ for (k = 0; k < n; ++k) {
+ if (isl_tab_select_facet(tabs[i], map->p[i]->n_eq + cuts[k]) < 0)
+ goto error;
+ if (isl_tab_detect_redundant(tabs[i]) < 0)
+ goto error;
+ set_is_redundant(tabs[i], map->p[i]->n_eq, cuts, n, k, 1);
+
+ isl_seq_neg(bound->el, map->p[i]->ineq[cuts[k]], 1 + total);
+ if (add_wraps(wraps, map->p[i], tabs[i], bound->el, set) < 0)
+ goto error;
+
+ set_is_redundant(tabs[i], map->p[i]->n_eq, cuts, n, k, 0);
+ if (isl_tab_rollback(tabs[i], snap_i) < 0)
+ goto error;
+
+ if (!wraps->n_row)
+ break;
+
+ isl_seq_cpy(bound->el, map->p[i]->ineq[cuts[k]], 1 + total);
+ isl_int_add_ui(bound->el[0], bound->el[0], 1);
+ tabs[j] = isl_tab_add_eq(tabs[j], bound->el);
+ if (isl_tab_detect_redundant(tabs[j]) < 0)
+ goto error;
+
+ if (!tabs[j]->empty &&
+ add_wraps(wraps, map->p[j], tabs[j], bound->el, set) < 0)
+ goto error;
+
+ if (isl_tab_rollback(tabs[j], snap_j) < 0)
+ goto error;
+
+ if (!wraps->n_row)
+ break;
+ }
+
+ if (k == n)
+ changed = fuse(map, i, j, tabs,
+ eq_i, ineq_i, eq_j, ineq_j, wraps);
+
+ isl_vec_free(bound);
+ isl_mat_free(wraps);
+ isl_set_free(set);
+
+ return changed;
+error:
+ isl_vec_free(bound);
+ isl_mat_free(wraps);
+ isl_set_free(set);
+ return -1;
+}
+
+/* Given two basic sets i and j such that i has not cut equalities,
+ * check if relaxing all the cut inequalities of i by one turns
+ * them into valid constraint for j and check if we can wrap in
+ * the bits that are sticking out.
* If so, replace the pair by their union.
*
- * We first check if j has a facet adjacent to the cut constraint of i.
- * If so, we try to wrap in the facet.
+ * We first check if all relaxed cut inequalities of i are valid for j
+ * and then try to wrap in the intersections of the relaxed cut inequalities
+ * with j.
+ *
+ * During this wrapping, we consider the points of j that lie at a distance
+ * of exactly 1 from i. In particular, we ignore the points that lie in
+ * between this lower-dimensional space and the basic map i.
+ * We can therefore only apply this to integer maps.
* ____ _____
* / ___|_ / \
* / | | / |
* \ | | => \ |
* \|____| \ |
* \___| \____/
+ *
+ * _____ ______
+ * | ____|_ | \
+ * | | | | |
+ * | | | => | |
+ * |_| | | |
+ * |_____| \______|
+ *
+ * _______
+ * | |
+ * | |\ |
+ * | | \ |
+ * | | \ |
+ * | | \|
+ * | | \
+ * | |_____\
+ * | |
+ * |_______|
+ *
+ * Wrapping can fail if the result of wrapping one of the facets
+ * around its edges does not produce any new facet constraint.
+ * In particular, this happens when we try to wrap in unbounded sets.
+ *
+ * _______________________________________________________________________
+ * |
+ * | ___
+ * | | |
+ * |_| |_________________________________________________________________
+ * |___|
+ *
+ * The following is not an acceptable result of coalescing the above two
+ * sets as it includes extra integer points.
+ * _______________________________________________________________________
+ * |
+ * |
+ * |
+ * |
+ * \______________________________________________________________________
*/
static int can_wrap_in_set(struct isl_map *map, int i, int j,
- struct isl_tab **tabs, int *ineq_i, int *ineq_j)
+ struct isl_tab **tabs, int *eq_i, int *ineq_i, int *eq_j, int *ineq_j)
{
int changed = 0;
- int k, l;
- unsigned total = isl_basic_map_total_dim(map->p[i]);
- struct isl_tab_undo *snap;
-
- for (k = 0; k < map->p[i]->n_ineq; ++k)
- if (ineq_i[k] == STATUS_CUT)
- break;
+ int k, m;
+ int n;
+ int *cuts = NULL;
- isl_assert(map->ctx, k < map->p[i]->n_ineq, return -1);
-
- isl_int_add_ui(map->p[i]->ineq[k][0], map->p[i]->ineq[k][0], 1);
- for (l = 0; l < map->p[j]->n_ineq; ++l)
- if (isl_seq_eq(map->p[i]->ineq[k],
- map->p[j]->ineq[l], 1 + total))
- break;
- isl_int_sub_ui(map->p[i]->ineq[k][0], map->p[i]->ineq[k][0], 1);
+ if (ISL_F_ISSET(map->p[i], ISL_BASIC_MAP_RATIONAL) ||
+ ISL_F_ISSET(map->p[j], ISL_BASIC_MAP_RATIONAL))
+ return 0;
- if (l >= map->p[j]->n_ineq)
+ n = count(ineq_i, map->p[i]->n_ineq, STATUS_CUT);
+ if (n == 0)
return 0;
- snap = isl_tab_snap(tabs[j]);
- tabs[j] = isl_tab_select_facet(tabs[j], map->p[j]->n_eq + l);
- if (isl_tab_detect_redundant(tabs[j]) < 0)
+ cuts = isl_alloc_array(map->ctx, int, n);
+ if (!cuts)
return -1;
- changed = can_wrap_in_facet(map, i, j, k, tabs, NULL, ineq_i, NULL, ineq_j);
+ for (k = 0, m = 0; m < n; ++k) {
+ enum isl_ineq_type type;
- if (!changed && isl_tab_rollback(tabs[j], snap) < 0)
- return -1;
+ if (ineq_i[k] != STATUS_CUT)
+ continue;
+
+ isl_int_add_ui(map->p[i]->ineq[k][0], map->p[i]->ineq[k][0], 1);
+ type = isl_tab_ineq_type(tabs[j], map->p[i]->ineq[k]);
+ isl_int_sub_ui(map->p[i]->ineq[k][0], map->p[i]->ineq[k][0], 1);
+ if (type == isl_ineq_error)
+ goto error;
+ if (type != isl_ineq_redundant)
+ break;
+ cuts[m] = k;
+ ++m;
+ }
+
+ if (m == n)
+ changed = wrap_in_facets(map, i, j, cuts, n, tabs,
+ eq_i, ineq_i, eq_j, ineq_j);
+
+ free(cuts);
return changed;
+error:
+ free(cuts);
+ return -1;
}
/* Check if either i or j has a single cut constraint that can
* if so, replace the pair by their union.
