X-Git-Url: http://review.tizen.org/git/?a=blobdiff_plain;f=isl_convex_hull.c;h=1980cca99838309fe52034c6a03027f75c515eb0;hb=7b55974acad42b968f06fe5b1b55ad3bebea7e3d;hp=477ec3ced42ced17b49d1e068c0c29cb81b6f699;hpb=95e960e70d9b7099739ce5c550e537b7a6371e9e;p=platform%2Fupstream%2Fisl.git

diff --git a/isl_convex_hull.c b/isl_convex_hull.c
index 477ec3c..1980cca 100644
--- a/isl_convex_hull.c
+++ b/isl_convex_hull.c
@@ -7,7 +7,7 @@
 #include "isl_equalities.h"
 #include "isl_tab.h"
 
-static struct isl_basic_set *uset_convex_hull_wrap(struct isl_set *set);
+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)
 {
@@ -50,7 +50,7 @@ int isl_basic_map_constraint_is_redundant(struct isl_basic_map **bmap,
 	if (i < total)
 		return 0;
 
-	res = isl_solve_lp(*bmap, 0, c+1, (*bmap)->ctx->one, opt_n, opt_d);
+	res = isl_solve_lp(*bmap, 0, c, (*bmap)->ctx->one, opt_n, opt_d);
 	if (res == isl_lp_unbounded)
 		return 0;
 	if (res == isl_lp_error)
@@ -59,10 +59,6 @@ int isl_basic_map_constraint_is_redundant(struct isl_basic_map **bmap,
 		*bmap = isl_basic_map_set_to_empty(*bmap);
 		return 0;
 	}
-	if (opt_d)
-		isl_int_addmul(*opt_n, *opt_d, c[0]);
-	else
-		isl_int_add(*opt_n, *opt_n, c[0]);
 	return !isl_int_is_neg(*opt_n);
 }
 
@@ -97,10 +93,10 @@ struct isl_basic_map *isl_basic_map_convex_hull(struct isl_basic_map *bmap)
 		return bmap;
 
 	tab = isl_tab_from_basic_map(bmap);
-	tab = isl_tab_detect_equalities(bmap->ctx, tab);
-	tab = isl_tab_detect_redundant(bmap->ctx, tab);
+	tab = isl_tab_detect_equalities(tab);
+	tab = isl_tab_detect_redundant(tab);
 	bmap = isl_basic_map_update_from_tab(bmap, tab);
-	isl_tab_free(bmap->ctx, 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;
@@ -116,8 +112,7 @@ struct isl_basic_set *isl_basic_set_convex_hull(struct isl_basic_set *bset)
  * constraint c and if so, set the constant term such that the
  * resulting constraint is a bounding constraint for the set.
  */
-static int uset_is_bound(struct isl_ctx *ctx, struct isl_set *set,
-	isl_int *c, unsigned len)
+static int uset_is_bound(struct isl_set *set, isl_int *c, unsigned len)
 {
 	int first;
 	int j;
@@ -134,7 +129,7 @@ static int uset_is_bound(struct isl_ctx *ctx, struct isl_set *set,
 			continue;
 
 		res = isl_solve_lp((struct isl_basic_map*)set->p[j],
-				0, c+1, ctx->one, &opt, &opt_denom);
+				0, c, set->ctx->one, &opt, &opt_denom);
 		if (res == isl_lp_unbounded)
 			break;
 		if (res == isl_lp_error)
@@ -147,13 +142,12 @@ static int uset_is_bound(struct isl_ctx *ctx, struct isl_set *set,
 		}
 		if (!isl_int_is_one(opt_denom))
 			isl_seq_scale(c, c, opt_denom, len);
-		if (first || isl_int_lt(opt, c[0]))
-			isl_int_set(c[0], opt);
+		if (first || isl_int_is_neg(opt))
+			isl_int_sub(c[0], c[0], opt);
 		first = 0;
 	}
 	isl_int_clear(opt);
 	isl_int_clear(opt_denom);
-	isl_int_neg(c[0], c[0]);
 	return j >= set->n;
 error:
 	isl_int_clear(opt);
@@ -161,15 +155,14 @@ error:
 	return -1;
 }
 
-/* Check if "c" is a direction with both a lower bound and an upper
- * bound in "set" that is independent of the previously found "n"
+/* 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_ctx *ctx,
-	struct isl_set *set, isl_int *c,
+static int is_independent_bound(struct isl_set *set, isl_int *c,
 	struct isl_mat *dirs, int n)
 {
 	int is_bound;
@@ -195,12 +188,7 @@ static int is_independent_bound(struct isl_ctx *ctx,
 		}
 	}
 
-	isl_seq_neg(dirs->row[n] + 1, dirs->row[n] + 1, dirs->n_col - 1);
-	is_bound = uset_is_bound(ctx, set, dirs->row[n], dirs->n_col);
-	isl_seq_neg(dirs->row[n] + 1, dirs->row[n] + 1, dirs->n_col - 1);
-	if (is_bound != 1)
-		return is_bound;
-	is_bound = uset_is_bound(ctx, set, dirs->row[n], dirs->n_col);
+	is_bound = uset_is_bound(set, dirs->row[n], dirs->n_col);
 	if (is_bound != 1)
 		return is_bound;
 	if (i < n) {
@@ -217,14 +205,13 @@ static int is_independent_bound(struct isl_ctx *ctx,
  * on the set "set", based on the constraints of the basic sets
  * in "set".
  */
-static struct isl_mat *independent_bounds(struct isl_ctx *ctx,
-	struct isl_set *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);
 
-	dirs = isl_mat_alloc(ctx, dim, 1+dim);
+	dirs = isl_mat_alloc(set->ctx, dim, 1+dim);
 	if (!dirs)
 		goto error;
 
@@ -234,16 +221,14 @@ static struct isl_mat *independent_bounds(struct isl_ctx *ctx,
 		struct isl_basic_set *bset = set->p[i];
 
 		for (j = 0; n < dim && j < bset->n_eq; ++j) {
-			f = is_independent_bound(ctx, set, bset->eq[j],
-						dirs, n);
+			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(ctx, set, bset->ineq[j],
-						dirs, n);
+			f = is_independent_bound(set, bset->ineq[j], dirs, n);
 			if (f < 0)
 				goto error;
 			if (f)
@@ -253,12 +238,11 @@ static struct isl_mat *independent_bounds(struct isl_ctx *ctx,
 	dirs->n_row = n;
 	return dirs;
 error:
-	isl_mat_free(ctx, dirs);
+	isl_mat_free(dirs);
 	return NULL;
 }
 
-static struct isl_basic_set *isl_basic_set_set_rational(
-	struct isl_basic_set *bset)
+struct isl_basic_set *isl_basic_set_set_rational(struct isl_basic_set *bset)
 {
 	if (!bset)
 		return NULL;
@@ -293,7 +277,7 @@ error:
 	return NULL;
 }
 
-static struct isl_basic_set *isl_basic_set_add_equality(struct isl_ctx *ctx,
+static struct isl_basic_set *isl_basic_set_add_equality(
 	struct isl_basic_set *bset, isl_int *c)
 {
 	int i;
@@ -306,6 +290,7 @@ static struct isl_basic_set *isl_basic_set_add_equality(struct isl_ctx *ctx,
 	isl_assert(ctx, isl_basic_set_n_param(bset) == 0, goto error);
 	isl_assert(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);
 	i = isl_basic_set_alloc_equality(bset);
 	if (i < 0)
@@ -317,8 +302,7 @@ error:
 	return NULL;
 }
 
-static struct isl_set *isl_set_add_equality(struct isl_ctx *ctx,
-	struct isl_set *set, isl_int *c)
+static struct isl_set *isl_set_add_equality(struct isl_set *set, isl_int *c)
 {
 	int i;
 
@@ -326,7 +310,7 @@ static struct isl_set *isl_set_add_equality(struct isl_ctx *ctx,
 	if (!set)
 		return NULL;
 	for (i = 0; i < set->n; ++i) {
-		set->p[i] = isl_basic_set_add_equality(ctx, set->p[i], c);
+		set->p[i] = isl_basic_set_add_equality(set->p[i], c);
 		if (!set->p[i])
 			goto error;
 	}
@@ -344,7 +328,7 @@ error:
  *				    [ 1 ]
  *				A_i [ x ]  >= 0
  *
- * then the resulting set is of dimension n*(1+d) and has as contraints
+ * then the resulting set is of dimension n*(1+d) and has as constraints
  *
  *				    [ a_i ]
  *				A_i [ x_i ] >= 0
@@ -353,8 +337,7 @@ error:
  *
  *			\sum_i x_{i,1} = 1
  */
-static struct isl_basic_set *wrap_constraints(struct isl_ctx *ctx,
-							struct isl_set *set)
+static struct isl_basic_set *wrap_constraints(struct isl_set *set)
 {
 	struct isl_basic_set *lp;
 	unsigned n_eq;
@@ -372,7 +355,7 @@ static struct isl_basic_set *wrap_constraints(struct isl_ctx *ctx,
 		n_eq += set->p[i]->n_eq;
 		n_ineq += set->p[i]->n_ineq;
 	}
-	lp = isl_basic_set_alloc(ctx, 0, dim * set->n, 0, n_eq, n_ineq);
+	lp = isl_basic_set_alloc(set->ctx, 0, dim * set->n, 0, n_eq, n_ineq);
 	if (!lp)
 		return NULL;
 	lp_dim = isl_basic_set_n_dim(lp);
@@ -458,12 +441,10 @@ static struct isl_basic_set *wrap_constraints(struct isl_ctx *ctx,
  * In the original space, we need to take the same combination of the
  * corresponding constraints "facet" and "ridge".
  *
- * 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.
+ * Note that a is always finite, since we only apply the wrapping
+ * technique to a union of polytopes.
  */
-static isl_int *wrap_facet(struct isl_ctx *ctx, struct isl_set *set,
-	isl_int *facet, isl_int *ridge)
+static isl_int *wrap_facet(struct isl_set *set, isl_int *facet, isl_int *ridge)
 {
 	int i;
 	struct isl_mat *T = NULL;
@@ -476,46 +457,46 @@ static isl_int *wrap_facet(struct isl_ctx *ctx, struct isl_set *set,
 	set = isl_set_copy(set);
 
