+/*
+ * 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/seq.h>
#include "isl_tab.h"
+#include <isl_mat_private.h>
#define STATUS_ERROR -1
#define STATUS_REDUNDANT 1
{
enum isl_ineq_type type = isl_tab_ineq_type(tab, ineq);
switch (type) {
+ default:
case isl_ineq_error: return STATUS_ERROR;
case isl_ineq_redundant: return STATUS_VALID;
case isl_ineq_separate: return STATUS_SEPARATE;
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) &&
ISL_F_SET(fused, ISL_BASIC_MAP_RATIONAL);
fused_tab = isl_tab_from_basic_map(fused);
- fused_tab = isl_tab_detect_redundant(fused_tab);
- if (!fused_tab)
+ if (isl_tab_detect_redundant(fused_tab) < 0)
goto error;
isl_basic_map_free(map->p[i]);
return 1;
error:
+ isl_tab_free(fused_tab);
isl_basic_map_free(fused);
return -1;
}
for (k = 0; k < map->p[i]->n_ineq; ++k) {
if (ineq_i[k] != STATUS_CUT)
continue;
- tabs[i] = isl_tab_select_facet(tabs[i], n_eq + k);
+ if (isl_tab_select_facet(tabs[i], n_eq + k) < 0)
+ return -1;
for (l = 0; l < map->p[j]->n_ineq; ++l) {
int stat;
if (ineq_j[l] != STATUS_CUT)
if (stat != STATUS_VALID)
break;
}
- isl_tab_rollback(tabs[i], snap);
+ if (isl_tab_rollback(tabs[i], snap) < 0)
+ return -1;
if (l < map->p[j]->n_ineq)
break;
}
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]);
+ if (isl_tab_select_facet(tabs[i], n_eq + k) < 0)
+ return -1;
+ 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;
+}
+
+/* Check if the constraints in "wraps" from "first" until the last
+ * are all valid for the basic set represented by "tab".
+ * If not, wraps->n_row is set to zero.
+ */
+static int check_wraps(__isl_keep isl_mat *wraps, int first,
+ struct isl_tab *tab)
+{
+ int i;
+
+ for (i = first; i < wraps->n_row; ++i) {
+ enum isl_ineq_type type;
+ type = isl_tab_ineq_type(tab, wraps->row[i]);
+ if (type == isl_ineq_error)
+ return -1;
+ if (type == isl_ineq_redundant)
+ continue;
+ wraps->n_row = 0;
+ return 0;
+ }
+
+ return 0;
+}
+
+/* Return a set that corresponds to the non-redudant constraints
+ * (as recorded in tab) of bmap.
+ *
+ * It's important to remove the redundant constraints as some
+ * of the other constraints may have been modified after the
+ * constraints were marked redundant.
+ * In particular, a constraint may have been relaxed.
+ * Redundant constraints are ignored when a constraint is relaxed
+ * and should therefore continue to be ignored ever after.
+ * Otherwise, the relaxation might be thwarted by some of
+ * these constraints.
+ */
+static __isl_give isl_set *set_from_updated_bmap(__isl_keep isl_basic_map *bmap,
+ struct isl_tab *tab)
+{
+ bmap = isl_basic_map_copy(bmap);
+ bmap = isl_basic_map_cow(bmap);
+ bmap = isl_basic_map_update_from_tab(bmap, tab);
+ return isl_set_from_basic_set(isl_basic_map_underlying_set(bmap));
+}
+
+/* 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.
+ *
+ * However, the constraints of j may not be valid for i and so
+ * we have to check that the wrapping constraints for j are valid for i.
+ *
+ * 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;
+ int n;
+
+ set_i = set_from_updated_bmap(map->p[i], tabs[i]);
+ set_j = set_from_updated_bmap(map->p[j], tabs[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;
+
+ snap = isl_tab_snap(tabs[i]);
+
+ if (isl_tab_select_facet(tabs[i], map->p[i]->n_eq + k) < 0)
+ goto error;
+ if (isl_tab_detect_redundant(tabs[i]) < 0)
+ goto error;
+
+ isl_seq_neg(bound->el, map->p[i]->ineq[k], 1 + total);
+
+ n = wraps->n_row;
+ if (add_wraps(wraps, map->p[i], tabs[i], bound->el, set_j) < 0)
+ goto error;
+
+ if (isl_tab_rollback(tabs[i], snap) < 0)
+ goto error;
+ if (check_wraps(wraps, n, tabs[i]) < 0)
+ goto error;
+ if (!wraps->n_row)
+ goto unbounded;
+
+ changed = fuse(map, i, j, tabs, eq_i, ineq_i, eq_j, ineq_j, wraps);
+
+unbounded:
+ 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;
+}
+
+/* Set the is_redundant property of the "n" constraints in "cuts",
+ * except "k" to "v".
