X-Git-Url: http://review.tizen.org/git/?a=blobdiff_plain;f=isl_map_simplify.c;h=4775efaa8b8501837bdb495903b12f3be5f27c79;hb=3769d58bc91ea9900b8c6aa0bf4d8b04596f7abf;hp=f37cb2ae29e2a28538f8519e6abea984deaa9ffb;hpb=11b961b0bcb5d791e5adc82a6ae8cec0fdf9077b;p=platform%2Fupstream%2Fisl.git

diff --git a/isl_map_simplify.c b/isl_map_simplify.c
index f37cb2a..4775efa 100644
--- a/isl_map_simplify.c
+++ b/isl_map_simplify.c
@@ -1,6 +1,16 @@
+/*
+ * Copyright 2008-2009 Katholieke Universiteit Leuven
+ *
+ * Use of this software is governed by the GNU LGPLv2.1 license
+ *
+ * Written by Sven Verdoolaege, K.U.Leuven, Departement
+ * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
+ */
+
 #include "isl_equalities.h"
 #include "isl_map.h"
 #include "isl_map_private.h"
+#include "isl_seq.h"
 #include "isl_tab.h"
 
 static void swap_equality(struct isl_basic_map *bmap, int a, int b)
@@ -110,7 +120,34 @@ error:
 	return NULL;
 }
 
-/* Drop n input dimensions starting at first.
+/* Move "n" divs starting at "first" to the end of the list of divs.
+ */
+static struct isl_basic_map *move_divs_last(struct isl_basic_map *bmap,
+	unsigned first, unsigned n)
+{
+	isl_int **div;
+	int i;
+
+	if (first + n == bmap->n_div)
+		return bmap;
+
+	div = isl_alloc_array(bmap->ctx, isl_int *, n);
+	if (!div)
+		goto error;
+	for (i = 0; i < n; ++i)
+		div[i] = bmap->div[first + i];
+	for (i = 0; i < bmap->n_div - first - n; ++i)
+		bmap->div[first + i] = bmap->div[first + n + i];
+	for (i = 0; i < n; ++i)
+		bmap->div[bmap->n_div - n + i] = div[i];
+	free(div);
+	return bmap;
+error:
+	isl_basic_map_free(bmap);
+	return NULL;
+}
+
+/* Drop "n" dimensions of type "type" starting at "first".
  *
  * In principle, this frees up some extra variables as the number
  * of columns remains constant, but we would have to extend
@@ -149,7 +186,13 @@ struct isl_basic_map *isl_basic_map_drop(struct isl_basic_map *bmap,
 	for (i = 0; i < bmap->n_div; ++i)
 		constraint_drop_vars(bmap->div[i]+1+offset, n, left);
 
-	bmap->dim = isl_dim_drop(bmap->dim, type, first, n);
+	if (type == isl_dim_div) {
+		bmap = move_divs_last(bmap, first, n);
+		if (!bmap)
+			goto error;
+		isl_basic_map_free_div(bmap, n);
+	} else
+		bmap->dim = isl_dim_drop(bmap->dim, type, first, n);
 	if (!bmap->dim)
 		goto error;
 
@@ -161,6 +204,13 @@ error:
 	return NULL;
 }
 
+__isl_give isl_basic_set *isl_basic_set_drop(__isl_take isl_basic_set *bset,
+	enum isl_dim_type type, unsigned first, unsigned n)
+{
+	return (isl_basic_set *)isl_basic_map_drop((isl_basic_map *)bset,
+							type, first, n);
+}
+
 struct isl_basic_map *isl_basic_map_drop_inputs(
 		struct isl_basic_map *bmap, unsigned first, unsigned n)
 {
@@ -199,6 +249,12 @@ error:
 	return NULL;
 }
 
+struct isl_set *isl_set_drop(struct isl_set *set,
+	enum isl_dim_type type, unsigned first, unsigned n)
+{
+	return (isl_set *)isl_map_drop((isl_map *)set, type, first, n);
+}
+
 struct isl_map *isl_map_drop_inputs(
 		struct isl_map *map, unsigned first, unsigned n)
 {
@@ -261,6 +317,9 @@ struct isl_basic_map *isl_basic_map_normalize_constraints(
 	isl_int gcd;
 	unsigned total = isl_basic_map_total_dim(bmap);
 
+	if (!bmap)
+		return NULL;
+
 	isl_int_init(gcd);
 	for (i = bmap->n_eq - 1; i >= 0; --i) {
 		isl_seq_gcd(bmap->eq[i]+1, total, &gcd);
@@ -308,36 +367,101 @@ struct isl_basic_map *isl_basic_map_normalize_constraints(
 struct isl_basic_set *isl_basic_set_normalize_constraints(
 	struct isl_basic_set *bset)
 {
-	(struct isl_basic_set *)isl_basic_map_normalize_constraints(
+	return (struct isl_basic_set *)isl_basic_map_normalize_constraints(
 		(struct isl_basic_map *)bset);
 }
 
-static void eliminate_div(struct isl_basic_map *bmap, isl_int *eq, unsigned div)
+/* Assumes divs have been ordered if keep_divs is set.
+ */
+static void eliminate_var_using_equality(struct isl_basic_map *bmap,
+	unsigned pos, isl_int *eq, int keep_divs, int *progress)
 {
-	int i;
-	unsigned pos = 1 + isl_dim_total(bmap->dim) + div;
-	unsigned len;
-	len = 1 + isl_basic_map_total_dim(bmap);
+	unsigned total;
+	int k;
+	int last_div;
 
-	for (i = 0; i < bmap->n_eq; ++i)
-		if (bmap->eq[i] != eq)
-			isl_seq_elim(bmap->eq[i], eq, pos, len, NULL);
+	total = isl_basic_map_total_dim(bmap);
+	last_div = isl_seq_last_non_zero(eq + 1 + isl_dim_total(bmap->dim),
+						bmap->n_div);
+	for (k = 0; k < bmap->n_eq; ++k) {
+		if (bmap->eq[k] == eq)
+			continue;
+		if (isl_int_is_zero(bmap->eq[k][1+pos]))
+			continue;
+		if (progress)
+			*progress = 1;
+		isl_seq_elim(bmap->eq[k], eq, 1+pos, 1+total, NULL);
+	}
 
-	for (i = 0; i < bmap->n_ineq; ++i)
-		isl_seq_elim(bmap->ineq[i], eq, pos, len, NULL);
+	for (k = 0; k < bmap->n_ineq; ++k) {
+		if (isl_int_is_zero(bmap->ineq[k][1+pos]))
+			continue;
+		if (progress)
+			*progress = 1;
+		isl_seq_elim(bmap->ineq[k], eq, 1+pos, 1+total, NULL);
+		ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
+	}
 
-	/* We need to be careful about circular definitions,
-	 * so for now we just remove the definitions of other divs that
-	 * depend on this div and (possibly) recompute them later.
-	 */
-	for (i = 0; i < bmap->n_div; ++i)
-		if (!isl_int_is_zero(bmap->div[i][0]) &&
-		    !isl_int_is_zero(bmap->div[i][1 + pos]))
-			isl_seq_clr(bmap->div[i], 1 + len);
+	for (k = 0; k < bmap->n_div; ++k) {
+		if (isl_int_is_zero(bmap->div[k][0]))
+			continue;
+		if (isl_int_is_zero(bmap->div[k][1+1+pos]))
+			continue;
+		if (progress)
+			*progress = 1;
+		/* We need to be careful about circular definitions,
+		 * so for now we just remove the definition of div k
+		 * if the equality contains any divs.
+		 * If keep_divs is set, then the divs have been ordered
+		 * and we can keep the definition as long as the result
+		 * is still ordered.
+		 */
+		if (last_div == -1 || (keep_divs && last_div < k))
+			isl_seq_elim(bmap->div[k]+1, eq,
+					1+pos, 1+total, &bmap->div[k][0]);
+		else
+			isl_seq_clr(bmap->div[k], 1 + total);
+		ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
+	}
+}
+
+/* Assumes divs have been ordered if keep_divs is set.
+ */
+static void eliminate_div(struct isl_basic_map *bmap, isl_int *eq,
+	unsigned div, int keep_divs)
+{
+	unsigned pos = isl_dim_total(bmap->dim) + div;
+
+	eliminate_var_using_equality(bmap, pos, eq, keep_divs, NULL);
 
