X-Git-Url: http://review.tizen.org/git/?a=blobdiff_plain;f=isl_map_simplify.c;h=47b13c0f93f7c5c211d4e9b9f765b4127544dbad;hb=de51a9bc4da5dd3f1f9f57c2362da6f9752c44e0;hp=37ec30ca4f9f6ebef82ef6ddb04ce43002b77b38;hpb=fd5ac025089b7b92de2ec25648ccc5727f76b2d3;p=platform%2Fupstream%2Fisl.git

diff --git a/isl_map_simplify.c b/isl_map_simplify.c
index 37ec30c..47b13c0 100644
--- a/isl_map_simplify.c
+++ b/isl_map_simplify.c
@@ -1,6 +1,23 @@
+/*
+ * Copyright 2008-2009 Katholieke Universiteit Leuven
+ * 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 Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
+ */
+
+#include <strings.h>
+#include <isl_ctx_private.h>
+#include <isl_map_private.h>
 #include "isl_equalities.h"
-#include "isl_map.h"
-#include "isl_map_private.h"
+#include <isl/map.h>
+#include <isl/seq.h>
+#include "isl_tab.h"
+#include <isl_space_private.h>
+#include <isl_mat_private.h>
 
 static void swap_equality(struct isl_basic_map *bmap, int a, int b)
 {
@@ -18,11 +35,6 @@ static void swap_inequality(struct isl_basic_map *bmap, int a, int b)
 	}
 }
 
-static void set_swap_inequality(struct isl_basic_set *bset, int a, int b)
-{
-	swap_inequality((struct isl_basic_map *)bset, a, b);
-}
-
 static void constraint_drop_vars(isl_int *c, unsigned n, unsigned rem)
 {
 	isl_seq_cpy(c, c + n, rem);
@@ -46,7 +58,7 @@ struct isl_basic_set *isl_basic_set_drop_dims(
 
 	isl_assert(bset->ctx, first + n <= bset->dim->n_out, goto error);
 
-	if (n == 0)
+	if (n == 0 && !isl_space_get_tuple_name(bset->dim, isl_dim_set))
 		return bset;
 
 	bset = isl_basic_set_cow(bset);
@@ -65,7 +77,7 @@ struct isl_basic_set *isl_basic_set_drop_dims(
 		constraint_drop_vars(bset->div[i]+1+1+bset->dim->nparam+first, n,
 				     (bset->dim->n_out-first-n)+bset->extra);
 
-	bset->dim = isl_dim_drop_outputs(bset->dim, first, n);
+	bset->dim = isl_space_drop_outputs(bset->dim, first, n);
 	if (!bset->dim)
 		goto error;
 
@@ -87,12 +99,12 @@ struct isl_set *isl_set_drop_dims(
 
 	isl_assert(set->ctx, first + n <= set->dim->n_out, goto error);
 
-	if (n == 0)
+	if (n == 0 && !isl_space_get_tuple_name(set->dim, isl_dim_set))
 		return set;
 	set = isl_set_cow(set);
 	if (!set)
 		goto error;
-	set->dim = isl_dim_drop_outputs(set->dim, first, n);
+	set->dim = isl_space_drop_outputs(set->dim, first, n);
 	if (!set->dim)
 		goto error;
 
@@ -109,7 +121,34 @@ 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
@@ -130,7 +169,7 @@ struct isl_basic_map *isl_basic_map_drop(struct isl_basic_map *bmap,
 	dim = isl_basic_map_dim(bmap, type);
 	isl_assert(bmap->ctx, first + n <= dim, goto error);
 
-	if (n == 0)
+	if (n == 0 && !isl_space_is_named_or_nested(bmap->dim, type))
 		return bmap;
 
 	bmap = isl_basic_map_cow(bmap);
@@ -148,7 +187,13 @@ 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_space_drop_dims(bmap->dim, type, first, n);
 	if (!bmap->dim)
 		goto error;
 
@@ -160,6 +205,13 @@ 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)
 {
@@ -176,12 +228,12 @@ struct isl_map *isl_map_drop(struct isl_map *map,
 
 	isl_assert(map->ctx, first + n <= isl_map_dim(map, type), goto error);
 
-	if (n == 0)
+	if (n == 0 && !isl_space_get_tuple_name(map->dim, type))
 		return map;
 	map = isl_map_cow(map);
 	if (!map)
 		goto error;
-	map->dim = isl_dim_drop(map->dim, type, first, n);
+	map->dim = isl_space_drop_dims(map->dim, type, first, n);
 	if (!map->dim)
 		goto error;
 
@@ -198,6 +250,12 @@ 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)
 {
@@ -216,7 +274,7 @@ static struct isl_basic_map *isl_basic_map_drop_div(
 	if (!bmap)
 		goto error;
 
-	pos = 1 + isl_dim_total(bmap->dim) + div;
+	pos = 1 + isl_space_dim(bmap->dim, isl_dim_all) + div;
 
 	isl_assert(bmap->ctx, div < bmap->n_div, goto error);
 
@@ -253,12 +311,16 @@ error:
 	return NULL;
 }
 
-static struct isl_basic_map *normalize_constraints(struct isl_basic_map *bmap)
+struct isl_basic_map *isl_basic_map_normalize_constraints(
+	struct isl_basic_map *bmap)
 {
 	int i;
 	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);
@@ -303,32 +365,169 @@ static struct isl_basic_map *normalize_constraints(struct isl_basic_map *bmap)
 	return bmap;
 }
 
-static void eliminate_div(struct isl_basic_map *bmap, isl_int *eq, unsigned div)
+struct isl_basic_set *isl_basic_set_normalize_constraints(
+	struct isl_basic_set *bset)
 {
-	int i;
-	unsigned pos = 1 + isl_dim_total(bmap->dim) + div;
-	unsigned len;
-	len = 1 + isl_basic_map_total_dim(bmap);
+	return (struct isl_basic_set *)isl_basic_map_normalize_constraints(
+		(struct isl_basic_map *)bset);
+}
 
