X-Git-Url: http://review.tizen.org/git/?a=blobdiff_plain;f=isl_coalesce.c;h=c2c3bb44d7366e169a2337b0f2feb1546011f6f7;hb=de51a9bc4da5dd3f1f9f57c2362da6f9752c44e0;hp=1ccd208b2e58da36845b9f1a08b8b288e7ea052e;hpb=331369e303691d8e084ba6cf488f37d829be601f;p=platform%2Fupstream%2Fisl.git

diff --git a/isl_coalesce.c b/isl_coalesce.c
index 1ccd208..c2c3bb4 100644
--- a/isl_coalesce.c
+++ b/isl_coalesce.c
@@ -1,5 +1,23 @@
+/*
+ * Copyright 2008-2009 Katholieke Universiteit Leuven
+ * Copyright 2010      INRIA Saclay
+ * Copyright 2012      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
@@ -13,6 +31,7 @@ static int status_in(isl_int *ineq, struct isl_tab *tab)
 {
 	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;
@@ -22,24 +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;
 		}
@@ -54,22 +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)
@@ -129,31 +149,44 @@ static void drop(struct isl_map *map, int i, struct isl_tab **tabs)
 	map->n--;
 }
 
-/* Replace the pair of basic maps i and j but the basic map bounded
- * by the valid constraints in both basic maps.
+/* Replace the pair of basic maps i and j by the basic map bounded
+ * by the valid constraints in both basic maps and the constraint
+ * in extra (if not NULL).
  */
-static int fuse(struct isl_map *map, int i, int j, struct isl_tab **tabs,
-	int *ineq_i, int *ineq_j)
+static int fuse(struct isl_map *map, int i, int j,
+	struct isl_tab **tabs, int *eq_i, int *ineq_i, int *eq_j, int *ineq_j,
+	__isl_keep isl_mat *extra)
 {
 	int k, l;
 	struct isl_basic_map *fused = NULL;
 	struct isl_tab *fused_tab = NULL;
 	unsigned total = isl_basic_map_total_dim(map->p[i]);
+	unsigned extra_rows = extra ? extra->n_row : 0;
 
-	fused = isl_basic_map_alloc_dim(isl_dim_copy(map->p[i]->dim),
+	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);
+			map->p[i]->n_ineq + map->p[j]->n_ineq + extra_rows);
 	if (!fused)
 		goto error;
 
 	for (k = 0; k < map->p[i]->n_eq; ++k) {
-		int l = isl_basic_map_alloc_equality(fused);
+		if (eq_i && (eq_i[2 * k] != STATUS_VALID ||
+			     eq_i[2 * k + 1] != STATUS_VALID))
+			continue;
+		l = isl_basic_map_alloc_equality(fused);
+		if (l < 0)
+			goto error;
 		isl_seq_cpy(fused->eq[l], map->p[i]->eq[k], 1 + total);
 	}
 
 	for (k = 0; k < map->p[j]->n_eq; ++k) {
-		int l = isl_basic_map_alloc_equality(fused);
+		if (eq_j && (eq_j[2 * k] != STATUS_VALID ||
+			     eq_j[2 * k + 1] != STATUS_VALID))
+			continue;
+		l = isl_basic_map_alloc_equality(fused);
+		if (l < 0)
+			goto error;
 		isl_seq_cpy(fused->eq[l], map->p[j]->eq[k], 1 + total);
 	}
 
@@ -161,6 +194,8 @@ static int fuse(struct isl_map *map, int i, int j, struct isl_tab **tabs,
 		if (ineq_i[k] != STATUS_VALID)
 			continue;
 		l = isl_basic_map_alloc_inequality(fused);
+		if (l < 0)
+			goto error;
 		isl_seq_cpy(fused->ineq[l], map->p[i]->ineq[k], 1 + total);
 	}
 