+ * This is a fairly tricky operation as it bypasses isl_tab.c.
+ * The reason we want to temporarily mark some constraints redundant
+ * is that we want to ignore them in add_wraps.
+ *
+ * Initially all cut constraints are non-redundant, but the
+ * selection of a facet right before the call to this function
+ * may have made some of them redundant.
+ * Likewise, the same constraints are marked non-redundant
+ * in the second call to this function, before they are officially
+ * made non-redundant again in the subsequent rollback.
+ */
+static void set_is_redundant(struct isl_tab *tab, unsigned n_eq,
+ int *cuts, int n, int k, int v)
+{
+ int l;
+
+ for (l = 0; l < n; ++l) {
+ if (l == k)
+ continue;
+ tab->con[n_eq + cuts[l]].is_redundant = v;
+ }
+}
+
+/* Given a pair of basic maps i and j such that j sticks out
+ * of i at n cut constraints, each time by at most one,
+ * try to compute wrapping constraints and replace the two
+ * basic maps by a single basic map.
+ * The other constraints of i are assumed to be valid for j.
+ *
+ * The facets of i corresponding to the cut constraints are
+ * wrapped around their ridges, except those ridges determined
+ * by any of the other cut constraints.
+ * The intersections of cut constraints need to be ignored
+ * as the result of wrapping one cut constraint around another
+ * would result in a constraint cutting the union.
+ * In each case, the facets are wrapped to include the union
+ * of the two basic maps.
+ *
+ * The pieces of j that lie at an offset of exactly one from
+ * one of the cut constraints of i are wrapped around their edges.
+ * Here, there is no need to ignore intersections because we
+ * are wrapping around the union of the two basic maps.
+ *
+ * If any wrapping fails, i.e., if we cannot wrap to touch
+ * the union, then we give up.
+ * Otherwise, the pair of basic maps is replaced by their union.
+ */
+static int wrap_in_facets(struct isl_map *map, int i, int j,
+ int *cuts, int n, struct isl_tab **tabs,
+ int *eq_i, int *ineq_i, int *eq_j, int *ineq_j)
+{
+ int changed = 0;
+ isl_mat *wraps = NULL;
+ isl_set *set = NULL;
+ isl_vec *bound = NULL;
+ unsigned total = isl_basic_map_total_dim(map->p[i]);
+ int max_wrap;
+ int k;
+ struct isl_tab_undo *snap_i, *snap_j;
+
+ if (isl_tab_extend_cons(tabs[j], 1) < 0)
+ goto error;
+
+ max_wrap = 2 * (map->p[i]->n_eq + map->p[j]->n_eq) +
+ map->p[i]->n_ineq + map->p[j]->n_ineq;
+ max_wrap *= n;
+
+ set = isl_set_union(set_from_updated_bmap(map->p[i], tabs[i]),
+ set_from_updated_bmap(map->p[j], tabs[j]));
+ wraps = isl_mat_alloc(map->ctx, max_wrap, 1 + total);
+ bound = isl_vec_alloc(map->ctx, 1 + total);
+ if (!set || !wraps || !bound)
+ goto error;
+
+ snap_i = isl_tab_snap(tabs[i]);
+ snap_j = isl_tab_snap(tabs[j]);
+
+ wraps->n_row = 0;
+
+ for (k = 0; k < n; ++k) {
+ if (isl_tab_select_facet(tabs[i], map->p[i]->n_eq + cuts[k]) < 0)
+ goto error;
+ if (isl_tab_detect_redundant(tabs[i]) < 0)
+ goto error;
+ set_is_redundant(tabs[i], map->p[i]->n_eq, cuts, n, k, 1);
+
+ isl_seq_neg(bound->el, map->p[i]->ineq[cuts[k]], 1 + total);
+ if (add_wraps(wraps, map->p[i], tabs[i], bound->el, set) < 0)
+ goto error;
+
+ set_is_redundant(tabs[i], map->p[i]->n_eq, cuts, n, k, 0);
+ if (isl_tab_rollback(tabs[i], snap_i) < 0)
+ goto error;
+
+ if (!wraps->n_row)
+ break;
+
+ isl_seq_cpy(bound->el, map->p[i]->ineq[cuts[k]], 1 + total);
+ isl_int_add_ui(bound->el[0], bound->el[0], 1);
