+/*
+ * Copyright 2008-2009 Katholieke Universiteit Leuven
+ * Copyright 2010 INRIA Saclay
+ *
+ * Use of this software is governed by the GNU LGPLv2.1 license
+ *
+ * Written by Sven Verdoolaege, K.U.Leuven, Departement
+ * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
+ * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
+ * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France
+ */
+
#include "isl_map_private.h"
#include "isl_seq.h"
#include "isl_tab.h"
map->n--;
}
-/* Replace the pair of basic maps i and j but the basic map bounded
- * by the valid constraints in both basic maps.
+/* Replace the pair of basic maps i and j by the basic map bounded
+ * by the valid constraints in both basic maps and the constraint
+ * in extra (if not NULL).
*/
-static int fuse(struct isl_map *map, int i, int j, struct isl_tab **tabs,
- int *ineq_i, int *ineq_j)
+static int fuse(struct isl_map *map, int i, int j,
+ struct isl_tab **tabs, int *eq_i, int *ineq_i, int *eq_j, int *ineq_j,
+ __isl_keep isl_mat *extra)
{
int k, l;
struct isl_basic_map *fused = NULL;
struct isl_tab *fused_tab = NULL;
unsigned total = isl_basic_map_total_dim(map->p[i]);
+ unsigned extra_rows = extra ? extra->n_row : 0;
fused = isl_basic_map_alloc_dim(isl_dim_copy(map->p[i]->dim),
map->p[i]->n_div,
map->p[i]->n_eq + map->p[j]->n_eq,
- map->p[i]->n_ineq + map->p[j]->n_ineq);
+ map->p[i]->n_ineq + map->p[j]->n_ineq + extra_rows);
if (!fused)
goto error;
for (k = 0; k < map->p[i]->n_eq; ++k) {
- int l = isl_basic_map_alloc_equality(fused);
+ if (eq_i && (eq_i[2 * k] != STATUS_VALID ||
+ eq_i[2 * k + 1] != STATUS_VALID))
+ continue;
+ l = isl_basic_map_alloc_equality(fused);
+ if (l < 0)
+ goto error;
isl_seq_cpy(fused->eq[l], map->p[i]->eq[k], 1 + total);
}
for (k = 0; k < map->p[j]->n_eq; ++k) {
- int l = isl_basic_map_alloc_equality(fused);
+ if (eq_j && (eq_j[2 * k] != STATUS_VALID ||
+ eq_j[2 * k + 1] != STATUS_VALID))
+ continue;
+ l = isl_basic_map_alloc_equality(fused);
+ if (l < 0)
+ goto error;
isl_seq_cpy(fused->eq[l], map->p[j]->eq[k], 1 + total);
}
if (ineq_i[k] != STATUS_VALID)
continue;
l = isl_basic_map_alloc_inequality(fused);
+ if (l < 0)
+ goto error;
isl_seq_cpy(fused->ineq[l], map->p[i]->ineq[k], 1 + total);
}
if (ineq_j[k] != STATUS_VALID)
continue;
l = isl_basic_map_alloc_inequality(fused);
+ if (l < 0)
+ goto error;
isl_seq_cpy(fused->ineq[l], map->p[j]->ineq[k], 1 + total);
}
for (k = 0; k < map->p[i]->n_div; ++k) {
int l = isl_basic_map_alloc_div(fused);
+ if (l < 0)
+ goto error;
isl_seq_cpy(fused->div[l], map->p[i]->div[k], 1 + 1 + total);
}
+ for (k = 0; k < extra_rows; ++k) {
+ l = isl_basic_map_alloc_inequality(fused);
+ if (l < 0)
+ goto error;
+ isl_seq_cpy(fused->ineq[l], extra->row[k], 1 + total);
+ }
+
fused = isl_basic_map_gauss(fused, NULL);
ISL_F_SET(fused, ISL_BASIC_MAP_FINAL);
if (ISL_F_ISSET(map->p[i], ISL_BASIC_MAP_RATIONAL) &&
if (k < map->p[i]->n_ineq)
/* BAD CUT PAIR */
return 0;
- return fuse(map, i, j, tabs, ineq_i, ineq_j);
+ return fuse(map, i, j, tabs, NULL, ineq_i, NULL, ineq_j, NULL);
}
/* Both basic maps have at least one inequality with and adjacent
;
else if (count(ineq_i, map->p[i]->n_ineq, STATUS_ADJ_INEQ) == 1 &&
count(ineq_j, map->p[j]->n_ineq, STATUS_ADJ_INEQ) == 1)
- changed = fuse(map, i, j, tabs, ineq_i, ineq_j);
+ changed = fuse(map, i, j, tabs, NULL, ineq_i, NULL, ineq_j, NULL);
/* else ADJ INEQ TOO MANY */
return changed;
return 1;
}
-/* At least one of the basic maps has an equality that is adjacent
- * to inequality. Make sure that only one of the basic maps has
- * such an equality and that the other basic map has exactly one
- * inequality adjacent to an equality.
