X-Git-Url: http://review.tizen.org/git/?a=blobdiff_plain;f=isl_convex_hull.c;h=dc8ac917a517b4396107f48526965ea278f649f8;hb=de51a9bc4da5dd3f1f9f57c2362da6f9752c44e0;hp=664ea4dd2ae2c35b9bb449afcd4dea22c8516aed;hpb=64e09ae0d4ab16682b8a4bbbf6ae524d67cd521a;p=platform%2Fupstream%2Fisl.git

diff --git a/isl_convex_hull.c b/isl_convex_hull.c
index 664ea4d..dc8ac91 100644
--- a/isl_convex_hull.c
+++ b/isl_convex_hull.c
@@ -1,25 +1,25 @@
-#include "isl_lp.h"
-#include "isl_map.h"
-#include "isl_map_private.h"
-#include "isl_mat.h"
-#include "isl_set.h"
-#include "isl_seq.h"
+/*
+ * Copyright 2008-2009 Katholieke Universiteit Leuven
+ *
+ * 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
+ */
+
+#include <isl_ctx_private.h>
+#include <isl_map_private.h>
+#include <isl/lp.h>
+#include <isl/map.h>
+#include <isl_mat_private.h>
+#include <isl/set.h>
+#include <isl/seq.h>
+#include <isl_options_private.h>
 #include "isl_equalities.h"
 #include "isl_tab.h"
 
 static struct isl_basic_set *uset_convex_hull_wrap_bounded(struct isl_set *set);
 
-static void swap_ineq(struct isl_basic_map *bmap, unsigned i, unsigned j)
-{
-	isl_int *t;
-
-	if (i != j) {
-		t = bmap->ineq[i];
-		bmap->ineq[i] = bmap->ineq[j];
-		bmap->ineq[j] = t;
-	}
-}
-
 /* Return 1 if constraint c is redundant with respect to the constraints
  * in bmap.  If c is a lower [upper] bound in some variable and bmap
  * does not have a lower [upper] bound in that variable, then c cannot
@@ -50,7 +50,8 @@ int isl_basic_map_constraint_is_redundant(struct isl_basic_map **bmap,
 	if (i < total)
 		return 0;
 
-	res = isl_solve_lp(*bmap, 0, c, (*bmap)->ctx->one, opt_n, opt_d);
+	res = isl_basic_map_solve_lp(*bmap, 0, c, (*bmap)->ctx->one,
+					opt_n, opt_d, NULL);
 	if (res == isl_lp_unbounded)
 		return 0;
 	if (res == isl_lp_error)
@@ -69,7 +70,7 @@ int isl_basic_set_constraint_is_redundant(struct isl_basic_set **bset,
 			(struct isl_basic_map **)bset, c, opt_n, opt_d);
 }
 
-/* Compute the convex hull of a basic map, by removing the redundant
+/* Remove redundant
  * constraints.  If the minimal value along the normal of a constraint
  * is the same if the constraint is removed, then the constraint is redundant.
  *
@@ -77,7 +78,8 @@ int isl_basic_set_constraint_is_redundant(struct isl_basic_set **bset,
  * corresponding equality and the checked if the dimension was that
  * of a facet.
  */
-struct isl_basic_map *isl_basic_map_convex_hull(struct isl_basic_map *bmap)
+__isl_give isl_basic_map *isl_basic_map_remove_redundancies(
+	__isl_take isl_basic_map *bmap)
 {
 	struct isl_tab *tab;
 
@@ -92,20 +94,40 @@ struct isl_basic_map *isl_basic_map_convex_hull(struct isl_basic_map *bmap)
 	if (bmap->n_ineq <= 1)
 		return bmap;
 
-	tab = isl_tab_from_basic_map(bmap);
-	tab = isl_tab_detect_equalities(tab);
-	tab = isl_tab_detect_redundant(tab);
+	tab = isl_tab_from_basic_map(bmap, 0);
+	if (isl_tab_detect_implicit_equalities(tab) < 0)
+		goto error;
+	if (isl_tab_detect_redundant(tab) < 0)
+		goto error;
 	bmap = isl_basic_map_update_from_tab(bmap, tab);
 	isl_tab_free(tab);
 	ISL_F_SET(bmap, ISL_BASIC_MAP_NO_IMPLICIT);
 	ISL_F_SET(bmap, ISL_BASIC_MAP_NO_REDUNDANT);
 	return bmap;
+error:
+	isl_tab_free(tab);
+	isl_basic_map_free(bmap);
+	return NULL;
 }
 
-struct isl_basic_set *isl_basic_set_convex_hull(struct isl_basic_set *bset)
+__isl_give isl_basic_set *isl_basic_set_remove_redundancies(
+	__isl_take isl_basic_set *bset)
 {
 	return (struct isl_basic_set *)
-		isl_basic_map_convex_hull((struct isl_basic_map *)bset);
+		isl_basic_map_remove_redundancies((struct isl_basic_map *)bset);
+}
+
+/* Remove redundant constraints in each of the basic maps.
+ */
+__isl_give isl_map *isl_map_remove_redundancies(__isl_take isl_map *map)
+{
+	return isl_map_inline_foreach_basic_map(map,
+					    &isl_basic_map_remove_redundancies);
+}
+
+__isl_give isl_set *isl_set_remove_redundancies(__isl_take isl_set *set)
+{
+	return isl_map_remove_redundancies(set);
 }
 
 /* Check if the set set is bound in the direction of the affine
@@ -128,8 +150,8 @@ static int uset_is_bound(struct isl_set *set, isl_int *c, unsigned len)
 		if (ISL_F_ISSET(set->p[j], ISL_BASIC_SET_EMPTY))
 			continue;
 
-		res = isl_solve_lp((struct isl_basic_map*)set->p[j],
-				0, c, set->ctx->one, &opt, &opt_denom);
+		res = isl_basic_set_solve_lp(set->p[j],
+				0, c, set->ctx->one, &opt, &opt_denom, NULL);
 		if (res == isl_lp_unbounded)
 			break;
 		if (res == isl_lp_error)
@@ -140,10 +162,11 @@ static int uset_is_bound(struct isl_set *set, isl_int *c, unsigned len)
 				goto error;
 			continue;
 		}
-		if (!isl_int_is_one(opt_denom))
-			isl_seq_scale(c, c, opt_denom, len);
-		if (first || isl_int_is_neg(opt))
+		if (first || isl_int_is_neg(opt)) {
+			if (!isl_int_is_one(opt_denom))
+				isl_seq_scale(c, c, opt_denom, len);
 			isl_int_sub(c[0], c[0], opt);
+		}
 		first = 0;
 	}
 	isl_int_clear(opt);
@@ -155,141 +178,67 @@ error:
 	return -1;
 }
 