 	dim = 1 + isl_set_n_dim(set);
-	T = isl_mat_alloc(ctx, 3, dim);
+	T = isl_mat_alloc(set->ctx, 3, dim);
 	if (!T)
 		goto error;
 	isl_int_set_si(T->row[0][0], 1);
 	isl_seq_clr(T->row[0]+1, dim - 1);
 	isl_seq_cpy(T->row[1], facet, dim);
 	isl_seq_cpy(T->row[2], ridge, dim);
-	T = isl_mat_right_inverse(ctx, T);
+	T = isl_mat_right_inverse(T);
 	set = isl_set_preimage(set, T);
 	T = NULL;
 	if (!set)
 		goto error;
-	lp = wrap_constraints(ctx, set);
-	obj = isl_vec_alloc(ctx, dim*set->n);
+	lp = wrap_constraints(set);
+	obj = isl_vec_alloc(set->ctx, 1 + dim*set->n);
 	if (!obj)
 		goto error;
+	isl_int_set_si(obj->block.data[0], 0);
 	for (i = 0; i < set->n; ++i) {
-		isl_seq_clr(obj->block.data+dim*i, 2);
-		isl_int_set_si(obj->block.data[dim*i+2], 1);
-		isl_seq_clr(obj->block.data+dim*i+3, dim-3);
+		isl_seq_clr(obj->block.data + 1 + dim*i, 2);
+		isl_int_set_si(obj->block.data[1 + dim*i+2], 1);
+		isl_seq_clr(obj->block.data + 1 + dim*i+3, dim-3);
 	}
 	isl_int_init(num);
 	isl_int_init(den);
 	res = isl_solve_lp((struct isl_basic_map *)lp, 0,
-					obj->block.data, ctx->one, &num, &den);
+				    obj->block.data, set->ctx->one, &num, &den);
 	if (res == isl_lp_ok) {
 		isl_int_neg(num, num);
 		isl_seq_combine(facet, num, facet, den, ridge, dim);
 	}
 	isl_int_clear(num);
 	isl_int_clear(den);
-	isl_vec_free(ctx, obj);
+	isl_vec_free(obj);
 	isl_basic_set_free(lp);
 	isl_set_free(set);
-	isl_assert(ctx, res == isl_lp_ok || res == isl_lp_unbounded, 
-		   return NULL);
+	isl_assert(set->ctx, res == isl_lp_ok, return NULL);
 	return facet;
 error:
 	isl_basic_set_free(lp);
-	isl_mat_free(ctx, T);
+	isl_mat_free(T);
 	isl_set_free(set);
 	return NULL;
 }
@@ -532,8 +513,8 @@ error:
  * The resulting linear combination of the bounding constraints will
  * correspond to a facet of the convex hull.
  */
-static struct isl_mat *initial_facet_constraint(struct isl_ctx *ctx,
-	struct isl_set *set, struct isl_mat *bounds)
+static struct isl_mat *initial_facet_constraint(struct isl_set *set,
+	struct isl_mat *bounds)
 {
 	struct isl_set *slice = NULL;
 	struct isl_basic_set *face = NULL;
@@ -546,7 +527,7 @@ static struct isl_mat *initial_facet_constraint(struct isl_ctx *ctx,
 
 	while (bounds->n_row > 1) {
 		slice = isl_set_copy(set);
-		slice = isl_set_add_equality(ctx, slice, bounds->row[0]);
+		slice = isl_set_add_equality(slice, bounds->row[0]);
 		face = isl_set_affine_hull(slice);
 		if (!face)
 			goto error;
@@ -554,29 +535,27 @@ static struct isl_mat *initial_facet_constraint(struct isl_ctx *ctx,
 			isl_basic_set_free(face);
 			break;
 		}
-		m = isl_mat_alloc(ctx, 1 + face->n_eq, 1 + dim);
+		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(ctx, m);
-		Q = isl_mat_right_inverse(ctx, isl_mat_copy(ctx, U));
-		U = isl_mat_drop_cols(ctx, U, 1 + face->n_eq,
-						dim - face->n_eq);
-		Q = isl_mat_drop_rows(ctx, Q, 1 + face->n_eq,
-						dim - face->n_eq);
-		U = isl_mat_drop_cols(ctx, U, 0, 1);
-		Q = isl_mat_drop_rows(ctx, Q, 0, 1);
-		bounds = isl_mat_product(ctx, bounds, U);
-		bounds = isl_mat_product(ctx, bounds, Q);
+		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(ctx, set, bounds->row[0],
+		if (!wrap_facet(set, bounds->row[0],
 					  bounds->row[bounds->n_row-1]))
 			goto error;
 		isl_basic_set_free(face);
@@ -585,7 +564,7 @@ static struct isl_mat *initial_facet_constraint(struct isl_ctx *ctx,
 	return bounds;
 error:
 	isl_basic_set_free(face);
-	isl_mat_free(ctx, bounds);
+	isl_mat_free(bounds);
 	return NULL;
 }
 
@@ -628,30 +607,33 @@ error:
  * After computing the facets of the facet in the z' space,
  * we convert them back to the x space through Q.
  */
-static struct isl_basic_set *compute_facet(struct isl_ctx *ctx,
-	struct isl_set *set, isl_int *c)
+static struct isl_basic_set *compute_facet(struct isl_set *set, isl_int *c)
 {
 	struct isl_mat *m, *U, *Q;
-	struct isl_basic_set *facet;
+	struct isl_basic_set *facet = NULL;
+	struct isl_ctx *ctx;
 	unsigned dim;
 
+	ctx = set->ctx;
 	set = isl_set_copy(set);
 	dim = isl_set_n_dim(set);
-	m = isl_mat_alloc(ctx, 2, 1 + dim);
+	m = isl_mat_alloc(set->ctx, 2, 1 + dim);
 	if (!m)
 		goto error;
 	isl_int_set_si(m->row[0][0], 1);
 	isl_seq_clr(m->row[0]+1, dim);
 	isl_seq_cpy(m->row[1], c, 1+dim);
-	U = isl_mat_right_inverse(ctx, m);
-	Q = isl_mat_right_inverse(ctx, isl_mat_copy(ctx, U));
-	U = isl_mat_drop_cols(ctx, U, 1, 1);
-	Q = isl_mat_drop_rows(ctx, Q, 1, 1);
+	U = isl_mat_right_inverse(m);
+	Q = isl_mat_right_inverse(isl_mat_copy(U));
+	U = isl_mat_drop_cols(U, 1, 1);
+	Q = isl_mat_drop_rows(Q, 1, 1);
 	set = isl_set_preimage(set, U);
-	facet = uset_convex_hull_wrap(set);
+	facet = uset_convex_hull_wrap_bounded(set);
 	facet = isl_basic_set_preimage(facet, Q);
+	isl_assert(ctx, facet->n_eq == 0, goto error);
 	return facet;
 error:
+	isl_basic_set_free(facet);
 	isl_set_free(set);
 	return NULL;
 }
@@ -661,6 +643,14 @@ error:
  * the adjacent facets through wrapping, adding those facets that we
  * hadn't already found before.
  *
+ * For each facet we have found so far, we first compute its facets
+ * in the resulting convex hull.  That is, we compute the ridges
+ * of the resulting convex hull contained in the facet.
+ * We also compute the corresponding facet in the current approximation
+ * of the convex hull.  There is no need to wrap around the ridges
+ * in this facet since that would result in a facet that is already
+ * present in the current approximation.
+ *
  * This function can still be significantly optimized by checking which of
  * the facets of the basic sets are also facets of the convex hull and
  * using all the facets so far to help in constructing the facets of the
@@ -669,63 +659,56 @@ error:
  * using the technique in section "3.1 Ridge Generation" of
  * "Extended Convex Hull" by Fukuda et al.
  */
-static struct isl_basic_set *extend(struct isl_ctx *ctx, struct isl_set *set,
-	struct isl_mat *initial)
+static struct isl_basic_set *extend(struct isl_basic_set *hull,
+	struct isl_set *set)
 {
 	int i, j, f;
 	int k;
-	struct isl_basic_set *hull = NULL;
 	struct isl_basic_set *facet = NULL;
-	unsigned n_ineq;
+	struct isl_basic_set *hull_facet = NULL;
 	unsigned total;
 	unsigned dim;
 
-	isl_assert(ctx, set->n > 0, goto error);
+	isl_assert(set->ctx, set->n > 0, goto error);
 