-	for (i = 0; i < bmap->n_eq; ++i)
-		if (bmap->eq[i] != eq)
-			isl_seq_elim(bmap->eq[i], eq, pos, len, NULL);
+/* Remove any common factor in numerator and denominator of the div expression,
+ * not taking into account the constant term.
+ * That is, if the div is of the form
+ *
+ *	floor((a + m f(x))/(m d))
+ *
+ * then replace it by
+ *
+ *	floor((floor(a/m) + f(x))/d)
+ *
+ * The difference {a/m}/d in the argument satisfies 0 <= {a/m}/d < 1/d
+ * and can therefore not influence the result of the floor.
+ */
+static void normalize_div_expression(__isl_keep isl_basic_map *bmap, int div)
+{
+	unsigned total = isl_basic_map_total_dim(bmap);
+	isl_ctx *ctx = bmap->ctx;
+
+	if (isl_int_is_zero(bmap->div[div][0]))
+		return;
+	isl_seq_gcd(bmap->div[div] + 2, total, &ctx->normalize_gcd);
+	isl_int_gcd(ctx->normalize_gcd, ctx->normalize_gcd, bmap->div[div][0]);
+	if (isl_int_is_one(ctx->normalize_gcd))
+		return;
+	isl_int_fdiv_q(bmap->div[div][1], bmap->div[div][1],
+			ctx->normalize_gcd);
+	isl_int_divexact(bmap->div[div][0], bmap->div[div][0],
+			ctx->normalize_gcd);
+	isl_seq_scale_down(bmap->div[div] + 2, bmap->div[div] + 2,
+			ctx->normalize_gcd, total);
+}
 
-	for (i = 0; i < bmap->n_ineq; ++i)
-		isl_seq_elim(bmap->ineq[i], eq, pos, len, NULL);
+/* Remove any common factor in numerator and denominator of a div expression,
+ * not taking into account the constant term.
+ * That is, look for any div of the form
+ *
+ *	floor((a + m f(x))/(m d))
+ *
+ * and replace it by
+ *
+ *	floor((floor(a/m) + f(x))/d)
+ *
+ * The difference {a/m}/d in the argument satisfies 0 <= {a/m}/d < 1/d
+ * and can therefore not influence the result of the floor.
+ */
+static __isl_give isl_basic_map *normalize_div_expressions(
+	__isl_take isl_basic_map *bmap)
+{
+	int i;
+
+	if (!bmap)
+		return NULL;
+	if (bmap->n_div == 0)
+		return bmap;
 
-	/* 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);
+		normalize_div_expression(bmap, i);
+
+	return bmap;
+}
+
+/* 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)
+{
+	unsigned total;
+	unsigned space_total;
+	int k;
+	int last_div;
+
+	total = isl_basic_map_total_dim(bmap);
+	space_total = isl_space_dim(bmap->dim, isl_dim_all);
+	last_div = isl_seq_last_non_zero(eq + 1 + space_total, 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);
+		isl_seq_normalize(bmap->ctx, bmap->eq[k], 1 + total);
+	}
+
+	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_seq_normalize(bmap->ctx, bmap->ineq[k], 1 + total);
+		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 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]);
+			normalize_div_expression(bmap, k);
+		} 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_space_dim(bmap->dim, isl_dim_all) + 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 space_total = isl_space_dim(bmap->dim, isl_dim_all);
+	unsigned pos = space_total + div;
+
+	last_div = isl_seq_last_non_zero(eq + 1 + space_total, 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(
@@ -339,19 +538,23 @@ static struct isl_basic_map *eliminate_divs_eq(
 	int modified = 0;
 	unsigned off;
 
+	bmap = isl_basic_map_order_divs(bmap);
+
 	if (!bmap)
 		return NULL;
 
-	off = 1 + isl_dim_total(bmap->dim);
+	off = 1 + isl_space_dim(bmap->dim, isl_dim_all);
 
 	for (d = bmap->n_div - 1; d >= 0 ; --d) {
 		for (i = 0; i < bmap->n_eq; ++i) {
 			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;
 		}
@@ -375,7 +578,7 @@ static struct isl_basic_map *eliminate_divs_ineq(
 		return NULL;
 
 	ctx = bmap->ctx;
-	off = 1 + isl_dim_total(bmap->dim);
+	off = 1 + isl_space_dim(bmap->dim, isl_dim_all);
 
 	for (d = bmap->n_div - 1; d >= 0 ; --d) {
 		for (i = 0; i < bmap->n_eq; ++i)
@@ -390,7 +593,7 @@ 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)
@@ -399,56 +602,6 @@ 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)
 {
@@ -458,6 +611,8 @@ struct isl_basic_map *isl_basic_map_gauss(
 	unsigned total_var;
 	unsigned total;
 
+	bmap = isl_basic_map_order_divs(bmap);
+
 	if (!bmap)
 		return NULL;
 
@@ -480,7 +635,7 @@ 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 &&
@@ -490,6 +645,8 @@ struct isl_basic_map *isl_basic_map_gauss(
 			isl_int_set_si(bmap->div[div][1+1+last_var], 0);
 			isl_int_set(bmap->div[div][0],
 				    bmap->eq[done][1+last_var]);
+			if (progress)
+				*progress = 1;
 			ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
 		}
 	}
@@ -556,13 +713,17 @@ 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)
+	bmap = isl_basic_map_order_divs(bmap);
+	if (!bmap || bmap->n_div <= 1)
 		return bmap;
 
+	total_var = isl_space_dim(bmap->dim, isl_dim_all);
+	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]))
@@ -606,7 +767,7 @@ 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, 1);
 		isl_int_set_si(eq.data[1+total_var+k], 0);
 		isl_int_set_si(eq.data[1+total_var+l], 0);
 	}
@@ -618,6 +779,23 @@ out:
 	return bmap;
 }
 