@@ -168,23 +203,33 @@ static int fuse(struct isl_map *map, int i, int j, struct isl_tab **tabs,
 		if (ineq_j[k] != STATUS_VALID)
 			continue;
 		l = isl_basic_map_alloc_inequality(fused);
+		if (l < 0)
+			goto error;
 		isl_seq_cpy(fused->ineq[l], map->p[j]->ineq[k], 1 + total);
 	}
 
 	for (k = 0; k < map->p[i]->n_div; ++k) {
 		int l = isl_basic_map_alloc_div(fused);
+		if (l < 0)
+			goto error;
 		isl_seq_cpy(fused->div[l], map->p[i]->div[k], 1 + 1 + total);
 	}
 
+	for (k = 0; k < extra_rows; ++k) {
+		l = isl_basic_map_alloc_inequality(fused);
+		if (l < 0)
+			goto error;
+		isl_seq_cpy(fused->ineq[l], extra->row[k], 1 + total);
+	}
+
 	fused = isl_basic_map_gauss(fused, NULL);
 	ISL_F_SET(fused, ISL_BASIC_MAP_FINAL);
 	if (ISL_F_ISSET(map->p[i], ISL_BASIC_MAP_RATIONAL) &&
 	    ISL_F_ISSET(map->p[j], ISL_BASIC_MAP_RATIONAL))
 		ISL_F_SET(fused, ISL_BASIC_MAP_RATIONAL);
 
-	fused_tab = isl_tab_from_basic_map(fused);
-	fused_tab = isl_tab_detect_redundant(fused_tab);
-	if (!fused_tab)
+	fused_tab = isl_tab_from_basic_map(fused, 0);
+	if (isl_tab_detect_redundant(fused_tab) < 0)
 		goto error;
 
 	isl_basic_map_free(map->p[i]);
@@ -195,6 +240,7 @@ static int fuse(struct isl_map *map, int i, int j, struct isl_tab **tabs,
 
 	return 1;
 error:
+	isl_tab_free(fused_tab);
 	isl_basic_map_free(fused);
 	return -1;
 }
@@ -230,7 +276,8 @@ static int check_facets(struct isl_map *map, int i, int j,
 	for (k = 0; k < map->p[i]->n_ineq; ++k) {
 		if (ineq_i[k] != STATUS_CUT)
 			continue;
-		tabs[i] = isl_tab_select_facet(tabs[i], n_eq + k);
+		if (isl_tab_select_facet(tabs[i], n_eq + k) < 0)
+			return -1;
 		for (l = 0; l < map->p[j]->n_ineq; ++l) {
 			int stat;
 			if (ineq_j[l] != STATUS_CUT)
@@ -239,7 +286,8 @@ static int check_facets(struct isl_map *map, int i, int j,
 			if (stat != STATUS_VALID)
 				break;
 		}
-		isl_tab_rollback(tabs[i], snap);
+		if (isl_tab_rollback(tabs[i], snap) < 0)
+			return -1;
 		if (l < map->p[j]->n_ineq)
 			break;
 	}
@@ -247,7 +295,7 @@ static int check_facets(struct isl_map *map, int i, int j,
 	if (k < map->p[i]->n_ineq)
 		/* BAD CUT PAIR */
 		return 0;
-	return fuse(map, i, j, tabs, ineq_i, ineq_j);
+	return fuse(map, i, j, tabs, NULL, ineq_i, NULL, ineq_j, NULL);
 }
 
 /* Both basic maps have at least one inequality with and adjacent
@@ -288,7 +336,7 @@ static int check_adj_ineq(struct isl_map *map, int i, int 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);
+		changed = fuse(map, i, j, tabs, NULL, ineq_i, NULL, ineq_j, NULL);
 	/* else ADJ INEQ TOO MANY */
 
 	return changed;
@@ -325,18 +373,13 @@ static int contains(struct isl_map *map, int i, int *ineq_i,
 	return 1;
 }
 
