#include "isl_map_private.h"
#include "isl_seq.h"
+/* Given a map that represents a path with the length of the path
+ * encoded as the difference between the last output coordindate
+ * and the last input coordinate, set this length to either
+ * exactly "length" (if "exactly" is set) or at least "length"
+ * (if "exactly" is not set).
+ */
+static __isl_give isl_map *set_path_length(__isl_take isl_map *map,
+ int exactly, int length)
+{
+ struct isl_dim *dim;
+ struct isl_basic_map *bmap;
+ unsigned d;
+ unsigned nparam;
+ int k;
+ isl_int *c;
+
+ 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);
+ if (exactly) {
+ k = isl_basic_map_alloc_equality(bmap);
+ c = bmap->eq[k];
+ } else {
+ k = isl_basic_map_alloc_inequality(bmap);
+ c = bmap->ineq[k];
+ }
+ if (k < 0)
+ goto error;
+ isl_seq_clr(c, 1 + isl_basic_map_total_dim(bmap));
+ isl_int_set_si(c[0], -length);
+ isl_int_set_si(c[1 + nparam + d - 1], -1);
+ isl_int_set_si(c[1 + nparam + d + d - 1], 1);
+
+ bmap = isl_basic_map_finalize(bmap);
+ map = isl_map_intersect(map, isl_map_from_basic_map(bmap));
+
+ return map;
+error:
+ isl_basic_map_free(bmap);
+ isl_map_free(map);
+ return NULL;
+}
+
+/* Check whether the overapproximation of the power of "map" is exactly
+ * the power of "map". Let R be "map" and A_k the overapproximation.
+ * The approximation is exact if
+ *
+ * A_1 = R
+ * A_k = A_{k-1} \circ R k >= 2
+ *
+ * Since A_k is known to be an overapproximation, we only need to check
+ *
+ * A_1 \subset R
+ * A_k \subset A_{k-1} \circ R k >= 2
+ *
+ * In practice, "app" has an extra input and output coordinate
+ * to encode the length of the path. So, we first need to add
+ * this coordinate to "map" and set the length of the path to
+ * one.
+ */
+static int check_power_exactness(__isl_take isl_map *map,
+ __isl_take isl_map *app)
+{
+ int exact;
+ 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 = set_path_length(map, 1, 1);
+
+ app_1 = set_path_length(isl_map_copy(app), 1, 1);
+
+ exact = isl_map_is_subset(app_1, map);
+ isl_map_free(app_1);
+
+ if (!exact || exact < 0) {
+ isl_map_free(app);
+ isl_map_free(map);
+ return exact;
+ }
+
+ app_1 = set_path_length(isl_map_copy(app), 0, 1);
+ app_2 = set_path_length(app, 0, 2);
+ app_1 = isl_map_apply_range(map, app_1);
+
+ exact = isl_map_is_subset(app_2, app_1);
+
+ isl_map_free(app_1);
+ isl_map_free(app_2);
+
+ return exact;
+}
+
+/* Check whether the overapproximation of the power of "map" is exactly
+ * the power of "map", possibly after projecting out the power (if "project"
+ * is set).
+ *
+ * If "project" is set and if "steps" can only result in acyclic paths,
+ * then we check
+ *
+ * A = R \cup (A \circ R)
+ *
+ * where A is the overapproximation with the power projected out, i.e.,
+ * an overapproximation of the transitive closure.
+ * More specifically, since A is known to be an overapproximation, we check
+ *
+ * A \subset R \cup (A \circ R)
+ *
+ * Otherwise, we check if the power is exact.
+ *
+ * Note that "app" has an extra input and output coordinate to encode
+ * the length of the part. If we are only interested in the transitive
+ * closure, then we can simply project out these coordinates first.
+ */
+static int check_exactness(__isl_take isl_map *map, __isl_take isl_map *app,
+ int project)
+{
+ isl_map *test;
+ int exact;
+ unsigned d;
+
+ if (!project)
+ return check_power_exactness(map, app);
+
+ d = isl_map_dim(map, isl_dim_in);
+ app = set_path_length(app, 0, 1);
+ app = isl_map_project_out(app, isl_dim_in, d, 1);
+ app = isl_map_project_out(app, isl_dim_out, d, 1);
+
+ test = isl_map_apply_range(isl_map_copy(map), isl_map_copy(app));
+ test = isl_map_union(test, isl_map_copy(map));
+
+ exact = isl_map_is_subset(app, test);
+
+ isl_map_free(app);
+ isl_map_free(test);
+
+ isl_map_free(map);
+
+ return exact;
+error:
+ isl_map_free(app);
+ isl_map_free(map);
+ return -1;
+}
+
/*
* The transitive closure implementation is based on the paper
* "Computing the Transitive Closure of a Union of Affine Integer
#define IMPURE 0
#define PURE_PARAM 1
#define PURE_VAR 2
+#define MIXED 3
/* 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
+ * variables are non-zero and if moreover the parametric constant
+ * can never attain positive values.