-	n_ineq = 1;
-	for (i = 0; i < set->n; ++i) {
-		n_ineq += set->p[i]->n_eq;
-		n_ineq += set->p[i]->n_ineq;
-	}
 	dim = isl_set_n_dim(set);
-	isl_assert(ctx, 1 + dim == initial->n_col, goto error);
-	hull = isl_basic_set_alloc(ctx, 0, dim, 0, 0, n_ineq);
-	hull = isl_basic_set_set_rational(hull);
-	if (!hull)
-		goto error;
-	k = isl_basic_set_alloc_inequality(hull);
-	if (k < 0)
-		goto error;
-	isl_seq_cpy(hull->ineq[k], initial->row[0], initial->n_col);
+
 	for (i = 0; i < hull->n_ineq; ++i) {
-		facet = compute_facet(ctx, set, hull->ineq[i]);
+		facet = compute_facet(set, hull->ineq[i]);
+		facet = isl_basic_set_add_equality(facet, hull->ineq[i]);
+		facet = isl_basic_set_gauss(facet, NULL);
+		facet = isl_basic_set_normalize_constraints(facet);
+		hull_facet = isl_basic_set_copy(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)
 			goto error;
-		if (facet->n_ineq + hull->n_ineq > n_ineq) {
-			hull = isl_basic_set_extend(hull,
-				0, dim, 0, 0, facet->n_ineq);
-			n_ineq = hull->n_ineq + facet->n_ineq;
-		}
+		hull = isl_basic_set_cow(hull);
+		hull = isl_basic_set_extend_dim(hull,
+			isl_dim_copy(hull->dim), 0, 0, facet->n_ineq);
 		for (j = 0; j < facet->n_ineq; ++j) {
+			for (f = 0; f < hull_facet->n_ineq; ++f)
+				if (isl_seq_eq(facet->ineq[j],
+						hull_facet->ineq[f], 1 + dim))
+					break;
+			if (f < hull_facet->n_ineq)
+				continue;
 			k = isl_basic_set_alloc_inequality(hull);
 			if (k < 0)
 				goto error;
 			isl_seq_cpy(hull->ineq[k], hull->ineq[i], 1+dim);
-			if (!wrap_facet(ctx, set, hull->ineq[k], facet->ineq[j]))
+			if (!wrap_facet(set, hull->ineq[k], facet->ineq[j]))
 				goto error;
-			for (f = 0; f < k; ++f)
-				if (isl_seq_eq(hull->ineq[f], hull->ineq[k],
-						1+dim))
-					break;
-			if (f < k)
-				isl_basic_set_free_inequality(hull, 1);
 		}
+		isl_basic_set_free(hull_facet);
 		isl_basic_set_free(facet);
 	}
 	hull = isl_basic_set_simplify(hull);
 	hull = isl_basic_set_finalize(hull);
 	return hull;
 error:
+	isl_basic_set_free(hull_facet);
 	isl_basic_set_free(facet);
 	isl_basic_set_free(hull);
 	return NULL;
@@ -735,8 +718,7 @@ error:
  * We simply collect the lower and upper bounds of each basic set
  * and the biggest of those.
  */
-static struct isl_basic_set *convex_hull_1d(struct isl_ctx *ctx,
-	struct isl_set *set)
+static struct isl_basic_set *convex_hull_1d(struct isl_set *set)
 {
 	struct isl_mat *c = NULL;
 	isl_int *lower = NULL;
@@ -753,13 +735,13 @@ static struct isl_basic_set *convex_hull_1d(struct isl_ctx *ctx,
 	set = isl_set_remove_empty_parts(set);
 	if (!set)
 		goto error;
-	isl_assert(ctx, set->n > 0, goto error);
-	c = isl_mat_alloc(ctx, 2, 2);
+	isl_assert(set->ctx, set->n > 0, goto error);
+	c = isl_mat_alloc(set->ctx, 2, 2);
 	if (!c)
 		goto error;
 
 	if (set->p[0]->n_eq > 0) {
-		isl_assert(ctx, set->p[0]->n_eq == 1, goto error);
+		isl_assert(set->ctx, set->p[0]->n_eq == 1, goto error);
 		lower = c->row[0];
 		upper = c->row[1];
 		if (isl_int_is_pos(set->p[0]->eq[0][1])) {
@@ -834,7 +816,7 @@ static struct isl_basic_set *convex_hull_1d(struct isl_ctx *ctx,
 	isl_int_clear(a);
 	isl_int_clear(b);
 
-	hull = isl_basic_set_alloc(ctx, 0, 1, 0, 0, 2);
+	hull = isl_basic_set_alloc(set->ctx, 0, 1, 0, 0, 2);
 	hull = isl_basic_set_set_rational(hull);
 	if (!hull)
 		goto error;
@@ -848,11 +830,11 @@ static struct isl_basic_set *convex_hull_1d(struct isl_ctx *ctx,
 	}
 	hull = isl_basic_set_finalize(hull);
 	isl_set_free(set);
-	isl_mat_free(ctx, c);
+	isl_mat_free(c);
 	return hull;
 error:
 	isl_set_free(set);
-	isl_mat_free(ctx, c);
+	isl_mat_free(c);
 	return NULL;
 }
 
@@ -887,7 +869,7 @@ static struct isl_basic_set *convex_hull_0d(struct isl_set *set)
  * to the two original basic sets, retaining only those corresponding
  * to the convex hull.
  */
-static struct isl_basic_set *convex_hull_pair(struct isl_basic_set *bset1,
+static struct isl_basic_set *convex_hull_pair_elim(struct isl_basic_set *bset1,
 	struct isl_basic_set *bset2)
 {
 	int i, j, k;
@@ -951,200 +933,999 @@ error:
 	return NULL;
 }
 
-/* Compute the convex hull of a set without any parameters or
- * integer divisions using Fourier-Motzkin elimination.
- * In each step, we combined two basic sets until only one
- * basic set is left.
+static int isl_basic_set_is_bounded(struct isl_basic_set *bset)
+{
+	struct isl_tab *tab;
+	int bounded;
+
+	tab = isl_tab_from_recession_cone((struct isl_basic_map *)bset);
+	bounded = isl_tab_cone_is_bounded(tab);
+	isl_tab_free(tab);
+	return bounded;
+}
+
+static int isl_set_is_bounded(struct isl_set *set)
+{
+	int i;
+
+	for (i = 0; i < set->n; ++i) {
+		int bounded = isl_basic_set_is_bounded(set->p[i]);
+		if (!bounded || bounded < 0)
+			return bounded;
+	}
+	return 1;
+}
+
+/* Compute the lineality space of the convex hull of bset1 and bset2.
+ *
+ * We first compute the intersection of the recession cone of bset1
+ * with the negative of the recession cone of bset2 and then compute
+ * the linear hull of the resulting cone.
  */
-static struct isl_basic_set *uset_convex_hull_elim(struct isl_set *set)
+static struct isl_basic_set *induced_lineality_space(
+	struct isl_basic_set *bset1, struct isl_basic_set *bset2)
 {
-	struct isl_basic_set *convex_hull = NULL;
+	int i, k;
+	struct isl_basic_set *lin = NULL;
+	unsigned dim;
 
-	convex_hull = isl_set_copy_basic_set(set);
-	set = isl_set_drop_basic_set(set, convex_hull);
-	if (!set)
+	if (!bset1 || !bset2)
 		goto error;
-	while (set->n > 0) {
-		struct isl_basic_set *t;
-		t = isl_set_copy_basic_set(set);
-		if (!t)
+
+	dim = isl_basic_set_total_dim(bset1);
+	lin = isl_basic_set_alloc_dim(isl_basic_set_get_dim(bset1), 0,
+					bset1->n_eq + bset2->n_eq,
+					bset1->n_ineq + bset2->n_ineq);
+	lin = isl_basic_set_set_rational(lin);
+	if (!lin)
+		goto error;
+	for (i = 0; i < bset1->n_eq; ++i) {
+		k = isl_basic_set_alloc_equality(lin);
+		if (k < 0)
 			goto error;
-		set = isl_set_drop_basic_set(set, t);
-		if (!set)
+		isl_int_set_si(lin->eq[k][0], 0);
+		isl_seq_cpy(lin->eq[k] + 1, bset1->eq[i] + 1, dim);
+	}
+	for (i = 0; i < bset1->n_ineq; ++i) {
+		k = isl_basic_set_alloc_inequality(lin);
+		if (k < 0)
 			goto error;
-		convex_hull = convex_hull_pair(convex_hull, t);
+		isl_int_set_si(lin->ineq[k][0], 0);
+		isl_seq_cpy(lin->ineq[k] + 1, bset1->ineq[i] + 1, dim);
 	}
-	isl_set_free(set);
-	return convex_hull;
+	for (i = 0; i < bset2->n_eq; ++i) {
+		k = isl_basic_set_alloc_equality(lin);
+		if (k < 0)
+			goto error;
+		isl_int_set_si(lin->eq[k][0], 0);
+		isl_seq_neg(lin->eq[k] + 1, bset2->eq[i] + 1, dim);
+	}
+	for (i = 0; i < bset2->n_ineq; ++i) {
+		k = isl_basic_set_alloc_inequality(lin);
+		if (k < 0)
+			goto error;
+		isl_int_set_si(lin->ineq[k][0], 0);
+		isl_seq_neg(lin->ineq[k] + 1, bset2->ineq[i] + 1, dim);
+	}
+
+	isl_basic_set_free(bset1);
+	isl_basic_set_free(bset2);
+	return isl_basic_set_affine_hull(lin);
 error:
-	isl_set_free(set);
-	isl_basic_set_free(convex_hull);
+	isl_basic_set_free(lin);
+	isl_basic_set_free(bset1);
+	isl_basic_set_free(bset2);
 	return NULL;
 }
 
-static struct isl_basic_set *uset_convex_hull_wrap_with_bounds(
-	struct isl_set *set, struct isl_mat *bounds)
+static struct isl_basic_set *uset_convex_hull(struct isl_set *set);
+
+/* Given a set and a linear space "lin" of dimension n > 0,
+ * project the linear space from the set, compute the convex hull
+ * and then map the set back to the original space.
+ *
+ * Let
+ *
+ *	M x = 0
+ *
+ * describe the linear space.  We first compute the Hermite normal
+ * form H = M U of M = H Q, to obtain
+ *
+ *	H Q x = 0
+ *
+ * The last n rows of H will be zero, so the last n variables of x' = Q x
+ * are the one we want to project out.  We do this by transforming each
+ * basic set A x >= b to A U x' >= b and then removing the last n dimensions.
+ * After computing the convex hull in x'_1, i.e., A' x'_1 >= b',
+ * we transform the hull back to the original space as A' Q_1 x >= b',
+ * with Q_1 all but the last n rows of Q.
+ */
+static struct isl_basic_set *modulo_lineality(struct isl_set *set,
+	struct isl_basic_set *lin)
 {
-	struct isl_basic_set *convex_hull = NULL;
+	unsigned total = isl_basic_set_total_dim(lin);
+	unsigned lin_dim;
+	struct isl_basic_set *hull;
+	struct isl_mat *M, *U, *Q;
 