+static int n_pure_div_eq(struct isl_basic_map *bmap)
+{
+	int i, j;
+	unsigned total;
+
+	total = isl_space_dim(bmap->dim, isl_dim_all);
+	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
@@ -693,29 +871,21 @@ static struct isl_basic_map *normalize_divs(
 	if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED_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;
+	total = isl_space_dim(bmap->dim, isl_dim_all);
+	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,
+		B = isl_mat_sub_alloc6(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;
 		}
 	}
@@ -728,20 +898,20 @@ static struct isl_basic_map *normalize_divs(
 			--j;
 		isl_int_set(d->block.data[i], bmap->eq[i][1 + total + j]);
 	}
-	B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, 0, div_eq, 0, 1 + total);
+	B = isl_mat_sub_alloc6(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);
@@ -753,6 +923,8 @@ 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) {
@@ -774,7 +946,7 @@ static struct isl_basic_map *normalize_divs(
 			needed++;
 	}
 	if (needed > dropped) {
-		bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim),
+		bmap = isl_basic_map_extend_space(bmap, isl_space_copy(bmap->dim),
 				needed, needed, 0);
 		if (!bmap)
 			goto error;
@@ -805,23 +977,110 @@ 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_space_dim(bmap->dim, isl_dim_all);
+
+	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_space_dim(bmap->dim, isl_dim_all);
+
+	/* 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_space_dim(bmap->dim, isl_dim_all);
+
+	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;
 }
 
 static struct isl_basic_map *remove_duplicate_constraints(
-	struct isl_basic_map *bmap, int *progress)
+	struct isl_basic_map *bmap, int *progress, int detect_divs)
 {
 	unsigned int size;
 	isl_int ***index;
@@ -829,12 +1088,14 @@ static struct isl_basic_map *remove_duplicate_constraints(
 	int bits;
 	unsigned total = isl_basic_map_total_dim(bmap);
 	isl_int sum;
+	isl_ctx *ctx;
 
-	if (bmap->n_ineq <= 1)
+	if (!bmap || bmap->n_ineq <= 1)
 		return bmap;
 
 	size = round_up(4 * (bmap->n_ineq+1) / 3 - 1);
 	bits = ffs(size) - 1;
+	ctx = isl_basic_map_get_ctx(bmap);
 	index = isl_calloc_array(ctx, isl_int **, size);
 	if (!index)
 		return bmap;
@@ -863,14 +1124,20 @@ 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)) {
+			if (detect_divs)
+				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
@@ -884,21 +1151,110 @@ static struct isl_basic_map *remove_duplicate_constraints(
 }
 
 
-struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
+/* Eliminate knowns divs from constraints where they appear with
+ * a (positive or negative) unit coefficient.
+ *
+ * That is, replace
+ *
+ *	floor(e/m) + f >= 0
+ *
+ * by
+ *
+ *	e + m f >= 0
+ *
+ * and
+ *
+ *	-floor(e/m) + f >= 0
+ *
+ * by
+ *
+ *	-e + m f + m - 1 >= 0
+ *
+ * The first conversion is valid because floor(e/m) >= -f is equivalent
+ * to e/m >= -f because -f is an integral expression.
+ * The second conversion follows from the fact that
+ *
+ *	-floor(e/m) = ceil(-e/m) = floor((-e + m - 1)/m)
+ *
+ *
+ * We skip integral divs, i.e., those with denominator 1, as we would
+ * risk eliminating the div from the div constraints.  We do not need
+ * to handle those divs here anyway since the div constraints will turn
+ * out to form an equality and this equality can then be use to eliminate
+ * the div from all constraints.
+ */
+static __isl_give isl_basic_map *eliminate_unit_divs(
+	__isl_take isl_basic_map *bmap, int *progress)
+{
+	int i, j;
+	isl_ctx *ctx;
+	unsigned total;
+
+	if (!bmap)
+		return NULL;
+
+	ctx = isl_basic_map_get_ctx(bmap);
+	total = 1 + isl_space_dim(bmap->dim, isl_dim_all);
+
+	for (i = 0; i < bmap->n_div; ++i) {
+		if (isl_int_is_zero(bmap->div[i][0]))
+			continue;
+		if (isl_int_is_one(bmap->div[i][0]))
+			continue;
+		for (j = 0; j < bmap->n_ineq; ++j) {
+			int s;
+
+			if (!isl_int_is_one(bmap->ineq[j][total + i]) &&
+			    !isl_int_is_negone(bmap->ineq[j][total + i]))
+				continue;
+
+			*progress = 1;
+
+			s = isl_int_sgn(bmap->ineq[j][total + i]);
+			isl_int_set_si(bmap->ineq[j][total + i], 0);
+			if (s < 0)
+				isl_seq_combine(bmap->ineq[j],
+					ctx->negone, bmap->div[i] + 1,
+					bmap->div[i][0], bmap->ineq[j],
+					total + bmap->n_div);
+			else
+				isl_seq_combine(bmap->ineq[j],
+					ctx->one, bmap->div[i] + 1,
+					bmap->div[i][0], bmap->ineq[j],
+					total + bmap->n_div);
+			if (s < 0) {
+				isl_int_add(bmap->ineq[j][0],
+					bmap->ineq[j][0], bmap->div[i][0]);
+				isl_int_sub_ui(bmap->ineq[j][0],
+					bmap->ineq[j][0], 1);
+			}
+		}
+	}
+
+	return bmap;
+}
+
+struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
 {
 	int progress = 1;
 	if (!bmap)
 		return NULL;
 	while (progress) {
 		progress = 0;
-		bmap = normalize_constraints(bmap);
+		if (!bmap)
+			break;
+		if (isl_basic_map_plain_is_empty(bmap))
+			break;
+		bmap = isl_basic_map_normalize_constraints(bmap);
+		bmap = normalize_div_expressions(bmap);
+		bmap = remove_duplicate_divs(bmap, &progress);
+		bmap = eliminate_unit_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);
+		bmap = remove_duplicate_constraints(bmap, &progress, 1);
 	}
 	return bmap;
 }
@@ -910,6 +1266,49 @@ 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_space_dim(bmap->dim, isl_dim_all) + 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;
+}
+
+int isl_basic_set_is_div_constraint(__isl_keep isl_basic_set *bset,
+	isl_int *constraint, unsigned div)
+{
+	return isl_basic_map_is_div_constraint(bset, constraint, div);
+}
+
+
 /* If the only constraints a div d=floor(f/m)
  * appears in are its two defining constraints
  *
@@ -921,7 +1320,7 @@ struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset)
 static int div_is_redundant(struct isl_basic_map *bmap, int div)
 {
 	int i;
-	unsigned pos = 1 + isl_dim_total(bmap->dim) + div;
+	unsigned pos = 1 + isl_space_dim(bmap->dim, isl_dim_all) + div;
 
 	for (i = 0; i < bmap->n_eq; ++i)
 		if (!isl_int_is_zero(bmap->eq[i][pos]))
@@ -930,33 +1329,16 @@ 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;
 	}
 
