X-Git-Url: http://review.tizen.org/git/?a=blobdiff_plain;f=isl_sample.c;h=c6a0f314425b0bc2d4683589997a3034b652abe0;hb=de51a9bc4da5dd3f1f9f57c2362da6f9752c44e0;hp=f66182fbdc1a1236a151aa83ea7880b91d039e9f;hpb=0ac9d8167135ae27ea5019bf5d6cc653da9eeea3;p=platform%2Fupstream%2Fisl.git

diff --git a/isl_sample.c b/isl_sample.c
index f66182f..c6a0f31 100644
--- a/isl_sample.c
+++ b/isl_sample.c
@@ -1,10 +1,34 @@
+/*
+ * Copyright 2008-2009 Katholieke Universiteit Leuven
+ *
+ * Use of this software is governed by the MIT license
+ *
+ * Written by Sven Verdoolaege, K.U.Leuven, Departement
+ * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
+ */
+
+#include <isl_ctx_private.h>
+#include <isl_map_private.h>
 #include "isl_sample.h"
 #include "isl_sample_piplib.h"
-#include "isl_vec.h"
-#include "isl_mat.h"
-#include "isl_seq.h"
-#include "isl_map_private.h"
+#include <isl/vec.h>
+#include <isl/mat.h>
+#include <isl/seq.h>
 #include "isl_equalities.h"
+#include "isl_tab.h"
+#include "isl_basis_reduction.h"
+#include <isl_factorization.h>
+#include <isl_point_private.h>
+#include <isl_options_private.h>
+
+static struct isl_vec *empty_sample(struct isl_basic_set *bset)
+{
+	struct isl_vec *vec;
+
+	vec = isl_vec_alloc(bset->ctx, 0);
+	isl_basic_set_free(bset);
+	return vec;
+}
 
 /* Construct a zero sample of the same dimension as bset.
  * As a special case, if bset is zero-dimensional, this
@@ -25,8 +49,7 @@ static struct isl_vec *zero_sample(struct isl_basic_set *bset)
 	return sample;
 }
 
-static struct isl_vec *interval_sample(struct isl_ctx *ctx,
-	struct isl_basic_set *bset)
+static struct isl_vec *interval_sample(struct isl_basic_set *bset)
 {
 	int i;
 	isl_int t;
@@ -35,13 +58,32 @@ static struct isl_vec *interval_sample(struct isl_ctx *ctx,
 	bset = isl_basic_set_simplify(bset);
 	if (!bset)
 		return NULL;
-	if (bset->n_eq > 0)
-		return isl_basic_set_sample(bset);
-	if (bset->n_ineq == 0)
+	if (isl_basic_set_plain_is_empty(bset))
+		return empty_sample(bset);
+	if (bset->n_eq == 0 && bset->n_ineq == 0)
 		return zero_sample(bset);
 
-	sample = isl_vec_alloc(ctx, 2);
+	sample = isl_vec_alloc(bset->ctx, 2);
+	if (!sample)
+		goto error;
+	if (!bset)
+		return NULL;
 	isl_int_set_si(sample->block.data[0], 1);
+
+	if (bset->n_eq > 0) {
+		isl_assert(bset->ctx, bset->n_eq == 1, goto error);
+		isl_assert(bset->ctx, bset->n_ineq == 0, goto error);
+		if (isl_int_is_one(bset->eq[0][1]))
+			isl_int_neg(sample->el[1], bset->eq[0][0]);
+		else {
+			isl_assert(bset->ctx, isl_int_is_negone(bset->eq[0][1]),
+				   goto error);
+			isl_int_set(sample->el[1], bset->eq[0][0]);
+		}
+		isl_basic_set_free(bset);
+		return sample;
+	}
+
 	isl_int_init(t);
 	if (isl_int_is_one(bset->ineq[0][1]))
 		isl_int_neg(sample->block.data[1], bset->ineq[0][0]);
@@ -56,31 +98,46 @@ static struct isl_vec *interval_sample(struct isl_ctx *ctx,
 	isl_int_clear(t);
 	if (i < bset->n_ineq) {
 		isl_vec_free(sample);
-		sample = isl_vec_alloc(ctx, 0);
+		return empty_sample(bset);
 	}
 
 	isl_basic_set_free(bset);
 	return sample;
+error:
+	isl_basic_set_free(bset);
+	isl_vec_free(sample);
+	return NULL;
 }
 
-static struct isl_mat *independent_bounds(struct isl_ctx *ctx,
-	struct isl_basic_set *bset)
+static struct isl_mat *independent_bounds(struct isl_basic_set *bset)
 {
 	int i, j, n;
 	struct isl_mat *dirs = NULL;
+	struct isl_mat *bounds = NULL;
 	unsigned dim;
 
 	if (!bset)
 		return NULL;
 
 	dim = isl_basic_set_n_dim(bset);
+	bounds = isl_mat_alloc(bset->ctx, 1+dim, 1+dim);
+	if (!bounds)
+		return NULL;
+
+	isl_int_set_si(bounds->row[0][0], 1);
+	isl_seq_clr(bounds->row[0]+1, dim);
+	bounds->n_row = 1;
+
 	if (bset->n_ineq == 0)
-		return isl_mat_alloc(ctx, 0, dim);
+		return bounds;
 
-	dirs = isl_mat_alloc(ctx, dim, dim);
-	if (!dirs)
+	dirs = isl_mat_alloc(bset->ctx, dim, dim);
+	if (!dirs) {
+		isl_mat_free(bounds);
 		return NULL;
+	}
 	isl_seq_cpy(dirs->row[0], bset->ineq[0]+1, dirs->n_col);
+	isl_seq_cpy(bounds->row[1], bset->ineq[0], bounds->n_col);
 	for (j = 1, n = 1; n < dim && j < bset->n_ineq; ++j) {
 		int pos;
 
@@ -112,91 +169,1299 @@ static struct isl_mat *independent_bounds(struct isl_ctx *ctx,
 			dirs->row[i] = t;
 		}
 		++n;
+		isl_seq_cpy(bounds->row[n], bset->ineq[j], bounds->n_col);
 	}
-	dirs->n_row = n;
-	return dirs;
+	isl_mat_free(dirs);
+	bounds->n_row = 1+n;
+	return bounds;
 }
 
-static struct isl_basic_set *remove_lineality(struct isl_ctx *ctx,
-	struct isl_basic_set *bset, struct isl_mat *bounds, struct isl_mat **T)
+static void swap_inequality(struct isl_basic_set *bset, int a, int b)
+{
+	isl_int *t = bset->ineq[a];
+	bset->ineq[a] = bset->ineq[b];
+	bset->ineq[b] = t;
+}
+
+/* Skew into positive orthant and project out lineality space.
+ *
+ * We perform a unimodular transformation that turns a selected
+ * maximal set of linearly independent bounds into constraints
+ * on the first dimensions that impose that these first dimensions
+ * are non-negative.  In particular, the constraint matrix is lower
+ * triangular with positive entries on the diagonal and negative
+ * entries below.
+ * If "bset" has a lineality space then these constraints (and therefore
+ * all constraints in bset) only involve the first dimensions.
+ * The remaining dimensions then do not appear in any constraints and
+ * we can select any value for them, say zero.  We therefore project
+ * out this final dimensions and plug in the value zero later.  This
+ * is accomplished by simply dropping the final columns of
+ * the unimodular transformation.
+ */
+static struct isl_basic_set *isl_basic_set_skew_to_positive_orthant(
+	struct isl_basic_set *bset, struct isl_mat **T)
 {
 	struct isl_mat *U = NULL;
+	struct isl_mat *bounds = NULL;
+	int i, j;
 	unsigned old_dim, new_dim;
 