- * We call the basic map that has the inequality "i" and the basic
- * map that has the equality "j".
- * If "i" has any "cut" inequality, then relaxing the inequality
- * by one would not result in a basic map that contains the other
- * basic map.
- * Otherwise, we relax the constraint, compute the corresponding
+/* Basic map "i" has an inequality "k" that is adjacent to some equality
+ * of basic map "j". All the other inequalities are valid for "j".
+ * Check if basic map "j" forms an extension of basic map "i".
+ *
+ * In particular, we relax constraint "k", compute the corresponding
* facet and check whether it is included in the other basic map.
- * If so, we know that relaxing the constraint extend the basic
+ * If so, we know that relaxing the constraint extends the basic
* map with exactly the other basic map (we already know that this
* other basic map is included in the extension, because there
* were no "cut" inequalities in "i") and we can replace the
* \ || \ |
* \___|| \____|
*/
-static int check_adj_eq(struct isl_map *map, int i, int j,
+static int is_extension(struct isl_map *map, int i, int j, int k,
struct isl_tab **tabs, int *eq_i, int *ineq_i, int *eq_j, int *ineq_j)
{
int changed = 0;
int super;
- int k;
struct isl_tab_undo *snap, *snap2;
unsigned n_eq = map->p[i]->n_eq;
+ snap = isl_tab_snap(tabs[i]);
+ tabs[i] = isl_tab_relax(tabs[i], n_eq + k);
+ snap2 = isl_tab_snap(tabs[i]);
+ tabs[i] = isl_tab_select_facet(tabs[i], n_eq + k);
+ super = contains(map, j, ineq_j, tabs[i]);
+ if (super) {
+ if (isl_tab_rollback(tabs[i], snap2) < 0)
+ return -1;
+ map->p[i] = isl_basic_map_cow(map->p[i]);
+ if (!map->p[i])
+ return -1;
+ isl_int_add_ui(map->p[i]->ineq[k][0], map->p[i]->ineq[k][0], 1);
+ ISL_F_SET(map->p[i], ISL_BASIC_MAP_FINAL);
+ drop(map, j, tabs);
+ changed = 1;
+ } else
+ if (isl_tab_rollback(tabs[i], snap) < 0)
+ return -1;
+
+ return changed;
+}
+
+/* For each non-redundant constraint in "bmap" (as determined by "tab"),
+ * wrap the constraint around "bound" such that it includes the whole
+ * set "set" and append the resulting constraint to "wraps".
+ * "wraps" is assumed to have been pre-allocated to the appropriate size.
+ * wraps->n_row is the number of actual wrapped constraints that have
+ * been added.
+ * If any of the wrapping problems results in a constraint that is
+ * identical to "bound", then this means that "set" is unbounded in such
+ * way that no wrapping is possible. If this happens then wraps->n_row
+ * is reset to zero.