 	isl_basic_map_drop_div(bmap, div);
 }
 
+/* Check if elimination of div "div" using equality "eq" would not
+ * result in a div depending on a later div.
+ */
+static int ok_to_eliminate_div(struct isl_basic_map *bmap, isl_int *eq,
+	unsigned div)
+{
+	int k;
+	int last_div;
+	unsigned pos = isl_dim_total(bmap->dim) + div;
+
+	last_div = isl_seq_last_non_zero(eq + 1 + isl_dim_total(bmap->dim),
+						bmap->n_div);
+	if (last_div < 0 || last_div <= div)
+		return 1;
+
+	for (k = 0; k <= last_div; ++k) {
+		if (isl_int_is_zero(bmap->div[k][0]))
+			return 1;
+		if (!isl_int_is_zero(bmap->div[k][1 + 1 + pos]))
+			return 0;
+	}
+
+	return 1;
+}
+
 /* Elimininate divs based on equalities
  */
 static struct isl_basic_map *eliminate_divs_eq(
@@ -348,6 +472,8 @@ static struct isl_basic_map *eliminate_divs_eq(
 	int modified = 0;
 	unsigned off;
 
+	bmap = isl_basic_map_order_divs(bmap);
+
 	if (!bmap)
 		return NULL;
 
@@ -358,9 +484,11 @@ static struct isl_basic_map *eliminate_divs_eq(
 			if (!isl_int_is_one(bmap->eq[i][off + d]) &&
 			    !isl_int_is_negone(bmap->eq[i][off + d]))
 				continue;
+			if (!ok_to_eliminate_div(bmap, bmap->eq[i], d))
+				continue;
 			modified = 1;
 			*progress = 1;
-			eliminate_div(bmap, bmap->eq[i], d);
+			eliminate_div(bmap, bmap->eq[i], d, 1);
 			isl_basic_map_drop_equality(bmap, i);
 			break;
 		}
@@ -399,7 +527,7 @@ static struct isl_basic_map *eliminate_divs_ineq(
 			continue;
 		*progress = 1;
 		bmap = isl_basic_map_eliminate_vars(bmap, (off-1)+d, 1);
-		if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
+		if (!bmap || ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
 			break;
 		bmap = isl_basic_map_drop_div(bmap, d);
 		if (!bmap)
@@ -408,56 +536,6 @@ static struct isl_basic_map *eliminate_divs_ineq(
 	return bmap;
 }
 
-static void eliminate_var_using_equality(struct isl_basic_map *bmap,
-	unsigned pos, isl_int *eq, int *progress)
-{
-	unsigned total;
-	int k;
-	int contains_divs;
-
-	total = isl_basic_map_total_dim(bmap);
-	contains_divs =
-		isl_seq_first_non_zero(eq + 1 + isl_dim_total(bmap->dim),
-						bmap->n_div) != -1;
-	for (k = 0; k < bmap->n_eq; ++k) {
-		if (bmap->eq[k] == eq)
-			continue;
-		if (isl_int_is_zero(bmap->eq[k][1+pos]))
-			continue;
-		if (progress)
-			*progress = 1;
-		isl_seq_elim(bmap->eq[k], eq, 1+pos, 1+total, NULL);
-	}
-
-	for (k = 0; k < bmap->n_ineq; ++k) {
-		if (isl_int_is_zero(bmap->ineq[k][1+pos]))
-			continue;
-		if (progress)
-			*progress = 1;
-		isl_seq_elim(bmap->ineq[k], eq, 1+pos, 1+total, NULL);
-		ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
-	}
-
-	for (k = 0; k < bmap->n_div; ++k) {
-		if (isl_int_is_zero(bmap->div[k][0]))
-			continue;
-		if (isl_int_is_zero(bmap->div[k][1+1+pos]))
-			continue;
-		if (progress)
-			*progress = 1;
-		/* We need to be careful about circular definitions,
-		 * so for now we just remove the definition of div k
-		 * if the equality contains any divs.
-		 */
-		if (contains_divs)
-			isl_seq_clr(bmap->div[k], 1 + total);
-		else
-			isl_seq_elim(bmap->div[k]+1, eq,
-					1+pos, 1+total, &bmap->div[k][0]);
-		ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
-	}
-}
-
 struct isl_basic_map *isl_basic_map_gauss(
 	struct isl_basic_map *bmap, int *progress)
 {
@@ -467,6 +545,8 @@ struct isl_basic_map *isl_basic_map_gauss(
 	unsigned total_var;
 	unsigned total;
 
+	bmap = isl_basic_map_order_divs(bmap);
+
 	if (!bmap)
 		return NULL;
 
@@ -489,7 +569,7 @@ struct isl_basic_map *isl_basic_map_gauss(
 		if (isl_int_is_neg(bmap->eq[done][1+last_var]))
 			isl_seq_neg(bmap->eq[done], bmap->eq[done], 1+total);
 
-		eliminate_var_using_equality(bmap, last_var, bmap->eq[done],
+		eliminate_var_using_equality(bmap, last_var, bmap->eq[done], 1,
 						progress);
 
 		if (last_var >= total_var &&
@@ -565,13 +645,16 @@ static struct isl_basic_map *remove_duplicate_divs(
 	int k, l, h;
 	int bits;
 	struct isl_blk eq;
-	unsigned total_var = isl_dim_total(bmap->dim);
-	unsigned total = total_var + bmap->n_div;
+	unsigned total_var;
+	unsigned total;
 	struct isl_ctx *ctx;
 
-	if (bmap->n_div <= 1)
+	if (!bmap || bmap->n_div <= 1)
 		return bmap;
 
+	total_var = isl_dim_total(bmap->dim);
+	total = total_var + bmap->n_div;
+
 	ctx = bmap->ctx;
 	for (k = bmap->n_div - 1; k >= 0; --k)
 		if (!isl_int_is_zero(bmap->div[k][0]))
@@ -615,7 +698,7 @@ static struct isl_basic_map *remove_duplicate_divs(
 		k = elim_for[l] - 1;
 		isl_int_set_si(eq.data[1+total_var+k], -1);
 		isl_int_set_si(eq.data[1+total_var+l], 1);
-		eliminate_div(bmap, eq.data, l);
+		eliminate_div(bmap, eq.data, l, 0);
 		isl_int_set_si(eq.data[1+total_var+k], 0);
 		isl_int_set_si(eq.data[1+total_var+l], 0);
 	}
@@ -627,6 +710,23 @@ out:
 	return bmap;
 }
 
+static int n_pure_div_eq(struct isl_basic_map *bmap)
+{
+	int i, j;
+	unsigned total;
+
+	total = isl_dim_total(bmap->dim);
+	for (i = 0, j = bmap->n_div-1; i < bmap->n_eq; ++i) {
+		while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
+			--j;
+		if (j < 0)
+			break;
+		if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total, j) != -1)
+			return 0;
+	}
+	return i;
+}
+
 /* Normalize divs that appear in equalities.
  *
  * In particular, we assume that bmap contains some equalities
@@ -703,28 +803,20 @@ static struct isl_basic_map *normalize_divs(
 		return bmap;
 
 	total = isl_dim_total(bmap->dim);
-	for (i = 0, j = bmap->n_div-1; i < bmap->n_eq; ++i) {
-		while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
-			--j;
-		if (j < 0)
-			break;
-		if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total, j) != -1)
-			goto done;
-	}
-	div_eq = i;
+	div_eq = n_pure_div_eq(bmap);
 	if (div_eq == 0)
 		return bmap;
 
 	if (div_eq < bmap->n_eq) {
 		B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, div_eq,
 					bmap->n_eq - div_eq, 0, 1 + total);
-		C = isl_mat_variable_compression(bmap->ctx, B, &C2);
+		C = isl_mat_variable_compression(B, &C2);
 		if (!C || !C2)
 			goto error;
 		if (C->n_col == 0) {
 			bmap = isl_basic_map_set_to_empty(bmap);
-			isl_mat_free(bmap->ctx, C);
-			isl_mat_free(bmap->ctx, C2);
+			isl_mat_free(C);
+			isl_mat_free(C2);
 			goto done;
 		}
 	}
@@ -740,17 +832,17 @@ static struct isl_basic_map *normalize_divs(
 	B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, 0, div_eq, 0, 1 + total);
 
 	if (C) {
-		B = isl_mat_product(bmap->ctx, B, C);
+		B = isl_mat_product(B, C);
 		C = NULL;
 	}
 
