X-Git-Url: http://review.tizen.org/git/?a=blobdiff_plain;f=isl_convex_hull.c;h=40cca1b74ed4fa4c51bc3e6645a6bcc1099cdc04;hb=a41dca96db00c891c58a4535bb8920b5ed70e682;hp=41427f19ea70bc464922273120842257eec6bf6d;hpb=f649bf1c93c9e5ff5bfa996a9e5cf6c55bc8f283;p=platform%2Fupstream%2Fisl.git

diff --git a/isl_convex_hull.c b/isl_convex_hull.c
index 41427f1..40cca1b 100644
--- a/isl_convex_hull.c
+++ b/isl_convex_hull.c
@@ -7,12 +7,12 @@
  * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
  */
 
-#include "isl_lp.h"
-#include "isl_map.h"
+#include <isl/lp.h>
+#include <isl/map.h>
 #include "isl_map_private.h"
-#include "isl_mat.h"
-#include "isl_set.h"
-#include "isl_seq.h"
+#include <isl_mat_private.h>
+#include <isl/set.h>
+#include <isl/seq.h>
 #include "isl_equalities.h"
 #include "isl_tab.h"
 
@@ -79,7 +79,7 @@ int isl_basic_set_constraint_is_redundant(struct isl_basic_set **bset,
 			(struct isl_basic_map **)bset, c, opt_n, opt_d);
 }
 
-/* Compute the convex hull of a basic map, by removing the redundant
+/* Remove redundant
  * constraints.  If the minimal value along the normal of a constraint
  * is the same if the constraint is removed, then the constraint is redundant.
  *
@@ -87,7 +87,8 @@ int isl_basic_set_constraint_is_redundant(struct isl_basic_set **bset,
  * corresponding equality and the checked if the dimension was that
  * of a facet.
  */
-struct isl_basic_map *isl_basic_map_convex_hull(struct isl_basic_map *bmap)
+__isl_give isl_basic_map *isl_basic_map_remove_redundancies(
+	__isl_take isl_basic_map *bmap)
 {
 	struct isl_tab *tab;
 
@@ -103,7 +104,8 @@ 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_implicit_equalities(tab);
+	if (isl_tab_detect_implicit_equalities(tab) < 0)
+		goto error;
 	if (isl_tab_detect_redundant(tab) < 0)
 		goto error;
 	bmap = isl_basic_map_update_from_tab(bmap, tab);
@@ -117,10 +119,11 @@ error:
 	return NULL;
 }
 
-struct isl_basic_set *isl_basic_set_convex_hull(struct isl_basic_set *bset)
+__isl_give isl_basic_set *isl_basic_set_remove_redundancies(
+	__isl_take isl_basic_set *bset)
 {
 	return (struct isl_basic_set *)
-		isl_basic_map_convex_hull((struct isl_basic_map *)bset);
+		isl_basic_map_remove_redundancies((struct isl_basic_map *)bset);
 }
 
 /* Check if the set set is bound in the direction of the affine
@@ -171,94 +174,6 @@ error:
 	return -1;
 }
 
-/* Check if "c" is a direction that is independent of the previously found "n"
- * bounds in "dirs".
- * If so, add it to the list, with the negative of the lower bound
- * in the constant position, i.e., such that c corresponds to a bounding
- * hyperplane (but not necessarily a facet).
- * Assumes set "set" is bounded.
- */
-static int is_independent_bound(struct isl_set *set, isl_int *c,
-	struct isl_mat *dirs, int n)
-{
-	int is_bound;
-	int i = 0;
-
-	isl_seq_cpy(dirs->row[n]+1, c+1, dirs->n_col-1);
-	if (n != 0) {
-		int pos = isl_seq_first_non_zero(dirs->row[n]+1, dirs->n_col-1);
-		if (pos < 0)
-			return 0;
-		for (i = 0; i < n; ++i) {
-			int pos_i;
-			pos_i = isl_seq_first_non_zero(dirs->row[i]+1, dirs->n_col-1);
-			if (pos_i < pos)
-				continue;
-			if (pos_i > pos)
-				break;
-			isl_seq_elim(dirs->row[n]+1, dirs->row[i]+1, pos,
-					dirs->n_col-1, NULL);
-			pos = isl_seq_first_non_zero(dirs->row[n]+1, dirs->n_col-1);
-			if (pos < 0)
-				return 0;
-		}
-	}
-
-	is_bound = uset_is_bound(set, dirs->row[n], dirs->n_col);
-	if (is_bound != 1)
-		return is_bound;
-	isl_seq_normalize(set->ctx, dirs->row[n], dirs->n_col);
-	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_set *set)
-{
-	int i, j, n;
-	struct isl_mat *dirs = NULL;
-	unsigned dim = isl_set_n_dim(set);
-
-	dirs = isl_mat_alloc(set->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(set, bset->eq[j], dirs, n);
-			if (f < 0)
-				goto error;
-			if (f)
-				++n;
-		}
-		for (j = 0; n < dim && j < bset->n_ineq; ++j) {
-			f = is_independent_bound(set, bset->ineq[j], dirs, n);
-			if (f < 0)
-				goto error;
-			if (f)
-				++n;
-		}
-	}
-	dirs->n_row = n;
-	return dirs;
-error:
-	isl_mat_free(dirs);
-	return NULL;
-}
-
 struct isl_basic_set *isl_basic_set_set_rational(struct isl_basic_set *bset)
 {
 	if (!bset)
@@ -300,6 +215,9 @@ static struct isl_basic_set *isl_basic_set_add_equality(
 	int i;
 	unsigned dim;
 