-/* At least one of the basic maps has an equality that is adjacent
- * to inequality.  Make sure that only one of the basic maps has
- * such an equality and that the other basic map has exactly one
- * inequality adjacent to an equality.
- * We call the basic map that has the inequality "i" and the basic
- * map that has the equality "j".
- * If "i" has any "cut" inequality, then relaxing the inequality
- * by one would not result in a basic map that contains the other
- * basic map.
- * Otherwise, we relax the constraint, compute the corresponding
+/* Basic map "i" has an inequality "k" that is adjacent to some equality
+ * of basic map "j".  All the other inequalities are valid for "j".
+ * Check if basic map "j" forms an extension of basic map "i".
+ *
+ * In particular, we relax constraint "k", compute the corresponding
  * facet and check whether it is included in the other basic map.
- * If so, we know that relaxing the constraint extend the basic
+ * If so, we know that relaxing the constraint extends the basic
  * map with exactly the other basic map (we already know that this
  * other basic map is included in the extension, because there
  * were no "cut" inequalities in "i") and we can replace the
@@ -348,15 +391,640 @@ static int contains(struct isl_map *map, int i, int *ineq_i,
  *       \    ||		 \     |
  *        \___||		  \____|
  */
-static int check_adj_eq(struct isl_map *map, int i, int j,
+static int is_extension(struct isl_map *map, int i, int j, int k,
 	struct isl_tab **tabs, int *eq_i, int *ineq_i, int *eq_j, int *ineq_j)
 {
 	int changed = 0;
 	int super;
-	int k;
 	struct isl_tab_undo *snap, *snap2;
 	unsigned n_eq = map->p[i]->n_eq;
 
+	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;
+}
+
+/* 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)
+ */
+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;
+	isl_int max_k;
+	unsigned total = isl_basic_map_total_dim(bmap);
+
+	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 < bmap->n_ineq; ++k) {
+		if (ineq[k] == STATUS_VALID || ineq[k] == STATUS_REDUNDANT)
+			continue;
+		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;
+}
+
+/* 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 can_wrap_in_facet(struct isl_map *map, int i, int j, int k,
+	struct isl_tab **tabs, int *eq_i, int *ineq_i, int *eq_j, int *ineq_j)
+{
+	int changed = 0;
+	struct isl_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_i, *snap_j;
+
+	if (isl_tab_extend_cons(tabs[j], 1) < 0)
+		goto error;
+
+	max_wrap = 2 * (map->p[i]->n_eq + map->p[j]->n_eq) +
+		    map->p[i]->n_ineq + map->p[j]->n_ineq;
+	max_wrap *= n;
+
+	set = isl_set_union(set_from_updated_bmap(map->p[i], tabs[i]),
+			    set_from_updated_bmap(map->p[j], tabs[j]));
+	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 */
@@ -368,11 +1036,12 @@ static int check_adj_eq(struct isl_map *map, int i, int j,
 
 	/* j has an equality adjacent to an inequality in i */
 
+	if (any(eq_i, 2 * map->p[i]->n_eq, STATUS_CUT))
+		return 0;
 	if (any(ineq_i, map->p[i]->n_ineq, STATUS_CUT))
 		/* ADJ EQ CUT */
 		return 0;
-	if (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 ||
+	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))
@@ -383,22 +1052,110 @@ static int check_adj_eq(struct isl_map *map, int i, int j,
 		if (ineq_i[k] == STATUS_ADJ_EQ)
 			break;
 
