X-Git-Url: http://review.tizen.org/git/?a=blobdiff_plain;f=isl_convex_hull.c;h=17212c36d5c94d000ac28547d59a0dc1e249293b;hb=d1374f24acec4c3b3e65f1c6f44b54406500470d;hp=b1aa2dfcfc414c28e3d42c73417276034b2e1941;hpb=e2a4cce46780d0dcfa561cfde7e68ed8161d5c50;p=platform%2Fupstream%2Fisl.git

diff --git a/isl_convex_hull.c b/isl_convex_hull.c
index b1aa2df..17212c3 100644
--- a/isl_convex_hull.c
+++ b/isl_convex_hull.c
@@ -1,3 +1,12 @@
+/*
+ * Copyright 2008-2009 Katholieke Universiteit Leuven
+ *
+ * Use of this software is governed by the GNU LGPLv2.1 license
+ *
+ * Written by Sven Verdoolaege, K.U.Leuven, Departement
+ * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
+ */
+
 #include "isl_lp.h"
 #include "isl_map.h"
 #include "isl_map_private.h"
@@ -50,7 +59,8 @@ int isl_basic_map_constraint_is_redundant(struct isl_basic_map **bmap,
 	if (i < total)
 		return 0;
 
-	res = isl_solve_lp(*bmap, 0, c+1, (*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)
@@ -59,10 +69,6 @@ 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);
 }
 
@@ -97,13 +103,18 @@ 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_implicit_equalities(tab);
+	if (isl_tab_detect_redundant(tab) < 0)
+		goto error;
 	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;
+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)
@@ -116,8 +127,7 @@ 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;
@@ -133,8 +143,8 @@ static int uset_is_bound(struct isl_ctx *ctx, struct isl_set *set,
 		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+1, 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)
@@ -145,15 +155,15 @@ static int uset_is_bound(struct isl_ctx *ctx, struct isl_set *set,
 				goto error;
 			continue;
 		}
-		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)) {
+			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);
 	isl_int_clear(opt_denom);
-	isl_int_neg(c[0], c[0]);
 	return j >= set->n;
 error:
 	isl_int_clear(opt);
@@ -161,99 +171,7 @@ 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_ctx *ctx,
-	struct isl_set *set, isl_int *c,
-	struct isl_mat *dirs, int n)
-{
-	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(ctx, 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;
-}
-
-/* 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_ctx *ctx,
-	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);
-	if (!dirs)
-		goto error;
-
-	n = 0;
-	for (i = 0; n < dim && i < set->n; ++i) {
-		int f;
-		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);
-			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);
-			if (f < 0)
-				goto error;
-			if (f)
-				++n;
-		}
-	}
-	dirs->n_row = n;
-	return dirs;
-error:
-	isl_mat_free(ctx, 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;
@@ -288,19 +206,19 @@ 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;
-	unsigned total;
 	unsigned dim;
 
 	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);
 	i = isl_basic_set_alloc_equality(bset);
 	if (i < 0)
@@ -312,8 +230,7 @@ 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_basic_set_equality(struct isl_set *set, isl_int *c)
 {
 	int i;
 
@@ -321,7 +238,7 @@ 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;
 	}
@@ -339,7 +256,7 @@ 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
@@ -456,7 +373,8 @@ static struct isl_basic_set *wrap_constraints(struct isl_set *set)
  * 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;
 	struct isl_mat *T = NULL;
@@ -467,6 +385,7 @@ static isl_int *wrap_facet(struct isl_set *set, isl_int *facet, isl_int *ridge)
 	unsigned dim;
 
 	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);
@@ -476,31 +395,32 @@ static isl_int *wrap_facet(struct isl_set *set, isl_int *facet, isl_int *ridge)
 	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(set->ctx, T);
+	T = isl_mat_right_inverse(T);
 	set = isl_set_preimage(set, T);
 	T = NULL;
 	if (!set)
 		goto error;
 	lp = wrap_constraints(set);
-	obj = isl_vec_alloc(set->ctx, dim*set->n);
+	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, set->ctx->one, &num, &den);
+	res = isl_basic_set_solve_lp(lp, 0,
+			    obj->block.data, set->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_int_clear(num);
 	isl_int_clear(den);
-	isl_vec_free(set->ctx, obj);
+	isl_vec_free(obj);
 	isl_basic_set_free(lp);
 	isl_set_free(set);
 	isl_assert(set->ctx, res == isl_lp_ok || res == isl_lp_unbounded, 
@@ -508,38 +428,49 @@ static isl_int *wrap_facet(struct isl_set *set, isl_int *facet, isl_int *ridge)
 	return facet;
 error:
 	isl_basic_set_free(lp);
-	isl_mat_free(set->ctx, T);
+	isl_mat_free(T);
 	isl_set_free(set);
 	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_ctx *ctx,
-	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;
 