-	isl_assert(set->ctx, bounds->n_row == isl_set_n_dim(set), goto error);
-	bounds = initial_facet_constraint(set->ctx, set, bounds);
-	if (!bounds)
+	if (!set || !lin)
 		goto error;
-	convex_hull = extend(set->ctx, set, bounds);
-	isl_mat_free(set->ctx, bounds);
-	isl_set_free(set);
+	lin_dim = total - lin->n_eq;
+	M = isl_mat_sub_alloc(set->ctx, lin->eq, 0, lin->n_eq, 1, total);
+	M = isl_mat_left_hermite(M, 0, &U, &Q);
+	if (!M)
+		goto error;
+	isl_mat_free(M);
+	isl_basic_set_free(lin);
 
-	return convex_hull;
+	Q = isl_mat_drop_rows(Q, Q->n_row - lin_dim, lin_dim);
+
+	U = isl_mat_lin_to_aff(U);
+	Q = isl_mat_lin_to_aff(Q);
+
+	set = isl_set_preimage(set, U);
+	set = isl_set_remove_dims(set, total - lin_dim, lin_dim);
+	hull = uset_convex_hull(set);
+	hull = isl_basic_set_preimage(hull, Q);
+
+	return hull;
 error:
+	isl_basic_set_free(lin);
 	isl_set_free(set);
 	return NULL;
 }
 
-/* Compute the convex hull of a set without any parameters or
- * integer divisions.  Depending on whether the set is bounded,
- * we pass control to the wrapping based convex hull or
- * the Fourier-Motzkin elimination based convex hull.
- * We also handle a few special cases before checking the boundedness.
+/* Given two polyhedra with as constraints h_{ij} x >= 0 in homegeneous space,
+ * set up an LP for solving
+ *
+ *	\sum_j \alpha_{1j} h_{1j} = \sum_j \alpha_{2j} h_{2j}
+ *
+ * \alpha{i0} corresponds to the (implicit) positivity constraint 1 >= 0
+ * The next \alpha{ij} correspond to the equalities and come in pairs.
+ * The final \alpha{ij} correspond to the inequalities.
  */
-static struct isl_basic_set *uset_convex_hull(struct isl_set *set)
+static struct isl_basic_set *valid_direction_lp(
+	struct isl_basic_set *bset1, struct isl_basic_set *bset2)
 {
-	int i;
-	struct isl_basic_set *convex_hull = NULL;
-	struct isl_mat *bounds;
-
-	if (isl_set_n_dim(set) == 0)
-		return convex_hull_0d(set);
-
-	set = isl_set_set_rational(set);
+	struct isl_dim *dim;
+	struct isl_basic_set *lp;
+	unsigned d;
+	int n;
+	int i, j, k;
 
-	if (!set)
+	if (!bset1 || !bset2)
 		goto error;
-	set = isl_set_normalize(set);
-	if (!set)
-		return NULL;
-	if (set->n == 1) {
-		convex_hull = isl_basic_set_copy(set->p[0]);
-		isl_set_free(set);
-		return convex_hull;
-	}
-	if (isl_set_n_dim(set) == 1)
-		return convex_hull_1d(set->ctx, set);
-
-	bounds = independent_bounds(set->ctx, set);
-	if (!bounds)
+	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);
+	if (!lp)
 		goto error;
-	if (bounds->n_row == isl_set_n_dim(set))
-		return uset_convex_hull_wrap_with_bounds(set, bounds);
-	isl_mat_free(set->ctx, bounds);
-
-	return uset_convex_hull_elim(set);
+	for (i = 0; i < n; ++i) {
+		k = isl_basic_set_alloc_inequality(lp);
+		if (k < 0)
+			goto error;
+		isl_seq_clr(lp->ineq[k] + 1, n);
+		isl_int_set_si(lp->ineq[k][0], -1);
+		isl_int_set_si(lp->ineq[k][1 + i], 1);
+	}
+	for (i = 0; i < d; ++i) {
+		k = isl_basic_set_alloc_equality(lp);
+		if (k < 0)
+			goto error;
+		n = 0;
+		isl_int_set_si(lp->eq[k][n++], 0);
+		/* positivity constraint 1 >= 0 */
+		isl_int_set_si(lp->eq[k][n++], i == 0);
+		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]);
+		}
+		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));
+		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]);
+		}
+		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);
+	isl_basic_set_free(bset2);
+	return lp;
 error:
-	isl_set_free(set);
-	isl_basic_set_free(convex_hull);
+	isl_basic_set_free(bset1);
+	isl_basic_set_free(bset2);
 	return NULL;
 }
 
-/* This is the core procedure, where "set" is a "pure" set, i.e.,
- * without parameters or divs and where the convex hull of set is
- * known to be full-dimensional.
+/* Compute a vector s in the homogeneous space such that <s, r> > 0
+ * for all rays in the homogeneous space of the two cones that correspond
+ * to the input polyhedra bset1 and bset2.
+ *
+ * We compute s as a vector that satisfies
+ *
+ *	s = \sum_j \alpha_{ij} h_{ij}	for i = 1,2			(*)
+ *
+ * with h_{ij} the normals of the facets of polyhedron i
+ * (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,
+ * 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 (*).
+ *
+ * Note that we simply pick any valid direction and make no attempt
+ * to pick a "good" or even the "best" valid direction.
  */
-static struct isl_basic_set *uset_convex_hull_wrap(struct isl_set *set)
+static struct isl_vec *valid_direction(
+	struct isl_basic_set *bset1, struct isl_basic_set *bset2)
 {
+	struct isl_basic_set *lp;
+	struct isl_tab *tab;
+	struct isl_vec *sample = NULL;
+	struct isl_vec *dir;
+	unsigned d;
 	int i;
-	struct isl_basic_set *convex_hull = NULL;
-	struct isl_mat *bounds;
+	int n;
 
-	if (isl_set_n_dim(set) == 0) {
-		convex_hull = isl_basic_set_universe(isl_dim_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)
+	if (!bset1 || !bset2)
 		goto error;
-	set = isl_set_normalize(set);
-	if (!set)
+	lp = valid_direction_lp(isl_basic_set_copy(bset1),
+				isl_basic_set_copy(bset2));
+	tab = isl_tab_from_basic_set(lp);
+	sample = isl_tab_get_sample_value(tab);
+	isl_tab_free(tab);
+	isl_basic_set_free(lp);
+	if (!sample)
 		goto error;
-	if (set->n == 1) {
-		convex_hull = isl_basic_set_copy(set->p[0]);
-		isl_set_free(set);
-		return convex_hull;
-	}
-	if (isl_set_n_dim(set) == 1)
-		return convex_hull_1d(set->ctx, set);
-
-	bounds = independent_bounds(set->ctx, set);
-	if (!bounds)
+	d = isl_basic_set_total_dim(bset1);
+	dir = isl_vec_alloc(bset1->ctx, 1 + d);
+	if (!dir)
 		goto error;
-	return uset_convex_hull_wrap_with_bounds(set, bounds);
+	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++]);
+	for (i = 0; i < bset1->n_eq; ++i) {
+		isl_int_sub(sample->block.data[n],
+			    sample->block.data[n], sample->block.data[n+1]);
+		isl_seq_combine(dir->block.data,
+				bset1->ctx->one, dir->block.data,
+				sample->block.data[n], bset1->eq[i], 1 + d);
+
+		n += 2;
+	}
+	for (i = 0; i < bset1->n_ineq; ++i)
+		isl_seq_combine(dir->block.data,
+				bset1->ctx->one, dir->block.data,
+				sample->block.data[n++], bset1->ineq[i], 1 + d);
+	isl_vec_free(sample);
+	isl_basic_set_free(bset1);
+	isl_basic_set_free(bset2);
+	isl_seq_normalize(dir->block.data + 1, dir->size - 1);
+	return dir;
 error:
-	isl_set_free(set);
+	isl_vec_free(sample);
+	isl_basic_set_free(bset1);
+	isl_basic_set_free(bset2);
 	return NULL;
 }
 
-/* Compute the convex hull of set "set" with affine hull "affine_hull",
- * We first remove the equalities (transforming the set), compute the
- * convex hull of the transformed set and then add the equalities back
- * (after performing the inverse transformation.
+/* Given a polyhedron b_i + A_i x >= 0 and a map T = S^{-1},
+ * compute b_i' + A_i' x' >= 0, with
+ *
+ *	[ b_i A_i ]        [ y' ]		              [ y' ]
+ *	[  1   0  ] S^{-1} [ x' ] >= 0	or	[ b_i' A_i' ] [ x' ] >= 0
+ *
+ * In particular, add the "positivity constraint" and then perform
+ * the mapping.
  */
-static struct isl_basic_set *modulo_affine_hull(struct isl_ctx *ctx,
-	struct isl_set *set, struct isl_basic_set *affine_hull)
+static struct isl_basic_set *homogeneous_map(struct isl_basic_set *bset,
+	struct isl_mat *T)
 {
-	struct isl_mat *T;
-	struct isl_mat *T2;
-	struct isl_basic_set *dummy;
-	struct isl_basic_set *convex_hull;
+	int k;
 