+ if (isl_tab_add_eq(tabs[j], bound->el) < 0)
+ goto error;
+ if (isl_tab_detect_redundant(tabs[j]) < 0)
+ goto error;
+
+ if (!tabs[j]->empty &&
+ add_wraps(wraps, map->p[j], tabs[j], bound->el, set) < 0)
+ goto error;
+
+ if (isl_tab_rollback(tabs[j], snap_j) < 0)
+ goto error;
+
+ if (!wraps->n_row)
+ break;
+ }
+
+ if (k == n)
+ changed = fuse(map, i, j, tabs,
+ eq_i, ineq_i, eq_j, ineq_j, wraps);
+
+ isl_vec_free(bound);
+ isl_mat_free(wraps);
+ isl_set_free(set);
+
+ return changed;
+error:
+ isl_vec_free(bound);
+ isl_mat_free(wraps);
+ isl_set_free(set);
+ return -1;
+}
+
+/* Given two basic sets i and j such that i has no cut equalities,
+ * check if relaxing all the cut inequalities of i by one turns
+ * them into valid constraint for j and check if we can wrap in
+ * the bits that are sticking out.
+ * If so, replace the pair by their union.
+ *
+ * We first check if all relaxed cut inequalities of i are valid for j
+ * and then try to wrap in the intersections of the relaxed cut inequalities
+ * with j.
+ *
+ * During this wrapping, we consider the points of j that lie at a distance
+ * of exactly 1 from i. In particular, we ignore the points that lie in
+ * between this lower-dimensional space and the basic map i.
+ * We can therefore only apply this to integer maps.
+ * ____ _____
+ * / ___|_ / \
+ * / | | / |
+ * \ | | => \ |
+ * \|____| \ |
+ * \___| \____/
+ *
+ * _____ ______
+ * | ____|_ | \
+ * | | | | |
+ * | | | => | |
+ * |_| | | |
+ * |_____| \______|
+ *
+ * _______
+ * | |
+ * | |\ |
+ * | | \ |
+ * | | \ |
+ * | | \|
+ * | | \
+ * | |_____\
+ * | |
+ * |_______|
+ *
+ * Wrapping can fail if the result of wrapping one of the facets
+ * around its edges does not produce any new facet constraint.
+ * In particular, this happens when we try to wrap in unbounded sets.
+ *
+ * _______________________________________________________________________
+ * |
+ * | ___
+ * | | |
+ * |_| |_________________________________________________________________
+ * |___|
+ *
+ * The following is not an acceptable result of coalescing the above two
+ * sets as it includes extra integer points.
+ * _______________________________________________________________________
+ * |
+ * |
+ * |
+ * |
+ * \______________________________________________________________________
+ */
+static int can_wrap_in_set(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, m;
+ int n;
+ int *cuts = NULL;
+
+ if (ISL_F_ISSET(map->p[i], ISL_BASIC_MAP_RATIONAL) ||
+ ISL_F_ISSET(map->p[j], ISL_BASIC_MAP_RATIONAL))
+ return 0;
+
+ n = count(ineq_i, map->p[i]->n_ineq, STATUS_CUT);
+ if (n == 0)
+ return 0;
+
+ cuts = isl_alloc_array(map->ctx, int, n);
+ if (!cuts)
+ return -1;
+
+ for (k = 0, m = 0; m < n; ++k) {
+ enum isl_ineq_type type;
+
+ if (ineq_i[k] != STATUS_CUT)
+ continue;
+
+ isl_int_add_ui(map->p[i]->ineq[k][0], map->p[i]->ineq[k][0], 1);
+ type = isl_tab_ineq_type(tabs[j], map->p[i]->ineq[k]);
+ isl_int_sub_ui(map->p[i]->ineq[k][0], map->p[i]->ineq[k][0], 1);
+ if (type == isl_ineq_error)
+ goto error;
+ if (type != isl_ineq_redundant)
+ break;
+ cuts[m] = k;
+ ++m;
+ }
+
+ if (m == n)
+ changed = wrap_in_facets(map, i, j, cuts, n, tabs,
+ eq_i, ineq_i, eq_j, ineq_j);
+
+ free(cuts);
+
+ return changed;
+error:
+ free(cuts);
+ return -1;
+}
+
+/* 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 *eq_i, int *ineq_i, int *eq_j, int *ineq_j)
+{
+ int changed = 0;
+
+ if (!any(eq_i, 2 * map->p[i]->n_eq, STATUS_CUT))
