return 0;
}
+/* The core of the Floyd-Warshall algorithm.
+ * Updates the given n x x matrix of relations in place.
+ *
+ * The algorithm iterates over all vertices. In each step, the whole
+ * matrix is updated to include all paths that go to the current vertex,
+ * possibly stay there a while (including passing through earlier vertices)
+ * and then come back. At the start of each iteration, the diagonal
+ * element corresponding to the current vertex is replaced by its
+ * transitive closure to account for all indirect paths that stay
+ * in the current vertex.
+ */
+static void floyd_warshall_iterate(isl_map ***grid, int n, int *exact)
+{
+ int r, p, q;
+
+ for (r = 0; r < n; ++r) {
+ int r_exact;
+ grid[r][r] = isl_map_transitive_closure(grid[r][r],
+ (exact && *exact) ? &r_exact : NULL);
+ if (exact && *exact && !r_exact)
+ *exact = 0;
+
+ for (p = 0; p < n; ++p)
+ for (q = 0; q < n; ++q) {
+ isl_map *loop;
+ if (p == r && q == r)
+ continue;
+ loop = isl_map_apply_range(
+ isl_map_copy(grid[p][r]),
+ isl_map_copy(grid[r][q]));
+ grid[p][q] = isl_map_union(grid[p][q], loop);
+ loop = isl_map_apply_range(
+ isl_map_copy(grid[p][r]),
+ isl_map_apply_range(
+ isl_map_copy(grid[r][r]),
+ isl_map_copy(grid[r][q])));
+ grid[p][q] = isl_map_union(grid[p][q], loop);
+ grid[p][q] = isl_map_coalesce(grid[p][q]);
+ }
+ }
+}
+
/* Given a partition of the domains and ranges of the basic maps in "map",
* apply the Floyd-Warshall algorithm with the elements in the partition
* as vertices.
* apply Floyd-Warshall on this matrix of relations and then take the
* union of all entries in the matrix as the final result.
*
- * The algorithm iterates over all vertices. In each step, the whole
- * matrix is updated to include all paths that go to the current vertex,
- * possibly stay there a while (including passing through earlier vertices)
- * and then come back. At the start of each iteration, the diagonal
- * element corresponding to the current vertex is replaced by its
- * transitive closure to account for all indirect paths that stay
- * in the current vertex.
- *
* If we are actually computing the power instead of the transitive closure,
* i.e., when "project" is not set, then the result should have the
* path lengths encoded as the difference between an extra pair of
__isl_keep isl_map *map, int *exact, int project, int *group, int n)
{
int i, j, k;
- int r, p, q;
isl_map ***grid = NULL;
isl_map *app;
if (!project && add_length(map, grid, n) < 0)
goto error;
- for (r = 0; r < n; ++r) {
- int r_exact;
- grid[r][r] = isl_map_transitive_closure(grid[r][r],
- (exact && *exact) ? &r_exact : NULL);
- if (exact && *exact && !r_exact)
- *exact = 0;
-
- for (p = 0; p < n; ++p)
- for (q = 0; q < n; ++q) {
- isl_map *loop;
- if (p == r && q == r)
- continue;
- loop = isl_map_apply_range(
- isl_map_copy(grid[p][r]),
- isl_map_copy(grid[r][q]));
- grid[p][q] = isl_map_union(grid[p][q], loop);
- loop = isl_map_apply_range(
- isl_map_copy(grid[p][r]),
- isl_map_apply_range(
- isl_map_copy(grid[r][r]),
- isl_map_copy(grid[r][q])));
- grid[p][q] = isl_map_union(grid[p][q], loop);
- grid[p][q] = isl_map_coalesce(grid[p][q]);
- }
- }
+ floyd_warshall_iterate(grid, n, exact);
app = isl_map_empty(isl_map_get_dim(map));
return NULL;
}
-/* Check if the domains and ranges of the basic maps in "map" can
- * be partitioned, and if so, apply Floyd-Warshall on the elements
- * of the partition. Note that we also apply this algorithm
- * if we want to compute the power, i.e., when "project" is not set.
- * However, the results are unlikely to be exact since the recursive
- * calls inside the Floyd-Warshall algorithm typically result in
- * non-linear path lengths quite quickly.
+/* Partition the domains and ranges of the n basic relations in list
+ * into disjoint cells.
*
* To find the partition, we simply consider all of the domains
* and ranges in turn and combine those that overlap.
* ranges in the corresponding group, or is equal to some l < k,
* with l another domain or range in the same group.