-/* Check if "c" is a direction that is independent of the previously found "n"
- * bounds in "dirs".
- * If so, add it to the list, with the negative of the lower bound
- * in the constant position, i.e., such that c corresponds to a bounding
- * hyperplane (but not necessarily a facet).
- * Assumes set "set" is bounded.
- */
-static int is_independent_bound(struct isl_set *set, isl_int *c,
-	struct isl_mat *dirs, int n)
+__isl_give isl_basic_map *isl_basic_map_set_rational(
+	__isl_take isl_basic_set *bmap)
 {
-	int is_bound;
-	int i = 0;
-
-	isl_seq_cpy(dirs->row[n]+1, c+1, dirs->n_col-1);
-	if (n != 0) {
-		int pos = isl_seq_first_non_zero(dirs->row[n]+1, dirs->n_col-1);
-		if (pos < 0)
-			return 0;
-		for (i = 0; i < n; ++i) {
-			int pos_i;
-			pos_i = isl_seq_first_non_zero(dirs->row[i]+1, dirs->n_col-1);
-			if (pos_i < pos)
-				continue;
-			if (pos_i > pos)
-				break;
-			isl_seq_elim(dirs->row[n]+1, dirs->row[i]+1, pos,
-					dirs->n_col-1, NULL);
-			pos = isl_seq_first_non_zero(dirs->row[n]+1, dirs->n_col-1);
-			if (pos < 0)
-				return 0;
-		}
-	}
-
-	is_bound = uset_is_bound(set, dirs->row[n], dirs->n_col);
-	if (is_bound != 1)
-		return is_bound;
-	if (i < n) {
-		int k;
-		isl_int *t = dirs->row[n];
-		for (k = n; k > i; --k)
-			dirs->row[k] = dirs->row[k-1];
-		dirs->row[i] = t;
-	}
-	return 1;
-}
+	if (!bmap)
+		return NULL;
 
-/* Compute and return a maximal set of linearly independent bounds
- * on the set "set", based on the constraints of the basic sets
- * in "set".
- */
-static struct isl_mat *independent_bounds(struct isl_set *set)
-{
-	int i, j, n;
-	struct isl_mat *dirs = NULL;
-	unsigned dim = isl_set_n_dim(set);
+	if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
+		return bmap;
 
-	dirs = isl_mat_alloc(set->ctx, dim, 1+dim);
-	if (!dirs)
-		goto error;
+	bmap = isl_basic_map_cow(bmap);
+	if (!bmap)
+		return NULL;
 
-	n = 0;
-	for (i = 0; n < dim && i < set->n; ++i) {
-		int f;
-		struct isl_basic_set *bset = set->p[i];
+	ISL_F_SET(bmap, ISL_BASIC_MAP_RATIONAL);
 
-		for (j = 0; n < dim && j < bset->n_eq; ++j) {
-			f = is_independent_bound(set, bset->eq[j], dirs, n);
-			if (f < 0)
-				goto error;
-			if (f)
-				++n;
-		}
-		for (j = 0; n < dim && j < bset->n_ineq; ++j) {
-			f = is_independent_bound(set, bset->ineq[j], dirs, n);
-			if (f < 0)
-				goto error;
-			if (f)
-				++n;
-		}
-	}
-	dirs->n_row = n;
-	return dirs;
-error:
-	isl_mat_free(dirs);
-	return NULL;
+	return isl_basic_map_finalize(bmap);
 }
 
-static struct isl_basic_set *isl_basic_set_set_rational(
-	struct isl_basic_set *bset)
+__isl_give isl_basic_set *isl_basic_set_set_rational(
+	__isl_take isl_basic_set *bset)
 {
-	if (!bset)
-		return NULL;
-
-	if (ISL_F_ISSET(bset, ISL_BASIC_MAP_RATIONAL))
-		return bset;
-
-	bset = isl_basic_set_cow(bset);
-	if (!bset)
-		return NULL;
-
-	ISL_F_SET(bset, ISL_BASIC_MAP_RATIONAL);
-
-	return isl_basic_set_finalize(bset);
+	return isl_basic_map_set_rational(bset);
 }
 
-static struct isl_set *isl_set_set_rational(struct isl_set *set)
+__isl_give isl_map *isl_map_set_rational(__isl_take isl_map *map)
 {
 	int i;
 
-	set = isl_set_cow(set);
-	if (!set)
+	map = isl_map_cow(map);
+	if (!map)
 		return NULL;
-	for (i = 0; i < set->n; ++i) {
-		set->p[i] = isl_basic_set_set_rational(set->p[i]);
-		if (!set->p[i])
+	for (i = 0; i < map->n; ++i) {
+		map->p[i] = isl_basic_map_set_rational(map->p[i]);
+		if (!map->p[i])
 			goto error;
 	}
-	return set;
+	return map;
 error:
-	isl_set_free(set);
+	isl_map_free(map);
 	return NULL;
 }
 
+__isl_give isl_set *isl_set_set_rational(__isl_take isl_set *set)
+{
+	return isl_map_set_rational(set);
+}
+
 static struct isl_basic_set *isl_basic_set_add_equality(
 	struct isl_basic_set *bset, isl_int *c)
 {
 	int i;
-	unsigned total;
 	unsigned dim;
 
+	if (!bset)
+		return NULL;
+
 	if (ISL_F_ISSET(bset, ISL_BASIC_SET_EMPTY))
 		return bset;
 
-	isl_assert(ctx, isl_basic_set_n_param(bset) == 0, goto error);
-	isl_assert(ctx, bset->n_div == 0, goto error);
+	isl_assert(bset->ctx, isl_basic_set_n_param(bset) == 0, goto error);
+	isl_assert(bset->ctx, bset->n_div == 0, goto error);
 	dim = isl_basic_set_n_dim(bset);
 	bset = isl_basic_set_cow(bset);
 	bset = isl_basic_set_extend(bset, 0, dim, 0, 1, 0);
@@ -303,7 +252,7 @@ error:
 	return NULL;
 }
 
-static struct isl_set *isl_set_add_equality(struct isl_set *set, isl_int *c)
+static struct isl_set *isl_set_add_basic_set_equality(struct isl_set *set, isl_int *c)
 {
 	int i;
 
@@ -357,6 +306,7 @@ static struct isl_basic_set *wrap_constraints(struct isl_set *set)
 		n_ineq += set->p[i]->n_ineq;
 	}
 	lp = isl_basic_set_alloc(set->ctx, 0, dim * set->n, 0, n_eq, n_ineq);
+	lp = isl_basic_set_set_rational(lp);
 	if (!lp)
 		return NULL;
 	lp_dim = isl_basic_set_n_dim(lp);
@@ -442,12 +392,15 @@ static struct isl_basic_set *wrap_constraints(struct isl_set *set)
  * In the original space, we need to take the same combination of the
  * corresponding constraints "facet" and "ridge".
  *
- * Note that a is always finite, since we only apply the wrapping
- * technique to a union of polytopes.
+ * If a = -infty = "-1/0", then we just return the original facet constraint.
+ * This means that the facet is unbounded, but has a bounded intersection
+ * with the union of sets.
  */
-static isl_int *wrap_facet(struct isl_set *set, isl_int *facet, isl_int *ridge)
+isl_int *isl_set_wrap_facet(__isl_keep isl_set *set,
+	isl_int *facet, isl_int *ridge)
 {
 	int i;
+	isl_ctx *ctx;
 	struct isl_mat *T = NULL;
 	struct isl_basic_set *lp = NULL;
 	struct isl_vec *obj;
@@ -455,10 +408,14 @@ static isl_int *wrap_facet(struct isl_set *set, isl_int *facet, isl_int *ridge)
 	isl_int num, den;
 	unsigned dim;
 