+	if (!bset)
+		return NULL;
+
 	if (ISL_F_ISSET(bset, ISL_BASIC_SET_EMPTY))
 		return bset;
 
@@ -465,6 +383,7 @@ isl_int *isl_set_wrap_facet(__isl_keep isl_set *set,
 	isl_int *facet, isl_int *ridge)
 {
 	int i;
+	isl_ctx *ctx;
 	struct isl_mat *T = NULL;
 	struct isl_basic_set *lp = NULL;
 	struct isl_vec *obj;
@@ -472,10 +391,14 @@ isl_int *isl_set_wrap_facet(__isl_keep isl_set *set,
 	isl_int num, den;
 	unsigned dim;
 
+	if (!set)
+		return NULL;
+	ctx = set->ctx;
 	set = isl_set_copy(set);
+	set = isl_set_set_rational(set);
 
 	dim = 1 + isl_set_n_dim(set);
-	T = isl_mat_alloc(set->ctx, 3, dim);
+	T = isl_mat_alloc(ctx, 3, dim);
 	if (!T)
 		goto error;
 	isl_int_set_si(T->row[0][0], 1);
@@ -488,7 +411,7 @@ isl_int *isl_set_wrap_facet(__isl_keep isl_set *set,
 	if (!set)
 		goto error;
 	lp = wrap_constraints(set);
-	obj = isl_vec_alloc(set->ctx, 1 + dim*set->n);
+	obj = isl_vec_alloc(ctx, 1 + dim*set->n);
 	if (!obj)
 		goto error;
 	isl_int_set_si(obj->block.data[0], 0);
@@ -500,17 +423,20 @@ isl_int *isl_set_wrap_facet(__isl_keep isl_set *set,
 	isl_int_init(num);
 	isl_int_init(den);
 	res = isl_basic_set_solve_lp(lp, 0,
-			    obj->block.data, set->ctx->one, &num, &den, NULL);
+			    obj->block.data, ctx->one, &num, &den, NULL);
 	if (res == isl_lp_ok) {
 		isl_int_neg(num, num);
 		isl_seq_combine(facet, num, facet, den, ridge, dim);
+		isl_seq_normalize(ctx, facet, dim);
 	}
 	isl_int_clear(num);
 	isl_int_clear(den);
 	isl_vec_free(obj);
 	isl_basic_set_free(lp);
 	isl_set_free(set);
-	isl_assert(set->ctx, res == isl_lp_ok || res == isl_lp_unbounded, 
+	if (res == isl_lp_error)
+		return NULL;
+	isl_assert(ctx, res == isl_lp_ok || res == isl_lp_unbounded, 
 		   return NULL);
 	return facet;
 error:
@@ -520,80 +446,43 @@ error:
 	return NULL;
 }
 