* Return IMPURE otherwise.
*/
-static int purity(__isl_keep isl_basic_set *bset, isl_int *c)
+static int purity(__isl_keep isl_basic_set *bset, isl_int *c, int eq)
{
unsigned d;
unsigned n_div;
unsigned nparam;
+ int k;
+ int empty;
n_div = isl_basic_set_dim(bset, isl_dim_div);
d = isl_basic_set_dim(bset, isl_dim_set);
return PURE_VAR;
if (isl_seq_first_non_zero(c + 1 + nparam, d) == -1)
return PURE_PARAM;
- return IMPURE;
+ 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);
+ 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;
}
/* Given a set of offsets "delta", construct a relation of the
* In particular, let delta be defined as
*
* \delta = [p] -> { [x] : A x + a >= and B p + b >= 0 and
- * C x + C'p + c >= 0 }
+ * C x + C'p + c >= 0 and
+ * D x + D'p + d >= 0 }
*
- * then the relation is constructed as
+ * where the constraints C x + C'p + c >= 0 are such that the parametric
+ * constant term of each constraint j, "C_j x + C'_j p + c_j",
+ * can never attain positive values, then the relation is constructed as
*
* { [x] -> [y] : exists [f, k] \in Z^{n+1} : y = x + f and
- * A f + k a >= 0 and B p + b >= 0 and k >= 1 }
+ * A f + k a >= 0 and B p + b >= 0 and
+ * C f + C'p + c >= 0 and k >= 1 }
* union { [x] -> [x] }
*
* Existentially quantified variables in \delta are currently ignored.
}
for (i = 0; i < delta->n_eq; ++i) {
- int p = purity(delta, delta->eq[i]);
+ int p = purity(delta, delta->eq[i], 1);
+ if (p < 0)
+ goto error;
if (p == IMPURE)
continue;
k = isl_basic_map_alloc_equality(path);
}
for (i = 0; i < delta->n_ineq; ++i) {
- int p = purity(delta, delta->ineq[i]);
+ int p = purity(delta, delta->ineq[i], 0);
+ if (p < 0)
+ goto error;
if (p == IMPURE)
continue;
k = isl_basic_map_alloc_inequality(path);
isl_seq_cpy(path->ineq[k] + off,
delta->ineq[i] + 1 + nparam, d);
isl_int_set(path->ineq[k][off + d], delta->ineq[i][0]);
- } else
+ } else if (p == PURE_PARAM) {
isl_seq_cpy(path->ineq[k], delta->ineq[i], 1 + nparam);
+ } else {
+ isl_seq_cpy(path->ineq[k] + off,
+ delta->ineq[i] + 1 + nparam, d);
+ isl_seq_cpy(path->ineq[k], delta->ineq[i], 1 + nparam);
+ }
}
k = isl_basic_map_alloc_inequality(path);
if (j < d) {
path = isl_map_apply_range(path,
path_along_delta(isl_dim_copy(dim), delta));
+ path = isl_map_coalesce(path);
} else {
isl_basic_set_free(delta);
++n;
/* 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
+ * construct a map that is the union of the identity map and
+ * 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}
+ * x in dom R and x + d in ran R } union
+ * { (x) -> (x) }
*/
-static __isl_give isl_map *construct_extended_power(__isl_take isl_dim *dim,
- __isl_keep isl_map *map, int *project)
+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) {
+ 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 = set_path_length(map, 1, 1);
+ 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);
- path = construct_extended_path(dim, map, project);
+ path = construct_extended_path(isl_dim_copy(dim), map,
+ exact && *exact ? &project : NULL);
app = isl_map_intersect(app, path);
- return app;
+ if (exact && *exact &&
+ (*exact = check_exactness(isl_map_copy(map), isl_map_copy(app),
+ project)) < 0)
+ goto error;
+
+ return isl_map_union(app, isl_map_identity(isl_dim_domain(dim)));
+error:
+ isl_dim_free(dim);
+ isl_map_free(app);
+ return NULL;
}
-/* Given a union of basic maps R = \cup_i R_i \subseteq D \times D,
- * construct a map that is an overapproximation of the map
- * that takes an element from the space D to another
- * element from the same space, such that the difference between
- * them is a strictly positive sum of differences between images
- * and pre-images in one of the R_i.
- * The number of differences in the sum is equated to parameter "param".
- * That is, let
+/* 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
+ */
+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)
+{
+ 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;
+
+ 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).