+	if (!set)
+		return NULL;
+	ctx = set->ctx;
 	set = isl_set_copy(set);
+	set = isl_set_set_rational(set);
 
 	dim = 1 + isl_set_n_dim(set);
-	T = isl_mat_alloc(set->ctx, 3, dim);
+	T = isl_mat_alloc(ctx, 3, dim);
 	if (!T)
 		goto error;
 	isl_int_set_si(T->row[0][0], 1);
@@ -471,7 +428,7 @@ static isl_int *wrap_facet(struct isl_set *set, isl_int *facet, isl_int *ridge)
 	if (!set)
 		goto error;
 	lp = wrap_constraints(set);
-	obj = isl_vec_alloc(set->ctx, 1 + dim*set->n);
+	obj = isl_vec_alloc(ctx, 1 + dim*set->n);
 	if (!obj)
 		goto error;
 	isl_int_set_si(obj->block.data[0], 0);
@@ -482,18 +439,22 @@ static isl_int *wrap_facet(struct isl_set *set, isl_int *facet, isl_int *ridge)
 	}
 	isl_int_init(num);
 	isl_int_init(den);
-	res = isl_solve_lp((struct isl_basic_map *)lp, 0,
-				    obj->block.data, set->ctx->one, &num, &den);
+	res = isl_basic_set_solve_lp(lp, 0,
+			    obj->block.data, ctx->one, &num, &den, NULL);
 	if (res == isl_lp_ok) {
 		isl_int_neg(num, num);
 		isl_seq_combine(facet, num, facet, den, ridge, dim);
+		isl_seq_normalize(ctx, facet, dim);
 	}
 	isl_int_clear(num);
 	isl_int_clear(den);
 	isl_vec_free(obj);
 	isl_basic_set_free(lp);
 	isl_set_free(set);
-	isl_assert(set->ctx, res == isl_lp_ok, return NULL);
+	if (res == isl_lp_error)
+		return NULL;
+	isl_assert(ctx, res == isl_lp_ok || res == isl_lp_unbounded, 
+		   return NULL);
 	return facet;
 error:
 	isl_basic_set_free(lp);
@@ -502,33 +463,45 @@ error:
 	return NULL;
 }
 
-/* Given a set of d linearly independent bounding constraints of the
- * convex hull of "set", compute the constraint of a facet of "set".
- *
- * We first compute the intersection with the first bounding hyperplane
- * and remove the component corresponding to this hyperplane from
- * other bounds (in homogeneous space).
- * We then wrap around one of the remaining bounding constraints
- * and continue the process until all bounding constraints have been
- * taken into account.
- * The resulting linear combination of the bounding constraints will
- * correspond to a facet of the convex hull.
+/* Compute the constraint of a facet of "set".
+ *
+ * We first compute the intersection with a bounding constraint
+ * that is orthogonal to one of the coordinate axes.
+ * If the affine hull of this intersection has only one equality,
+ * we have found a facet.
+ * Otherwise, we wrap the current bounding constraint around
+ * one of the equalities of the face (one that is not equal to
+ * the current bounding constraint).
+ * This process continues until we have found a facet.
+ * The dimension of the intersection increases by at least
+ * one on each iteration, so termination is guaranteed.
  */
-static struct isl_mat *initial_facet_constraint(struct isl_set *set,
-	struct isl_mat *bounds)
+static __isl_give isl_mat *initial_facet_constraint(__isl_keep isl_set *set)
 {
 	struct isl_set *slice = NULL;
 	struct isl_basic_set *face = NULL;
-	struct isl_mat *m, *U, *Q;
 	int i;
 	unsigned dim = isl_set_n_dim(set);
+	int is_bound;
+	isl_mat *bounds = NULL;
+
+	isl_assert(set->ctx, set->n > 0, goto error);
+	bounds = isl_mat_alloc(set->ctx, 1, 1 + dim);
+	if (!bounds)
+		return NULL;
 
-	isl_assert(ctx, set->n > 0, goto error);
-	isl_assert(ctx, bounds->n_row == dim, goto error);
+	isl_seq_clr(bounds->row[0], dim);
+	isl_int_set_si(bounds->row[0][1 + dim - 1], 1);
+	is_bound = uset_is_bound(set, bounds->row[0], 1 + dim);
+	if (is_bound < 0)
+		goto error;
+	isl_assert(set->ctx, is_bound, goto error);
+	isl_seq_normalize(set->ctx, bounds->row[0], 1 + dim);
+	bounds->n_row = 1;
 
-	while (bounds->n_row > 1) {
+	for (;;) {
 		slice = isl_set_copy(set);
-		slice = isl_set_add_equality(slice, bounds->row[0]);
+		slice = isl_set_add_basic_set_equality(slice, bounds->row[0]);
 		face = isl_set_affine_hull(slice);
 		if (!face)
 			goto error;
@@ -536,32 +509,18 @@ static struct isl_mat *initial_facet_constraint(struct isl_set *set,
 			isl_basic_set_free(face);
 			break;
 		}
-		m = isl_mat_alloc(set->ctx, 1 + face->n_eq, 1 + dim);
-		if (!m)
-			goto error;
-		isl_int_set_si(m->row[0][0], 1);
-		isl_seq_clr(m->row[0]+1, dim);
 		for (i = 0; i < face->n_eq; ++i)
-			isl_seq_cpy(m->row[1 + i], face->eq[i], 1 + dim);
-		U = isl_mat_right_inverse(m);
-		Q = isl_mat_right_inverse(isl_mat_copy(U));
-		U = isl_mat_drop_cols(U, 1 + face->n_eq, dim - face->n_eq);
-		Q = isl_mat_drop_rows(Q, 1 + face->n_eq, dim - face->n_eq);
-		U = isl_mat_drop_cols(U, 0, 1);
-		Q = isl_mat_drop_rows(Q, 0, 1);
-		bounds = isl_mat_product(bounds, U);
-		bounds = isl_mat_product(bounds, Q);
-		while (isl_seq_first_non_zero(bounds->row[bounds->n_row-1],
-					      bounds->n_col) == -1) {
-			bounds->n_row--;
-			isl_assert(ctx, bounds->n_row > 1, goto error);
-		}
-		if (!wrap_facet(set, bounds->row[0],
-					  bounds->row[bounds->n_row-1]))
+			if (!isl_seq_eq(bounds->row[0], face->eq[i], 1 + dim) &&
+			    !isl_seq_is_neg(bounds->row[0],
+						face->eq[i], 1 + dim))
+				break;
+		isl_assert(set->ctx, i < face->n_eq, goto error);
+		if (!isl_set_wrap_facet(set, bounds->row[0], face->eq[i]))
 			goto error;
+		isl_seq_normalize(set->ctx, bounds->row[0], bounds->n_col);
 		isl_basic_set_free(face);
-		bounds->n_row--;
 	}
+
 	return bounds;
 error:
 	isl_basic_set_free(face);
@@ -631,7 +590,8 @@ static struct isl_basic_set *compute_facet(struct isl_set *set, isl_int *c)
 	set = isl_set_preimage(set, U);
 	facet = uset_convex_hull_wrap_bounded(set);
 	facet = isl_basic_set_preimage(facet, Q);
-	isl_assert(ctx, facet->n_eq == 0, goto error);
+	if (facet)
+		isl_assert(ctx, facet->n_eq == 0, goto error);
 	return facet;
 error:
 	isl_basic_set_free(facet);
@@ -667,9 +627,11 @@ static struct isl_basic_set *extend(struct isl_basic_set *hull,
 	int k;
 	struct isl_basic_set *facet = NULL;
 	struct isl_basic_set *hull_facet = NULL;
-	unsigned total;
 	unsigned dim;
 