-	for (i = 0; i < bmap->n_div; ++i)
+	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+pos]))
 			return 0;
+	}
 
 	return 1;
 }
@@ -1032,22 +1414,24 @@ 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);
+
+	if (!bmap)
+		return NULL;
 
 	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;
 }
@@ -1061,6 +1445,7 @@ struct isl_basic_map *isl_basic_map_eliminate_vars(
 	int d;
 	int i, j, k;
 	unsigned total;
+	int need_gauss = 0;
 
 	if (n == 0)
 		return bmap;
@@ -1071,6 +1456,8 @@ struct isl_basic_map *isl_basic_map_eliminate_vars(
 	bmap = isl_basic_map_cow(bmap);
 	for (d = pos + n - 1; d >= 0 && d >= pos; --d)
 		bmap = remove_dependent_vars(bmap, d);
+	if (!bmap)
+		return NULL;
 
 	for (d = pos + n - 1;
 	     d >= 0 && d >= total - bmap->n_div && d >= pos; --d)
@@ -1082,8 +1469,9 @@ 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);
+			need_gauss = 1;
 			break;
 		}
 		if (i < bmap->n_eq)
@@ -1098,6 +1486,8 @@ 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]))
@@ -1122,10 +1512,11 @@ struct isl_basic_map *isl_basic_map_eliminate_vars(
 			i = last + 1;
 		}
 		if (n_lower > 0 && n_upper > 0) {
-			bmap = normalize_constraints(bmap);
-			bmap = remove_duplicate_constraints(bmap, NULL);
+			bmap = isl_basic_map_normalize_constraints(bmap);
+			bmap = remove_duplicate_constraints(bmap, NULL, 0);
 			bmap = isl_basic_map_gauss(bmap, NULL);
-			bmap = isl_basic_map_convex_hull(bmap);
+			bmap = isl_basic_map_remove_redundancies(bmap);
+			need_gauss = 0;
 			if (!bmap)
 				goto error;
 			if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
@@ -1133,6 +1524,8 @@ struct isl_basic_map *isl_basic_map_eliminate_vars(
 		}
 	}
 	ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
+	if (need_gauss)
+		bmap = isl_basic_map_gauss(bmap, NULL);
 	return bmap;
 error:
 	isl_basic_map_free(bmap);
@@ -1146,16 +1539,62 @@ struct isl_basic_set *isl_basic_set_eliminate_vars(
 			(struct isl_basic_map *)bset, pos, n);
 }
 
+/* Eliminate the specified n dimensions starting at first from the
+ * constraints, without removing the dimensions from the space.
+ * If the set is rational, the dimensions are eliminated using Fourier-Motzkin.
+ * Otherwise, they are projected out and the original space is restored.
+ */
+__isl_give isl_basic_map *isl_basic_map_eliminate(
+	__isl_take isl_basic_map *bmap,
+	enum isl_dim_type type, unsigned first, unsigned n)
+{
+	isl_space *space;
+
+	if (!bmap)
+		return NULL;
+	if (n == 0)
+		return bmap;
+
+	if (first + n > isl_basic_map_dim(bmap, type) || first + n < first)
+		isl_die(bmap->ctx, isl_error_invalid,
+			"index out of bounds", goto error);
+
+	if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL)) {
+		first += isl_basic_map_offset(bmap, type) - 1;
+		bmap = isl_basic_map_eliminate_vars(bmap, first, n);
+		return isl_basic_map_finalize(bmap);
+	}
+
+	space = isl_basic_map_get_space(bmap);
+	bmap = isl_basic_map_project_out(bmap, type, first, n);
+	bmap = isl_basic_map_insert_dims(bmap, type, first, n);
+	bmap = isl_basic_map_reset_space(bmap, space);
+	return bmap;
+error:
+	isl_basic_map_free(bmap);
+	return NULL;
+}
+
+__isl_give isl_basic_set *isl_basic_set_eliminate(
+	__isl_take isl_basic_set *bset,
+	enum isl_dim_type type, unsigned first, unsigned n)
+{
+	return isl_basic_map_eliminate(bset, type, first, n);
+}
+
+/* Don't assume equalities are in order, because align_divs
+ * may have changed the order of the divs.
+ */
 static void compute_elimination_index(struct isl_basic_map *bmap, int *elim)
 {
 	int d, i;
 	unsigned total;
 
-	total = isl_dim_total(bmap->dim);
+	total = isl_space_dim(bmap->dim, isl_dim_all);
 	for (d = 0; d < total; ++d)
 		elim[d] = -1;
-	for (d = total - 1, i = 0; d >= 0 && i < bmap->n_eq; ++i) {
-		for (; d >= 0; --d) {
+	for (i = 0; i < bmap->n_eq; ++i) {
+		for (d = total - 1; d >= 0; --d) {
 			if (isl_int_is_zero(bmap->eq[i][1+d]))
 				continue;
 			elim[d] = i;
@@ -1166,17 +1605,17 @@ 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;
 
-	total = isl_dim_total(bmap->dim);
+	total = isl_space_dim(bmap->dim, isl_dim_all);
 	for (d = total - 1; d >= 0; --d) {
 		if (isl_int_is_zero(src[1+d]))
 			continue;
@@ -1207,11 +1646,16 @@ 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);
@@ -1239,12 +1683,14 @@ static struct isl_basic_set *remove_shifted_constraints(
 	isl_int ***index;
 	int bits;
 	int k, h, l;
+	isl_ctx *ctx;
 
 	if (!bset)
 		return NULL;
 
 	size = round_up(4 * (context->n_ineq+1) / 3 - 1);
 	bits = ffs(size) - 1;
+	ctx = isl_basic_set_get_ctx(bset);
 	index = isl_calloc_array(ctx, isl_int **, size);
 	if (!index)
 		return bset;
@@ -1273,55 +1719,285 @@ error:
 	return bset;
 }
 
-static struct isl_basic_set *uset_gist(struct isl_basic_set *bset,
-	struct isl_basic_set *context);
+/* Does the (linear part of a) constraint "c" involve any of the "len"
+ * "relevant" dimensions?
+ */
+static int is_related(isl_int *c, int len, int *relevant)
+{
+	int i;
+
+	for (i = 0; i < len; ++i) {
+		if (!relevant[i])
+			continue;
+		if (!isl_int_is_zero(c[i]))
+			return 1;
+	}
+
+	return 0;
+}
 
