#include "isl_map.h"
#include "isl_map_private.h"
#include "isl_seq.h"
+#include <isl_dim_private.h>
#include <isl_lp.h>
+#include <isl_union_map.h>
+#include <isl_mat_private.h>
+
+int isl_map_is_transitively_closed(__isl_keep isl_map *map)
+{
+ isl_map *map2;
+ int closed;
+
+ map2 = isl_map_apply_range(isl_map_copy(map), isl_map_copy(map));
+ closed = isl_map_is_subset(map2, map);
+ isl_map_free(map2);
+
+ return closed;
+}
+
+int isl_union_map_is_transitively_closed(__isl_keep isl_union_map *umap)
+{
+ isl_union_map *umap2;
+ int closed;
+
+ umap2 = isl_union_map_apply_range(isl_union_map_copy(umap),
+ isl_union_map_copy(umap));
+ closed = isl_union_map_is_subset(umap2, umap);
+ isl_union_map_free(umap2);
+
+ return closed;
+}
/* Given a map that represents a path with the length of the path
* encoded as the difference between the last output coordindate
isl_map *app_1;
isl_map *app_2;
- map = isl_map_add(map, isl_dim_in, 1);
- map = isl_map_add(map, isl_dim_out, 1);
+ map = isl_map_add_dims(map, isl_dim_in, 1);
+ map = isl_map_add_dims(map, isl_dim_out, 1);
map = set_path_length(map, 1, 1);
app_1 = set_path_length(isl_map_copy(app), 1, 1);
app = isl_map_project_out(app, isl_dim_in, d, 1);
app = isl_map_project_out(app, isl_dim_out, d, 1);
+ app = isl_map_reset_dim(app, isl_map_get_dim(map));
+
test = isl_map_apply_range(isl_map_copy(map), isl_map_copy(app));
test = isl_map_union(test, isl_map_copy(map));
isl_map_free(map);
return exact;
-error:
- isl_map_free(app);
- isl_map_free(map);
- return -1;
}
/*
#define PURE_VAR 2
#define MIXED 3
+/* Check whether the parametric constant term of constraint c is never
+ * positive in "bset".
+ */
+static int parametric_constant_never_positive(__isl_keep isl_basic_set *bset,
+ isl_int *c, int *div_purity)
+{
+ unsigned d;
+ unsigned n_div;
+ unsigned nparam;
+ int i;
+ int k;
+ int empty;
+
+ n_div = isl_basic_set_dim(bset, isl_dim_div);
+ d = isl_basic_set_dim(bset, isl_dim_set);
+ nparam = isl_basic_set_dim(bset, isl_dim_param);
+
+ bset = isl_basic_set_copy(bset);
+ bset = isl_basic_set_cow(bset);
+ bset = isl_basic_set_extend_constraints(bset, 0, 1);
+ k = isl_basic_set_alloc_inequality(bset);
+ if (k < 0)
+ goto error;
+ isl_seq_clr(bset->ineq[k], 1 + isl_basic_set_total_dim(bset));
+ isl_seq_cpy(bset->ineq[k], c, 1 + nparam);
+ for (i = 0; i < n_div; ++i) {
+ if (div_purity[i] != PURE_PARAM)
+ continue;
+ isl_int_set(bset->ineq[k][1 + nparam + d + i],
+ c[1 + nparam + d + i]);
+ }
+ isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
+ empty = isl_basic_set_is_empty(bset);
+ isl_basic_set_free(bset);
+
+ return empty;
+error:
+ isl_basic_set_free(bset);
+ return -1;
+}
+
/* Return PURE_PARAM if only the coefficients of the parameters are non-zero.
* Return PURE_VAR if only the coefficients of the set variables are non-zero.
* Return MIXED if only the coefficients of the parameters and the set
unsigned d;
unsigned n_div;
unsigned nparam;
- int k;
int empty;
int i;
int p = 0, v = 0;
return PURE_VAR;
if (!v && isl_seq_first_non_zero(c + 1 + nparam, d) == -1)
return PURE_PARAM;
- if (eq)
- return IMPURE;
- bset = isl_basic_set_copy(bset);
- bset = isl_basic_set_cow(bset);
- bset = isl_basic_set_extend_constraints(bset, 0, 1);
- k = isl_basic_set_alloc_inequality(bset);
- if (k < 0)
- goto error;
- isl_seq_clr(bset->ineq[k], 1 + isl_basic_set_total_dim(bset));
- isl_seq_cpy(bset->ineq[k], c, 1 + nparam);
- for (i = 0; i < n_div; ++i) {
- if (div_purity[i] != PURE_PARAM)
- continue;
- isl_int_set(bset->ineq[k][1 + nparam + d + i],
- c[1 + nparam + d + i]);
+ empty = parametric_constant_never_positive(bset, c, div_purity);
+ if (eq && empty >= 0 && !empty) {
+ isl_seq_neg(c, c, 1 + nparam + d + n_div);
+ empty = parametric_constant_never_positive(bset, c, div_purity);
}
- isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
- empty = isl_basic_set_is_empty(bset);
- isl_basic_set_free(bset);
return empty < 0 ? -1 : empty ? MIXED : IMPURE;
-error:
- isl_basic_set_free(bset);
- return -1;
}
/* Return an array of integers indicating the type of each div in bset.
* check if setting the length to zero results in only the identity
* mapping.
*/
-int empty_path_is_identity(__isl_keep isl_basic_map *path, unsigned pos)
+static int empty_path_is_identity(__isl_keep isl_basic_map *path, unsigned pos)
{
isl_basic_map *test = NULL;
isl_basic_map *id = NULL;
isl_seq_clr(test->eq[k], 1 + isl_basic_map_total_dim(test));
isl_int_set_si(test->eq[k][pos], 1);
id = isl_basic_map_identity(isl_dim_domain(isl_basic_map_get_dim(path)));
- is_id = isl_basic_map_is_subset(test, id);
+ is_id = isl_basic_map_is_equal(test, id);
isl_basic_map_free(test);
isl_basic_map_free(id);
return is_id;
return -1;
}
-__isl_give isl_basic_map *add_delta_constraints(__isl_take isl_basic_map *path,
+static __isl_give isl_basic_map *add_delta_constraints(
+ __isl_take isl_basic_map *path,
__isl_keep isl_basic_set *delta, unsigned off, unsigned nparam,
unsigned d, int *div_purity, int eq)
{
int i, k;
int n = eq ? delta->n_eq : delta->n_ineq;
isl_int **delta_c = eq ? delta->eq : delta->ineq;
- isl_int **path_c = eq ? path->eq : path->ineq;
unsigned n_div;
n_div = isl_basic_set_dim(delta, isl_dim_div);
for (i = 0; i < n; ++i) {
+ isl_int *path_c;
int p = purity(delta, delta_c[i], div_purity, eq);
if (p < 0)
goto error;
if (p == IMPURE)
continue;
- if (eq)
+ if (eq && p != MIXED) {
k = isl_basic_map_alloc_equality(path);
- else
+ path_c = path->eq[k];
+ } else {
k = isl_basic_map_alloc_inequality(path);
+ path_c = path->ineq[k];
+ }
if (k < 0)
goto error;
- isl_seq_clr(path_c[k], 1 + isl_basic_map_total_dim(path));
+ isl_seq_clr(path_c, 1 + isl_basic_map_total_dim(path));
if (p == PURE_VAR) {
- isl_seq_cpy(path_c[k] + off,
+ isl_seq_cpy(path_c + off,
delta_c[i] + 1 + nparam, d);
- isl_int_set(path_c[k][off + d], delta_c[i][0]);
+ isl_int_set(path_c[off + d], delta_c[i][0]);
} else if (p == PURE_PARAM) {
- isl_seq_cpy(path_c[k], delta_c[i], 1 + nparam);
+ isl_seq_cpy(path_c, delta_c[i], 1 + nparam);
} else {
- isl_seq_cpy(path_c[k] + off,
+ isl_seq_cpy(path_c + off,
delta_c[i] + 1 + nparam, d);
- isl_seq_cpy(path_c[k], delta_c[i], 1 + nparam);
+ isl_seq_cpy(path_c, delta_c[i], 1 + nparam);
}
- isl_seq_cpy(path_c[k] + off - n_div,
+ isl_seq_cpy(path_c + off - n_div,
delta_c[i] + 1 + nparam + d, n_div);
}
d = isl_basic_set_dim(delta, isl_dim_set);
nparam = isl_basic_set_dim(delta, isl_dim_param);
path = isl_basic_map_alloc_dim(isl_dim_copy(dim), n_div + d + 1,
- d + 1 + delta->n_eq, delta->n_ineq + 1);
+ d + 1 + delta->n_eq, delta->n_eq + delta->n_ineq + 1);
off = 1 + nparam + 2 * (d + 1) + n_div;
for (i = 0; i < n_div + d + 1; ++i) {
return NULL;
}
-/* Given a dimenion specification Z^{n+1} -> Z^{n+1} and a parameter "param",
+/* Given a dimension specification Z^{n+1} -> Z^{n+1} and a parameter "param",
* construct a map that equates the parameter to the difference
* in the final coordinates and imposes that this difference is positive.
