X-Git-Url: http://review.tizen.org/git/?a=blobdiff_plain;f=isl_sample.c;h=c6a0f314425b0bc2d4683589997a3034b652abe0;hb=de51a9bc4da5dd3f1f9f57c2362da6f9752c44e0;hp=d19d585b2933a1bee38d0eaa8842b327f872dc35;hpb=7eb3527926a43d4163e68936adbb2db20af2b251;p=platform%2Fupstream%2Fisl.git

diff --git a/isl_sample.c b/isl_sample.c
index d19d585..c6a0f31 100644
--- a/isl_sample.c
+++ b/isl_sample.c
@@ -1,12 +1,25 @@
+/*
+ * 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)
 {
@@ -45,12 +58,16 @@ static struct isl_vec *interval_sample(struct isl_basic_set *bset)
 	bset = isl_basic_set_simplify(bset);
 	if (!bset)
 		return NULL;
-	if (isl_basic_set_fast_is_empty(bset))
+	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(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) {
@@ -257,179 +274,476 @@ static struct isl_vec *sample_eq(struct isl_basic_set *bset,
 	return sample;
 }
 
-/* Given a basic set "bset" and an affine function "f"/"denom",
- * check if bset is bounded and non-empty and if so, return the minimal
- * and maximal value attained by the affine function in "min" and "max".
- * The minimal value is rounded up to the nearest integer, while the
- * maximal value is rounded down.
- * The return value indicates whether the set was empty or unbounded.
- *
- * If we happen to find an integer point while looking for the minimal
- * or maximal value, then we record that value in "bset" and return early.
+/* 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 enum isl_lp_result basic_set_range(struct isl_basic_set *bset,
-	isl_int *f, isl_int denom, isl_int *min, isl_int *max)
+static struct isl_mat *tab_equalities(struct isl_tab *tab)
 {
-	unsigned dim;
-	struct isl_tab *tab;
-	enum isl_lp_result res;
+	int i, j;
+	int n_eq;
+	struct isl_mat *eq;
+	struct isl_basic_set *bset;
 
-	if (!bset)
-		return isl_lp_error;
-	if (isl_basic_set_fast_is_empty(bset))
-		return isl_lp_empty;
+	if (!tab)
+		return NULL;
 
-	tab = isl_tab_from_basic_set(bset);
-	res = isl_tab_min(tab, f, denom, min, NULL, 0);
-	if (res != isl_lp_ok)
-		goto done;
+	bset = isl_tab_peek_bset(tab);
+	isl_assert(tab->mat->ctx, bset, return NULL);
 
-	if (isl_tab_sample_is_integer(tab)) {
-		isl_vec_free(bset->sample);
-		bset->sample = isl_tab_get_sample_value(tab);
-		if (!bset->sample)
-			goto error;
-		isl_int_set(*max, *min);
-		goto done;
+	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;
+}
 
-	dim = isl_basic_set_total_dim(bset);
-	isl_seq_neg(f, f, 1 + dim);
-	res = isl_tab_min(tab, f, denom, max, NULL, 0);
-	isl_seq_neg(f, f, 1 + dim);
-	isl_int_neg(*max, *max);
+/* 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);
 
-	if (isl_tab_sample_is_integer(tab)) {
-		isl_vec_free(bset->sample);
-		bset->sample = isl_tab_get_sample_value(tab);
-		if (!bset->sample)
-			goto error;
-	}
+	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]);
 
-done:
-	isl_tab_free(tab);
 	return res;
-error:
-	isl_tab_free(tab);
-	return isl_lp_error;
 }
 
-/* Perform a basis reduction on "bset" and return the inverse of
- * the new basis, i.e., an affine mapping from the new coordinates to the old,
- * in *T.
+/* 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 struct isl_basic_set *basic_set_reduced(struct isl_basic_set *bset,
-	struct isl_mat **T)
+static int greedy_search(isl_ctx *ctx, struct isl_tab *tab,
+	__isl_keep isl_vec *min, __isl_keep isl_vec *max, int level)
 {
-	unsigned gbr_only_first;
+	struct isl_tab_undo *snap;
+	enum isl_lp_result res;
 
