/*
* Copyright 2010 INRIA Saclay
*
- * Use of this software is governed by the GNU LGPLv2.1 license
+ * Use of this software is governed by the MIT license
*
* Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
* Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
* 91893 Orsay, France
*/
-#include "isl_map.h"
-#include "isl_map_private.h"
-#include "isl_seq.h"
-#include <isl_lp.h>
+#include <isl_ctx_private.h>
+#include <isl_map_private.h>
+#include <isl/map.h>
+#include <isl/seq.h>
+#include <isl_space_private.h>
+#include <isl/lp.h>
+#include <isl/union_map.h>
+#include <isl_mat_private.h>
+#include <isl_options_private.h>
+#include <isl_tarjan.h>
int isl_map_is_transitively_closed(__isl_keep isl_map *map)
{
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
static __isl_give isl_map *set_path_length(__isl_take isl_map *map,
int exactly, int length)
{
- struct isl_dim *dim;
+ isl_space *dim;
struct isl_basic_map *bmap;
unsigned d;
unsigned nparam;
if (!map)
return NULL;
- dim = isl_map_get_dim(map);
- d = isl_dim_size(dim, isl_dim_in);
- nparam = isl_dim_size(dim, isl_dim_param);
- bmap = isl_basic_map_alloc_dim(dim, 0, 1, 1);
+ dim = isl_map_get_space(map);
+ d = isl_space_dim(dim, isl_dim_in);
+ nparam = isl_space_dim(dim, isl_dim_param);
+ bmap = isl_basic_map_alloc_space(dim, 0, 1, 1);
if (exactly) {
k = isl_basic_map_alloc_equality(bmap);
c = bmap->eq[k];
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_space(app, isl_map_get_space(map));
+
test = isl_map_apply_range(isl_map_copy(map), isl_map_copy(app));
test = isl_map_union(test, isl_map_copy(map));
* For any element in this relation, the number of steps taken
* is equal to the difference in the final coordinates.
*/
-static __isl_give isl_map *path_along_steps(__isl_take isl_dim *dim,
+static __isl_give isl_map *path_along_steps(__isl_take isl_space *dim,
__isl_keep isl_mat *steps)
{
int i, j, k;
if (!dim || !steps)
goto error;
- d = isl_dim_size(dim, isl_dim_in);
+ d = isl_space_dim(dim, isl_dim_in);
n = steps->n_row;
- nparam = isl_dim_size(dim, isl_dim_param);
+ nparam = isl_space_dim(dim, isl_dim_param);
- path = isl_basic_map_alloc_dim(isl_dim_copy(dim), n, d, n);
+ path = isl_basic_map_alloc_space(isl_space_copy(dim), n, d, n);
for (i = 0; i < n; ++i) {
k = isl_basic_map_alloc_div(path);
isl_int_set_si(path->ineq[k][1 + nparam + 2 * d + i], 1);
}
- isl_dim_free(dim);
+ isl_space_free(dim);
path = isl_basic_map_simplify(path);
path = isl_basic_map_finalize(path);
return isl_map_from_basic_map(path);
error:
- isl_dim_free(dim);
+ isl_space_free(dim);
isl_basic_map_free(path);
return NULL;
}
* variables are non-zero and if moreover the parametric constant
* can never attain positive values.
* Return IMPURE otherwise.
+ *
+ * If div_purity is NULL then we are dealing with a non-parametric set
+ * and so the constraint is obviously PURE_VAR.
*/
static int purity(__isl_keep isl_basic_set *bset, isl_int *c, int *div_purity,
int eq)
int i;
int p = 0, v = 0;
+ if (!div_purity)
+ return PURE_VAR;
+
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);
* 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;
goto error;
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)));
+ id = isl_basic_map_identity(isl_basic_map_get_space(path));
is_id = isl_basic_map_is_equal(test, id);
isl_basic_map_free(test);
isl_basic_map_free(id);
return -1;
}
-__isl_give isl_basic_map *add_delta_constraints(__isl_take isl_basic_map *path,
+/* If any of the constraints is found to be impure then this function
+ * sets *impurity to 1.