* That is, construct
return NULL;
}
+static int isl_set_overlaps(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
+{
+ isl_set *i;
+ int no_overlap;
+
+ if (!isl_dim_tuple_match(set1->dim, isl_dim_set, set2->dim, isl_dim_set))
+ return 0;
+
+ i = isl_set_intersect(isl_set_copy(set1), isl_set_copy(set2));
+ no_overlap = isl_set_is_empty(i);
+ isl_set_free(i);
+
+ return no_overlap < 0 ? -1 : !no_overlap;
+}
+
/* 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 the union of the identity map and
- * an overapproximation of the map
+ * construct a map that is an overapproximation of the map
* that takes an element from the dom R \times Z to an
* element from ran R \times Z, such that the first n coordinates of the
* difference between them is a sum of differences between images
*
* { (x) -> (x + d) | \exists k_i >= 0, \delta_i \in \Delta_i :
* d = (\sum_i k_i \delta_i, \sum_i k_i) and
- * x in dom R and x + d in ran R } union
- * { (x) -> (x) }
+ * x in dom R and x + d in ran R and
+ * \sum_i k_i >= 1 }
*/
static __isl_give isl_map *construct_component(__isl_take isl_dim *dim,
__isl_keep isl_map *map, int *exact, int project)
{
struct isl_set *domain = NULL;
struct isl_set *range = NULL;
- struct isl_set *overlap;
struct isl_map *app = NULL;
struct isl_map *path = NULL;
domain = isl_set_coalesce(domain);
range = isl_map_range(isl_map_copy(map));
range = isl_set_coalesce(range);
- overlap = isl_set_intersect(isl_set_copy(domain), isl_set_copy(range));
- if (isl_set_is_empty(overlap) == 1) {
+ if (!isl_set_overlaps(domain, range)) {
isl_set_free(domain);
isl_set_free(range);
- isl_set_free(overlap);
+ isl_dim_free(dim);
map = isl_map_copy(map);
- map = isl_map_add(map, isl_dim_in, 1);
- map = isl_map_add(map, isl_dim_out, 1);
+ map = isl_map_add_dims(map, isl_dim_in, 1);
+ map = isl_map_add_dims(map, isl_dim_out, 1);
map = set_path_length(map, 1, 1);
- map = isl_map_union(map, isl_map_identity(isl_dim_domain(dim)));
return map;
}
- isl_set_free(overlap);
app = isl_map_from_domain_and_range(domain, range);
- app = isl_map_add(app, isl_dim_in, 1);
- app = isl_map_add(app, isl_dim_out, 1);
+ app = isl_map_add_dims(app, isl_dim_in, 1);
+ app = isl_map_add_dims(app, isl_dim_out, 1);
path = construct_extended_path(isl_dim_copy(dim), map,
exact && *exact ? &project : NULL);
project)) < 0)
goto error;
- return isl_map_union(app, isl_map_identity(isl_dim_domain(dim)));
+ isl_dim_free(dim);
+ app = set_path_length(app, 0, 1);
+ return app;
error:
isl_dim_free(dim);
isl_map_free(app);
return NULL;
}
-/* Structure for representing the nodes in the graph being traversed
- * using Tarjan's algorithm.
- * index represents the order in which nodes are visited.
- * min_index is the index of the root of a (sub)component.
- * on_stack indicates whether the node is currently on the stack.
- */
-struct basic_map_sort_node {
- int index;
- int min_index;
- int on_stack;
-};
-/* Structure for representing the graph being traversed
- * using Tarjan's algorithm.
- * len is the number of nodes
- * node is an array of nodes
- * stack contains the nodes on the path from the root to the current node
- * sp is the stack pointer
- * index is the index of the last node visited
- * order contains the elements of the components separated by -1
- * op represents the current position in order
+/* Call construct_component and, if "project" is set, project out
+ * the final coordinates.
*/
-struct basic_map_sort {
- int len;
- struct basic_map_sort_node *node;
- int *stack;
- int sp;
- int index;
- int *order;
- int op;
-};
-
-static void basic_map_sort_free(struct basic_map_sort *s)
+static __isl_give isl_map *construct_projected_component(
+ __isl_take isl_dim *dim,
+ __isl_keep isl_map *map, int *exact, int project)
{
- if (!s)
- return;
- free(s->node);
- free(s->stack);
- free(s->order);
- free(s);
+ isl_map *app;
+ unsigned d;
+
+ if (!dim)
+ return NULL;
+ d = isl_dim_size(dim, isl_dim_in);
+
+ app = construct_component(dim, map, exact, project);
+ if (project) {
+ app = isl_map_project_out(app, isl_dim_in, d - 1, 1);
+ app = isl_map_project_out(app, isl_dim_out, d - 1, 1);
+ }
+ return app;
}
-static struct basic_map_sort *basic_map_sort_alloc(struct isl_ctx *ctx, int len)
+/* Compute an extended version, i.e., with path lengths, of
+ * an overapproximation of the transitive closure of "bmap"
+ * with path lengths greater than or equal to zero and with
+ * domain and range equal to "dom".
+ */
+static __isl_give isl_map *q_closure(__isl_take isl_dim *dim,
+ __isl_take isl_set *dom, __isl_keep isl_basic_map *bmap, int *exact)
{
- struct basic_map_sort *s;
- int i;
+ int project = 1;
+ isl_map *path;
+ isl_map *map;
+ isl_map *app;
- s = isl_calloc_type(ctx, struct basic_map_sort);
- if (!s)
- return NULL;
- s->len = len;
- s->node = isl_alloc_array(ctx, struct basic_map_sort_node, len);
- if (!s->node)
- goto error;
- for (i = 0; i < len; ++i)
- s->node[i].index = -1;
- s->stack = isl_alloc_array(ctx, int, len);
- if (!s->stack)
- goto error;
- s->order = isl_alloc_array(ctx, int, 2 * len);
- if (!s->order)
- goto error;
+ dom = isl_set_add_dims(dom, isl_dim_set, 1);
+ app = isl_map_from_domain_and_range(dom, isl_set_copy(dom));
+ map = isl_map_from_basic_map(isl_basic_map_copy(bmap));
+ path = construct_extended_path(dim, map, &project);
+ app = isl_map_intersect(app, path);
- s->sp = 0;
- s->index = 0;
- s->op = 0;
+ if ((*exact = check_exactness(map, isl_map_copy(app), project)) < 0)
+ goto error;
- return s;
+ return app;
error:
- basic_map_sort_free(s);
+ isl_map_free(app);
return NULL;
}
-/* Check whether in the computation of the transitive closure
- * "bmap1" (R_1) should follow (or be part of the same component as)
- * "bmap2" (R_2).
- *
- * That is check whether
- *
- * R_1 \circ R_2
- *
- * is a subset of
- *
- * R_2 \circ R_1
- *
- * If so, then there is no reason for R_1 to immediately follow R_2
- * in any path.
+/* Check whether qc has any elements of length at least one
+ * with domain and/or range outside of dom and ran.
*/
-static int basic_map_follows(__isl_keep isl_basic_map *bmap1,
- __isl_keep isl_basic_map *bmap2)
+static int has_spurious_elements(__isl_keep isl_map *qc,
+ __isl_keep isl_set *dom, __isl_keep isl_set *ran)
{
- struct isl_map *map12 = NULL;
- struct isl_map *map21 = NULL;
+ isl_set *s;
int subset;
+ unsigned d;
- map21 = isl_map_from_basic_map(
- isl_basic_map_apply_range(
- isl_basic_map_copy(bmap2),
- isl_basic_map_copy(bmap1)));
- subset = isl_map_is_empty(map21);
+ if (!qc || !dom || !ran)
+ return -1;
+
+ d = isl_map_dim(qc, isl_dim_in);
+
+ qc = isl_map_copy(qc);
+ qc = set_path_length(qc, 0, 1);
+ qc = isl_map_project_out(qc, isl_dim_in, d - 1, 1);
+ qc = isl_map_project_out(qc, isl_dim_out, d - 1, 1);
+
+ s = isl_map_domain(isl_map_copy(qc));
+ subset = isl_set_is_subset(s, dom);
+ isl_set_free(s);
if (subset < 0)
goto error;
- if (subset) {
- isl_map_free(map21);
- return 0;
+ if (!subset) {
+ isl_map_free(qc);
+ return 1;
}
- map12 = isl_map_from_basic_map(
- isl_basic_map_apply_range(
- isl_basic_map_copy(bmap1),
- isl_basic_map_copy(bmap2)));
-
- subset = isl_map_is_subset(map21, map12);
-
- isl_map_free(map12);
- isl_map_free(map21);
+ s = isl_map_range(qc);
+ subset = isl_set_is_subset(s, ran);
+ isl_set_free(s);
return subset < 0 ? -1 : !subset;
error:
- isl_map_free(map21);
+ isl_map_free(qc);
return -1;
}
-/* Perform Tarjan's algorithm for computing the strongly connected components
- * in the graph with the disjuncts of "map" as vertices and with an
- * edge between any pair of disjuncts such that the first has
- * to be applied after the second.
