+/*
+ * Copyright 2008-2009 Katholieke Universiteit Leuven
+ * Copyright 2010 INRIA Saclay
+ * Copyright 2012-2013 Ecole Normale Superieure
+ *
+ * Use of this software is governed by the MIT 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
+ * and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
+ */
+
#include "isl_map_private.h"
+#include <isl/seq.h>
+#include <isl/options.h>
#include "isl_tab.h"
+#include <isl_mat_private.h>
+#include <isl_local_space_private.h>
#define STATUS_ERROR -1
#define STATUS_REDUNDANT 1
#define STATUS_ADJ_EQ 5
#define STATUS_ADJ_INEQ 6
-static int status_in(struct isl_ctx *ctx, isl_int *ineq, struct isl_tab *tab)
+static int status_in(isl_int *ineq, struct isl_tab *tab)
{
- enum isl_ineq_type type = isl_tab_ineq_type(ctx, tab, ineq);
+ 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;
}
}
-/* Compute the position of the equalities of basic set "i"
- * with respect to basic set "j".
+/* Compute the position of the equalities of basic map "bmap_i"
+ * with respect to the basic map represented by "tab_j".
* The resulting array has twice as many entries as the number
* of equalities corresponding to the two inequalties to which
* each equality corresponds.
*/
-static int *eq_status_in(struct isl_set *set, int i, int j,
- struct isl_tab **tabs)
+static int *eq_status_in(__isl_keep isl_basic_map *bmap_i,
+ struct isl_tab *tab_j)
{
int k, l;
- int *eq = isl_calloc_array(set->ctx, int, 2 * set->p[i]->n_eq);
+ int *eq = isl_calloc_array(bmap_i->ctx, int, 2 * bmap_i->n_eq);
unsigned dim;
- dim = isl_basic_set_total_dim(set->p[i]);
- for (k = 0; k < set->p[i]->n_eq; ++k) {
+ dim = isl_basic_map_total_dim(bmap_i);
+ for (k = 0; k < bmap_i->n_eq; ++k) {
for (l = 0; l < 2; ++l) {
- isl_seq_neg(set->p[i]->eq[k], set->p[i]->eq[k], 1+dim);
- eq[2 * k + l] = status_in(set->ctx, set->p[i]->eq[k],
- tabs[j]);
+ isl_seq_neg(bmap_i->eq[k], bmap_i->eq[k], 1+dim);
+ eq[2 * k + l] = status_in(bmap_i->eq[k], tab_j);
if (eq[2 * k + l] == STATUS_ERROR)
goto error;
}
return NULL;
}
-/* Compute the position of the inequalities of basic set "i"
- * with respect to basic set "j".
+/* Compute the position of the inequalities of basic map "bmap_i"
+ * (also represented by "tab_i", if not NULL) with respect to the basic map
+ * represented by "tab_j".
*/
-static int *ineq_status_in(struct isl_set *set, int i, int j,
- struct isl_tab **tabs)
+static int *ineq_status_in(__isl_keep isl_basic_map *bmap_i,
+ struct isl_tab *tab_i, struct isl_tab *tab_j)
{
int k;
- unsigned n_eq = set->p[i]->n_eq;
- int *ineq = isl_calloc_array(set->ctx, int, set->p[i]->n_ineq);
+ unsigned n_eq = bmap_i->n_eq;
+ int *ineq = isl_calloc_array(bmap_i->ctx, int, bmap_i->n_ineq);
- for (k = 0; k < set->p[i]->n_ineq; ++k) {
- if (isl_tab_is_redundant(set->ctx, tabs[i], n_eq + k)) {
+ for (k = 0; k < bmap_i->n_ineq; ++k) {
+ if (tab_i && isl_tab_is_redundant(tab_i, n_eq + k)) {
ineq[k] = STATUS_REDUNDANT;
continue;
}
- ineq[k] = status_in(set->ctx, set->p[i]->ineq[k], tabs[j]);
+ ineq[k] = status_in(bmap_i->ineq[k], tab_j);
if (ineq[k] == STATUS_ERROR)
goto error;
if (ineq[k] == STATUS_SEPARATE)
return 1;
}
-static void drop(struct isl_set *set, int i, struct isl_tab **tabs)
+static void drop(struct isl_map *map, int i, struct isl_tab **tabs)
{
- isl_basic_set_free(set->p[i]);
- isl_tab_free(set->ctx, tabs[i]);
+ isl_basic_map_free(map->p[i]);
+ isl_tab_free(tabs[i]);
- if (i != set->n - 1) {
- set->p[i] = set->p[set->n - 1];
- tabs[i] = tabs[set->n - 1];
+ if (i != map->n - 1) {
+ map->p[i] = map->p[map->n - 1];
+ tabs[i] = tabs[map->n - 1];
}
- tabs[set->n - 1] = NULL;
- set->n--;
+ tabs[map->n - 1] = NULL;
+ map->n--;
}
-/* Replace the pair of basic sets i and j but the basic set bounded
- * by the valid constraints in both basic sets.