+ */
+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)
+ unsigned d, int *div_purity, int eq, int *impurity)
{
int i, k;
int n = eq ? delta->n_eq : delta->n_ineq;
int p = purity(delta, delta_c[i], div_purity, eq);
if (p < 0)
goto error;
+ if (p != PURE_VAR && p != PURE_PARAM && !*impurity)
+ *impurity = 1;
if (p == IMPURE)
continue;
if (eq && p != MIXED) {
*
* In particular, let delta be defined as
*
- * \delta = [p] -> { [x] : A x + a >= and B p + b >= 0 and
+ * \delta = [p] -> { [x] : A x + a >= 0 and B p + b >= 0 and
* C x + C'p + c >= 0 and
* D x + D'p + d >= 0 }
*
* parameter dependent and others. Constraints containing
* any of the other existentially quantified variables are removed.
* This is safe, but leads to an additional overapproximation.
+ *
+ * If there are any impure constraints, then we also eliminate
+ * the parameters from \delta, resulting in a set
+ *
+ * \delta' = { [x] : E x + e >= 0 }
+ *
+ * and add the constraints
+ *
+ * E f + k e >= 0
+ *
+ * to the constructed relation.
*/
-static __isl_give isl_map *path_along_delta(__isl_take isl_dim *dim,
+static __isl_give isl_map *path_along_delta(__isl_take isl_space *dim,
__isl_take isl_basic_set *delta)
{
isl_basic_map *path = NULL;
int i, k;
int is_id;
int *div_purity = NULL;
+ int impurity = 0;
if (!delta)
goto error;
n_div = isl_basic_set_dim(delta, isl_dim_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,
+ path = isl_basic_map_alloc_space(isl_space_copy(dim), n_div + d + 1,
d + 1 + delta->n_eq, delta->n_eq + delta->n_ineq + 1);
off = 1 + nparam + 2 * (d + 1) + n_div;
if (!div_purity)
goto error;
- path = add_delta_constraints(path, delta, off, nparam, d, div_purity, 1);
- path = add_delta_constraints(path, delta, off, nparam, d, div_purity, 0);
+ path = add_delta_constraints(path, delta, off, nparam, d,
+ div_purity, 1, &impurity);
+ path = add_delta_constraints(path, delta, off, nparam, d,
+ div_purity, 0, &impurity);
+ if (impurity) {
+ isl_space *dim = isl_basic_set_get_space(delta);
+ delta = isl_basic_set_project_out(delta,
+ isl_dim_param, 0, nparam);
+ delta = isl_basic_set_add_dims(delta, isl_dim_param, nparam);
+ delta = isl_basic_set_reset_space(delta, dim);
+ if (!delta)
+ goto error;
+ path = isl_basic_map_extend_constraints(path, delta->n_eq,
+ delta->n_ineq + 1);
+ path = add_delta_constraints(path, delta, off, nparam, d,
+ NULL, 1, &impurity);
+ path = add_delta_constraints(path, delta, off, nparam, d,
+ NULL, 0, &impurity);
+ path = isl_basic_map_gauss(path, NULL);
+ }
is_id = empty_path_is_identity(path, off + d);
if (is_id < 0)
isl_basic_set_free(delta);
path = isl_basic_map_finalize(path);
if (is_id) {
- isl_dim_free(dim);
+ isl_space_free(dim);
return isl_map_from_basic_map(path);
}
- return isl_basic_map_union(path,
- isl_basic_map_identity(isl_dim_domain(dim)));
+ return isl_basic_map_union(path, isl_basic_map_identity(dim));
error:
free(div_purity);
- isl_dim_free(dim);
+ isl_space_free(dim);
isl_basic_set_free(delta);
isl_basic_map_free(path);
return NULL;
*
* { [x,x_s] -> [y,y_s] : k = y_s - x_s > 0 }
*/
-static __isl_give isl_map *equate_parameter_to_length(__isl_take isl_dim *dim,
+static __isl_give isl_map *equate_parameter_to_length(__isl_take isl_space *dim,
unsigned param)
{
struct isl_basic_map *bmap;
unsigned nparam;
int k;
- d = isl_dim_size(dim, isl_dim_in);
- nparam = isl_dim_size(dim, isl_dim_param);
- bmap = isl_basic_map_alloc_dim(dim, 0, 1, 1);
+ d = isl_space_dim(dim, isl_dim_in);
+ nparam = isl_space_dim(dim, isl_dim_param);
+ bmap = isl_basic_map_alloc_space(dim, 0, 1, 1);
k = isl_basic_map_alloc_equality(bmap);
if (k < 0)
goto error;
* Since each of these paths performs an addition, composition is
* symmetric and we can simply compose all resulting paths in any order.