+#define LEFT 2
+#define RIGHT 1
+
+/* For each basic map in "map", except i, check whether it combines
+ * with the transitive closure that is reflexive on C combines
+ * to the left and to the right.
+ *
+ * In particular, if
+ *
+ * dom map_j \subseteq C
+ *
+ * then right[j] is set to 1. Otherwise, if
+ *
+ * ran map_i \cap dom map_j = \emptyset
+ *
+ * then right[j] is set to 0. Otherwise, composing to the right
+ * is impossible.
+ *
+ * Similar, for composing to the left, we have if
+ *
+ * ran map_j \subseteq C
+ *
+ * then left[j] is set to 1. Otherwise, if
+ *
+ * dom map_i \cap ran map_j = \emptyset
+ *
+ * then left[j] is set to 0. Otherwise, composing to the left
+ * is impossible.
+ *
+ * The return value is or'd with LEFT if composing to the left
+ * is possible and with RIGHT if composing to the right is possible.
*/
-static int power_components_tarjan(struct basic_map_sort *s,
- __isl_keep isl_map *map, int i)
+static int composability(__isl_keep isl_set *C, int i,
+ isl_set **dom, isl_set **ran, int *left, int *right,
+ __isl_keep isl_map *map)
{
int j;
+ int ok;
- s->node[i].index = s->index;
- s->node[i].min_index = s->index;
- s->node[i].on_stack = 1;
- s->index++;
- s->stack[s->sp++] = i;
-
- for (j = s->len - 1; j >= 0; --j) {
- int f;
-
+ ok = LEFT | RIGHT;
+ for (j = 0; j < map->n && ok; ++j) {
+ int overlaps, subset;
if (j == i)
continue;
- if (s->node[j].index >= 0 &&
- (!s->node[j].on_stack ||
- s->node[j].index > s->node[i].min_index))
- continue;
- f = basic_map_follows(map->p[i], map->p[j]);
- if (f < 0)
- return -1;
- if (!f)
- continue;
+ if (ok & RIGHT) {
+ if (!dom[j])
+ dom[j] = isl_set_from_basic_set(
+ isl_basic_map_domain(
+ isl_basic_map_copy(map->p[j])));
+ if (!dom[j])
+ return -1;
+ overlaps = isl_set_overlaps(ran[i], dom[j]);
+ if (overlaps < 0)
+ return -1;
+ if (!overlaps)
+ right[j] = 0;
+ else {
+ subset = isl_set_is_subset(dom[j], C);
+ if (subset < 0)
+ return -1;
+ if (subset)
+ right[j] = 1;
+ else
+ ok &= ~RIGHT;
+ }
+ }
- if (s->node[j].index < 0) {
- power_components_tarjan(s, map, 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)
- s->node[i].min_index = s->node[j].index;
+ if (ok & LEFT) {
+ if (!ran[j])
+ ran[j] = isl_set_from_basic_set(
+ isl_basic_map_range(
+ isl_basic_map_copy(map->p[j])));
+ if (!ran[j])
+ return -1;
+ overlaps = isl_set_overlaps(dom[i], ran[j]);
+ if (overlaps < 0)
+ return -1;
+ if (!overlaps)
+ left[j] = 0;
+ else {
+ subset = isl_set_is_subset(ran[j], C);
+ if (subset < 0)
+ return -1;
+ if (subset)
+ left[j] = 1;
+ else
+ ok &= ~LEFT;
+ }
+ }
}
- if (s->node[i].index != s->node[i].min_index)
- return 0;
-
- do {
- j = s->stack[--s->sp];
- s->node[j].on_stack = 0;
- s->order[s->op++] = j;
- } while (j != i);
- s->order[s->op++] = -1;
+ return ok;
+}
+
+static __isl_give isl_map *anonymize(__isl_take isl_map *map)
+{
+ map = isl_map_reset(map, isl_dim_in);
+ map = isl_map_reset(map, isl_dim_out);
+ return map;
+}
+
+/* Return a map that is a union of the basic maps in "map", except i,
+ * composed to left and right with qc based on the entries of "left"
+ * and "right".
+ */
+static __isl_give isl_map *compose(__isl_keep isl_map *map, int i,
+ __isl_take isl_map *qc, int *left, int *right)
+{
+ int j;
+ isl_map *comp;
+
+ comp = isl_map_empty(isl_map_get_dim(map));
+ for (j = 0; j < map->n; ++j) {
+ isl_map *map_j;
+
+ if (j == i)
+ continue;
+
+ map_j = isl_map_from_basic_map(isl_basic_map_copy(map->p[j]));
+ map_j = anonymize(map_j);
+ if (left && left[j])
+ map_j = isl_map_apply_range(map_j, isl_map_copy(qc));
+ if (right && right[j])
+ map_j = isl_map_apply_range(isl_map_copy(qc), map_j);
+ comp = isl_map_union(comp, map_j);
+ }
+
+ comp = isl_map_compute_divs(comp);
+ comp = isl_map_coalesce(comp);
+
+ isl_map_free(qc);
+
+ return comp;
+}
+
+/* Compute the transitive closure of "map" incrementally by
+ * computing
+ *
+ * map_i^+ \cup qc^+
+ *
+ * or
+ *
+ * map_i^+ \cup ((id \cup map_i^) \circ qc^+)
+ *
+ * or
+ *
+ * map_i^+ \cup (qc^+ \circ (id \cup map_i^))
+ *
+ * depending on whether left or right are NULL.
+ */
+static __isl_give isl_map *compute_incremental(
+ __isl_take isl_dim *dim, __isl_keep isl_map *map,
+ int i, __isl_take isl_map *qc, int *left, int *right, int *exact)
+{
+ isl_map *map_i;
+ isl_map *tc;
+ isl_map *rtc = NULL;
+
+ if (!map)
+ goto error;
+ isl_assert(map->ctx, left || right, goto error);
+
+ map_i = isl_map_from_basic_map(isl_basic_map_copy(map->p[i]));
+ tc = construct_projected_component(isl_dim_copy(dim), map_i,
+ exact, 1);
+ isl_map_free(map_i);
+
+ if (*exact)
+ qc = isl_map_transitive_closure(qc, exact);
+
+ if (!*exact) {
+ isl_dim_free(dim);
+ isl_map_free(tc);
+ isl_map_free(qc);
+ return isl_map_universe(isl_map_get_dim(map));
+ }
+
+ if (!left || !right)
+ rtc = isl_map_union(isl_map_copy(tc),
+ isl_map_identity(isl_dim_domain(isl_map_get_dim(tc))));
+ if (!right)
+ qc = isl_map_apply_range(rtc, qc);
+ if (!left)
+ qc = isl_map_apply_range(qc, rtc);
+ qc = isl_map_union(tc, qc);
+
+ isl_dim_free(dim);
+
+ return qc;
+error:
+ isl_dim_free(dim);
+ isl_map_free(qc);
+ return NULL;
+}
+
+/* Given a map "map", try to find a basic map such that
+ * map^+ can be computed as
+ *
+ * map^+ = map_i^+ \cup
+ * \bigcup_j ((map_i^+ \cup Id_C)^+ \circ map_j \circ (map_i^+ \cup Id_C))^+
+ *
+ * with C the simple hull of the domain and range of the input map.
+ * map_i^ \cup Id_C is computed by allowing the path lengths to be zero
+ * and by intersecting domain and range with C.
+ * Of course, we need to check that this is actually equal to map_i^ \cup Id_C.
+ * Also, we only use the incremental computation if all the transitive
+ * closures are exact and if the number of basic maps in the union,
+ * after computing the integer divisions, is smaller than the number
+ * of basic maps in the input map.
+ */
+static int incemental_on_entire_domain(__isl_keep isl_dim *dim,
+ __isl_keep isl_map *map,
+ isl_set **dom, isl_set **ran, int *left, int *right,
+ __isl_give isl_map **res)
+{
+ int i;
+ isl_set *C;
+ unsigned d;
+
+ *res = NULL;
+
+ C = isl_set_union(isl_map_domain(isl_map_copy(map)),
+ isl_map_range(isl_map_copy(map)));
+ C = isl_set_from_basic_set(isl_set_simple_hull(C));
+ if (!C)
+ return -1;
+ if (C->n != 1) {
+ isl_set_free(C);
+ return 0;
+ }
+
+ d = isl_map_dim(map, isl_dim_in);
+
+ for (i = 0; i < map->n; ++i) {
+ isl_map *qc;
+ int exact_i, spurious;
+ int j;
+ dom[i] = isl_set_from_basic_set(isl_basic_map_domain(
+ isl_basic_map_copy(map->p[i])));
+ ran[i] = isl_set_from_basic_set(isl_basic_map_range(
+ isl_basic_map_copy(map->p[i])));
+ qc = q_closure(isl_dim_copy(dim), isl_set_copy(C),
+ map->p[i], &exact_i);
+ if (!qc)
+ goto error;
+ if (!exact_i) {
+ isl_map_free(qc);
+ continue;
+ }
+ spurious = has_spurious_elements(qc, dom[i], ran[i]);
+ if (spurious) {
+ isl_map_free(qc);
+ if (spurious < 0)
+ goto error;
+ continue;
+ }
+ qc = isl_map_project_out(qc, isl_dim_in, d, 1);
+ qc = isl_map_project_out(qc, isl_dim_out, d, 1);
+ qc = isl_map_compute_divs(qc);
+ for (j = 0; j < map->n; ++j)
+ left[j] = right[j] = 1;
+ qc = compose(map, i, qc, left, right);
+ if (!qc)
+ goto error;
+ if (qc->n >= map->n) {
+ isl_map_free(qc);
+ continue;
+ }
+ *res = compute_incremental(isl_dim_copy(dim), map, i, qc,
+ left, right, &exact_i);
+ if (!*res)
+ goto error;
+ if (exact_i)
+ break;
+ isl_map_free(*res);
+ *res = NULL;
+ }
+
+ isl_set_free(C);
+
+ return *res != NULL;
+error:
+ isl_set_free(C);
+ return -1;
+}
+
+/* Try and compute the transitive closure of "map" as
+ *
+ * map^+ = map_i^+ \cup
+ * \bigcup_j ((map_i^+ \cup Id_C)^+ \circ map_j \circ (map_i^+ \cup Id_C))^+
+ *
+ * with C either the simple hull of the domain and range of the entire
+ * map or the simple hull of domain and range of map_i.