+ */
+static int add_wraps(__isl_keep isl_mat *wraps, __isl_keep isl_basic_map *bmap,
+ struct isl_tab *tab, isl_int *bound, __isl_keep isl_set *set)
+{
+ int l;
+ int w;
+ unsigned total = isl_basic_map_total_dim(bmap);
+
+ w = wraps->n_row;
+
+ for (l = 0; l < bmap->n_ineq; ++l) {
+ if (isl_seq_is_neg(bound, bmap->ineq[l], 1 + total))
+ continue;
+ if (isl_seq_eq(bound, bmap->ineq[l], 1 + total))
+ continue;
+ if (isl_tab_is_redundant(tab, bmap->n_eq + l))
+ continue;
+
+ isl_seq_cpy(wraps->row[w], bound, 1 + total);
+ if (!isl_set_wrap_facet(set, wraps->row[w], bmap->ineq[l]))
+ return -1;
+ if (isl_seq_eq(wraps->row[w], bound, 1 + total))
+ goto unbounded;
+ ++w;
+ }
+ for (l = 0; l < bmap->n_eq; ++l) {
+ if (isl_seq_is_neg(bound, bmap->eq[l], 1 + total))
+ continue;
+ if (isl_seq_eq(bound, bmap->eq[l], 1 + total))
+ continue;
+
+ isl_seq_cpy(wraps->row[w], bound, 1 + total);
+ isl_seq_neg(wraps->row[w + 1], bmap->eq[l], 1 + total);
+ if (!isl_set_wrap_facet(set, wraps->row[w], wraps->row[w + 1]))
+ return -1;
+ if (isl_seq_eq(wraps->row[w], bound, 1 + total))
+ goto unbounded;
+ ++w;
+
+ isl_seq_cpy(wraps->row[w], bound, 1 + total);
+ if (!isl_set_wrap_facet(set, wraps->row[w], bmap->eq[l]))
+ return -1;
+ if (isl_seq_eq(wraps->row[w], bound, 1 + total))
+ goto unbounded;
+ ++w;
+ }
+
+ wraps->n_row = w;
+ return 0;
+unbounded:
+ wraps->n_row = 0;
+ return 0;
+}
+
+/* Given a basic set i with a constraint k that is adjacent to either the
+ * whole of basic set j or a facet of basic set j, check if we can wrap
+ * both the facet corresponding to k and the facet of j (or the whole of j)
+ * around their ridges to include the other set.
+ * If so, replace the pair of basic sets by their union.
+ *
+ * All constraints of i (except k) are assumed to be valid for j.
+ *
+ * In the case where j has a facet adjacent to i, tab[j] is assumed
+ * to have been restricted to this facet, so that the non-redundant
+ * constraints in tab[j] are the ridges of the facet.
+ * Note that for the purpose of wrapping, it does not matter whether
+ * we wrap the ridges of i around the whole of j or just around
+ * the facet since all the other constraints are assumed to be valid for j.
+ * In practice, we wrap to include the whole of j.
+ * ____ _____
+ * / | / \
+ * / || / |
+ * \ || => \ |
+ * \ || \ |
+ * \___|| \____|
+ *
+ */
+static int can_wrap_in_facet(struct isl_map *map, int i, int j, int k,
+ struct isl_tab **tabs, int *eq_i, int *ineq_i, int *eq_j, int *ineq_j)
+{
+ int changed = 0;
+ struct isl_mat *wraps = NULL;
+ struct isl_set *set_i = NULL;
+ struct isl_set *set_j = NULL;
+ struct isl_vec *bound = NULL;
+ unsigned total = isl_basic_map_total_dim(map->p[i]);
+ struct isl_tab_undo *snap;
+
+ snap = isl_tab_snap(tabs[i]);
+
+ set_i = isl_set_from_basic_set(
+ isl_basic_map_underlying_set(isl_basic_map_copy(map->p[i])));
+ set_j = isl_set_from_basic_set(
+ isl_basic_map_underlying_set(isl_basic_map_copy(map->p[j])));
+ wraps = isl_mat_alloc(map->ctx, 2 * (map->p[i]->n_eq + map->p[j]->n_eq) +
+ map->p[i]->n_ineq + map->p[j]->n_ineq,
+ 1 + total);
+ bound = isl_vec_alloc(map->ctx, 1 + total);
+ if (!set_i || !set_j || !wraps || !bound)
+ goto error;
+
+ isl_seq_cpy(bound->el, map->p[i]->ineq[k], 1 + total);
+ isl_int_add_ui(bound->el[0], bound->el[0], 1);