*/
-static __isl_give isl_map *construct_extended_path(__isl_take isl_dim *dim,
+static __isl_give isl_map *construct_extended_path(__isl_take isl_space *dim,
__isl_keep isl_map *map, int *project)
{
struct isl_mat *steps = NULL;
d = isl_map_dim(map, isl_dim_in);
- path = isl_map_identity(isl_dim_domain(isl_dim_copy(dim)));
+ path = isl_map_identity(isl_space_copy(dim));
steps = isl_mat_alloc(map->ctx, map->n, d);
if (!steps)
for (j = 0; j < d; ++j) {
int fixed;
- fixed = isl_basic_set_fast_dim_is_fixed(delta, j,
+ fixed = isl_basic_set_plain_dim_is_fixed(delta, j,
&steps->row[n][j]);
if (fixed < 0) {
isl_basic_set_free(delta);
if (j < d) {
path = isl_map_apply_range(path,
- path_along_delta(isl_dim_copy(dim), delta));
+ path_along_delta(isl_space_copy(dim), delta));
path = isl_map_coalesce(path);
} else {
isl_basic_set_free(delta);
if (n > 0) {
steps->n_row = n;
path = isl_map_apply_range(path,
- path_along_steps(isl_dim_copy(dim), steps));
+ path_along_steps(isl_space_copy(dim), steps));
}
if (project && *project) {
goto error;
}
- isl_dim_free(dim);
+ isl_space_free(dim);
isl_mat_free(steps);
return path;
error:
- isl_dim_free(dim);
+ isl_space_free(dim);
isl_mat_free(steps);
isl_map_free(path);
return NULL;
isl_set *i;
int no_overlap;
+ if (!isl_space_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);
* 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,
+static __isl_give isl_map *construct_component(__isl_take isl_space *dim,
__isl_keep isl_map *map, int *exact, int project)
{
struct isl_set *domain = NULL;
if (!isl_set_overlaps(domain, range)) {
isl_set_free(domain);
isl_set_free(range);
- isl_dim_free(dim);
+ isl_space_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);
return map;
}
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,
+ path = construct_extended_path(isl_space_copy(dim), map,
exact && *exact ? &project : NULL);
app = isl_map_intersect(app, path);
project)) < 0)
goto error;
- isl_dim_free(dim);
+ isl_space_free(dim);
app = set_path_length(app, 0, 1);
return app;
error:
- isl_dim_free(dim);
+ isl_space_free(dim);
isl_map_free(app);
return NULL;
}
* the final coordinates.
*/
static __isl_give isl_map *construct_projected_component(
- __isl_take isl_dim *dim,
+ __isl_take isl_space *dim,
__isl_keep isl_map *map, int *exact, int project)
{
isl_map *app;
if (!dim)
return NULL;
- d = isl_dim_size(dim, isl_dim_in);
+ d = isl_space_dim(dim, isl_dim_in);
app = construct_component(dim, map, exact, project);
if (project) {
* 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,
+static __isl_give isl_map *q_closure(__isl_take isl_space *dim,
__isl_take isl_set *dom, __isl_keep isl_basic_map *bmap, int *exact)
{
int project = 1;
isl_map *map;
isl_map *app;
- dom = isl_set_add(dom, isl_dim_set, 1);
+ 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);
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".