+	if (!hull)
+		return NULL;
+
 	isl_assert(set->ctx, set->n > 0, goto error);
 
 	dim = isl_set_n_dim(set);
@@ -683,11 +645,13 @@ static struct isl_basic_set *extend(struct isl_basic_set *hull,
 		hull_facet = isl_basic_set_add_equality(hull_facet, hull->ineq[i]);
 		hull_facet = isl_basic_set_gauss(hull_facet, NULL);
 		hull_facet = isl_basic_set_normalize_constraints(hull_facet);
-		if (!facet)
+		if (!facet || !hull_facet)
 			goto error;
 		hull = isl_basic_set_cow(hull);
-		hull = isl_basic_set_extend_dim(hull,
-			isl_dim_copy(hull->dim), 0, 0, facet->n_ineq);
+		hull = isl_basic_set_extend_space(hull,
+			isl_space_copy(hull->dim), 0, 0, facet->n_ineq);
+		if (!hull)
+			goto error;
 		for (j = 0; j < facet->n_ineq; ++j) {
 			for (f = 0; f < hull_facet->n_ineq; ++f)
 				if (isl_seq_eq(facet->ineq[j],
@@ -699,7 +663,7 @@ static struct isl_basic_set *extend(struct isl_basic_set *hull,
 			if (k < 0)
 				goto error;
 			isl_seq_cpy(hull->ineq[k], hull->ineq[i], 1+dim);
-			if (!wrap_facet(set, hull->ineq[k], facet->ineq[j]))
+			if (!isl_set_wrap_facet(set, hull->ineq[k], facet->ineq[j]))
 				goto error;
 		}
 		isl_basic_set_free(hull_facet);
@@ -839,13 +803,6 @@ error:
 	return NULL;
 }
 
-/* Project out final n dimensions using Fourier-Motzkin */
-static struct isl_set *set_project_out(struct isl_ctx *ctx,
-	struct isl_set *set, unsigned n)
-{
-	return isl_set_remove_dims(set, isl_set_n_dim(set) - n, n);
-}
-
 static struct isl_basic_set *convex_hull_0d(struct isl_set *set)
 {
 	struct isl_basic_set *convex_hull;
@@ -854,9 +811,9 @@ static struct isl_basic_set *convex_hull_0d(struct isl_set *set)
 		return NULL;
 
 	if (isl_set_is_empty(set))
-		convex_hull = isl_basic_set_empty(isl_dim_copy(set->dim));
+		convex_hull = isl_basic_set_empty(isl_space_copy(set->dim));
 	else
-		convex_hull = isl_basic_set_universe(isl_dim_copy(set->dim));
+		convex_hull = isl_basic_set_universe(isl_space_copy(set->dim));
 	isl_set_free(set);
 	return convex_hull;
 }
@@ -922,8 +879,8 @@ static struct isl_basic_set *convex_hull_pair_elim(struct isl_basic_set *bset1,
 		isl_int_set_si(hull->eq[k][2*(1+dim)+j], 1);
 	}
 	hull = isl_basic_set_set_rational(hull);
-	hull = isl_basic_set_remove_dims(hull, dim, 2*(1+dim));
-	hull = isl_basic_set_convex_hull(hull);
+	hull = isl_basic_set_remove_dims(hull, isl_dim_set, dim, 2*(1+dim));
+	hull = isl_basic_set_remove_redundancies(hull);
 	isl_basic_set_free(bset1);
 	isl_basic_set_free(bset2);
 	return hull;
@@ -934,21 +891,52 @@ error:
 	return NULL;
 }
 
-static int isl_basic_set_is_bounded(struct isl_basic_set *bset)
+/* Is the set bounded for each value of the parameters?
+ */
+int isl_basic_set_is_bounded(__isl_keep isl_basic_set *bset)
 {
 	struct isl_tab *tab;
 	int bounded;
 
-	tab = isl_tab_from_recession_cone((struct isl_basic_map *)bset);
+	if (!bset)
+		return -1;
+	if (isl_basic_set_plain_is_empty(bset))
+		return 1;
+
+	tab = isl_tab_from_recession_cone(bset, 1);
 	bounded = isl_tab_cone_is_bounded(tab);
 	isl_tab_free(tab);
 	return bounded;
 }
 
-static int isl_set_is_bounded(struct isl_set *set)
+/* Is the image bounded for each value of the parameters and
+ * the domain variables?
+ */
+int isl_basic_map_image_is_bounded(__isl_keep isl_basic_map *bmap)
+{
+	unsigned nparam = isl_basic_map_dim(bmap, isl_dim_param);
+	unsigned n_in = isl_basic_map_dim(bmap, isl_dim_in);
+	int bounded;
+
+	bmap = isl_basic_map_copy(bmap);
+	bmap = isl_basic_map_cow(bmap);
+	bmap = isl_basic_map_move_dims(bmap, isl_dim_param, nparam,
+					isl_dim_in, 0, n_in);
+	bounded = isl_basic_set_is_bounded((isl_basic_set *)bmap);
+	isl_basic_map_free(bmap);
+
+	return bounded;
+}
+
+/* Is the set bounded for each value of the parameters?
+ */
+int isl_set_is_bounded(__isl_keep isl_set *set)
 {
 	int i;
 
+	if (!set)
+		return -1;
+
 	for (i = 0; i < set->n; ++i) {
 		int bounded = isl_basic_set_is_bounded(set->p[i]);
 		if (!bounded || bounded < 0)
@@ -974,7 +962,7 @@ static struct isl_basic_set *induced_lineality_space(
 		goto error;
 
 	dim = isl_basic_set_total_dim(bset1);
-	lin = isl_basic_set_alloc_dim(isl_basic_set_get_dim(bset1), 0,
+	lin = isl_basic_set_alloc_space(isl_basic_set_get_space(bset1), 0,
 					bset1->n_eq + bset2->n_eq,
 					bset1->n_ineq + bset2->n_ineq);
 	lin = isl_basic_set_set_rational(lin);
@@ -1052,7 +1040,7 @@ static struct isl_basic_set *modulo_lineality(struct isl_set *set,
 	if (!set || !lin)
 		goto error;
 	lin_dim = total - lin->n_eq;
-	M = isl_mat_sub_alloc(set->ctx, lin->eq, 0, lin->n_eq, 1, total);
+	M = isl_mat_sub_alloc6(set->ctx, lin->eq, 0, lin->n_eq, 1, total);
 	M = isl_mat_left_hermite(M, 0, &U, &Q);
 	if (!M)
 		goto error;
@@ -1065,7 +1053,7 @@ static struct isl_basic_set *modulo_lineality(struct isl_set *set,
 	Q = isl_mat_lin_to_aff(Q);
 
 	set = isl_set_preimage(set, U);
-	set = isl_set_remove_dims(set, total - lin_dim, lin_dim);
+	set = isl_set_remove_dims(set, isl_dim_set, total - lin_dim, lin_dim);
 	hull = uset_convex_hull(set);
 	hull = isl_basic_set_preimage(hull, Q);
 