+ */
+static __isl_give isl_map *incremental_closure(__isl_take isl_dim *dim,
+ __isl_keep isl_map *map, int *exact, int project)
+{
+ int i;
+ isl_set **dom = NULL;
+ isl_set **ran = NULL;
+ int *left = NULL;
+ int *right = NULL;
+ isl_set *C;
+ unsigned d;
+ isl_map *res = NULL;
+
+ if (!project)
+ return construct_projected_component(dim, map, exact, project);
+
+ if (!map)
+ goto error;
+ if (map->n <= 1)
+ return construct_projected_component(dim, map, exact, project);
+
+ d = isl_map_dim(map, isl_dim_in);
+
+ dom = isl_calloc_array(map->ctx, isl_set *, map->n);
+ ran = isl_calloc_array(map->ctx, isl_set *, map->n);
+ left = isl_calloc_array(map->ctx, int, map->n);
+ right = isl_calloc_array(map->ctx, int, map->n);
+ if (!ran || !dom || !left || !right)
+ goto error;
+
+ if (incemental_on_entire_domain(dim, map, dom, ran, left, right, &res) < 0)
+ goto error;
+
+ for (i = 0; !res && i < map->n; ++i) {
+ isl_map *qc;
+ int exact_i, spurious, comp;
+ if (!dom[i])
+ dom[i] = isl_set_from_basic_set(
+ isl_basic_map_domain(
+ isl_basic_map_copy(map->p[i])));
+ if (!dom[i])
+ goto error;
+ if (!ran[i])
+ ran[i] = isl_set_from_basic_set(
+ isl_basic_map_range(
+ isl_basic_map_copy(map->p[i])));
+ if (!ran[i])
+ goto error;
+ C = isl_set_union(isl_set_copy(dom[i]),
+ isl_set_copy(ran[i]));
+ C = isl_set_from_basic_set(isl_set_simple_hull(C));
+ if (!C)
+ goto error;
+ if (C->n != 1) {
+ isl_set_free(C);
+ continue;
+ }
+ comp = composability(C, i, dom, ran, left, right, map);
+ if (!comp || comp < 0) {
+ isl_set_free(C);
+ if (comp < 0)
+ goto error;
+ continue;
+ }
+ qc = q_closure(isl_dim_copy(dim), C, map->p[i], &exact_i);
+ if (!qc)
+ goto error;
+ if (!exact_i) {
+ isl_map_free(qc);
+ continue;
+ }
+ spurious = has_spurious_elements(qc, dom[i], ran[i]);
+ if (spurious) {
+ isl_map_free(qc);
+ if (spurious < 0)
+ goto error;
+ continue;
+ }
+ qc = isl_map_project_out(qc, isl_dim_in, d, 1);
+ qc = isl_map_project_out(qc, isl_dim_out, d, 1);
+ qc = isl_map_compute_divs(qc);
+ qc = compose(map, i, qc, (comp & LEFT) ? left : NULL,
+ (comp & RIGHT) ? right : NULL);
+ if (!qc)
+ goto error;
+ if (qc->n >= map->n) {
+ isl_map_free(qc);
+ continue;
+ }
+ res = compute_incremental(isl_dim_copy(dim), map, i, qc,
+ (comp & LEFT) ? left : NULL,
+ (comp & RIGHT) ? right : NULL, &exact_i);
+ if (!res)
+ goto error;
+ if (exact_i)
+ break;
+ isl_map_free(res);
+ res = NULL;
+ }
+
+ for (i = 0; i < map->n; ++i) {
+ isl_set_free(dom[i]);
+ isl_set_free(ran[i]);
+ }
+ free(dom);
+ free(ran);
+ free(left);
+ free(right);
+
+ if (res) {
+ isl_dim_free(dim);
+ return res;
+ }
+
+ return construct_projected_component(dim, map, exact, project);
+error:
+ if (dom)
+ for (i = 0; i < map->n; ++i)
+ isl_set_free(dom[i]);
+ free(dom);
+ if (ran)
+ for (i = 0; i < map->n; ++i)
+ isl_set_free(ran[i]);
+ free(ran);
+ free(left);
+ free(right);
+ isl_dim_free(dim);
+ return NULL;
+}
+
+/* Given an array of sets "set", add "dom" at position "pos"
+ * and search for elements at earlier positions that overlap with "dom".
+ * If any can be found, then merge all of them, together with "dom", into
+ * a single set and assign the union to the first in the array,
+ * which becomes the new group leader for all groups involved in the merge.
+ * During the search, we only consider group leaders, i.e., those with
+ * group[i] = i, as the other sets have already been combined
+ * with one of the group leaders.
+ */
+static int merge(isl_set **set, int *group, __isl_take isl_set *dom, int pos)
+{
+ int i;
+
+ group[pos] = pos;
+ set[pos] = isl_set_copy(dom);
+
+ for (i = pos - 1; i >= 0; --i) {
+ int o;
+
+ if (group[i] != i)
+ continue;
+
+ o = isl_set_overlaps(set[i], dom);
+ if (o < 0)
+ goto error;
+ if (!o)
+ continue;
+
+ set[i] = isl_set_union(set[i], set[group[pos]]);
+ set[group[pos]] = NULL;
+ if (!set[i])
+ goto error;
+ group[group[pos]] = i;
+ group[pos] = i;
+ }
+
+ isl_set_free(dom);
+ return 0;
+error:
+ isl_set_free(dom);
+ return -1;
+}
+
+/* Replace each entry in the n by n grid of maps by the cross product
+ * with the relation { [i] -> [i + 1] }.
+ */
+static int add_length(__isl_keep isl_map *map, isl_map ***grid, int n)
+{
+ int i, j, k;
+ isl_dim *dim;
+ isl_basic_map *bstep;
+ isl_map *step;
+ unsigned nparam;
+
+ if (!map)
+ return -1;
+
+ dim = isl_map_get_dim(map);
+ nparam = isl_dim_size(dim, isl_dim_param);
+ dim = isl_dim_drop(dim, isl_dim_in, 0, isl_dim_size(dim, isl_dim_in));
+ dim = isl_dim_drop(dim, isl_dim_out, 0, isl_dim_size(dim, isl_dim_out));
+ dim = isl_dim_add(dim, isl_dim_in, 1);
+ dim = isl_dim_add(dim, isl_dim_out, 1);
+ bstep = isl_basic_map_alloc_dim(dim, 0, 1, 0);
+ k = isl_basic_map_alloc_equality(bstep);
+ if (k < 0) {
+ isl_basic_map_free(bstep);
+ return -1;
+ }
+ isl_seq_clr(bstep->eq[k], 1 + isl_basic_map_total_dim(bstep));
+ isl_int_set_si(bstep->eq[k][0], 1);
+ isl_int_set_si(bstep->eq[k][1 + nparam], 1);
+ isl_int_set_si(bstep->eq[k][1 + nparam + 1], -1);
+ bstep = isl_basic_map_finalize(bstep);
+ step = isl_map_from_basic_map(bstep);
+
+ for (i = 0; i < n; ++i)
+ for (j = 0; j < n; ++j)
+ grid[i][j] = isl_map_product(grid[i][j],
+ isl_map_copy(step));
+
+ isl_map_free(step);
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.
+ *
+ * In particular, there are "n" elements in the partition and "group" is
+ * an array of length 2 * map->n with entries in [0,n-1].
+ *
+ * We first construct a matrix of relations based on the partition information,
+ * apply Floyd-Warshall on this matrix of relations and then take the
+ * union of all entries in the matrix as the final result.
+ *
+ * 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
+ * coordinates. We therefore apply the nested transitive closures
+ * to relations that include these lengths. In particular, we replace
+ * the input relation by the cross product with the unit length relation
+ * { [i] -> [i + 1] }.