int j;
isl_map *comp;
- comp = isl_map_empty(isl_map_get_dim(map));
+ comp = isl_map_empty(isl_map_get_space(map));
for (j = 0; j < map->n; ++j) {
isl_map *map_j;
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])
* 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,
+ __isl_take isl_space *dim, __isl_keep isl_map *map,
int i, __isl_take isl_map *qc, int *left, int *right, int *exact)
{
isl_map *map_i;
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,
+ tc = construct_projected_component(isl_space_copy(dim), map_i,
exact, 1);
isl_map_free(map_i);
qc = isl_map_transitive_closure(qc, exact);
if (!*exact) {
- isl_dim_free(dim);
+ isl_space_free(dim);
isl_map_free(tc);
isl_map_free(qc);
- return isl_map_universe(isl_map_get_dim(map));
+ return isl_map_universe(isl_map_get_space(map));
}
if (!left || !right)
rtc = isl_map_union(isl_map_copy(tc),
- isl_map_identity(isl_dim_domain(isl_map_get_dim(tc))));
+ isl_map_identity(isl_map_get_space(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);
+ isl_space_free(dim);
return qc;
error:
- isl_dim_free(dim);
+ isl_space_free(dim);
isl_map_free(qc);
return NULL;
}
* 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,
+static int incemental_on_entire_domain(__isl_keep isl_space *dim,
__isl_keep isl_map *map,
isl_set **dom, isl_set **ran, int *left, int *right,
__isl_give isl_map **res)
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),
+ qc = q_closure(isl_space_copy(dim), isl_set_copy(C),
map->p[i], &exact_i);
if (!qc)
goto error;
isl_map_free(qc);
continue;
}
- *res = compute_incremental(isl_dim_copy(dim), map, i, qc,
+ *res = compute_incremental(isl_space_copy(dim), map, i, qc,
left, right, &exact_i);
if (!*res)
goto error;
* 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,
+static __isl_give isl_map *incremental_closure(__isl_take isl_space *dim,
__isl_keep isl_map *map, int *exact, int project)
{
int i;
goto error;
continue;
}
- qc = q_closure(isl_dim_copy(dim), C, map->p[i], &exact_i);
+ qc = q_closure(isl_space_copy(dim), C, map->p[i], &exact_i);
if (!qc)
goto error;
if (!exact_i) {
isl_map_free(qc);
continue;
}
- res = compute_incremental(isl_dim_copy(dim), map, i, qc,
+ res = compute_incremental(isl_space_copy(dim), map, i, qc,
(comp & LEFT) ? left : NULL,
(comp & RIGHT) ? right : NULL, &exact_i);
if (!res)
free(right);
if (res) {
- isl_dim_free(dim);
+ isl_space_free(dim);
return res;
}
free(ran);
free(left);
free(right);
- isl_dim_free(dim);
+ isl_space_free(dim);
return NULL;
}
continue;
set[i] = isl_set_union(set[i], set[group[pos]]);
+ set[group[pos]] = NULL;
if (!set[i])
goto error;
- set[group[pos]] = NULL;
group[group[pos]] = i;
group[pos] = i;
}
static int add_length(__isl_keep isl_map *map, isl_map ***grid, int n)
{
int i, j, k;
- isl_dim *dim;
+ isl_space *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);
+ dim = isl_map_get_space(map);
+ nparam = isl_space_dim(dim, isl_dim_param);
+ dim = isl_space_drop_dims(dim, isl_dim_in, 0, isl_space_dim(dim, isl_dim_in));
+ dim = isl_space_drop_dims(dim, isl_dim_out, 0, isl_space_dim(dim, isl_dim_out));
+ dim = isl_space_add_dims(dim, isl_dim_in, 1);
+ dim = isl_space_add_dims(dim, isl_dim_out, 1);
+ bstep = isl_basic_map_alloc_space(dim, 0, 1, 0);
k = isl_basic_map_alloc_equality(bstep);
if (k < 0) {
isl_basic_map_free(bstep);
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
* 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,
+static __isl_give isl_map *floyd_warshall_with_groups(__isl_take isl_space *dim,
__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 (!grid[i])
goto error;
