X-Git-Url: http://review.tizen.org/git/?a=blobdiff_plain;f=isl_tab_pip.c;h=f6e238a26a6a2180e7ae80438914d65ad2502787;hb=f6cbdb2ed96a00ac5aa0136c06605bd552d33d84;hp=4758106803d774368802f99a24779a0691a5f3be;hpb=5838a24b6ca93204c2e7422550426d8885558bf2;p=platform%2Fupstream%2Fisl.git

diff --git a/isl_tab_pip.c b/isl_tab_pip.c
index 4758106..f6e238a 100644
--- a/isl_tab_pip.c
+++ b/isl_tab_pip.c
@@ -1,7 +1,21 @@
+/*
+ * Copyright 2008-2009 Katholieke Universiteit Leuven
+ * Copyright 2010      INRIA Saclay
+ *
+ * Use of this software is governed by the GNU LGPLv2.1 license
+ *
+ * Written by Sven Verdoolaege, K.U.Leuven, Departement
+ * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
+ * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
+ * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France 
+ */
+
+#include <isl_ctx_private.h>
 #include "isl_map_private.h"
-#include "isl_seq.h"
+#include <isl/seq.h>
 #include "isl_tab.h"
 #include "isl_sample.h"
+#include <isl_mat_private.h>
 
 /*
  * The implementation of parametric integer linear programming in this file
@@ -12,7 +26,7 @@
  * The strategy used for obtaining a feasible solution is different
  * from the one used in isl_tab.c.  In particular, in isl_tab.c,
  * upon finding a constraint that is not yet satisfied, we pivot
- * in a row that increases the constant term of row holding the
+ * in a row that increases the constant term of the row holding the
  * constraint, making sure the sample solution remains feasible
  * for all the constraints it already satisfied.
  * Here, we always pivot in the row holding the constraint,
@@ -26,10 +40,10 @@
  * then the initial sample value may be chosen equal to zero.
  * However, we will not make this assumption.  Instead, we apply
  * the "big parameter" trick.  Any variable x is then not directly
- * used in the tableau, but instead it its represented by another
+ * used in the tableau, but instead it is represented by another
  * variable x' = M + x, where M is an arbitrarily large (positive)
  * value.  x' is therefore always non-negative, whatever the value of x.
- * Taking as initial smaple value x' = 0 corresponds to x = -M,
+ * Taking as initial sample value x' = 0 corresponds to x = -M,
  * which is always smaller than any possible value of x.
  *
  * The big parameter trick is used in the main tableau and
@@ -71,9 +85,8 @@ struct isl_context_op {
 	/* return index of a div that corresponds to "div" */
 	int (*get_div)(struct isl_context *context, struct isl_tab *tab,
 			struct isl_vec *div);
-	/* add div "div" to context and return index and non-negativity */
-	int (*add_div)(struct isl_context *context, struct isl_vec *div,
-			int *nonneg);
+	/* add div "div" to context and return non-negativity */
+	int (*add_div)(struct isl_context *context, struct isl_vec *div);
 	int (*detect_equalities)(struct isl_context *context,
 			struct isl_tab *tab);
 	/* return row index of "best" split */
@@ -440,17 +453,17 @@ static void sol_add(struct isl_sol *sol, struct isl_tab *tab)
 
 		isl_seq_clr(mat->row[1 + row], mat->n_col);
 		if (!tab->var[i].is_row) {
-			/* no unbounded */
-			isl_assert(mat->ctx, !tab->M, goto error2);
+			if (tab->M)
+				isl_die(mat->ctx, isl_error_invalid,
+					"unbounded optimum", goto error2);
 			continue;
 		}
 
 		r = tab->var[i].index;
-		/* no unbounded */
-		if (tab->M)
-			isl_assert(mat->ctx, isl_int_eq(tab->mat->row[r][2],
-					                tab->mat->row[r][0]),
-				    goto error2);
+		if (tab->M &&
+		    isl_int_ne(tab->mat->row[r][2], tab->mat->row[r][0]))
+			isl_die(mat->ctx, isl_error_invalid,
+				"unbounded optimum", goto error2);
 		isl_int_gcd(m, mat->row[0][0], tab->mat->row[r][0]);
 		isl_int_divexact(m, tab->mat->row[r][0], m);
 		scale_rows(mat, m, 1 + row);
@@ -486,7 +499,7 @@ error2:
 error:
 	isl_basic_set_free(bset);
 	isl_mat_free(mat);
-	sol_free(sol);
+	sol->error = 1;
 }
 
 struct isl_sol_map {
@@ -497,6 +510,8 @@ struct isl_sol_map {
 
 static void sol_map_free(struct isl_sol_map *sol_map)
 {
+	if (!sol_map)
+		return;
 	if (sol_map->sol.context)
 		sol_map->sol.context->op->free(sol_map->sol.context);
 	isl_map_free(sol_map->map);
@@ -523,7 +538,7 @@ static void sol_map_add_empty(struct isl_sol_map *sol,
 	sol->empty = isl_set_grow(sol->empty, 1);
 	bset = isl_basic_set_simplify(bset);
 	bset = isl_basic_set_finalize(bset);
-	sol->empty = isl_set_add(sol->empty, isl_basic_set_copy(bset));
+	sol->empty = isl_set_add_basic_set(sol->empty, isl_basic_set_copy(bset));
 	if (!sol->empty)
 		goto error;
 	isl_basic_set_free(bset);
@@ -539,6 +554,18 @@ static void sol_map_add_empty_wrap(struct isl_sol *sol,
 	sol_map_add_empty((struct isl_sol_map *)sol, bset);
 }
 
+/* Add bset to sol's empty, but only if we are actually collecting
+ * the empty set.
+ */
+static void sol_map_add_empty_if_needed(struct isl_sol_map *sol,
+	struct isl_basic_set *bset)
+{
+	if (sol->empty)
+		sol_map_add_empty(sol, bset);
+	else
+		isl_basic_set_free(bset);
+}
+
 /* Given a basic map "dom" that represents the context and an affine
  * matrix "M" that maps the dimensions of the context to the
  * output variables, construct a basic map with the same parameters
@@ -621,7 +648,7 @@ static void sol_map_add(struct isl_sol_map *sol,
 	bmap = isl_basic_map_simplify(bmap);
 	bmap = isl_basic_map_finalize(bmap);
 	sol->map = isl_map_grow(sol->map, 1);
-	sol->map = isl_map_add(sol->map, bmap);
+	sol->map = isl_map_add_basic_map(sol->map, bmap);
 	if (!sol->map)
 		goto error;
 	isl_basic_set_free(dom);
@@ -1050,7 +1077,7 @@ error:
 }
 
 /* Return the first known violated constraint, i.e., a non-negative
- * contraint that currently has an either obviously negative value
+ * constraint that currently has an either obviously negative value
  * or a previously determined to be negative value.
  *
  * If any constraint has a negative coefficient for the big parameter,
@@ -1064,8 +1091,11 @@ static int first_neg(struct isl_tab *tab)
 		for (row = tab->n_redundant; row < tab->n_row; ++row) {
 			if (!isl_tab_var_from_row(tab, row)->is_nonneg)
 				continue;
-			if (isl_int_is_neg(tab->mat->row[row][2]))
-				return row;
+			if (!isl_int_is_neg(tab->mat->row[row][2]))
+				continue;
+			if (tab->row_sign)
+				tab->row_sign[row] = isl_tab_row_neg;
+			return row;
 		}
 	for (row = tab->n_redundant; row < tab->n_row; ++row) {
 		if (!isl_tab_var_from_row(tab, row)->is_nonneg)
@@ -1083,9 +1113,45 @@ static int first_neg(struct isl_tab *tab)
 	return -1;
 }
 
+/* Check whether the invariant that all columns are lexico-positive
+ * is satisfied.  This function is not called from the current code
+ * but is useful during debugging.
+ */
+static void check_lexpos(struct isl_tab *tab)
+{
+	unsigned off = 2 + tab->M;
+	int col;
+	int var;
+	int row;
+
+	for (col = tab->n_dead; col < tab->n_col; ++col) {
+		if (tab->col_var[col] >= 0 &&
+		    (tab->col_var[col] < tab->n_param ||
+		     tab->col_var[col] >= tab->n_var - tab->n_div))
+			continue;
+		for (var = tab->n_param; var < tab->n_var - tab->n_div; ++var) {
+			if (!tab->var[var].is_row) {
+				if (tab->var[var].index == col)
+					break;
+				else
+					continue;
+			}
+			row = tab->var[var].index;
+			if (isl_int_is_zero(tab->mat->row[row][off + col]))
+				continue;
+			if (isl_int_is_pos(tab->mat->row[row][off + col]))
+				break;
+			fprintf(stderr, "lexneg column %d (row %d)\n",
+				col, row);
+		}
+		if (var >= tab->n_var - tab->n_div)
+			fprintf(stderr, "zero column %d\n", col);
+	}
+}
+
 /* Resolve all known or obviously violated constraints through pivoting.
  * In particular, as long as we can find any violated constraint, we
- * look for a pivoting column that would result in the lexicographicallly
+ * look for a pivoting column that would result in the lexicographically
  * smallest increment in the sample point.  If there is no such column
  * then the tableau is infeasible.
  */
@@ -1100,8 +1166,11 @@ static struct isl_tab *restore_lexmin(struct isl_tab *tab)
 		return tab;
 	while ((row = first_neg(tab)) != -1) {
 		col = lexmin_pivot_col(tab, row);
-		if (col >= tab->n_col)
-			return isl_tab_mark_empty(tab);
+		if (col >= tab->n_col) {
+			if (isl_tab_mark_empty(tab) < 0)
+				goto error;
+			return tab;
+		}
 		if (col < 0)
 			goto error;
 		if (isl_tab_pivot(tab, row, col) < 0)
@@ -1194,8 +1263,6 @@ static struct isl_tab *add_lexmin_valid_eq(struct isl_tab *tab, isl_int *eq)
 		if (isl_tab_kill_col(tab, i) < 0)
 			goto error;
 		tab->n_eq++;
-
-		tab = restore_lexmin(tab);
 	}
 