-	dummy = isl_basic_set_remove_equalities(
-			isl_basic_set_copy(affine_hull), &T, &T2);
-	if (!dummy)
+	if (!bset)
 		goto error;
-	isl_basic_set_free(dummy);
-	set = isl_set_preimage(set, T);
-	convex_hull = uset_convex_hull(set);
-	convex_hull = isl_basic_set_preimage(convex_hull, T2);
-	convex_hull = isl_basic_set_intersect(convex_hull, affine_hull);
-	return convex_hull;
+	bset = isl_basic_set_extend_constraints(bset, 0, 1);
+	k = isl_basic_set_alloc_inequality(bset);
+	if (k < 0)
+		goto error;
+	isl_seq_clr(bset->ineq[k] + 1, isl_basic_set_total_dim(bset));
+	isl_int_set_si(bset->ineq[k][0], 1);
+	bset = isl_basic_set_preimage(bset, T);
+	return bset;
 error:
-	isl_basic_set_free(affine_hull);
-	isl_set_free(set);
+	isl_mat_free(T);
+	isl_basic_set_free(bset);
 	return NULL;
 }
 
-/* Compute the convex hull of a map.
+/* Compute the convex hull of a pair of basic sets without any parameters or
+ * integer divisions, where the convex hull is known to be pointed,
+ * but the basic sets may be unbounded.
  *
- * The implementation was inspired by "Extended Convex Hull" by Fukuda et al.,
- * specifically, the wrapping of facets to obtain new facets.
+ * We turn this problem into the computation of a convex hull of a pair
+ * _bounded_ polyhedra by "changing the direction of the homogeneous
+ * dimension".  This idea is due to Matthias Koeppe.
+ *
+ * Consider the cones in homogeneous space that correspond to the
+ * input polyhedra.  The rays of these cones are also rays of the
+ * polyhedra if the coordinate that corresponds to the homogeneous
+ * dimension is zero.  That is, if the inner product of the rays
+ * with the homogeneous direction is zero.
+ * The cones in the homogeneous space can also be considered to
+ * correspond to other pairs of polyhedra by chosing a different
+ * homogeneous direction.  To ensure that both of these polyhedra
+ * are bounded, we need to make sure that all rays of the cones
+ * correspond to vertices and not to rays.
+ * Let s be a direction such that <s, r> > 0 for all rays r of both cones.
+ * Then using s as a homogeneous direction, we obtain a pair of polytopes.
+ * The vector s is computed in valid_direction.
+ *
+ * Note that we need to consider _all_ rays of the cones and not just
+ * the rays that correspond to rays in the polyhedra.  If we were to
+ * only consider those rays and turn them into vertices, then we
+ * may inadvertently turn some vertices into rays.
+ *
+ * The standard homogeneous direction is the unit vector in the 0th coordinate.
+ * We therefore transform the two polyhedra such that the selected
+ * direction is mapped onto this standard direction and then proceed
+ * with the normal computation.
+ * Let S be a non-singular square matrix with s as its first row,
+ * then we want to map the polyhedra to the space
+ *
+ *	[ y' ]     [ y ]		[ y ]          [ y' ]
+ *	[ x' ] = S [ x ]	i.e.,	[ x ] = S^{-1} [ x' ]
+ *
+ * We take S to be the unimodular completion of s to limit the growth
+ * of the coefficients in the following computations.
+ *
+ * Let b_i + A_i x >= 0 be the constraints of polyhedron i.
+ * We first move to the homogeneous dimension
+ *
+ *	b_i y + A_i x >= 0		[ b_i A_i ] [ y ]    [ 0 ]
+ *	    y         >= 0	or	[  1   0  ] [ x ] >= [ 0 ]
+ *
+ * Then we change directoin
+ *
+ *	[ b_i A_i ]        [ y' ]		              [ y' ]
+ *	[  1   0  ] S^{-1} [ x' ] >= 0	or	[ b_i' A_i' ] [ x' ] >= 0
+ *
+ * Then we compute the convex hull of the polytopes b_i' + A_i' x' >= 0
+ * resulting in b' + A' x' >= 0, which we then convert back
+ *
+ *	            [ y ]		        [ y ]
+ *	[ b' A' ] S [ x ] >= 0	or	[ b A ] [ x ] >= 0
+ *
+ * The polyhedron b + A x >= 0 is then the convex hull of the input polyhedra.
  */
-struct isl_basic_map *isl_map_convex_hull(struct isl_map *map)
+static struct isl_basic_set *convex_hull_pair_pointed(
+	struct isl_basic_set *bset1, struct isl_basic_set *bset2)
 {
-	struct isl_basic_set *bset;
-	struct isl_basic_map *model = NULL;
-	struct isl_basic_set *affine_hull = NULL;
-	struct isl_basic_map *convex_hull = NULL;
-	struct isl_set *set = NULL;
-	struct isl_ctx *ctx;
+	struct isl_ctx *ctx = NULL;
+	struct isl_vec *dir = NULL;
+	struct isl_mat *T = NULL;
+	struct isl_mat *T2 = NULL;
+	struct isl_basic_set *hull;
+	struct isl_set *set;
 