for (j = 0; j < n; ++j)
- grid[i][j] = isl_map_empty(isl_map_get_dim(map));
+ grid[i][j] = isl_map_empty(isl_map_get_space(map));
}
for (k = 0; k < map->n; ++k) {
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));
+ app = isl_map_empty(isl_map_get_space(map));
for (i = 0; i < n; ++i) {
for (j = 0; j < n; ++j)
free(grid);
free(group);
- isl_dim_free(dim);
+ isl_space_free(dim);
return app;
error:
}
free(grid);
free(group);
- isl_dim_free(dim);
+ isl_space_free(dim);
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;
-
- if (!map)
- goto error;
- if (map->n <= 1)
- return incremental_closure(dim, map, exact, project);
+ int g;
- set = isl_calloc_array(map->ctx, isl_set *, 2 * map->n);
- group = isl_alloc_array(map->ctx, int, 2 * map->n);
+ *set = isl_calloc_array(ctx, isl_set *, 2 * n);
+ group = isl_alloc_array(ctx, int, 2 * 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)
- if (group[i] == i)
- group[i] = n++;
- else
+ 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]];
- for (i = 0; i < 2 * map->n; ++i)
- isl_set_free(set[i]);
-
- free(set);
+ *n_group = g;
- return floyd_warshall_with_groups(dim, map, exact, project, group, n);
+ return group;
error:
- for (i = 0; i < 2 * map->n; ++i)
- isl_set_free(set[i]);
- free(set);
+ if (*set) {
+ for (i = 0; i < 2 * n; ++i)
+ isl_set_free((*set)[i]);
+ free(*set);
+ *set = NULL;
+ }
free(group);
- 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
+/* 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.
*/
-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)
+static __isl_give isl_map *floyd_warshall(__isl_take isl_space *dim,
+ __isl_keep isl_map *map, int *exact, int project)
{
- struct basic_map_sort *s;
int i;
+ isl_set **set = NULL;
+ int *group = NULL;
+ int n;
- 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)
+ if (!map)
goto error;
- s->order = isl_alloc_array(ctx, int, 2 * len);
- if (!s->order)
+ 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;
- s->sp = 0;
- s->index = 0;
- s->op = 0;
+ for (i = 0; i < 2 * map->n; ++i)
+ isl_set_free(set[i]);
- s->check_closed = 0;
+ free(set);
- return s;
+ return floyd_warshall_with_groups(dim, map, exact, project, group, n);
error:
- basic_map_sort_free(s);
+ isl_space_free(dim);
return NULL;
}
+/* Structure for representing the nodes of the graph of which
+ * strongly connected components are being computed.
+ *
+ * list contains the actual nodes
+ * check_closed is set if we may have used the fact that
+ * a pair of basic maps can be interchanged
+ */
+struct isl_tc_follows_data {
+ isl_basic_map **list;
+ int check_closed;
+};
+
/* 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).
+ * "list[i]" (R_1) should follow (or be part of the same component as)
+ * "list[j]" (R_2).
*
* That is check whether
*
* *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)
+static int basic_map_follows(int i, int j, void *user)
{
+ struct isl_tc_follows_data *data = user;
struct isl_map *map12 = NULL;
struct isl_map *map21 = NULL;
int subset;
+ if (!isl_space_tuple_match(data->list[i]->dim, isl_dim_in,
+ data->list[j]->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)));
+ isl_basic_map_copy(data->list[j]),
+ isl_basic_map_copy(data->list[i])));
subset = isl_map_is_empty(map21);
if (subset < 0)
goto error;
return 0;
}
+ if (!isl_space_tuple_match(data->list[i]->dim, isl_dim_in,
+ data->list[i]->dim, isl_dim_out) ||
+ !isl_space_tuple_match(data->list[j]->dim, isl_dim_in,
+ data->list[j]->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)));
+ isl_basic_map_copy(data->list[i]),