-	*T = NULL;
-	if (!bset)
+	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_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;
+	}
 
-	gbr_only_first = bset->ctx->gbr_only_first;
-	bset->ctx->gbr_only_first = bset->ctx->gbr == ISL_GBR_ONCE;
-	*T = isl_basic_set_reduced_basis(bset);
-	bset->ctx->gbr_only_first = gbr_only_first;
+	if (isl_tab_extend_cons(tab, dim + 1) < 0)
+		return NULL;
 
-	*T = isl_mat_lin_to_aff(*T);
-	*T = isl_mat_right_inverse(*T);
+	min = isl_vec_alloc(ctx, dim);
+	max = isl_vec_alloc(ctx, dim);
+	snap = isl_alloc_array(ctx, struct isl_tab_undo *, dim);
 
-	bset = isl_basic_set_preimage(bset, isl_mat_copy(*T));
-	if (!bset)
+	if (!min || !max || !snap)
 		goto error;
 
-	return bset;
+	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:
-	isl_mat_free(*T);
-	*T = NULL;
+	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);
 
-/* Given a basic set "bset" whose first coordinate ranges between
- * "min" and "max", step through all values from min to max, until
- * the slice of bset with the first coordinate fixed to one of these
- * values contains an integer point.  If such a point is found, return it.
- * If none of the slices contains any integer point, then bset itself
- * doesn't contain any integer point and an empty sample is returned.
+/* Compute a sample point of the given basic set, based on the given,
+ * non-trivial factorization.
  */
-static struct isl_vec *sample_scan(struct isl_basic_set *bset,
-	isl_int min, isl_int max)
+static __isl_give isl_vec *factored_sample(__isl_take isl_basic_set *bset,
+	__isl_take isl_factorizer *f)
 {
-	unsigned total;
-	struct isl_basic_set *slice = NULL;
-	struct isl_vec *sample = NULL;
-	isl_int tmp;
+	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;
 
-	total = isl_basic_set_total_dim(bset);
+	nparam = isl_basic_set_dim(bset, isl_dim_param);
+	nvar = isl_basic_set_dim(bset, isl_dim_set);
 
-	isl_int_init(tmp);
-	for (isl_int_set(tmp, min); isl_int_le(tmp, max);
-	     isl_int_add_ui(tmp, tmp, 1)) {
-		int k;
+	sample = isl_vec_alloc(ctx, 1 + isl_basic_set_total_dim(bset));
+	if (!sample)
+		goto error;
+	isl_int_set_si(sample->el[0], 1);
 
-		slice = isl_basic_set_copy(bset);
-		slice = isl_basic_set_cow(slice);
-		slice = isl_basic_set_extend_constraints(slice, 1, 0);
-		k = isl_basic_set_alloc_equality(slice);
-		if (k < 0)
-			goto error;
-		isl_int_set(slice->eq[k][0], tmp);
-		isl_int_set_si(slice->eq[k][1], -1);
-		isl_seq_clr(slice->eq[k] + 2, total - 1);
-		slice = isl_basic_set_simplify(slice);
-		sample = sample_bounded(slice);
-		slice = NULL;
-		if (!sample)
+	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->size > 0)
-			break;
-		isl_vec_free(sample);
-		sample = NULL;
+		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];
 	}
-	if (!sample)
-		sample = empty_sample(bset);
-	else
-		isl_basic_set_free(bset);
-	isl_int_clear(tmp);
+
+	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_basic_set_free(slice);
-	isl_int_clear(tmp);
+	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 check the range of the
- * first coordinate.  If this coordinate can only attain one integer
- * value, we are happy.  Otherwise, we perform basis reduction and
- * determine the new range.
- *
- * Then we step through all possible values in the range in sample_scan.
- *
- * If any basis reduction was performed, the sample value found, if any,
- * is transformed back to the original space.
+ * 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;
-	unsigned gbr;
 	struct isl_ctx *ctx;
 	struct isl_vec *sample;
-	struct isl_vec *obj = NULL;
-	struct isl_mat *T = NULL;
-	isl_int min, max;
-	enum isl_lp_result res;
+	struct isl_tab *tab = NULL;
+	isl_factorizer *f;
 
 	if (!bset)
 		return NULL;
 