-	if (!map)
+	if (!bset1 || !bset2)
 		goto error;
-
-	ctx = map->ctx;
-	if (map->n == 0) {
-		convex_hull = isl_basic_map_empty_like_map(map);
-		isl_map_free(map);
-		return convex_hull;
-	}
-
-	map = isl_map_align_divs(map);
-	model = isl_basic_map_copy(map->p[0]);
-	set = isl_map_underlying_set(map);
-	if (!set)
+	ctx = bset1->ctx;
+	dir = valid_direction(isl_basic_set_copy(bset1),
+				isl_basic_set_copy(bset2));
+	if (!dir)
 		goto error;
-
+	T = isl_mat_alloc(bset1->ctx, dir->size, dir->size);
+	if (!T)
+		goto error;
+	isl_seq_cpy(T->row[0], dir->block.data, dir->size);
+	T = isl_mat_unimodular_complete(T, 1);
+	T2 = isl_mat_right_inverse(isl_mat_copy(T));
+
+	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);
+	hull = uset_convex_hull(set);
+	hull = isl_basic_set_preimage(hull, T);
+	 
+	isl_vec_free(dir);
+
+	return hull;
+error:
+	isl_vec_free(dir);
+	isl_basic_set_free(bset1);
+	isl_basic_set_free(bset2);
+	return NULL;
+}
+
+/* Compute the convex hull of a pair of basic sets without any parameters or
+ * integer divisions.
+ *
+ * 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;
+
+	if (isl_basic_set_is_bounded(bset1) || isl_basic_set_is_bounded(bset2))
+		return convex_hull_pair_pointed(bset1, bset2);
+
+	lin = induced_lineality_space(isl_basic_set_copy(bset1),
+				      isl_basic_set_copy(bset2));
+	if (!lin)
+		goto error;
+	if (isl_basic_set_is_universe(lin)) {
+		isl_basic_set_free(bset1);
+		isl_basic_set_free(bset2);
+		return lin;
+	}
+	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);
+		return modulo_lineality(set, lin);
+	}
+	isl_basic_set_free(lin);
+
+	return convex_hull_pair_pointed(bset1, bset2);
+error:
+	isl_basic_set_free(bset1);
+	isl_basic_set_free(bset2);
+	return NULL;
+}
+
+/* Compute the lineality space of a basic set.
+ * We currently do not allow the basic set to have any divs.
+ * We basically just drop the constants and turn every inequality
+ * into an equality.
+ */
+struct isl_basic_set *isl_basic_set_lineality_space(struct isl_basic_set *bset)
+{
+	int i, k;
+	struct isl_basic_set *lin = NULL;
+	unsigned dim;
+
+	if (!bset)
+		goto error;
+	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);
+	if (!lin)
+		goto error;
+	for (i = 0; i < bset->n_eq; ++i) {
+		k = isl_basic_set_alloc_equality(lin);
+		if (k < 0)
+			goto error;
+		isl_int_set_si(lin->eq[k][0], 0);
+		isl_seq_cpy(lin->eq[k] + 1, bset->eq[i] + 1, dim);
+	}
+	lin = isl_basic_set_gauss(lin, NULL);
+	if (!lin)
+		goto error;
+	for (i = 0; i < bset->n_ineq && lin->n_eq < dim; ++i) {
+		k = isl_basic_set_alloc_equality(lin);
+		if (k < 0)
+			goto error;
+		isl_int_set_si(lin->eq[k][0], 0);
+		isl_seq_cpy(lin->eq[k] + 1, bset->ineq[i] + 1, dim);
+		lin = isl_basic_set_gauss(lin, NULL);
+		if (!lin)
+			goto error;
+	}
+	isl_basic_set_free(bset);
+	return lin;
+error:
+	isl_basic_set_free(lin);
+	isl_basic_set_free(bset);
+	return NULL;
+}
+
+/* Compute the (linear) hull of the lineality spaces of the basic sets in the
+ * "underlying" set "set".
+ */
+static struct isl_basic_set *uset_combined_lineality_space(struct isl_set *set)
+{
+	int i;
+	struct isl_set *lin = NULL;
+
+	if (!set)
+		return NULL;
+	if (set->n == 0) {
+		struct isl_dim *dim = isl_set_get_dim(set);
+		isl_set_free(set);
+		return isl_basic_set_empty(dim);
+	}
+
+	lin = isl_set_alloc_dim(isl_set_get_dim(set), set->n, 0);
+	for (i = 0; i < set->n; ++i)
+		lin = isl_set_add(lin,
+		    isl_basic_set_lineality_space(isl_basic_set_copy(set->p[i])));
+	isl_set_free(set);
+	return isl_set_affine_hull(lin);
+}
+
+/* Compute the convex hull of a set without any parameters or
+ * integer divisions.
+ * In each step, we combined two basic sets until only one
+ * basic set is left.
+ * The input basic sets are assumed not to have a non-trivial
+ * lineality space.  If any of the intermediate results has
+ * a non-trivial lineality space, it is projected out.
+ */
+static struct isl_basic_set *uset_convex_hull_unbounded(struct isl_set *set)
+{
+	struct isl_basic_set *convex_hull = NULL;
+
+	convex_hull = isl_set_copy_basic_set(set);
+	set = isl_set_drop_basic_set(set, convex_hull);
+	if (!set)
+		goto error;
+	while (set->n > 0) {
+		struct isl_basic_set *t;
+		t = isl_set_copy_basic_set(set);
+		if (!t)
+			goto error;
+		set = isl_set_drop_basic_set(set, t);
+		if (!set)
+			goto error;
+		convex_hull = convex_hull_pair(convex_hull, t);
+		if (set->n == 0)
+			break;
+		t = isl_basic_set_lineality_space(isl_basic_set_copy(convex_hull));
+		if (!t)
+			goto error;
+		if (isl_basic_set_is_universe(t)) {
+			isl_basic_set_free(convex_hull);
+			convex_hull = t;
+			break;
+		}
+		if (t->n_eq < isl_basic_set_total_dim(t)) {
+			set = isl_set_add(set, convex_hull);
+			return modulo_lineality(set, t);
+		}
+		isl_basic_set_free(t);
+	}
+	isl_set_free(set);
+	return convex_hull;
+error:
+	isl_set_free(set);
+	isl_basic_set_free(convex_hull);
+	return NULL;
+}
+
+/* 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.
+ */
+static struct isl_basic_set *initial_hull(struct isl_basic_set *hull,
+	struct isl_set *set)
+{
+	struct isl_mat *bounds = NULL;
+	unsigned dim;
+	int k;
+
+	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);
+	if (!bounds)
+		goto error;
+	k = isl_basic_set_alloc_inequality(hull);
+	if (k < 0)
+		goto error;
+	dim = isl_set_n_dim(set);
+	isl_assert(set->ctx, 1 + dim == bounds->n_col, goto error);
+	isl_seq_cpy(hull->ineq[k], bounds->row[0], bounds->n_col);
+	isl_mat_free(bounds);
+
+	return hull;
+error:
+	isl_basic_set_free(hull);
+	isl_mat_free(bounds);
+	return NULL;
+}
+
+struct max_constraint {
+	struct isl_mat *c;
+	int	 	count;
+	int		ineq;
+};
+
+static int max_constraint_equal(const void *entry, const void *val)
+{
+	struct max_constraint *a = (struct max_constraint *)entry;
+	isl_int *b = (isl_int *)val;
+
+	return isl_seq_eq(a->c->row[0] + 1, b, a->c->n_col - 1);
+}
+
+static void update_constraint(struct isl_ctx *ctx, struct isl_hash_table *table,
+	isl_int *con, unsigned len, int n, int ineq)
+{
+	struct isl_hash_table_entry *entry;
+	struct max_constraint *c;
+	uint32_t c_hash;
+
+	c_hash = isl_seq_hash(con + 1, len, isl_hash_init());
+	entry = isl_hash_table_find(ctx, table, c_hash, max_constraint_equal,
+			con + 1, 0);
+	if (!entry)
+		return;
+	c = entry->data;
+	if (c->count < n) {
+		isl_hash_table_remove(ctx, table, entry);
+		return;
+	}
+	c->count++;
+	if (isl_int_gt(c->c->row[0][0], con[0]))
+		return;
+	if (isl_int_eq(c->c->row[0][0], con[0])) {
+		if (ineq)
+			c->ineq = ineq;
+		return;
+	}
+	c->c = isl_mat_cow(c->c);
+	isl_int_set(c->c->row[0][0], con[0]);
+	c->ineq = ineq;
+}
+
+/* Check whether the constraint hash table "table" constains the constraint
+ * "con".
+ */
+static int has_constraint(struct isl_ctx *ctx, struct isl_hash_table *table,
+	isl_int *con, unsigned len, int n)
+{
+	struct isl_hash_table_entry *entry;
+	struct max_constraint *c;
+	uint32_t c_hash;
+
+	c_hash = isl_seq_hash(con + 1, len, isl_hash_init());
+	entry = isl_hash_table_find(ctx, table, c_hash, max_constraint_equal,
+			con + 1, 0);
+	if (!entry)
+		return 0;
+	c = entry->data;
+	if (c->count < n)
+		return 0;
+	return isl_int_eq(c->c->row[0][0], con[0]);
+}
+
+/* Check for inequality constraints of a basic set without equalities
+ * such that the same or more stringent copies of the constraint appear
+ * in all of the basic sets.  Such constraints are necessarily facet
+ * constraints of the convex hull.
+ *
+ * If the resulting basic set is by chance identical to one of
+ * the basic sets in "set", then we know that this basic set contains
+ * all other basic sets and is therefore the convex hull of set.
+ * In this case we set *is_hull to 1.
+ */
+static struct isl_basic_set *common_constraints(struct isl_basic_set *hull,
+	struct isl_set *set, int *is_hull)
+{
+	int i, j, s, n;
+	int min_constraints;
+	int best;
+	struct max_constraint *constraints = NULL;
+	struct isl_hash_table *table = NULL;
+	unsigned total;
+
+	*is_hull = 0;
+
+	for (i = 0; i < set->n; ++i)
+		if (set->p[i]->n_eq == 0)
+			break;
+	if (i >= set->n)
+		return hull;
+	min_constraints = set->p[i]->n_ineq;
+	best = i;
+	for (i = best + 1; i < set->n; ++i) {
+		if (set->p[i]->n_eq != 0)
+			continue;
+		if (set->p[i]->n_ineq >= min_constraints)
+			continue;
+		min_constraints = set->p[i]->n_ineq;
+		best = i;
+	}
+	constraints = isl_calloc_array(hull->ctx, struct max_constraint,
+					min_constraints);
+	if (!constraints)
+		return hull;
+	table = isl_alloc_type(hull->ctx, struct isl_hash_table);
+	if (isl_hash_table_init(hull->ctx, table, min_constraints))
+		goto error;
+
+	total = isl_dim_total(set->dim);
+	for (i = 0; i < set->p[best]->n_ineq; ++i) {
+		constraints[i].c = isl_mat_sub_alloc(hull->ctx,
+			set->p[best]->ineq + i, 0, 1, 0, 1 + total);
+		if (!constraints[i].c)
+			goto error;
+		constraints[i].ineq = 1;
+	}
+	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());
+		entry = isl_hash_table_find(hull->ctx, table, c_hash,
+			max_constraint_equal, constraints[i].c->row[0] + 1, 1);
+		if (!entry)
+			goto error;
+		isl_assert(hull->ctx, !entry->data, goto error);
+		entry->data = &constraints[i];
+	}
+
+	n = 0;
+	for (s = 0; s < set->n; ++s) {
+		if (s == best)
+			continue;
+
+		for (i = 0; i < set->p[s]->n_eq; ++i) {
+			isl_int *eq = set->p[s]->eq[i];
+			for (j = 0; j < 2; ++j) {
+				isl_seq_neg(eq, eq, 1 + total);
+				update_constraint(hull->ctx, table,
+							    eq, total, n, 0);
+			}
+		}
+		for (i = 0; i < set->p[s]->n_ineq; ++i) {
+			isl_int *ineq = set->p[s]->ineq[i];
+			update_constraint(hull->ctx, table, ineq, total, n,
+				set->p[s]->n_eq == 0);
+		}
+		++n;
+	}
+
+	for (i = 0; i < min_constraints; ++i) {
+		if (constraints[i].count < n)
+			continue;
+		if (!constraints[i].ineq)
+			continue;
+		j = isl_basic_set_alloc_inequality(hull);
+		if (j < 0)
+			goto error;
+		isl_seq_cpy(hull->ineq[j], constraints[i].c->row[0], 1 + total);
+	}
+
+	for (s = 0; s < set->n; ++s) {
+		if (set->p[s]->n_eq)
+			continue;
+		if (set->p[s]->n_ineq != hull->n_ineq)
+			continue;
+		for (i = 0; i < set->p[s]->n_ineq; ++i) {
+			isl_int *ineq = set->p[s]->ineq[i];
+			if (!has_constraint(hull->ctx, table, ineq, total, n))
+				break;
+		}
+		if (i == set->p[s]->n_ineq)
+			*is_hull = 1;
+	}
+
+	isl_hash_table_clear(table);
+	for (i = 0; i < min_constraints; ++i)
+		isl_mat_free(constraints[i].c);
+	free(constraints);
+	free(table);
+	return hull;
+error:
+	isl_hash_table_clear(table);
+	free(table);
+	if (constraints)
+		for (i = 0; i < min_constraints; ++i)
+			isl_mat_free(constraints[i].c);
+	free(constraints);
+	return hull;
+}
+
+/* Create a template for the convex hull of "set" and fill it up
+ * obvious facet constraints, if any.  If the result happens to
+ * be the convex hull of "set" then *is_hull is set to 1.
+ */
+static struct isl_basic_set *proto_hull(struct isl_set *set, int *is_hull)
+{
+	struct isl_basic_set *hull;
+	unsigned n_ineq;
+	int i;
+
+	n_ineq = 1;
+	for (i = 0; i < set->n; ++i) {
+		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_set_rational(hull);
+	if (!hull)
+		return NULL;
+	return common_constraints(hull, set, is_hull);
+}
+
+static struct isl_basic_set *uset_convex_hull_wrap(struct isl_set *set)
+{
+	struct isl_basic_set *hull;
+	int is_hull;
+
+	hull = proto_hull(set, &is_hull);
+	if (hull && !is_hull) {
+		if (hull->n_ineq == 0)
+			hull = initial_hull(hull, set);
+		hull = extend(hull, set);
+	}
+	isl_set_free(set);
+
+	return hull;
+}
+
+/* Compute the convex hull of a set without any parameters or
+ * integer divisions.  Depending on whether the set is bounded,
+ * we pass control to the wrapping based convex hull or
+ * the Fourier-Motzkin elimination based convex hull.
+ * We also handle a few special cases before checking the boundedness.
+ */
+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;
+
+	if (isl_set_n_dim(set) == 0)
+		return convex_hull_0d(set);
+
+	set = isl_set_coalesce(set);
+	set = isl_set_set_rational(set);
+
+	if (!set)
+		goto error;
+	if (!set)
+		return NULL;
+	if (set->n == 1) {
+		convex_hull = isl_basic_set_copy(set->p[0]);
+		isl_set_free(set);
+		return convex_hull;
+	}
+	if (isl_set_n_dim(set) == 1)
+		return convex_hull_1d(set);
+
+	if (isl_set_is_bounded(set))
+		return uset_convex_hull_wrap(set);
+
+	lin = uset_combined_lineality_space(isl_set_copy(set));
+	if (!lin)
+		goto error;
+	if (isl_basic_set_is_universe(lin)) {
+		isl_set_free(set);
+		return lin;
+	}
+	if (lin->n_eq < isl_basic_set_total_dim(lin))
+		return modulo_lineality(set, lin);
+	isl_basic_set_free(lin);
+
+	return uset_convex_hull_unbounded(set);
+error:
+	isl_set_free(set);
+	isl_basic_set_free(convex_hull);
+	return NULL;
+}
+
+/* This is the core procedure, where "set" is a "pure" set, i.e.,
+ * without parameters or divs and where the convex hull of set is
+ * known to be full-dimensional.
+ */
+static struct isl_basic_set *uset_convex_hull_wrap_bounded(struct isl_set *set)
+{
+	int i;
+	struct isl_basic_set *convex_hull = NULL;
+
+	if (isl_set_n_dim(set) == 0) {
+		convex_hull = isl_basic_set_universe(isl_dim_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_coalesce(set);
+	if (!set)
+		goto error;
+	if (set->n == 1) {
+		convex_hull = isl_basic_set_copy(set->p[0]);
+		isl_set_free(set);
+		return convex_hull;
+	}
+	if (isl_set_n_dim(set) == 1)
+		return convex_hull_1d(set);
+
+	return uset_convex_hull_wrap(set);
+error:
+	isl_set_free(set);
+	return NULL;
+}
+
+/* Compute the convex hull of set "set" with affine hull "affine_hull",
+ * We first remove the equalities (transforming the set), compute the
+ * 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,
+	struct isl_set *set, struct isl_basic_set *affine_hull)
+{
+	struct isl_mat *T;
+	struct isl_mat *T2;
+	struct isl_basic_set *dummy;
+	struct isl_basic_set *convex_hull;
+
+	dummy = isl_basic_set_remove_equalities(
+			isl_basic_set_copy(affine_hull), &T, &T2);
+	if (!dummy)
+		goto error;
+	isl_basic_set_free(dummy);
+	set = isl_set_preimage(set, T);
+	convex_hull = uset_convex_hull(set);
+	convex_hull = isl_basic_set_preimage(convex_hull, T2);
+	convex_hull = isl_basic_set_intersect(convex_hull, affine_hull);
+	return convex_hull;
+error:
+	isl_basic_set_free(affine_hull);
+	isl_set_free(set);
+	return NULL;
+}
+
+/* Compute the convex hull of a map.
+ *
+ * The implementation was inspired by "Extended Convex Hull" by Fukuda et al.,
+ * specifically, the wrapping of facets to obtain new facets.
+ */
+struct isl_basic_map *isl_map_convex_hull(struct isl_map *map)
+{
+	struct isl_basic_set *bset;
+	struct isl_basic_map *model = NULL;
+	struct isl_basic_set *affine_hull = NULL;
+	struct isl_basic_map *convex_hull = NULL;
+	struct isl_set *set = NULL;
+	struct isl_ctx *ctx;
+
+	if (!map)
+		goto error;
+
+	ctx = map->ctx;
+	if (map->n == 0) {
+		convex_hull = isl_basic_map_empty_like_map(map);
+		isl_map_free(map);
+		return convex_hull;
+	}
+
+	map = isl_map_detect_equalities(map);
+	map = isl_map_align_divs(map);
+	model = isl_basic_map_copy(map->p[0]);
+	set = isl_map_underlying_set(map);
+	if (!set)
+		goto error;
+
 	affine_hull = isl_set_affine_hull(isl_set_copy(set));
 	if (!affine_hull)
 		goto error;
@@ -1157,6 +1938,8 @@ struct isl_basic_map *isl_map_convex_hull(struct isl_map *map)
 