 	return tab;
@@ -1243,8 +1310,11 @@ static struct isl_tab *add_lexmin_eq(struct isl_tab *tab, isl_int *eq)
 	row = tab->con[r1].index;
 	if (is_constant(tab, row)) {
 		if (!isl_int_is_zero(tab->mat->row[row][1]) ||
-		    (tab->M && !isl_int_is_zero(tab->mat->row[row][2])))
-			return isl_tab_mark_empty(tab);
+		    (tab->M && !isl_int_is_zero(tab->mat->row[row][2]))) {
+			if (isl_tab_mark_empty(tab) < 0)
+				goto error;
+			return tab;
+		}
 		if (isl_tab_rollback(tab, snap) < 0)
 			goto error;
 		return tab;
@@ -1273,30 +1343,18 @@ static struct isl_tab *add_lexmin_eq(struct isl_tab *tab, isl_int *eq)
 	} else if (!tab->con[r2].is_row) {
 		if (isl_tab_kill_col(tab, tab->con[r2].index) < 0)
 			goto error;
-	} else if (isl_int_is_zero(tab->mat->row[tab->con[r1].index][1])) {
-		unsigned off = 2 + tab->M;
-		int i;
-		int row = tab->con[r1].index;
-		i = isl_seq_first_non_zero(tab->mat->row[row]+off+tab->n_dead,
-						tab->n_col - tab->n_dead);
-		if (i != -1) {
-			if (isl_tab_pivot(tab, row, tab->n_dead + i) < 0)
-				goto error;
-			if (isl_tab_kill_col(tab, tab->n_dead + i) < 0)
-				goto error;
-		}
 	}
 
-	if (tab->bset) {
-		tab->bset = isl_basic_set_add_ineq(tab->bset, eq);
-		if (isl_tab_push(tab, isl_tab_undo_bset_ineq) < 0)
+	if (tab->bmap) {
+		tab->bmap = isl_basic_map_add_ineq(tab->bmap, eq);
+		if (isl_tab_push(tab, isl_tab_undo_bmap_ineq) < 0)
 			goto error;
 		isl_seq_neg(eq, eq, 1 + tab->n_var);
-		tab->bset = isl_basic_set_add_ineq(tab->bset, eq);
+		tab->bmap = isl_basic_map_add_ineq(tab->bmap, eq);
 		isl_seq_neg(eq, eq, 1 + tab->n_var);
-		if (isl_tab_push(tab, isl_tab_undo_bset_ineq) < 0)
+		if (isl_tab_push(tab, isl_tab_undo_bmap_ineq) < 0)
 			goto error;
-		if (!tab->bset)
+		if (!tab->bmap)
 			goto error;
 	}
 
@@ -1315,11 +1373,11 @@ static struct isl_tab *add_lexmin_ineq(struct isl_tab *tab, isl_int *ineq)
 
 	if (!tab)
 		return NULL;
-	if (tab->bset) {
-		tab->bset = isl_basic_set_add_ineq(tab->bset, ineq);
-		if (isl_tab_push(tab, isl_tab_undo_bset_ineq) < 0)
+	if (tab->bmap) {
+		tab->bmap = isl_basic_map_add_ineq(tab->bmap, ineq);
+		if (isl_tab_push(tab, isl_tab_undo_bmap_ineq) < 0)
 			goto error;
-		if (!tab->bset)
+		if (!tab->bmap)
 			goto error;
 	}
 	r = isl_tab_add_row(tab, ineq);
@@ -1404,8 +1462,9 @@ static int integer_constant(struct isl_tab *tab, int row)
 #define I_PAR	1 << 1
 #define I_VAR	1 << 2
 
-/* Check for first (non-parameter) variable that is non-integer and
- * therefore requires a cut.
+/* Check for next (non-parameter) variable after "var" (first if var == -1)
+ * that is non-integer and therefore requires a cut and return
+ * the index of the variable.
  * For parametric tableaus, there are three parts in a row,
  * the constant, the coefficients of the parameters and the rest.
  * For each part, we check whether the coefficients in that part
@@ -1414,16 +1473,16 @@ static int integer_constant(struct isl_tab *tab, int row)
  * current sample value is integral and no cut is required
  * (irrespective of whether the variable part is integral).
  */
-static int first_non_integer(struct isl_tab *tab, int *f)
+static int next_non_integer_var(struct isl_tab *tab, int var, int *f)
 {
-	int i;
+	var = var < 0 ? tab->n_param : var + 1;
 
-	for (i = tab->n_param; i < tab->n_var - tab->n_div; ++i) {
+	for (; var < tab->n_var - tab->n_div; ++var) {
 		int flags = 0;
 		int row;
-		if (!tab->var[i].is_row)
+		if (!tab->var[var].is_row)
 			continue;
-		row = tab->var[i].index;
+		row = tab->var[var].index;
 		if (integer_constant(tab, row))
 			ISL_FL_SET(flags, I_CST);
 		if (integer_parameter(tab, row))
@@ -1433,11 +1492,28 @@ static int first_non_integer(struct isl_tab *tab, int *f)
 		if (integer_variable(tab, row))
 			ISL_FL_SET(flags, I_VAR);
 		*f = flags;
-		return row;
+		return var;
 	}
 	return -1;
 }
 
+/* Check for first (non-parameter) variable that is non-integer and
+ * therefore requires a cut and return the corresponding row.
+ * For parametric tableaus, there are three parts in a row,
+ * the constant, the coefficients of the parameters and the rest.
+ * For each part, we check whether the coefficients in that part
+ * are all integral and if so, set the corresponding flag in *f.
+ * If the constant and the parameter part are integral, then the
+ * current sample value is integral and no cut is required
+ * (irrespective of whether the variable part is integral).
+ */
+static int first_non_integer_row(struct isl_tab *tab, int *f)
+{
+	int var = next_non_integer_var(tab, -1, f);
+
+	return var < 0 ? -1 : tab->var[var].index;
+}
+
 /* Add a (non-parametric) cut to cut away the non-integral sample
  * value of the given row.
  *
@@ -1497,15 +1573,17 @@ static int add_cut(struct isl_tab *tab, int row)
  * sample point is obtained or until the tableau is determined
  * to be integer infeasible.
  * As long as there is any non-integer value in the sample point,
- * we add an appropriate cut, if possible and resolve the violated
- * cut constraint using restore_lexmin.
+ * we add appropriate cuts, if possible, for each of these
+ * non-integer values and then resolve the violated
+ * cut constraints using restore_lexmin.
  * If one of the corresponding rows is equal to an integral
  * combination of variables/constraints plus a non-integral constant,
- * then there is no way to obtain an integer point an we return
+ * then there is no way to obtain an integer point and we return
  * a tableau that is marked empty.
  */
 static struct isl_tab *cut_to_integer_lexmin(struct isl_tab *tab)
 {
+	int var;
 	int row;
 	int flags;
 
@@ -1514,12 +1592,18 @@ static struct isl_tab *cut_to_integer_lexmin(struct isl_tab *tab)
 	if (tab->empty)
 		return tab;
 
-	while ((row = first_non_integer(tab, &flags)) != -1) {
-		if (ISL_FL_ISSET(flags, I_VAR))
-			return isl_tab_mark_empty(tab);
-		row = add_cut(tab, row);
-		if (row < 0)
-			goto error;
+	while ((var = next_non_integer_var(tab, -1, &flags)) != -1) {
+		do {
+			if (ISL_FL_ISSET(flags, I_VAR)) {
+				if (isl_tab_mark_empty(tab) < 0)
+					goto error;
+				return tab;
+			}
+			row = tab->var[var].index;
+			row = add_cut(tab, row);
+			if (row < 0)
+				goto error;
+		} while ((var = next_non_integer_var(tab, var, &flags)) != -1);
 		tab = restore_lexmin(tab);
 		if (!tab || tab->empty)
 			break;
@@ -1542,7 +1626,7 @@ static struct isl_tab *check_samples(struct isl_tab *tab, isl_int *ineq, int eq)
 	if (!tab)
 		return NULL;
 
-	isl_assert(tab->mat->ctx, tab->bset, goto error);
+	isl_assert(tab->mat->ctx, tab->bmap, goto error);
 	isl_assert(tab->mat->ctx, tab->samples, goto error);
 	isl_assert(tab->mat->ctx, tab->samples->n_col == 1 + tab->n_var, goto error);
 
@@ -1641,7 +1725,7 @@ static int tab_has_valid_sample(struct isl_tab *tab, isl_int *ineq, int eq)
 	if (!tab)
 		return -1;
 