+ isl_basic_map_copy(data->list[j])));
subset = isl_map_is_subset(map21, map12);
isl_map_free(map21);
if (subset)
- *check_closed = 1;
+ data->check_closed = 1;
return subset < 0 ? -1 : !subset;
error:
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_map *map, 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(map->p[i], map->p[j], &s->check_closed);
- if (f < 0)
- return -1;
- if (!f)
- continue;
-
- 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 (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;
-}
-
/* 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
* 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,
+static __isl_give isl_map *construct_power_components(__isl_take isl_space *dim,
__isl_keep isl_map *map, int *exact, int project)
{
int i, n, c;
struct isl_map *path = NULL;
- struct basic_map_sort *s = NULL;
+ struct isl_tc_follows_data data;
+ struct isl_tarjan_graph *g = NULL;
int *orig_exact;
int local_exact;
if (map->n <= 1)
return floyd_warshall(dim, map, exact, project);
- s = basic_map_sort_alloc(map->ctx, map->n);
- if (!s)
+ data.list = map->p;
+ data.check_closed = 0;
+ g = isl_tarjan_graph_init(map->ctx, map->n, &basic_map_follows, &data);
+ if (!g)
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)
+ if (data.check_closed && !exact)
exact = &local_exact;
c = 0;
i = 0;
n = map->n;
if (project)
- path = isl_map_empty(isl_map_get_dim(map));
+ path = isl_map_empty(isl_map_get_space(map));
else
- path = isl_map_empty(isl_dim_copy(dim));
+ path = isl_map_empty(isl_space_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_alloc_space(isl_map_get_space(map), n, 0);
+ while (g->order[i] != -1) {
comp = isl_map_add_basic_map(comp,
- isl_basic_map_copy(map->p[s->order[i]]));
+ isl_basic_map_copy(map->p[g->order[i]]));
--n;
++i;
}
- path_comp = floyd_warshall(isl_dim_copy(dim),
+ path_comp = floyd_warshall(isl_space_copy(dim),
comp, exact, project);
+ path_comp = anonymize(path_comp);
path_comb = isl_map_apply_range(isl_map_copy(path),
isl_map_copy(path_comp));
path = isl_map_union(path, path_comp);
++c;
}
- if (c > 1 && s->check_closed && !*exact) {
+ if (c > 1 && data.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_tarjan_graph_free(g);
isl_map_free(path);
return floyd_warshall(dim, map, orig_exact, project);
}
}
- basic_map_sort_free(s);
- isl_dim_free(dim);
+ isl_tarjan_graph_free(g);
+ isl_space_free(dim);
return path;
error:
- basic_map_sort_free(s);
- isl_dim_free(dim);
+ isl_tarjan_graph_free(g);
+ isl_space_free(dim);
isl_map_free(path);
return NULL;
}
int *exact, int project)
{
struct isl_map *app = NULL;
- struct isl_dim *dim = NULL;
+ isl_space *dim = NULL;
unsigned d;
if (!map)
return NULL;
- dim = isl_map_get_dim(map);
+ dim = isl_map_get_space(map);
- d = isl_dim_size(dim, isl_dim_in);
- dim = isl_dim_add(dim, isl_dim_in, 1);
- dim = isl_dim_add(dim, isl_dim_out, 1);
+ d = isl_space_dim(dim, isl_dim_in);
+ dim = isl_space_add_dims(dim, isl_dim_in, 1);
+ dim = isl_space_add_dims(dim, isl_dim_out, 1);
- app = construct_power_components(isl_dim_copy(dim), map,
+ app = construct_power_components(isl_space_copy(dim), map,
exact, project);
- isl_dim_free(dim);
+ isl_space_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.
+ * The result maps the exponent to a nested copy of the corresponding power.
+ * 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.
+ * In the final step, this difference is equated to an extra parameter
+ * and made positive. The extra coordinates are subsequently projected out
+ * and the parameter is turned into the domain of the result.