 	convex_hull = isl_basic_map_overlying_set(bset, model);
 
+	ISL_F_SET(convex_hull, ISL_BASIC_MAP_NO_IMPLICIT);
+	ISL_F_SET(convex_hull, ISL_BASIC_MAP_ALL_EQUALITIES);
 	ISL_F_CLR(convex_hull, ISL_BASIC_MAP_RATIONAL);
 	return convex_hull;
 error:
@@ -1171,22 +1954,334 @@ struct isl_basic_set *isl_set_convex_hull(struct isl_set *set)
 		isl_map_convex_hull((struct isl_map *)set);
 }
 
+struct sh_data_entry {
+	struct isl_hash_table	*table;
+	struct isl_tab		*tab;
+};
+
+/* Holds the data needed during the simple hull computation.
+ * In particular,
+ *	n		the number of basic sets in the original set
+ *	hull_table	a hash table of already computed constraints
+ *			in the simple hull
+ *	p		for each basic set,
+ *		table		a hash table of the constraints
+ *		tab		the tableau corresponding to the basic set
+ */
+struct sh_data {
+	struct isl_ctx		*ctx;
+	unsigned		n;
+	struct isl_hash_table	*hull_table;
+	struct sh_data_entry	p[0];
+};
+
+static void sh_data_free(struct sh_data *data)
+{
+	int i;
+
+	if (!data)
+		return;
+	isl_hash_table_free(data->ctx, data->hull_table);
+	for (i = 0; i < data->n; ++i) {
+		isl_hash_table_free(data->ctx, data->p[i].table);
+		isl_tab_free(data->p[i].tab);
+	}
+	free(data);
+}
+
+struct ineq_cmp_data {
+	unsigned	len;
+	isl_int		*p;
+};
+
+static int has_ineq(const void *entry, const void *val)
+{
+	isl_int *row = (isl_int *)entry;
+	struct ineq_cmp_data *v = (struct ineq_cmp_data *)val;
+
+	return isl_seq_eq(row + 1, v->p + 1, v->len) ||
+	       isl_seq_is_neg(row + 1, v->p + 1, v->len);
+}
+
+static int hash_ineq(struct isl_ctx *ctx, struct isl_hash_table *table,
+			isl_int *ineq, unsigned len)
+{
+	uint32_t c_hash;
+	struct ineq_cmp_data v;
+	struct isl_hash_table_entry *entry;
+
+	v.len = len;
+	v.p = ineq;
+	c_hash = isl_seq_hash(ineq + 1, len, isl_hash_init());
+	entry = isl_hash_table_find(ctx, table, c_hash, has_ineq, &v, 1);
+	if (!entry)
+		return - 1;
+	entry->data = ineq;
+	return 0;
+}
+
+/* Fill hash table "table" with the constraints of "bset".
+ * Equalities are added as two inequalities.
+ * The value in the hash table is a pointer to the (in)equality of "bset".
+ */
+static int hash_basic_set(struct isl_hash_table *table,
+				struct isl_basic_set *bset)
+{
+	int i, j;
+	unsigned dim = isl_basic_set_total_dim(bset);
+
+	for (i = 0; i < bset->n_eq; ++i) {
+		for (j = 0; j < 2; ++j) {
+			isl_seq_neg(bset->eq[i], bset->eq[i], 1 + dim);
+			if (hash_ineq(bset->ctx, table, bset->eq[i], dim) < 0)
+				return -1;
+		}
+	}
+	for (i = 0; i < bset->n_ineq; ++i) {
+		if (hash_ineq(bset->ctx, table, bset->ineq[i], dim) < 0)
+			return -1;
+	}
+	return 0;
+}
+
+static struct sh_data *sh_data_alloc(struct isl_set *set, unsigned n_ineq)
+{
+	struct sh_data *data;
+	int i;
+
+	data = isl_calloc(set->ctx, struct sh_data,
+		sizeof(struct sh_data) + set->n * sizeof(struct sh_data_entry));
+	if (!data)
+		return NULL;
+	data->ctx = set->ctx;
+	data->n = set->n;
+	data->hull_table = isl_hash_table_alloc(set->ctx, n_ineq);
+	if (!data->hull_table)
+		goto error;
+	for (i = 0; i < set->n; ++i) {
+		data->p[i].table = isl_hash_table_alloc(set->ctx,
+				    2 * set->p[i]->n_eq + set->p[i]->n_ineq);
+		if (!data->p[i].table)
+			goto error;
+		if (hash_basic_set(data->p[i].table, set->p[i]) < 0)
+			goto error;
+	}
+	return data;
+error:
+	sh_data_free(data);
+	return NULL;
+}
+
+/* Check if inequality "ineq" is a bound for basic set "j" or if
+ * 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.
+ * 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)
+{
+	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]);
+		if (!data->p[j].tab)
+			return -1;
+	}
+
+	isl_int_init(opt);
+
+	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);
+
+	isl_int_clear(opt);
+
+	return res == isl_lp_ok ? 1 :
+	       res == isl_lp_unbounded ? 0 : -1;
+}
+
+/* Check if inequality "ineq" from basic set "i" can be relaxed to
+ * become a bound on the whole set.  If so, add the (relaxed) inequality
+ * to "hull".
+ *
+ * We first check if "hull" already contains a translate of the inequality.
+ * If so, we are done.
+ * Then, we check if any of the previous basic sets contains a translate
+ * of the inequality.  If so, then we have already considered this
+ * inequality and we are done.
+ * Otherwise, for each basic set other than "i", we check if the inequality
+ * is a bound on the basic set.
+ * For previous basic sets, we know that they do not contain a translate
+ * of the inequality, so we directly call is_bound.
+ * For following basic sets, we first check if a translate of the
+ * inequality appears in its description and if so directly update
+ * 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)
+{
+	uint32_t c_hash;
+	struct ineq_cmp_data v;
+	struct isl_hash_table_entry *entry;
+	int j, k;
+
+	if (!hull)
+		return NULL;
+
+	v.len = isl_basic_set_total_dim(hull);
+	v.p = ineq;
+	c_hash = isl_seq_hash(ineq + 1, v.len, isl_hash_init());
+
+	entry = isl_hash_table_find(hull->ctx, data->hull_table, c_hash,
+					has_ineq, &v, 0);
+	if (entry)
+		return hull;
+
+	for (j = 0; j < i; ++j) {
+		entry = isl_hash_table_find(hull->ctx, data->p[j].table,
+						c_hash, has_ineq, &v, 0);
+		if (entry)
+			break;
+	}
+	if (j < i)
+		return hull;
+
+	k = isl_basic_set_alloc_inequality(hull);
+	isl_seq_cpy(hull->ineq[k], ineq, 1 + v.len);
+	if (k < 0)
+		goto error;
+
+	for (j = 0; j < i; ++j) {
+		int bound;
+		bound = is_bound(data, set, j, hull->ineq[k]);
+		if (bound < 0)
+			goto error;
+		if (!bound)
+			break;
+	}
+	if (j < i) {
+		isl_basic_set_free_inequality(hull, 1);
+		return hull;
+	}
+
+	for (j = i + 1; j < set->n; ++j) {
+		int bound, neg;
+		isl_int *ineq_j;
+		entry = isl_hash_table_find(hull->ctx, data->p[j].table,
+						c_hash, has_ineq, &v, 0);
+		if (entry) {
+			ineq_j = entry->data;
+			neg = isl_seq_is_neg(ineq_j + 1,
+					     hull->ineq[k] + 1, v.len);
+			if (neg)
+				isl_int_neg(ineq_j[0], ineq_j[0]);
+			if (isl_int_gt(ineq_j[0], hull->ineq[k][0]))
+				isl_int_set(hull->ineq[k][0], ineq_j[0]);
+			if (neg)
+				isl_int_neg(ineq_j[0], ineq_j[0]);
+			continue;
+		}
+		bound = is_bound(data, set, j, hull->ineq[k]);
+		if (bound < 0)
+			goto error;
+		if (!bound)
+			break;
+	}
+	if (j < set->n) {
+		isl_basic_set_free_inequality(hull, 1);
+		return hull;
+	}
+
+	entry = isl_hash_table_find(hull->ctx, data->hull_table, c_hash,
+					has_ineq, &v, 1);
+	if (!entry)
+		goto error;
+	entry->data = hull->ineq[k];
+
+	return hull;
+error:
+	isl_basic_set_free(hull);
+	return NULL;
+}
+
+/* Check if any inequality from basic set "i" can be relaxed to
+ * become a bound on the whole set.  If so, add the (relaxed) inequality
+ * to "hull".
+ */
+static struct isl_basic_set *add_bounds(struct isl_basic_set *bset,
+	struct sh_data *data, struct isl_set *set, int i)
+{
+	int j, k;
+	unsigned dim = isl_basic_set_total_dim(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]);
+		}
+	}
+	for (j = 0; j < set->p[i]->n_ineq; ++j)
+		add_bound(bset, data, set, i, set->p[i]->ineq[j]);
+	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.
+ */
+static struct isl_basic_set *uset_simple_hull(struct isl_set *set)
+{
+	struct sh_data *data = NULL;
+	struct isl_basic_set *hull = NULL;
+	unsigned n_ineq;
+	int i, j;
+
+	if (!set)
+		return NULL;
+
+	n_ineq = 0;
+	for (i = 0; i < set->n; ++i) {
+		if (!set->p[i])
+			goto error;
+		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);
+	if (!hull)
+		goto error;
+
+	data = sh_data_alloc(set, n_ineq);
+	if (!data)
+		goto error;
+
+	for (i = 0; i < set->n; ++i)
+		hull = add_bounds(hull, data, set, i);
+
+	sh_data_free(data);
+	isl_set_free(set);
+
+	return hull;
+error:
+	sh_data_free(data);
+	isl_basic_set_free(hull);
+	isl_set_free(set);
+	return NULL;
+}
+
 /* Compute a superset of the convex hull of map that is described
  * by only translates of the constraints in the constituents of map.
- *
- * The implementation is not very efficient.  In particular, if
- * constraints with the same normal appear in more than one
- * basic map, they will be (re)examined each time.
  */
 struct isl_basic_map *isl_map_simple_hull(struct isl_map *map)
 {
 	struct isl_set *set = NULL;
 	struct isl_basic_map *model = NULL;
 	struct isl_basic_map *hull;
+	struct isl_basic_map *affine_hull;
 	struct isl_basic_set *bset = NULL;
-	int i, j;
-	unsigned n_ineq;
-	unsigned dim;
 