-/* Drop rows in "rows" that are redundant with respect to earlier rows,
- * assuming that "rows" is of full column rank.
- *
- * We compute the column echelon form.  The non-redundant rows are
- * those that are the first to contain a non-zero entry in a column.
- * All the other rows can be removed.
+/* 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 __isl_give isl_mat *drop_redundant_rows(__isl_take isl_mat *rows)
-{
-	struct isl_mat *H = NULL;
-	int col;
-	int row;
-	int last_row;
-
-	if (!rows)
-		return NULL;
-
-	isl_assert(rows->ctx, rows->n_row >= rows->n_col, goto error);
-
-	if (rows->n_row == rows->n_col)
-		return rows;
-
-	H = isl_mat_left_hermite(isl_mat_copy(rows), 0, NULL, NULL);
-	if (!H)
-		goto error;
-
-	last_row = rows->n_row;
-	for (col = rows->n_col - 1; col >= 0; --col) {
-		for (row = col; row < last_row; ++row)
-			if (!isl_int_is_zero(H->row[row][col]))
-				break;
-		isl_assert(rows->ctx, row < last_row, goto error);
-		if (row + 1 < last_row) {
-			rows = isl_mat_drop_rows(rows, row + 1, last_row - (row + 1));
-			if (rows->n_row == rows->n_col)
-				break;
-		}
-		last_row = row;
-	}
-
-	isl_mat_free(H);
-
-	return rows;
-error:
-	isl_mat_free(H);
-	isl_mat_free(rows);
-	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.
- */
-static struct isl_mat *initial_facet_constraint(struct isl_set *set,
-	struct isl_mat *bounds)
+static __isl_give isl_mat *initial_facet_constraint(__isl_keep isl_set *set)
 {
 	struct isl_set *slice = NULL;
 	struct isl_basic_set *face = NULL;
-	struct isl_mat *m, *U, *Q;
 	int i;
 	unsigned dim = isl_set_n_dim(set);
+	int is_bound;
+	isl_mat *bounds;
 
 	isl_assert(set->ctx, set->n > 0, goto error);
-	isl_assert(set->ctx, bounds->n_row == dim, goto error);
+	bounds = isl_mat_alloc(set->ctx, 1, 1 + dim);
+	if (!bounds)
+		return NULL;
+
+	isl_seq_clr(bounds->row[0], dim);
+	isl_int_set_si(bounds->row[0][1 + dim - 1], 1);
+	is_bound = uset_is_bound(set, bounds->row[0], 1 + dim);
+	if (is_bound < 0)
+		goto error;
+	isl_assert(set->ctx, is_bound, goto error);
+	isl_seq_normalize(set->ctx, bounds->row[0], 1 + dim);
+	bounds->n_row = 1;
 
-	while (bounds->n_row > 1) {
+	for (;;) {
 		slice = isl_set_copy(set);
 		slice = isl_set_add_basic_set_equality(slice, bounds->row[0]);
 		face = isl_set_affine_hull(slice);
@@ -603,29 +492,18 @@ static struct isl_mat *initial_facet_constraint(struct isl_set *set,
 			isl_basic_set_free(face);
 			break;
 		}
-		m = isl_mat_alloc(set->ctx, 1 + face->n_eq, 1 + dim);
-		if (!m)
-			goto error;
-		isl_int_set_si(m->row[0][0], 1);
-		isl_seq_clr(m->row[0]+1, dim);
 		for (i = 0; i < face->n_eq; ++i)
-			isl_seq_cpy(m->row[1 + i], face->eq[i], 1 + dim);
-		U = isl_mat_right_inverse(m);
-		Q = isl_mat_right_inverse(isl_mat_copy(U));
-		U = isl_mat_drop_cols(U, 1 + face->n_eq, dim - face->n_eq);
-		Q = isl_mat_drop_rows(Q, 1 + face->n_eq, dim - face->n_eq);
-		U = isl_mat_drop_cols(U, 0, 1);
-		Q = isl_mat_drop_rows(Q, 0, 1);
-		bounds = isl_mat_product(bounds, U);
-		bounds = drop_redundant_rows(bounds);
-		bounds = isl_mat_product(bounds, Q);
-		isl_assert(set->ctx, bounds->n_row > 1, goto error);
-		if (!isl_set_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);
@@ -695,7 +573,8 @@ static struct isl_basic_set *compute_facet(struct isl_set *set, isl_int *c)
 	set = isl_set_preimage(set, U);
 	facet = uset_convex_hull_wrap_bounded(set);
 	facet = isl_basic_set_preimage(facet, Q);
-	isl_assert(ctx, facet->n_eq == 0, goto error);
+	if (facet)
+		isl_assert(ctx, facet->n_eq == 0, goto error);
 	return facet;
 error:
 	isl_basic_set_free(facet);
@@ -749,11 +628,13 @@ static struct isl_basic_set *extend(struct isl_basic_set *hull,
 		hull_facet = isl_basic_set_add_equality(hull_facet, hull->ineq[i]);
 		hull_facet = isl_basic_set_gauss(hull_facet, NULL);
 		hull_facet = isl_basic_set_normalize_constraints(hull_facet);
-		if (!facet)
+		if (!facet || !hull_facet)
 			goto error;
 		hull = isl_basic_set_cow(hull);
 		hull = isl_basic_set_extend_dim(hull,
 			isl_dim_copy(hull->dim), 0, 0, facet->n_ineq);
+		if (!hull)
+			goto error;
 		for (j = 0; j < facet->n_ineq; ++j) {
 			for (f = 0; f < hull_facet->n_ineq; ++f)
 				if (isl_seq_eq(facet->ineq[j],
@@ -909,7 +790,7 @@ error:
 static struct isl_set *set_project_out(struct isl_ctx *ctx,
 	struct isl_set *set, unsigned n)
 {
-	return isl_set_remove_dims(set, isl_set_n_dim(set) - n, n);
+	return isl_set_remove_dims(set, isl_dim_set, isl_set_n_dim(set) - n, n);
 }
 