-	isl_assert(tab->mat->ctx, tab->bset, return -1);
+	isl_assert(tab->mat->ctx, tab->bmap, return -1);
 	isl_assert(tab->mat->ctx, tab->samples, return -1);
 	isl_assert(tab->mat->ctx, tab->samples->n_col == 1 + tab->n_var, return -1);
 
@@ -1659,78 +1743,21 @@ static int tab_has_valid_sample(struct isl_tab *tab, isl_int *ineq, int eq)
 	return i < tab->n_sample;
 }
 
-/* For a div d = floor(f/m), add the constraints
- *
- *		f - m d >= 0
- *		-(f-(m-1)) + m d >= 0
- *
- * Note that the second constraint is the negation of
- *
- *		f - m d >= m
- */
-static void add_div_constraints(struct isl_context *context, unsigned div)
-{
-	unsigned total;
-	unsigned div_pos;
-	struct isl_vec *ineq;
-	struct isl_basic_set *bset;
-
-	bset = context->op->peek_basic_set(context);
-	if (!bset)
-		goto error;
-
-	total = isl_basic_set_total_dim(bset);
-	div_pos = 1 + total - bset->n_div + div;
-
-	ineq = ineq_for_div(bset, div);
-	if (!ineq)
-		goto error;
-
-	context->op->add_ineq(context, ineq->el, 0, 0);
-
-	isl_seq_neg(ineq->el, bset->div[div] + 1, 1 + total);
-	isl_int_set(ineq->el[div_pos], bset->div[div][0]);
-	isl_int_add(ineq->el[0], ineq->el[0], ineq->el[div_pos]);
-	isl_int_sub_ui(ineq->el[0], ineq->el[0], 1);
-
-	context->op->add_ineq(context, ineq->el, 0, 0);
-
-	isl_vec_free(ineq);
-
-	return;
-error:
-	context->op->invalidate(context);
-}
-
-/* Add a div specifed by "div" to the tableau "tab" and return
- * the index of the new div.  *nonneg is set to 1 if the div
- * is obviously non-negative.
+/* Add a div specified by "div" to the tableau "tab" and return
+ * 1 if the div is obviously non-negative.
  */
 static int context_tab_add_div(struct isl_tab *tab, struct isl_vec *div,
-	int *nonneg)
+	int (*add_ineq)(void *user, isl_int *), void *user)
 {
 	int i;
 	int r;
-	int k;
 	struct isl_mat *samples;
+	int nonneg;
 
-	for (i = 0; i < tab->n_var; ++i) {
-		if (isl_int_is_zero(div->el[2 + i]))
-			continue;
-		if (!tab->var[i].is_nonneg)
-			break;
-	}
-	*nonneg = i == tab->n_var;
-
-	if (isl_tab_extend_cons(tab, 3) < 0)
-		return -1;
-	if (isl_tab_extend_vars(tab, 1) < 0)
-		return -1;
-	r = isl_tab_allocate_var(tab);
+	r = isl_tab_add_div(tab, div, add_ineq, user);
 	if (r < 0)
 		return -1;
-	if (*nonneg)
-		tab->var[r].is_nonneg = 1;
+	nonneg = tab->var[r].is_nonneg;
 	tab->var[r].frozen = 1;
 
 	samples = isl_mat_extend(tab->samples,
@@ -1745,16 +1772,7 @@ static int context_tab_add_div(struct isl_tab *tab, struct isl_vec *div,
 			       samples->row[i][samples->n_col - 1], div->el[0]);
 	}
 
-	tab->bset = isl_basic_set_extend_dim(tab->bset,
-		isl_basic_set_get_dim(tab->bset), 1, 0, 2);
-	k = isl_basic_set_alloc_div(tab->bset);
-	if (k < 0)
-		return -1;
-	isl_seq_cpy(tab->bset->div[k], div->el, div->size);
-	if (isl_tab_push(tab, isl_tab_undo_bset_div) < 0)
-		return -1;
-
-	return k;
+	return nonneg;
 }
 
 /* Add a div specified by "div" to both the main tableau and
@@ -1767,14 +1785,11 @@ static int add_div(struct isl_tab *tab, struct isl_context *context,
 	struct isl_vec *div)
 {
 	int r;
-	int k;
 	int nonneg;
 
-	k = context->op->add_div(context, div, &nonneg);
-	if (k < 0)
+	if ((nonneg = context->op->add_div(context, div)) < 0)
 		goto error;
 
-	add_div_constraints(context, k);
 	if (!context->op->is_ok(context))
 		goto error;
 
@@ -1797,12 +1812,12 @@ error:
 static int find_div(struct isl_tab *tab, isl_int *div, isl_int denom)
 {
 	int i;
-	unsigned total = isl_basic_set_total_dim(tab->bset);
+	unsigned total = isl_basic_map_total_dim(tab->bmap);
 
-	for (i = 0; i < tab->bset->n_div; ++i) {
-		if (isl_int_ne(tab->bset->div[i][0], denom))
+	for (i = 0; i < tab->bmap->n_div; ++i) {
+		if (isl_int_ne(tab->bmap->div[i][0], denom))
 			continue;
-		if (!isl_seq_eq(tab->bset->div[i] + 1, div, total))
+		if (!isl_seq_eq(tab->bmap->div[i] + 1, div, 1 + total))
 			continue;
 		return i;
 	}
@@ -1979,8 +1994,11 @@ static struct isl_tab *tab_for_lexmin(struct isl_basic_map *bmap,
 		if (!tab->row_sign)
 			goto error;
 	}
-	if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
-		return isl_tab_mark_empty(tab);
+	if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY)) {
+		if (isl_tab_mark_empty(tab) < 0)
+			goto error;
+		return tab;
+	}
 
 	for (i = tab->n_param; i < tab->n_var - tab->n_div; ++i) {
 		tab->var[i].is_nonneg = 1;
@@ -1999,6 +2017,8 @@ static struct isl_tab *tab_for_lexmin(struct isl_basic_map *bmap,
 		if (!tab || tab->empty)
 			return tab;
 	}
+	if (bmap->n_eq)
+		tab = restore_lexmin(tab);
 	for (i = 0; i < bmap->n_ineq; ++i) {
 		if (max)
 			isl_seq_neg(bmap->ineq[i] + 1 + tab->n_param,
@@ -2051,6 +2071,7 @@ static int best_split(struct isl_tab *tab, struct isl_tab *context_tab)
 		struct isl_tab_undo *snap2;
 		struct isl_vec *ineq = NULL;
 		int r = 0;
+		int ok;
 
 		if (!isl_tab_var_from_row(tab, split)->is_nonneg)
 			continue;
@@ -2060,8 +2081,10 @@ static int best_split(struct isl_tab *tab, struct isl_tab *context_tab)
 		ineq = get_row_parameter_ineq(tab, split);
 		if (!ineq)
 			return -1;
-		context_tab = isl_tab_add_ineq(context_tab, ineq->el);
+		ok = isl_tab_add_ineq(context_tab, ineq->el) >= 0;
 		isl_vec_free(ineq);
+		if (!ok)
+			return -1;
 
 		snap2 = isl_tab_snap(context_tab);
 
@@ -2078,8 +2101,10 @@ static int best_split(struct isl_tab *tab, struct isl_tab *context_tab)
 			ineq = get_row_parameter_ineq(tab, row);
 			if (!ineq)
 				return -1;
-			context_tab = isl_tab_add_ineq(context_tab, ineq->el);
+			ok = isl_tab_add_ineq(context_tab, ineq->el) >= 0;
 			isl_vec_free(ineq);
+			if (!ok)
+				return -1;
 			var = &context_tab->con[context_tab->n_con - 1];
 			if (!context_tab->empty &&
 			    !isl_tab_min_at_most_neg_one(context_tab, var))
@@ -2104,7 +2129,7 @@ static struct isl_basic_set *context_lex_peek_basic_set(
 	struct isl_context_lex *clex = (struct isl_context_lex *)context;
 	if (!clex->tab)
 		return NULL;
-	return clex->tab->bset;
+	return isl_tab_peek_bset(clex->tab);
 }
 
 static struct isl_tab *context_lex_peek_tab(struct isl_context *context)
@@ -2168,6 +2193,13 @@ error:
 	clex->tab = NULL;
 }
 
+static int context_lex_add_ineq_wrap(void *user, isl_int *ineq)
+{
+	struct isl_context *context = (struct isl_context *)user;
+	context_lex_add_ineq(context, ineq, 0, 0);
+	return context->op->is_ok(context) ? 0 : -1;
+}
+
 /* Check which signs can be obtained by "ineq" on all the currently
  * active sample values.  See row_sign for more information.
  */
@@ -2177,10 +2209,11 @@ static enum isl_tab_row_sign tab_ineq_sign(struct isl_tab *tab, isl_int *ineq,
 	int i;
 	int sgn;
 	isl_int tmp;
-	int res = isl_tab_row_unknown;
+	enum isl_tab_row_sign res = isl_tab_row_unknown;
 