@@ -1088,7 +1076,7 @@ error:
 static struct isl_basic_set *valid_direction_lp(
 	struct isl_basic_set *bset1, struct isl_basic_set *bset2)
 {
-	struct isl_dim *dim;
+	isl_space *dim;
 	struct isl_basic_set *lp;
 	unsigned d;
 	int n;
@@ -1099,8 +1087,8 @@ static struct isl_basic_set *valid_direction_lp(
 	d = 1 + isl_basic_set_total_dim(bset1);
 	n = 2 +
 	    2 * bset1->n_eq + bset1->n_ineq + 2 * bset2->n_eq + bset2->n_ineq;
-	dim = isl_dim_set_alloc(bset1->ctx, 0, n);
-	lp = isl_basic_set_alloc_dim(dim, 0, d, n);
+	dim = isl_space_set_alloc(bset1->ctx, 0, n);
+	lp = isl_basic_set_alloc_space(dim, 0, d, n);
 	if (!lp)
 		goto error;
 	for (i = 0; i < n; ++i) {
@@ -1116,23 +1104,25 @@ static struct isl_basic_set *valid_direction_lp(
 		if (k < 0)
 			goto error;
 		n = 0;
-		isl_int_set_si(lp->eq[k][n++], 0);
+		isl_int_set_si(lp->eq[k][n], 0); n++;
 		/* positivity constraint 1 >= 0 */
-		isl_int_set_si(lp->eq[k][n++], i == 0);
+		isl_int_set_si(lp->eq[k][n], i == 0); n++;
 		for (j = 0; j < bset1->n_eq; ++j) {
-			isl_int_set(lp->eq[k][n++], bset1->eq[j][i]);
-			isl_int_neg(lp->eq[k][n++], bset1->eq[j][i]);
+			isl_int_set(lp->eq[k][n], bset1->eq[j][i]); n++;
+			isl_int_neg(lp->eq[k][n], bset1->eq[j][i]); n++;
+		}
+		for (j = 0; j < bset1->n_ineq; ++j) {
+			isl_int_set(lp->eq[k][n], bset1->ineq[j][i]); n++;
 		}
-		for (j = 0; j < bset1->n_ineq; ++j)
-			isl_int_set(lp->eq[k][n++], bset1->ineq[j][i]);
 		/* positivity constraint 1 >= 0 */
-		isl_int_set_si(lp->eq[k][n++], -(i == 0));
+		isl_int_set_si(lp->eq[k][n], -(i == 0)); n++;
 		for (j = 0; j < bset2->n_eq; ++j) {
-			isl_int_neg(lp->eq[k][n++], bset2->eq[j][i]);
-			isl_int_set(lp->eq[k][n++], bset2->eq[j][i]);
+			isl_int_neg(lp->eq[k][n], bset2->eq[j][i]); n++;
+			isl_int_set(lp->eq[k][n], bset2->eq[j][i]); n++;
+		}
+		for (j = 0; j < bset2->n_ineq; ++j) {
+			isl_int_neg(lp->eq[k][n], bset2->ineq[j][i]); n++;
 		}
-		for (j = 0; j < bset2->n_ineq; ++j)
-			isl_int_neg(lp->eq[k][n++], bset2->ineq[j][i]);
 	}
 	lp = isl_basic_set_gauss(lp, NULL);
 	isl_basic_set_free(bset1);
@@ -1156,7 +1146,7 @@ error:
  * (including the "positivity constraint" 1 >= 0) and \alpha_{ij}
  * strictly positive numbers.  For simplicity we impose \alpha_{ij} >= 1.
  * We first set up an LP with as variables the \alpha{ij}.
- * In this formulateion, for each polyhedron i,
+ * In this formulation, for each polyhedron i,
  * the first constraint is the positivity constraint, followed by pairs
  * of variables for the equalities, followed by variables for the inequalities.
  * We then simply pick a feasible solution and compute s using (*).
@@ -1179,7 +1169,7 @@ static struct isl_vec *valid_direction(
 		goto error;
 	lp = valid_direction_lp(isl_basic_set_copy(bset1),
 				isl_basic_set_copy(bset2));
-	tab = isl_tab_from_basic_set(lp);
+	tab = isl_tab_from_basic_set(lp, 0);
 	sample = isl_tab_get_sample_value(tab);
 	isl_tab_free(tab);
 	isl_basic_set_free(lp);
@@ -1192,7 +1182,7 @@ static struct isl_vec *valid_direction(
 	isl_seq_clr(dir->block.data + 1, dir->size - 1);
 	n = 1;
 	/* positivity constraint 1 >= 0 */
-	isl_int_set(dir->block.data[0], sample->block.data[n++]);
+	isl_int_set(dir->block.data[0], sample->block.data[n]); n++;
 	for (i = 0; i < bset1->n_eq; ++i) {
 		isl_int_sub(sample->block.data[n],
 			    sample->block.data[n], sample->block.data[n+1]);
@@ -1207,9 +1197,9 @@ static struct isl_vec *valid_direction(
 				bset1->ctx->one, dir->block.data,
 				sample->block.data[n++], bset1->ineq[i], 1 + d);
 	isl_vec_free(sample);
+	isl_seq_normalize(bset1->ctx, dir->el, dir->size);
 	isl_basic_set_free(bset1);
 	isl_basic_set_free(bset2);
-	isl_seq_normalize(dir->block.data + 1, dir->size - 1);
 	return dir;
 error:
 	isl_vec_free(sample);
@@ -1333,9 +1323,9 @@ static struct isl_basic_set *convex_hull_pair_pointed(
 
 	bset1 = homogeneous_map(bset1, isl_mat_copy(T2));
 	bset2 = homogeneous_map(bset2, T2);
-	set = isl_set_alloc_dim(isl_basic_set_get_dim(bset1), 2, 0);
-	set = isl_set_add(set, bset1);
-	set = isl_set_add(set, bset2);
+	set = isl_set_alloc_space(isl_basic_set_get_space(bset1), 2, 0);
+	set = isl_set_add_basic_set(set, bset1);
+	set = isl_set_add_basic_set(set, bset2);
 	hull = uset_convex_hull(set);
 	hull = isl_basic_set_preimage(hull, T);
 	 
@@ -1349,18 +1339,50 @@ error:
 	return NULL;
 }
 
+static struct isl_basic_set *uset_convex_hull_wrap(struct isl_set *set);
+static struct isl_basic_set *modulo_affine_hull(
+	struct isl_set *set, struct isl_basic_set *affine_hull);
+
 /* Compute the convex hull of a pair of basic sets without any parameters or
  * integer divisions.
  *
+ * This function is called from uset_convex_hull_unbounded, which
+ * means that the complete convex hull is unbounded.  Some pairs
+ * of basic sets may still be bounded, though.
+ * They may even lie inside a lower dimensional space, in which
+ * case they need to be handled inside their affine hull since
+ * the main algorithm assumes that the result is full-dimensional.
+ *
  * If the convex hull of the two basic sets would have a non-trivial
  * lineality space, we first project out this lineality space.
  */
 static struct isl_basic_set *convex_hull_pair(struct isl_basic_set *bset1,
 	struct isl_basic_set *bset2)
 {
-	struct isl_basic_set *lin;
+	isl_basic_set *lin, *aff;
+	int bounded1, bounded2;
+
+	if (bset1->ctx->opt->convex == ISL_CONVEX_HULL_FM)
+		return convex_hull_pair_elim(bset1, bset2);
+
+	aff = isl_set_affine_hull(isl_basic_set_union(isl_basic_set_copy(bset1),
+						    isl_basic_set_copy(bset2)));
+	if (!aff)
+		goto error;
+	if (aff->n_eq != 0) 
+		return modulo_affine_hull(isl_basic_set_union(bset1, bset2), aff);
+	isl_basic_set_free(aff);
 