+ */
+static __isl_give isl_map *floyd_warshall_with_groups(__isl_take isl_dim *dim,
+ __isl_keep isl_map *map, int *exact, int project, int *group, int n)
+{
+ int i, j, k;
+ isl_map ***grid = NULL;
+ isl_map *app;
+
+ if (!map)
+ goto error;
+
+ if (n == 1) {
+ free(group);
+ return incremental_closure(dim, map, exact, project);
+ }
+
+ grid = isl_calloc_array(map->ctx, isl_map **, n);
+ if (!grid)
+ goto error;
+ for (i = 0; i < n; ++i) {
+ grid[i] = isl_calloc_array(map->ctx, isl_map *, n);
+ if (!grid[i])
+ goto error;
+ for (j = 0; j < n; ++j)
+ grid[i][j] = isl_map_empty(isl_map_get_dim(map));
+ }
+
+ for (k = 0; k < map->n; ++k) {
+ i = group[2 * k];
+ j = group[2 * k + 1];
+ grid[i][j] = isl_map_union(grid[i][j],
+ isl_map_from_basic_map(
+ isl_basic_map_copy(map->p[k])));
+ }
+
+ if (!project && add_length(map, grid, n) < 0)
+ goto error;
+
+ floyd_warshall_iterate(grid, n, exact);
+
+ app = isl_map_empty(isl_map_get_dim(map));
+
+ for (i = 0; i < n; ++i) {
+ for (j = 0; j < n; ++j)
+ app = isl_map_union(app, grid[i][j]);
+ free(grid[i]);
+ }
+ free(grid);
+
+ free(group);
+ isl_dim_free(dim);
+
+ return app;
+error:
+ if (grid)
+ for (i = 0; i < n; ++i) {
+ if (!grid[i])
+ continue;
+ for (j = 0; j < n; ++j)
+ isl_map_free(grid[i][j]);
+ free(grid[i]);
+ }
+ free(grid);
+ free(group);
+ isl_dim_free(dim);
+ return NULL;
+}
+
+/* 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.
+ * "set" contains the partition elements and "group" indicates
+ * to which partition element a given domain or range belongs.
+ * The domain of basic map i corresponds to element 2 * i in these arrays,
+ * while the domain corresponds to element 2 * i + 1.
+ * During the construction group[k] is either equal to k,
+ * in which case set[k] contains the union of all the domains and
+ * ranges in the corresponding group, or is equal to some l < k,
+ * with l another domain or range in the same group.
+ */
+static int *setup_groups(isl_ctx *ctx, __isl_keep isl_basic_map **list, int n,
+ isl_set ***set, int *n_group)
+{
+ int i;
+ int *group = NULL;
+ int g;
+
+ *set = isl_calloc_array(ctx, isl_set *, 2 * n);
+ group = isl_alloc_array(ctx, int, 2 * n);
+
+ if (!*set || !group)
+ goto error;
+
+ for (i = 0; i < n; ++i) {
+ isl_set *dom;
+ dom = isl_set_from_basic_set(isl_basic_map_domain(
+ 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(list[i])));
+ if (merge(*set, group, dom, 2 * i + 1) < 0)
+ goto error;
+ }
+
+ g = 0;
+ for (i = 0; i < 2 * n; ++i)
+ if (group[i] == i) {
+ if (g != i) {
+ (*set)[g] = (*set)[i];
+ (*set)[i] = NULL;
+ }
+ 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]);
+
+ free(set);
+
+ return floyd_warshall_with_groups(dim, map, exact, project, group, n);
+error:
+ isl_dim_free(dim);
+ return NULL;
+}
+
+/* Structure for representing the nodes in the graph being traversed
+ * using Tarjan's algorithm.
+ * index represents the order in which nodes are visited.
+ * min_index is the index of the root of a (sub)component.
+ * on_stack indicates whether the node is currently on the stack.
+ */
+struct basic_map_sort_node {
+ int index;
+ int min_index;
+ int on_stack;
+};
+/* Structure for representing the graph being traversed
+ * using Tarjan's algorithm.
+ * len is the number of nodes
+ * node is an array of nodes
+ * stack contains the nodes on the path from the root to the current node
+ * sp is the stack pointer
+ * index is the index of the last node visited
+ * order contains the elements of the components separated by -1
+ * op represents the current position in order
+ *
+ * check_closed is set if we may have used the fact that
+ * a pair of basic maps can be interchanged
+ */
+struct basic_map_sort {
+ int len;
+ struct basic_map_sort_node *node;
+ int *stack;
+ int sp;
+ int index;
+ int *order;
+ int op;
+ int check_closed;
+};
+
+static void basic_map_sort_free(struct basic_map_sort *s)
+{
+ if (!s)
+ return;
+ free(s->node);
+ free(s->stack);
+ free(s->order);
+ free(s);
+}
+
+static struct basic_map_sort *basic_map_sort_alloc(struct isl_ctx *ctx, int len)
+{
+ struct basic_map_sort *s;
+ int i;
+
+ s = isl_calloc_type(ctx, struct basic_map_sort);
+ if (!s)
+ return NULL;
+ s->len = len;
+ s->node = isl_alloc_array(ctx, struct basic_map_sort_node, len);
+ if (!s->node)
+ goto error;
+ for (i = 0; i < len; ++i)
+ s->node[i].index = -1;
+ s->stack = isl_alloc_array(ctx, int, len);
+ if (!s->stack)
+ goto error;
+ s->order = isl_alloc_array(ctx, int, 2 * len);
+ if (!s->order)
+ goto error;
+
+ s->sp = 0;
+ s->index = 0;
+ s->op = 0;
+
+ s->check_closed = 0;
+
+ return s;
+error:
+ basic_map_sort_free(s);
+ return NULL;
+}
+
+/* Check whether in the computation of the transitive closure
+ * "bmap1" (R_1) should follow (or be part of the same component as)
+ * "bmap2" (R_2).
+ *
+ * That is check whether
+ *
+ * R_1 \circ R_2
+ *
+ * is a subset of
+ *
+ * R_2 \circ R_1
+ *
+ * If so, then there is no reason for R_1 to immediately follow R_2
+ * in any path.
+ *
+ * *check_closed is set if the subset relation holds while
+ * R_1 \circ R_2 is not empty.
+ */
+static int basic_map_follows(__isl_keep isl_basic_map *bmap1,
+ __isl_keep isl_basic_map *bmap2, int *check_closed)
+{
+ struct isl_map *map12 = NULL;
+ struct isl_map *map21 = NULL;
+ int subset;
+
+ if (!isl_dim_tuple_match(bmap1->dim, isl_dim_in, bmap2->dim, isl_dim_out))
+ return 0;
+
+ map21 = isl_map_from_basic_map(
+ isl_basic_map_apply_range(
+ isl_basic_map_copy(bmap2),
+ isl_basic_map_copy(bmap1)));
+ subset = isl_map_is_empty(map21);
+ if (subset < 0)
+ goto error;
+ if (subset) {
+ isl_map_free(map21);
+ return 0;
+ }
+
+ if (!isl_dim_tuple_match(bmap1->dim, isl_dim_in, bmap1->dim, isl_dim_out) ||
+ !isl_dim_tuple_match(bmap2->dim, isl_dim_in, bmap2->dim, isl_dim_out)) {
+ isl_map_free(map21);
+ return 1;
+ }
+
+ map12 = isl_map_from_basic_map(
+ isl_basic_map_apply_range(
+ isl_basic_map_copy(bmap1),
+ isl_basic_map_copy(bmap2)));
+
+ subset = isl_map_is_subset(map21, map12);
+
+ isl_map_free(map12);
+ isl_map_free(map21);
+
+ if (subset)
+ *check_closed = 1;
+
+ return subset < 0 ? -1 : !subset;
+error:
+ isl_map_free(map21);
+ return -1;
+}
+
+/* Perform Tarjan's algorithm for computing the strongly connected components
+ * in the graph with the disjuncts of "map" as vertices and with an
+ * edge between any pair of disjuncts such that the first has
+ * to be applied after the second.
+ */
+static int power_components_tarjan(struct basic_map_sort *s,
+ __isl_keep isl_basic_map **list, int i)
+{
+ int j;
+
+ s->node[i].index = s->index;
+ s->node[i].min_index = s->index;
+ s->node[i].on_stack = 1;
+ s->index++;
+ s->stack[s->sp++] = i;
+
+ for (j = s->len - 1; j >= 0; --j) {
+ int f;
+
+ if (j == i)
+ continue;
+ if (s->node[j].index >= 0 &&
+ (!s->node[j].on_stack ||
+ s->node[j].index > s->node[i].min_index))
+ continue;
+
+ 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, 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)
+ s->node[i].min_index = s->node[j].index;
+ }
+
+ if (s->node[i].index != s->node[i].min_index)
+ return 0;
+
+ do {
+ j = s->stack[--s->sp];
+ s->node[j].on_stack = 0;
+ s->order[s->op++] = j;
+ } while (j != i);
+ s->order[s->op++] = -1;
+
+ 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 the union of the identity map and
- * an overapproximation of the map
+ * construct a map that is an overapproximation of the map
* that takes an element from the dom R \times Z to an
* element from ran R \times Z, such that the first n coordinates of the
* difference between them is a sum of differences between images
* and pre-images in one of the R_i and such that the last coordinate
* is equal to the number of steps taken.