-static struct isl_basic_set *uset_gist_context_eq(struct isl_basic_set *bset,
-	struct isl_basic_set *context)
+/* Drop constraints from "bset" that do not involve any of
+ * the dimensions marked "relevant".
+ */
+static __isl_give isl_basic_set *drop_unrelated_constraints(
+	__isl_take isl_basic_set *bset, int *relevant)
 {
-	struct isl_mat *T;
-	struct isl_mat *T2;
-	struct isl_ctx *ctx = context->ctx;
-	struct isl_basic_set *reduced_context;
-	reduced_context = isl_basic_set_remove_equalities(
-				isl_basic_set_copy(context), &T, &T2);
-	if (!reduced_context)
-		goto error;
-	bset = isl_basic_set_preimage(bset, T);
-	bset = uset_gist(bset, reduced_context);
-	bset = isl_basic_set_preimage(bset, T2);
-	bset = isl_basic_set_reduce_using_equalities(bset, context);
+	int i, dim;
+
+	dim = isl_basic_set_dim(bset, isl_dim_set);
+	for (i = 0; i < dim; ++i)
+		if (!relevant[i])
+			break;
+	if (i >= dim)
+		return bset;
+
+	for (i = bset->n_eq - 1; i >= 0; --i)
+		if (!is_related(bset->eq[i] + 1, dim, relevant))
+			isl_basic_set_drop_equality(bset, i);
+
+	for (i = bset->n_ineq - 1; i >= 0; --i)
+		if (!is_related(bset->ineq[i] + 1, dim, relevant))
+			isl_basic_set_drop_inequality(bset, i);
+
 	return bset;
+}
+
+/* Update the groups in "group" based on the (linear part of a) constraint "c".
+ *
+ * In particular, for any variable involved in the constraint,
+ * find the actual group id from before and replace the group
+ * of the corresponding variable by the minimal group of all
+ * the variables involved in the constraint considered so far
+ * (if this minimum is smaller) or replace the minimum by this group
+ * (if the minimum is larger).
+ *
+ * At the end, all the variables in "c" will (indirectly) point
+ * to the minimal of the groups that they referred to originally.
+ */
+static void update_groups(int dim, int *group, isl_int *c)
+{
+	int j;
+	int min = dim;
+
+	for (j = 0; j < dim; ++j) {
+		if (isl_int_is_zero(c[j]))
+			continue;
+		while (group[j] >= 0 && group[group[j]] != group[j])
+			group[j] = group[group[j]];
+		if (group[j] == min)
+			continue;
+		if (group[j] < min) {
+			if (min >= 0 && min < dim)
+				group[min] = group[j];
+			min = group[j];
+		} else
+			group[group[j]] = min;
+	}
+}
+
+/* Drop constraints from "context" that are irrelevant for computing
+ * the gist of "bset".
+ *
+ * In particular, drop constraints in variables that are not related
+ * to any of the variables involved in the constraints of "bset"
+ * in the sense that there is no sequence of constraints that connects them.
+ *
+ * We construct groups of variables that collect variables that
+ * (indirectly) appear in some common constraint of "context".
+ * Each group is identified by the first variable in the group,
+ * except for the special group of variables that appear in "bset"
+ * (or are related to those variables), which is identified by -1.
+ * If group[i] is equal to i (or -1), then the group of i is i (or -1),
+ * otherwise the group of i is the group of group[i].
+ *
+ * We first initialize the -1 group with the variables that appear in "bset".
+ * Then we initialize groups for the remaining variables.
+ * Then we iterate over the constraints of "context" and update the
+ * group of the variables in the constraint by the smallest group.
+ * Finally, we resolve indirect references to groups by running over
+ * the variables.
+ *
+ * After computing the groups, we drop constraints that do not involve
+ * any variables in the -1 group.
+ */
+static __isl_give isl_basic_set *drop_irrelevant_constraints(
+	__isl_take isl_basic_set *context, __isl_keep isl_basic_set *bset)
+{
+	isl_ctx *ctx;
+	int *group;
+	int dim;
+	int i, j;
+	int last;
+
+	if (!context || !bset)
+		return isl_basic_set_free(context);
+
+	dim = isl_basic_set_dim(bset, isl_dim_set);
+	ctx = isl_basic_set_get_ctx(bset);
+	group = isl_calloc_array(ctx, int, dim);
+
+	if (!group)
+		goto error;
+
+	for (i = 0; i < dim; ++i) {
+		for (j = 0; j < bset->n_eq; ++j)
+			if (!isl_int_is_zero(bset->eq[j][1 + i]))
+				break;
+		if (j < bset->n_eq) {
+			group[i] = -1;
+			continue;
+		}
+		for (j = 0; j < bset->n_ineq; ++j)
+			if (!isl_int_is_zero(bset->ineq[j][1 + i]))
+				break;
+		if (j < bset->n_ineq)
+			group[i] = -1;
+	}
+
+	last = -1;
+	for (i = 0; i < dim; ++i)
+		if (group[i] >= 0)
+			last = group[i] = i;
+	if (last < 0) {
+		free(group);
+		return context;
+	}
+
+	for (i = 0; i < context->n_eq; ++i)
+		update_groups(dim, group, context->eq[i] + 1);
+	for (i = 0; i < context->n_ineq; ++i)
+		update_groups(dim, group, context->ineq[i] + 1);
+
+	for (i = 0; i < dim; ++i)
+		if (group[i] >= 0)
+			group[i] = group[group[i]];
+
+	for (i = 0; i < dim; ++i)
+		group[i] = group[i] == -1;
+
+	context = drop_unrelated_constraints(context, group);
+
+	free(group);
+	return context;
 error:
-	isl_basic_set_free(context);
-	isl_basic_set_free(bset);
-	return NULL;
+	free(group);
+	return isl_basic_set_free(context);
 }
 