-	isl_assert(tab->mat->ctx, tab->samples, return 0);
-	isl_assert(tab->mat->ctx, tab->samples->n_col == 1 + tab->n_var, return 0);
+	isl_assert(tab->mat->ctx, tab->samples, return isl_tab_row_unknown);
+	isl_assert(tab->mat->ctx, tab->samples->n_col == 1 + tab->n_var,
+			return isl_tab_row_unknown);
 
 	isl_int_init(tmp);
 	for (i = tab->n_outside; i < tab->n_sample; ++i) {
@@ -2249,11 +2282,25 @@ static int context_lex_get_div(struct isl_context *context, struct isl_tab *tab,
 	return get_div(tab, context, div);
 }
 
-static int context_lex_add_div(struct isl_context *context, struct isl_vec *div,
-	int *nonneg)
+/* Add a div specified by "div" to the context tableau and return
+ * 1 if the div is obviously non-negative.
+ * context_tab_add_div will always return 1, because all variables
+ * in a isl_context_lex tableau are non-negative.
+ * However, if we are using a big parameter in the context, then this only
+ * reflects the non-negativity of the variable used to _encode_ the
+ * div, i.e., div' = M + div, so we can't draw any conclusions.
+ */
+static int context_lex_add_div(struct isl_context *context, struct isl_vec *div)
 {
 	struct isl_context_lex *clex = (struct isl_context_lex *)context;
-	return context_tab_add_div(clex->tab, div, nonneg);
+	int nonneg;
+	nonneg = context_tab_add_div(clex->tab, div,
+					context_lex_add_ineq_wrap, context);
+	if (nonneg < 0)
+		return -1;
+	if (clex->tab->M)
+		return 0;
+	return nonneg;
 }
 
 static int context_lex_detect_equalities(struct isl_context *context,
@@ -2274,7 +2321,7 @@ static int context_lex_best_split(struct isl_context *context,
 		return -1;
 	r = best_split(tab, clex->tab);
 
-	if (isl_tab_rollback(clex->tab, snap) < 0)
+	if (r >= 0 && isl_tab_rollback(clex->tab, snap) < 0)
 		return -1;
 
 	return r;
@@ -2347,7 +2394,8 @@ static struct isl_tab *tab_detect_nonnegative_parameters(struct isl_tab *tab,
 	isl_seq_clr(ineq->el, ineq->size);
 	for (i = 0; i < context_tab->n_var; ++i) {
 		isl_int_set_si(ineq->el[1 + i], 1);
-		context_tab = isl_tab_add_ineq(context_tab, ineq->el);
+		if (isl_tab_add_ineq(context_tab, ineq->el) < 0)
+			goto error;
 		var = &context_tab->con[context_tab->n_con - 1];
 		if (!context_tab->empty &&
 		    !isl_tab_min_at_most_neg_one(context_tab, var)) {
@@ -2381,6 +2429,9 @@ static struct isl_tab *context_lex_detect_nonnegative_parameters(
 	struct isl_context_lex *clex = (struct isl_context_lex *)context;
 	struct isl_tab_undo *snap;
 
+	if (!tab)
+		return NULL;
+
 	snap = isl_tab_snap(clex->tab);
 	if (isl_tab_push_basis(clex->tab) < 0)
 		goto error;
@@ -2440,7 +2491,8 @@ static struct isl_tab *context_tab_for_lexmin(struct isl_basic_set *bset)
 	tab = tab_for_lexmin((struct isl_basic_map *)bset, NULL, 1, 0);
 	if (!tab)
 		goto error;
-	tab->bset = bset;
+	if (isl_tab_track_bset(tab, bset) < 0)
+		goto error;
 	tab = isl_tab_init_samples(tab);
 	return tab;
 error:
@@ -2484,6 +2536,8 @@ static struct isl_tab *context_gbr_detect_nonnegative_parameters(
 	struct isl_context *context, struct isl_tab *tab)
 {
 	struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
+	if (!tab)
+		return NULL;
 	return tab_detect_nonnegative_parameters(tab, cgbr->tab);
 }
 
@@ -2493,7 +2547,7 @@ static struct isl_basic_set *context_gbr_peek_basic_set(
 	struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
 	if (!cgbr->tab)
 		return NULL;
-	return cgbr->tab->bset;
+	return isl_tab_peek_bset(cgbr->tab);
 }
 
 static struct isl_tab *context_gbr_peek_tab(struct isl_context *context)
@@ -2512,7 +2566,7 @@ static void gbr_init_shifted(struct isl_context_gbr *cgbr)
 {
 	int i, j;
 	struct isl_vec *cst;
-	struct isl_basic_set *bset = cgbr->tab->bset;
+	struct isl_basic_set *bset = isl_tab_peek_bset(cgbr->tab);
 	unsigned dim = isl_basic_set_total_dim(bset);
 
 	cst = isl_vec_alloc(cgbr->tab->mat->ctx, bset->n_ineq);
@@ -2576,7 +2630,7 @@ static struct isl_basic_set *drop_constant_terms(struct isl_basic_set *bset)
 
 static int use_shifted(struct isl_context_gbr *cgbr)
 {
-	return cgbr->tab->bset->n_eq == 0 && cgbr->tab->bset->n_div == 0;
+	return cgbr->tab->bmap->n_eq == 0 && cgbr->tab->bmap->n_div == 0;
 }
 
 static struct isl_vec *gbr_get_sample(struct isl_context_gbr *cgbr)
@@ -2598,13 +2652,14 @@ static struct isl_vec *gbr_get_sample(struct isl_context_gbr *cgbr)
 	}
 
 	if (!cgbr->cone) {
-		cgbr->cone = isl_tab_from_recession_cone(cgbr->tab->bset);
+		bset = isl_tab_peek_bset(cgbr->tab);
+		cgbr->cone = isl_tab_from_recession_cone(bset, 0);
 		if (!cgbr->cone)
 			return NULL;
-		cgbr->cone->bset = isl_basic_set_dup(cgbr->tab->bset);
+		if (isl_tab_track_bset(cgbr->cone, isl_basic_set_dup(bset)) < 0)
+			return NULL;
 	}
-	cgbr->cone = isl_tab_detect_implicit_equalities(cgbr->cone);
-	if (!cgbr->cone)
+	if (isl_tab_detect_implicit_equalities(cgbr->cone) < 0)
 		return NULL;
 
 	if (cgbr->cone->n_dead == cgbr->cone->n_col) {
@@ -2615,10 +2670,9 @@ static struct isl_vec *gbr_get_sample(struct isl_context_gbr *cgbr)
 			if (cgbr->tab->basis->n_col != 1 + cgbr->tab->n_var) {
 				isl_mat_free(cgbr->tab->basis);
 				cgbr->tab->basis = NULL;
-			} else {
-				cgbr->tab->n_zero = 0;
-				cgbr->tab->n_unbounded = 0;
 			}
+			cgbr->tab->n_zero = 0;
+			cgbr->tab->n_unbounded = 0;
 		}
 
 		snap = isl_tab_snap(cgbr->tab);
@@ -2633,13 +2687,13 @@ static struct isl_vec *gbr_get_sample(struct isl_context_gbr *cgbr)
 		return sample;
 	}
 
-	cone = isl_basic_set_dup(cgbr->cone->bset);
+	cone = isl_basic_set_dup(isl_tab_peek_bset(cgbr->cone));
 	cone = drop_constant_terms(cone);
 	cone = isl_basic_set_update_from_tab(cone, cgbr->cone);
 	cone = isl_basic_set_underlying_set(cone);
 	cone = isl_basic_set_gauss(cone, NULL);
 
-	bset = isl_basic_set_dup(cgbr->tab->bset);
+	bset = isl_basic_set_dup(isl_tab_peek_bset(cgbr->tab));
 	bset = isl_basic_set_update_from_tab(bset, cgbr->tab);
 	bset = isl_basic_set_underlying_set(bset);
 	bset = isl_basic_set_gauss(bset, NULL);
@@ -2663,7 +2717,8 @@ static void check_gbr_integer_feasible(struct isl_context_gbr *cgbr)
 
 	if (sample->size == 0) {
 		isl_vec_free(sample);
-		cgbr->tab = isl_tab_mark_empty(cgbr->tab);
+		if (isl_tab_mark_empty(cgbr->tab) < 0)
+			goto error;
 		return;
 	}
 
@@ -2685,7 +2740,8 @@ static struct isl_tab *add_gbr_eq(struct isl_tab *tab, isl_int *eq)
 	if (isl_tab_extend_cons(tab, 2) < 0)
 		goto error;
 
-	tab = isl_tab_add_eq(tab, eq);
+	if (isl_tab_add_eq(tab, eq) < 0)
+		goto error;
 
 	return tab;
 error:
@@ -2703,7 +2759,8 @@ static void context_gbr_add_eq(struct isl_context *context, isl_int *eq,
 	if (cgbr->cone && cgbr->cone->n_col != cgbr->cone->n_dead) {
 		if (isl_tab_extend_cons(cgbr->cone, 2) < 0)
 			goto error;
-		cgbr->cone = isl_tab_add_eq(cgbr->cone, eq);
+		if (isl_tab_add_eq(cgbr->cone, eq) < 0)
+			goto error;
 	}
 
 	if (check) {
@@ -2729,12 +2786,13 @@ static void add_gbr_ineq(struct isl_context_gbr *cgbr, isl_int *ineq)
 	if (isl_tab_extend_cons(cgbr->tab, 1) < 0)
 		goto error;
 