-	old_dim = isl_basic_set_n_dim(bset);
-	new_dim = bounds->n_row;
 	*T = NULL;
-	bounds = isl_mat_left_hermite(ctx, bounds, 0, &U, NULL);
+	if (!bset)
+		return NULL;
+
+	isl_assert(bset->ctx, isl_basic_set_n_param(bset) == 0, goto error);
+	isl_assert(bset->ctx, bset->n_div == 0, goto error);
+	isl_assert(bset->ctx, bset->n_eq == 0, goto error);
+	
+	old_dim = isl_basic_set_n_dim(bset);
+	/* Try to move (multiples of) unit rows up. */
+	for (i = 0, j = 0; i < bset->n_ineq; ++i) {
+		int pos = isl_seq_first_non_zero(bset->ineq[i]+1, old_dim);
+		if (pos < 0)
+			continue;
+		if (isl_seq_first_non_zero(bset->ineq[i]+1+pos+1,
+						old_dim-pos-1) >= 0)
+			continue;
+		if (i != j)
+			swap_inequality(bset, i, j);
+		++j;
+	}
+	bounds = independent_bounds(bset);
+	if (!bounds)
+		goto error;
+	new_dim = bounds->n_row - 1;
+	bounds = isl_mat_left_hermite(bounds, 1, &U, NULL);
 	if (!bounds)
 		goto error;
-	U = isl_mat_lin_to_aff(ctx, U);
-	U = isl_mat_drop_cols(ctx, U, 1 + new_dim, old_dim - new_dim);
-	bset = isl_basic_set_preimage(bset, isl_mat_copy(ctx, U));
+	U = isl_mat_drop_cols(U, 1 + new_dim, old_dim - new_dim);
+	bset = isl_basic_set_preimage(bset, isl_mat_copy(U));
 	if (!bset)
 		goto error;
 	*T = U;
-	isl_mat_free(ctx, bounds);
+	isl_mat_free(bounds);
 	return bset;
 error:
-	isl_mat_free(ctx, bounds);
-	isl_mat_free(ctx, U);
+	isl_mat_free(bounds);
+	isl_mat_free(U);
 	isl_basic_set_free(bset);
 	return NULL;
 }
 