+/* 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_set *set, 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_set *fused = NULL;
+ struct isl_basic_map *fused = NULL;
struct isl_tab *fused_tab = NULL;
- unsigned total = isl_basic_set_total_dim(set->p[i]);
+ unsigned total = isl_basic_map_total_dim(map->p[i]);
+ unsigned extra_rows = extra ? extra->n_row : 0;
- fused = isl_basic_set_alloc_dim(isl_dim_copy(set->p[i]->dim),
- set->p[i]->n_div,
- set->p[i]->n_eq + set->p[j]->n_eq,
- set->p[i]->n_ineq + set->p[j]->n_ineq);
+ fused = isl_basic_map_alloc_space(isl_space_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 + extra_rows);
if (!fused)
goto error;
- for (k = 0; k < set->p[i]->n_eq; ++k) {
- int l = isl_basic_set_alloc_equality(fused);
- isl_seq_cpy(fused->eq[l], set->p[i]->eq[k], 1 + total);
+ for (k = 0; k < map->p[i]->n_eq; ++k) {
+ 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 < set->p[j]->n_eq; ++k) {
- int l = isl_basic_set_alloc_equality(fused);
- isl_seq_cpy(fused->eq[l], set->p[j]->eq[k], 1 + total);
+ for (k = 0; k < map->p[j]->n_eq; ++k) {
+ 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);
}
- for (k = 0; k < set->p[i]->n_ineq; ++k) {
+ for (k = 0; k < map->p[i]->n_ineq; ++k) {
if (ineq_i[k] != STATUS_VALID)
continue;
- l = isl_basic_set_alloc_inequality(fused);
- isl_seq_cpy(fused->ineq[l], set->p[i]->ineq[k], 1 + total);
+ 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);
}
- for (k = 0; k < set->p[j]->n_ineq; ++k) {
+ for (k = 0; k < map->p[j]->n_ineq; ++k) {
if (ineq_j[k] != STATUS_VALID)
continue;
- l = isl_basic_set_alloc_inequality(fused);
- isl_seq_cpy(fused->ineq[l], set->p[j]->ineq[k], 1 + total);
+ 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 < set->p[i]->n_div; ++k) {
- int l = isl_basic_set_alloc_div(fused);
- isl_seq_cpy(fused->div[l], set->p[i]->div[k], 1 + 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);
}
- fused = isl_basic_set_gauss(fused, NULL);
- ISL_F_SET(fused, ISL_BASIC_SET_FINAL);
+ 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_tab = isl_tab_from_basic_set(fused);
- fused_tab = isl_tab_detect_redundant(set->ctx, fused_tab);
- if (!fused_tab)
+ 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_ISSET(map->p[j], ISL_BASIC_MAP_RATIONAL))
+ ISL_F_SET(fused, ISL_BASIC_MAP_RATIONAL);
+
+ fused_tab = isl_tab_from_basic_map(fused, 0);
+ if (isl_tab_detect_redundant(fused_tab) < 0)
goto error;
- isl_basic_set_free(set->p[i]);
- set->p[i] = fused;
- isl_tab_free(set->ctx, tabs[i]);
+ isl_basic_map_free(map->p[i]);
+ map->p[i] = fused;
+ isl_tab_free(tabs[i]);
tabs[i] = fused_tab;
- drop(set, j, tabs);
+ drop(map, j, tabs);
return 1;
error:
- isl_basic_set_free(fused);
+ isl_tab_free(fused_tab);
+ isl_basic_map_free(fused);
return -1;
}
-/* Given a pair of basic sets i and j such that all constraints are either
+/* Given a pair of basic maps i and j such that all constraints are either
* "valid" or "cut", check if the facets corresponding to the "cut"
- * constraints of i lie entirely within basic set j.
- * If so, replace the pair by the basic set consisting of the valid
- * constraints in both basic sets.
+ * constraints of i lie entirely within basic map j.
+ * If so, replace the pair by the basic map consisting of the valid
+ * constraints in both basic maps.
*
* To see that we are not introducing any extra points, call the
- * two basic sets A and B and the resulting set U and let x
+ * two basic maps A and B and the resulting map U and let x
* be an element of U \setminus ( A \cup B ).
* Then there is a pair of cut constraints c_1 and c_2 in A and B such that x
* violates them. Let X be the intersection of U with the opposites
* c_2 must be opposites of each other, but then x could not violate
* both of them.
*/
-static int check_facets(struct isl_set *set, int i, int j,
+static int check_facets(struct isl_map *map, int i, int j,
struct isl_tab **tabs, int *ineq_i, int *ineq_j)
{
int k, l;
struct isl_tab_undo *snap;
- unsigned n_eq = set->p[i]->n_eq;
+ unsigned n_eq = map->p[i]->n_eq;
- snap = isl_tab_snap(set->ctx, tabs[i]);
+ snap = isl_tab_snap(tabs[i]);
- for (k = 0; k < set->p[i]->n_ineq; ++k) {
+ for (k = 0; k < map->p[i]->n_ineq; ++k) {
if (ineq_i[k] != STATUS_CUT)
continue;
- tabs[i] = isl_tab_select_facet(set->ctx, tabs[i], n_eq + k);
- for (l = 0; l < set->p[j]->n_ineq; ++l) {
+ 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)
continue;
- stat = status_in(set->ctx, set->p[j]->ineq[l], tabs[i]);
+ stat = status_in(map->p[j]->ineq[l], tabs[i]);
if (stat != STATUS_VALID)
break;
}
- isl_tab_rollback(set->ctx, tabs[i], snap);
- if (l < set->p[j]->n_ineq)
+ if (isl_tab_rollback(tabs[i], snap) < 0)
+ return -1;
+ if (l < map->p[j]->n_ineq)
break;
}
- if (k < set->p[i]->n_ineq)
+ if (k < map->p[i]->n_ineq)
/* BAD CUT PAIR */
return 0;
- return fuse(set, i, j, tabs, ineq_i, ineq_j);
+ return fuse(map, i, j, tabs, NULL, ineq_i, NULL, ineq_j, NULL);
+}
+
+/* Check if basic map "i" contains the basic map represented
+ * by the tableau "tab".
+ */
+static int contains(struct isl_map *map, int i, int *ineq_i,
+ struct isl_tab *tab)
+{
+ int k, l;
+ unsigned dim;
+
+ dim = isl_basic_map_total_dim(map->p[i]);
+ for (k = 0; k < map->p[i]->n_eq; ++k) {
+ for (l = 0; l < 2; ++l) {
+ int stat;
+ isl_seq_neg(map->p[i]->eq[k], map->p[i]->eq[k], 1+dim);
+ stat = status_in(map->p[i]->eq[k], tab);
+ if (stat != STATUS_VALID)
+ return 0;
+ }
+ }
+
+ for (k = 0; k < map->p[i]->n_ineq; ++k) {
+ int stat;
+ if (ineq_i[k] == STATUS_REDUNDANT)
+ continue;
+ stat = status_in(map->p[i]->ineq[k], tab);
+ if (stat != STATUS_VALID)
+ return 0;
+ }
+ return 1;
+}
+
+/* Basic map "i" has an inequality (say "k") that is adjacent
+ * to some inequality of basic map "j". All the other inequalities
+ * are valid for "j".
+ * Check if basic map "j" forms an extension of basic map "i".
+ *
+ * Note that this function is only called if some of the equalities or
+ * inequalities of basic map "j" do cut basic map "i". The function is
+ * correct even if there are no such cut constraints, but in that case
+ * the additional checks performed by this function are overkill.
+ *
+ * In particular, we replace constraint k, say f >= 0, by constraint
+ * f <= -1, add the inequalities of "j" that are valid for "i"
+ * and check if the result is a subset of basic map "j".
+ * If so, then we know that this result is exactly equal to basic map "j"
+ * since all its constraints are valid for basic map "j".
+ * By combining the valid constraints of "i" (all equalities and all
+ * inequalities except "k") and the valid constraints of "j" we therefore
+ * obtain a basic map that is equal to their union.
+ * In this case, there is no need to perform a rollback of the tableau
+ * since it is going to be destroyed in fuse().