-	isl_assert(ctx, set->n > 0, goto error);
-	isl_assert(ctx, bounds->n_row == dim, goto error);
+	isl_assert(set->ctx, set->n > 0, goto error);
+	bounds = isl_mat_alloc(set->ctx, 1, 1 + dim);
+	if (!bounds)
+		return NULL;
 
-	while (bounds->n_row > 1) {
+	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);
+	isl_assert(set->ctx, is_bound == 1, goto error);
+	isl_seq_normalize(set->ctx, bounds->row[0], 1 + dim);
+	bounds->n_row = 1;
+
+	for (;;) {
 		slice = isl_set_copy(set);
-		slice = isl_set_add_equality(ctx, 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;
@@ -547,38 +478,22 @@ 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);
-		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);
-		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);
-	isl_mat_free(ctx, bounds);
+	isl_mat_free(bounds);
 	return NULL;
 }
 
@@ -637,10 +552,10 @@ static struct isl_basic_set *compute_facet(struct isl_set *set, isl_int *c)
 	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(set->ctx, m);
-	Q = isl_mat_right_inverse(set->ctx, isl_mat_copy(set->ctx, U));
-	U = isl_mat_drop_cols(set->ctx, U, 1, 1);
-	Q = isl_mat_drop_rows(set->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_bounded(set);
 	facet = isl_basic_set_preimage(facet, Q);
@@ -680,27 +595,29 @@ 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);
 
 	for (i = 0; i < hull->n_ineq; ++i) {
 		facet = compute_facet(set, hull->ineq[i]);
-		facet = isl_basic_set_add_equality(facet->ctx, facet, 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->ctx, hull_facet, hull->ineq[i]);
+		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 > hull->c_size)
-			hull = isl_basic_set_extend_dim(hull,
-				isl_dim_copy(hull->dim), 0, 0, 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],
@@ -712,7 +629,7 @@ 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);
@@ -732,8 +649,7 @@ 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;
@@ -750,13 +666,13 @@ 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])) {
@@ -831,7 +747,7 @@ 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;
@@ -845,11 +761,11 @@ 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;
 }
 
@@ -884,7 +800,7 @@ 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;
@@ -948,12 +864,574 @@ error:
 	return NULL;
 }
 