-	if (isl_basic_set_fast_is_empty(bset))
+	if (isl_basic_set_plain_is_empty(bset))
 		return empty_sample(bset);
 
 	dim = isl_basic_set_total_dim(bset);
@@ -440,74 +754,43 @@ static struct isl_vec *sample_bounded(struct isl_basic_set *bset)
 	if (bset->n_eq > 0)
 		return sample_eq(bset, sample_bounded);
 
-	ctx = bset->ctx;
-	gbr = ctx->gbr;
-
-	isl_int_init(min);
-	isl_int_init(max);
-	obj = isl_vec_alloc(bset->ctx, 1 + dim);
-	if (!obj)
+	f = isl_basic_set_factorizer(bset);
+	if (!f)
 		goto error;
-	isl_seq_clr(obj->el, 1+ dim);
-	isl_int_set_si(obj->el[1], 1);
+	if (f->n_group != 0)
+		return factored_sample(bset, f);
+	isl_factorizer_free(f);
+		
+	ctx = bset->ctx;
 
-	res = basic_set_range(bset, obj->el, bset->ctx->one, &min, &max);
-	if (res == isl_lp_error)
-		goto error;
-	isl_assert(bset->ctx, res != isl_lp_unbounded, goto error);
-	if (bset->sample) {
-		sample = isl_vec_copy(bset->sample);
+	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);
-		goto out;
-	}
-	if (res == isl_lp_empty || isl_int_lt(max, min)) {
-		sample = empty_sample(bset);
-		goto out;
+		return sample;
 	}
 
-	if (ctx->gbr != ISL_GBR_NEVER && isl_int_ne(min, max)) {
-		if (ctx->gbr == ISL_GBR_ONCE)
-			ctx->gbr = ISL_GBR_NEVER;
-
-		bset = basic_set_reduced(bset, &T);
-		if (!bset)
+	if (!ISL_F_ISSET(bset, ISL_BASIC_SET_NO_IMPLICIT))
+		if (isl_tab_detect_implicit_equalities(tab) < 0)
 			goto error;
 
-		res = basic_set_range(bset, obj->el, bset->ctx->one, &min, &max);
-		if (res == isl_lp_error)
-			goto error;
-		isl_assert(bset->ctx, res != isl_lp_unbounded, goto error);
-		if (bset->sample) {
-			sample = isl_vec_copy(bset->sample);
-			isl_basic_set_free(bset);
-			goto out;
-		}
-		if (res == isl_lp_empty || isl_int_lt(max, min)) {
-			sample = empty_sample(bset);
-			goto out;
-		}
-	}
+	sample = isl_tab_sample(tab);
+	if (!sample)
+		goto error;
 
-	sample = sample_scan(bset, min, max);
-out:
-	if (T) {
-		if (!sample || sample->size == 0)
-			isl_mat_free(T);
-		else
-			sample = isl_mat_vec_product(T, sample);
+	if (sample->size > 0) {
+		isl_vec_free(bset->sample);
+		bset->sample = isl_vec_copy(sample);
 	}
-	isl_vec_free(obj);
-	isl_int_clear(min);
-	isl_int_clear(max);
-	ctx->gbr = gbr;
+
+	isl_basic_set_free(bset);
+	isl_tab_free(tab);
 	return sample;
 error:
-	ctx->gbr = gbr;
-	isl_mat_free(T);
 	isl_basic_set_free(bset);
-	isl_vec_free(obj);
-	isl_int_clear(min);
-	isl_int_clear(max);
+	isl_tab_free(tab);
 	return NULL;
 }
 
@@ -567,7 +850,7 @@ static struct isl_vec *rational_sample(struct isl_basic_set *bset)
 	if (!bset)
 		return NULL;
 
-	tab = isl_tab_from_basic_set(bset);
+	tab = isl_tab_from_basic_set(bset, 0);
 	sample = isl_tab_get_sample_value(tab);
 	isl_tab_free(tab);
 
@@ -624,7 +907,7 @@ static struct isl_basic_set *shift_cone(struct isl_basic_set *cone,
 
 	total = isl_basic_set_total_dim(cone);
 