-	cgbr->tab = isl_tab_add_ineq(cgbr->tab, ineq);
+	if (isl_tab_add_ineq(cgbr->tab, ineq) < 0)
+		goto error;
 
 	if (cgbr->shifted && !cgbr->shifted->empty && use_shifted(cgbr)) {
 		int i;
 		unsigned dim;
-		dim = isl_basic_set_total_dim(cgbr->tab->bset);
+		dim = isl_basic_map_total_dim(cgbr->tab->bmap);
 
 		if (isl_tab_extend_cons(cgbr->shifted, 1) < 0)
 			goto error;
@@ -2745,7 +2803,8 @@ static void add_gbr_ineq(struct isl_context_gbr *cgbr, isl_int *ineq)
 			isl_int_add(ineq[0], ineq[0], ineq[1 + i]);
 		}
 
-		cgbr->shifted = isl_tab_add_ineq(cgbr->shifted, ineq);
+		if (isl_tab_add_ineq(cgbr->shifted, ineq) < 0)
+			goto error;
 
 		for (i = 0; i < dim; ++i) {
 			if (!isl_int_is_neg(ineq[1 + i]))
@@ -2757,7 +2816,8 @@ static void add_gbr_ineq(struct isl_context_gbr *cgbr, isl_int *ineq)
 	if (cgbr->cone && cgbr->cone->n_col != cgbr->cone->n_dead) {
 		if (isl_tab_extend_cons(cgbr->cone, 1) < 0)
 			goto error;
-		cgbr->cone = isl_tab_add_ineq(cgbr->cone, ineq);
+		if (isl_tab_add_ineq(cgbr->cone, ineq) < 0)
+			goto error;
 	}
 
 	return;
@@ -2790,6 +2850,13 @@ error:
 	cgbr->tab = NULL;
 }
 
+static int context_gbr_add_ineq_wrap(void *user, isl_int *ineq)
+{
+	struct isl_context *context = (struct isl_context *)user;
+	context_gbr_add_ineq(context, ineq, 0, 0);
+	return context->op->is_ok(context) ? 0 : -1;
+}
+
 static enum isl_tab_row_sign context_gbr_ineq_sign(struct isl_context *context,
 			isl_int *ineq, int strict)
 {
@@ -2893,20 +2960,20 @@ static void propagate_equalities(struct isl_context_gbr *cgbr,
 	if (!eq)
 		goto error;
 
-	if (isl_tab_extend_cons(tab, (cgbr->tab->bset->n_ineq - first)/2) < 0)
+	if (isl_tab_extend_cons(tab, (cgbr->tab->bmap->n_ineq - first)/2) < 0)
 		goto error;
 
 	isl_seq_clr(eq->el + 1 + tab->n_param,
 		    tab->n_var - tab->n_param - tab->n_div);
-	for (i = first; i < cgbr->tab->bset->n_ineq; i += 2) {
+	for (i = first; i < cgbr->tab->bmap->n_ineq; i += 2) {
 		int j;
 		int r;
 		struct isl_tab_undo *snap;
 		snap = isl_tab_snap(tab);
 
-		isl_seq_cpy(eq->el, cgbr->tab->bset->ineq[i], 1 + tab->n_param);
+		isl_seq_cpy(eq->el, cgbr->tab->bmap->ineq[i], 1 + tab->n_param);
 		isl_seq_cpy(eq->el + 1 + tab->n_var - tab->n_div,
-			    cgbr->tab->bset->ineq[i] + 1 + tab->n_param,
+			    cgbr->tab->bmap->ineq[i] + 1 + tab->n_param,
 			    tab->n_div);
 
 		r = isl_tab_add_row(tab, eq->el);
@@ -2951,16 +3018,19 @@ static int context_gbr_detect_equalities(struct isl_context *context,
 	ctx = cgbr->tab->mat->ctx;
 
 	if (!cgbr->cone) {
-		cgbr->cone = isl_tab_from_recession_cone(cgbr->tab->bset);
+		struct isl_basic_set *bset = isl_tab_peek_bset(cgbr->tab);
+		cgbr->cone = isl_tab_from_recession_cone(bset, 0);
 		if (!cgbr->cone)
 			goto error;
-		cgbr->cone->bset = isl_basic_set_dup(cgbr->tab->bset);
+		if (isl_tab_track_bset(cgbr->cone, isl_basic_set_dup(bset)) < 0)
+			goto error;
 	}
-	cgbr->cone = isl_tab_detect_implicit_equalities(cgbr->cone);
+	if (isl_tab_detect_implicit_equalities(cgbr->cone) < 0)
+		goto error;
 
-	n_ineq = cgbr->tab->bset->n_ineq;
+	n_ineq = cgbr->tab->bmap->n_ineq;
 	cgbr->tab = isl_tab_detect_equalities(cgbr->tab, cgbr->cone);
-	if (cgbr->tab && cgbr->tab->bset->n_ineq > n_ineq)
+	if (cgbr->tab && cgbr->tab->bmap->n_ineq > n_ineq)
 		propagate_equalities(cgbr, tab, n_ineq);
 
 	return 0;
@@ -2976,8 +3046,7 @@ static int context_gbr_get_div(struct isl_context *context, struct isl_tab *tab,
 	return get_div(tab, context, div);
 }
 
-static int context_gbr_add_div(struct isl_context *context, struct isl_vec *div,
-	int *nonneg)
+static int context_gbr_add_div(struct isl_context *context, struct isl_vec *div)
 {
 	struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
 	if (cgbr->cone) {
@@ -2990,16 +3059,17 @@ static int context_gbr_add_div(struct isl_context *context, struct isl_vec *div,
 		if (isl_tab_allocate_var(cgbr->cone) <0)
 			return -1;
 
-		cgbr->cone->bset = isl_basic_set_extend_dim(cgbr->cone->bset,
-			isl_basic_set_get_dim(cgbr->cone->bset), 1, 0, 2);
-		k = isl_basic_set_alloc_div(cgbr->cone->bset);
+		cgbr->cone->bmap = isl_basic_map_extend_dim(cgbr->cone->bmap,
+			isl_basic_map_get_dim(cgbr->cone->bmap), 1, 0, 2);
+		k = isl_basic_map_alloc_div(cgbr->cone->bmap);
 		if (k < 0)
 			return -1;
-		isl_seq_cpy(cgbr->cone->bset->div[k], div->el, div->size);
-		if (isl_tab_push(cgbr->cone, isl_tab_undo_bset_div) < 0)
+		isl_seq_cpy(cgbr->cone->bmap->div[k], div->el, div->size);
+		if (isl_tab_push(cgbr->cone, isl_tab_undo_bmap_div) < 0)
 			return -1;
 	}
-	return context_tab_add_div(cgbr->tab, div, nonneg);
+	return context_tab_add_div(cgbr->tab, div,
+					context_gbr_add_ineq_wrap, context);
 }
 
 static int context_gbr_best_split(struct isl_context *context,
@@ -3012,7 +3082,7 @@ static int context_gbr_best_split(struct isl_context *context,
 	snap = isl_tab_snap(cgbr->tab);
 	r = best_split(tab, cgbr->tab);
 
-	if (isl_tab_rollback(cgbr->tab, snap) < 0)
+	if (r >= 0 && isl_tab_rollback(cgbr->tab, snap) < 0)
 		return -1;
 
 	return r;
@@ -3158,8 +3228,8 @@ static struct isl_context *isl_context_gbr_alloc(struct isl_basic_set *dom)
 	cgbr->tab = isl_tab_init_samples(cgbr->tab);
 	if (!cgbr->tab)
 		goto error;
-	cgbr->tab->bset = isl_basic_set_cow(isl_basic_set_copy(dom));
-	if (!cgbr->tab->bset)
+	if (isl_tab_track_bset(cgbr->tab,
+				isl_basic_set_cow(isl_basic_set_copy(dom))) < 0)
 		goto error;
 	check_gbr_integer_feasible(cgbr);
 
@@ -3190,9 +3260,12 @@ static struct isl_context *isl_context_alloc(struct isl_basic_set *dom)
 static struct isl_sol_map *sol_map_init(struct isl_basic_map *bmap,
 	struct isl_basic_set *dom, int track_empty, int max)
 {
-	struct isl_sol_map *sol_map;
+	struct isl_sol_map *sol_map = NULL;
 
-	sol_map = isl_calloc_type(bset->ctx, struct isl_sol_map);
+	if (!bmap)
+		goto error;
+
+	sol_map = isl_calloc_type(bmap->ctx, struct isl_sol_map);
 	if (!sol_map)
 		goto error;
 
@@ -3332,7 +3405,7 @@ static enum isl_tab_row_sign row_sign(struct isl_tab *tab,
 	struct isl_sol *sol, int row)
 {
 	struct isl_vec *ineq = NULL;
-	int res = isl_tab_row_unknown;
+	enum isl_tab_row_sign res = isl_tab_row_unknown;
 	int critical;
 	int strict;
 	int row2;
@@ -3396,7 +3469,7 @@ static enum isl_tab_row_sign row_sign(struct isl_tab *tab,
 	return res;
 error:
 	isl_vec_free(ineq);
-	return 0;
+	return isl_tab_row_unknown;
 }
 
 static void find_solutions(struct isl_sol *sol, struct isl_tab *tab);
@@ -3431,7 +3504,8 @@ static void find_in_pos(struct isl_sol *sol, struct isl_tab *tab, isl_int *ineq)
 
 	find_solutions(sol, tab);
 