-static struct isl_basic_set *uset_gist_set_eq(struct isl_basic_set *bset,
-	struct isl_basic_set *context)
+/* Remove all information from bset that is redundant in the context
+ * of context.  Both bset and context are assumed to be full-dimensional.
+ *
+ * We first remove the inequalities from "bset"
+ * that are obviously redundant with respect to some inequality in "context".
+ * Then we remove those constraints from "context" that have become
+ * irrelevant for computing the gist of "bset".
+ * Note that this removal of constraints cannot be replaced by
+ * a factorization because factors in "bset" may still be connected
+ * to each other through constraints 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 inequalities, we freeze all constraints such that
+ * they won't be considered redundant in terms of the constraints of "bset".
+ * 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 __isl_give isl_basic_set *uset_gist_full(__isl_take isl_basic_set *bset,
+	__isl_take isl_basic_set *context)
 {
-	struct isl_mat *T;
-	struct isl_mat *T2;
-	struct isl_ctx *ctx = context->ctx;
-	struct isl_basic_set *affine_hull = NULL;
+	int i, k;
+	isl_basic_set *combined = NULL;
+	struct isl_tab *tab = NULL;
+	unsigned context_ineq;
+	unsigned total;
+
+	if (!bset || !context)
+		goto error;
 
-	affine_hull = isl_basic_set_copy(bset);
-	affine_hull = isl_basic_set_cow(affine_hull);
-	if (!affine_hull)
+	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;
-	isl_basic_set_free_inequality(affine_hull, affine_hull->n_ineq);
+	if (bset->n_ineq == 0)
+		goto done;
+
+	context = drop_irrelevant_constraints(context, bset);
+	if (!context)
+		goto error;
+	if (isl_basic_set_is_universe(context)) {
+		isl_basic_set_free(context);
+		return bset;
+	}
 
-	bset = isl_basic_set_remove_equalities(bset, &T, &T2);
+	context_ineq = context->n_ineq;
+	combined = isl_basic_set_cow(isl_basic_set_copy(context));
+	combined = isl_basic_set_extend_constraints(combined, 0, bset->n_ineq);
+	tab = isl_tab_from_basic_set(combined, 0);
+	for (i = 0; i < context_ineq; ++i)
+		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)
+		if (isl_tab_add_ineq(tab, bset->ineq[i]) < 0)
+			goto error;
+	bset = isl_basic_set_add_constraints(combined, bset, 0);
+	combined = NULL;
 	if (!bset)
 		goto error;
-	context = isl_basic_set_preimage(context, T);
-	bset = uset_gist(bset, context);
-	bset = isl_basic_set_preimage(bset, T2);
-	bset = isl_basic_set_intersect(bset, affine_hull);
+	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;
+	}
+	for (i = 0; i < context_ineq; ++i)
+		tab->con[i].is_redundant = 1;
+	bset = isl_basic_set_update_from_tab(bset, tab);
+	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_basic_set_free(affine_hull);
+	isl_tab_free(tab);
+	isl_basic_set_free(combined);
 	isl_basic_set_free(context);
 	isl_basic_set_free(bset);
 	return NULL;
@@ -1332,63 +2008,127 @@ error:
  * of those in context are removed.  Then the inequalities that are
  * redundant in the context of the equalities and inequalities of
  * context are removed.
+ *
+ * First of all, we drop those constraints from "context"
+ * that are irrelevant for computing the gist of "bset".
+ * Alternatively, we could factorize the intersection of "context" and "bset".
+ *
+ * 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.
+ *
+ * If two constraints are mutually redundant, then uset_gist_full
+ * will remove the second of those constraints.  We therefore first
+ * sort the constraints so that constraints not involving existentially
+ * quantified variables are given precedence over those that do.
+ * We have to perform this sorting before the variable compression,
+ * because that may effect the order of the variables.
  */
-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(__isl_take isl_basic_set *bset,
+	__isl_take isl_basic_set *context)
 {
-	int i;
-	isl_int opt;
-	struct isl_basic_set *combined;
-	struct isl_ctx *ctx;
+	isl_mat *eq;
+	isl_mat *T, *T2;
+	isl_basic_set *aff;
+	isl_basic_set *aff_context;
+	unsigned total;
 
 	if (!bset || !context)
 		goto error;
 
-	if (context->n_eq > 0)
-		return uset_gist_context_eq(bset, context);
-	if (!context->n_ineq)
-		goto done;
-	if (bset->n_eq > 0)
-		return uset_gist_set_eq(bset, context);
-	bset = remove_shifted_constraints(bset, context);
-	combined = isl_basic_set_extend_constraints(isl_basic_set_copy(bset),
-			context->n_eq, context->n_ineq);
-	context = isl_basic_set_add_constraints(combined, context, 0);
-	if (!context)
+	context = drop_irrelevant_constraints(context, bset);
+
+	bset = isl_basic_set_intersect(bset, isl_basic_set_copy(context));
+	if (isl_basic_set_plain_is_empty(bset)) {
+		isl_basic_set_free(context);
+		return bset;
+	}
+	bset = isl_basic_set_sort_constraints(bset);
+	aff = isl_basic_set_affine_hull(isl_basic_set_copy(bset));
+	if (!aff)
 		goto error;
-	ctx = context->ctx;
-	isl_int_init(opt);
-	for (i = bset->n_ineq-1; i >= 0; --i) {
-		int redundant;
-		set_swap_inequality(context, i, context->n_ineq-1);
-		context->n_ineq--;
-		redundant = isl_basic_set_constraint_is_redundant(&context,
-				context->ineq[context->n_ineq], &opt, NULL);
-		if (redundant == -1) {
-			isl_int_clear(opt);
-			goto error;
-		}
-		if (ISL_F_ISSET(context, ISL_BASIC_MAP_EMPTY)) {
-			bset = isl_basic_set_set_to_empty(bset);
-			break;
-		}
-		context->n_ineq++;
-		set_swap_inequality(context, i, context->n_ineq-1);
-		if (redundant) {
-			isl_basic_set_drop_inequality(context, i);
-			isl_basic_set_drop_inequality(bset, i);
-		}
+	if (isl_basic_set_plain_is_empty(aff)) {
+		isl_basic_set_free(aff);
+		isl_basic_set_free(context);
+		return bset;
 	}
-	isl_int_clear(opt);
-done:
-	isl_basic_set_free(context);
+	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_alloc6(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(context);
 	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);
+		if (k < 0)
+			return isl_basic_map_free(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)
 {
@@ -1397,6 +2137,25 @@ struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
 	if (!bmap || !context)
 		goto error;
 