-	if (isl_basic_set_is_bounded(bset1) || isl_basic_set_is_bounded(bset2))
+	bounded1 = isl_basic_set_is_bounded(bset1);
+	bounded2 = isl_basic_set_is_bounded(bset2);
+
+	if (bounded1 < 0 || bounded2 < 0)
+		goto error;
+
+	if (bounded1 && bounded2)
+		uset_convex_hull_wrap(isl_basic_set_union(bset1, bset2));
+
+	if (bounded1 || bounded2)
 		return convex_hull_pair_pointed(bset1, bset2);
 
 	lin = induced_lineality_space(isl_basic_set_copy(bset1),
@@ -1374,9 +1396,9 @@ static struct isl_basic_set *convex_hull_pair(struct isl_basic_set *bset1,
 	}
 	if (lin->n_eq < isl_basic_set_total_dim(lin)) {
 		struct isl_set *set;
-		set = isl_set_alloc_dim(isl_basic_set_get_dim(bset1), 2, 0);
-		set = isl_set_add(set, bset1);
-		set = isl_set_add(set, bset2);
+		set = isl_set_alloc_space(isl_basic_set_get_space(bset1), 2, 0);
+		set = isl_set_add_basic_set(set, bset1);
+		set = isl_set_add_basic_set(set, bset2);
 		return modulo_lineality(set, lin);
 	}
 	isl_basic_set_free(lin);
@@ -1404,7 +1426,7 @@ struct isl_basic_set *isl_basic_set_lineality_space(struct isl_basic_set *bset)
 	isl_assert(bset->ctx, bset->n_div == 0, goto error);
 	dim = isl_basic_set_total_dim(bset);
 
-	lin = isl_basic_set_alloc_dim(isl_basic_set_get_dim(bset), 0, dim, 0);
+	lin = isl_basic_set_alloc_space(isl_basic_set_get_space(bset), 0, dim, 0);
 	if (!lin)
 		goto error;
 	for (i = 0; i < bset->n_eq; ++i) {
@@ -1446,14 +1468,14 @@ static struct isl_basic_set *uset_combined_lineality_space(struct isl_set *set)
 	if (!set)
 		return NULL;
 	if (set->n == 0) {
-		struct isl_dim *dim = isl_set_get_dim(set);
+		isl_space *dim = isl_set_get_space(set);
 		isl_set_free(set);
 		return isl_basic_set_empty(dim);
 	}
 
-	lin = isl_set_alloc_dim(isl_set_get_dim(set), set->n, 0);
+	lin = isl_set_alloc_space(isl_set_get_space(set), set->n, 0);
 	for (i = 0; i < set->n; ++i)
-		lin = isl_set_add(lin,
+		lin = isl_set_add_basic_set(lin,
 		    isl_basic_set_lineality_space(isl_basic_set_copy(set->p[i])));
 	isl_set_free(set);
 	return isl_set_affine_hull(lin);
@@ -1495,7 +1517,7 @@ static struct isl_basic_set *uset_convex_hull_unbounded(struct isl_set *set)
 			break;
 		}
 		if (t->n_eq < isl_basic_set_total_dim(t)) {
-			set = isl_set_add(set, convex_hull);
+			set = isl_set_add_basic_set(set, convex_hull);
 			return modulo_lineality(set, t);
 		}
 		isl_basic_set_free(t);
@@ -1509,13 +1531,8 @@ error:
 }
 
 /* Compute an initial hull for wrapping containing a single initial
- * facet by first computing bounds on the set and then using these
- * bounds to construct an initial facet.
- * This function is a remnant of an older implementation where the
- * bounds were also used to check whether the set was bounded.
- * Since this function will now only be called when we know the
- * set to be bounded, the initial facet should probably be constructed 
- * by simply using the coordinate directions instead.
+ * facet.
+ * This function assumes that the given set is bounded.
  */
 static struct isl_basic_set *initial_hull(struct isl_basic_set *hull,
 	struct isl_set *set)
@@ -1526,11 +1543,7 @@ static struct isl_basic_set *initial_hull(struct isl_basic_set *hull,
 
 	if (!hull)
 		goto error;
-	bounds = independent_bounds(set);
-	if (!bounds)
-		goto error;
-	isl_assert(set->ctx, bounds->n_row == isl_set_n_dim(set), goto error);
-	bounds = initial_facet_constraint(set, bounds);
+	bounds = initial_facet_constraint(set);
 	if (!bounds)
 		goto error;
 	k = isl_basic_set_alloc_inequality(hull);
@@ -1569,7 +1582,7 @@ static void update_constraint(struct isl_ctx *ctx, struct isl_hash_table *table,
 	struct max_constraint *c;
 	uint32_t c_hash;
 
-	c_hash = isl_seq_hash(con + 1, len, isl_hash_init());
+	c_hash = isl_seq_get_hash(con + 1, len);
 	entry = isl_hash_table_find(ctx, table, c_hash, max_constraint_equal,
 			con + 1, 0);
 	if (!entry)
@@ -1602,7 +1615,7 @@ static int has_constraint(struct isl_ctx *ctx, struct isl_hash_table *table,
 	struct max_constraint *c;
 	uint32_t c_hash;
 
-	c_hash = isl_seq_hash(con + 1, len, isl_hash_init());
+	c_hash = isl_seq_get_hash(con + 1, len);
 	entry = isl_hash_table_find(ctx, table, c_hash, max_constraint_equal,
 			con + 1, 0);
 	if (!entry)
@@ -1658,9 +1671,9 @@ static struct isl_basic_set *common_constraints(struct isl_basic_set *hull,
 	if (isl_hash_table_init(hull->ctx, table, min_constraints))
 		goto error;
 
-	total = isl_dim_total(set->dim);
+	total = isl_space_dim(set->dim, isl_dim_all);
 	for (i = 0; i < set->p[best]->n_ineq; ++i) {
-		constraints[i].c = isl_mat_sub_alloc(hull->ctx,
+		constraints[i].c = isl_mat_sub_alloc6(hull->ctx,
 			set->p[best]->ineq + i, 0, 1, 0, 1 + total);
 		if (!constraints[i].c)
 			goto error;
@@ -1669,8 +1682,7 @@ static struct isl_basic_set *common_constraints(struct isl_basic_set *hull,
 	for (i = 0; i < min_constraints; ++i) {
 		struct isl_hash_table_entry *entry;
 		uint32_t c_hash;
-		c_hash = isl_seq_hash(constraints[i].c->row[0] + 1, total,
-					isl_hash_init());
+		c_hash = isl_seq_get_hash(constraints[i].c->row[0] + 1, total);
 		entry = isl_hash_table_find(hull->ctx, table, c_hash,
 			max_constraint_equal, constraints[i].c->row[0] + 1, 1);
 		if (!entry)
@@ -1756,7 +1768,7 @@ static struct isl_basic_set *proto_hull(struct isl_set *set, int *is_hull)
 		n_ineq += set->p[i]->n_eq;
 		n_ineq += set->p[i]->n_ineq;
 	}
-	hull = isl_basic_set_alloc_dim(isl_dim_copy(set->dim), 0, 0, n_ineq);
+	hull = isl_basic_set_alloc_space(isl_space_copy(set->dim), 0, 0, n_ineq);
 	hull = isl_basic_set_set_rational(hull);
 	if (!hull)
 		return NULL;
@@ -1787,7 +1799,6 @@ static struct isl_basic_set *uset_convex_hull_wrap(struct isl_set *set)
  */
 static struct isl_basic_set *uset_convex_hull(struct isl_set *set)
 {
-	int i;
 	struct isl_basic_set *convex_hull = NULL;
 	struct isl_basic_set *lin;
 