-	shift = isl_basic_set_alloc_dim(isl_basic_set_get_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) {
@@ -684,7 +967,8 @@ static struct isl_vec *round_up_in_cone(struct isl_vec *vec,
 
 	total = isl_basic_set_total_dim(cone);
 	cone = isl_basic_set_preimage(cone, U);
-	cone = isl_basic_set_remove_dims(cone, 0, total - (vec->size - 1));
+	cone = isl_basic_set_remove_dims(cone, isl_dim_set,
+					 0, total - (vec->size - 1));
 
 	cone = shift_cone(cone, vec);
 
@@ -729,28 +1013,6 @@ error:
 	return NULL;
 }
 
-/* Drop all constraints in bset that involve any of the dimensions
- * first to first+n-1.
- */
-static struct isl_basic_set *drop_constraints_involving
-	(struct isl_basic_set *bset, unsigned first, unsigned n)
-{
-	int i;
-
-	if (!bset)
-		return NULL;
-
-	bset = isl_basic_set_cow(bset);
-
-	for (i = bset->n_ineq - 1; i >= 0; --i) {
-		if (isl_seq_first_non_zero(bset->ineq[i] + 1 + first, n) == -1)
-			continue;
-		isl_basic_set_drop_inequality(bset, i);
-	}
-
-	return bset;
-}
-
 /* Give a basic set "bset" with recession cone "cone", compute and
  * return an integer point in bset, if any.
  *
@@ -788,8 +1050,8 @@ static struct isl_basic_set *drop_constraints_involving
  * then combined into a single sample point and transformed back
  * to the original space.
  */
-static struct isl_vec *sample_with_cone(struct isl_basic_set *bset,
-	struct isl_basic_set *cone)
+__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;
@@ -806,7 +1068,7 @@ static struct isl_vec *sample_with_cone(struct isl_basic_set *bset,
 	total = isl_basic_set_total_dim(cone);
 	cone_dim = total - cone->n_eq;
 
-	M = isl_mat_sub_alloc(bset->ctx, cone->eq, 0, cone->n_eq, 1, total);
+	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;
@@ -816,7 +1078,8 @@ static struct isl_vec *sample_with_cone(struct isl_basic_set *bset,
 	bset = isl_basic_set_preimage(bset, isl_mat_copy(U));
 
 	bounded = isl_basic_set_copy(bset);
-	bounded = drop_constraints_involving(bounded, total - cone_dim, cone_dim);
+	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) {
@@ -837,6 +1100,133 @@ error:
 	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
@@ -851,12 +1241,17 @@ static struct isl_vec *gbr_sample(struct isl_basic_set *bset)
 	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 sample_with_cone(bset, cone);
+		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)
@@ -888,7 +1283,7 @@ static struct isl_vec *basic_set_sample(struct isl_basic_set *bset, int bounded)
 		return NULL;
 
 	ctx = bset->ctx;
-	if (isl_basic_set_fast_is_empty(bset))
+	if (isl_basic_set_plain_is_empty(bset))
 		return empty_sample(bset);
 
 	dim = isl_basic_set_n_dim(bset);
@@ -909,13 +1304,14 @@ static struct isl_vec *basic_set_sample(struct isl_basic_set *bset, int bounded)
 	bset->sample = NULL;
 
 	if (bset->n_eq > 0)
-		return sample_eq(bset, isl_basic_set_sample_vec);
+		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(bset);
 
-	switch (bset->ctx->ilp_solver) {
+	switch (bset->ctx->opt->ilp_solver) {
 	case ISL_ILP_PIP:
 		return pip_sample(bset);
 	case ISL_ILP_GBR:
@@ -965,7 +1361,7 @@ __isl_give isl_basic_set *isl_basic_set_from_vec(__isl_take isl_vec *vec)
 		isl_int_neg(bset->eq[k][0], vec->el[1 + i]);
 		isl_int_set(bset->eq[k][1 + i], vec->el[0]);
 	}
-	isl_vec_free(vec);
+	bset->sample = vec;
 
 	return bset;
 error:
@@ -997,6 +1393,11 @@ error:
 	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;
@@ -1026,3 +1427,41 @@ __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;
+}