 	if (!map)
 		return NULL;
@@ -1201,63 +2296,107 @@ struct isl_basic_map *isl_map_simple_hull(struct isl_map *map)
 		return hull;
 	}
 
+	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]);
 
-	n_ineq = 0;
-	for (i = 0; i < map->n; ++i) {
-		if (!map->p[i])
-			goto error;
-		n_ineq += map->p[i]->n_ineq;
-	}
-
 	set = isl_map_underlying_set(map);
-	if (!set)
-		goto error;
 
-	bset = isl_set_affine_hull(isl_set_copy(set));
-	if (!bset)
-		goto error;
-	dim = isl_basic_set_n_dim(bset);
-	bset = isl_basic_set_extend(bset, 0, dim, 0, 0, n_ineq);
-	if (!bset)
+	bset = uset_simple_hull(set);
+
+	hull = isl_basic_map_overlying_set(bset, model);
+
+	hull = isl_basic_map_intersect(hull, affine_hull);
+	hull = isl_basic_map_convex_hull(hull);
+	ISL_F_SET(hull, ISL_BASIC_MAP_NO_IMPLICIT);
+	ISL_F_SET(hull, ISL_BASIC_MAP_ALL_EQUALITIES);
+
+	return hull;
+}
+
+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);
+}
+
+/* Given a set "set", return parametric bounds on the dimension "dim".
+ */
+static struct isl_basic_set *set_bounds(struct isl_set *set, int dim)
+{
+	unsigned set_dim = isl_set_dim(set, isl_dim_set);
+	set = isl_set_copy(set);
+	set = isl_set_eliminate_dims(set, dim + 1, set_dim - (dim + 1));
+	set = isl_set_eliminate_dims(set, 0, dim);
+	return isl_set_convex_hull(set);
+}
+
+/* Computes a "simple hull" and then check if each dimension in the
+ * resulting hull is bounded by a symbolic constant.  If not, the
+ * hull is intersected with the corresponding bounds on the whole set.
+ */
+struct isl_basic_set *isl_set_bounded_simple_hull(struct isl_set *set)
+{
+	int i, j;
+	struct isl_basic_set *hull;
+	unsigned nparam, left;
+	int removed_divs = 0;
+
+	hull = isl_set_simple_hull(isl_set_copy(set));
+	if (!hull)
 		goto error;
 
-	for (i = 0; i < set->n; ++i) {
-		for (j = 0; j < set->p[i]->n_ineq; ++j) {
-			int k;
-			int is_bound;
+	nparam = isl_basic_set_dim(hull, isl_dim_param);
+	for (i = 0; i < isl_basic_set_dim(hull, isl_dim_set); ++i) {
+		int lower = 0, upper = 0;
+		struct isl_basic_set *bounds;
 
-			k = isl_basic_set_alloc_inequality(bset);
-			if (k < 0)
-				goto error;
-			isl_seq_cpy(bset->ineq[k], set->p[i]->ineq[j], 1 + dim);
-			is_bound = uset_is_bound(set->ctx, set, bset->ineq[k],
-							1 + dim);
-			if (is_bound < 0)
-				goto error;
-			if (!is_bound)
-				isl_basic_set_free_inequality(bset, 1);
+		left = isl_basic_set_total_dim(hull) - nparam - i - 1;
+		for (j = 0; j < hull->n_eq; ++j) {
+			if (isl_int_is_zero(hull->eq[j][1 + nparam + i]))
+				continue;
+			if (isl_seq_first_non_zero(hull->eq[j]+1+nparam+i+1,
+						    left) == -1)
+				break;
+		}
+		if (j < hull->n_eq)
+			continue;
+
+		for (j = 0; j < hull->n_ineq; ++j) {
+			if (isl_int_is_zero(hull->ineq[j][1 + nparam + i]))
+				continue;
+			if (isl_seq_first_non_zero(hull->ineq[j]+1+nparam+i+1,
+						    left) != -1 ||
+			    isl_seq_first_non_zero(hull->ineq[j]+1+nparam,
+						    i) != -1)
+				continue;
+			if (isl_int_is_pos(hull->ineq[j][1 + nparam + i]))
+				lower = 1;
+			else
+				upper = 1;
+			if (lower && upper)
+				break;
 		}
-	}
 
-	bset = isl_basic_set_simplify(bset);
-	bset = isl_basic_set_finalize(bset);
-	bset = isl_basic_set_convex_hull(bset);
+		if (lower && upper)
+			continue;
 
-	hull = isl_basic_map_overlying_set(bset, model);
+		if (!removed_divs) {
+			set = isl_set_remove_divs(set);
+			if (!set)
+				goto error;
+			removed_divs = 1;
+		}
+		bounds = set_bounds(set, i);
+		hull = isl_basic_set_intersect(hull, bounds);
+		if (!hull)
+			goto error;
+	}
 
 	isl_set_free(set);
 	return hull;
 error:
-	isl_basic_set_free(bset);
 	isl_set_free(set);
-	isl_basic_map_free(model);
 	return NULL;
 }
-
-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);
-}