-	T = isl_mat_parameter_compression(bmap->ctx, B, d);
+	T = isl_mat_parameter_compression(B, d);
 	if (!T)
 		goto error;
 	if (T->n_col == 0) {
 		bmap = isl_basic_map_set_to_empty(bmap);
-		isl_mat_free(bmap->ctx, C2);
-		isl_mat_free(bmap->ctx, T);
+		isl_mat_free(C2);
+		isl_mat_free(T);
 		goto done;
 	}
 	isl_int_init(v);
@@ -762,6 +854,8 @@ static struct isl_basic_map *normalize_divs(
 	}
 	isl_int_clear(v);
 	pos = isl_alloc_array(bmap->ctx, int, T->n_row);
+	if (!pos)
+		goto error;
 	/* We have to be careful because dropping equalities may reorder them */
 	dropped = 0;
 	for (j = bmap->n_div - 1; j >= 0; --j) {
@@ -814,18 +908,105 @@ static struct isl_basic_map *normalize_divs(
 		isl_int_set(bmap->eq[j][pos[i]], bmap->div[k][0]);
 	}
 	free(pos);
-	isl_mat_free(bmap->ctx, C2);
-	isl_mat_free(bmap->ctx, T);
+	isl_mat_free(C2);
+	isl_mat_free(T);
 
-	*progress = 1;
+	if (progress)
+		*progress = 1;
 done:
 	ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
 
 	return bmap;
 error:
-	isl_mat_free(bmap->ctx, C);
-	isl_mat_free(bmap->ctx, C2);
-	isl_mat_free(bmap->ctx, T);
+	isl_mat_free(C);
+	isl_mat_free(C2);
+	isl_mat_free(T);
+	return bmap;
+}
+
+static struct isl_basic_map *set_div_from_lower_bound(
+	struct isl_basic_map *bmap, int div, int ineq)
+{
+	unsigned total = 1 + isl_dim_total(bmap->dim);
+
+	isl_seq_neg(bmap->div[div] + 1, bmap->ineq[ineq], total + bmap->n_div);
+	isl_int_set(bmap->div[div][0], bmap->ineq[ineq][total + div]);
+	isl_int_add(bmap->div[div][1], bmap->div[div][1], bmap->div[div][0]);
+	isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
+	isl_int_set_si(bmap->div[div][1 + total + div], 0);
+
+	return bmap;
+}
+
+/* Check whether it is ok to define a div based on an inequality.
+ * To avoid the introduction of circular definitions of divs, we
+ * do not allow such a definition if the resulting expression would refer to
+ * any other undefined divs or if any known div is defined in
+ * terms of the unknown div.
+ */
+static int ok_to_set_div_from_bound(struct isl_basic_map *bmap,
+	int div, int ineq)
+{
+	int j;
+	unsigned total = 1 + isl_dim_total(bmap->dim);
+
+	/* Not defined in terms of unknown divs */
+	for (j = 0; j < bmap->n_div; ++j) {
+		if (div == j)
+			continue;
+		if (isl_int_is_zero(bmap->ineq[ineq][total + j]))
+			continue;
+		if (isl_int_is_zero(bmap->div[j][0]))
+			return 0;
+	}
+
+	/* No other div defined in terms of this one => avoid loops */
+	for (j = 0; j < bmap->n_div; ++j) {
+		if (div == j)
+			continue;
+		if (isl_int_is_zero(bmap->div[j][0]))
+			continue;
+		if (!isl_int_is_zero(bmap->div[j][1 + total + div]))
+			return 0;
+	}
+
+	return 1;
+}
+
+/* Given two constraints "k" and "l" that are opposite to each other,
+ * except for the constant term, check if we can use them
+ * to obtain an expression for one of the hitherto unknown divs.
+ * "sum" is the sum of the constant terms of the constraints.
+ * If this sum is strictly smaller than the coefficient of one
+ * of the divs, then this pair can be used define the div.
+ * To avoid the introduction of circular definitions of divs, we
+ * do not use the pair if the resulting expression would refer to
+ * any other undefined divs or if any known div is defined in
+ * terms of the unknown div.
+ */
+static struct isl_basic_map *check_for_div_constraints(
+	struct isl_basic_map *bmap, int k, int l, isl_int sum, int *progress)
+{
+	int i;
+	unsigned total = 1 + isl_dim_total(bmap->dim);
+
+	for (i = 0; i < bmap->n_div; ++i) {
+		if (!isl_int_is_zero(bmap->div[i][0]))
+			continue;
+		if (isl_int_is_zero(bmap->ineq[k][total + i]))
+			continue;
+		if (isl_int_abs_ge(sum, bmap->ineq[k][total + i]))
+			continue;
+		if (!ok_to_set_div_from_bound(bmap, i, k))
+			break;
+		if (isl_int_is_pos(bmap->ineq[k][total + i]))
+			bmap = set_div_from_lower_bound(bmap, i, k);
+		else
+			bmap = set_div_from_lower_bound(bmap, i, l);
+		if (progress)
+			*progress = 1;
+		break;
+	}
 	return bmap;
 }
 
@@ -839,7 +1020,7 @@ static struct isl_basic_map *remove_duplicate_constraints(
 	unsigned total = isl_basic_map_total_dim(bmap);
 	isl_int sum;
 
-	if (bmap->n_ineq <= 1)
+	if (!bmap || bmap->n_ineq <= 1)
 		return bmap;
 
 	size = round_up(4 * (bmap->n_ineq+1) / 3 - 1);
@@ -872,14 +1053,19 @@ static struct isl_basic_map *remove_duplicate_constraints(
 			continue;
 		l = index[h] - &bmap->ineq[0];
 		isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0]);
-		if (isl_int_is_pos(sum))
+		if (isl_int_is_pos(sum)) {
+			bmap = check_for_div_constraints(bmap, k, l, sum,
+							 progress);
 			continue;
+		}
 		if (isl_int_is_zero(sum)) {
 			/* We need to break out of the loop after these
 			 * changes since the contents of the hash
 			 * will no longer be valid.
 			 * Plus, we probably we want to regauss first.
 			 */
+			if (progress)
+				*progress = 1;
 			isl_basic_map_drop_inequality(bmap, l);
 			isl_basic_map_inequality_to_equality(bmap, k);
 		} else
@@ -901,12 +1087,12 @@ struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
 	while (progress) {
 		progress = 0;
 		bmap = isl_basic_map_normalize_constraints(bmap);
+		bmap = remove_duplicate_divs(bmap, &progress);
 		bmap = eliminate_divs_eq(bmap, &progress);
 		bmap = eliminate_divs_ineq(bmap, &progress);
 		bmap = isl_basic_map_gauss(bmap, &progress);
 		/* requires equalities in normal form */
 		bmap = normalize_divs(bmap, &progress);
-		bmap = remove_duplicate_divs(bmap, &progress);
 		bmap = remove_duplicate_constraints(bmap, &progress);
 	}
 	return bmap;
@@ -919,6 +1105,43 @@ struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset)
 }
 