-	sol->context->op->restore(sol->context, saved);
+	if (!sol->error)
+		sol->context->op->restore(sol->context, saved);
 	return;
 error:
 	sol->error = 1;
@@ -3446,7 +3520,7 @@ static void no_sol_in_strict(struct isl_sol *sol,
 	int empty;
 	void *saved;
 
-	if (!sol->context)
+	if (!sol->context || sol->error)
 		goto error;
 	saved = sol->context->op->save(sol->context);
 
@@ -3543,7 +3617,7 @@ error:
  * coefficient are integral, then there is nothing that can be done
  * and the tableau has no integral solution.
  * If, on the other hand, one or more of the other columns have rational
- * coeffcients, but the parameter coefficients are all integral, then
+ * coefficients, but the parameter coefficients are all integral, then
  * we can perform a regular (non-parametric) cut.
  * Finally, if there is any parameter coefficient that is non-integral,
  * then we need to involve the context tableau.  There are two cases here.
@@ -3580,7 +3654,7 @@ static void find_solutions(struct isl_sol *sol, struct isl_tab *tab)
 	for (; tab && !tab->empty; tab = restore_lexmin(tab)) {
 		int flags;
 		int row;
-		int sgn;
+		enum isl_tab_row_sign sgn;
 		int split = -1;
 		int n_split = 0;
 
@@ -3623,7 +3697,8 @@ static void find_solutions(struct isl_sol *sol, struct isl_tab *tab)
 			row = split;
 			isl_seq_neg(ineq->el, ineq->el, ineq->size);
 			isl_int_sub_ui(ineq->el[0], ineq->el[0], 1);
-			context->op->add_ineq(context, ineq->el, 0, 1);
+			if (!sol->error)
+				context->op->add_ineq(context, ineq->el, 0, 1);
 			isl_vec_free(ineq);
 			if (sol->error)
 				goto error;
@@ -3631,12 +3706,13 @@ static void find_solutions(struct isl_sol *sol, struct isl_tab *tab)
 		}
 		if (tab->rational)
 			break;
-		row = first_non_integer(tab, &flags);
+		row = first_non_integer_row(tab, &flags);
 		if (row < 0)
 			break;
 		if (ISL_FL_ISSET(flags, I_PAR)) {
 			if (ISL_FL_ISSET(flags, I_VAR)) {
-				tab = isl_tab_mark_empty(tab);
+				if (isl_tab_mark_empty(tab) < 0)
+					goto error;
 				break;
 			}
 			row = add_cut(tab, row);
@@ -3652,6 +3728,8 @@ static void find_solutions(struct isl_sol *sol, struct isl_tab *tab)
 			if (d < 0)
 				goto error;
 			ineq = ineq_for_div(context->op->peek_basic_set(context), d);
+			if (!ineq)
+				goto error;
 			sol_inc_level(sol);
 			no_sol_in_strict(sol, tab, ineq);
 			isl_seq_neg(ineq->el, ineq->el, ineq->size);
@@ -3660,6 +3738,8 @@ static void find_solutions(struct isl_sol *sol, struct isl_tab *tab)
 			if (sol->error || !context->op->is_ok(context))
 				goto error;
 			tab = set_row_cst_to_div(tab, row, d);
+			if (context->op->is_empty(context))
+				break;
 		} else
 			row = add_parametric_cut(tab, row, context);
 		if (row < 0)
@@ -3671,7 +3751,7 @@ done:
 	return;
 error:
 	isl_tab_free(tab);
-	sol_free(sol);
+	sol->error = 1;
 }
 
 /* Compute the lexicographic minimum of the set represented by the main
@@ -3689,6 +3769,9 @@ static void find_solutions_main(struct isl_sol *sol, struct isl_tab *tab)
 {
 	int row;
 
+	if (!tab)
+		goto error;
+
 	sol->level = 0;
 
 	for (row = tab->n_redundant; row < tab->n_row; ++row) {
@@ -3707,6 +3790,8 @@ static void find_solutions_main(struct isl_sol *sol, struct isl_tab *tab)
 				+ tab->n_param - (tab->n_var - tab->n_div);
 
 		eq = isl_vec_alloc(tab->mat->ctx, 1+tab->n_param+tab->n_div);
+		if (!eq)
+			goto error;
 		get_row_parameter_line(tab, row, eq->el);
 		isl_int_neg(eq->el[1 + p], tab->mat->row[row][0]);
 		eq = isl_vec_normalize(eq);
@@ -3740,7 +3825,7 @@ static void find_solutions_main(struct isl_sol *sol, struct isl_tab *tab)
 	return;
 error:
 	isl_tab_free(tab);
-	sol_free(sol);
+	sol->error = 1;
 }
 
 static void sol_map_find_solutions(struct isl_sol_map *sol_map,
@@ -3825,43 +3910,21 @@ error:
 	return NULL;
 }
 
-/* Compute the lexicographic minimum (or maximum if "max" is set)
- * of "bmap" over the domain "dom" and return the result as a map.
- * If "empty" is not NULL, then *empty is assigned a set that
- * contains those parts of the domain where there is no solution.
- * If "bmap" is marked as rational (ISL_BASIC_MAP_RATIONAL),
- * then we compute the rational optimum.  Otherwise, we compute
- * the integral optimum.
+/* Base case of isl_tab_basic_map_partial_lexopt, after removing
+ * some obvious symmetries.
  *
- * We perform some preprocessing.  As the PILP solver does not
- * handle implicit equalities very well, we first make sure all
- * the equalities are explicitly available.
- * We also make sure the divs in the domain are properly order,
+ * We make sure the divs in the domain are properly ordered,
  * because they will be added one by one in the given order
  * during the construction of the solution map.
  */
-struct isl_map *isl_tab_basic_map_partial_lexopt(
-		struct isl_basic_map *bmap, struct isl_basic_set *dom,
-		struct isl_set **empty, int max)
+static __isl_give isl_map *basic_map_partial_lexopt_base(
+	__isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
+	__isl_give isl_set **empty, int max)
 {
+	isl_map *result = NULL;
 	struct isl_tab *tab;
-	struct isl_map *result = NULL;
 	struct isl_sol_map *sol_map = NULL;
 	struct isl_context *context;
-	struct isl_basic_map *eq;
-
-	if (empty)
-		*empty = NULL;
-	if (!bmap || !dom)
-		goto error;
-
-	isl_assert(bmap->ctx,
-	    isl_basic_map_compatible_domain(bmap, dom), goto error);
-
-	eq = isl_basic_map_copy(bmap);
-	eq = isl_basic_map_intersect_domain(eq, isl_basic_set_copy(dom));
-	eq = isl_basic_map_affine_hull(eq);
-	bmap = isl_basic_map_intersect(bmap, eq);
 
 	if (dom->n_div) {
 		dom = isl_basic_set_order_divs(dom);
@@ -3875,8 +3938,8 @@ struct isl_map *isl_tab_basic_map_partial_lexopt(
 	if (isl_basic_set_fast_is_empty(context->op->peek_basic_set(context)))
 		/* nothing */;
 	else if (isl_basic_map_fast_is_empty(bmap))
-		sol_map_add_empty(sol_map,
-		    isl_basic_set_dup(context->op->peek_basic_set(context)));
+		sol_map_add_empty_if_needed(sol_map,
+		    isl_basic_set_copy(context->op->peek_basic_set(context)));
 	else {
 		tab = tab_for_lexmin(bmap,
 				    context->op->peek_basic_set(context), 1, max);
@@ -3898,6 +3961,515 @@ error:
 	return NULL;
 }
 