+ *
+ *
+ * |\__ |\__
+ * | \__ | \__
+ * | \_ => | \__
+ * |_______| _ |_________\
+ *
+ *
+ * |\ |\
+ * | \ | \
+ * | \ | \
+ * | | | \
+ * | ||\ => | \
+ * | || \ | \
+ * | || | | |
+ * |__||_/ |_____/
+ */
+static int is_adj_ineq_extension(__isl_keep 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;
+ struct isl_tab_undo *snap;
+ unsigned n_eq = map->p[i]->n_eq;
+ unsigned total = isl_basic_map_total_dim(map->p[i]);
+ int r;
+
+ if (isl_tab_extend_cons(tabs[i], 1 + map->p[j]->n_ineq) < 0)
+ return -1;
+
+ for (k = 0; k < map->p[i]->n_ineq; ++k)
+ if (ineq_i[k] == STATUS_ADJ_INEQ)
+ break;
+ if (k >= map->p[i]->n_ineq)
+ isl_die(isl_map_get_ctx(map), isl_error_internal,
+ "ineq_i should have exactly one STATUS_ADJ_INEQ",
+ return -1);
+
+ snap = isl_tab_snap(tabs[i]);
+
+ if (isl_tab_unrestrict(tabs[i], n_eq + k) < 0)
+ return -1;
+
+ isl_seq_neg(map->p[i]->ineq[k], map->p[i]->ineq[k], 1 + total);
+ isl_int_sub_ui(map->p[i]->ineq[k][0], map->p[i]->ineq[k][0], 1);
+ r = isl_tab_add_ineq(tabs[i], map->p[i]->ineq[k]);
+ isl_seq_neg(map->p[i]->ineq[k], map->p[i]->ineq[k], 1 + total);
+ isl_int_sub_ui(map->p[i]->ineq[k][0], map->p[i]->ineq[k][0], 1);
+ if (r < 0)
+ return -1;
+
+ for (k = 0; k < map->p[j]->n_ineq; ++k) {
+ if (ineq_j[k] != STATUS_VALID)
+ continue;
+ if (isl_tab_add_ineq(tabs[i], map->p[j]->ineq[k]) < 0)
+ return -1;
+ }
+
+ if (contains(map, j, ineq_j, tabs[i]))
+ return fuse(map, i, j, tabs, eq_i, ineq_i, eq_j, ineq_j, NULL);
+
+ if (isl_tab_rollback(tabs[i], snap) < 0)
+ return -1;
+
+ return 0;
}
-/* Both basic sets have at least one inequality with and adjacent
- * (but opposite) inequality in the other basic set.
+
+/* Both basic maps have at least one inequality with and adjacent
+ * (but opposite) inequality in the other basic map.
* Check that there are no cut constraints and that there is only
* a single pair of adjacent inequalities.
- * If so, we can replace the pair by a single basic set described
+ * If so, we can replace the pair by a single basic map described
* by all but the pair of adjacent inequalities.
* Any additional points introduced lie strictly between the two
* adjacent hyperplanes and can therefore be integral.
* \___||_/ \_____/
*
* The test for a single pair of adjancent inequalities is important
- * for avoiding the combination of two basic sets like the following
+ * for avoiding the combination of two basic maps like the following
*
* /|
* / |
* | |
* | |
* |___|
+ *
+ * If there are some cut constraints on one side, then we may
+ * still be able to fuse the two basic maps, but we need to perform
+ * some additional checks in is_adj_ineq_extension.
*/
-static int check_adj_ineq(struct isl_set *set, int i, int j,
- struct isl_tab **tabs, int *ineq_i, int *ineq_j)
+static int check_adj_ineq(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 count_i, count_j;
+ int cut_i, cut_j;
+
+ count_i = count(ineq_i, map->p[i]->n_ineq, STATUS_ADJ_INEQ);
+ count_j = count(ineq_j, map->p[j]->n_ineq, STATUS_ADJ_INEQ);
+
+ if (count_i != 1 && count_j != 1)
+ return 0;
+
+ cut_i = any(eq_i, 2 * map->p[i]->n_eq, STATUS_CUT) ||
+ any(ineq_i, map->p[i]->n_ineq, STATUS_CUT);
+ cut_j = any(eq_j, 2 * map->p[j]->n_eq, STATUS_CUT) ||
+ any(ineq_j, map->p[j]->n_ineq, STATUS_CUT);
+
+ if (!cut_i && !cut_j && count_i == 1 && count_j == 1)
+ return fuse(map, i, j, tabs, NULL, ineq_i, NULL, ineq_j, NULL);
+
+ if (count_i == 1 && !cut_i)
+ return is_adj_ineq_extension(map, i, j, tabs,
+ eq_i, ineq_i, eq_j, ineq_j);
+
+ if (count_j == 1 && !cut_j)
+ return is_adj_ineq_extension(map, j, i, tabs,
+ eq_j, ineq_j, eq_i, ineq_i);
+
+ return 0;
+}
+
+/* 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 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
+ * two basic maps by this extension.
+ * ____ _____
+ * / || / |
+ * / || / |
+ * \ || => \ |
+ * \ || \ |
+ * \___|| \____|
+ */
+static int is_adj_eq_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;
+ struct isl_tab_undo *snap, *snap2;
+ unsigned n_eq = map->p[i]->n_eq;
- if (any(ineq_i, set->p[i]->n_ineq, STATUS_CUT) ||
- any(ineq_j, set->p[j]->n_ineq, STATUS_CUT))
- /* ADJ INEQ CUT */
- ;
- else if (count(ineq_i, set->p[i]->n_ineq, STATUS_ADJ_INEQ) == 1 &&
- count(ineq_j, set->p[j]->n_ineq, STATUS_ADJ_INEQ) == 1)
- changed = fuse(set, i, j, tabs, ineq_i, ineq_j);
- /* else ADJ INEQ TOO MANY */
+ if (isl_tab_is_equality(tabs[i], n_eq + k))
+ return 0;
+
+ 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;
}
-/* Check if basic set "i" contains the basic set represented
- * by the tableau "tab".
+/* Data structure that keeps track of the wrapping constraints
+ * and of information to bound the coefficients of those constraints.
+ *
+ * bound is set if we want to apply a bound on the coefficients
+ * mat contains the wrapping constraints
+ * max is the bound on the coefficients (if bound is set)
*/
-static int contains(struct isl_set *set, int i, int *ineq_i,
- struct isl_tab *tab)
+struct isl_wraps {
+ int bound;
+ isl_mat *mat;
+ isl_int max;
+};
+
+/* Update wraps->max to be greater than or equal to the coefficients
+ * in the equalities and inequalities of bmap that can be removed if we end up
+ * applying wrapping.