 
+int isl_basic_map_is_div_constraint(__isl_keep isl_basic_map *bmap,
+	isl_int *constraint, unsigned div)
+{
+	unsigned pos;
+
+	if (!bmap)
+		return -1;
+
+	pos = 1 + isl_dim_total(bmap->dim) + div;
+
+	if (isl_int_eq(constraint[pos], bmap->div[div][0])) {
+		int neg;
+		isl_int_sub(bmap->div[div][1],
+				bmap->div[div][1], bmap->div[div][0]);
+		isl_int_add_ui(bmap->div[div][1], bmap->div[div][1], 1);
+		neg = isl_seq_is_neg(constraint, bmap->div[div]+1, pos);
+		isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
+		isl_int_add(bmap->div[div][1],
+				bmap->div[div][1], bmap->div[div][0]);
+		if (!neg)
+			return 0;
+		if (isl_seq_first_non_zero(constraint+pos+1,
+					    bmap->n_div-div-1) != -1)
+			return 0;
+	} else if (isl_int_abs_eq(constraint[pos], bmap->div[div][0])) {
+		if (!isl_seq_eq(constraint, bmap->div[div]+1, pos))
+			return 0;
+		if (isl_seq_first_non_zero(constraint+pos+1,
+					    bmap->n_div-div-1) != -1)
+			return 0;
+	} else
+		return 0;
+
+	return 1;
+}
+
+
 /* If the only constraints a div d=floor(f/m)
  * appears in are its two defining constraints
  *
@@ -939,27 +1162,7 @@ static int div_is_redundant(struct isl_basic_map *bmap, int div)
 	for (i = 0; i < bmap->n_ineq; ++i) {
 		if (isl_int_is_zero(bmap->ineq[i][pos]))
 			continue;
-		if (isl_int_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
-			int neg;
-			isl_int_sub(bmap->div[div][1],
-					bmap->div[div][1], bmap->div[div][0]);
-			isl_int_add_ui(bmap->div[div][1], bmap->div[div][1], 1);
-			neg = isl_seq_is_neg(bmap->ineq[i], bmap->div[div]+1, pos);
-			isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
-			isl_int_add(bmap->div[div][1],
-					bmap->div[div][1], bmap->div[div][0]);
-			if (!neg)
-				return 0;
-			if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
-						    bmap->n_div-div-1) != -1)
-				return 0;
-		} else if (isl_int_abs_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
-			if (!isl_seq_eq(bmap->ineq[i], bmap->div[div]+1, pos))
-				return 0;
-			if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
-						    bmap->n_div-div-1) != -1)
-				return 0;
-		} else
+		if (!isl_basic_map_is_div_constraint(bmap, bmap->ineq[i], div))
 			return 0;
 	}
 
@@ -1041,22 +1244,21 @@ error:
 }
 
 
-/* Remove any div that is defined in terms of the given variable.
+/* Remove definition of any div that is defined in terms of the given variable.
+ * The div itself is not removed.  Functions such as
+ * eliminate_divs_ineq depend on the other divs remaining in place.
  */
 static struct isl_basic_map *remove_dependent_vars(struct isl_basic_map *bmap,
 									int pos)
 {
 	int i;
-	unsigned dim = isl_dim_total(bmap->dim);
 
 	for (i = 0; i < bmap->n_div; ++i) {
 		if (isl_int_is_zero(bmap->div[i][0]))
 			continue;
 		if (isl_int_is_zero(bmap->div[i][1+1+pos]))
 			continue;
-		bmap = isl_basic_map_eliminate_vars(bmap, dim + i, 1);
-		if (!bmap)
-			return NULL;
+		isl_int_set_si(bmap->div[i][0], 0);
 	}
 	return bmap;
 }
@@ -1091,7 +1293,7 @@ struct isl_basic_map *isl_basic_map_eliminate_vars(
 		for (i = 0; i < bmap->n_eq; ++i) {
 			if (isl_int_is_zero(bmap->eq[i][1+d]))
 				continue;
-			eliminate_var_using_equality(bmap, d, bmap->eq[i], NULL);
+			eliminate_var_using_equality(bmap, d, bmap->eq[i], 0, NULL);
 			isl_basic_map_drop_equality(bmap, i);
 			break;
 		}
@@ -1107,6 +1309,8 @@ struct isl_basic_map *isl_basic_map_eliminate_vars(
 		}
 		bmap = isl_basic_map_extend_constraints(bmap,
 				0, n_lower * n_upper);
+		if (!bmap)
+			goto error;
 		for (i = bmap->n_ineq - 1; i >= 0; --i) {
 			int last;
 			if (isl_int_is_zero(bmap->ineq[i][1+d]))
@@ -1134,7 +1338,7 @@ struct isl_basic_map *isl_basic_map_eliminate_vars(
 			bmap = isl_basic_map_normalize_constraints(bmap);
 			bmap = remove_duplicate_constraints(bmap, NULL);
 			bmap = isl_basic_map_gauss(bmap, NULL);
-			bmap = isl_basic_map_convex_hull(bmap);
+			bmap = isl_basic_map_remove_redundancies(bmap);
 			if (!bmap)
 				goto error;
 			if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
@@ -1178,13 +1382,13 @@ static void compute_elimination_index(struct isl_basic_map *bmap, int *elim)
 
 static void set_compute_elimination_index(struct isl_basic_set *bset, int *elim)
 {
-	return compute_elimination_index((struct isl_basic_map *)bset, elim);
+	compute_elimination_index((struct isl_basic_map *)bset, elim);
 }
 
 static int reduced_using_equalities(isl_int *dst, isl_int *src,
 	struct isl_basic_map *bmap, int *elim)
 {
-	int d, i;
+	int d;
 	int copied = 0;
 	unsigned total;
 
@@ -1219,11 +1423,16 @@ static struct isl_basic_set *isl_basic_set_reduce_using_equalities(
 	if (!bset || !context)
 		goto error;
 
+	if (context->n_eq == 0) {
+		isl_basic_set_free(context);
+		return bset;
+	}
+
 	bset = isl_basic_set_cow(bset);
 	if (!bset)
 		goto error;
 
-	elim = isl_alloc_array(ctx, int, isl_basic_set_n_dim(bset));
+	elim = isl_alloc_array(bset->ctx, int, isl_basic_set_n_dim(bset));
 	if (!elim)
 		goto error;
 	set_compute_elimination_index(context, elim);
@@ -1336,22 +1545,25 @@ static struct isl_basic_set *normalize_constraints_in_compressed_space(
 	if (ISL_F_ISSET(bset, ISL_BASIC_SET_RATIONAL))
 		return bset;
 
+	if (!bset->n_ineq)
+		return bset;
+
 	bset = isl_basic_set_cow(bset);
 	if (!bset)
 		return NULL;
 
 	total = isl_basic_set_total_dim(bset);
 	B = isl_mat_sub_alloc(bset->ctx, bset->eq, 0, bset->n_eq, 0, 1 + total);
-	C = isl_mat_variable_compression(bset->ctx, B, NULL);
+	C = isl_mat_variable_compression(B, NULL);
 	if (!C)
 		return bset;
 	if (C->n_col == 0) {
-		isl_mat_free(bset->ctx, C);
+		isl_mat_free(C);
 		return isl_basic_set_set_to_empty(bset);
 	}
 	B = isl_mat_sub_alloc(bset->ctx, bset->ineq,
 						0, bset->n_ineq, 0, 1 + total);
-	C = isl_mat_product(bset->ctx, B, C);
+	C = isl_mat_product(B, C);
 	if (!C)
 		return bset;
 
@@ -1365,117 +1577,227 @@ static struct isl_basic_set *normalize_constraints_in_compressed_space(
 	}
 	isl_int_clear(gcd);
 
-	isl_mat_free(bset->ctx, C);
+	isl_mat_free(C);
 
 	return bset;
 }
 
 /* Remove all information from bset that is redundant in the context
- * of context.  In particular, equalities that are linear combinations
- * of those in context are removed.  Then the inequalities that are
- * redundant in the context of the equalities and inequalities of
- * context are removed.
+ * of context.  Both bset and context are assumed to be full-dimensional.
  *
- * We first simplify the constraints of "bset" in the context of the
- * equalities of "context".
- * Then we simplify the inequalities of the context in the context
- * of the equalities of bset and remove the inequalities from "bset"
+ * We first * remove the inequalities from "bset"
  * that are obviously redundant with respect to some inequality in "context".
  *
  * If there are any inequalities left, we construct a tableau for
  * the context and then add the inequalities of "bset".
- * Before adding these equalities, we freeze all constraints such that
+ * Before adding these inequalities, we freeze all constraints such that
  * they won't be considered redundant in terms of the constraints of "bset".
- * Then we detect all equalities and redundant constraints (among the
- * constraints that weren't frozen) and update bset according to the results.
- * We have to be careful here because we don't want any of the context
- * constraints to remain and because we haven't added the equalities of "bset"
- * to the tableau so we temporarily have to pretend that there were no
- * equalities.
+ * Then we detect all redundant constraints (among the
+ * constraints that weren't frozen), first by checking for redundancy in the
+ * the tableau and then by checking if replacing a constraint by its negation
+ * would lead to an empty set.  This last step is fairly expensive
+ * and could be optimized by more reuse of the tableau.
+ * Finally, we update bset according to the results.
  */
-static struct isl_basic_set *uset_gist(struct isl_basic_set *bset,
-	struct isl_basic_set *context)
+static __isl_give isl_basic_set *uset_gist_full(__isl_take isl_basic_set *bset,
+	__isl_take isl_basic_set *context)
 {
-	int i;
-	struct isl_tab *tab;
-	unsigned context_ineq, bset_eq;
-	struct isl_basic_set *combined = NULL;
+	int i, k;
+	isl_basic_set *combined = NULL;
+	struct isl_tab *tab = NULL;
+	unsigned context_ineq;
+	unsigned total;
 
