X-Git-Url: http://review.tizen.org/git/?a=blobdiff_plain;f=isl_tab.c;h=e4cc386679d8760504af441f0741f9241120f479;hb=ca90b151a05f17ccc1c3215ff24dc5d7b9198ff4;hp=695f7bac5ff6b0090a46a037b443d982a9dd66a8;hpb=c3bbf920555f83634940f3e3993c649f6e3cc699;p=platform%2Fupstream%2Fisl.git

diff --git a/isl_tab.c b/isl_tab.c
index 695f7ba..e4cc386 100644
--- a/isl_tab.c
+++ b/isl_tab.c
@@ -1,16 +1,20 @@
 /*
  * Copyright 2008-2009 Katholieke Universiteit Leuven
+ * Copyright 2013      Ecole Normale Superieure
  *
- * Use of this software is governed by the GNU LGPLv2.1 license
+ * 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
+ * and Ecole Normale Superieure, 45 rue d'Ulm, 75230 Paris, France
  */
 
-#include "isl_mat.h"
+#include <isl_ctx_private.h>
+#include <isl_mat_private.h>
 #include "isl_map_private.h"
 #include "isl_tab.h"
-#include "isl_seq.h"
+#include <isl/seq.h>
+#include <isl_config.h>
 
 /*
  * The implementation of tableaus in this file was inspired by Section 8
@@ -85,13 +89,20 @@ error:
 	return NULL;
 }
 
+isl_ctx *isl_tab_get_ctx(struct isl_tab *tab)
+{
+	return tab ? isl_mat_get_ctx(tab->mat) : NULL;
+}
+
 int isl_tab_extend_cons(struct isl_tab *tab, unsigned n_new)
 {
-	unsigned off = 2 + tab->M;
+	unsigned off;
 
 	if (!tab)
 		return -1;
 
+	off = 2 + tab->M;
+
 	if (tab->max_con < tab->n_con + n_new) {
 		struct isl_tab_var *con;
 
@@ -169,13 +180,24 @@ struct isl_tab *isl_tab_extend(struct isl_tab *tab, unsigned n_new)
 	return NULL;
 }
 
+static void free_undo_record(struct isl_tab_undo *undo)
+{
+	switch (undo->type) {
+	case isl_tab_undo_saved_basis:
+		free(undo->u.col_var);
+		break;
+	default:;
+	}
+	free(undo);
+}
+
 static void free_undo(struct isl_tab *tab)
 {
 	struct isl_tab_undo *undo, *next;
 
 	for (undo = tab->top; undo && undo != &tab->bottom; undo = next) {
 		next = undo->next;
-		free(undo);
+		free_undo_record(undo);
 	}
 	tab->top = undo;
 }
@@ -310,6 +332,8 @@ static struct isl_mat *tab_mat_product(struct isl_mat *mat1,
 
 	prod = isl_mat_alloc(mat1->ctx, mat1->n_row + mat2->n_row,
 					off + col1 + col2);
+	if (!prod)
+		return NULL;
 
 	n = 0;
 	for (i = 0; i < r1; ++i) {
@@ -770,6 +794,8 @@ static int push_union(struct isl_tab *tab,
 {
 	struct isl_tab_undo *undo;
 
+	if (!tab)
+		return -1;
 	if (!tab->need_undo)
 		return 0;
 
@@ -922,7 +948,7 @@ int isl_tab_mark_redundant(struct isl_tab *tab, int row)
 	struct isl_tab_var *var = isl_tab_var_from_row(tab, row);
 	var->is_redundant = 1;
 	isl_assert(tab->mat->ctx, row >= tab->n_redundant, return -1);
-	if (tab->need_undo || tab->row_var[row] >= 0) {
+	if (tab->preserve || tab->need_undo || tab->row_var[row] >= 0) {
 		if (tab->row_var[row] >= 0 && !var->is_nonneg) {
 			var->is_nonneg = 1;
 			if (isl_tab_push_var(tab, isl_tab_undo_nonneg, var) < 0)
@@ -1079,6 +1105,11 @@ int isl_tab_pivot(struct isl_tab *tab, int row, int col)
 	struct isl_tab_var *var;
 	unsigned off = 2 + tab->M;
 