+ */
+static void wraps_update_max(struct isl_wraps *wraps,
+ __isl_keep isl_basic_map *bmap, int *eq, int *ineq)
{
- int k, l;
- unsigned dim;
+ int k;
+ isl_int max_k;
+ unsigned total = isl_basic_map_total_dim(bmap);
- dim = isl_basic_set_total_dim(set->p[i]);
- for (k = 0; k < set->p[i]->n_eq; ++k) {
- for (l = 0; l < 2; ++l) {
- int stat;
- isl_seq_neg(set->p[i]->eq[k], set->p[i]->eq[k], 1+dim);
- stat = status_in(set->ctx, set->p[i]->eq[k], tab);
- if (stat != STATUS_VALID)
- return 0;
- }
+ isl_int_init(max_k);
+
+ for (k = 0; k < bmap->n_eq; ++k) {
+ if (eq[2 * k] == STATUS_VALID &&
+ eq[2 * k + 1] == STATUS_VALID)
+ continue;
+ isl_seq_abs_max(bmap->eq[k] + 1, total, &max_k);
+ if (isl_int_abs_gt(max_k, wraps->max))
+ isl_int_set(wraps->max, max_k);
}
- for (k = 0; k < set->p[i]->n_ineq; ++k) {
- int stat;
- if (ineq_i[l] == STATUS_REDUNDANT)
+ for (k = 0; k < bmap->n_ineq; ++k) {
+ if (ineq[k] == STATUS_VALID || ineq[k] == STATUS_REDUNDANT)
continue;
- stat = status_in(set->ctx, set->p[i]->ineq[k], tab);
- if (stat != STATUS_VALID)
- return 0;
+ isl_seq_abs_max(bmap->ineq[k] + 1, total, &max_k);
+ if (isl_int_abs_gt(max_k, wraps->max))
+ isl_int_set(wraps->max, max_k);
}
+
+ isl_int_clear(max_k);
+}
+
+/* Initialize the isl_wraps data structure.
+ * If we want to bound the coefficients of the wrapping constraints,
+ * we set wraps->max to the largest coefficient
+ * in the equalities and inequalities that can be removed if we end up
+ * applying wrapping.
+ */
+static void wraps_init(struct isl_wraps *wraps, __isl_take isl_mat *mat,
+ __isl_keep isl_map *map, int i, int j,
+ int *eq_i, int *ineq_i, int *eq_j, int *ineq_j)
+{
+ isl_ctx *ctx;
+
+ wraps->bound = 0;
+ wraps->mat = mat;
+ if (!mat)
+ return;
+ ctx = isl_mat_get_ctx(mat);
+ wraps->bound = isl_options_get_coalesce_bounded_wrapping(ctx);
+ if (!wraps->bound)
+ return;
+ isl_int_init(wraps->max);
+ isl_int_set_si(wraps->max, 0);
+ wraps_update_max(wraps, map->p[i], eq_i, ineq_i);
+ wraps_update_max(wraps, map->p[j], eq_j, ineq_j);
+}
+
+/* Free the contents of the isl_wraps data structure.
+ */
+static void wraps_free(struct isl_wraps *wraps)
+{
+ isl_mat_free(wraps->mat);
+ if (wraps->bound)
+ isl_int_clear(wraps->max);
+}
+
+/* Is the wrapping constraint in row "row" allowed?
+ *
+ * If wraps->bound is set, we check that none of the coefficients
+ * is greater than wraps->max.
+ */
+static int allow_wrap(struct isl_wraps *wraps, int row)
+{
+ int i;
+
+ if (!wraps->bound)
+ return 1;
+
+ for (i = 1; i < wraps->mat->n_col; ++i)
+ if (isl_int_abs_gt(wraps->mat->row[row][i], wraps->max))
+ return 0;
+
return 1;
}
-/* At least one of the basic sets has an equality that is adjacent
- * to inequality. Make sure that only one of the basic sets has
- * such an equality and that the other basic set has exactly one
- * inequality adjacent to an equality.
- * We call the basic set that has the inequality "i" and the basic
- * set that has the equality "j".
- * If "i" has any "cut" inequality, then relaxing the inequality
- * by one would not result in a basic set that contains the other
- * basic set.
- * Otherwise, we relax the constraint, compute the corresponding
- * facet and check whether it is included in the other basic set.
- * If so, we know that relaxing the constraint extend the basic
- * set with exactly the other basic set (we already know that this
- * other basic set is included in the extension, because there
- * were no "cut" inequalities in "i") and we can replace the
- * two basic sets by thie extension.
+/* 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.
+ * Similarly, if we want to bound the coefficients of the wrapping
+ * constraints and a newly added wrapping constraint does not
+ * satisfy the bound, then wraps->n_row is also reset to zero.
+ */
+static int add_wraps(struct isl_wraps *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->mat->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->mat->row[w], bound, 1 + total);
+ if (!isl_set_wrap_facet(set, wraps->mat->row[w], bmap->ineq[l]))
+ return -1;
+ if (isl_seq_eq(wraps->mat->row[w], bound, 1 + total))
+ goto unbounded;
+ if (!allow_wrap(wraps, w))
+ 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->mat->row[w], bound, 1 + total);
+ isl_seq_neg(wraps->mat->row[w + 1], bmap->eq[l], 1 + total);
+ if (!isl_set_wrap_facet(set, wraps->mat->row[w],
+ wraps->mat->row[w + 1]))
+ return -1;
+ if (isl_seq_eq(wraps->mat->row[w], bound, 1 + total))
+ goto unbounded;
+ if (!allow_wrap(wraps, w))
+ goto unbounded;
+ ++w;
+
+ isl_seq_cpy(wraps->mat->row[w], bound, 1 + total);
+ if (!isl_set_wrap_facet(set, wraps->mat->row[w], bmap->eq[l]))
+ return -1;
+ if (isl_seq_eq(wraps->mat->row[w], bound, 1 + total))
+ goto unbounded;
+ if (!allow_wrap(wraps, w))
+ goto unbounded;
+ ++w;
+ }
+
+ wraps->mat->n_row = w;
+ return 0;
+unbounded:
+ wraps->mat->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 check_adj_eq(struct isl_set *set, int i, int 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;
- int super;
+ struct isl_wraps wraps;
+ isl_mat *mat;
+ 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]);
+ mat = 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);
+ wraps_init(&wraps, mat, map, i, j, eq_i, ineq_i, eq_j, ineq_j);
+ bound = isl_vec_alloc(map->ctx, 1 + total);