+
+ isl_seq_cpy(wraps->row[0], bound->el, 1 + total);
+ wraps->n_row = 1;
+
+ if (add_wraps(wraps, map->p[j], tabs[j], bound->el, set_i) < 0)
+ goto error;
+ if (!wraps->n_row)
+ goto unbounded;
+
+ tabs[i] = isl_tab_select_facet(tabs[i], map->p[i]->n_eq + k);
+ if (isl_tab_detect_redundant(tabs[i]) < 0)
+ goto error;
+
+ isl_seq_neg(bound->el, map->p[i]->ineq[k], 1 + total);
+
+ if (add_wraps(wraps, map->p[i], tabs[i], bound->el, set_j) < 0)
+ goto error;
+ if (!wraps->n_row)
+ goto unbounded;
+
+ changed = fuse(map, i, j, tabs, eq_i, ineq_i, eq_j, ineq_j, wraps);
+
+ if (!changed) {
+unbounded:
+ if (isl_tab_rollback(tabs[i], snap) < 0)
+ goto error;
+ }
+
+ isl_mat_free(wraps);
+
+ isl_set_free(set_i);
+ isl_set_free(set_j);
+
+ isl_vec_free(bound);
+
+ return changed;
+error:
+ isl_vec_free(bound);
+ isl_mat_free(wraps);
+ isl_set_free(set_i);
+ isl_set_free(set_j);
+ return -1;
+}
+
+/* Given two basic sets i and j such that i has exactly one cut constraint,
+ * check if we can wrap the corresponding facet around its ridges to include
+ * the other basic set (and nothing else).
+ * If so, replace the pair by their union.
+ *
+ * We first check if j has a facet adjacent to the cut constraint of i.
+ * If so, we try to wrap in the facet.
+ * ____ _____
+ * / ___|_ / \
+ * / | | / |
+ * \ | | => \ |
+ * \|____| \ |
+ * \___| \____/
+ */
+static int can_wrap_in_set(struct isl_map *map, int i, int j,
+ struct isl_tab **tabs, int *ineq_i, int *ineq_j)
+{
+ int changed = 0;
+ int k, l;
+ unsigned total = isl_basic_map_total_dim(map->p[i]);
+ struct isl_tab_undo *snap;
+
+ for (k = 0; k < map->p[i]->n_ineq; ++k)
+ if (ineq_i[k] == STATUS_CUT)
+ break;
+
+ isl_assert(map->ctx, k < map->p[i]->n_ineq, return -1);
+
+ isl_int_add_ui(map->p[i]->ineq[k][0], map->p[i]->ineq[k][0], 1);
+ for (l = 0; l < map->p[j]->n_ineq; ++l) {
+ if (isl_tab_is_redundant(tabs[j], map->p[j]->n_eq + l))
+ continue;
+ if (isl_seq_eq(map->p[i]->ineq[k],
+ map->p[j]->ineq[l], 1 + total))
+ break;
+ }
+ isl_int_sub_ui(map->p[i]->ineq[k][0], map->p[i]->ineq[k][0], 1);
+
+ if (l >= map->p[j]->n_ineq)
+ return 0;
+
+ snap = isl_tab_snap(tabs[j]);
+ tabs[j] = isl_tab_select_facet(tabs[j], map->p[j]->n_eq + l);
+ if (isl_tab_detect_redundant(tabs[j]) < 0)
+ return -1;
+
+ changed = can_wrap_in_facet(map, i, j, k, tabs, NULL, ineq_i, NULL, ineq_j);
+
+ if (!changed && isl_tab_rollback(tabs[j], snap) < 0)
+ return -1;
+
+ return changed;
+}
+
+/* Check if either i or j has a single cut constraint that can
+ * be used to wrap in (a facet of) the other basic set.
+ * if so, replace the pair by their union.
+ */
+static int check_wrap(struct isl_map *map, int i, int j,
+ struct isl_tab **tabs, int *ineq_i, int *ineq_j)
+{
+ int changed = 0;
+
+ if (count(ineq_i, map->p[i]->n_ineq, STATUS_CUT) == 1)
+ changed = can_wrap_in_set(map, i, j, tabs, ineq_i, ineq_j);
+ if (changed)
+ return changed;
+
+ if (count(ineq_j, map->p[j]->n_ineq, STATUS_CUT) == 1)
+ changed = can_wrap_in_set(map, j, i, tabs, ineq_j, ineq_i);
+ return changed;
+}
+
+/* At least one of the basic maps has an equality that is adjacent
+ * to inequality. Make sure that only one of the basic maps has
+ * such an equality and that the other basic map has exactly one
+ * inequality adjacent to an equality.
