X-Git-Url: http://review.tizen.org/git/?a=blobdiff_plain;f=isl_coalesce.c;h=ed80560c022a2abfdf34efe739eab0fe215e295a;hb=da1dc20cb7aa4509e375f703c35beaf27dfa4a15;hp=8d06e2e843c9e0c3bb766e2a6201a1606170241a;hpb=6817c5f804b1f77ab174af03b960e7c2e10fe342;p=platform%2Fupstream%2Fisl.git

diff --git a/isl_coalesce.c b/isl_coalesce.c
index 8d06e2e..ed80560 100644
--- a/isl_coalesce.c
+++ b/isl_coalesce.c
@@ -1,13 +1,15 @@
 /*
  * Copyright 2008-2009 Katholieke Universiteit Leuven
  * Copyright 2010      INRIA Saclay
+ * Copyright 2012-2013 Ecole Normale Superieure
  *
- * Use of this software is governed by the GNU LGPLv2.1 license
+ * Use of this software is governed by the MIT license
  *
  * Written by Sven Verdoolaege, 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"
@@ -15,6 +17,7 @@
 #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
@@ -38,24 +41,24 @@ static int status_in(isl_int *ineq, struct isl_tab *tab)
 	}
 }
 
-/* Compute the position of the equalities of basic map "i"
- * with respect to basic map "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_map *map, 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(map->ctx, int, 2 * map->p[i]->n_eq);
+	int *eq = isl_calloc_array(bmap_i->ctx, int, 2 * bmap_i->n_eq);
 	unsigned dim;
 
-	dim = isl_basic_map_total_dim(map->p[i]);
-	for (k = 0; k < map->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(map->p[i]->eq[k], map->p[i]->eq[k], 1+dim);
-			eq[2 * k + l] = status_in(map->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;
 		}
@@ -70,22 +73,23 @@ error:
 	return NULL;
 }
 
-/* Compute the position of the inequalities of basic map "i"
- * with respect to basic map "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_map *map, 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 = map->p[i]->n_eq;
-	int *ineq = isl_calloc_array(map->ctx, int, map->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 < map->p[i]->n_ineq; ++k) {
-		if (isl_tab_is_redundant(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(map->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)
@@ -294,6 +298,124 @@ static int check_facets(struct isl_map *map, int i, int 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 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
@@ -320,53 +442,40 @@ static int check_facets(struct isl_map *map, int i, int j,
  *         |   |
  *         |   |
  *         |___|
+ *
+ * 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_map *map, int i, int j,
-	struct isl_tab **tabs, int *ineq_i, int *ineq_j)
+	struct isl_tab **tabs, int *eq_i, int *ineq_i, int *eq_j, int *ineq_j)
 {
-	int changed = 0;
+	int count_i, count_j;
+	int cut_i, cut_j;
 
-	if (any(ineq_i, map->p[i]->n_ineq, STATUS_CUT) ||
-	    any(ineq_j, map->p[j]->n_ineq, STATUS_CUT))
-		/* ADJ INEQ CUT */
-		;
-	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, NULL, ineq_i, NULL, ineq_j, NULL);
-	/* else ADJ INEQ TOO MANY */
+	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);
 
-	return changed;
-}
+	if (count_i != 1 && count_j != 1)
+		return 0;
 
-/* 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;
+	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);
 
-	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;
-		}
-	}
+	if (!cut_i && !cut_j && count_i == 1 && count_j == 1)
+		return fuse(map, i, j, tabs, NULL, ineq_i, NULL, ineq_j, NULL);
 
-	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;
+	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
@@ -379,7 +488,7 @@ static int contains(struct isl_map *map, int i, int *ineq_i,
  * 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 thie extension.
+ * two basic maps by this extension.
  *        ____			  _____
  *       /    || 		 /     |
  *      /     ||  		/      |
@@ -387,7 +496,7 @@ static int contains(struct isl_map *map, int i, int *ineq_i,
  *       \    ||		 \     |
  *        \___||		  \____|
  */
-static int is_extension(struct isl_map *map, int i, int j, int k,
+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;
@@ -1044,11 +1153,12 @@ static int check_adj_eq(struct isl_map *map, int i, int j,
 		/* ADJ EQ TOO MANY */
 		return 0;
 