 static struct isl_basic_set *convex_hull_0d(struct isl_set *set)
@@ -988,8 +869,8 @@ static struct isl_basic_set *convex_hull_pair_elim(struct isl_basic_set *bset1,
 		isl_int_set_si(hull->eq[k][2*(1+dim)+j], 1);
 	}
 	hull = isl_basic_set_set_rational(hull);
-	hull = isl_basic_set_remove_dims(hull, dim, 2*(1+dim));
-	hull = isl_basic_set_convex_hull(hull);
+	hull = isl_basic_set_remove_dims(hull, isl_dim_set, dim, 2*(1+dim));
+	hull = isl_basic_set_remove_redundancies(hull);
 	isl_basic_set_free(bset1);
 	isl_basic_set_free(bset2);
 	return hull;
@@ -1000,21 +881,52 @@ error:
 	return NULL;
 }
 
-static int isl_basic_set_is_bounded(struct isl_basic_set *bset)
+/* Is the set bounded for each value of the parameters?
+ */
+int isl_basic_set_is_bounded(__isl_keep isl_basic_set *bset)
 {
 	struct isl_tab *tab;
 	int bounded;
 
-	tab = isl_tab_from_recession_cone(bset);
+	if (!bset)
+		return -1;
+	if (isl_basic_set_fast_is_empty(bset))
+		return 1;
+
+	tab = isl_tab_from_recession_cone(bset, 1);
 	bounded = isl_tab_cone_is_bounded(tab);
 	isl_tab_free(tab);
 	return bounded;
 }
 
-static int isl_set_is_bounded(struct isl_set *set)
+/* Is the image bounded for each value of the parameters and
+ * the domain variables?
+ */
+int isl_basic_map_image_is_bounded(__isl_keep isl_basic_map *bmap)
+{
+	unsigned nparam = isl_basic_map_dim(bmap, isl_dim_param);
+	unsigned n_in = isl_basic_map_dim(bmap, isl_dim_in);
+	int bounded;
+
+	bmap = isl_basic_map_copy(bmap);
+	bmap = isl_basic_map_cow(bmap);
+	bmap = isl_basic_map_move_dims(bmap, isl_dim_param, nparam,
+					isl_dim_in, 0, n_in);
+	bounded = isl_basic_set_is_bounded((isl_basic_set *)bmap);
+	isl_basic_map_free(bmap);
+
+	return bounded;
+}
+
+/* Is the set bounded for each value of the parameters?
+ */
+int isl_set_is_bounded(__isl_keep isl_set *set)
 {
 	int i;
 
+	if (!set)
+		return -1;
+
 	for (i = 0; i < set->n; ++i) {
 		int bounded = isl_basic_set_is_bounded(set->p[i]);
 		if (!bounded || bounded < 0)
@@ -1131,7 +1043,7 @@ static struct isl_basic_set *modulo_lineality(struct isl_set *set,
 	Q = isl_mat_lin_to_aff(Q);
 
 	set = isl_set_preimage(set, U);
-	set = isl_set_remove_dims(set, total - lin_dim, lin_dim);
+	set = isl_set_remove_dims(set, isl_dim_set, total - lin_dim, lin_dim);
 	hull = uset_convex_hull(set);
 	hull = isl_basic_set_preimage(hull, Q);
 