-struct isl_vec *isl_basic_set_sample(struct isl_basic_set *bset)
+/* Find a sample integer point, if any, in bset, which is known
+ * to have equalities.  If bset contains no integer points, then
+ * return a zero-length vector.
+ * We simply remove the known equalities, compute a sample
+ * in the resulting bset, using the specified recurse function,
+ * and then transform the sample back to the original space.
+ */
+static struct isl_vec *sample_eq(struct isl_basic_set *bset,
+	struct isl_vec *(*recurse)(struct isl_basic_set *))
 {
+	struct isl_mat *T;
+	struct isl_vec *sample;
+
+	if (!bset)
+		return NULL;
+
+	bset = isl_basic_set_remove_equalities(bset, &T, NULL);
+	sample = recurse(bset);
+	if (!sample || sample->size == 0)
+		isl_mat_free(T);
+	else
+		sample = isl_mat_vec_product(T, sample);
+	return sample;
+}
+
+/* Return a matrix containing the equalities of the tableau
+ * in constraint form.  The tableau is assumed to have
+ * an associated bset that has been kept up-to-date.
+ */
+static struct isl_mat *tab_equalities(struct isl_tab *tab)
+{
+	int i, j;
+	int n_eq;
+	struct isl_mat *eq;
+	struct isl_basic_set *bset;
+
+	if (!tab)
+		return NULL;
+
+	bset = isl_tab_peek_bset(tab);
+	isl_assert(tab->mat->ctx, bset, return NULL);
+
+	n_eq = tab->n_var - tab->n_col + tab->n_dead;
+	if (tab->empty || n_eq == 0)
+		return isl_mat_alloc(tab->mat->ctx, 0, tab->n_var);
+	if (n_eq == tab->n_var)
+		return isl_mat_identity(tab->mat->ctx, tab->n_var);
+
+	eq = isl_mat_alloc(tab->mat->ctx, n_eq, tab->n_var);
+	if (!eq)
+		return NULL;
+	for (i = 0, j = 0; i < tab->n_con; ++i) {
+		if (tab->con[i].is_row)
+			continue;
+		if (tab->con[i].index >= 0 && tab->con[i].index >= tab->n_dead)
+			continue;
+		if (i < bset->n_eq)
+			isl_seq_cpy(eq->row[j], bset->eq[i] + 1, tab->n_var);
+		else
+			isl_seq_cpy(eq->row[j],
+				    bset->ineq[i - bset->n_eq] + 1, tab->n_var);
+		++j;
+	}
+	isl_assert(bset->ctx, j == n_eq, goto error);
+	return eq;
+error:
+	isl_mat_free(eq);
+	return NULL;
+}
+
+/* Compute and return an initial basis for the bounded tableau "tab".
+ *
+ * If the tableau is either full-dimensional or zero-dimensional,
+ * the we simply return an identity matrix.
+ * Otherwise, we construct a basis whose first directions correspond
+ * to equalities.
+ */
+static struct isl_mat *initial_basis(struct isl_tab *tab)
+{
+	int n_eq;
+	struct isl_mat *eq;
+	struct isl_mat *Q;
+
+	tab->n_unbounded = 0;
+	tab->n_zero = n_eq = tab->n_var - tab->n_col + tab->n_dead;
+	if (tab->empty || n_eq == 0 || n_eq == tab->n_var)
+		return isl_mat_identity(tab->mat->ctx, 1 + tab->n_var);
+
+	eq = tab_equalities(tab);
+	eq = isl_mat_left_hermite(eq, 0, NULL, &Q);
+	if (!eq)
+		return NULL;
+	isl_mat_free(eq);
+
+	Q = isl_mat_lin_to_aff(Q);
+	return Q;
+}
+
+/* Compute the minimum of the current ("level") basis row over "tab"
+ * and store the result in position "level" of "min".
+ */
+static enum isl_lp_result compute_min(isl_ctx *ctx, struct isl_tab *tab,
+	__isl_keep isl_vec *min, int level)
+{
+	return isl_tab_min(tab, tab->basis->row[1 + level],
+			    ctx->one, &min->el[level], NULL, 0);
+}
+
+/* Compute the maximum of the current ("level") basis row over "tab"
+ * and store the result in position "level" of "max".
+ */
+static enum isl_lp_result compute_max(isl_ctx *ctx, struct isl_tab *tab,
+	__isl_keep isl_vec *max, int level)
+{
+	enum isl_lp_result res;
+	unsigned dim = tab->n_var;
+
+	isl_seq_neg(tab->basis->row[1 + level] + 1,
+		    tab->basis->row[1 + level] + 1, dim);
+	res = isl_tab_min(tab, tab->basis->row[1 + level],
+		    ctx->one, &max->el[level], NULL, 0);
+	isl_seq_neg(tab->basis->row[1 + level] + 1,
+		    tab->basis->row[1 + level] + 1, dim);
+	isl_int_neg(max->el[level], max->el[level]);
+
+	return res;
+}
+
+/* Perform a greedy search for an integer point in the set represented
+ * by "tab", given that the minimal rational value (rounded up to the
+ * nearest integer) at "level" is smaller than the maximal rational
+ * value (rounded down to the nearest integer).
+ *
+ * Return 1 if we have found an integer point (if tab->n_unbounded > 0
+ * then we may have only found integer values for the bounded dimensions
+ * and it is the responsibility of the caller to extend this solution
+ * to the unbounded dimensions).
+ * Return 0 if greedy search did not result in a solution.
+ * Return -1 if some error occurred.
+ *
+ * We assign a value half-way between the minimum and the maximum
+ * to the current dimension and check if the minimal value of the
+ * next dimension is still smaller than (or equal) to the maximal value.
+ * We continue this process until either
+ * - the minimal value (rounded up) is greater than the maximal value
+ *	(rounded down).  In this case, greedy search has failed.
+ * - we have exhausted all bounded dimensions, meaning that we have
+ *	found a solution.
+ * - the sample value of the tableau is integral.
+ * - some error has occurred.
+ */
+static int greedy_search(isl_ctx *ctx, struct isl_tab *tab,
+	__isl_keep isl_vec *min, __isl_keep isl_vec *max, int level)
+{
+	struct isl_tab_undo *snap;
+	enum isl_lp_result res;
+
+	snap = isl_tab_snap(tab);
+
+	do {
+		isl_int_add(tab->basis->row[1 + level][0],
+			    min->el[level], max->el[level]);
+		isl_int_fdiv_q_ui(tab->basis->row[1 + level][0],
+			    tab->basis->row[1 + level][0], 2);
+		isl_int_neg(tab->basis->row[1 + level][0],
+			    tab->basis->row[1 + level][0]);
+		if (isl_tab_add_valid_eq(tab, tab->basis->row[1 + level]) < 0)
+			return -1;
+		isl_int_set_si(tab->basis->row[1 + level][0], 0);
+
+		if (++level >= tab->n_var - tab->n_unbounded)
+			return 1;
+		if (isl_tab_sample_is_integer(tab))
+			return 1;
+
+		res = compute_min(ctx, tab, min, level);
+		if (res == isl_lp_error)
+			return -1;
+		if (res != isl_lp_ok)
+			isl_die(ctx, isl_error_internal,
+				"expecting bounded rational solution",
+				return -1);
+		res = compute_max(ctx, tab, max, level);
+		if (res == isl_lp_error)
+			return -1;
+		if (res != isl_lp_ok)
+			isl_die(ctx, isl_error_internal,
+				"expecting bounded rational solution",
+				return -1);
+	} while (isl_int_le(min->el[level], max->el[level]));
+
+	if (isl_tab_rollback(tab, snap) < 0)
+		return -1;
+
+	return 0;
+}
+
+/* Given a tableau representing a set, find and return
+ * an integer point in the set, if there is any.
+ *
+ * We perform a depth first search
+ * for an integer point, by scanning all possible values in the range
+ * attained by a basis vector, where an initial basis may have been set
+ * by the calling function.  Otherwise an initial basis that exploits
+ * the equalities in the tableau is created.
+ * tab->n_zero is currently ignored and is clobbered by this function.
+ *
+ * The tableau is allowed to have unbounded direction, but then
+ * the calling function needs to set an initial basis, with the
+ * unbounded directions last and with tab->n_unbounded set
+ * to the number of unbounded directions.
+ * Furthermore, the calling functions needs to add shifted copies
+ * of all constraints involving unbounded directions to ensure
+ * that any feasible rational value in these directions can be rounded
+ * up to yield a feasible integer value.
+ * In particular, let B define the given basis x' = B x
+ * and let T be the inverse of B, i.e., X = T x'.
+ * Let a x + c >= 0 be a constraint of the set represented by the tableau,
+ * or a T x' + c >= 0 in terms of the given basis.  Assume that
+ * the bounded directions have an integer value, then we can safely
+ * round up the values for the unbounded directions if we make sure
+ * that x' not only satisfies the original constraint, but also
+ * the constraint "a T x' + c + s >= 0" with s the sum of all
+ * negative values in the last n_unbounded entries of "a T".
+ * The calling function therefore needs to add the constraint
+ * a x + c + s >= 0.  The current function then scans the first
+ * directions for an integer value and once those have been found,
+ * it can compute "T ceil(B x)" to yield an integer point in the set.
+ * Note that during the search, the first rows of B may be changed
+ * by a basis reduction, but the last n_unbounded rows of B remain
+ * unaltered and are also not mixed into the first rows.
+ *
+ * The search is implemented iteratively.  "level" identifies the current
+ * basis vector.  "init" is true if we want the first value at the current
+ * level and false if we want the next value.
+ *
+ * At the start of each level, we first check if we can find a solution
+ * using greedy search.  If not, we continue with the exhaustive search.
+ *
+ * The initial basis is the identity matrix.  If the range in some direction
+ * contains more than one integer value, we perform basis reduction based
+ * on the value of ctx->opt->gbr
+ *	- ISL_GBR_NEVER:	never perform basis reduction
+ *	- ISL_GBR_ONCE:		only perform basis reduction the first
+ *				time such a range is encountered