+ changed = can_wrap_in_set(map, i, j, tabs,
+ eq_i, ineq_i, eq_j, ineq_j);
+ if (changed)
+ return changed;
+
+ if (!any(eq_j, 2 * map->p[j]->n_eq, STATUS_CUT))
+ changed = can_wrap_in_set(map, j, i, tabs,
+ eq_j, ineq_j, eq_i, 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" (in)equality, 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 */
/* j has an equality adjacent to an inequality in i */
+ if (any(eq_i, 2 * map->p[i]->n_eq, STATUS_CUT))
+ return 0;
if (any(ineq_i, map->p[i]->n_ineq, STATUS_CUT))
/* ADJ EQ CUT */
return 0;
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) {
- isl_tab_rollback(tabs[i], snap2);
- 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
- isl_tab_rollback(tabs[i], snap);
+ 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;
+}
+
+/* The two basic maps lie on adjacent hyperplanes. In particular,
+ * basic map "i" has an equality that lies parallel to basic map "j".
+ * Check if we can wrap the facets around the parallel hyperplanes
+ * to include the other set.
+ *
+ * We perform basically the same operations as can_wrap_in_facet,
+ * except that we don't need to select a facet of one of the sets.
+ * _
+ * \\ \\
+ * \\ => \\
+ * \ \|
+ *
+ * We only allow one equality of "i" to be adjacent to an equality of "j"
+ * to avoid coalescing
+ *
+ * [m, n] -> { [x, y] -> [x, 1 + y] : x >= 1 and y >= 1 and
+ * x <= 10 and y <= 10;
+ * [x, y] -> [1 + x, y] : x >= 1 and x <= 20 and
+ * y >= 5 and y <= 15 }
+ *
+ * to
+ *
+ * [m, n] -> { [x, y] -> [x2, y2] : x >= 1 and 10y2 <= 20 - x + 10y and
+ * 4y2 >= 5 + 3y and 5y2 <= 15 + 4y and
+ * y2 <= 1 + x + y - x2 and y2 >= y and
+ * y2 >= 1 + x + y - x2 }
+ */
+static int check_eq_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 k;
+ 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]);
+
+ if (count(eq_i, 2 * map->p[i]->n_eq, STATUS_ADJ_EQ) != 1)
+ return 0;
+
+ for (k = 0; k < 2 * map->p[i]->n_eq ; ++k)
+ if (eq_i[k] == STATUS_ADJ_EQ)
+ break;
+
+ set_i = set_from_updated_bmap(map->p[i], tabs[i]);
+ set_j = set_from_updated_bmap(map->p[j], tabs[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;
+
+ if (k % 2 == 0)
+ isl_seq_neg(bound->el, map->p[i]->eq[k / 2], 1 + total);
+ else
+ isl_seq_cpy(bound->el, map->p[i]->eq[k / 2], 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;
+
+ isl_int_sub_ui(bound->el[0], bound->el[0], 1);
+ isl_seq_neg(bound->el, bound->el, 1 + total);
+
+ isl_seq_cpy(wraps->row[wraps->n_row], bound->el, 1 + total);
+ wraps->n_row++;
+
+ 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 (0) {
+error: changed = -1;
+ }
+unbounded:
+
+ isl_mat_free(wraps);
+ isl_set_free(set_i);
+ isl_set_free(set_j);
+ isl_vec_free(bound);
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 seven 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 extends beyond the other by at most one.
+ * Moreover, the facets corresponding to the cut constraints and
+ * the pieces of the other basic map at offset one from these cut
+ * constraints can be wrapped around their ridges to include
+ * the union of the two basic maps
+ * => the pair can be replaced by a basic map consisting
+ * of the valid constraints in both basic maps together
+ * with all wrapping constraints
+ *
+ * 7. the two basic maps live in adjacent hyperplanes. In principle
+ * such sets can always be combined through wrapping, but we impose
+ * that there is only one such pair, to avoid overeager coalescing.