-	snap = isl_tab_snap(tabs[i]);
-	tabs[i] = isl_tab_relax(tabs[i], n_eq + k);
-	snap2 = isl_tab_snap(tabs[i]);
-	tabs[i] = isl_tab_select_facet(tabs[i], n_eq + k);
-	super = contains(map, j, ineq_j, tabs[i]);
-	if (super) {
-		isl_tab_rollback(tabs[i], snap2);
-		map->p[i] = isl_basic_map_cow(map->p[i]);
-		if (!map->p[i])
-			return -1;
-		isl_int_add_ui(map->p[i]->ineq[k][0], map->p[i]->ineq[k][0], 1);
-		ISL_F_SET(map->p[i], ISL_BASIC_MAP_FINAL);
-		drop(map, j, tabs);
-		changed = 1;
-	} else
-		isl_tab_rollback(tabs[i], snap);
+	changed = is_extension(map, i, j, k, tabs, eq_i, ineq_i, eq_j, ineq_j);
+	if (changed)
+		return changed;
+
+	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;
+}
+
+/* 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;
 }
@@ -407,6 +1164,7 @@ static int check_adj_eq(struct isl_map *map, int i, int j,
  * 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.
@@ -425,7 +1183,7 @@ static int check_adj_eq(struct isl_map *map, int i, int j,
  *	adj_ineq	the given constraint is adjacent (on the outside)
  *			to an inequality of the other basic map
  *
- * We consider four cases in which we can replace the pair by a single
+ * We consider seven cases in which we can replace the pair by a single
  * basic map.  We ignore all "redundant" constraints.
  *
  *	1. all constraints of one basic map are valid
@@ -450,11 +1208,33 @@ static int check_adj_eq(struct isl_map *map, int i, int j,
  *		=> the pair can be replaced by the basic map containing
  *		   the inequality, with the inequality relaxed.
  *
+ *	5. there is a single adjacent pair of an inequality and an equality,
+ *	   the other constraints of the basic map containing the inequality are
+ *	   "valid".  Moreover, the facets corresponding to both
+ *	   the inequality and the equality can be wrapped around their
+ *	   ridges to include the other basic map
+ *		=> the pair can be replaced by a basic map consisting
+ *		   of the valid constraints in both basic maps together
+ *		   with all wrapping constraints
+ *
+ *	6. one of the basic maps extends beyond the other by at most one.
+ *	   Moreover, the facets corresponding to the cut constraints and
+ *	   the pieces of the other basic map at offset one from these cut
+ *	   constraints can be wrapped around their ridges to include
+ *	   the union of the two basic maps
+ *		=> the pair can be replaced by a basic map consisting
+ *		   of the valid constraints in both basic maps together
+ *		   with all wrapping constraints
+ *
+ *	7. the two basic maps live in adjacent hyperplanes.  In principle
+ *	   such sets can always be combined through wrapping, but we impose
+ *	   that there is only one such pair, to avoid overeager coalescing.
+ *
  * Throughout the computation, we maintain a collection of tableaus
  * corresponding to the basic maps.  When the basic maps are dropped
  * or combined, the tableaus are modified accordingly.
  */
-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;
@@ -463,25 +1243,33 @@ 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))
 		goto error;
 	if (any(eq_i, 2 * map->p[i]->n_eq, STATUS_SEPARATE))
 		goto done;
 