-	if (!context || !bset)
+	if (!bset || !context)
 		goto error;
 
-	if (context->n_eq > 0)
-		bset = isl_basic_set_reduce_using_equalities(bset,
-					isl_basic_set_copy(context));
+	if (isl_basic_set_is_universe(bset)) {
+		isl_basic_set_free(context);
+		return bset;
+	}
+
+	if (isl_basic_set_is_universe(context)) {
+		isl_basic_set_free(context);
+		return bset;
+	}
+
+	bset = remove_shifted_constraints(bset, context);
 	if (!bset)
 		goto error;
+	if (bset->n_ineq == 0)
+		goto done;
 
-	if (bset->n_eq > 0) {
-		struct isl_basic_set *affine_hull;
-		affine_hull = isl_basic_set_copy(bset);
-		affine_hull = isl_basic_set_cow(affine_hull);
-		if (!affine_hull)
-			goto error;
-		isl_basic_set_free_inequality(affine_hull, affine_hull->n_ineq);
-		context = isl_basic_set_intersect(context, affine_hull);
-		context = isl_basic_set_gauss(context, NULL);
-		context = normalize_constraints_in_compressed_space(context);
-	}
-	if (!context)
-		goto error;
-	if (ISL_F_ISSET(context, ISL_BASIC_SET_EMPTY)) {
-		isl_basic_set_free(bset);
-		return context;
-	}
-	if (!context->n_ineq)
-		goto done;
-	bset = remove_shifted_constraints(bset, context);
-	if (!bset->n_ineq)
-		goto done;
-	isl_basic_set_free_equality(context, context->n_eq);
 	context_ineq = context->n_ineq;
 	combined = isl_basic_set_cow(isl_basic_set_copy(context));
-	combined = isl_basic_set_extend_constraints(combined,
-						    bset->n_eq, bset->n_ineq);
+	combined = isl_basic_set_extend_constraints(combined, 0, bset->n_ineq);
 	tab = isl_tab_from_basic_set(combined);
-	if (!tab)
-		goto error;
 	for (i = 0; i < context_ineq; ++i)
-		tab->con[i].frozen = 1;
-	tab = isl_tab_extend(bset->ctx, tab, bset->n_ineq);
-	if (!tab)
-		goto error;
+		if (isl_tab_freeze_constraint(tab, i) < 0)
+			goto error;
+	tab = isl_tab_extend(tab, bset->n_ineq);
 	for (i = 0; i < bset->n_ineq; ++i)
-		tab = isl_tab_add_ineq(bset->ctx, tab, bset->ineq[i]);
+		if (isl_tab_add_ineq(tab, bset->ineq[i]) < 0)
+			goto error;
 	bset = isl_basic_set_add_constraints(combined, bset, 0);
-	tab = isl_tab_detect_equalities(bset->ctx, tab);
-	tab = isl_tab_detect_redundant(bset->ctx, tab);
-	if (!tab)
-		goto error2;
-	for (i = 0; i < context_ineq; ++i) {
-		tab->con[i].is_zero = 0;
+	combined = NULL;
+	if (!bset)
+		goto error;
+	if (isl_tab_detect_redundant(tab) < 0)
+		goto error;
+	total = isl_basic_set_total_dim(bset);
+	for (i = context_ineq; i < bset->n_ineq; ++i) {
+		int is_empty;
+		if (tab->con[i].is_redundant)
+			continue;
 		tab->con[i].is_redundant = 1;
+		combined = isl_basic_set_dup(bset);
+		combined = isl_basic_set_update_from_tab(combined, tab);
+		combined = isl_basic_set_extend_constraints(combined, 0, 1);
+		k = isl_basic_set_alloc_inequality(combined);
+		if (k < 0)
+			goto error;
+		isl_seq_neg(combined->ineq[k], bset->ineq[i], 1 + total);
+		isl_int_sub_ui(combined->ineq[k][0], combined->ineq[k][0], 1);
+		is_empty = isl_basic_set_is_empty(combined);
+		if (is_empty < 0)
+			goto error;
+		isl_basic_set_free(combined);
+		combined = NULL;
+		if (!is_empty)
+			tab->con[i].is_redundant = 0;
 	}
-	bset_eq = bset->n_eq;
-	bset->n_eq = 0;
+	for (i = 0; i < context_ineq; ++i)
+		tab->con[i].is_redundant = 1;
 	bset = isl_basic_set_update_from_tab(bset, tab);
-	bset->n_eq = bset_eq;
-	isl_tab_free(bset->ctx, tab);
-	ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
-	ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
+	if (bset) {
+		ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
+		ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
+	}
+
+	isl_tab_free(tab);
 done:
 	bset = isl_basic_set_simplify(bset);
 	bset = isl_basic_set_finalize(bset);
 	isl_basic_set_free(context);
 	return bset;
 error:
+	isl_tab_free(tab);
 	isl_basic_set_free(combined);
-error2:
+	isl_basic_set_free(context);
+	isl_basic_set_free(bset);
+	return NULL;
+}
+
+/* Remove all information from bset that is redundant in the context
+ * of context.  In particular, equalities that are linear combinations
+ * of those in context are removed.  Then the inequalities that are
+ * redundant in the context of the equalities and inequalities of
+ * context are removed.
+ *
+ * We first compute the integer affine hull of the intersection,
+ * compute the gist inside this affine hull and then add back
+ * those equalities that are not implied by the context.
+ */
+static __isl_give isl_basic_set *uset_gist(__isl_take isl_basic_set *bset,
+	__isl_take isl_basic_set *context)
+{
+	isl_mat *eq;
+	isl_mat *T, *T2;
+	isl_basic_set *aff;
+	isl_basic_set *aff_context;
+	unsigned total;
+
+	if (!bset || !context)
+		goto error;
+
+	bset = isl_basic_set_intersect(bset, isl_basic_set_copy(context));
+	if (isl_basic_set_fast_is_empty(bset)) {
+		isl_basic_set_free(context);
+		return bset;
+	}
+	aff = isl_basic_set_affine_hull(isl_basic_set_copy(bset));
+	if (!aff)
+		goto error;
+	if (isl_basic_set_fast_is_empty(aff)) {
+		isl_basic_set_free(aff);
+		isl_basic_set_free(context);
+		return bset;
+	}
+	if (aff->n_eq == 0) {
+		isl_basic_set_free(aff);
+		return uset_gist_full(bset, context);
+	}
+	total = isl_basic_set_total_dim(bset);
+	eq = isl_mat_sub_alloc(bset->ctx, aff->eq, 0, aff->n_eq, 0, 1 + total);
+	eq = isl_mat_cow(eq);
+	T = isl_mat_variable_compression(eq, &T2);
+	if (T && T->n_col == 0) {
+		isl_mat_free(T);
+		isl_mat_free(T2);
+		isl_basic_set_free(context);
+		isl_basic_set_free(aff);
+		return isl_basic_set_set_to_empty(bset);
+	}
+
+	aff_context = isl_basic_set_affine_hull(isl_basic_set_copy(context));
+
+	bset = isl_basic_set_preimage(bset, isl_mat_copy(T));
+	context = isl_basic_set_preimage(context, T);
+
+	bset = uset_gist_full(bset, context);
+	bset = isl_basic_set_preimage(bset, T2);
+	bset = isl_basic_set_intersect(bset, aff);
+	bset = isl_basic_set_reduce_using_equalities(bset, aff_context);
+
+	if (bset) {
+		ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
+		ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
+	}
+
+	return bset;
+error:
 	isl_basic_set_free(bset);
 	isl_basic_set_free(context);
 	return NULL;
 }
 