@@ -1809,7 +1820,8 @@ static struct isl_basic_set *uset_convex_hull(struct isl_set *set)
 	if (isl_set_n_dim(set) == 1)
 		return convex_hull_1d(set);
 
-	if (isl_set_is_bounded(set))
+	if (isl_set_is_bounded(set) &&
+	    set->ctx->opt->convex == ISL_CONVEX_HULL_WRAP)
 		return uset_convex_hull_wrap(set);
 
 	lin = uset_combined_lineality_space(isl_set_copy(set));
@@ -1836,26 +1848,26 @@ error:
  */
 static struct isl_basic_set *uset_convex_hull_wrap_bounded(struct isl_set *set)
 {
-	int i;
 	struct isl_basic_set *convex_hull = NULL;
 
+	if (!set)
+		goto error;
+
 	if (isl_set_n_dim(set) == 0) {
-		convex_hull = isl_basic_set_universe(isl_dim_copy(set->dim));
+		convex_hull = isl_basic_set_universe(isl_space_copy(set->dim));
 		isl_set_free(set);
 		convex_hull = isl_basic_set_set_rational(convex_hull);
 		return convex_hull;
 	}
 
 	set = isl_set_set_rational(set);
-
-	if (!set)
-		goto error;
-	set = isl_set_normalize(set);
+	set = isl_set_coalesce(set);
 	if (!set)
 		goto error;
 	if (set->n == 1) {
 		convex_hull = isl_basic_set_copy(set->p[0]);
 		isl_set_free(set);
+		convex_hull = isl_basic_map_remove_redundancies(convex_hull);
 		return convex_hull;
 	}
 	if (isl_set_n_dim(set) == 1)
@@ -1872,7 +1884,7 @@ error:
  * convex hull of the transformed set and then add the equalities back
  * (after performing the inverse transformation.
  */
-static struct isl_basic_set *modulo_affine_hull(struct isl_ctx *ctx,
+static struct isl_basic_set *modulo_affine_hull(
 	struct isl_set *set, struct isl_basic_set *affine_hull)
 {
 	struct isl_mat *T;
@@ -1922,6 +1934,8 @@ struct isl_basic_map *isl_map_convex_hull(struct isl_map *map)
 
 	map = isl_map_detect_equalities(map);
 	map = isl_map_align_divs(map);
+	if (!map)
+		goto error;
 	model = isl_basic_map_copy(map->p[0]);
 	set = isl_map_underlying_set(map);
 	if (!set)
@@ -1931,13 +1945,15 @@ struct isl_basic_map *isl_map_convex_hull(struct isl_map *map)
 	if (!affine_hull)
 		goto error;
 	if (affine_hull->n_eq != 0)
-		bset = modulo_affine_hull(ctx, set, affine_hull);
+		bset = modulo_affine_hull(set, affine_hull);
 	else {
 		isl_basic_set_free(affine_hull);
 		bset = uset_convex_hull(set);
 	}
 
 	convex_hull = isl_basic_map_overlying_set(bset, model);
+	if (!convex_hull)
+		return NULL;
 
 	ISL_F_SET(convex_hull, ISL_BASIC_MAP_NO_IMPLICIT);
 	ISL_F_SET(convex_hull, ISL_BASIC_MAP_ALL_EQUALITIES);
@@ -1955,6 +1971,19 @@ struct isl_basic_set *isl_set_convex_hull(struct isl_set *set)
 		isl_map_convex_hull((struct isl_map *)set);
 }
 
+__isl_give isl_basic_map *isl_map_polyhedral_hull(__isl_take isl_map *map)
+{
+	isl_basic_map *hull;
+
+	hull = isl_map_convex_hull(map);
+	return isl_basic_map_remove_divs(hull);
+}
+
+__isl_give isl_basic_set *isl_set_polyhedral_hull(__isl_take isl_set *set)
+{
+	return (isl_basic_set *)isl_map_polyhedral_hull((isl_map *)set);
+}
+
 struct sh_data_entry {
 	struct isl_hash_table	*table;
 	struct isl_tab		*tab;
@@ -1973,7 +2002,7 @@ struct sh_data {
 	struct isl_ctx		*ctx;
 	unsigned		n;
 	struct isl_hash_table	*hull_table;
-	struct sh_data_entry	p[0];
+	struct sh_data_entry	p[1];
 };
 
 static void sh_data_free(struct sh_data *data)
@@ -2013,7 +2042,7 @@ static int hash_ineq(struct isl_ctx *ctx, struct isl_hash_table *table,
 
 	v.len = len;
 	v.p = ineq;
-	c_hash = isl_seq_hash(ineq + 1, len, isl_hash_init());
+	c_hash = isl_seq_get_hash(ineq + 1, len);
 	entry = isl_hash_table_find(ctx, table, c_hash, has_ineq, &v, 1);
 	if (!entry)
 		return - 1;
@@ -2051,7 +2080,8 @@ static struct sh_data *sh_data_alloc(struct isl_set *set, unsigned n_ineq)
 	int i;
 
 	data = isl_calloc(set->ctx, struct sh_data,
-		sizeof(struct sh_data) + set->n * sizeof(struct sh_data_entry));
+		sizeof(struct sh_data) +
+		(set->n - 1) * sizeof(struct sh_data_entry));
 	if (!data)
 		return NULL;
 	data->ctx = set->ctx;
@@ -2077,18 +2107,20 @@ error:
  * it can be relaxed (by increasing the constant term) to become
  * a bound for that basic set.  In the latter case, the constant
  * term is updated.
+ * Relaxation of the constant term is only allowed if "shift" is set.
+ *
  * Return 1 if "ineq" is a bound
  *	  0 if "ineq" may attain arbitrarily small values on basic set "j"
  *	 -1 if some error occurred
  */
 static int is_bound(struct sh_data *data, struct isl_set *set, int j,
-			isl_int *ineq)
+	isl_int *ineq, int shift)
 {
 	enum isl_lp_result res;
 	isl_int opt;
 
 	if (!data->p[j].tab) {
-		data->p[j].tab = isl_tab_from_basic_set(set->p[j]);
+		data->p[j].tab = isl_tab_from_basic_set(set->p[j], 0);
 		if (!data->p[j].tab)
 			return -1;
 	}
@@ -2097,18 +2129,22 @@ static int is_bound(struct sh_data *data, struct isl_set *set, int j,
 
 	res = isl_tab_min(data->p[j].tab, ineq, data->ctx->one,
 				&opt, NULL, 0);
-	if (res == isl_lp_ok && isl_int_is_neg(opt))
-		isl_int_sub(ineq[0], ineq[0], opt);
+	if (res == isl_lp_ok && isl_int_is_neg(opt)) {
+		if (shift)
+			isl_int_sub(ineq[0], ineq[0], opt);
+		else
+			res = isl_lp_unbounded;
+	}
 
 	isl_int_clear(opt);
 
-	return res == isl_lp_ok ? 1 :
+	return (res == isl_lp_ok || res == isl_lp_empty) ? 1 :
 	       res == isl_lp_unbounded ? 0 : -1;
 }
 