+ * If "project" is set, then these final coordinates are not included,
+ * i.e., a relation of type Z^n -> Z^n is returned.
* That is, let
*
* \Delta_i = { y - x | (x, y) in R_i }
*
* { (x) -> (x + d) | \exists k_i >= 0, \delta_i \in \Delta_i :
* d = (\sum_i k_i \delta_i, \sum_i k_i) and
- * x in dom R and x + d in ran R } union
- * { (x) -> (x) }
+ * x in dom R and x + d in ran R }
+ *
+ * or
+ *
+ * { (x) -> (x + d) | \exists k_i >= 0, \delta_i \in \Delta_i :
+ * d = (\sum_i k_i \delta_i) and
+ * x in dom R and x + d in ran R }
+ *
+ * if "project" is set.
*
* We first split the map into strongly connected components, perform
- * the above on each component and the join the results in the correct
- * order. The power of each of the components needs to be extended
- * with the identity map because a path in the global result need
- * not go through every component.
- * The final result will then also contain the identity map, but
- * this part will be removed when the length of the path is forced
- * to be strictly positive.
+ * the above on each component and then join the results in the correct
+ * order, at each join also taking in the union of both arguments
+ * to allow for paths that do not go through one of the two arguments.
*/
static __isl_give isl_map *construct_power_components(__isl_take isl_dim *dim,
__isl_keep isl_map *map, int *exact, int project)
{
- int i, n;
+ int i, n, c;
struct isl_map *path = NULL;
struct basic_map_sort *s = NULL;
+ int *orig_exact;
+ int local_exact;
if (!map)
goto error;
if (map->n <= 1)
- return construct_component(dim, map, exact, project);
+ 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)
+ exact = &local_exact;
+
+ c = 0;
i = 0;
n = map->n;
- path = isl_map_identity(isl_dim_domain(isl_dim_copy(dim)));
+ if (project)
+ path = isl_map_empty(isl_map_get_dim(map));
+ else
+ path = isl_map_empty(isl_dim_copy(dim));
+ path = anonymize(path);
while (n) {
struct isl_map *comp;
+ isl_map *path_comp, *path_comb;
comp = isl_map_alloc_dim(isl_map_get_dim(map), n, 0);
while (s->order[i] != -1) {
comp = isl_map_add_basic_map(comp,
--n;
++i;
}
- path = isl_map_apply_range(path,
- construct_component(isl_dim_copy(dim), comp,
- exact, project));
+ path_comp = floyd_warshall(isl_dim_copy(dim),
+ comp, exact, project);
+ path_comb = isl_map_apply_range(isl_map_copy(path),
+ isl_map_copy(path_comp));
+ path = isl_map_union(path, path_comp);
+ path = isl_map_union(path, path_comb);
isl_map_free(comp);
++i;
+ ++c;
+ }
+
+ if (c > 1 && s->check_closed && !*exact) {
+ int closed;
+
+ closed = isl_map_is_transitively_closed(path);
+ if (closed < 0)
+ goto error;
+ if (!closed) {
+ basic_map_sort_free(s);
+ isl_map_free(path);
+ return floyd_warshall(dim, map, orig_exact, project);
+ }
}
basic_map_sort_free(s);
error:
basic_map_sort_free(s);
isl_dim_free(dim);
+ isl_map_free(path);
return NULL;
}
*
* if "project" is set.
*
- * We first construct an extended mapping with an extra coordinate
+ * If "project" is not set, then
+ * we construct an extended mapping with an extra coordinate
* that indicates the number of steps taken. In particular,
* the difference in the last coordinate is equal to the number
* of steps taken to move from a domain element to the corresponding
* image element(s).
- * In the final step, this difference is equated to the parameter "param"
- * and made positive (unless project is set).
- * The extra coordinates are subsequently projected out.
*/
static __isl_give isl_map *construct_power(__isl_keep isl_map *map,
- unsigned param, int *exact, int project)
+ int *exact, int project)
{
struct isl_map *app = NULL;
- struct isl_map *diff;
struct isl_dim *dim = NULL;
unsigned d;
app = construct_power_components(isl_dim_copy(dim), map,
exact, project);
- if (project) {
- isl_dim_free(dim);
- app = set_path_length(app, 0, 1);
- } else {
- diff = equate_parameter_to_length(dim, param);
- app = isl_map_intersect(app, diff);
- }
- app = isl_map_project_out(app, isl_dim_in, d, 1);
- app = isl_map_project_out(app, isl_dim_out, d, 1);
+ isl_dim_free(dim);
return app;
}
/* Compute the positive powers of "map", or an overapproximation.
- * The power is given by parameter "param". If the result is exact,
- * then *exact is set to 1.
+ * If the result is exact, then *exact is set to 1.
*
* If project is set, then we are actually interested in the transitive
* closure, so we can use a more relaxed exactness check.
* The lengths of the paths are also projected out instead of being
- * equated to "param" (which is then ignored in this case).
+ * encoded as the difference between an extra pair of final coordinates.
*/
-static __isl_give isl_map *map_power(__isl_take isl_map *map, unsigned param,
+static __isl_give isl_map *map_power(__isl_take isl_map *map,
int *exact, int project)
{
struct isl_map *app = NULL;
if (exact)
*exact = 1;
- map = isl_map_coalesce(map);
if (!map)
return NULL;
+ isl_assert(map->ctx,
+ isl_map_dim(map, isl_dim_in) == isl_map_dim(map, isl_dim_out),
+ goto error);
+
+ app = construct_power(map, exact, project);
+
+ isl_map_free(map);
+ return app;
+error:
+ isl_map_free(map);
+ isl_map_free(app);
+ return NULL;
+}
+
+/* Compute the positive powers of "map", or an overapproximation.
+ * The power is given by parameter "param". If the result is exact,
+ * then *exact is set to 1.
+ * map_power constructs an extended relation with the path lengths
+ * encoded as the difference between the final coordinates.
+ * In the final step, this difference is equated to the parameter "param"
+ * and made positive. The extra coordinates are subsequently projected out.
+ */
+__isl_give isl_map *isl_map_power(__isl_take isl_map *map, unsigned param,
+ int *exact)
+{
+ isl_dim *target_dim;
+ isl_dim *dim;
+ isl_map *diff;
+ unsigned d;
+
+ if (!map)
+ return NULL;
+
+ isl_assert(map->ctx, param < isl_map_dim(map, isl_dim_param),
+ goto error);
+
+ d = isl_map_dim(map, isl_dim_in);
+
+ map = isl_map_compute_divs(map);
+ map = isl_map_coalesce(map);
+
if (isl_map_fast_is_empty(map))
return map;
- isl_assert(map->ctx, project || param < isl_map_dim(map, isl_dim_param),
- goto error);
- isl_assert(map->ctx,
- isl_map_dim(map, isl_dim_in) == isl_map_dim(map, isl_dim_out),
- goto error);
+ target_dim = isl_map_get_dim(map);
+ map = map_power(map, exact, 0);
- app = construct_power(map, param, exact, project);
+ dim = isl_map_get_dim(map);
+ diff = equate_parameter_to_length(dim, param);
+ map = isl_map_intersect(map, diff);
+ map = isl_map_project_out(map, isl_dim_in, d, 1);
+ map = isl_map_project_out(map, isl_dim_out, d, 1);
- isl_map_free(map);
- return app;
+ map = isl_map_reset_dim(map, target_dim);
+
+ return map;
error:
isl_map_free(map);
- isl_map_free(app);
return NULL;
}
-/* Compute the positive powers of "map", or an overapproximation.
- * The power is given by parameter "param". If the result is exact,
- * then *exact is set to 1.
+/* Compute a relation that maps each element in the range of the input
+ * relation to the lengths of all paths composed of edges in the input
+ * relation that end up in the given range element.
+ * The result may be an overapproximation, in which case *exact is set to 0.
+ * The resulting relation is very similar to the power relation.
+ * The difference are that the domain has been projected out, the
+ * range has become the domain and the exponent is the range instead
+ * of a parameter.
*/
-__isl_give isl_map *isl_map_power(__isl_take isl_map *map, unsigned param,
+__isl_give isl_map *isl_map_reaching_path_lengths(__isl_take isl_map *map,
int *exact)
{
- return map_power(map, param, exact, 0);
+ isl_dim *dim;
+ isl_map *diff;
+ unsigned d;
+ unsigned param;
+
+ if (!map)
+ return NULL;
+
+ d = isl_map_dim(map, isl_dim_in);
+ param = isl_map_dim(map, isl_dim_param);
+
+ map = isl_map_compute_divs(map);
+ map = isl_map_coalesce(map);
+
+ if (isl_map_fast_is_empty(map)) {
+ if (exact)
+ *exact = 1;
+ map = isl_map_project_out(map, isl_dim_out, 0, d);
+ map = isl_map_add_dims(map, isl_dim_out, 1);
+ return map;
+ }
+
+ map = map_power(map, exact, 0);
+
+ map = isl_map_add_dims(map, isl_dim_param, 1);
+ dim = isl_map_get_dim(map);
+ diff = equate_parameter_to_length(dim, param);
+ map = isl_map_intersect(map, diff);
+ map = isl_map_project_out(map, isl_dim_in, 0, d + 1);
+ map = isl_map_project_out(map, isl_dim_out, d, 1);
+ map = isl_map_reverse(map);
+ map = isl_map_move_dims(map, isl_dim_out, 0, isl_dim_param, param, 1);
+
+ return map;
}
/* Check whether equality i of bset is a pure stride constraint
* k L <= j - i <= k U and exists a: j_p - i_p = M_p a_p }
*
* and intersect domain and range of this transitive closure with
- * domain and range of the original map.