+/* Normalize the divs in "bmap" in the context of the equalities in "context".
+ * We simply add the equalities in context to bmap and then do a regular
+ * div normalizations.  Better results can be obtained by normalizing
+ * only the divs in bmap than do not also appear in context.
+ * We need to be careful to reduce the divs using the equalities
+ * so that later calls to isl_basic_map_overlying_set wouldn't introduce
+ * spurious constraints.
+ */
+static struct isl_basic_map *normalize_divs_in_context(
+	struct isl_basic_map *bmap, struct isl_basic_map *context)
+{
+	int i;
+	unsigned total_context;
+	int div_eq;
+
+	div_eq = n_pure_div_eq(bmap);
+	if (div_eq == 0)
+		return bmap;
+
+	if (context->n_div > 0)
+		bmap = isl_basic_map_align_divs(bmap, context);
+
+	total_context = isl_basic_map_total_dim(context);
+	bmap = isl_basic_map_extend_constraints(bmap, context->n_eq, 0);
+	for (i = 0; i < context->n_eq; ++i) {
+		int k;
+		k = isl_basic_map_alloc_equality(bmap);
+		isl_seq_cpy(bmap->eq[k], context->eq[i], 1 + total_context);
+		isl_seq_clr(bmap->eq[k] + 1 + total_context,
+				isl_basic_map_total_dim(bmap) - total_context);
+	}
+	bmap = isl_basic_map_gauss(bmap, NULL);
+	bmap = normalize_divs(bmap, NULL);
+	bmap = isl_basic_map_gauss(bmap, NULL);
+	return bmap;
+}
+
 struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
 	struct isl_basic_map *context)
 {
@@ -1503,8 +1825,11 @@ struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
 		return bmap;
 	}
 
-	bmap = isl_basic_map_convex_hull(bmap);
-	context = isl_basic_map_convex_hull(context);
+	bmap = isl_basic_map_remove_redundancies(bmap);
+	context = isl_basic_map_remove_redundancies(context);
+
+	if (context->n_eq)
+		bmap = normalize_divs_in_context(bmap, context);
 
 	context = isl_basic_map_align_divs(context, bmap);
 	bmap = isl_basic_map_align_divs(bmap, context);
@@ -1522,7 +1847,8 @@ error:
 /*
  * Assumes context has no implicit divs.
  */
-struct isl_map *isl_map_gist(struct isl_map *map, struct isl_basic_map *context)
+__isl_give isl_map *isl_map_gist_basic_map(__isl_take isl_map *map,
+	__isl_take isl_basic_map *context)
 {
 	int i;
 
@@ -1540,7 +1866,7 @@ struct isl_map *isl_map_gist(struct isl_map *map, struct isl_basic_map *context)
 		return isl_map_universe(dim);
 	}
 
-	context = isl_basic_map_convex_hull(context);
+	context = isl_basic_map_remove_redundancies(context);
 	map = isl_map_cow(map);
 	if (!map || !context)
 		goto error;;
@@ -1563,6 +1889,12 @@ error:
 	return NULL;
 }
 
+__isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
+	__isl_take isl_map *context)
+{
+	return isl_map_gist_basic_map(map, isl_map_convex_hull(context));
+}
+
 struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
 						struct isl_basic_set *context)
 {
@@ -1570,12 +1902,20 @@ struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
 		(struct isl_basic_map *)bset, (struct isl_basic_map *)context);
 }
 
-struct isl_set *isl_set_gist(struct isl_set *set, struct isl_basic_set *context)
+__isl_give isl_set *isl_set_gist_basic_set(__isl_take isl_set *set,
+	__isl_take isl_basic_set *context)
 {
-	return (struct isl_set *)isl_map_gist((struct isl_map *)set,
+	return (struct isl_set *)isl_map_gist_basic_map((struct isl_map *)set,
 					(struct isl_basic_map *)context);
 }
 
+__isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
+	__isl_take isl_set *context)
+{
+	return (struct isl_set *)isl_map_gist((struct isl_map *)set,
+					(struct isl_map *)context);
+}
+
 /* Quick check to see if two basic maps are disjoint.
  * In particular, we reduce the equalities and inequalities of
  * one basic map in the context of the equalities of the other
@@ -1587,7 +1927,7 @@ int isl_basic_map_fast_is_disjoint(struct isl_basic_map *bmap1,
 	struct isl_vec *v = NULL;
 	int *elim = NULL;
 	unsigned total;
-	int d, i;
+	int i;
 