+ *	- ISL_GBR_ALWAYS:	always perform basis reduction when
+ *				such a range is encountered
+ *
+ * When ctx->opt->gbr is set to ISL_GBR_ALWAYS, then we allow the basis
+ * reduction computation to return early.  That is, as soon as it
+ * finds a reasonable first direction.
+ */ 
+struct isl_vec *isl_tab_sample(struct isl_tab *tab)
+{
+	unsigned dim;
+	unsigned gbr;
 	struct isl_ctx *ctx;
-	struct isl_mat *bounds;
+	struct isl_vec *sample;
+	struct isl_vec *min;
+	struct isl_vec *max;
+	enum isl_lp_result res;
+	int level;
+	int init;
+	int reduced;
+	struct isl_tab_undo **snap;
+
+	if (!tab)
+		return NULL;
+	if (tab->empty)
+		return isl_vec_alloc(tab->mat->ctx, 0);
+
+	if (!tab->basis)
+		tab->basis = initial_basis(tab);
+	if (!tab->basis)
+		return NULL;
+	isl_assert(tab->mat->ctx, tab->basis->n_row == tab->n_var + 1,
+		    return NULL);
+	isl_assert(tab->mat->ctx, tab->basis->n_col == tab->n_var + 1,
+		    return NULL);
+
+	ctx = tab->mat->ctx;
+	dim = tab->n_var;
+	gbr = ctx->opt->gbr;
+
+	if (tab->n_unbounded == tab->n_var) {
+		sample = isl_tab_get_sample_value(tab);
+		sample = isl_mat_vec_product(isl_mat_copy(tab->basis), sample);
+		sample = isl_vec_ceil(sample);
+		sample = isl_mat_vec_inverse_product(isl_mat_copy(tab->basis),
+							sample);
+		return sample;
+	}
+
+	if (isl_tab_extend_cons(tab, dim + 1) < 0)
+		return NULL;
+
+	min = isl_vec_alloc(ctx, dim);
+	max = isl_vec_alloc(ctx, dim);
+	snap = isl_alloc_array(ctx, struct isl_tab_undo *, dim);
+
+	if (!min || !max || !snap)
+		goto error;
+
+	level = 0;
+	init = 1;
+	reduced = 0;
+
+	while (level >= 0) {
+		if (init) {
+			int choice;
+
+			res = compute_min(ctx, tab, min, level);
+			if (res == isl_lp_error)
+				goto error;
+			if (res != isl_lp_ok)
+				isl_die(ctx, isl_error_internal,
+					"expecting bounded rational solution",
+					goto error);
+			if (isl_tab_sample_is_integer(tab))
+				break;
+			res = compute_max(ctx, tab, max, level);
+			if (res == isl_lp_error)
+				goto error;
+			if (res != isl_lp_ok)
+				isl_die(ctx, isl_error_internal,
+					"expecting bounded rational solution",
+					goto error);
+			if (isl_tab_sample_is_integer(tab))
+				break;
+			choice = isl_int_lt(min->el[level], max->el[level]);
+			if (choice) {
+				int g;
+				g = greedy_search(ctx, tab, min, max, level);
+				if (g < 0)
+					goto error;
+				if (g)
+					break;
+			}
+			if (!reduced && choice &&
+			    ctx->opt->gbr != ISL_GBR_NEVER) {
+				unsigned gbr_only_first;
+				if (ctx->opt->gbr == ISL_GBR_ONCE)
+					ctx->opt->gbr = ISL_GBR_NEVER;
+				tab->n_zero = level;
+				gbr_only_first = ctx->opt->gbr_only_first;
+				ctx->opt->gbr_only_first =
+					ctx->opt->gbr == ISL_GBR_ALWAYS;
+				tab = isl_tab_compute_reduced_basis(tab);
+				ctx->opt->gbr_only_first = gbr_only_first;
+				if (!tab || !tab->basis)
+					goto error;
+				reduced = 1;
+				continue;
+			}
+			reduced = 0;
+			snap[level] = isl_tab_snap(tab);
+		} else
+			isl_int_add_ui(min->el[level], min->el[level], 1);
+
+		if (isl_int_gt(min->el[level], max->el[level])) {
+			level--;
+			init = 0;
+			if (level >= 0)
+				if (isl_tab_rollback(tab, snap[level]) < 0)
+					goto error;
+			continue;
+		}
+		isl_int_neg(tab->basis->row[1 + level][0], min->el[level]);
+		if (isl_tab_add_valid_eq(tab, tab->basis->row[1 + level]) < 0)
+			goto error;
+		isl_int_set_si(tab->basis->row[1 + level][0], 0);
+		if (level + tab->n_unbounded < dim - 1) {
+			++level;
+			init = 1;
+			continue;
+		}
+		break;
+	}
+
+	if (level >= 0) {
+		sample = isl_tab_get_sample_value(tab);
+		if (!sample)
+			goto error;
+		if (tab->n_unbounded && !isl_int_is_one(sample->el[0])) {
+			sample = isl_mat_vec_product(isl_mat_copy(tab->basis),
+						     sample);
+			sample = isl_vec_ceil(sample);
+			sample = isl_mat_vec_inverse_product(
+					isl_mat_copy(tab->basis), sample);
+		}
+	} else
+		sample = isl_vec_alloc(ctx, 0);
+
+	ctx->opt->gbr = gbr;
+	isl_vec_free(min);
+	isl_vec_free(max);
+	free(snap);
+	return sample;
+error:
+	ctx->opt->gbr = gbr;
+	isl_vec_free(min);
+	isl_vec_free(max);
+	free(snap);
+	return NULL;
+}
+
+static struct isl_vec *sample_bounded(struct isl_basic_set *bset);
+
+/* Compute a sample point of the given basic set, based on the given,
+ * non-trivial factorization.
+ */
+static __isl_give isl_vec *factored_sample(__isl_take isl_basic_set *bset,
+	__isl_take isl_factorizer *f)
+{
+	int i, n;
+	isl_vec *sample = NULL;
+	isl_ctx *ctx;
+	unsigned nparam;
+	unsigned nvar;
+
+	ctx = isl_basic_set_get_ctx(bset);
+	if (!ctx)
+		goto error;
+
+	nparam = isl_basic_set_dim(bset, isl_dim_param);
+	nvar = isl_basic_set_dim(bset, isl_dim_set);
+
+	sample = isl_vec_alloc(ctx, 1 + isl_basic_set_total_dim(bset));
+	if (!sample)
+		goto error;
+	isl_int_set_si(sample->el[0], 1);
+
+	bset = isl_morph_basic_set(isl_morph_copy(f->morph), bset);
+
+	for (i = 0, n = 0; i < f->n_group; ++i) {
+		isl_basic_set *bset_i;
+		isl_vec *sample_i;
+
+		bset_i = isl_basic_set_copy(bset);
+		bset_i = isl_basic_set_drop_constraints_involving(bset_i,
+			    nparam + n + f->len[i], nvar - n - f->len[i]);
+		bset_i = isl_basic_set_drop_constraints_involving(bset_i,
+			    nparam, n);
+		bset_i = isl_basic_set_drop(bset_i, isl_dim_set,
+			    n + f->len[i], nvar - n - f->len[i]);
+		bset_i = isl_basic_set_drop(bset_i, isl_dim_set, 0, n);
+
+		sample_i = sample_bounded(bset_i);
+		if (!sample_i)
+			goto error;
+		if (sample_i->size == 0) {
+			isl_basic_set_free(bset);
+			isl_factorizer_free(f);
+			isl_vec_free(sample);
+			return sample_i;
+		}
+		isl_seq_cpy(sample->el + 1 + nparam + n,
+			    sample_i->el + 1, f->len[i]);
+		isl_vec_free(sample_i);
+
+		n += f->len[i];
+	}
+
+	f->morph = isl_morph_inverse(f->morph);
+	sample = isl_morph_vec(isl_morph_copy(f->morph), sample);
+
+	isl_basic_set_free(bset);
+	isl_factorizer_free(f);
+	return sample;
+error:
+	isl_basic_set_free(bset);
+	isl_factorizer_free(f);
+	isl_vec_free(sample);
+	return NULL;
+}
+
+/* Given a basic set that is known to be bounded, find and return
+ * an integer point in the basic set, if there is any.
+ *
+ * After handling some trivial cases, we construct a tableau
+ * and then use isl_tab_sample to find a sample, passing it
+ * the identity matrix as initial basis.
+ */ 
+static struct isl_vec *sample_bounded(struct isl_basic_set *bset)
+{
 	unsigned dim;
+	struct isl_ctx *ctx;
+	struct isl_vec *sample;
+	struct isl_tab *tab = NULL;
+	isl_factorizer *f;
+
+	if (!bset)
+		return NULL;
+
+	if (isl_basic_set_plain_is_empty(bset))
+		return empty_sample(bset);
+
+	dim = isl_basic_set_total_dim(bset);
+	if (dim == 0)
+		return zero_sample(bset);
+	if (dim == 1)
+		return interval_sample(bset);
+	if (bset->n_eq > 0)
+		return sample_eq(bset, sample_bounded);
+
+	f = isl_basic_set_factorizer(bset);
+	if (!f)
+		goto error;
+	if (f->n_group != 0)
+		return factored_sample(bset, f);
+	isl_factorizer_free(f);
+		
+	ctx = bset->ctx;
+
+	tab = isl_tab_from_basic_set(bset, 1);
+	if (tab && tab->empty) {
+		isl_tab_free(tab);
+		ISL_F_SET(bset, ISL_BASIC_SET_EMPTY);
+		sample = isl_vec_alloc(bset->ctx, 0);
+		isl_basic_set_free(bset);
+		return sample;
+	}
+
+	if (!ISL_F_ISSET(bset, ISL_BASIC_SET_NO_IMPLICIT))
+		if (isl_tab_detect_implicit_equalities(tab) < 0)
+			goto error;
+
+	sample = isl_tab_sample(tab);
+	if (!sample)
+		goto error;
+
+	if (sample->size > 0) {
+		isl_vec_free(bset->sample);
+		bset->sample = isl_vec_copy(sample);
+	}
+
+	isl_basic_set_free(bset);
+	isl_tab_free(tab);
+	return sample;
+error:
+	isl_basic_set_free(bset);
+	isl_tab_free(tab);
+	return NULL;
+}
+
+/* Given a basic set "bset" and a value "sample" for the first coordinates
+ * of bset, plug in these values and drop the corresponding coordinates.
+ *
+ * We do this by computing the preimage of the transformation
+ *
+ *	     [ 1 0 ]
+ *	x =  [ s 0 ] x'
+ *	     [ 0 I ]
+ *
+ * where [1 s] is the sample value and I is the identity matrix of the
+ * appropriate dimension.
+ */
+static struct isl_basic_set *plug_in(struct isl_basic_set *bset,
+	struct isl_vec *sample)
+{
+	int i;
+	unsigned total;
+	struct isl_mat *T;
+
+	if (!bset || !sample)
+		goto error;
+
+	total = isl_basic_set_total_dim(bset);
+	T = isl_mat_alloc(bset->ctx, 1 + total, 1 + total - (sample->size - 1));
+	if (!T)
+		goto error;
+
+	for (i = 0; i < sample->size; ++i) {
+		isl_int_set(T->row[i][0], sample->el[i]);
+		isl_seq_clr(T->row[i] + 1, T->n_col - 1);
+	}
+	for (i = 0; i < T->n_col - 1; ++i) {
+		isl_seq_clr(T->row[sample->size + i], T->n_col);
+		isl_int_set_si(T->row[sample->size + i][1 + i], 1);
+	}
+	isl_vec_free(sample);
+
+	bset = isl_basic_set_preimage(bset, T);
+	return bset;
+error:
+	isl_basic_set_free(bset);
+	isl_vec_free(sample);
+	return NULL;
+}
+
+/* Given a basic set "bset", return any (possibly non-integer) point
+ * in the basic set.
+ */
+static struct isl_vec *rational_sample(struct isl_basic_set *bset)
+{
+	struct isl_tab *tab;
+	struct isl_vec *sample;
+
 	if (!bset)
 		return NULL;
 