-/* Check if inequality "ineq" from basic set "i" can be relaxed to
+/* Check if inequality "ineq" from basic set "i" is or can be relaxed to
  * become a bound on the whole set.  If so, add the (relaxed) inequality
- * to "hull".
+ * to "hull".  Relaxation is only allowed if "shift" is set.
  *
  * We first check if "hull" already contains a translate of the inequality.
  * If so, we are done.
@@ -2124,7 +2160,8 @@ static int is_bound(struct sh_data *data, struct isl_set *set, int j,
  * the inequality accordingly.
  */
 static struct isl_basic_set *add_bound(struct isl_basic_set *hull,
-	struct sh_data *data, struct isl_set *set, int i, isl_int *ineq)
+	struct sh_data *data, struct isl_set *set, int i, isl_int *ineq,
+	int shift)
 {
 	uint32_t c_hash;
 	struct ineq_cmp_data v;
@@ -2136,7 +2173,7 @@ static struct isl_basic_set *add_bound(struct isl_basic_set *hull,
 
 	v.len = isl_basic_set_total_dim(hull);
 	v.p = ineq;
-	c_hash = isl_seq_hash(ineq + 1, v.len, isl_hash_init());
+	c_hash = isl_seq_get_hash(ineq + 1, v.len);
 
 	entry = isl_hash_table_find(hull->ctx, data->hull_table, c_hash,
 					has_ineq, &v, 0);
@@ -2159,7 +2196,7 @@ static struct isl_basic_set *add_bound(struct isl_basic_set *hull,
 
 	for (j = 0; j < i; ++j) {
 		int bound;
-		bound = is_bound(data, set, j, hull->ineq[k]);
+		bound = is_bound(data, set, j, hull->ineq[k], shift);
 		if (bound < 0)
 			goto error;
 		if (!bound)
@@ -2187,7 +2224,7 @@ static struct isl_basic_set *add_bound(struct isl_basic_set *hull,
 				isl_int_neg(ineq_j[0], ineq_j[0]);
 			continue;
 		}
-		bound = is_bound(data, set, j, hull->ineq[k]);
+		bound = is_bound(data, set, j, hull->ineq[k], shift);
 		if (bound < 0)
 			goto error;
 		if (!bound)
@@ -2210,12 +2247,12 @@ error:
 	return NULL;
 }
 
-/* Check if any inequality from basic set "i" can be relaxed to
+/* Check if any inequality from basic set "i" is or can be relaxed to
  * become a bound on the whole set.  If so, add the (relaxed) inequality
- * to "hull".
+ * to "hull".  Relaxation is only allowed if "shift" is set.
  */
 static struct isl_basic_set *add_bounds(struct isl_basic_set *bset,
-	struct sh_data *data, struct isl_set *set, int i)
+	struct sh_data *data, struct isl_set *set, int i, int shift)
 {
 	int j, k;
 	unsigned dim = isl_basic_set_total_dim(bset);
@@ -2223,23 +2260,26 @@ static struct isl_basic_set *add_bounds(struct isl_basic_set *bset,
 	for (j = 0; j < set->p[i]->n_eq; ++j) {
 		for (k = 0; k < 2; ++k) {
 			isl_seq_neg(set->p[i]->eq[j], set->p[i]->eq[j], 1+dim);
-			add_bound(bset, data, set, i, set->p[i]->eq[j]);
+			bset = add_bound(bset, data, set, i, set->p[i]->eq[j],
+					    shift);
 		}
 	}
 	for (j = 0; j < set->p[i]->n_ineq; ++j)
-		add_bound(bset, data, set, i, set->p[i]->ineq[j]);
+		bset = add_bound(bset, data, set, i, set->p[i]->ineq[j], shift);
 	return bset;
 }
 
 /* Compute a superset of the convex hull of set that is described
- * by only translates of the constraints in the constituents of set.
+ * by only (translates of) the constraints in the constituents of set.
+ * Translation is only allowed if "shift" is set.
  */
-static struct isl_basic_set *uset_simple_hull(struct isl_set *set)
+static __isl_give isl_basic_set *uset_simple_hull(__isl_take isl_set *set,
+	int shift)
 {
 	struct sh_data *data = NULL;
 	struct isl_basic_set *hull = NULL;
 	unsigned n_ineq;
-	int i, j;
+	int i;
 
 	if (!set)
 		return NULL;
@@ -2251,7 +2291,7 @@ static struct isl_basic_set *uset_simple_hull(struct isl_set *set)
 		n_ineq += 2 * set->p[i]->n_eq + set->p[i]->n_ineq;
 	}
 
-	hull = isl_basic_set_alloc_dim(isl_dim_copy(set->dim), 0, 0, n_ineq);
+	hull = isl_basic_set_alloc_space(isl_space_copy(set->dim), 0, 0, n_ineq);
 	if (!hull)
 		goto error;
 
@@ -2260,7 +2300,7 @@ static struct isl_basic_set *uset_simple_hull(struct isl_set *set)
 		goto error;
 
 	for (i = 0; i < set->n; ++i)
-		hull = add_bounds(hull, data, set, i);
+		hull = add_bounds(hull, data, set, i, shift);
 
 	sh_data_free(data);
 	isl_set_free(set);
@@ -2274,9 +2314,11 @@ error:
 }
 
 /* Compute a superset of the convex hull of map that is described
- * by only translates of the constraints in the constituents of map.
+ * by only (translates of) the constraints in the constituents of map.
+ * Translation is only allowed if "shift" is set.
  */
-struct isl_basic_map *isl_map_simple_hull(struct isl_map *map)
+static __isl_give isl_basic_map *map_simple_hull(__isl_take isl_map *map,
+	int shift)
 {
 	struct isl_set *set = NULL;
 	struct isl_basic_map *model = NULL;
@@ -2300,28 +2342,54 @@ struct isl_basic_map *isl_map_simple_hull(struct isl_map *map)
 	map = isl_map_detect_equalities(map);
 	affine_hull = isl_map_affine_hull(isl_map_copy(map));
 	map = isl_map_align_divs(map);
-	model = isl_basic_map_copy(map->p[0]);
+	model = map ? isl_basic_map_copy(map->p[0]) : NULL;
 
 	set = isl_map_underlying_set(map);
 
-	bset = uset_simple_hull(set);
+	bset = uset_simple_hull(set, shift);
 
 	hull = isl_basic_map_overlying_set(bset, model);
 
 	hull = isl_basic_map_intersect(hull, affine_hull);
-	hull = isl_basic_map_convex_hull(hull);
+	hull = isl_basic_map_remove_redundancies(hull);
+
+	if (!hull)
+		return NULL;
 	ISL_F_SET(hull, ISL_BASIC_MAP_NO_IMPLICIT);
 	ISL_F_SET(hull, ISL_BASIC_MAP_ALL_EQUALITIES);
 
 	return hull;
 }
 
+/* Compute a superset of the convex hull of map that is described
+ * by only translates of the constraints in the constituents of map.
+ */
+__isl_give isl_basic_map *isl_map_simple_hull(__isl_take isl_map *map)
+{
+	return map_simple_hull(map, 1);
+}
+
 struct isl_basic_set *isl_set_simple_hull(struct isl_set *set)
 {
 	return (struct isl_basic_set *)
 		isl_map_simple_hull((struct isl_map *)set);
 }
 
+/* Compute a superset of the convex hull of map that is described
+ * by only the constraints in the constituents of map.
+ */
+__isl_give isl_basic_map *isl_map_unshifted_simple_hull(
+	__isl_take isl_map *map)
+{
+	return map_simple_hull(map, 0);
+}
+
+__isl_give isl_basic_set *isl_set_unshifted_simple_hull(
+	__isl_take isl_set *set)
+{
+	return isl_map_unshifted_simple_hull(set);
+}
+
 /* Given a set "set", return parametric bounds on the dimension "dim".
  */
 static struct isl_basic_set *set_bounds(struct isl_set *set, int dim)