 	if (!bmap1 || !bmap2)
 		return -1;
@@ -1633,15 +1973,15 @@ int isl_basic_map_fast_is_disjoint(struct isl_basic_map *bmap1,
 		    isl_seq_first_non_zero(v->block.data + 1, total) == -1)
 			goto disjoint;
 	}
-	isl_vec_free(bmap1->ctx, v);
+	isl_vec_free(v);
 	free(elim);
 	return 0;
 disjoint:
-	isl_vec_free(bmap1->ctx, v);
+	isl_vec_free(v);
 	free(elim);
 	return 1;
 error:
-	isl_vec_free(bmap1->ctx, v);
+	isl_vec_free(v);
 	free(elim);
 	return -1;
 }
@@ -1679,3 +2019,547 @@ int isl_set_fast_is_disjoint(struct isl_set *set1, struct isl_set *set2)
 	return isl_map_fast_is_disjoint((struct isl_map *)set1,
 					(struct isl_map *)set2);
 }
+
+/* Check if we can combine a given div with lower bound l and upper
+ * bound u with some other div and if so return that other div.
+ * Otherwise return -1.
+ *
+ * We first check that
+ *	- the bounds are opposites of each other (except for the constant
+ *	  term)
+ *	- the bounds do not reference any other div
+ *	- no div is defined in terms of this div
+ *
+ * Let m be the size of the range allowed on the div by the bounds.
+ * That is, the bounds are of the form
+ *
+ *	e <= a <= e + m - 1
+ *
+ * with e some expression in the other variables.
+ * We look for another div b such that no third div is defined in terms
+ * of this second div b and such that in any constraint that contains
+ * a (except for the given lower and upper bound), also contains b
+ * with a coefficient that is m times that of b.
+ * That is, all constraints (execpt for the lower and upper bound)
+ * are of the form
+ *
+ *	e + f (a + m b) >= 0
+ *
+ * If so, we return b so that "a + m b" can be replaced by
+ * a single div "c = a + m b".
+ */
+static int div_find_coalesce(struct isl_basic_map *bmap, int *pairs,
+	unsigned div, unsigned l, unsigned u)
+{
+	int i, j;
+	unsigned dim;
+	int coalesce = -1;
+
+	if (bmap->n_div <= 1)
+		return -1;
+	dim = isl_dim_total(bmap->dim);
+	if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim, div) != -1)
+		return -1;
+	if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim + div + 1,
+				   bmap->n_div - div - 1) != -1)
+		return -1;
+	if (!isl_seq_is_neg(bmap->ineq[l] + 1, bmap->ineq[u] + 1,
+			    dim + bmap->n_div))
+		return -1;
+
+	for (i = 0; i < bmap->n_div; ++i) {
+		if (isl_int_is_zero(bmap->div[i][0]))
+			continue;
+		if (!isl_int_is_zero(bmap->div[i][1 + 1 + dim + div]))
+			return -1;
+	}
+
+	isl_int_add(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
+	if (isl_int_is_neg(bmap->ineq[l][0])) {
+		isl_int_sub(bmap->ineq[l][0],
+			    bmap->ineq[l][0], bmap->ineq[u][0]);
+		bmap = isl_basic_map_copy(bmap);
+		bmap = isl_basic_map_set_to_empty(bmap);
+		isl_basic_map_free(bmap);
+		return -1;
+	}
+	isl_int_add_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
+	for (i = 0; i < bmap->n_div; ++i) {
+		if (i == div)
+			continue;
+		if (!pairs[i])
+			continue;
+		for (j = 0; j < bmap->n_div; ++j) {
+			if (isl_int_is_zero(bmap->div[j][0]))
+				continue;
+			if (!isl_int_is_zero(bmap->div[j][1 + 1 + dim + i]))
+				break;
+		}
+		if (j < bmap->n_div)
+			continue;
+		for (j = 0; j < bmap->n_ineq; ++j) {
+			int valid;
+			if (j == l || j == u)
+				continue;
+			if (isl_int_is_zero(bmap->ineq[j][1 + dim + div]))
+				continue;
+			if (isl_int_is_zero(bmap->ineq[j][1 + dim + i]))
+				break;
+			isl_int_mul(bmap->ineq[j][1 + dim + div],
+				    bmap->ineq[j][1 + dim + div],
+				    bmap->ineq[l][0]);
+			valid = isl_int_eq(bmap->ineq[j][1 + dim + div],
+					   bmap->ineq[j][1 + dim + i]);
+			isl_int_divexact(bmap->ineq[j][1 + dim + div],
+					 bmap->ineq[j][1 + dim + div],
+					 bmap->ineq[l][0]);
+			if (!valid)
+				break;
+		}
+		if (j < bmap->n_ineq)
+			continue;
+		coalesce = i;
+		break;
+	}
+	isl_int_sub_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
+	isl_int_sub(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
+	return coalesce;
+}
+
+/* Given a lower and an upper bound on div i, construct an inequality
+ * that when nonnegative ensures that this pair of bounds always allows
+ * for an integer value of the given div.
+ * The lower bound is inequality l, while the upper bound is inequality u.
+ * The constructed inequality is stored in ineq.
+ * g, fl, fu are temporary scalars.
+ *
+ * Let the upper bound be
+ *
+ *	-n_u a + e_u >= 0
+ *
+ * and the lower bound
+ *
+ *	n_l a + e_l >= 0
+ *
+ * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
+ * We have
+ *
+ *	- f_u e_l <= f_u f_l g a <= f_l e_u
+ *
+ * Since all variables are integer valued, this is equivalent to
+ *
+ *	- f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
+ *
+ * If this interval is at least f_u f_l g, then it contains at least
+ * one integer value for a.
+ * That is, the test constraint is
+ *
+ *	f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
+ */
+static void construct_test_ineq(struct isl_basic_map *bmap, int i,
+	int l, int u, isl_int *ineq, isl_int g, isl_int fl, isl_int fu)
+{
+	unsigned dim;
+	dim = isl_dim_total(bmap->dim);
+
+	isl_int_gcd(g, bmap->ineq[l][1 + dim + i], bmap->ineq[u][1 + dim + i]);
+	isl_int_divexact(fl, bmap->ineq[l][1 + dim + i], g);
+	isl_int_divexact(fu, bmap->ineq[u][1 + dim + i], g);
+	isl_int_neg(fu, fu);
+	isl_seq_combine(ineq, fl, bmap->ineq[u], fu, bmap->ineq[l],
+			1 + dim + bmap->n_div);
+	isl_int_add(ineq[0], ineq[0], fl);
+	isl_int_add(ineq[0], ineq[0], fu);
+	isl_int_sub_ui(ineq[0], ineq[0], 1);
+	isl_int_mul(g, g, fl);
+	isl_int_mul(g, g, fu);
+	isl_int_sub(ineq[0], ineq[0], g);
+}
+
+/* Remove more kinds of divs that are not strictly needed.
+ * In particular, if all pairs of lower and upper bounds on a div
+ * are such that they allow at least one integer value of the div,
+ * the we can eliminate the div using Fourier-Motzkin without
+ * introducing any spurious solutions.
+ */
+static struct isl_basic_map *drop_more_redundant_divs(
+	struct isl_basic_map *bmap, int *pairs, int n)
+{
+	struct isl_tab *tab = NULL;
+	struct isl_vec *vec = NULL;
+	unsigned dim;
+	int remove = -1;
+	isl_int g, fl, fu;
+
+	isl_int_init(g);
+	isl_int_init(fl);
+	isl_int_init(fu);
+
+	if (!bmap)
+		goto error;
+
+	dim = isl_dim_total(bmap->dim);
+	vec = isl_vec_alloc(bmap->ctx, 1 + dim + bmap->n_div);
+	if (!vec)
+		goto error;
+
+	tab = isl_tab_from_basic_map(bmap);
+
+	while (n > 0) {
+		int i, l, u;
+		int best = -1;
+		enum isl_lp_result res;
+
+		for (i = 0; i < bmap->n_div; ++i) {
+			if (!pairs[i])
+				continue;
+			if (best >= 0 && pairs[best] <= pairs[i])
+				continue;
+			best = i;
+		}
+
+		i = best;
+		for (l = 0; l < bmap->n_ineq; ++l) {
+			if (!isl_int_is_pos(bmap->ineq[l][1 + dim + i]))
+				continue;
+			for (u = 0; u < bmap->n_ineq; ++u) {
+				if (!isl_int_is_neg(bmap->ineq[u][1 + dim + i]))
+					continue;
+				construct_test_ineq(bmap, i, l, u,
+						    vec->el, g, fl, fu);
+				res = isl_tab_min(tab, vec->el,
+						  bmap->ctx->one, &g, NULL, 0);
+				if (res == isl_lp_error)
+					goto error;
+				if (res == isl_lp_empty) {
+					bmap = isl_basic_map_set_to_empty(bmap);
+					break;
+				}
+				if (res != isl_lp_ok || isl_int_is_neg(g))
+					break;
+			}
+			if (u < bmap->n_ineq)
+				break;
+		}
+		if (l == bmap->n_ineq) {
+			remove = i;
+			break;
+		}
+		pairs[i] = 0;
+		--n;
+	}
+
+	isl_tab_free(tab);
+	isl_vec_free(vec);
+
+	isl_int_clear(g);
+	isl_int_clear(fl);
+	isl_int_clear(fu);
+
+	free(pairs);
+
+	if (remove < 0)
+		return bmap;
+
+	bmap = isl_basic_map_remove(bmap, isl_dim_div, remove, 1);
+	return isl_basic_map_drop_redundant_divs(bmap);
+error:
+	free(pairs);
+	isl_basic_map_free(bmap);
+	isl_tab_free(tab);
+	isl_vec_free(vec);
+	isl_int_clear(g);
+	isl_int_clear(fl);
+	isl_int_clear(fu);
+	return NULL;
+}
+
+/* Given a pair of divs div1 and div2 such that, expect for the lower bound l
+ * and the upper bound u, div1 always occurs together with div2 in the form 
+ * (div1 + m div2), where m is the constant range on the variable div1