+	tab = isl_tab_from_basic_set(bset, 0);
+	sample = isl_tab_get_sample_value(tab);
+	isl_tab_free(tab);
+
+	isl_basic_set_free(bset);
+
+	return sample;
+}
+
+/* Given a linear cone "cone" and a rational point "vec",
+ * construct a polyhedron with shifted copies of the constraints in "cone",
+ * i.e., a polyhedron with "cone" as its recession cone, such that each
+ * point x in this polyhedron is such that the unit box positioned at x
+ * lies entirely inside the affine cone 'vec + cone'.
+ * Any rational point in this polyhedron may therefore be rounded up
+ * to yield an integer point that lies inside said affine cone.
+ *
+ * Denote the constraints of cone by "<a_i, x> >= 0" and the rational
+ * point "vec" by v/d.
+ * Let b_i = <a_i, v>.  Then the affine cone 'vec + cone' is given
+ * by <a_i, x> - b/d >= 0.
+ * The polyhedron <a_i, x> - ceil{b/d} >= 0 is a subset of this affine cone.
+ * We prefer this polyhedron over the actual affine cone because it doesn't
+ * require a scaling of the constraints.
+ * If each of the vertices of the unit cube positioned at x lies inside
+ * this polyhedron, then the whole unit cube at x lies inside the affine cone.
+ * We therefore impose that x' = x + \sum e_i, for any selection of unit
+ * vectors lies inside the polyhedron, i.e.,
+ *
+ *	<a_i, x'> - ceil{b/d} = <a_i, x> + sum a_i - ceil{b/d} >= 0
+ *
+ * The most stringent of these constraints is the one that selects
+ * all negative a_i, so the polyhedron we are looking for has constraints
+ *
+ *	<a_i, x> + sum_{a_i < 0} a_i - ceil{b/d} >= 0
+ *
+ * Note that if cone were known to have only non-negative rays
+ * (which can be accomplished by a unimodular transformation),
+ * then we would only have to check the points x' = x + e_i
+ * and we only have to add the smallest negative a_i (if any)
+ * instead of the sum of all negative a_i.
+ */
+static struct isl_basic_set *shift_cone(struct isl_basic_set *cone,
+	struct isl_vec *vec)
+{
+	int i, j, k;
+	unsigned total;
+
+	struct isl_basic_set *shift = NULL;
+
+	if (!cone || !vec)
+		goto error;
+
+	isl_assert(cone->ctx, cone->n_eq == 0, goto error);
+
+	total = isl_basic_set_total_dim(cone);
+
+	shift = isl_basic_set_alloc_space(isl_basic_set_get_space(cone),
+					0, 0, cone->n_ineq);
+
+	for (i = 0; i < cone->n_ineq; ++i) {
+		k = isl_basic_set_alloc_inequality(shift);
+		if (k < 0)
+			goto error;
+		isl_seq_cpy(shift->ineq[k] + 1, cone->ineq[i] + 1, total);
+		isl_seq_inner_product(shift->ineq[k] + 1, vec->el + 1, total,
+				      &shift->ineq[k][0]);
+		isl_int_cdiv_q(shift->ineq[k][0],
+			       shift->ineq[k][0], vec->el[0]);
+		isl_int_neg(shift->ineq[k][0], shift->ineq[k][0]);
+		for (j = 0; j < total; ++j) {
+			if (isl_int_is_nonneg(shift->ineq[k][1 + j]))
+				continue;
+			isl_int_add(shift->ineq[k][0],
+				    shift->ineq[k][0], shift->ineq[k][1 + j]);
+		}
+	}
+
+	isl_basic_set_free(cone);
+	isl_vec_free(vec);
+
+	return isl_basic_set_finalize(shift);
+error:
+	isl_basic_set_free(shift);
+	isl_basic_set_free(cone);
+	isl_vec_free(vec);
+	return NULL;
+}
+
+/* Given a rational point vec in a (transformed) basic set,
+ * such that cone is the recession cone of the original basic set,
+ * "round up" the rational point to an integer point.
+ *
+ * We first check if the rational point just happens to be integer.
+ * If not, we transform the cone in the same way as the basic set,
+ * pick a point x in this cone shifted to the rational point such that
+ * the whole unit cube at x is also inside this affine cone.
+ * Then we simply round up the coordinates of x and return the
+ * resulting integer point.
+ */
+static struct isl_vec *round_up_in_cone(struct isl_vec *vec,
+	struct isl_basic_set *cone, struct isl_mat *U)
+{
+	unsigned total;
+
+	if (!vec || !cone || !U)
+		goto error;
+
+	isl_assert(vec->ctx, vec->size != 0, goto error);
+	if (isl_int_is_one(vec->el[0])) {
+		isl_mat_free(U);
+		isl_basic_set_free(cone);
+		return vec;
+	}
+
+	total = isl_basic_set_total_dim(cone);
+	cone = isl_basic_set_preimage(cone, U);
+	cone = isl_basic_set_remove_dims(cone, isl_dim_set,
+					 0, total - (vec->size - 1));
+
+	cone = shift_cone(cone, vec);
+
+	vec = rational_sample(cone);
+	vec = isl_vec_ceil(vec);
+	return vec;
+error:
+	isl_mat_free(U);
+	isl_vec_free(vec);
+	isl_basic_set_free(cone);
+	return NULL;
+}
+
+/* Concatenate two integer vectors, i.e., two vectors with denominator
+ * (stored in element 0) equal to 1.
+ */
+static struct isl_vec *vec_concat(struct isl_vec *vec1, struct isl_vec *vec2)
+{
+	struct isl_vec *vec;
+
+	if (!vec1 || !vec2)
+		goto error;
+	isl_assert(vec1->ctx, vec1->size > 0, goto error);
+	isl_assert(vec2->ctx, vec2->size > 0, goto error);
+	isl_assert(vec1->ctx, isl_int_is_one(vec1->el[0]), goto error);
+	isl_assert(vec2->ctx, isl_int_is_one(vec2->el[0]), goto error);
+
+	vec = isl_vec_alloc(vec1->ctx, vec1->size + vec2->size - 1);
+	if (!vec)
+		goto error;
+
+	isl_seq_cpy(vec->el, vec1->el, vec1->size);
+	isl_seq_cpy(vec->el + vec1->size, vec2->el + 1, vec2->size - 1);
+
+	isl_vec_free(vec1);
+	isl_vec_free(vec2);
+
+	return vec;
+error:
+	isl_vec_free(vec1);
+	isl_vec_free(vec2);
+	return NULL;
+}
+
+/* Give a basic set "bset" with recession cone "cone", compute and
+ * return an integer point in bset, if any.
+ *
+ * If the recession cone is full-dimensional, then we know that
+ * bset contains an infinite number of integer points and it is
+ * fairly easy to pick one of them.
+ * If the recession cone is not full-dimensional, then we first
+ * transform bset such that the bounded directions appear as
+ * the first dimensions of the transformed basic set.
+ * We do this by using a unimodular transformation that transforms
+ * the equalities in the recession cone to equalities on the first
+ * dimensions.
+ *
+ * The transformed set is then projected onto its bounded dimensions.
+ * Note that to compute this projection, we can simply drop all constraints
+ * involving any of the unbounded dimensions since these constraints
+ * cannot be combined to produce a constraint on the bounded dimensions.
+ * To see this, assume that there is such a combination of constraints
+ * that produces a constraint on the bounded dimensions.  This means
+ * that some combination of the unbounded dimensions has both an upper
+ * bound and a lower bound in terms of the bounded dimensions, but then
+ * this combination would be a bounded direction too and would have been
+ * transformed into a bounded dimensions.
+ *
+ * We then compute a sample value in the bounded dimensions.
+ * If no such value can be found, then the original set did not contain
+ * any integer points and we are done.
+ * Otherwise, we plug in the value we found in the bounded dimensions,
+ * project out these bounded dimensions and end up with a set with
+ * a full-dimensional recession cone.
+ * A sample point in this set is computed by "rounding up" any
+ * rational point in the set.
+ *
+ * The sample points in the bounded and unbounded dimensions are
+ * then combined into a single sample point and transformed back
+ * to the original space.
+ */
+__isl_give isl_vec *isl_basic_set_sample_with_cone(
+	__isl_take isl_basic_set *bset, __isl_take isl_basic_set *cone)
+{
+	unsigned total;
+	unsigned cone_dim;
+	struct isl_mat *M, *U;
+	struct isl_vec *sample;
+	struct isl_vec *cone_sample;
+	struct isl_ctx *ctx;
+	struct isl_basic_set *bounded;
+
+	if (!bset || !cone)
+		goto error;
+
 	ctx = bset->ctx;
-	if (ISL_F_ISSET(bset, ISL_BASIC_SET_EMPTY)) {
+	total = isl_basic_set_total_dim(cone);
+	cone_dim = total - cone->n_eq;
+
+	M = isl_mat_sub_alloc6(bset->ctx, cone->eq, 0, cone->n_eq, 1, total);
+	M = isl_mat_left_hermite(M, 0, &U, NULL);
+	if (!M)
+		goto error;
+	isl_mat_free(M);
+
+	U = isl_mat_lin_to_aff(U);
+	bset = isl_basic_set_preimage(bset, isl_mat_copy(U));
+
+	bounded = isl_basic_set_copy(bset);
+	bounded = isl_basic_set_drop_constraints_involving(bounded,
+						   total - cone_dim, cone_dim);
+	bounded = isl_basic_set_drop_dims(bounded, total - cone_dim, cone_dim);
+	sample = sample_bounded(bounded);
+	if (!sample || sample->size == 0) {
 		isl_basic_set_free(bset);
-		return isl_vec_alloc(ctx, 0);
+		isl_basic_set_free(cone);
+		isl_mat_free(U);
+		return sample;
+	}
+	bset = plug_in(bset, isl_vec_copy(sample));
+	cone_sample = rational_sample(bset);
+	cone_sample = round_up_in_cone(cone_sample, cone, isl_mat_copy(U));
+	sample = vec_concat(sample, cone_sample);
+	sample = isl_mat_vec_product(U, sample);
+	return sample;
+error:
+	isl_basic_set_free(cone);
+	isl_basic_set_free(bset);
+	return NULL;
+}
+
+static void vec_sum_of_neg(struct isl_vec *v, isl_int *s)
+{
+	int i;
+
+	isl_int_set_si(*s, 0);
+
+	for (i = 0; i < v->size; ++i)
+		if (isl_int_is_neg(v->el[i]))
+			isl_int_add(*s, *s, v->el[i]);
+}
+
+/* Given a tableau "tab", a tableau "tab_cone" that corresponds
+ * to the recession cone and the inverse of a new basis U = inv(B),
+ * with the unbounded directions in B last,
+ * add constraints to "tab" that ensure any rational value
+ * in the unbounded directions can be rounded up to an integer value.
+ *
+ * The new basis is given by x' = B x, i.e., x = U x'.
+ * For any rational value of the last tab->n_unbounded coordinates
+ * in the update tableau, the value that is obtained by rounding
+ * up this value should be contained in the original tableau.
+ * For any constraint "a x + c >= 0", we therefore need to add
+ * a constraint "a x + c + s >= 0", with s the sum of all negative
+ * entries in the last elements of "a U".
+ *
+ * Since we are not interested in the first entries of any of the "a U",
+ * we first drop the columns of U that correpond to bounded directions.
+ */
+static int tab_shift_cone(struct isl_tab *tab,
+	struct isl_tab *tab_cone, struct isl_mat *U)
+{
+	int i;
+	isl_int v;
+	struct isl_basic_set *bset = NULL;
+
+	if (tab && tab->n_unbounded == 0) {
+		isl_mat_free(U);
+		return 0;
+	}
+	isl_int_init(v);
+	if (!tab || !tab_cone || !U)
+		goto error;
+	bset = isl_tab_peek_bset(tab_cone);
+	U = isl_mat_drop_cols(U, 0, tab->n_var - tab->n_unbounded);
+	for (i = 0; i < bset->n_ineq; ++i) {
+		int ok;
+		struct isl_vec *row = NULL;
+		if (isl_tab_is_equality(tab_cone, tab_cone->n_eq + i))
+			continue;
+		row = isl_vec_alloc(bset->ctx, tab_cone->n_var);
+		if (!row)
+			goto error;
+		isl_seq_cpy(row->el, bset->ineq[i] + 1, tab_cone->n_var);
+		row = isl_vec_mat_product(row, isl_mat_copy(U));
+		if (!row)
+			goto error;
+		vec_sum_of_neg(row, &v);
+		isl_vec_free(row);
+		if (isl_int_is_zero(v))
+			continue;
+		tab = isl_tab_extend(tab, 1);
+		isl_int_add(bset->ineq[i][0], bset->ineq[i][0], v);
+		ok = isl_tab_add_ineq(tab, bset->ineq[i]) >= 0;
+		isl_int_sub(bset->ineq[i][0], bset->ineq[i][0], v);
+		if (!ok)
+			goto error;
+	}
+
+	isl_mat_free(U);
+	isl_int_clear(v);
+	return 0;
+error:
+	isl_mat_free(U);
+	isl_int_clear(v);
+	return -1;
+}
+
+/* Compute and return an initial basis for the possibly
+ * unbounded tableau "tab".  "tab_cone" is a tableau
+ * for the corresponding recession cone.
+ * Additionally, add constraints to "tab" that ensure
+ * that any rational value for the unbounded directions
+ * can be rounded up to an integer value.
+ *
+ * If the tableau is bounded, i.e., if the recession cone
+ * is zero-dimensional, then we just use inital_basis.
+ * Otherwise, we construct a basis whose first directions
+ * correspond to equalities, followed by bounded directions,
+ * i.e., equalities in the recession cone.
+ * The remaining directions are then unbounded.
+ */
+int isl_tab_set_initial_basis_with_cone(struct isl_tab *tab,
+	struct isl_tab *tab_cone)
+{
+	struct isl_mat *eq;
+	struct isl_mat *cone_eq;
+	struct isl_mat *U, *Q;
+
+	if (!tab || !tab_cone)
+		return -1;
+
+	if (tab_cone->n_col == tab_cone->n_dead) {
+		tab->basis = initial_basis(tab);
+		return tab->basis ? 0 : -1;
 	}
 