*
- * \Delta_i = { y - x | (x, y) in R_i }
+ * That is check whether
*
- * then the constructed map is an overapproximation of
+ * R_1 \circ R_2
*
- * { (x) -> (x + d) | \exists k_i >= 0, \delta_i \in \Delta_i :
- * d = \sum_i k_i \delta_i and k = \sum_i k_i > 0 }
+ * is a subset of
*
- * We first 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. The extra coordinates are subsequently projected out.
+ * R_2 \circ R_1
+ *
+ * If so, then there is no reason for R_1 to immediately follow R_2
+ * in any path.
*/
-static __isl_give isl_map *construct_power(__isl_keep isl_map *map,
- unsigned param, int *project)
+static int basic_map_follows(__isl_keep isl_basic_map *bmap1,
+ __isl_keep isl_basic_map *bmap2)
{
- struct isl_map *app = NULL;
- struct isl_map *diff;
- struct isl_dim *dim = NULL;
- unsigned d;
+ struct isl_map *map12 = NULL;
+ struct isl_map *map21 = NULL;
+ int subset;
+
+ 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 (!map)
- return NULL;
+ map12 = isl_map_from_basic_map(
+ isl_basic_map_apply_range(
+ isl_basic_map_copy(bmap1),
+ isl_basic_map_copy(bmap2)));
- dim = isl_map_get_dim(map);
+ subset = isl_map_is_subset(map21, map12);
- 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);
-
- app = construct_extended_power(isl_dim_copy(dim), map, project);
+ isl_map_free(map12);
+ isl_map_free(map21);
- 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);
-
- return app;
+ return subset < 0 ? -1 : !subset;
+error:
+ isl_map_free(map21);
+ return -1;
}
-/* Shift variable at position "pos" up by one.
- * That is, replace the corresponding variable v by v - 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 __isl_give isl_basic_map *basic_map_shift_pos(
- __isl_take isl_basic_map *bmap, unsigned pos)
+static int power_components_tarjan(struct basic_map_sort *s,
+ __isl_keep isl_map *map, int i)
{
- int i;
+ int j;
- bmap = isl_basic_map_cow(bmap);
- if (!bmap)
- return NULL;
+ 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 (i = 0; i < bmap->n_eq; ++i)
- isl_int_sub(bmap->eq[i][0], bmap->eq[i][0], bmap->eq[i][pos]);
+ for (j = s->len - 1; j >= 0; --j) {
+ int f;
- for (i = 0; i < bmap->n_ineq; ++i)
- isl_int_sub(bmap->ineq[i][0],
- bmap->ineq[i][0], bmap->ineq[i][pos]);
+ 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;
- for (i = 0; i < bmap->n_div; ++i) {
- if (isl_int_is_zero(bmap->div[i][0]))
+ f = basic_map_follows(map->p[i], map->p[j]);
+ if (f < 0)
+ return -1;
+ if (!f)
continue;
- isl_int_sub(bmap->div[i][1],
- bmap->div[i][1], bmap->div[i][1 + pos]);
+
+ 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;
}
- return bmap;
-}
+ if (s->node[i].index != s->node[i].min_index)
+ return 0;
-/* Shift variable at position "pos" up by one.
- * That is, replace the corresponding variable v by v - 1.
- */
-static __isl_give isl_map *map_shift_pos(__isl_take isl_map *map, unsigned pos)
-{
- int i;
+ 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;
- map = isl_map_cow(map);
- if (!map)
- return NULL;
-
- for (i = 0; i < map->n; ++i) {
- map->p[i] = basic_map_shift_pos(map->p[i], pos);
- if (!map->p[i])
- goto error;
- }
- ISL_F_CLR(map, ISL_MAP_NORMALIZED);
- return map;
-error:
- isl_map_free(map);
- return NULL;
+ return 0;
}
-/* Check whether the overapproximation of the power of "map" is exactly
- * the power of "map". Let R be "map" and A_k the overapproximation.
- * The approximation is exact if
+/* 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
+ * 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.
+ * That is, let
*
- * A_1 = R
- * A_k = A_{k-1} \circ R k >= 2
+ * \Delta_i = { y - x | (x, y) in R_i }
*
- * Since A_k is known to be an overapproximation, we only need to check
+ * then the constructed map is an overapproximation of
*
- * A_1 \subset R
- * A_k \subset A_{k-1} \circ R k >= 2
+ * { (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) }
*
+ * 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.