+ if (!set_i || !set_j || !wraps.mat || !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.mat->row[0], bound->el, 1 + total);
+ wraps.mat->n_row = 1;
+
+ if (add_wraps(&wraps, map->p[j], tabs[j], bound->el, set_i) < 0)
+ goto error;
+ if (!wraps.mat->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.mat->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.mat, n, tabs[i]) < 0)
+ goto error;
+ if (!wraps.mat->n_row)
+ goto unbounded;
+
+ changed = fuse(map, i, j, tabs, eq_i, ineq_i, eq_j, ineq_j, wraps.mat);
+
+unbounded:
+ wraps_free(&wraps);
+
+ isl_set_free(set_i);
+ isl_set_free(set_j);
+
+ isl_vec_free(bound);
+
+ return changed;
+error:
+ wraps_free(&wraps);
+ isl_vec_free(bound);
+ 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;
+ struct isl_wraps wraps;
+ isl_mat *mat;
+ 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, *snap2;
- unsigned n_eq = set->p[i]->n_eq;
+ 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;
- if (any(eq_i, 2 * set->p[i]->n_eq, STATUS_ADJ_INEQ) &&
- any(eq_j, 2 * set->p[j]->n_eq, STATUS_ADJ_INEQ))
+ set = isl_set_union(set_from_updated_bmap(map->p[i], tabs[i]),
+ set_from_updated_bmap(map->p[j], tabs[j]));
+ mat = isl_mat_alloc(map->ctx, max_wrap, 1 + total);
+ wraps_init(&wraps, mat, map, i, j, eq_i, ineq_i, eq_j, ineq_j);
+ bound = isl_vec_alloc(map->ctx, 1 + total);
+ if (!set || !wraps.mat || !bound)
+ goto error;
+
+ snap_i = isl_tab_snap(tabs[i]);
+ snap_j = isl_tab_snap(tabs[j]);
+
+ wraps.mat->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 (!tabs[i]->empty &&
+ 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 (tabs[i]->empty)
+ break;
+ if (!wraps.mat->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.mat->n_row)
+ break;
+ }
+
+ if (k == n)
+ changed = fuse(map, i, j, tabs,
+ eq_i, ineq_i, eq_j, ineq_j, wraps.mat);
+
+ isl_vec_free(bound);
+ wraps_free(&wraps);
+ isl_set_free(set);
+
+ return changed;
+error:
+ isl_vec_free(bound);
+ wraps_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 */
return 0;
- if (any(eq_i, 2 * set->p[i]->n_eq, STATUS_ADJ_INEQ))
- return check_adj_eq(set, j, i, tabs,
+ if (any(eq_i, 2 * map->p[i]->n_eq, STATUS_ADJ_INEQ))
+ return check_adj_eq(map, j, i, tabs,
eq_j, ineq_j, eq_i, ineq_i);
/* j has an equality adjacent to an inequality in i */
- if (any(ineq_i, set->p[i]->n_ineq, STATUS_CUT))
+ 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 (count(eq_j, 2 * set->p[j]->n_eq, STATUS_ADJ_INEQ) != 1 ||
- count(ineq_i, set->p[i]->n_ineq, STATUS_ADJ_EQ) != 1 ||
- any(ineq_j, set->p[j]->n_ineq, STATUS_ADJ_EQ) ||
- any(ineq_i, set->p[i]->n_ineq, STATUS_ADJ_INEQ) ||
- any(ineq_j, set->p[j]->n_ineq, STATUS_ADJ_INEQ))
+ if (count(ineq_i, map->p[i]->n_ineq, STATUS_ADJ_EQ) != 1 ||
+ any(ineq_j, map->p[j]->n_ineq, STATUS_ADJ_EQ) ||
+ any(ineq_i, map->p[i]->n_ineq, STATUS_ADJ_INEQ) ||
+ any(ineq_j, map->p[j]->n_ineq, STATUS_ADJ_INEQ))
/* ADJ EQ TOO MANY */
return 0;
- for (k = 0; k < set->p[i]->n_ineq ; ++k)
+ for (k = 0; k < map->p[i]->n_ineq; ++k)
if (ineq_i[k] == STATUS_ADJ_EQ)
break;
- snap = isl_tab_snap(set->ctx, tabs[i]);
- tabs[i] = isl_tab_relax(set->ctx, tabs[i], n_eq + k);
- snap2 = isl_tab_snap(set->ctx, tabs[i]);
- tabs[i] = isl_tab_select_facet(set->ctx, tabs[i], n_eq + k);
- super = contains(set, j, ineq_j, tabs[i]);
- if (super) {
- isl_tab_rollback(set->ctx, tabs[i], snap2);
- set->p[i] = isl_basic_set_cow(set->p[i]);
- if (!set->p[i])
- return -1;
- isl_int_add_ui(set->p[i]->ineq[k][0], set->p[i]->ineq[k][0], 1);
- ISL_F_SET(set->p[i], ISL_BASIC_SET_FINAL);
- drop(set, j, tabs);
- changed = 1;
- } else
- isl_tab_rollback(set->ctx, tabs[i], snap);
+ changed = is_adj_eq_extension(map, i, j, k, tabs,
+ eq_i, ineq_i, eq_j, ineq_j);
+ if (changed)
+ return changed;
+
+ if (count(eq_j, 2 * map->p[j]->n_eq, STATUS_ADJ_INEQ) != 1)
+ return 0;
+
+ changed = can_wrap_in_facet(map, i, j, k, tabs, eq_i, ineq_i, eq_j, ineq_j);
return changed;
}
-/* Check if the union of the given pair of basic sets
- * can be represented by a single basic set.
- * If so, replace the pair by the single basic set and return 1.
+/* 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_wraps wraps;
+ isl_mat *mat;
+ 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]);
+ mat = 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);
+ wraps_init(&wraps, mat, map, i, j, eq_i, ineq_i, eq_j, ineq_j);
+ bound = isl_vec_alloc(map->ctx, 1 + total);
+ if (!set_i || !set_j || !wraps.mat || !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.mat->row[0], bound->el, 1 + total);
+ wraps.mat->n_row = 1;
+
+ if (add_wraps(&wraps, map->p[j], tabs[j], bound->el, set_i) < 0)
+ goto error;
+ if (!wraps.mat->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.mat->row[wraps.mat->n_row], bound->el, 1 + total);
+ wraps.mat->n_row++;
+
+ if (add_wraps(&wraps, map->p[i], tabs[i], bound->el, set_j) < 0)
+ goto error;
+ if (!wraps.mat->n_row)
+ goto unbounded;
+
+ changed = fuse(map, i, j, tabs, eq_i, ineq_i, eq_j, ineq_j, wraps.mat);
+
+ if (0) {
+error: changed = -1;
+ }
+unbounded:
+
+ wraps_free(&wraps);
+ isl_set_free(set_i);
+ isl_set_free(set_j);
+ isl_vec_free(bound);
+
+ return changed;
+}
+
+/* Check if the union of the given pair of basic maps
+ * can be represented by a single basic map.
+ * If so, replace the pair by the single basic map and return 1.