+	eq = tab_equalities(tab);
+	if (!eq)
+		return -1;
+	tab->n_zero = eq->n_row;
+	cone_eq = tab_equalities(tab_cone);
+	eq = isl_mat_concat(eq, cone_eq);
+	if (!eq)
+		return -1;
+	tab->n_unbounded = tab->n_var - (eq->n_row - tab->n_zero);
+	eq = isl_mat_left_hermite(eq, 0, &U, &Q);
+	if (!eq)
+		return -1;
+	isl_mat_free(eq);
+	tab->basis = isl_mat_lin_to_aff(Q);
+	if (tab_shift_cone(tab, tab_cone, U) < 0)
+		return -1;
+	if (!tab->basis)
+		return -1;
+	return 0;
+}
+
+/* Compute and return a sample point in bset using generalized basis
+ * reduction.  We first check if the input set has a non-trivial
+ * recession cone.  If so, we perform some extra preprocessing in
+ * sample_with_cone.  Otherwise, we directly perform generalized basis
+ * reduction.
+ */
+static struct isl_vec *gbr_sample(struct isl_basic_set *bset)
+{
+	unsigned dim;
+	struct isl_basic_set *cone;
+
+	dim = isl_basic_set_total_dim(bset);
+
+	cone = isl_basic_set_recession_cone(isl_basic_set_copy(bset));
+	if (!cone)
+		goto error;
+
+	if (cone->n_eq < dim)
+		return isl_basic_set_sample_with_cone(bset, cone);
+
+	isl_basic_set_free(cone);
+	return sample_bounded(bset);
+error:
+	isl_basic_set_free(bset);
+	return NULL;
+}
+
+static struct isl_vec *pip_sample(struct isl_basic_set *bset)
+{
+	struct isl_mat *T;
+	struct isl_ctx *ctx;
+	struct isl_vec *sample;
+
+	bset = isl_basic_set_skew_to_positive_orthant(bset, &T);
+	if (!bset)
+		return NULL;
+
+	ctx = bset->ctx;
+	sample = isl_pip_basic_set_sample(bset);
+
+	if (sample && sample->size != 0)
+		sample = isl_mat_vec_product(T, sample);
+	else
+		isl_mat_free(T);
+
+	return sample;
+}
+
+static struct isl_vec *basic_set_sample(struct isl_basic_set *bset, int bounded)
+{
+	struct isl_ctx *ctx;
+	unsigned dim;
+	if (!bset)
+		return NULL;
+
+	ctx = bset->ctx;
+	if (isl_basic_set_plain_is_empty(bset))
+		return empty_sample(bset);
+
 	dim = isl_basic_set_n_dim(bset);
 	isl_assert(ctx, isl_basic_set_n_param(bset) == 0, goto error);
 	isl_assert(ctx, bset->n_div == 0, goto error);
 