+ * allowed by l and u, replace the pair div1 and div2 by a single
+ * div that is equal to div1 + m div2.
+ *
+ * The new div will appear in the location that contains div2.
+ * We need to modify all constraints that contain
+ * div2 = (div - div1) / m
+ * (If a constraint does not contain div2, it will also not contain div1.)
+ * If the constraint also contains div1, then we know they appear
+ * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
+ * i.e., the coefficient of div is f.
+ *
+ * Otherwise, we first need to introduce div1 into the constraint.
+ * Let the l be
+ *
+ *	div1 + f >=0
+ *
+ * and u
+ *
+ *	-div1 + f' >= 0
+ *
+ * A lower bound on div2
+ *
+ *	n div2 + t >= 0
+ *
+ * can be replaced by
+ *
+ *	(n * (m div 2 + div1) + m t + n f)/g >= 0
+ *
+ * with g = gcd(m,n).
+ * An upper bound
+ *
+ *	-n div2 + t >= 0
+ *
+ * can be replaced by
+ *
+ *	(-n * (m div2 + div1) + m t + n f')/g >= 0
+ *
+ * These constraint are those that we would obtain from eliminating
+ * div1 using Fourier-Motzkin.
+ *
+ * After all constraints have been modified, we drop the lower and upper
+ * bound and then drop div1.
+ */
+static struct isl_basic_map *coalesce_divs(struct isl_basic_map *bmap,
+	unsigned div1, unsigned div2, unsigned l, unsigned u)
+{
+	isl_int a;
+	isl_int b;
+	isl_int m;
+	unsigned dim, total;
+	int i;
+
+	dim = isl_dim_total(bmap->dim);
+	total = 1 + dim + bmap->n_div;
+
+	isl_int_init(a);
+	isl_int_init(b);
+	isl_int_init(m);
+	isl_int_add(m, bmap->ineq[l][0], bmap->ineq[u][0]);
+	isl_int_add_ui(m, m, 1);
+
+	for (i = 0; i < bmap->n_ineq; ++i) {
+		if (i == l || i == u)
+			continue;
+		if (isl_int_is_zero(bmap->ineq[i][1 + dim + div2]))
+			continue;
+		if (isl_int_is_zero(bmap->ineq[i][1 + dim + div1])) {
+			isl_int_gcd(b, m, bmap->ineq[i][1 + dim + div2]);
+			isl_int_divexact(a, m, b);
+			isl_int_divexact(b, bmap->ineq[i][1 + dim + div2], b);
+			if (isl_int_is_pos(b)) {
+				isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
+						b, bmap->ineq[l], total);
+			} else {
+				isl_int_neg(b, b);
+				isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
+						b, bmap->ineq[u], total);
+			}
+		}
+		isl_int_set(bmap->ineq[i][1 + dim + div2],
+			    bmap->ineq[i][1 + dim + div1]);
+		isl_int_set_si(bmap->ineq[i][1 + dim + div1], 0);
+	}
+
+	isl_int_clear(a);
+	isl_int_clear(b);
+	isl_int_clear(m);
+	if (l > u) {
+		isl_basic_map_drop_inequality(bmap, l);
+		isl_basic_map_drop_inequality(bmap, u);
+	} else {
+		isl_basic_map_drop_inequality(bmap, u);
+		isl_basic_map_drop_inequality(bmap, l);
+	}
+	bmap = isl_basic_map_drop_div(bmap, div1);
+	return bmap;
+}
+
+/* First check if we can coalesce any pair of divs and
+ * then continue with dropping more redundant divs.
+ *
+ * We loop over all pairs of lower and upper bounds on a div
+ * with coefficient 1 and -1, respectively, check if there
+ * is any other div "c" with which we can coalesce the div
+ * and if so, perform the coalescing.
+ */
+static struct isl_basic_map *coalesce_or_drop_more_redundant_divs(
+	struct isl_basic_map *bmap, int *pairs, int n)
+{
+	int i, l, u;
+	unsigned dim;
+
+	dim = isl_dim_total(bmap->dim);
+
+	for (i = 0; i < bmap->n_div; ++i) {
+		if (!pairs[i])
+			continue;
+		for (l = 0; l < bmap->n_ineq; ++l) {
+			if (!isl_int_is_one(bmap->ineq[l][1 + dim + i]))
+				continue;
+			for (u = 0; u < bmap->n_ineq; ++u) {
+				int c;
+
+				if (!isl_int_is_negone(bmap->ineq[u][1+dim+i]))
+					continue;
+				c = div_find_coalesce(bmap, pairs, i, l, u);
+				if (c < 0)
+					continue;
+				free(pairs);
+				bmap = coalesce_divs(bmap, i, c, l, u);
+				return isl_basic_map_drop_redundant_divs(bmap);
+			}
+		}
+	}
+
+	if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
+		return bmap;
+
+	return drop_more_redundant_divs(bmap, pairs, n);
+}
+
+/* Remove divs that are not strictly needed.
+ * In particular, if a div only occurs positively (or negatively)
+ * in constraints, then it can simply be dropped.
+ * Also, if a div occurs only occurs in two constraints and if moreover
+ * those two constraints are opposite to each other, except for the constant
+ * term and if the sum of the constant terms is such that for any value
+ * of the other values, there is always at least one integer value of the
+ * div, i.e., if one plus this sum is greater than or equal to
+ * the (absolute value) of the coefficent of the div in the constraints,
+ * then we can also simply drop the div.
+ *
+ * If any divs are left after these simple checks then we move on
+ * to more complicated cases in drop_more_redundant_divs.
+ */
+struct isl_basic_map *isl_basic_map_drop_redundant_divs(
+	struct isl_basic_map *bmap)
+{
+	int i, j;
+	unsigned off;
+	int *pairs = NULL;
+	int n = 0;
+
+	if (!bmap)
+		goto error;
+
+	off = isl_dim_total(bmap->dim);
+	pairs = isl_calloc_array(bmap->ctx, int, bmap->n_div);
+	if (!pairs)
+		goto error;
+
+	for (i = 0; i < bmap->n_div; ++i) {
+		int pos, neg;
+		int last_pos, last_neg;
+		int redundant;
+		int defined;
+
+		defined = !isl_int_is_zero(bmap->div[i][0]);
+		for (j = 0; j < bmap->n_eq; ++j)
+			if (!isl_int_is_zero(bmap->eq[j][1 + off + i]))
+				break;
+		if (j < bmap->n_eq)
+			continue;
+		++n;
+		pos = neg = 0;
+		for (j = 0; j < bmap->n_ineq; ++j) {
+			if (isl_int_is_pos(bmap->ineq[j][1 + off + i])) {
+				last_pos = j;
+				++pos;
+			}
+			if (isl_int_is_neg(bmap->ineq[j][1 + off + i])) {
+				last_neg = j;
+				++neg;
+			}
+		}
+		pairs[i] = pos * neg;
+		if (pairs[i] == 0) {
+			for (j = bmap->n_ineq - 1; j >= 0; --j)
+				if (!isl_int_is_zero(bmap->ineq[j][1+off+i]))
+					isl_basic_map_drop_inequality(bmap, j);
+			bmap = isl_basic_map_drop_div(bmap, i);
+			free(pairs);
+			return isl_basic_map_drop_redundant_divs(bmap);
+		}
+		if (pairs[i] != 1)
+			continue;
+		if (!isl_seq_is_neg(bmap->ineq[last_pos] + 1,
+				    bmap->ineq[last_neg] + 1,
+				    off + bmap->n_div))
+			continue;
+
+		isl_int_add(bmap->ineq[last_pos][0],
+			    bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
+		isl_int_add_ui(bmap->ineq[last_pos][0],
+			       bmap->ineq[last_pos][0], 1);
+		redundant = isl_int_ge(bmap->ineq[last_pos][0],
+				bmap->ineq[last_pos][1+off+i]);
+		isl_int_sub_ui(bmap->ineq[last_pos][0],
+			       bmap->ineq[last_pos][0], 1);
+		isl_int_sub(bmap->ineq[last_pos][0],
+			    bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
+		if (!redundant) {
+			if (defined ||
+			    !ok_to_set_div_from_bound(bmap, i, last_pos)) {
+				pairs[i] = 0;
+				--n;
+				continue;
+			}
+			bmap = set_div_from_lower_bound(bmap, i, last_pos);
+			bmap = isl_basic_map_simplify(bmap);
+			free(pairs);
+			return isl_basic_map_drop_redundant_divs(bmap);
+		}
+		if (last_pos > last_neg) {
+			isl_basic_map_drop_inequality(bmap, last_pos);
+			isl_basic_map_drop_inequality(bmap, last_neg);
+		} else {
+			isl_basic_map_drop_inequality(bmap, last_neg);
+			isl_basic_map_drop_inequality(bmap, last_pos);
+		}
+		bmap = isl_basic_map_drop_div(bmap, i);
+		free(pairs);
+		return isl_basic_map_drop_redundant_divs(bmap);
+	}
+
+	if (n > 0)
+		return coalesce_or_drop_more_redundant_divs(bmap, pairs, n);
+
+	free(pairs);
+	return bmap;
+error:
+	free(pairs);
+	isl_basic_map_free(bmap);
+	return NULL;
+}
+
+struct isl_basic_set *isl_basic_set_drop_redundant_divs(
+	struct isl_basic_set *bset)
+{
+	return (struct isl_basic_set *)
+	    isl_basic_map_drop_redundant_divs((struct isl_basic_map *)bset);
+}
+
+struct isl_map *isl_map_drop_redundant_divs(struct isl_map *map)
+{
+	int i;
+
+	if (!map)
+		return NULL;
+	for (i = 0; i < map->n; ++i) {
+		map->p[i] = isl_basic_map_drop_redundant_divs(map->p[i]);
+		if (!map->p[i])
+			goto error;
+	}
+	ISL_F_CLR(map, ISL_MAP_NORMALIZED);
+	return map;
+error:
+	isl_map_free(map);
+	return NULL;
+}
+
+struct isl_set *isl_set_drop_redundant_divs(struct isl_set *set)
+{
+	return (struct isl_set *)
+	    isl_map_drop_redundant_divs((struct isl_map *)set);
+}