@@ -1182,23 +1094,25 @@ static struct isl_basic_set *valid_direction_lp(
 		if (k < 0)
 			goto error;
 		n = 0;
-		isl_int_set_si(lp->eq[k][n++], 0);
+		isl_int_set_si(lp->eq[k][n], 0); n++;
 		/* positivity constraint 1 >= 0 */
-		isl_int_set_si(lp->eq[k][n++], i == 0);
+		isl_int_set_si(lp->eq[k][n], i == 0); n++;
 		for (j = 0; j < bset1->n_eq; ++j) {
-			isl_int_set(lp->eq[k][n++], bset1->eq[j][i]);
-			isl_int_neg(lp->eq[k][n++], bset1->eq[j][i]);
+			isl_int_set(lp->eq[k][n], bset1->eq[j][i]); n++;
+			isl_int_neg(lp->eq[k][n], bset1->eq[j][i]); n++;
+		}
+		for (j = 0; j < bset1->n_ineq; ++j) {
+			isl_int_set(lp->eq[k][n], bset1->ineq[j][i]); n++;
 		}
-		for (j = 0; j < bset1->n_ineq; ++j)
-			isl_int_set(lp->eq[k][n++], bset1->ineq[j][i]);
 		/* positivity constraint 1 >= 0 */
-		isl_int_set_si(lp->eq[k][n++], -(i == 0));
+		isl_int_set_si(lp->eq[k][n], -(i == 0)); n++;
 		for (j = 0; j < bset2->n_eq; ++j) {
-			isl_int_neg(lp->eq[k][n++], bset2->eq[j][i]);
-			isl_int_set(lp->eq[k][n++], bset2->eq[j][i]);
+			isl_int_neg(lp->eq[k][n], bset2->eq[j][i]); n++;
+			isl_int_set(lp->eq[k][n], bset2->eq[j][i]); n++;
+		}
+		for (j = 0; j < bset2->n_ineq; ++j) {
+			isl_int_neg(lp->eq[k][n], bset2->ineq[j][i]); n++;
 		}
-		for (j = 0; j < bset2->n_ineq; ++j)
-			isl_int_neg(lp->eq[k][n++], bset2->ineq[j][i]);
 	}
 	lp = isl_basic_set_gauss(lp, NULL);
 	isl_basic_set_free(bset1);
@@ -1222,7 +1136,7 @@ error:
  * (including the "positivity constraint" 1 >= 0) and \alpha_{ij}
  * strictly positive numbers.  For simplicity we impose \alpha_{ij} >= 1.
  * We first set up an LP with as variables the \alpha{ij}.
- * In this formulateion, for each polyhedron i,
+ * In this formulation, for each polyhedron i,
  * the first constraint is the positivity constraint, followed by pairs
  * of variables for the equalities, followed by variables for the inequalities.
  * We then simply pick a feasible solution and compute s using (*).
@@ -1258,7 +1172,7 @@ static struct isl_vec *valid_direction(
 	isl_seq_clr(dir->block.data + 1, dir->size - 1);
 	n = 1;
 	/* positivity constraint 1 >= 0 */
-	isl_int_set(dir->block.data[0], sample->block.data[n++]);
+	isl_int_set(dir->block.data[0], sample->block.data[n]); n++;
 	for (i = 0; i < bset1->n_eq; ++i) {
 		isl_int_sub(sample->block.data[n],
 			    sample->block.data[n], sample->block.data[n+1]);
@@ -1273,7 +1187,7 @@ static struct isl_vec *valid_direction(
 				bset1->ctx->one, dir->block.data,
 				sample->block.data[n++], bset1->ineq[i], 1 + d);
 	isl_vec_free(sample);
-	isl_seq_normalize(bset1->ctx, dir->block.data + 1, dir->size - 1);
+	isl_seq_normalize(bset1->ctx, dir->el, dir->size);
 	isl_basic_set_free(bset1);
 	isl_basic_set_free(bset2);
 	return dir;
@@ -1415,18 +1329,47 @@ error:
 	return NULL;
 }
 