+/* Structure used during detection of parallel constraints.
+ * n_in: number of "input" variables: isl_dim_param + isl_dim_in
+ * n_out: number of "output" variables: isl_dim_out + isl_dim_div
+ * val: the coefficients of the output variables
+ */
+struct isl_constraint_equal_info {
+	isl_basic_map *bmap;
+	unsigned n_in;
+	unsigned n_out;
+	isl_int *val;
+};
+
+/* Check whether the coefficients of the output variables
+ * of the constraint in "entry" are equal to info->val.
+ */
+static int constraint_equal(const void *entry, const void *val)
+{
+	isl_int **row = (isl_int **)entry;
+	const struct isl_constraint_equal_info *info = val;
+
+	return isl_seq_eq((*row) + 1 + info->n_in, info->val, info->n_out);
+}
+
+/* Check whether "bmap" has a pair of constraints that have
+ * the same coefficients for the output variables.
+ * Note that the coefficients of the existentially quantified
+ * variables need to be zero since the existentially quantified
+ * of the result are usually not the same as those of the input.
+ * the isl_dim_out and isl_dim_div dimensions.
+ * If so, return 1 and return the row indices of the two constraints
+ * in *first and *second.
+ */
+static int parallel_constraints(__isl_keep isl_basic_map *bmap,
+	int *first, int *second)
+{
+	int i;
+	isl_ctx *ctx = isl_basic_map_get_ctx(bmap);
+	struct isl_hash_table *table = NULL;
+	struct isl_hash_table_entry *entry;
+	struct isl_constraint_equal_info info;
+	unsigned n_out;
+	unsigned n_div;
+
+	ctx = isl_basic_map_get_ctx(bmap);
+	table = isl_hash_table_alloc(ctx, bmap->n_ineq);
+	if (!table)
+		goto error;
+
+	info.n_in = isl_basic_map_dim(bmap, isl_dim_param) +
+		    isl_basic_map_dim(bmap, isl_dim_in);
+	info.bmap = bmap;
+	n_out = isl_basic_map_dim(bmap, isl_dim_out);
+	n_div = isl_basic_map_dim(bmap, isl_dim_div);
+	info.n_out = n_out + n_div;
+	for (i = 0; i < bmap->n_ineq; ++i) {
+		uint32_t hash;
+
+		info.val = bmap->ineq[i] + 1 + info.n_in;
+		if (isl_seq_first_non_zero(info.val, n_out) < 0)
+			continue;
+		if (isl_seq_first_non_zero(info.val + n_out, n_div) >= 0)
+			continue;
+		hash = isl_seq_get_hash(info.val, info.n_out);
+		entry = isl_hash_table_find(ctx, table, hash,
+					    constraint_equal, &info, 1);
+		if (!entry)
+			goto error;
+		if (entry->data)
+			break;
+		entry->data = &bmap->ineq[i];
+	}
+
+	if (i < bmap->n_ineq) {
+		*first = ((isl_int **)entry->data) - bmap->ineq; 
+		*second = i;
+	}
+
+	isl_hash_table_free(ctx, table);
+
+	return i < bmap->n_ineq;
+error:
+	isl_hash_table_free(ctx, table);
+	return -1;
+}
+
+/* Given a set of upper bounds on the last "input" variable m,
+ * construct a set that assigns the minimal upper bound to m, i.e.,
+ * construct a set that divides the space into cells where one
+ * of the upper bounds is smaller than all the others and assign
+ * this upper bound to m.
+ *
+ * In particular, if there are n bounds b_i, then the result
+ * consists of n basic sets, each one of the form
+ *
+ *	m = b_i
+ *	b_i <= b_j	for j > i
+ *	b_i <  b_j	for j < i
+ */
+static __isl_give isl_set *set_minimum(__isl_take isl_dim *dim,
+	__isl_take isl_mat *var)
+{
+	int i, j, k;
+	isl_basic_set *bset = NULL;
+	isl_ctx *ctx;
+	isl_set *set = NULL;
+
+	if (!dim || !var)
+		goto error;
+
+	ctx = isl_dim_get_ctx(dim);
+	set = isl_set_alloc_dim(isl_dim_copy(dim),
+				var->n_row, ISL_SET_DISJOINT);
+
+	for (i = 0; i < var->n_row; ++i) {
+		bset = isl_basic_set_alloc_dim(isl_dim_copy(dim), 0,
+					       1, var->n_row - 1);
+		k = isl_basic_set_alloc_equality(bset);
+		if (k < 0)
+			goto error;
+		isl_seq_cpy(bset->eq[k], var->row[i], var->n_col);
+		isl_int_set_si(bset->eq[k][var->n_col], -1);
+		for (j = 0; j < var->n_row; ++j) {
+			if (j == i)
+				continue;
+			k = isl_basic_set_alloc_inequality(bset);
+			if (k < 0)
+				goto error;
+			isl_seq_combine(bset->ineq[k], ctx->one, var->row[j],
+					ctx->negone, var->row[i],
+					var->n_col);
+			isl_int_set_si(bset->ineq[k][var->n_col], 0);
+			if (j < i)
+				isl_int_sub_ui(bset->ineq[k][0],
+					       bset->ineq[k][0], 1);
+		}
+		bset = isl_basic_set_finalize(bset);
+		set = isl_set_add_basic_set(set, bset);
+	}
+
+	isl_dim_free(dim);
+	isl_mat_free(var);
+	return set;
+error:
+	isl_basic_set_free(bset);
+	isl_set_free(set);
+	isl_dim_free(dim);
+	isl_mat_free(var);
+	return NULL;
+}
+
+/* Given that the last input variable of "bmap" represents the minimum
+ * of the bounds in "cst", check whether we need to split the domain
+ * based on which bound attains the minimum.
+ *
+ * A split is needed when the minimum appears in an integer division
+ * or in an equality.  Otherwise, it is only needed if it appears in
+ * an upper bound that is different from the upper bounds on which it
+ * is defined.
+ */
+static int need_split_map(__isl_keep isl_basic_map *bmap,
+	__isl_keep isl_mat *cst)
+{
+	int i, j;
+	unsigned total;
+	unsigned pos;
+
+	pos = cst->n_col - 1;
+	total = isl_basic_map_dim(bmap, isl_dim_all);
+
+	for (i = 0; i < bmap->n_div; ++i)
+		if (!isl_int_is_zero(bmap->div[i][2 + pos]))
+			return 1;
+
+	for (i = 0; i < bmap->n_eq; ++i)
+		if (!isl_int_is_zero(bmap->eq[i][1 + pos]))
+			return 1;
+
+	for (i = 0; i < bmap->n_ineq; ++i) {
+		if (isl_int_is_nonneg(bmap->ineq[i][1 + pos]))
+			continue;
+		if (!isl_int_is_negone(bmap->ineq[i][1 + pos]))
+			return 1;
+		if (isl_seq_first_non_zero(bmap->ineq[i] + 1 + pos + 1,
+					   total - pos - 1) >= 0)
+			return 1;
+
+		for (j = 0; j < cst->n_row; ++j)
+			if (isl_seq_eq(bmap->ineq[i], cst->row[j], cst->n_col))
+				break;
+		if (j >= cst->n_row)
+			return 1;
+	}
+
+	return 0;
+}
+
+static int need_split_set(__isl_keep isl_basic_set *bset,
+	__isl_keep isl_mat *cst)
+{
+	return need_split_map((isl_basic_map *)bset, cst);
+}
+
+/* Given a set of which the last set variable is the minimum
+ * of the bounds in "cst", split each basic set in the set
+ * in pieces where one of the bounds is (strictly) smaller than the others.
+ * This subdivision is given in "min_expr".
+ * The variable is subsequently projected out.
+ *
+ * We only do the split when it is needed.
+ * For example if the last input variable m = min(a,b) and the only
+ * constraints in the given basic set are lower bounds on m,
+ * i.e., l <= m = min(a,b), then we can simply project out m
+ * to obtain l <= a and l <= b, without having to split on whether
+ * m is equal to a or b.
+ */
+static __isl_give isl_set *split(__isl_take isl_set *empty,
+	__isl_take isl_set *min_expr, __isl_take isl_mat *cst)
+{
+	int n_in;
+	int i;
+	isl_dim *dim;
+	isl_set *res;
+
+	if (!empty || !min_expr || !cst)
+		goto error;
+
+	n_in = isl_set_dim(empty, isl_dim_set);
+	dim = isl_set_get_dim(empty);
+	dim = isl_dim_drop(dim, isl_dim_set, n_in - 1, 1);
+	res = isl_set_empty(dim);
+
+	for (i = 0; i < empty->n; ++i) {
+		isl_set *set;
+
+		set = isl_set_from_basic_set(isl_basic_set_copy(empty->p[i]));
+		if (need_split_set(empty->p[i], cst))
+			set = isl_set_intersect(set, isl_set_copy(min_expr));
+		set = isl_set_remove_dims(set, isl_dim_set, n_in - 1, 1);
+
+		res = isl_set_union_disjoint(res, set);
+	}
+
+	isl_set_free(empty);
+	isl_set_free(min_expr);
+	isl_mat_free(cst);
+	return res;
+error:
+	isl_set_free(empty);
+	isl_set_free(min_expr);
+	isl_mat_free(cst);
+	return NULL;
+}
+
+/* Given a map of which the last input variable is the minimum
+ * of the bounds in "cst", split each basic set in the set
+ * in pieces where one of the bounds is (strictly) smaller than the others.
+ * This subdivision is given in "min_expr".
+ * The variable is subsequently projected out.
+ *
+ * The implementation is essentially the same as that of "split".
+ */
+static __isl_give isl_map *split_domain(__isl_take isl_map *opt,
+	__isl_take isl_set *min_expr, __isl_take isl_mat *cst)
+{
+	int n_in;
+	int i;
+	isl_dim *dim;
+	isl_map *res;
+
+	if (!opt || !min_expr || !cst)
+		goto error;
+
+	n_in = isl_map_dim(opt, isl_dim_in);
+	dim = isl_map_get_dim(opt);
+	dim = isl_dim_drop(dim, isl_dim_in, n_in - 1, 1);
+	res = isl_map_empty(dim);
+