*/
-static __isl_give isl_map *floyd_warshall(__isl_take isl_dim *dim,
- __isl_keep isl_map *map, int *exact, int project)
+static int *setup_groups(isl_ctx *ctx, __isl_keep isl_basic_map **list, int n,
+ isl_set ***set, int *n_group)
{
int i;
- isl_set **set = NULL;
int *group = NULL;
- int n;
+ int g;
- if (!map)
- goto error;
- if (map->n <= 1)
- return incremental_closure(dim, map, exact, project);
+ *set = isl_calloc_array(ctx, isl_set *, 2 * n);
+ group = isl_alloc_array(ctx, int, 2 * n);
- set = isl_calloc_array(map->ctx, isl_set *, 2 * map->n);
- group = isl_alloc_array(map->ctx, int, 2 * map->n);
-
- if (!set || !group)
+ if (!*set || !group)
goto error;
- for (i = 0; i < map->n; ++i) {
+ for (i = 0; i < n; ++i) {
isl_set *dom;
dom = isl_set_from_basic_set(isl_basic_map_domain(
- isl_basic_map_copy(map->p[i])));
- if (merge(set, group, dom, 2 * i) < 0)
+ isl_basic_map_copy(list[i])));
+ if (merge(*set, group, dom, 2 * i) < 0)
goto error;
dom = isl_set_from_basic_set(isl_basic_map_range(
- isl_basic_map_copy(map->p[i])));
- if (merge(set, group, dom, 2 * i + 1) < 0)
+ isl_basic_map_copy(list[i])));
+ if (merge(*set, group, dom, 2 * i + 1) < 0)
goto error;
}
- n = 0;
- for (i = 0; i < 2 * map->n; ++i)
+ g = 0;
+ for (i = 0; i < 2 * n; ++i)
if (group[i] == i)
- group[i] = n++;
+ group[i] = g++;
else
group[i] = group[group[i]];
+ *n_group = g;
+
+ return group;
+error:
+ if (*set) {
+ for (i = 0; i < 2 * n; ++i)
+ isl_set_free((*set)[i]);
+ free(*set);
+ *set = NULL;
+ }
+ free(group);
+ return NULL;
+}
+
+/* Check if the domains and ranges of the basic maps in "map" can
+ * be partitioned, and if so, apply Floyd-Warshall on the elements
+ * of the partition. Note that we also apply this algorithm
+ * if we want to compute the power, i.e., when "project" is not set.
+ * However, the results are unlikely to be exact since the recursive
+ * calls inside the Floyd-Warshall algorithm typically result in
+ * non-linear path lengths quite quickly.
+ */
+static __isl_give isl_map *floyd_warshall(__isl_take isl_dim *dim,
+ __isl_keep isl_map *map, int *exact, int project)
+{
+ int i;
+ isl_set **set = NULL;
+ int *group = NULL;
+ int n;
+
+ if (!map)
+ goto error;
+ if (map->n <= 1)
+ return incremental_closure(dim, map, exact, project);
+
+ group = setup_groups(map->ctx, map->p, map->n, &set, &n);
+ if (!group)
+ goto error;
+
for (i = 0; i < 2 * map->n; ++i)
isl_set_free(set[i]);
return floyd_warshall_with_groups(dim, map, exact, project, group, n);
error:
- for (i = 0; i < 2 * map->n; ++i)
- isl_set_free(set[i]);
- free(set);
- free(group);
isl_dim_free(dim);
return NULL;
}
* to be applied after the second.
*/
static int power_components_tarjan(struct basic_map_sort *s,
- __isl_keep isl_map *map, int i)
+ __isl_keep isl_basic_map **list, int i)
{
int j;
s->node[j].index > s->node[i].min_index))
continue;
- f = basic_map_follows(map->p[i], map->p[j], &s->check_closed);
+ f = basic_map_follows(list[i], list[j], &s->check_closed);
if (f < 0)
return -1;
if (!f)
continue;
if (s->node[j].index < 0) {
- power_components_tarjan(s, map, j);
+ power_components_tarjan(s, list, j);
if (s->node[j].min_index < s->node[i].min_index)
s->node[i].min_index = s->node[j].min_index;
} else if (s->node[j].index < s->node[i].min_index)
return 0;
}
+/* Decompose the "len" basic relations in "list" into strongly connected
+ * components.
+ */
+static struct basic_map_sort *basic_map_sort_init(isl_ctx *ctx, int len,
+ __isl_keep isl_basic_map **list)
+{
+ int i;
+ struct basic_map_sort *s = NULL;
+
+ s = basic_map_sort_alloc(ctx, len);
+ if (!s)
+ return NULL;
+ for (i = len - 1; i >= 0; --i) {
+ if (s->node[i].index >= 0)
+ continue;
+ if (power_components_tarjan(s, list, i) < 0)
+ goto error;
+ }
+
+ return s;
+error:
+ basic_map_sort_free(s);
+ return NULL;
+}
+
/* Given a union of basic maps R = \cup_i R_i \subseteq D \times D
* and a dimension specification (Z^{n+1} -> Z^{n+1}),
* construct a map that is an overapproximation of the map
if (map->n <= 1)
return floyd_warshall(dim, map, exact, project);
- s = basic_map_sort_alloc(map->ctx, map->n);
+ s = basic_map_sort_init(map->ctx, map->n, map->p);
if (!s)
goto error;
- for (i = map->n - 1; i >= 0; --i) {
- if (s->node[i].index >= 0)
- continue;
- if (power_components_tarjan(s, map, i) < 0)
- goto error;
- }
orig_exact = exact;
if (s->check_closed && !exact)
projects / platform / upstream / isl.git / commitdiff