* Otherwise, return 0;
+ * The two basic maps are assumed to live in the same local space.
*
- * We first check the effect of each constraint of one basic set
- * on the other basic set.
+ * We first check the effect of each constraint of one basic map
+ * on the other basic map.
* The constraint may be
* redundant the constraint is redundant in its own
- * basic set and should be ignore and removed
+ * basic map and should be ignore and removed
* in the end
- * valid all (integer) points of the other basic set
+ * valid all (integer) points of the other basic map
* satisfy the constraint
- * separate no (integer) point of the other basic set
+ * separate no (integer) point of the other basic map
* satisfies the constraint
- * cut some but not all points of the other basic set
+ * cut some but not all points of the other basic map
* satisfy the constraint
* adj_eq the given constraint is adjacent (on the outside)
- * to an equality of the other basic set
+ * to an equality of the other basic map
* adj_ineq the given constraint is adjacent (on the outside)
- * to an inequality of the other basic set
+ * to an inequality of the other basic map
*
- * We consider four cases in which we can replace the pair by a single
- * basic set. We ignore all "redundant" constraints.
+ * 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 set are valid
- * => the other basic set is a subset and can be removed
+ * 1. all constraints of one basic map are valid
+ * => the other basic map is a subset and can be removed
*
- * 2. all constraints of both basic sets are either "valid" or "cut"
+ * 2. all constraints of both basic maps are either "valid" or "cut"
* and the facets corresponding to the "cut" constraints
- * of one of the basic sets lies entirely inside the other basic set
- * => the pair can be replaced by a basic set consisting
- * of the valid constraints in both basic sets
+ * of one of the basic maps lies entirely inside the other basic map
+ * => the pair can be replaced by a basic map consisting
+ * of the valid constraints in both basic maps
*
* 3. there is a single pair of adjacent inequalities
* (all other constraints are "valid")
- * => the pair can be replaced by a basic set consisting
- * of the valid constraints in both basic sets
+ * => the pair can be replaced by a basic map consisting
+ * of the valid constraints in both basic maps
*
- * 4. there is a single adjacent pair of an inequality and an equality,
- * the other constraints of the basic set containing the equality are
- * "valid". Moreover, if the inequality the basic set is relaxed
+ * 4. one basic map has a single adjacent inequality, while the other
+ * constraints are "valid". The other basic map has some
+ * "cut" constraints, but replacing the adjacent inequality by
+ * its opposite and adding the valid constraints of the other
+ * basic map results in a subset of the other basic map
+ * => the pair can be replaced by a basic map consisting
+ * of the valid constraints in both basic maps
+ *
+ * 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, if the inequality the basic map is relaxed
* and then turned into an equality, then resulting facet lies
- * entirely inside the other basic set
- * => the pair can be replaced by the basic set containing
+ * entirely inside the other basic map
+ * => the pair can be replaced by the basic map containing
* the inequality, with the inequality relaxed.
*
+ * 6. 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
+ *
+ * 7. 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
+ *
+ * 8. 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 sets. When the basic sets are dropped
+ * corresponding to the basic maps. When the basic maps are dropped
* or combined, the tableaus are modified accordingly.
*/
-static int coalesce_pair(struct isl_set *set, int i, int j,
+static int coalesce_local_pair(__isl_keep isl_map *map, int i, int j,
struct isl_tab **tabs)
{
int changed = 0;
int *ineq_i = NULL;
int *ineq_j = NULL;
- eq_i = eq_status_in(set, i, j, tabs);
- if (any(eq_i, 2 * set->p[i]->n_eq, STATUS_ERROR))
+ eq_i = eq_status_in(map->p[i], tabs[j]);
+ if (!eq_i)
goto error;
- if (any(eq_i, 2 * set->p[i]->n_eq, STATUS_SEPARATE))
+ 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(set, j, i, tabs);
- if (any(eq_j, 2 * set->p[j]->n_eq, STATUS_ERROR))
+ eq_j = eq_status_in(map->p[j], tabs[i]);
+ if (!eq_j)
+ goto error;
+ if (any(eq_j, 2 * map->p[j]->n_eq, STATUS_ERROR))
goto error;
- if (any(eq_j, 2 * set->p[j]->n_eq, STATUS_SEPARATE))
+ if (any(eq_j, 2 * map->p[j]->n_eq, STATUS_SEPARATE))
goto done;
- ineq_i = ineq_status_in(set, i, j, tabs);
- if (any(ineq_i, set->p[i]->n_ineq, STATUS_ERROR))
+ ineq_i = ineq_status_in(map->p[i], tabs[i], tabs[j]);
+ if (!ineq_i)
+ goto error;
+ if (any(ineq_i, map->p[i]->n_ineq, STATUS_ERROR))
goto error;
- if (any(ineq_i, set->p[i]->n_ineq, STATUS_SEPARATE))
+ if (any(ineq_i, map->p[i]->n_ineq, STATUS_SEPARATE))
goto done;
- ineq_j = ineq_status_in(set, j, i, tabs);
- if (any(ineq_j, set->p[j]->n_ineq, STATUS_ERROR))
+ ineq_j = ineq_status_in(map->p[j], tabs[j], tabs[i]);
+ if (!ineq_j)
goto error;
- if (any(ineq_j, set->p[j]->n_ineq, STATUS_SEPARATE))
+ if (any(ineq_j, map->p[j]->n_ineq, STATUS_ERROR))
+ goto error;
+ if (any(ineq_j, map->p[j]->n_ineq, STATUS_SEPARATE))
goto done;
- if (all(eq_i, 2 * set->p[i]->n_eq, STATUS_VALID) &&
- all(ineq_i, set->p[i]->n_ineq, STATUS_VALID)) {
- drop(set, j, tabs);
+ if (all(eq_i, 2 * map->p[i]->n_eq, STATUS_VALID) &&
+ all(ineq_i, map->p[i]->n_ineq, STATUS_VALID)) {
+ drop(map, j, tabs);
changed = 1;
- } else if (all(eq_j, 2 * set->p[j]->n_eq, STATUS_VALID) &&
- all(ineq_j, set->p[j]->n_ineq, STATUS_VALID)) {
- drop(set, i, tabs);
+ } else if (all(eq_j, 2 * map->p[j]->n_eq, STATUS_VALID) &&
+ all(ineq_j, map->p[j]->n_ineq, STATUS_VALID)) {
+ drop(map, i, tabs);
changed = 1;
- } else if (any(eq_i, 2 * set->p[i]->n_eq, STATUS_CUT) ||
- any(eq_j, 2 * set->p[j]->n_eq, STATUS_CUT)) {
- /* BAD CUT */
- } else if (any(eq_i, 2 * set->p[i]->n_eq, STATUS_ADJ_EQ) ||
- any(eq_j, 2 * set->p[j]->n_eq, STATUS_ADJ_EQ)) {
- /* ADJ EQ PAIR */
- } else if (any(eq_i, 2 * set->p[i]->n_eq, STATUS_ADJ_INEQ) ||
- any(eq_j, 2 * set->p[j]->n_eq, STATUS_ADJ_INEQ)) {
- changed = check_adj_eq(set, i, j, tabs,
+ } 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,
eq_i, ineq_i, eq_j, ineq_j);
- } else if (any(ineq_i, set->p[i]->n_ineq, STATUS_ADJ_EQ) ||
- any(ineq_j, set->p[j]->n_ineq, STATUS_ADJ_EQ)) {
+ } else if (any(ineq_i, map->p[i]->n_ineq, STATUS_ADJ_EQ) ||
+ any(ineq_j, map->p[j]->n_ineq, STATUS_ADJ_EQ)) {
/* Can't happen */
/* BAD ADJ INEQ */
- } else if (any(ineq_i, set->p[i]->n_ineq, STATUS_ADJ_INEQ) ||
- any(ineq_j, set->p[j]->n_ineq, STATUS_ADJ_INEQ)) {
- changed = check_adj_ineq(set, i, j, tabs, ineq_i, ineq_j);
- } else
- changed = check_facets(set, i, j, tabs, ineq_i, ineq_j);
+ } 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,
+ eq_i, ineq_i, eq_j, 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);
return -1;
}
-static struct isl_set *coalesce(struct isl_set *set, struct isl_tab **tabs)
+/* Do the two basic maps live in the same local space, i.e.,
+ * do they have the same (known) divs?