-	if (bset->n_eq > 0) {
-		struct isl_mat *T;
-		struct isl_vec *sample;
-
-		bset = isl_basic_set_remove_equalities(bset, &T, NULL);
-		sample = isl_basic_set_sample(bset);
-		if (sample && sample->size != 0)
-			sample = isl_mat_vec_product(ctx, T, sample);
-		else
-			isl_mat_free(ctx, T);
-		return sample;
+	if (bset->sample && bset->sample->size == 1 + dim) {
+		int contains = isl_basic_set_contains(bset, bset->sample);
+		if (contains < 0)
+			goto error;
+		if (contains) {
+			struct isl_vec *sample = isl_vec_copy(bset->sample);
+			isl_basic_set_free(bset);
+			return sample;
+		}
 	}
+	isl_vec_free(bset->sample);
+	bset->sample = NULL;
+
+	if (bset->n_eq > 0)
+		return sample_eq(bset, bounded ? isl_basic_set_sample_bounded
+					       : isl_basic_set_sample_vec);
 	if (dim == 0)
 		return zero_sample(bset);
 	if (dim == 1)
-		return interval_sample(ctx, bset);
-	bounds = independent_bounds(ctx, bset);
-	if (!bounds)
+		return interval_sample(bset);
+
+	switch (bset->ctx->opt->ilp_solver) {
+	case ISL_ILP_PIP:
+		return pip_sample(bset);
+	case ISL_ILP_GBR:
+		return bounded ? sample_bounded(bset) : gbr_sample(bset);
+	}
+	isl_assert(bset->ctx, 0, );
+error:
+	isl_basic_set_free(bset);
+	return NULL;
+}
+
+__isl_give isl_vec *isl_basic_set_sample_vec(__isl_take isl_basic_set *bset)
+{
+	return basic_set_sample(bset, 0);
+}
+
+/* Compute an integer sample in "bset", where the caller guarantees
+ * that "bset" is bounded.
+ */
+struct isl_vec *isl_basic_set_sample_bounded(struct isl_basic_set *bset)
+{
+	return basic_set_sample(bset, 1);
+}
+
+__isl_give isl_basic_set *isl_basic_set_from_vec(__isl_take isl_vec *vec)
+{
+	int i;
+	int k;
+	struct isl_basic_set *bset = NULL;
+	struct isl_ctx *ctx;
+	unsigned dim;
+
+	if (!vec)
+		return NULL;
+	ctx = vec->ctx;
+	isl_assert(ctx, vec->size != 0, goto error);
+
+	bset = isl_basic_set_alloc(ctx, 0, vec->size - 1, 0, vec->size - 1, 0);
+	if (!bset)
 		goto error;
-	if (bounds->n_row == dim)
-		isl_mat_free(ctx, bounds);
-	else {
-		struct isl_mat *T;
-		struct isl_vec *sample;
+	dim = isl_basic_set_n_dim(bset);
+	for (i = dim - 1; i >= 0; --i) {
+		k = isl_basic_set_alloc_equality(bset);
+		if (k < 0)
+			goto error;
+		isl_seq_clr(bset->eq[k], 1 + dim);
+		isl_int_neg(bset->eq[k][0], vec->el[1 + i]);
+		isl_int_set(bset->eq[k][1 + i], vec->el[0]);
+	}
+	bset->sample = vec;
 