+ * the given domain and range.
*
* If with_id is set, then try to include as much of the identity mapping
* as possible, by computing
* { i -> j : exists k >= 0:
* k L <= j - i <= k U and exists a: j_p - i_p = M_p a_p }
*
- * instead (i.e., allow k = 0) and by intersecting domain and range
- * with the union of the domain and the range of the original map.
+ * instead (i.e., allow k = 0).
*
* In practice, we compute the difference set
*
* (constant) lower and upper bounds for each individual dimension,
* adding a constraint for each bound not equal to infinity.
*/
-static __isl_give isl_map *box_closure(__isl_take isl_map *map, int with_id)
+static __isl_give isl_map *box_closure_on_domain(__isl_take isl_map *map,
+ __isl_take isl_set *dom, __isl_take isl_set *ran, int with_id)
{
int i;
int k;
unsigned total;
isl_dim *dim;
isl_set *delta;
- isl_set *domain = NULL;
- isl_set *range = NULL;
isl_map *app = NULL;
isl_basic_set *aff = NULL;
isl_basic_map *bmap = NULL;
isl_int_set_si(bmap->ineq[k][0], -1);
isl_int_set_si(bmap->ineq[k][1 + nparam + 2 * d + aff->n_div], 1);
- domain = isl_map_domain(isl_map_copy(map));
- domain = isl_set_coalesce(domain);
- range = isl_map_range(isl_map_copy(map));
- range = isl_set_coalesce(range);
- if (with_id) {
- domain = isl_set_union(domain, range);
- domain = isl_set_coalesce(domain);
- range = isl_set_copy(domain);
- }
- app = isl_map_from_domain_and_range(domain, range);
+ app = isl_map_from_domain_and_range(dom, ran);
isl_vec_free(obj);
isl_basic_set_free(aff);
isl_vec_free(obj);
isl_basic_map_free(bmap);
isl_basic_set_free(aff);
+ isl_set_free(dom);
+ isl_set_free(ran);
isl_map_free(map);
isl_set_free(delta);
isl_int_clear(opt);
return NULL;
}
+/* Given a map, compute the smallest superset of this map that is of the form
+ *
+ * { i -> j : L <= j - i <= U and exists a_p: j_p - i_p = M_p a_p }
+ *
+ * (where p ranges over the (non-parametric) dimensions),
+ * compute the transitive closure of this map, i.e.,
+ *
+ * { i -> j : exists k > 0:
+ * k L <= j - i <= k U and exists a: j_p - i_p = M_p a_p }
+ *
+ * and intersect domain and range of this transitive closure with
+ * domain and range of the original map.
+ */
+static __isl_give isl_map *box_closure(__isl_take isl_map *map)
+{
+ isl_set *domain;
+ isl_set *range;
+
+ domain = isl_map_domain(isl_map_copy(map));
+ domain = isl_set_coalesce(domain);
+ range = isl_map_range(isl_map_copy(map));
+ range = isl_set_coalesce(range);
+
+ return box_closure_on_domain(map, domain, range, 0);
+}
+
+/* Given a map, compute the smallest superset of this map that is of the form
+ *
+ * { i -> j : L <= j - i <= U and exists a_p: j_p - i_p = M_p a_p }
+ *
+ * (where p ranges over the (non-parametric) dimensions),
+ * compute the transitive and partially reflexive closure of this map, i.e.,
+ *
+ * { i -> j : exists k >= 0:
+ * k L <= j - i <= k U and exists a: j_p - i_p = M_p a_p }
+ *
+ * and intersect domain and range of this transitive closure with
+ * the given domain.
+ */
+static __isl_give isl_map *box_closure_with_identity(__isl_take isl_map *map,
+ __isl_take isl_set *dom)
+{
+ return box_closure_on_domain(map, dom, isl_set_copy(dom), 1);
+}
+
/* Check whether app is the transitive closure of map.
* In particular, check that app is acyclic and, if so,
* check that
static int can_be_split_off(__isl_keep isl_map *map, int i,
__isl_give isl_map **tc, __isl_give isl_map **qc)
{
- isl_map *map_i, *id;
+ isl_map *map_i, *id = NULL;
int j = -1;
+ isl_set *C;
+
+ *tc = NULL;
+ *qc = NULL;
+
+ C = isl_set_union(isl_map_domain(isl_map_copy(map)),
+ isl_map_range(isl_map_copy(map)));
+ C = isl_set_from_basic_set(isl_set_simple_hull(C));
+ if (!C)
+ goto error;
map_i = isl_map_from_basic_map(isl_basic_map_copy(map->p[i]));
- *tc = box_closure(isl_map_copy(map_i), 0);
- *qc = box_closure(map_i, 1);
+ *tc = box_closure(isl_map_copy(map_i));
+ *qc = box_closure_with_identity(map_i, C);
id = isl_map_subtract(isl_map_copy(*qc), isl_map_copy(*tc));
if (!id || !*qc)
return -1;
}
+static __isl_give isl_map *box_closure_with_check(__isl_take isl_map *map,
+ int *exact)
+{
+ isl_map *app;
+
+ app = box_closure(isl_map_copy(map));
+ if (exact)
+ *exact = check_exactness_omega(map, app);
+
+ isl_map_free(map);
+ return app;
+}
+
/* Compute an overapproximation of the transitive closure of "map"
* using a variation of the algorithm from
* "Transitive Closure of Infinite Graphs and its Applications"
*
* If not, we simply call box_closure on the whole map.
*/
-static __isl_give isl_map *compute_closure_omega(__isl_take isl_map *map)
+static __isl_give isl_map *transitive_closure_omega(__isl_take isl_map *map,
+ int *exact)
{
int i, j;
+ int exact_i;
+ isl_map *app;
if (!map)
return NULL;
if (map->n == 1)
- return box_closure(map, 0);
-
- map = isl_map_cow(map);
- if (!map)
- goto error;
+ return box_closure_with_check(map, exact);
for (i = 0; i < map->n; ++i) {
int ok;
if (!ok)
continue;
- isl_basic_map_free(map->p[i]);
- if (i != map->n - 1)
- map->p[i] = map->p[map->n - 1];
- map->n--;
+ app = isl_map_alloc_dim(isl_map_get_dim(map), map->n - 1, 0);
+
+ for (j = 0; j < map->n; ++j) {
+ if (j == i)
+ continue;
+ app = isl_map_add_basic_map(app,
+ isl_basic_map_copy(map->p[j]));
+ }
- map = isl_map_apply_range(isl_map_copy(qc), map);
- map = isl_map_apply_range(map, qc);
+ app = isl_map_apply_range(isl_map_copy(qc), app);
+ app = isl_map_apply_range(app, qc);
- return isl_map_union(tc, compute_closure_omega(map));
+ app = isl_map_union(tc, transitive_closure_omega(app, NULL));
+ exact_i = check_exactness_omega(map, app);
+ if (exact_i == 1) {
+ if (exact)
+ *exact = exact_i;
+ isl_map_free(map);
+ return app;
+ }
+ isl_map_free(app);
+ if (exact_i < 0)
+ goto error;
}
- return box_closure(map, 0);
+ return box_closure_with_check(map, exact);
error:
isl_map_free(map);
return NULL;
}
-/* Compute an overapproximation of the transitive closure of "map"
- * using a variation of the algorithm from
- * "Transitive Closure of Infinite Graphs and its Applications"
- * by Kelly et al. and check whether the result is definitely exact.
- */
-static __isl_give isl_map *transitive_closure_omega(__isl_take isl_map *map,
- int *exact)
-{
- isl_map *app;
-
- app = compute_closure_omega(isl_map_copy(map));
-
- if (exact)
- *exact = check_exactness_omega(map, app);
-
- isl_map_free(map);
- return app;
-}
-
/* Compute the transitive closure of "map", or an overapproximation.
* If the result is exact, then *exact is set to 1.