+ * If either basic map has any unknown divs, then we can only assume
+ * that they do not live in the same local space.
+ */
+static int same_divs(__isl_keep isl_basic_map *bmap1,
+ __isl_keep isl_basic_map *bmap2)
+{
+ int i;
+ int known;
+ int total;
+
+ if (!bmap1 || !bmap2)
+ return -1;
+ if (bmap1->n_div != bmap2->n_div)
+ return 0;
+
+ if (bmap1->n_div == 0)
+ return 1;
+
+ known = isl_basic_map_divs_known(bmap1);
+ if (known < 0 || !known)
+ return known;
+ known = isl_basic_map_divs_known(bmap2);
+ if (known < 0 || !known)
+ return known;
+
+ total = isl_basic_map_total_dim(bmap1);
+ for (i = 0; i < bmap1->n_div; ++i)
+ if (!isl_seq_eq(bmap1->div[i], bmap2->div[i], 2 + total))
+ return 0;
+
+ return 1;
+}
+
+/* Given two basic maps "i" and "j", where the divs of "i" form a subset
+ * of those of "j", check if basic map "j" is a subset of basic map "i"
+ * and, if so, drop basic map "j".
+ *
+ * We first expand the divs of basic map "i" to match those of basic map "j",
+ * using the divs and expansion computed by the caller.
+ * Then we check if all constraints of the expanded "i" are valid for "j".
+ */
+static int coalesce_subset(__isl_keep isl_map *map, int i, int j,
+ struct isl_tab **tabs, __isl_keep isl_mat *div, int *exp)
+{
+ isl_basic_map *bmap;
+ int changed = 0;
+ int *eq_i = NULL;
+ int *ineq_i = NULL;
+
+ bmap = isl_basic_map_copy(map->p[i]);
+ bmap = isl_basic_set_expand_divs(bmap, isl_mat_copy(div), exp);
+
+ if (!bmap)
+ goto error;
+
+ eq_i = eq_status_in(bmap, tabs[j]);
+ if (!eq_i)
+ goto error;
+ if (any(eq_i, 2 * bmap->n_eq, STATUS_ERROR))
+ goto error;
+ if (any(eq_i, 2 * bmap->n_eq, STATUS_SEPARATE))
+ goto done;
+
+ ineq_i = ineq_status_in(bmap, NULL, tabs[j]);
+ if (!ineq_i)
+ goto error;
+ if (any(ineq_i, bmap->n_ineq, STATUS_ERROR))
+ goto error;
+ if (any(ineq_i, bmap->n_ineq, STATUS_SEPARATE))
+ goto done;
+
+ if (all(eq_i, 2 * map->p[i]->n_eq, STATUS_VALID) &&
+ all(ineq_i, map->p[i]->n_ineq, STATUS_VALID)) {
+ drop(map, j, tabs);
+ changed = 1;
+ }
+
+done:
+ isl_basic_map_free(bmap);
+ free(eq_i);
+ free(ineq_i);
+ return 0;
+error:
+ isl_basic_map_free(bmap);
+ free(eq_i);
+ free(ineq_i);
+ return -1;
+}
+
+/* Check if the basic map "j" is a subset of basic map "i",
+ * assuming that "i" has fewer divs that "j".
+ * If not, then we change the order.
+ *
+ * If the two basic maps have the same number of divs, then
+ * they must necessarily be different. Otherwise, we would have
+ * called coalesce_local_pair. We therefore don't do try anyhing
+ * in this case.
+ *
+ * We first check if the divs of "i" are all known and form a subset
+ * of those of "j". If so, we pass control over to coalesce_subset.
+ */
+static int check_coalesce_subset(__isl_keep isl_map *map, int i, int j,
+ struct isl_tab **tabs)
+{
+ int known;
+ isl_mat *div_i, *div_j, *div;
+ int *exp1 = NULL;
+ int *exp2 = NULL;
+ isl_ctx *ctx;
+ int subset;
+
+ if (map->p[i]->n_div == map->p[j]->n_div)
+ return 0;
+ if (map->p[j]->n_div < map->p[i]->n_div)
+ return check_coalesce_subset(map, j, i, tabs);
+
+ known = isl_basic_map_divs_known(map->p[i]);
+ if (known < 0 || !known)
+ return known;
+
+ ctx = isl_map_get_ctx(map);
+
+ div_i = isl_basic_map_get_divs(map->p[i]);
+ div_j = isl_basic_map_get_divs(map->p[j]);
+
+ if (!div_i || !div_j)
+ goto error;
+
+ exp1 = isl_alloc_array(ctx, int, div_i->n_row);
+ exp2 = isl_alloc_array(ctx, int, div_j->n_row);
+ if (!exp1 || !exp2)
+ goto error;
+
+ div = isl_merge_divs(div_i, div_j, exp1, exp2);
+ if (!div)
+ goto error;
+
+ if (div->n_row == div_j->n_row)
+ subset = coalesce_subset(map, i, j, tabs, div, exp1);
+ else
+ subset = 0;
+
+ isl_mat_free(div);
+
+ isl_mat_free(div_i);
+ isl_mat_free(div_j);
+
+ free(exp2);
+ free(exp1);
+
+ return subset;
+error:
+ isl_mat_free(div_i);
+ isl_mat_free(div_j);
+ free(exp1);
+ free(exp2);
+ return -1;
+}
+
+/* Check if the union of the given pair of basic maps
+ * can be represented by a single basic map.