+	if (isl_basic_map_is_universe(bmap)) {
+		isl_basic_map_free(context);
+		return bmap;
+	}
+	if (isl_basic_map_plain_is_empty(context)) {
+		isl_basic_map_free(bmap);
+		return context;
+	}
+	if (isl_basic_map_plain_is_empty(bmap)) {
+		isl_basic_map_free(context);
+		return bmap;
+	}
+
+	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);
 
@@ -1413,22 +2172,40 @@ 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;
 
+	if (!map || !context)
+		goto error;;
+
+	if (isl_basic_map_plain_is_empty(context)) {
+		isl_map_free(map);
+		return isl_map_from_basic_map(context);
+	}
+
+	context = isl_basic_map_remove_redundancies(context);
 	map = isl_map_cow(map);
 	if (!map || !context)
-		return NULL;
-	isl_assert(map->ctx, isl_dim_equal(map->dim, context->dim), goto error);
+		goto error;;
+	isl_assert(map->ctx, isl_space_is_equal(map->dim, context->dim), goto error);
 	map = isl_map_compute_divs(map);
+	if (!map)
+		goto error;
 	for (i = 0; i < map->n; ++i)
 		context = isl_basic_map_align_divs(context, map->p[i]);
-	for (i = 0; i < map->n; ++i) {
+	for (i = map->n - 1; i >= 0; --i) {
 		map->p[i] = isl_basic_map_gist(map->p[i],
 						isl_basic_map_copy(context));
 		if (!map->p[i])
 			goto error;
+		if (isl_basic_map_plain_is_empty(map->p[i])) {
+			isl_basic_map_free(map->p[i]);
+			if (i != map->n - 1)
+				map->p[i] = map->p[map->n - 1];
+			map->n--;
+		}
 	}
 	isl_basic_map_free(context);
 	ISL_F_CLR(map, ISL_MAP_NORMALIZED);
@@ -1439,42 +2216,140 @@ error:
 	return NULL;
 }
 
-struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
-						struct isl_basic_set *context)
-{
+/* Return a map that has the same intersection with "context" as "map"
+ * and that as "simple" as possible.
+ *
+ * If "map" is already the universe, then we cannot make it any simpler.
+ * Similarly, if "context" is the universe, then we cannot exploit it
+ * to simplify "map"
+ * If "map" and "context" are identical to each other, then we can
+ * return the corresponding universe.
+ *
+ * If none of these cases apply, we have to work a bit harder.
+ */
+static __isl_give isl_map *map_gist(__isl_take isl_map *map,
+	__isl_take isl_map *context)
+{
+	int equal;
+	int is_universe;
+
+	is_universe = isl_map_plain_is_universe(map);
+	if (is_universe >= 0 && !is_universe)
+		is_universe = isl_map_plain_is_universe(context);
+	if (is_universe < 0)
+		goto error;
+	if (is_universe) {
+		isl_map_free(context);
+		return map;
+	}
+
+	equal = isl_map_plain_is_equal(map, context);
+	if (equal < 0)
+		goto error;
+	if (equal) {
+		isl_map *res = isl_map_universe(isl_map_get_space(map));
+		isl_map_free(map);
+		isl_map_free(context);
+		return res;
+	}
+
+	context = isl_map_compute_divs(context);
+	return isl_map_gist_basic_map(map, isl_map_simple_hull(context));
+error:
+	isl_map_free(map);
+	isl_map_free(context);
+	return NULL;
+}
+
+__isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
+	__isl_take isl_map *context)
+{
+	return isl_map_align_params_map_map_and(map, context, &map_gist);
+}
+
+struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
+						struct isl_basic_set *context)
+{
 	return (struct isl_basic_set *)isl_basic_map_gist(
 		(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_params_basic_set(__isl_take isl_set *set,
+	__isl_take isl_basic_set *context)
+{
+	isl_space *space = isl_set_get_space(set);
+	isl_basic_set *dom_context = isl_basic_set_universe(space);
+	dom_context = isl_basic_set_intersect_params(dom_context, context);
+	return isl_set_gist_basic_set(set, dom_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);
+}
+
+__isl_give isl_map *isl_map_gist_domain(__isl_take isl_map *map,
+	__isl_take isl_set *context)
+{
+	isl_map *map_context = isl_map_universe(isl_map_get_space(map));
+	map_context = isl_map_intersect_domain(map_context, context);
+	return isl_map_gist(map, map_context);
+}
+
+__isl_give isl_map *isl_map_gist_range(__isl_take isl_map *map,
+	__isl_take isl_set *context)
+{
+	isl_map *map_context = isl_map_universe(isl_map_get_space(map));
+	map_context = isl_map_intersect_range(map_context, context);
+	return isl_map_gist(map, map_context);
+}
+
+__isl_give isl_map *isl_map_gist_params(__isl_take isl_map *map,
+	__isl_take isl_set *context)
+{
+	isl_map *map_context = isl_map_universe(isl_map_get_space(map));
+	map_context = isl_map_intersect_params(map_context, context);
+	return isl_map_gist(map, map_context);
+}
+
+__isl_give isl_set *isl_set_gist_params(__isl_take isl_set *set,
+	__isl_take isl_set *context)
+{
+	return isl_map_gist_params(set, 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
  * basic map and check if we get a contradiction.
  */
-int isl_basic_map_fast_is_disjoint(struct isl_basic_map *bmap1,
-	struct isl_basic_map *bmap2)
+int isl_basic_map_plain_is_disjoint(__isl_keep isl_basic_map *bmap1,
+	__isl_keep isl_basic_map *bmap2)
 {
 	struct isl_vec *v = NULL;
 	int *elim = NULL;
 	unsigned total;
-	int d, i;
+	int i;
 
 	if (!bmap1 || !bmap2)
 		return -1;
-	isl_assert(bmap1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim),
+	isl_assert(bmap1->ctx, isl_space_is_equal(bmap1->dim, bmap2->dim),
 			return -1);
 	if (bmap1->n_div || bmap2->n_div)
 		return 0;
 	if (!bmap1->n_eq && !bmap2->n_eq)
 		return 0;
 