*/
-static int check_power_exactness(__isl_take isl_map *map,
- __isl_take isl_map *app, unsigned param)
+static __isl_give isl_map *construct_power_components(__isl_take isl_dim *dim,
+ __isl_keep isl_map *map, int *exact, int project)
{
- int exact;
- isl_map *app_1;
- isl_map *app_2;
-
- app_1 = isl_map_fix_si(isl_map_copy(app), isl_dim_param, param, 1);
+ int i, n;
+ struct isl_map *path = NULL;
+ struct basic_map_sort *s = NULL;
- exact = isl_map_is_subset(app_1, map);
- isl_map_free(app_1);
+ if (!map)
+ goto error;
+ if (map->n <= 1)
+ return construct_component(dim, map, exact, project);
- if (!exact || exact < 0) {
- isl_map_free(app);
- isl_map_free(map);
- return exact;
+ s = basic_map_sort_alloc(map->ctx, map->n);
+ 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;
}
- app_2 = isl_map_lower_bound_si(isl_map_copy(app),
- isl_dim_param, param, 2);
- app_1 = map_shift_pos(app, 1 + param);
- app_1 = isl_map_apply_range(map, app_1);
-
- exact = isl_map_is_subset(app_2, app_1);
+ i = 0;
+ n = map->n;
+ path = isl_map_identity(isl_dim_domain(isl_dim_copy(dim)));
+ while (n) {
+ struct isl_map *comp;
+ comp = isl_map_alloc_dim(isl_map_get_dim(map), n, 0);
+ while (s->order[i] != -1) {
+ comp = isl_map_add_basic_map(comp,
+ isl_basic_map_copy(map->p[s->order[i]]));
+ --n;
+ ++i;
+ }
+ path = isl_map_apply_range(path,
+ construct_component(isl_dim_copy(dim), comp,
+ exact, project));
+ isl_map_free(comp);
+ ++i;
+ }
- isl_map_free(app_1);
- isl_map_free(app_2);
+ basic_map_sort_free(s);
+ isl_dim_free(dim);
- return exact;
+ return path;
+error:
+ basic_map_sort_free(s);
+ isl_dim_free(dim);
+ return NULL;
}
-/* Check whether the overapproximation of the power of "map" is exactly
- * the power of "map", possibly after projecting out the power (if "project"
- * is set).
- *
- * If "project" is set and if "steps" can only result in acyclic paths,
- * then we check
+/* Given a union of basic maps R = \cup_i R_i \subseteq D \times D,
+ * construct a map that is an overapproximation of the map
+ * that takes an element from the space D to another
+ * element from the same space, such that the difference between
+ * them is a strictly positive sum of differences between images
+ * and pre-images in one of the R_i.
+ * The number of differences in the sum is equated to parameter "param".
+ * That is, let
*
- * A = R \cup (A \circ R)
+ * \Delta_i = { y - x | (x, y) in R_i }
*
- * where A is the overapproximation with the power projected out, i.e.,
- * an overapproximation of the transitive closure.
- * More specifically, since A is known to be an overapproximation, we check
+ * then the constructed map is an overapproximation of
*
- * A \subset R \cup (A \circ R)
+ * { (x) -> (x + d) | \exists k_i >= 0, \delta_i \in \Delta_i :
+ * d = \sum_i k_i \delta_i and k = \sum_i k_i > 0 }
*
- * Otherwise, we check if the power is exact.
+ * We first 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. The extra coordinates are subsequently projected out.
*/
-static int check_exactness(__isl_take isl_map *map, __isl_take isl_map *app,
- unsigned param, int project)
+static __isl_give isl_map *construct_power(__isl_keep isl_map *map,
+ unsigned param, int *exact, int project)
{
- isl_map *test;
- int exact;
-
- if (!project)
- return check_power_exactness(map, app, param);
+ struct isl_map *app = NULL;
+ struct isl_map *diff;
+ struct isl_dim *dim = NULL;
+ unsigned d;
- map = isl_map_project_out(map, isl_dim_param, param, 1);
- app = isl_map_project_out(app, isl_dim_param, param, 1);
+ if (!map)
+ return NULL;
- test = isl_map_apply_range(isl_map_copy(map), isl_map_copy(app));
- test = isl_map_union(test, isl_map_copy(map));
+ dim = isl_map_get_dim(map);
- exact = isl_map_is_subset(app, test);
+ 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);
- isl_map_free(app);
- isl_map_free(test);
+ app = construct_power_components(isl_dim_copy(dim), map,
+ exact, project);
- isl_map_free(map);
+ 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);
- return exact;
-error:
- isl_map_free(app);
- isl_map_free(map);
- return -1;
+ return app;
}
/* Compute the positive powers of "map", or an overapproximation.
isl_map_dim(map, isl_dim_in) == isl_map_dim(map, isl_dim_out),
goto error);
- app = construct_power(map, param, exact ? &project : NULL);
-
- if (exact &&
- (*exact = check_exactness(isl_map_copy(map), isl_map_copy(app),
- param, project)) < 0)
- goto error;
+ app = construct_power(map, param, exact, project);
isl_map_free(map);
return app;
projects / platform / upstream / isl.git / blobdiff