+ * If so, replace the pair by the single basic map and return 1.
+ * Otherwise, return 0;
+ *
+ * We first check if the two basic maps live in the same local space.
+ * If so, we do the complete check. Otherwise, we check if one is
+ * an obvious subset of the other.
+ */
+static int coalesce_pair(__isl_keep isl_map *map, int i, int j,
+ struct isl_tab **tabs)
+{
+ int same;
+
+ same = same_divs(map->p[i], map->p[j]);
+ if (same < 0)
+ return -1;
+ if (same)
+ return coalesce_local_pair(map, i, j, tabs);
+
+ return check_coalesce_subset(map, i, j, tabs);
+}
+
+static struct isl_map *coalesce(struct isl_map *map, struct isl_tab **tabs)
{
int i, j;
- for (i = 0; i < set->n - 1; ++i)
- for (j = i + 1; j < set->n; ++j) {
+ for (i = map->n - 2; i >= 0; --i)
+restart:
+ for (j = i + 1; j < map->n; ++j) {
int changed;
- changed = coalesce_pair(set, i, j, tabs);
+ changed = coalesce_pair(map, i, j, tabs);
if (changed < 0)
goto error;
if (changed)
- return coalesce(set, tabs);
+ goto restart;
}
- return set;
+ return map;
error:
- isl_set_free(set);
+ isl_map_free(map);
return NULL;
}
-/* For each pair of basic sets in the set, check if the union of the two
- * can be represented by a single basic set.
- * If so, replace the pair by the single basic set and start over.
+/* For each pair of basic maps in the map, check if the union of the two
+ * can be represented by a single basic map.
+ * If so, replace the pair by the single basic map and start over.
+ *
+ * Since we are constructing the tableaus of the basic maps anyway,
+ * we exploit them to detect implicit equalities and redundant constraints.
+ * This also helps the coalescing as it can ignore the redundant constraints.
+ * In order to avoid confusion, we make all implicit equalities explicit
+ * in the basic maps. We don't call isl_basic_map_gauss, though,
+ * as that may affect the number of constraints.
+ * This means that we have to call isl_basic_map_gauss at the end
+ * of the computation to ensure that the basic maps are not left
+ * in an unexpected state.
*/
-struct isl_set *isl_set_coalesce(struct isl_set *set)
+struct isl_map *isl_map_coalesce(struct isl_map *map)
{
int i;
unsigned n;
- struct isl_ctx *ctx;
struct isl_tab **tabs = NULL;
- if (!set)
+ map = isl_map_remove_empty_parts(map);
+ if (!map)
return NULL;
- if (set->n <= 1)
- return set;
+ if (map->n <= 1)
+ return map;
- set = isl_set_align_divs(set);
+ map = isl_map_sort_divs(map);
+ map = isl_map_cow(map);
- tabs = isl_calloc_array(set->ctx, struct isl_tab *, set->n);
+ tabs = isl_calloc_array(map->ctx, struct isl_tab *, map->n);
if (!tabs)
goto error;
- n = set->n;
- ctx = set->ctx;
- for (i = 0; i < set->n; ++i) {
- tabs[i] = isl_tab_from_basic_set(set->p[i]);
+ n = map->n;
+ for (i = 0; i < map->n; ++i) {
+ tabs[i] = isl_tab_from_basic_map(map->p[i], 0);
if (!tabs[i])
goto error;
- if (!ISL_F_ISSET(set->p[i], ISL_BASIC_SET_NO_IMPLICIT))
- tabs[i] = isl_tab_detect_equalities(set->ctx, tabs[i]);
- if (!ISL_F_ISSET(set->p[i], ISL_BASIC_SET_NO_REDUNDANT))
- tabs[i] = isl_tab_detect_redundant(set->ctx, tabs[i]);
+ if (!ISL_F_ISSET(map->p[i], ISL_BASIC_MAP_NO_IMPLICIT))
+ if (isl_tab_detect_implicit_equalities(tabs[i]) < 0)
+ goto error;
+ map->p[i] = isl_tab_make_equalities_explicit(tabs[i],
+ map->p[i]);
+ if (!map->p[i])
+ goto error;
+ if (!ISL_F_ISSET(map->p[i], ISL_BASIC_MAP_NO_REDUNDANT))
+ if (isl_tab_detect_redundant(tabs[i]) < 0)
+ goto error;
}
- for (i = set->n - 1; i >= 0; --i)
+ for (i = map->n - 1; i >= 0; --i)
if (tabs[i]->empty)
- drop(set, i, tabs);
+ drop(map, i, tabs);
- set = coalesce(set, tabs);
+ map = coalesce(map, tabs);
- if (set)
- for (i = 0; i < set->n; ++i) {
- set->p[i] = isl_basic_set_update_from_tab(set->p[i],
+ if (map)
+ for (i = 0; i < map->n; ++i) {
+ map->p[i] = isl_basic_map_update_from_tab(map->p[i],
tabs[i]);
- if (!set->p[i])
+ map->p[i] = isl_basic_map_gauss(map->p[i], NULL);
+ map->p[i] = isl_basic_map_finalize(map->p[i]);
+ if (!map->p[i])
goto error;
- ISL_F_SET(set->p[i], ISL_BASIC_SET_NO_IMPLICIT);
- ISL_F_SET(set->p[i], ISL_BASIC_SET_NO_REDUNDANT);
+ ISL_F_SET(map->p[i], ISL_BASIC_MAP_NO_IMPLICIT);
+ ISL_F_SET(map->p[i], ISL_BASIC_MAP_NO_REDUNDANT);
}
for (i = 0; i < n; ++i)
- isl_tab_free(ctx, tabs[i]);
+ isl_tab_free(tabs[i]);
free(tabs);
- return set;
+ return map;
error:
if (tabs)
for (i = 0; i < n; ++i)
- isl_tab_free(ctx, tabs[i]);
+ isl_tab_free(tabs[i]);
free(tabs);
+ isl_map_free(map);
return NULL;
}
+
+/* For each pair of basic sets in the set, check if the union of the two
+ * can be represented by a single basic set.
+ * If so, replace the pair by the single basic set and start over.
+ */
+struct isl_set *isl_set_coalesce(struct isl_set *set)
+{
+ return (struct isl_set *)isl_map_coalesce((struct isl_map *)set);
+}
projects / platform / upstream / isl.git / blobdiff