-	for (k = 0; k < map->p[i]->n_ineq ; ++k)
+	for (k = 0; k < map->p[i]->n_ineq; ++k)
 		if (ineq_i[k] == STATUS_ADJ_EQ)
 			break;
 
-	changed = is_extension(map, i, j, k, tabs, eq_i, ineq_i, eq_j, ineq_j);
+	changed = is_adj_eq_extension(map, i, j, k, tabs,
+					eq_i, ineq_i, eq_j, ineq_j);
 	if (changed)
 		return changed;
 
@@ -1160,6 +1270,7 @@ unbounded:
  * 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 map
  * on the other basic map.
@@ -1195,7 +1306,15 @@ unbounded:
  *		=> 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,
+ *	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
@@ -1203,7 +1322,7 @@ unbounded:
  *		=> 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,
+ *	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
@@ -1212,7 +1331,7 @@ unbounded:
  *		   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.
+ *	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
@@ -1221,7 +1340,7 @@ unbounded:
  *		   of the valid constraints in both basic maps together
  *		   with all wrapping constraints
  *
- *	7. the two basic maps live in adjacent hyperplanes.  In principle
+ *	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.
  *
@@ -1229,7 +1348,7 @@ unbounded:
  * corresponding to the basic maps.  When the basic maps are dropped
  * or combined, the tableaus are modified accordingly.
  */
-static int coalesce_pair(struct isl_map *map, 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;
@@ -1238,7 +1357,7 @@ static int coalesce_pair(struct isl_map *map, int i, int j,
 	int *ineq_i = NULL;
 	int *ineq_j = NULL;
 
-	eq_i = eq_status_in(map, i, j, tabs);
+	eq_i = eq_status_in(map->p[i], tabs[j]);
 	if (!eq_i)
 		goto error;
 	if (any(eq_i, 2 * map->p[i]->n_eq, STATUS_ERROR))
@@ -1246,7 +1365,7 @@ static int coalesce_pair(struct isl_map *map, int i, int j,
 	if (any(eq_i, 2 * map->p[i]->n_eq, STATUS_SEPARATE))
 		goto done;
 
-	eq_j = eq_status_in(map, j, i, tabs);
+	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))
@@ -1254,7 +1373,7 @@ static int coalesce_pair(struct isl_map *map, int i, int j,
 	if (any(eq_j, 2 * map->p[j]->n_eq, STATUS_SEPARATE))
 		goto done;
 
-	ineq_i = ineq_status_in(map, i, j, tabs);
+	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))
@@ -1262,7 +1381,7 @@ static int coalesce_pair(struct isl_map *map, int i, int j,
 	if (any(ineq_i, map->p[i]->n_ineq, STATUS_SEPARATE))
 		goto done;
 
-	ineq_j = ineq_status_in(map, j, i, tabs);
+	ineq_j = ineq_status_in(map->p[j], tabs[j], tabs[i]);
 	if (!ineq_j)
 		goto error;
 	if (any(ineq_j, map->p[j]->n_ineq, STATUS_ERROR))
@@ -1294,10 +1413,8 @@ static int coalesce_pair(struct isl_map *map, int i, int j,
 		/* 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)) {
-		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);
+		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))
@@ -1321,6 +1438,190 @@ error:
 	return -1;
 }
 
+/* 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;
@@ -1344,6 +1645,16 @@ error:
 /* 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_map *isl_map_coalesce(struct isl_map *map)
 {
@@ -1358,7 +1669,8 @@ struct isl_map *isl_map_coalesce(struct isl_map *map)
 	if (map->n <= 1)
 		return map;
 
-	map = isl_map_align_divs(map);
+	map = isl_map_sort_divs(map);
+	map = isl_map_cow(map);
 
 	tabs = isl_calloc_array(map->ctx, struct isl_tab *, map->n);
 	if (!tabs)
@@ -1372,6 +1684,10 @@ struct isl_map *isl_map_coalesce(struct isl_map *map)
 		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;
@@ -1386,6 +1702,7 @@ struct isl_map *isl_map_coalesce(struct isl_map *map)
 		for (i = 0; i < map->n; ++i) {
 			map->p[i] = isl_basic_map_update_from_tab(map->p[i],
 								    tabs[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;