-	eq_j = eq_status_in(map, j, i, tabs);
+	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 * 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))
 		goto error;
 	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))
 		goto error;
 	if (any(ineq_j, map->p[j]->n_ineq, STATUS_SEPARATE))
@@ -495,12 +1283,12 @@ static int coalesce_pair(struct isl_map *map, int i, int j,
 		   all(ineq_j, map->p[j]->n_ineq, STATUS_VALID)) {
 		drop(map, i, tabs);
 		changed = 1;
-	} else if (any(eq_i, 2 * map->p[i]->n_eq, STATUS_CUT) ||
-		   any(eq_j, 2 * map->p[j]->n_eq, STATUS_CUT)) {
-		/* BAD CUT */
-	} else if (any(eq_i, 2 * map->p[i]->n_eq, STATUS_ADJ_EQ) ||
-		   any(eq_j, 2 * map->p[j]->n_eq, STATUS_ADJ_EQ)) {
-		/* ADJ EQ PAIR */
+	} else if (any(eq_i, 2 * map->p[i]->n_eq, STATUS_ADJ_EQ)) {
+		changed = check_eq_adj_eq(map, i, j, tabs,
+					eq_i, ineq_i, eq_j, ineq_j);
+	} else if (any(eq_j, 2 * map->p[j]->n_eq, STATUS_ADJ_EQ)) {
+		changed = check_eq_adj_eq(map, j, i, tabs,
+					eq_j, ineq_j, eq_i, ineq_i);
 	} else if (any(eq_i, 2 * map->p[i]->n_eq, STATUS_ADJ_INEQ) ||
 		   any(eq_j, 2 * map->p[j]->n_eq, STATUS_ADJ_INEQ)) {
 		changed = check_adj_eq(map, i, j, tabs,
@@ -511,9 +1299,18 @@ 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)) {
-		changed = check_adj_ineq(map, i, j, tabs, ineq_i, ineq_j);
-	} else
-		changed = check_facets(map, i, j, tabs, ineq_i, ineq_j);
+		if (!any(eq_i, 2 * map->p[i]->n_eq, STATUS_CUT) &&
+		    !any(eq_j, 2 * map->p[j]->n_eq, STATUS_CUT))
+			changed = check_adj_ineq(map, i, j, tabs,
+						 ineq_i, ineq_j);
+	} else {
+		if (!any(eq_i, 2 * map->p[i]->n_eq, STATUS_CUT) &&
+		    !any(eq_j, 2 * map->p[j]->n_eq, STATUS_CUT))
+			changed = check_facets(map, i, j, tabs, ineq_i, ineq_j);
+		if (!changed)
+			changed = check_wrap(map, i, j, tabs,
+						eq_i, ineq_i, eq_j, ineq_j);
+	}
 
 done:
 	free(eq_i);
@@ -529,18 +1326,203 @@ 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;
 
-	for (i = 0; i < map->n - 1; ++i)
+	for (i = map->n - 2; i >= 0; --i)
+restart:
 		for (j = i + 1; j < map->n; ++j) {
 			int changed;
 			changed = coalesce_pair(map, i, j, tabs);
 			if (changed < 0)
 				goto error;
 			if (changed)
-				return coalesce(map, tabs);
+				goto restart;
 		}
 	return map;
 error:
@@ -551,6 +1533,16 @@ 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)
 {
@@ -558,13 +1550,15 @@ struct isl_map *isl_map_coalesce(struct isl_map *map)
 	unsigned n;
 	struct isl_tab **tabs = NULL;
 
+	map = isl_map_remove_empty_parts(map);
 	if (!map)
 		return NULL;
 
 	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)
@@ -572,13 +1566,19 @@ struct isl_map *isl_map_coalesce(struct isl_map *map)
 
 	n = map->n;
 	for (i = 0; i < map->n; ++i) {
-		tabs[i] = isl_tab_from_basic_map(map->p[i]);
+		tabs[i] = isl_tab_from_basic_map(map->p[i], 0);
 		if (!tabs[i])
 			goto error;
 		if (!ISL_F_ISSET(map->p[i], ISL_BASIC_MAP_NO_IMPLICIT))
-			tabs[i] = isl_tab_detect_equalities(tabs[i]);
+			if (isl_tab_detect_implicit_equalities(tabs[i]) < 0)
+				goto error;
+		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))
-			tabs[i] = isl_tab_detect_redundant(tabs[i]);
+			if (isl_tab_detect_redundant(tabs[i]) < 0)
+				goto error;
 	}
 	for (i = map->n - 1; i >= 0; --i)
 		if (tabs[i]->empty)
@@ -590,6 +1590,7 @@ 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;
@@ -608,6 +1609,7 @@ error:
 		for (i = 0; i < n; ++i)
 			isl_tab_free(tabs[i]);
 	free(tabs);
+	isl_map_free(map);
 	return NULL;
 }
 
@@ -617,5 +1619,5 @@ error:
  */
 struct isl_set *isl_set_coalesce(struct isl_set *set)
 {
-	(struct isl_set *)isl_map_coalesce((struct isl_map *)set);
+	return (struct isl_set *)isl_map_coalesce((struct isl_map *)set);
 }