*/
static int check_wrap(struct isl_map *map, int i, int j,
- struct isl_tab **tabs, int *ineq_i, int *ineq_j)
+ struct isl_tab **tabs, int *eq_i, int *ineq_i, int *eq_j, int *ineq_j)
{
int changed = 0;
- if (count(ineq_i, map->p[i]->n_ineq, STATUS_CUT) == 1)
- changed = can_wrap_in_set(map, i, j, tabs, ineq_i, ineq_j);
+ if (!any(eq_i, 2 * map->p[i]->n_eq, STATUS_CUT))
+ changed = can_wrap_in_set(map, i, j, tabs,
+ eq_i, ineq_i, eq_j, ineq_j);
if (changed)
return changed;
- if (count(ineq_j, map->p[j]->n_ineq, STATUS_CUT) == 1)
- changed = can_wrap_in_set(map, j, i, tabs, ineq_j, ineq_i);
+ if (!any(eq_j, 2 * map->p[j]->n_eq, STATUS_CUT))
+ changed = can_wrap_in_set(map, j, i, tabs,
+ eq_j, ineq_j, eq_i, ineq_i);
return changed;
}
* inequality adjacent to an equality.
* We call the basic map that has the inequality "i" and the basic
* map that has the equality "j".
- * If "i" has any "cut" inequality, then relaxing the inequality
+ * If "i" has any "cut" (in)equality, then relaxing the inequality
* by one would not result in a basic map that contains the other
* basic map.
*/
/* j has an equality adjacent to an inequality in i */
+ if (any(eq_i, 2 * map->p[i]->n_eq, STATUS_CUT))
+ return 0;
if (any(ineq_i, map->p[i]->n_ineq, STATUS_CUT))
/* ADJ EQ CUT */
return 0;
* of the valid constraints in both basic maps together
* with all wrapping constraints
*
- * 6. one of the basic maps has a single cut constraint and
- * the other basic map has a constraint adjacent to this constraint.
- * Moreover, the facets corresponding to both constraints
- * can be wrapped around their ridges to include the other basic map
+ * 6. one of the basic maps extends beyond the other by at most one.
+ * Moreover, the facets corresponding to the cut constraints and
+ * the pieces of the other basic map at offset one from these cut
+ * constraints can be wrapped around their ridges to include
+ * the unione of the two basic maps
* => the pair can be replaced by a basic map consisting
* of the valid constraints in both basic maps together
* with all wrapping constraints
all(ineq_j, map->p[j]->n_ineq, STATUS_VALID)) {
drop(map, i, tabs);
changed = 1;
- } else if (any(eq_i, 2 * map->p[i]->n_eq, STATUS_CUT) ||
- any(eq_j, 2 * map->p[j]->n_eq, STATUS_CUT)) {
- /* BAD CUT */
} else if (any(eq_i, 2 * map->p[i]->n_eq, STATUS_ADJ_EQ) ||
any(eq_j, 2 * map->p[j]->n_eq, STATUS_ADJ_EQ)) {
/* ADJ EQ PAIR */
/* BAD ADJ INEQ */
} else if (any(ineq_i, map->p[i]->n_ineq, STATUS_ADJ_INEQ) ||
any(ineq_j, map->p[j]->n_ineq, STATUS_ADJ_INEQ)) {
- changed = check_adj_ineq(map, i, j, tabs, ineq_i, ineq_j);
+ if (!any(eq_i, 2 * map->p[i]->n_eq, STATUS_CUT) &&
+ !any(eq_j, 2 * map->p[j]->n_eq, STATUS_CUT))
+ changed = check_adj_ineq(map, i, j, tabs,
+ ineq_i, ineq_j);
} else {
- changed = check_facets(map, i, j, tabs, ineq_i, ineq_j);
+ if (!any(eq_i, 2 * map->p[i]->n_eq, STATUS_CUT) &&
+ !any(eq_j, 2 * map->p[j]->n_eq, STATUS_CUT))
+ changed = check_facets(map, i, j, tabs, ineq_i, ineq_j);
if (!changed)
- changed = check_wrap(map, i, j, tabs, ineq_i, ineq_j);
+ changed = check_wrap(map, i, j, tabs,
+ eq_i, ineq_i, eq_j, ineq_j);
}
done:
{
int i, j;
- for (i = 0; i < map->n - 1; ++i)
+ for (i = map->n - 2; i >= 0; --i)
+restart:
for (j = i + 1; j < map->n; ++j) {
int changed;
changed = coalesce_pair(map, i, j, tabs);
if (changed < 0)
goto error;
if (changed)
- return coalesce(map, tabs);
+ goto restart;
}
return map;
error: