add isl_map_coalesce

2 files changed, 229 insertions, 218 deletions

diff --git a/include/isl_map.h b/include/isl_map.h
index d027f1a0..000e4178 100644
--- a/include/isl_map.h
+++ b/include/isl_map.h
@@ -265,6 +265,8 @@ void isl_map_dump(struct isl_map *map, FILE *out, int indent);
 int isl_map_fast_input_is_fixed(struct isl_map *map,
 		unsigned in, isl_int *val);
 
+struct isl_map *isl_map_coalesce(struct isl_map *map);
+
 int isl_map_fast_is_equal(struct isl_map *map1, struct isl_map *map2);
 
 #if defined(__cplusplus)
diff --git a/isl_coalesce.c b/isl_coalesce.c
index 0d5da2f5..3bb18b83 100644
--- a/isl_coalesce.c
+++ b/isl_coalesce.c
@@ -22,24 +22,24 @@ static int status_in(struct isl_ctx *ctx, isl_int *ineq, struct isl_tab *tab)
 	}
 }
 
-/* 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 "i"
+ * with respect to basic map "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,
+static int *eq_status_in(struct isl_map *map, int i, int j,
 	struct isl_tab **tabs)
 {
 	int k, l;
-	int *eq = isl_calloc_array(set->ctx, int, 2 * set->p[i]->n_eq);
+	int *eq = isl_calloc_array(map->ctx, int, 2 * map->p[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(map->p[i]);
+	for (k = 0; k < map->p[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],
+			isl_seq_neg(map->p[i]->eq[k], map->p[i]->eq[k], 1+dim);
+			eq[2 * k + l] = status_in(map->ctx, map->p[i]->eq[k],
 								    tabs[j]);
 			if (eq[2 * k + l] == STATUS_ERROR)
 				goto error;
@@ -55,22 +55,22 @@ 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 "i"
+ * with respect to basic map "j".
  */
-static int *ineq_status_in(struct isl_set *set, int i, int j,
+static int *ineq_status_in(struct isl_map *map, int i, int j,
 	struct isl_tab **tabs)
 {
 	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 = map->p[i]->n_eq;
+	int *ineq = isl_calloc_array(map->ctx, int, map->p[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 < map->p[i]->n_ineq; ++k) {
+		if (isl_tab_is_redundant(map->ctx, tabs[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(map->ctx, map->p[i]->ineq[k], tabs[j]);
 		if (ineq[k] == STATUS_ERROR)
 			goto error;
 		if (ineq[k] == STATUS_SEPARATE)
@@ -117,94 +117,94 @@ static int all(int *con, unsigned len, int status)
 	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(map->ctx, 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 but the basic map bounded
+ * by the valid constraints in both basic maps.
  */
-static int fuse(struct isl_set *set, int i, int j, struct isl_tab **tabs,
+static int fuse(struct isl_map *map, int i, int j, struct isl_tab **tabs,
 	int *ineq_i, int *ineq_j)
 {
 	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]);
 
-	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_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);
 	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) {
+		int l = isl_basic_map_alloc_equality(fused);
+		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) {
+		int l = isl_basic_map_alloc_equality(fused);
+		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);
+		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);
+		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);
+		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);
+	fused = isl_basic_map_gauss(fused, NULL);
+	ISL_F_SET(fused, ISL_BASIC_MAP_FINAL);
 
-	fused_tab = isl_tab_from_basic_set(fused);
-	fused_tab = isl_tab_detect_redundant(set->ctx, fused_tab);
+	fused_tab = isl_tab_from_basic_map(fused);
+	fused_tab = isl_tab_detect_redundant(map->ctx, fused_tab);
 	if (!fused_tab)
 		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(map->ctx, tabs[i]);
 	tabs[i] = fused_tab;
-	drop(set, j, tabs);
+	drop(map, j, tabs);
 
 	return 1;
 error:
-	isl_basic_set_free(fused);
+	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
@@ -216,43 +216,43 @@ error:
  * 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(map->ctx, 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) {
+		tabs[i] = isl_tab_select_facet(map->ctx, tabs[i], n_eq + k);
+		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->ctx, 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)
+		isl_tab_rollback(map->ctx, tabs[i], snap);
+		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, ineq_i, ineq_j);
 }
 
-/* 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.
@@ -265,7 +265,7 @@ static int check_facets(struct isl_set *set, int i, int j,
  *        \___||_/		  \_____/
  *
  * 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
  *
  *       /|
  *      / |
@@ -275,70 +275,70 @@ static int check_facets(struct isl_set *set, int i, int j,
  *         |   |
  *         |___|
  */
-static int check_adj_ineq(struct isl_set *set, int i, int j,
+static int check_adj_ineq(struct isl_map *map, int i, int j,
 	struct isl_tab **tabs, int *ineq_i, int *ineq_j)
 {
 	int changed = 0;
 