-	total = isl_dim_total(bmap1->dim);
+	total = isl_space_dim(bmap1->dim, isl_dim_all);
 	if (total == 0)
 		return 0;
 	v = isl_vec_alloc(bmap1->ctx, 1 + total);
@@ -1509,39 +2384,80 @@ 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;
 }
 
-int isl_basic_set_fast_is_disjoint(struct isl_basic_set *bset1,
-	struct isl_basic_set *bset2)
+int isl_basic_set_plain_is_disjoint(__isl_keep isl_basic_set *bset1,
+	__isl_keep isl_basic_set *bset2)
 {
-	return isl_basic_map_fast_is_disjoint((struct isl_basic_map *)bset1,
+	return isl_basic_map_plain_is_disjoint((struct isl_basic_map *)bset1,
 					      (struct isl_basic_map *)bset2);
 }
 
-int isl_map_fast_is_disjoint(struct isl_map *map1, struct isl_map *map2)
+/* Are "map1" and "map2" obviously disjoint?
+ *
+ * If one of them is empty or if they live in different spaces (ignoring
+ * parameters), then they are clearly disjoint.
+ *
+ * If they have different parameters, then we skip any further tests.
+ *
+ * If they are obviously equal, but not obviously empty, then we will
+ * not be able to detect if they are disjoint.
+ *
+ * Otherwise we check if each basic map in "map1" is obviously disjoint
+ * from each basic map in "map2".
+ */
+int isl_map_plain_is_disjoint(__isl_keep isl_map *map1,
+	__isl_keep isl_map *map2)
 {
 	int i, j;
+	int disjoint;
+	int intersect;
+	int match;
 
 	if (!map1 || !map2)
 		return -1;
 
-	if (isl_map_fast_is_equal(map1, map2))
-		return 0;
+	disjoint = isl_map_plain_is_empty(map1);
+	if (disjoint < 0 || disjoint)
+		return disjoint;
+
+	disjoint = isl_map_plain_is_empty(map2);
+	if (disjoint < 0 || disjoint)
+		return disjoint;
+
+	match = isl_space_tuple_match(map1->dim, isl_dim_in,
+				map2->dim, isl_dim_in);
+	if (match < 0 || !match)
+		return match < 0 ? -1 : 1;
+
+	match = isl_space_tuple_match(map1->dim, isl_dim_out,
+				map2->dim, isl_dim_out);
+	if (match < 0 || !match)
+		return match < 0 ? -1 : 1;
+
+	match = isl_space_match(map1->dim, isl_dim_param,
+				map2->dim, isl_dim_param);
+	if (match < 0 || !match)
+		return match < 0 ? -1 : 0;
+
+	intersect = isl_map_plain_is_equal(map1, map2);
+	if (intersect < 0 || intersect)
+		return intersect < 0 ? -1 : 0;
 
 	for (i = 0; i < map1->n; ++i) {
 		for (j = 0; j < map2->n; ++j) {
-			int d = isl_basic_map_fast_is_disjoint(map1->p[i],
+			int d = isl_basic_map_plain_is_disjoint(map1->p[i],
 							       map2->p[j]);
 			if (d != 1)
 				return d;
@@ -1550,8 +2466,614 @@ int isl_map_fast_is_disjoint(struct isl_map *map1, struct isl_map *map2)
 	return 1;
 }
 
-int isl_set_fast_is_disjoint(struct isl_set *set1, struct isl_set *set2)
+/* Are "map1" and "map2" disjoint?
+ *
+ * They are disjoint if they are "obviously disjoint" or if one of them
+ * is empty.  Otherwise, they are not disjoint if one of them is universal.
+ * If none of these cases apply, we compute the intersection and see if
+ * the result is empty.
+ */
+int isl_map_is_disjoint(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
+{
+	int disjoint;
+	int intersect;
+	isl_map *test;
+
+	disjoint = isl_map_plain_is_disjoint(map1, map2);
+	if (disjoint < 0 || disjoint)
+		return disjoint;
+
+	disjoint = isl_map_is_empty(map1);
+	if (disjoint < 0 || disjoint)
+		return disjoint;
+
+	disjoint = isl_map_is_empty(map2);
+	if (disjoint < 0 || disjoint)
+		return disjoint;
+
+	intersect = isl_map_plain_is_universe(map1);
+	if (intersect < 0 || intersect)
+		return intersect < 0 ? -1 : 0;
+
+	intersect = isl_map_plain_is_universe(map2);
+	if (intersect < 0 || intersect)
+		return intersect < 0 ? -1 : 0;
+
+	test = isl_map_intersect(isl_map_copy(map1), isl_map_copy(map2));
+	disjoint = isl_map_is_empty(test);
+	isl_map_free(test);
+
+	return disjoint;
+}
+
+int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
+	__isl_keep isl_set *set2)
 {
-	return isl_map_fast_is_disjoint((struct isl_map *)set1,
+	return isl_map_plain_is_disjoint((struct isl_map *)set1,
 					(struct isl_map *)set2);
 }
+
+/* Are "set1" and "set2" disjoint?
+ */
+int isl_set_is_disjoint(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
+{
+	return isl_map_is_disjoint(set1, set2);
+}
+
+int isl_set_fast_is_disjoint(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
+{
+	return isl_set_plain_is_disjoint(set1, 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_space_dim(bmap->dim, isl_dim_all);
+	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_space_dim(bmap->dim, isl_dim_all);
+
+	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_space_dim(bmap->dim, isl_dim_all);
+	vec = isl_vec_alloc(bmap->ctx, 1 + dim + bmap->n_div);
+	if (!vec)
+		goto error;
+
+	tab = isl_tab_from_basic_map(bmap, 0);
+
+	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_dims(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_space_dim(bmap->dim, isl_dim_all);
+	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_space_dim(bmap->dim, isl_dim_all);
+
+	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 in only 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.
+ *
+ * We skip divs that appear in equalities or in the definition of other divs.
+ * Divs that appear in the definition of other divs usually occur in at least
+ * 4 constraints, but the constraints may have been simplified.
+ *
+ * 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_space_dim(bmap->dim, isl_dim_all);
+	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 = i; j < bmap->n_div; ++j)
+			if (!isl_int_is_zero(bmap->div[j][1 + 1 + off + i]))
+				break;
+		if (j < bmap->n_div)
+			continue;
+		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);
+}