+static int isl_basic_set_is_bounded(struct isl_basic_set *bset)
+{
+	struct isl_tab *tab;
+	int bounded;
+
+	if (!bset)
+		return -1;
+	if (isl_basic_set_fast_is_empty(bset))
+		return 1;
+
+	tab = isl_tab_from_recession_cone(bset);
+	bounded = isl_tab_cone_is_bounded(tab);
+	isl_tab_free(tab);
+	return bounded;
+}
+
+int isl_set_is_bounded(__isl_keep 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 *induced_lineality_space(
+	struct isl_basic_set *bset1, struct isl_basic_set *bset2)
+{
+	int i, k;
+	struct isl_basic_set *lin = NULL;
+	unsigned dim;
+
+	if (!bset1 || !bset2)
+		goto error;
+
+	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;
+		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;
+		isl_int_set_si(lin->ineq[k][0], 0);
+		isl_seq_cpy(lin->ineq[k] + 1, bset1->ineq[i] + 1, dim);
+	}
+	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_basic_set_free(lin);
+	isl_basic_set_free(bset1);
+	isl_basic_set_free(bset2);
+	return NULL;
+}
+
+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)
+{
+	unsigned total = isl_basic_set_total_dim(lin);
+	unsigned lin_dim;
+	struct isl_basic_set *hull;
+	struct isl_mat *M, *U, *Q;
+
+	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_left_hermite(M, 0, &U, &Q);
+	if (!M)
+		goto error;
+	isl_mat_free(M);
+	isl_basic_set_free(lin);
+
+	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;
+}
+
+/* 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 *valid_direction_lp(
+	struct isl_basic_set *bset1, struct isl_basic_set *bset2)
+{
+	struct isl_dim *dim;
+	struct isl_basic_set *lp;
+	unsigned d;
+	int n;
+	int i, j, k;
+
+	if (!bset1 || !bset2)
+		goto error;
+	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;
+	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_basic_set_free(bset1);
+	isl_basic_set_free(bset2);
+	return NULL;
+}
+
+/* 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 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 (*).
+ *
+ * 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_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;
+	int n;
+
+	if (!bset1 || !bset2)
+		goto error;
+	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;
+	d = isl_basic_set_total_dim(bset1);
+	dir = isl_vec_alloc(bset1->ctx, 1 + d);
+	if (!dir)
+		goto error;
+	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_seq_normalize(bset1->ctx, dir->el, dir->size);
+	isl_basic_set_free(bset1);
+	isl_basic_set_free(bset2);
+	return dir;
+error:
+	isl_vec_free(sample);
+	isl_basic_set_free(bset1);
+	isl_basic_set_free(bset2);
+	return NULL;
+}
+
+/* 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 *homogeneous_map(struct isl_basic_set *bset,
+	struct isl_mat *T)
+{
+	int k;
+
+	if (!bset)
+		goto error;
+	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_mat_free(T);
+	isl_basic_set_free(bset);
+	return NULL;
+}
+
+/* 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.
+ *
+ * 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.
+ */
+static struct isl_basic_set *convex_hull_pair_pointed(
+	struct isl_basic_set *bset1, struct isl_basic_set *bset2)
+{
+	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 (!bset1 || !bset2)
+		goto error;
+	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_basic_set(set, bset1);
+	set = isl_set_add_basic_set(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;
+}
+
+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)
+{
+	isl_basic_set *lin, *aff;
+	int bounded1, bounded2;
+
+	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);
+
+	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),
+				      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_basic_set(set, bset1);
+		set = isl_set_add_basic_set(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_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);
+}
+
 /* Compute the convex hull of a set without any parameters or
- * integer divisions using Fourier-Motzkin elimination.
+ * 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_elim(struct isl_set *set)
+static struct isl_basic_set *uset_convex_hull_unbounded(struct isl_set *set)
 {
 	struct isl_basic_set *convex_hull = NULL;
 
@@ -970,6 +1448,21 @@ static struct isl_basic_set *uset_convex_hull_elim(struct isl_set *set)
 		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_basic_set(set, convex_hull);
+			return modulo_lineality(set, t);
+		}
+		isl_basic_set_free(t);
 	}
 	isl_set_free(set);
 	return convex_hull;
@@ -980,13 +1473,8 @@ 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)
@@ -997,11 +1485,7 @@ static struct isl_basic_set *initial_hull(struct isl_basic_set *hull,
 
 	if (!hull)
 		goto error;
-	bounds = independent_bounds(set->ctx, set);
-	if (!bounds)
-		goto error;
-	isl_assert(set->ctx, bounds->n_row == isl_set_n_dim(set), goto error);
-	bounds = initial_facet_constraint(set->ctx, set, bounds);
+	bounds = initial_facet_constraint(set);
 	if (!bounds)
 		goto error;
 	k = isl_basic_set_alloc_inequality(hull);
@@ -1010,12 +1494,12 @@ static struct isl_basic_set *initial_hull(struct isl_basic_set *hull,
 	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(set->ctx, bounds);
+	isl_mat_free(bounds);
 
 	return hull;
 error:
 	isl_basic_set_free(hull);
-	isl_mat_free(set->ctx, bounds);
+	isl_mat_free(bounds);
 	return NULL;
 }
 
@@ -1040,7 +1524,7 @@ 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)
@@ -1058,7 +1542,7 @@ static void update_constraint(struct isl_ctx *ctx, struct isl_hash_table *table,
 			c->ineq = ineq;
 		return;
 	}
-	c->c = isl_mat_cow(ctx, c->c);
+	c->c = isl_mat_cow(c->c);
 	isl_int_set(c->c->row[0][0], con[0]);
 	c->ineq = ineq;
 }
@@ -1073,7 +1557,7 @@ 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)
@@ -1140,8 +1624,7 @@ 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)
@@ -1198,7 +1681,7 @@ static struct isl_basic_set *common_constraints(struct isl_basic_set *hull,
 
 	isl_hash_table_clear(table);
 	for (i = 0; i < min_constraints; ++i)
-		isl_mat_free(hull->ctx, constraints[i].c);
+		isl_mat_free(constraints[i].c);
 	free(constraints);
 	free(table);
 	return hull;
@@ -1207,7 +1690,7 @@ error:
 	free(table);
 	if (constraints)
 		for (i = 0; i < min_constraints; ++i)
-			isl_mat_free(hull->ctx, constraints[i].c);
+			isl_mat_free(constraints[i].c);
 	free(constraints);
 	return hull;
 }
@@ -1250,29 +1733,6 @@ static struct isl_basic_set *uset_convex_hull_wrap(struct isl_set *set)
 	return hull;
 }
 