+ * We call the basic map that has the inequality "i" and the basic
+ * map that has the equality "j".
+ * If "i" has any "cut" inequality, then relaxing the inequality
+ * by one would not result in a basic map that contains the other
+ * basic map.
+ */
+static int check_adj_eq(struct isl_map *map, int i, int j,
+ struct isl_tab **tabs, int *eq_i, int *ineq_i, int *eq_j, int *ineq_j)
+{
+ int changed = 0;
+ int k;
+
if (any(eq_i, 2 * map->p[i]->n_eq, STATUS_ADJ_INEQ) &&
any(eq_j, 2 * map->p[j]->n_eq, STATUS_ADJ_INEQ))
/* ADJ EQ TOO MANY */
if (ineq_i[k] == STATUS_ADJ_EQ)
break;
- snap = isl_tab_snap(tabs[i]);
- tabs[i] = isl_tab_relax(tabs[i], n_eq + k);
- snap2 = isl_tab_snap(tabs[i]);
- tabs[i] = isl_tab_select_facet(tabs[i], n_eq + k);
- super = contains(map, j, ineq_j, tabs[i]);
- if (super) {
- if (isl_tab_rollback(tabs[i], snap2) < 0)
- return -1;
- map->p[i] = isl_basic_map_cow(map->p[i]);
- if (!map->p[i])
- return -1;
- isl_int_add_ui(map->p[i]->ineq[k][0], map->p[i]->ineq[k][0], 1);
- ISL_F_SET(map->p[i], ISL_BASIC_MAP_FINAL);
- drop(map, j, tabs);
- changed = 1;
- } else
- if (isl_tab_rollback(tabs[i], snap) < 0)
- return -1;
+ changed = is_extension(map, i, j, k, tabs, eq_i, ineq_i, eq_j, ineq_j);
+ if (changed)
+ return changed;
+
+ changed = can_wrap_in_facet(map, i, j, k, tabs, eq_i, ineq_i, eq_j, ineq_j);
return changed;
}
* adj_ineq the given constraint is adjacent (on the outside)
* to an inequality of the other basic map
*
- * We consider four cases in which we can replace the pair by a single
+ * We consider six cases in which we can replace the pair by a single
* basic map. We ignore all "redundant" constraints.
*
* 1. all constraints of one basic map are valid
* => the pair can be replaced by the basic map containing
* the inequality, with the inequality relaxed.
*
+ * 5. there is a single adjacent pair of an inequality and an equality,
+ * the other constraints of the basic map containing the inequality are
+ * "valid". Moreover, the facets corresponding to both
+ * the inequality and the equality can be wrapped around their
+ * ridges to include the other basic map
+ * => the pair can be replaced by a basic map consisting
+ * of the valid constraints in both basic maps together
+ * with all wrapping constraints
+ *
+ * 6. one of the basic maps has a single cut constraint and
+ * the other basic map has a constraint adjacent to this constraint.
+ * Moreover, the facets corresponding to both constraints
+ * can be wrapped around their ridges to include the other basic map
+ * => the pair can be replaced by a basic map consisting
+ * of the valid constraints in both basic maps together
+ * with all wrapping constraints
+ *
* Throughout the computation, we maintain a collection of tableaus
* corresponding to the basic maps. When the basic maps are dropped
* or combined, the tableaus are modified accordingly.
} else if (any(ineq_i, map->p[i]->n_ineq, STATUS_ADJ_INEQ) ||
any(ineq_j, map->p[j]->n_ineq, STATUS_ADJ_INEQ)) {
changed = check_adj_ineq(map, i, j, tabs, ineq_i, ineq_j);
- } else
+ } else {
changed = check_facets(map, i, j, tabs, ineq_i, ineq_j);
+ if (!changed)
+ changed = check_wrap(map, i, j, tabs, ineq_i, ineq_j);
+ }
done:
free(eq_i);
projects / platform / upstream / isl.git / blobdiff