-		bset = remove_lineality(ctx, bset, bounds, &T);
-		sample = isl_basic_set_sample(bset);
-		if (sample && sample->size != 0)
-			sample = isl_mat_vec_product(ctx, T, sample);
-		else
-			isl_mat_free(ctx, T);
+	return bset;
+error:
+	isl_basic_set_free(bset);
+	isl_vec_free(vec);
+	return NULL;
+}
+
+__isl_give isl_basic_map *isl_basic_map_sample(__isl_take isl_basic_map *bmap)
+{
+	struct isl_basic_set *bset;
+	struct isl_vec *sample_vec;
+
+	bset = isl_basic_map_underlying_set(isl_basic_map_copy(bmap));
+	sample_vec = isl_basic_set_sample_vec(bset);
+	if (!sample_vec)
+		goto error;
+	if (sample_vec->size == 0) {
+		struct isl_basic_map *sample;
+		sample = isl_basic_map_empty_like(bmap);
+		isl_vec_free(sample_vec);
+		isl_basic_map_free(bmap);
 		return sample;
 	}
-	return isl_pip_basic_set_sample(bset);
+	bset = isl_basic_set_from_vec(sample_vec);
+	return isl_basic_map_overlying_set(bset, bmap);
 error:
-	isl_basic_set_free(bset);
+	isl_basic_map_free(bmap);
+	return NULL;
+}
+
+__isl_give isl_basic_set *isl_basic_set_sample(__isl_take isl_basic_set *bset)
+{
+	return isl_basic_map_sample(bset);
+}
+
+__isl_give isl_basic_map *isl_map_sample(__isl_take isl_map *map)
+{
+	int i;
+	isl_basic_map *sample = NULL;
+
+	if (!map)
+		goto error;
+
+	for (i = 0; i < map->n; ++i) {
+		sample = isl_basic_map_sample(isl_basic_map_copy(map->p[i]));
+		if (!sample)
+			goto error;
+		if (!ISL_F_ISSET(sample, ISL_BASIC_MAP_EMPTY))
+			break;
+		isl_basic_map_free(sample);
+	}
+	if (i == map->n)
+		sample = isl_basic_map_empty_like_map(map);
+	isl_map_free(map);
+	return sample;
+error:
+	isl_map_free(map);
+	return NULL;
+}
+
+__isl_give isl_basic_set *isl_set_sample(__isl_take isl_set *set)
+{
+	return (isl_basic_set *) isl_map_sample((isl_map *)set);
+}
+
+__isl_give isl_point *isl_basic_set_sample_point(__isl_take isl_basic_set *bset)
+{
+	isl_vec *vec;
+	isl_space *dim;
+
+	dim = isl_basic_set_get_space(bset);
+	bset = isl_basic_set_underlying_set(bset);
+	vec = isl_basic_set_sample_vec(bset);
+
+	return isl_point_alloc(dim, vec);
+}
+
+__isl_give isl_point *isl_set_sample_point(__isl_take isl_set *set)
+{
+	int i;
+	isl_point *pnt;
+
+	if (!set)
+		return NULL;
+
+	for (i = 0; i < set->n; ++i) {
+		pnt = isl_basic_set_sample_point(isl_basic_set_copy(set->p[i]));
+		if (!pnt)
+			goto error;
+		if (!isl_point_is_void(pnt))
+			break;
+		isl_point_free(pnt);
+	}
+	if (i == set->n)
+		pnt = isl_point_void(isl_set_get_space(set));
+
+	isl_set_free(set);
+	return pnt;
+error:
+	isl_set_free(set);
 	return NULL;
 }