+static struct isl_basic_set *uset_convex_hull_wrap(struct isl_set *set);
+static struct isl_basic_set *modulo_affine_hull(
+	struct isl_set *set, struct isl_basic_set *affine_hull);
+
 /* Compute the convex hull of a pair of basic sets without any parameters or
  * integer divisions.
  *
+ * This function is called from uset_convex_hull_unbounded, which
+ * means that the complete convex hull is unbounded.  Some pairs
+ * of basic sets may still be bounded, though.
+ * They may even lie inside a lower dimensional space, in which
+ * case they need to be handled inside their affine hull since
+ * the main algorithm assumes that the result is full-dimensional.
+ *
  * If the convex hull of the two basic sets would have a non-trivial
  * lineality space, we first project out this lineality space.
  */
 static struct isl_basic_set *convex_hull_pair(struct isl_basic_set *bset1,
 	struct isl_basic_set *bset2)
 {
-	struct isl_basic_set *lin;
+	isl_basic_set *lin, *aff;
+	int bounded1, bounded2;
+
+	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 (isl_basic_set_is_bounded(bset1) || 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),
@@ -1575,13 +1518,8 @@ 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)
@@ -1592,11 +1530,7 @@ static struct isl_basic_set *initial_hull(struct isl_basic_set *hull,
 
 	if (!hull)
 		goto error;
-	bounds = independent_bounds(set);
-	if (!bounds)
-		goto error;
-	isl_assert(set->ctx, bounds->n_row == isl_set_n_dim(set), goto error);
-	bounds = initial_facet_constraint(set, bounds);
+	bounds = initial_facet_constraint(set);
 	if (!bounds)
 		goto error;
 	k = isl_basic_set_alloc_inequality(hull);
@@ -1902,6 +1836,9 @@ static struct isl_basic_set *uset_convex_hull_wrap_bounded(struct isl_set *set)
 {
 	struct isl_basic_set *convex_hull = NULL;
 
+	if (!set)
+		goto error;
+
 	if (isl_set_n_dim(set) == 0) {
 		convex_hull = isl_basic_set_universe(isl_dim_copy(set->dim));
 		isl_set_free(set);
@@ -1910,9 +1847,6 @@ static struct isl_basic_set *uset_convex_hull_wrap_bounded(struct isl_set *set)
 	}
 
 	set = isl_set_set_rational(set);
-
-	if (!set)
-		goto error;
 	set = isl_set_coalesce(set);
 	if (!set)
 		goto error;
@@ -1935,7 +1869,7 @@ 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;
@@ -1985,6 +1919,8 @@ struct isl_basic_map *isl_map_convex_hull(struct isl_map *map)
 
 	map = isl_map_detect_equalities(map);
 	map = isl_map_align_divs(map);
+	if (!map)
+		goto error;
 	model = isl_basic_map_copy(map->p[0]);
 	set = isl_map_underlying_set(map);
 	if (!set)
@@ -1994,13 +1930,15 @@ struct isl_basic_map *isl_map_convex_hull(struct isl_map *map)
 	if (!affine_hull)
 		goto error;
 	if (affine_hull->n_eq != 0)
-		bset = modulo_affine_hull(ctx, set, affine_hull);
+		bset = modulo_affine_hull(set, affine_hull);
 	else {
 		isl_basic_set_free(affine_hull);
 		bset = uset_convex_hull(set);
 	}
 
 	convex_hull = isl_basic_map_overlying_set(bset, model);
+	if (!convex_hull)
+		return NULL;
 
 	ISL_F_SET(convex_hull, ISL_BASIC_MAP_NO_IMPLICIT);
 	ISL_F_SET(convex_hull, ISL_BASIC_MAP_ALL_EQUALITIES);
@@ -2018,6 +1956,19 @@ struct isl_basic_set *isl_set_convex_hull(struct isl_set *set)
 		isl_map_convex_hull((struct isl_map *)set);
 }
 
+__isl_give isl_basic_map *isl_map_polyhedral_hull(__isl_take isl_map *map)
+{
+	isl_basic_map *hull;
+
+	hull = isl_map_convex_hull(map);
+	return isl_basic_map_remove_divs(hull);
+}
+
+__isl_give isl_basic_set *isl_set_polyhedral_hull(__isl_take isl_set *set)
+{
+	return (isl_basic_set *)isl_map_polyhedral_hull((isl_map *)set);
+}
+
 struct sh_data_entry {
 	struct isl_hash_table	*table;
 	struct isl_tab		*tab;
@@ -2166,7 +2117,7 @@ static int is_bound(struct sh_data *data, struct isl_set *set, int j,
 
 	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;
 }
 
@@ -2287,11 +2238,11 @@ 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;
 }
 
@@ -2373,7 +2324,7 @@ 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);
+	hull = isl_basic_map_remove_redundancies(hull);
 	ISL_F_SET(hull, ISL_BASIC_MAP_NO_IMPLICIT);
 	ISL_F_SET(hull, ISL_BASIC_MAP_ALL_EQUALITIES);