+ *
* 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.
int *ineq_j = NULL;
eq_i = eq_status_in(map, i, j, tabs);
+ if (!eq_i)
+ goto error;
if (any(eq_i, 2 * map->p[i]->n_eq, STATUS_ERROR))
goto error;
if (any(eq_i, 2 * map->p[i]->n_eq, STATUS_SEPARATE))
goto done;
eq_j = eq_status_in(map, j, i, tabs);
+ if (!eq_j)
+ goto error;
if (any(eq_j, 2 * map->p[j]->n_eq, STATUS_ERROR))
goto error;
if (any(eq_j, 2 * map->p[j]->n_eq, STATUS_SEPARATE))
goto done;
ineq_i = ineq_status_in(map, i, j, tabs);
+ if (!ineq_i)
+ goto error;
if (any(ineq_i, map->p[i]->n_ineq, STATUS_ERROR))
goto error;
if (any(ineq_i, map->p[i]->n_ineq, STATUS_SEPARATE))
goto done;
ineq_j = ineq_status_in(map, j, i, tabs);
+ if (!ineq_j)
+ goto error;
if (any(ineq_j, map->p[j]->n_ineq, STATUS_ERROR))
goto error;
if (any(ineq_j, map->p[j]->n_ineq, STATUS_SEPARATE))
all(ineq_j, map->p[j]->n_ineq, STATUS_VALID)) {
drop(map, i, tabs);
changed = 1;
- } else if (any(eq_i, 2 * map->p[i]->n_eq, STATUS_CUT) ||
- any(eq_j, 2 * map->p[j]->n_eq, STATUS_CUT)) {
- /* BAD CUT */
- } else if (any(eq_i, 2 * map->p[i]->n_eq, STATUS_ADJ_EQ) ||
- any(eq_j, 2 * map->p[j]->n_eq, STATUS_ADJ_EQ)) {
- /* ADJ EQ PAIR */
+ } else if (any(eq_i, 2 * map->p[i]->n_eq, STATUS_ADJ_EQ)) {
+ changed = check_eq_adj_eq(map, i, j, tabs,
+ eq_i, ineq_i, eq_j, ineq_j);
+ } else if (any(eq_j, 2 * map->p[j]->n_eq, STATUS_ADJ_EQ)) {
+ changed = check_eq_adj_eq(map, j, i, tabs,
+ eq_j, ineq_j, eq_i, ineq_i);
} else 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)) {
changed = check_adj_eq(map, i, j, tabs,
/* BAD ADJ INEQ */
} 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
- changed = check_facets(map, i, j, tabs, ineq_i, ineq_j);
+ if (!any(eq_i, 2 * map->p[i]->n_eq, STATUS_CUT) &&
+ !any(eq_j, 2 * map->p[j]->n_eq, STATUS_CUT))
+ changed = check_adj_ineq(map, i, j, tabs,
+ ineq_i, ineq_j);
+ } else {
+ if (!any(eq_i, 2 * map->p[i]->n_eq, STATUS_CUT) &&
+ !any(eq_j, 2 * map->p[j]->n_eq, STATUS_CUT))
+ changed = check_facets(map, i, j, tabs, ineq_i, ineq_j);
+ if (!changed)
+ changed = check_wrap(map, i, j, tabs,
+ eq_i, ineq_i, eq_j, ineq_j);
+ }
done:
free(eq_i);
{
int i, j;
- for (i = 0; i < map->n - 1; ++i)
+ for (i = map->n - 2; i >= 0; --i)
+restart:
for (j = i + 1; j < map->n; ++j) {
int changed;
changed = coalesce_pair(map, i, j, tabs);
if (changed < 0)
goto error;
if (changed)
- return coalesce(map, tabs);
+ goto restart;
}
return map;
error:
if (!tabs[i])
goto error;
if (!ISL_F_ISSET(map->p[i], ISL_BASIC_MAP_NO_IMPLICIT))
- tabs[i] = isl_tab_detect_equalities(tabs[i]);
+ if (isl_tab_detect_implicit_equalities(tabs[i]) < 0)
+ goto error;
if (!ISL_F_ISSET(map->p[i], ISL_BASIC_MAP_NO_REDUNDANT))
- tabs[i] = isl_tab_detect_redundant(tabs[i]);
+ if (isl_tab_detect_redundant(tabs[i]) < 0)
+ goto error;
}
for (i = map->n - 1; i >= 0; --i)
if (tabs[i]->empty)
projects / platform / upstream / isl.git / blobdiff