*/
-__isl_give isl_map *isl_map_power(__isl_take isl_map *map, unsigned param,
- int *exact)
+__isl_give isl_map *isl_map_power(__isl_take isl_map *map, int *exact)
{
- isl_dim *dim;
+ isl_space *target_dim;
+ isl_space *dim;
isl_map *diff;
unsigned d;
+ unsigned param;
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);
+ 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 (isl_map_plain_is_empty(map)) {
+ map = isl_map_from_range(isl_map_wrap(map));
+ map = isl_map_add_dims(map, isl_dim_in, 1);
+ map = isl_map_set_dim_name(map, isl_dim_in, 0, "k");
return map;
+ }
+
+ target_dim = isl_map_get_space(map);
+ target_dim = isl_space_from_range(isl_space_wrap(target_dim));
+ target_dim = isl_space_add_dims(target_dim, isl_dim_in, 1);
+ target_dim = isl_space_set_dim_name(target_dim, isl_dim_in, 0, "k");
map = map_power(map, exact, 0);
- dim = isl_map_get_dim(map);
+ map = isl_map_add_dims(map, isl_dim_param, 1);
+ dim = isl_map_get_space(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);
+ map = isl_map_from_range(isl_map_wrap(map));
+ map = isl_map_move_dims(map, isl_dim_in, 0, isl_dim_param, param, 1);
+
+ map = isl_map_reset_space(map, target_dim);
+
+ return map;
+}
+
+/* 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_reaching_path_lengths(__isl_take isl_map *map,
+ int *exact)
+{
+ isl_space *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_plain_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_space(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;
-error:
- isl_map_free(map);
- return NULL;
}
/* Check whether equality i of bset is a pure stride constraint
*/
static int is_eq_stride(__isl_keep isl_basic_set *bset, int i)
{
- int k;
unsigned nparam;
unsigned d;
unsigned n_div;
unsigned d;
unsigned nparam;
unsigned total;
- isl_dim *dim;
+ isl_space *dim;
isl_set *delta;
isl_map *app = NULL;
isl_basic_set *aff = NULL;
aff = isl_set_affine_hull(isl_set_copy(delta));
if (!aff)
goto error;
- dim = isl_map_get_dim(map);
- d = isl_dim_size(dim, isl_dim_in);
- nparam = isl_dim_size(dim, isl_dim_param);
- total = isl_dim_total(dim);
- bmap = isl_basic_map_alloc_dim(dim,
+ dim = isl_map_get_space(map);
+ d = isl_space_dim(dim, isl_dim_in);
+ nparam = isl_space_dim(dim, isl_dim_param);
+ total = isl_space_dim(dim, isl_dim_all);
+ bmap = isl_basic_map_alloc_space(dim,
aff->n_div + 1, aff->n_div, 2 * d + 1);
for (i = 0; i < aff->n_div + 1; ++i) {
k = isl_basic_map_alloc_div(bmap);
if (!ok)
continue;
- app = isl_map_alloc_dim(isl_map_get_dim(map), map->n - 1, 0);
+ app = isl_map_alloc_space(isl_map_get_space(map), map->n - 1, 0);
for (j = 0; j < map->n; ++j) {
if (j == i)
__isl_give isl_map *isl_map_transitive_closure(__isl_take isl_map *map,
int *exact)
{
+ isl_space *target_dim;
int closed;
if (!map)
goto error;
- if (map->ctx->opt->closure == ISL_CLOSURE_OMEGA)
+ if (map->ctx->opt->closure == ISL_CLOSURE_BOX)
return transitive_closure_omega(map, exact);
map = isl_map_compute_divs(map);
return map;
}
+ target_dim = isl_map_get_space(map);
map = map_power(map, exact, 1);
+ map = isl_map_reset_space(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(ctx, isl_map *, n_group);
+ if (!grid[i])
+ goto error;
+ for (j = 0; j < n_group; ++j) {
+ isl_space *dim1, *dim2, *dim;
+ dim1 = isl_space_reverse(isl_set_get_space(set[i]));
+ dim2 = isl_set_get_space(set[j]);
+ dim = isl_space_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_space(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 = NULL;
+ 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 = NULL;
+ isl_basic_map **next;
+ isl_union_map *path = NULL;
+ struct isl_tc_follows_data data;
+ struct isl_tarjan_graph *g = 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;
+
+ data.list = list;
+ data.check_closed = 0;
+ g = isl_tarjan_graph_init(ctx, n, &basic_map_follows, &data);
+ if (!g)
+ goto error;
+
+ c = 0;
+ i = 0;
+ l = n;
+ path = isl_union_map_empty(isl_union_map_get_space(umap));
+ while (l) {
+ isl_union_map *comp;
+ isl_union_map *path_comp, *path_comb;
+ comp = isl_union_map_empty(isl_union_map_get_space(umap));
+ while (g->order[i] != -1) {
+ comp = isl_union_map_add_map(comp,
+ isl_map_from_basic_map(
+ isl_basic_map_copy(list[g->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 && data.check_closed && !*exact) {
+ int closed;
+
+ closed = isl_union_map_is_transitively_closed(path);
+ if (closed < 0)
+ goto error;
+ recheck = !closed;
+ }
+
+ isl_tarjan_graph_free(g);
+
+ 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:
+ isl_tarjan_graph_free(g);
+ 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;
+}
+
+struct isl_union_power {
+ isl_union_map *pow;
+ int *exact;
+};
+
+static int power(__isl_take isl_map *map, void *user)
+{
+ struct isl_union_power *up = user;
+
+ map = isl_map_power(map, up->exact);
+ up->pow = isl_union_map_from_map(map);
+
+ return -1;
+}
+
+/* Construct a map [x] -> [x+1], with parameters prescribed by "dim".