+	for (i = 0; i < opt->n; ++i) {
+		isl_map *map;
+
+		map = isl_map_from_basic_map(isl_basic_map_copy(opt->p[i]));
+		if (need_split_map(opt->p[i], cst))
+			map = isl_map_intersect_domain(map,
+						       isl_set_copy(min_expr));
+		map = isl_map_remove_dims(map, isl_dim_in, n_in - 1, 1);
+
+		res = isl_map_union_disjoint(res, map);
+	}
+
+	isl_map_free(opt);
+	isl_set_free(min_expr);
+	isl_mat_free(cst);
+	return res;
+error:
+	isl_map_free(opt);
+	isl_set_free(min_expr);
+	isl_mat_free(cst);
+	return NULL;
+}
+
+static __isl_give isl_map *basic_map_partial_lexopt(
+	__isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
+	__isl_give isl_set **empty, int max);
+
+/* Given a basic map with at least two parallel constraints (as found
+ * by the function parallel_constraints), first look for more constraints
+ * parallel to the two constraint and replace the found list of parallel
+ * constraints by a single constraint with as "input" part the minimum
+ * of the input parts of the list of constraints.  Then, recursively call
+ * basic_map_partial_lexopt (possibly finding more parallel constraints)
+ * and plug in the definition of the minimum in the result.
+ *
+ * More specifically, given a set of constraints
+ *
+ *	a x + b_i(p) >= 0
+ *
+ * Replace this set by a single constraint
+ *
+ *	a x + u >= 0
+ *
+ * with u a new parameter with constraints
+ *
+ *	u <= b_i(p)
+ *
+ * Any solution to the new system is also a solution for the original system
+ * since
+ *
+ *	a x >= -u >= -b_i(p)
+ *
+ * Moreover, m = min_i(b_i(p)) satisfies the constraints on u and can
+ * therefore be plugged into the solution.
+ */
+static __isl_give isl_map *basic_map_partial_lexopt_symm(
+	__isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
+	__isl_give isl_set **empty, int max, int first, int second)
+{
+	int i, n, k;
+	int *list = NULL;
+	unsigned n_in, n_out, n_div;
+	isl_ctx *ctx;
+	isl_vec *var = NULL;
+	isl_mat *cst = NULL;
+	isl_map *opt;
+	isl_set *min_expr;
+	isl_dim *map_dim, *set_dim;
+
+	map_dim = isl_basic_map_get_dim(bmap);
+	set_dim = empty ? isl_basic_set_get_dim(dom) : NULL;
+
+	n_in = isl_basic_map_dim(bmap, isl_dim_param) +
+	       isl_basic_map_dim(bmap, isl_dim_in);
+	n_out = isl_basic_map_dim(bmap, isl_dim_all) - n_in;
+
+	ctx = isl_basic_map_get_ctx(bmap);
+	list = isl_alloc_array(ctx, int, bmap->n_ineq);
+	var = isl_vec_alloc(ctx, n_out);
+	if (!list || !var)
+		goto error;
+
+	list[0] = first;
+	list[1] = second;
+	isl_seq_cpy(var->el, bmap->ineq[first] + 1 + n_in, n_out);
+	for (i = second + 1, n = 2; i < bmap->n_ineq; ++i) {
+		if (isl_seq_eq(var->el, bmap->ineq[i] + 1 + n_in, n_out))
+			list[n++] = i;
+	}
+
+	cst = isl_mat_alloc(ctx, n, 1 + n_in);
+	if (!cst)
+		goto error;
+
+	for (i = 0; i < n; ++i)
+		isl_seq_cpy(cst->row[i], bmap->ineq[list[i]], 1 + n_in);
+
+	bmap = isl_basic_map_cow(bmap);
+	if (!bmap)
+		goto error;
+	for (i = n - 1; i >= 0; --i)
+		if (isl_basic_map_drop_inequality(bmap, list[i]) < 0)
+			goto error;
+
+	bmap = isl_basic_map_add(bmap, isl_dim_in, 1);
+	bmap = isl_basic_map_extend_constraints(bmap, 0, 1);
+	k = isl_basic_map_alloc_inequality(bmap);
+	if (k < 0)
+		goto error;
+	isl_seq_clr(bmap->ineq[k], 1 + n_in);
+	isl_int_set_si(bmap->ineq[k][1 + n_in], 1);
+	isl_seq_cpy(bmap->ineq[k] + 1 + n_in + 1, var->el, n_out);
+	bmap = isl_basic_map_finalize(bmap);
+
+	n_div = isl_basic_set_dim(dom, isl_dim_div);
+	dom = isl_basic_set_add(dom, isl_dim_set, 1);
+	dom = isl_basic_set_extend_constraints(dom, 0, n);
+	for (i = 0; i < n; ++i) {
+		k = isl_basic_set_alloc_inequality(dom);
+		if (k < 0)
+			goto error;
+		isl_seq_cpy(dom->ineq[k], cst->row[i], 1 + n_in);
+		isl_int_set_si(dom->ineq[k][1 + n_in], -1);
+		isl_seq_clr(dom->ineq[k] + 1 + n_in + 1, n_div);
+	}
+
+	min_expr = set_minimum(isl_basic_set_get_dim(dom), isl_mat_copy(cst));
+
+	isl_vec_free(var);
+	free(list);
+
+	opt = basic_map_partial_lexopt(bmap, dom, empty, max);
+
+	if (empty) {
+		*empty = split(*empty,
+			       isl_set_copy(min_expr), isl_mat_copy(cst));
+		*empty = isl_set_reset_dim(*empty, set_dim);
+	}
+
+	opt = split_domain(opt, min_expr, cst);
+	opt = isl_map_reset_dim(opt, map_dim);
+
+	return opt;
+error:
+	isl_dim_free(map_dim);
+	isl_dim_free(set_dim);
+	isl_mat_free(cst);
+	isl_vec_free(var);
+	free(list);
+	isl_basic_set_free(dom);
+	isl_basic_map_free(bmap);
+	return NULL;
+}
+
+/* Recursive part of isl_tab_basic_map_partial_lexopt, after detecting
+ * equalities and removing redundant constraints.
+ *
+ * We first check if there are any parallel constraints (left).
+ * If not, we are in the base case.
+ * If there are parallel constraints, we replace them by a single
+ * constraint in basic_map_partial_lexopt_symm and then call
+ * this function recursively to look for more parallel constraints.
+ */
+static __isl_give isl_map *basic_map_partial_lexopt(
+	__isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
+	__isl_give isl_set **empty, int max)
+{
+	int par = 0;
+	int first, second;
+
+	if (!bmap)
+		goto error;
+
+	if (bmap->ctx->opt->pip_symmetry)
+		par = parallel_constraints(bmap, &first, &second);
+	if (par < 0)
+		goto error;
+	if (!par)
+		return basic_map_partial_lexopt_base(bmap, dom, empty, max);
+	
+	return basic_map_partial_lexopt_symm(bmap, dom, empty, max,
+					     first, second);
+error:
+	isl_basic_set_free(dom);
+	isl_basic_map_free(bmap);
+	return NULL;
+}
+
+/* Compute the lexicographic minimum (or maximum if "max" is set)
+ * of "bmap" over the domain "dom" and return the result as a map.
+ * If "empty" is not NULL, then *empty is assigned a set that
+ * contains those parts of the domain where there is no solution.
+ * If "bmap" is marked as rational (ISL_BASIC_MAP_RATIONAL),
+ * then we compute the rational optimum.  Otherwise, we compute
+ * the integral optimum.
+ *
+ * We perform some preprocessing.  As the PILP solver does not
+ * handle implicit equalities very well, we first make sure all
+ * the equalities are explicitly available.
+ *
+ * We also add context constraints to the basic map and remove
+ * redundant constraints.  This is only needed because of the
+ * way we handle simple symmetries.  In particular, we currently look
+ * for symmetries on the constraints, before we set up the main tableau.
+ * It is then no good to look for symmetries on possibly redundant constraints.
+ */
+struct isl_map *isl_tab_basic_map_partial_lexopt(
+		struct isl_basic_map *bmap, struct isl_basic_set *dom,
+		struct isl_set **empty, int max)
+{
+	if (empty)
+		*empty = NULL;
+	if (!bmap || !dom)
+		goto error;
+
+	isl_assert(bmap->ctx,
+	    isl_basic_map_compatible_domain(bmap, dom), goto error);
+
+	if (isl_basic_set_dim(dom, isl_dim_all) == 0)
+		return basic_map_partial_lexopt(bmap, dom, empty, max);
+
+	bmap = isl_basic_map_intersect_domain(bmap, isl_basic_set_copy(dom));
+	bmap = isl_basic_map_detect_equalities(bmap);
+	bmap = isl_basic_map_remove_redundancies(bmap);
+
+	return basic_map_partial_lexopt(bmap, dom, empty, max);
+error:
+	isl_basic_set_free(dom);
+	isl_basic_map_free(bmap);
+	return NULL;
+}
+
 struct isl_sol_for {
 	struct isl_sol	sol;
 	int		(*fn)(__isl_take isl_basic_set *dom,
@@ -3923,7 +4495,7 @@ static void sol_for_free_wrap(struct isl_sol *sol)
  *
  * Instead of constructing a basic map, this function calls a user
  * defined function with the current context as a basic set and
- * an affine matrix reprenting the relation between the input and output.
+ * an affine matrix representing the relation between the input and output.
  * The number of rows in this matrix is equal to one plus the number
  * of output variables.  The number of columns is equal to one plus
  * the total dimension of the context, i.e., the number of parameters,
@@ -3967,7 +4539,7 @@ static struct isl_sol_for *sol_for_init(struct isl_basic_map *bmap, int max,
 	struct isl_dim *dom_dim;
 	struct isl_basic_set *dom = NULL;
 
-	sol_for = isl_calloc_type(bset->ctx, struct isl_sol_for);
+	sol_for = isl_calloc_type(bmap->ctx, struct isl_sol_for);
 	if (!sol_for)
 		goto error;