-	if (any(ineq_i, set->p[i]->n_ineq, STATUS_CUT) ||
-	    any(ineq_j, set->p[j]->n_ineq, STATUS_CUT))
+	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, 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 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);
 	/* else ADJ INEQ TOO MANY */
 
 	return changed;
 }
 
-/* Check if basic set "i" contains the basic set represented
+/* Check if basic map "i" contains the basic map represented
  * by the tableau "tab".
  */
-static int contains(struct isl_set *set, int i, int *ineq_i,
+static int contains(struct isl_map *map, int i, int *ineq_i,
 	struct isl_tab *tab)
 {
 	int k, l;
 	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(map->p[i]);
+	for (k = 0; k < map->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);
+			isl_seq_neg(map->p[i]->eq[k], map->p[i]->eq[k], 1+dim);
+			stat = status_in(map->ctx, map->p[i]->eq[k], tab);
 			if (stat != STATUS_VALID)
 				return 0;
 		}
 	}
 
-	for (k = 0; k < set->p[i]->n_ineq; ++k) {
+	for (k = 0; k < map->p[i]->n_ineq; ++k) {
 		int stat;
 		if (ineq_i[l] == STATUS_REDUNDANT)
 			continue;
-		stat = status_in(set->ctx, set->p[i]->ineq[k], tab);
+		stat = status_in(map->ctx, map->p[i]->ineq[k], tab);
 		if (stat != STATUS_VALID)
 			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
+/* 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 set that has the inequality "i" and the basic
- * set that has the equality "j".
+ * 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 set that contains the other
- * basic set.
+ * by one would not result in a basic map that contains the other
+ * basic map.
  * Otherwise, we relax the constraint, compute the corresponding
- * facet and check whether it is included in the other basic set.
+ * facet and check whether it is included in the other basic map.
  * 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
+ * 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 sets by thie extension.
+ * two basic maps by thie extension.
  *        ____			  _____
  *       /    || 		 /     |
  *      /     ||  		/      |
@@ -346,113 +346,113 @@ static int contains(struct isl_set *set, int i, int *ineq_i,
  *       \    ||		 \     |
  *        \___||		  \____|
  */
-static int check_adj_eq(struct isl_set *set, int i, int j,
+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 super;
 	int k;
 	struct isl_tab_undo *snap, *snap2;
-	unsigned n_eq = set->p[i]->n_eq;
+	unsigned n_eq = map->p[i]->n_eq;
 
-	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))
+	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(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(eq_j, 2 * map->p[j]->n_eq, STATUS_ADJ_INEQ) != 1 ||
+	    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]);
+	snap = isl_tab_snap(map->ctx, tabs[i]);
+	tabs[i] = isl_tab_relax(map->ctx, tabs[i], n_eq + k);
+	snap2 = isl_tab_snap(map->ctx, tabs[i]);
+	tabs[i] = isl_tab_select_facet(map->ctx, tabs[i], n_eq + k);
+	super = contains(map, 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])
+		isl_tab_rollback(map->ctx, tabs[i], snap2);
+		map->p[i] = isl_basic_map_cow(map->p[i]);
+		if (!map->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);
+		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(set->ctx, tabs[i], snap);
+		isl_tab_rollback(map->ctx, tabs[i], snap);
 
 	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.
+/* 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 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.
+ * 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 inequality are
- *	   "valid".  Moreover, if the inequality the basic set is relaxed
+ *	   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.
  *
  * 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_pair(struct isl_map *map, int i, int j,
 	struct isl_tab **tabs)
 {
 	int changed = 0;
@@ -461,57 +461,57 @@ static int coalesce_pair(struct isl_set *set, int i, int j,
 	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, i, j, tabs);
+	if (any(eq_i, 2 * map->p[i]->n_eq, STATUS_ERROR))
 		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_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, j, i, tabs);
+	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, i, j, tabs);
+	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, j, i, tabs);
+	if (any(ineq_j, map->p[j]->n_ineq, STATUS_ERROR))
 		goto error;
-	if (any(ineq_j, set->p[j]->n_ineq, STATUS_SEPARATE))
+	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)) {
+	} 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 * set->p[i]->n_eq, STATUS_ADJ_EQ) ||
-		   any(eq_j, 2 * set->p[j]->n_eq, STATUS_ADJ_EQ)) {
+	} 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 * 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_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 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(set, i, j, tabs, ineq_i, ineq_j);
+		changed = check_facets(map, i, j, tabs, ineq_i, ineq_j);
 
 done:
 	free(eq_i);
@@ -527,73 +527,73 @@ error:
 	return -1;
 }
 
-static struct isl_set *coalesce(struct isl_set *set, struct isl_tab **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 = 0; i < map->n - 1; ++i)
+		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);
+				return coalesce(map, tabs);
 		}
-	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.
  */
-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)
+	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_align_divs(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;
+	ctx = map->ctx;
+	for (i = 0; i < map->n; ++i) {
+		tabs[i] = isl_tab_from_basic_map(map->p[i]);
 		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))
+			tabs[i] = isl_tab_detect_equalities(map->ctx, tabs[i]);
+		if (!ISL_F_ISSET(map->p[i], ISL_BASIC_MAP_NO_REDUNDANT))
+			tabs[i] = isl_tab_detect_redundant(map->ctx, tabs[i]);
 	}
-	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])
+			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)
@@ -601,7 +601,7 @@ struct isl_set *isl_set_coalesce(struct isl_set *set)
 
 	free(tabs);
 
-	return set;
+	return map;
 error:
 	if (tabs)
 		for (i = 0; i < n; ++i)
@@ -609,3 +609,12 @@ error:
 	free(tabs);
 	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)
+{
+	(struct isl_set *)isl_map_coalesce((struct isl_map *)set);
+}