* Simply use map_power to compute the powers of map, but tell
__isl_give isl_map *isl_map_transitive_closure(__isl_take isl_map *map,
int *exact)
{
- unsigned param;
+ isl_dim *target_dim;
+ int closed;
if (!map)
goto error;
if (map->ctx->opt->closure == ISL_CLOSURE_OMEGA)
return transitive_closure_omega(map, exact);
- param = isl_map_dim(map, isl_dim_param);
- map = map_power(map, param, exact, 1);
+ map = isl_map_compute_divs(map);
+ map = isl_map_coalesce(map);
+ closed = isl_map_is_transitively_closed(map);
+ if (closed < 0)
+ goto error;
+ if (closed) {
+ if (exact)
+ *exact = 1;
+ return map;
+ }
+
+ target_dim = isl_map_get_dim(map);
+ map = map_power(map, exact, 1);
+ map = isl_map_reset_dim(map, target_dim);
return map;
error:
isl_map_free(map);
return NULL;
}
+
+static int inc_count(__isl_take isl_map *map, void *user)
+{
+ int *n = user;
+
+ *n += map->n;
+
+ isl_map_free(map);
+
+ return 0;
+}
+
+static int collect_basic_map(__isl_take isl_map *map, void *user)
+{
+ int i;
+ isl_basic_map ***next = user;
+
+ for (i = 0; i < map->n; ++i) {
+ **next = isl_basic_map_copy(map->p[i]);
+ if (!**next)
+ goto error;
+ (*next)++;
+ }
+
+ isl_map_free(map);
+ return 0;
+error:
+ isl_map_free(map);
+ return -1;
+}
+
+/* Perform Floyd-Warshall on the given list of basic relations.
+ * The basic relations may live in different dimensions,
+ * but basic relations that get assigned to the diagonal of the
+ * grid have domains and ranges of the same dimension and so
+ * the standard algorithm can be used because the nested transitive
+ * closures are only applied to diagonal elements and because all
+ * compositions are peformed on relations with compatible domains and ranges.
+ */
+static __isl_give isl_union_map *union_floyd_warshall_on_list(isl_ctx *ctx,
+ __isl_keep isl_basic_map **list, int n, int *exact)
+{
+ int i, j, k;
+ int n_group;
+ int *group = NULL;
+ isl_set **set = NULL;
+ isl_map ***grid = NULL;
+ isl_union_map *app;
+
+ group = setup_groups(ctx, list, n, &set, &n_group);
+ if (!group)
+ goto error;
+
+ grid = isl_calloc_array(ctx, isl_map **, n_group);
+ if (!grid)
+ goto error;
+ for (i = 0; i < n_group; ++i) {
+ grid[i] = isl_calloc_array(map->ctx, isl_map *, n_group);
+ if (!grid[i])
+ goto error;
+ for (j = 0; j < n_group; ++j) {
+ isl_dim *dim1, *dim2, *dim;
+ dim1 = isl_dim_reverse(isl_set_get_dim(set[i]));
+ dim2 = isl_set_get_dim(set[j]);
+ dim = isl_dim_join(dim1, dim2);
+ grid[i][j] = isl_map_empty(dim);
+ }
+ }
+
+ for (k = 0; k < n; ++k) {
+ i = group[2 * k];
+ j = group[2 * k + 1];
+ grid[i][j] = isl_map_union(grid[i][j],
+ isl_map_from_basic_map(
+ isl_basic_map_copy(list[k])));
+ }
+
+ floyd_warshall_iterate(grid, n_group, exact);
+
+ app = isl_union_map_empty(isl_map_get_dim(grid[0][0]));
+
+ for (i = 0; i < n_group; ++i) {
+ for (j = 0; j < n_group; ++j)
+ app = isl_union_map_add_map(app, grid[i][j]);
+ free(grid[i]);
+ }
+ free(grid);
+
+ for (i = 0; i < 2 * n; ++i)
+ isl_set_free(set[i]);
+ free(set);
+
+ free(group);
+ return app;
+error:
+ if (grid)
+ for (i = 0; i < n_group; ++i) {
+ if (!grid[i])
+ continue;
+ for (j = 0; j < n_group; ++j)
+ isl_map_free(grid[i][j]);
+ free(grid[i]);
+ }
+ free(grid);
+ if (set) {
+ for (i = 0; i < 2 * n; ++i)
+ isl_set_free(set[i]);
+ free(set);
+ }
+ free(group);
+ return NULL;
+}
+
+/* Perform Floyd-Warshall on the given union relation.
+ * The implementation is very similar to that for non-unions.
+ * The main difference is that it is applied unconditionally.
+ * We first extract a list of basic maps from the union map
+ * and then perform the algorithm on this list.
+ */
+static __isl_give isl_union_map *union_floyd_warshall(
+ __isl_take isl_union_map *umap, int *exact)
+{
+ int i, n;
+ isl_ctx *ctx;
+ isl_basic_map **list;
+ isl_basic_map **next;
+ isl_union_map *res;
+
+ n = 0;
+ if (isl_union_map_foreach_map(umap, inc_count, &n) < 0)
+ goto error;
+
+ ctx = isl_union_map_get_ctx(umap);
+ list = isl_calloc_array(ctx, isl_basic_map *, n);
+ if (!list)
+ goto error;
+
+ next = list;
+ if (isl_union_map_foreach_map(umap, collect_basic_map, &next) < 0)
+ goto error;
+
+ res = union_floyd_warshall_on_list(ctx, list, n, exact);
+
+ if (list) {
+ for (i = 0; i < n; ++i)
+ isl_basic_map_free(list[i]);
+ free(list);
+ }
+
+ isl_union_map_free(umap);
+ return res;
+error:
+ if (list) {
+ for (i = 0; i < n; ++i)
+ isl_basic_map_free(list[i]);
+ free(list);
+ }
+ isl_union_map_free(umap);
+ return NULL;
+}
+
+/* Decompose the give union relation into strongly connected components.
+ * The implementation is essentially the same as that of
+ * construct_power_components with the major difference that all
+ * operations are performed on union maps.
+ */
+static __isl_give isl_union_map *union_components(
+ __isl_take isl_union_map *umap, int *exact)
+{
+ int i;
+ int n;
+ isl_ctx *ctx;
+ isl_basic_map **list;
+ isl_basic_map **next;
+ isl_union_map *path = NULL;
+ struct basic_map_sort *s = NULL;
+ int c, l;
+ int recheck = 0;
+
+ n = 0;
+ if (isl_union_map_foreach_map(umap, inc_count, &n) < 0)
+ goto error;
+
+ if (n <= 1)
+ return union_floyd_warshall(umap, exact);
+
+ ctx = isl_union_map_get_ctx(umap);
+ list = isl_calloc_array(ctx, isl_basic_map *, n);
+ if (!list)
+ goto error;
+
+ next = list;
+ if (isl_union_map_foreach_map(umap, collect_basic_map, &next) < 0)
+ goto error;
+
+ s = basic_map_sort_init(ctx, n, list);
+ if (!s)
+ goto error;
+
+ c = 0;
+ i = 0;
+ l = n;
+ path = isl_union_map_empty(isl_union_map_get_dim(umap));
+ while (l) {
+ isl_union_map *comp;
+ isl_union_map *path_comp, *path_comb;
+ comp = isl_union_map_empty(isl_union_map_get_dim(umap));
+ while (s->order[i] != -1) {
+ comp = isl_union_map_add_map(comp,
+ isl_map_from_basic_map(
+ isl_basic_map_copy(list[s->order[i]])));
+ --l;
+ ++i;
+ }
+ path_comp = union_floyd_warshall(comp, exact);
+ path_comb = isl_union_map_apply_range(isl_union_map_copy(path),
+ isl_union_map_copy(path_comp));
+ path = isl_union_map_union(path, path_comp);
+ path = isl_union_map_union(path, path_comb);
+ ++i;
+ ++c;
+ }
+
+ if (c > 1 && s->check_closed && !*exact) {
+ int closed;
+
+ closed = isl_union_map_is_transitively_closed(path);
+ if (closed < 0)
+ goto error;
+ recheck = !closed;
+ }
+
+ basic_map_sort_free(s);
+
+ for (i = 0; i < n; ++i)
+ isl_basic_map_free(list[i]);
+ free(list);
+
+ if (recheck) {
+ isl_union_map_free(path);
+ return union_floyd_warshall(umap, exact);
+ }
+
+ isl_union_map_free(umap);
+
+ return path;
+error:
+ basic_map_sort_free(s);
+ if (list) {
+ for (i = 0; i < n; ++i)
+ isl_basic_map_free(list[i]);
+ free(list);
+ }
+ isl_union_map_free(umap);
+ isl_union_map_free(path);
+ return NULL;
+}
+
+/* Compute the transitive closure of "umap", or an overapproximation.
+ * If the result is exact, then *exact is set to 1.
+ */
+__isl_give isl_union_map *isl_union_map_transitive_closure(
+ __isl_take isl_union_map *umap, int *exact)
+{
+ int closed;
+
+ if (!umap)
+ return NULL;
+
+ if (exact)
+ *exact = 1;
+
+ umap = isl_union_map_compute_divs(umap);
+ umap = isl_union_map_coalesce(umap);
+ closed = isl_union_map_is_transitively_closed(umap);
+ if (closed < 0)
+ goto error;
+ if (closed)
+ return umap;
+ umap = union_components(umap, exact);
+ return umap;
+error:
+ isl_union_map_free(umap);
+ return NULL;
+}
projects / platform / upstream / isl.git / blobdiff