+ */
+static __isl_give isl_union_map *increment(__isl_take isl_space *dim)
+{
+ int k;
+ isl_basic_map *bmap;
+
+ dim = isl_space_add_dims(dim, isl_dim_in, 1);
+ dim = isl_space_add_dims(dim, isl_dim_out, 1);
+ bmap = isl_basic_map_alloc_space(dim, 0, 1, 0);
+ k = isl_basic_map_alloc_equality(bmap);
+ if (k < 0)
+ goto error;
+ isl_seq_clr(bmap->eq[k], isl_basic_map_total_dim(bmap));
+ isl_int_set_si(bmap->eq[k][0], 1);
+ isl_int_set_si(bmap->eq[k][isl_basic_map_offset(bmap, isl_dim_in)], 1);
+ isl_int_set_si(bmap->eq[k][isl_basic_map_offset(bmap, isl_dim_out)], -1);
+ return isl_union_map_from_map(isl_map_from_basic_map(bmap));
+error:
+ isl_basic_map_free(bmap);
+ return NULL;
+}
+
+/* Construct a map [[x]->[y]] -> [y-x], with parameters prescribed by "dim".
+ */
+static __isl_give isl_union_map *deltas_map(__isl_take isl_space *dim)
+{
+ isl_basic_map *bmap;
+
+ dim = isl_space_add_dims(dim, isl_dim_in, 1);
+ dim = isl_space_add_dims(dim, isl_dim_out, 1);
+ bmap = isl_basic_map_universe(dim);
+ bmap = isl_basic_map_deltas_map(bmap);
+
+ return isl_union_map_from_map(isl_map_from_basic_map(bmap));
+}
+
+/* Compute the positive powers of "map", or an overapproximation.
+ * The result maps the exponent to a nested copy of the corresponding power.
+ * If the result is exact, then *exact is set to 1.
+ */
+__isl_give isl_union_map *isl_union_map_power(__isl_take isl_union_map *umap,
+ int *exact)
+{
+ int n;
+ isl_union_map *inc;
+ isl_union_map *dm;
+
+ if (!umap)
+ return NULL;
+ n = isl_union_map_n_map(umap);
+ if (n == 0)
+ return umap;
+ if (n == 1) {
+ struct isl_union_power up = { NULL, exact };
+ isl_union_map_foreach_map(umap, &power, &up);
+ isl_union_map_free(umap);
+ return up.pow;
+ }
+ inc = increment(isl_union_map_get_space(umap));
+ umap = isl_union_map_product(inc, umap);
+ umap = isl_union_map_transitive_closure(umap, exact);
+ umap = isl_union_map_zip(umap);
+ dm = deltas_map(isl_union_map_get_space(umap));
+ umap = isl_union_map_apply_domain(umap, dm);
+
+ return umap;
+}
+
+#undef TYPE
+#define TYPE isl_map
+#include "isl_power_templ.c"
+
+#undef TYPE
+#define TYPE isl_union_map
+#include "isl_power_templ.c"
projects / platform / upstream / isl.git / blobdiff