-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(bset->ctx, tab);
-	isl_tab_free(bset->ctx, 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 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
@@ -1281,17 +1741,17 @@ static int isl_set_is_bounded(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;
 
 	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;
-	set = isl_set_normalize(set);
 	if (!set)
 		return NULL;
 	if (set->n == 1) {
@@ -1300,12 +1760,23 @@ static struct isl_basic_set *uset_convex_hull(struct isl_set *set)
 		return convex_hull;
 	}
 	if (isl_set_n_dim(set) == 1)
-		return convex_hull_1d(set->ctx, set);
+		return convex_hull_1d(set);
 
-	if (!isl_set_is_bounded(set))
-		return uset_convex_hull_elim(set);
+	if (isl_set_is_bounded(set))
+		return uset_convex_hull_wrap(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);
@@ -1318,7 +1789,6 @@ 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 (isl_set_n_dim(set) == 0) {
@@ -1332,7 +1802,7 @@ static struct isl_basic_set *uset_convex_hull_wrap_bounded(struct isl_set *set)
 
 	if (!set)
 		goto error;
-	set = isl_set_normalize(set);
+	set = isl_set_coalesce(set);
 	if (!set)
 		goto error;
 	if (set->n == 1) {
@@ -1341,7 +1811,7 @@ static struct isl_basic_set *uset_convex_hull_wrap_bounded(struct isl_set *set)
 		return convex_hull;
 	}
 	if (isl_set_n_dim(set) == 1)
-		return convex_hull_1d(set->ctx, set);
+		return convex_hull_1d(set);
 
 	return uset_convex_hull_wrap(set);
 error:
@@ -1354,7 +1824,7 @@ 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;
@@ -1402,6 +1872,7 @@ struct isl_basic_map *isl_map_convex_hull(struct isl_map *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);
@@ -1412,7 +1883,7 @@ 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);
@@ -1420,6 +1891,8 @@ 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:
@@ -1452,7 +1925,7 @@ 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)
@@ -1464,7 +1937,7 @@ static void sh_data_free(struct sh_data *data)
 	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->ctx, data->p[i].tab);
+		isl_tab_free(data->p[i].tab);
 	}
 	free(data);
 }
@@ -1492,7 +1965,7 @@ 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;
@@ -1530,7 +2003,8 @@ 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;
@@ -1574,14 +2048,14 @@ static int is_bound(struct sh_data *data, struct isl_set *set, int j,
 
 	isl_int_init(opt);
 
-	res = isl_tab_min(data->ctx, data->p[j].tab, ineq, data->ctx->one,
-				&opt, NULL);
+	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 :
+	return (res == isl_lp_ok || res == isl_lp_empty) ? 1 :
 	       res == isl_lp_unbounded ? 0 : -1;
 }
 
@@ -1615,7 +2089,7 @@ 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);
@@ -1702,11 +2176,11 @@ 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]);
 		}
 	}
 	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]);
 	return bset;
 }
 
@@ -1718,7 +2192,7 @@ 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;
+	int i;
 
 	if (!set)
 		return NULL;
@@ -1730,25 +2204,17 @@ 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_set_affine_hull(isl_set_copy(set));
-	if (!hull)
-		goto error;
-	hull = isl_basic_set_extend_dim(hull, isl_dim_copy(hull->dim),
-					0, 0, 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;
-	if (hash_basic_set(data->hull_table, hull) < 0)
-		goto error;
 
 	for (i = 0; i < set->n; ++i)
 		hull = add_bounds(hull, data, set, i);
 
-	hull = isl_basic_set_convex_hull(hull);
-
 	sh_data_free(data);
 	isl_set_free(set);
 
@@ -1768,6 +2234,7 @@ 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;
 
 	if (!map)
@@ -1783,6 +2250,8 @@ 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]);
 
@@ -1792,6 +2261,11 @@ struct isl_basic_map *isl_map_simple_hull(struct isl_map *map)
 
 	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;
 }
 
@@ -1800,3 +2274,83 @@ 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;
+
+	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;
+
+		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;
+		}
+
+		if (lower && upper)
+			continue;
+
+		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_set_free(set);
+	return NULL;
+}