+	if (tab->mat->ctx->abort) {
+		isl_ctx_set_error(tab->mat->ctx, isl_error_abort);
+		return -1;
+	}
+
 	isl_int_swap(mat->row[row][0], mat->row[row][off + col]);
 	sgn = isl_int_sgn(mat->row[row][0]);
 	if (sgn < 0) {
@@ -1166,6 +1197,11 @@ static int to_row(struct isl_tab *tab, struct isl_tab_var *var, int sign)
 	return isl_tab_pivot(tab, r, var->index);
 }
 
+/* Check whether all variables that are marked as non-negative
+ * also have a non-negative sample value.  This function is not
+ * called from the current code but is useful during debugging.
+ */
+static void check_table(struct isl_tab *tab) __attribute__ ((unused));
 static void check_table(struct isl_tab *tab)
 {
 	int i;
@@ -1513,6 +1549,43 @@ int isl_tab_kill_col(struct isl_tab *tab, int col)
 	}
 }
 
+static int row_is_manifestly_non_integral(struct isl_tab *tab, int row)
+{
+	unsigned off = 2 + tab->M;
+
+	if (tab->M && !isl_int_eq(tab->mat->row[row][2],
+				  tab->mat->row[row][0]))
+		return 0;
+	if (isl_seq_first_non_zero(tab->mat->row[row] + off + tab->n_dead,
+				    tab->n_col - tab->n_dead) != -1)
+		return 0;
+
+	return !isl_int_is_divisible_by(tab->mat->row[row][1],
+					tab->mat->row[row][0]);
+}
+
+/* For integer tableaus, check if any of the coordinates are stuck
+ * at a non-integral value.
+ */
+static int tab_is_manifestly_empty(struct isl_tab *tab)
+{
+	int i;
+
+	if (tab->empty)
+		return 1;
+	if (tab->rational)
+		return 0;
+
+	for (i = 0; i < tab->n_var; ++i) {
+		if (!tab->var[i].is_row)
+			continue;
+		if (row_is_manifestly_non_integral(tab, tab->var[i].index))
+			return 1;
+	}
+
+	return 0;
+}
+
 /* Row variable "var" is non-negative and cannot attain any values
  * larger than zero.  This means that the coefficients of the unrestricted
  * column variables are zero and that the coefficients of the non-negative
@@ -1547,6 +1620,8 @@ static int close_row(struct isl_tab *tab, struct isl_tab_var *var)
 	}
 	if (isl_tab_mark_redundant(tab, var->index) < 0)
 		return -1;
+	if (tab_is_manifestly_empty(tab) && isl_tab_mark_empty(tab) < 0)
+		return -1;
 	return 0;
 }
 
@@ -1626,6 +1701,9 @@ int isl_tab_allocate_var(struct isl_tab *tab)
  *		d_r   d_r        d_r d_x/g                m
  *
  *	with g the gcd of d_r and d_x and m the lcm of d_r and d_x.
+ *
+ * If tab->M is set, then, internally, each variable x is represented
+ * as x' - M.  We then also need no subtract k d_r from the coefficient of M.
  */
 int isl_tab_add_row(struct isl_tab *tab, isl_int *line)
 {
@@ -1829,24 +1907,24 @@ static int row_is_manifestly_zero(struct isl_tab *tab, int row)
 
 /* Add an equality that is known to be valid for the given tableau.
  */
-struct isl_tab *isl_tab_add_valid_eq(struct isl_tab *tab, isl_int *eq)
+int isl_tab_add_valid_eq(struct isl_tab *tab, isl_int *eq)
 {
 	struct isl_tab_var *var;
 	int r;
 
 	if (!tab)
-		return NULL;
+		return -1;
 	r = isl_tab_add_row(tab, eq);
 	if (r < 0)
-		goto error;
+		return -1;
 
 	var = &tab->con[r];
 	r = var->index;
 	if (row_is_manifestly_zero(tab, r)) {
 		var->is_zero = 1;
 		if (isl_tab_mark_redundant(tab, r) < 0)
-			goto error;
-		return tab;
+			return -1;
+		return 0;
 	}
 
 	if (isl_int_is_neg(tab->mat->row[r][1])) {
@@ -1856,15 +1934,12 @@ struct isl_tab *isl_tab_add_valid_eq(struct isl_tab *tab, isl_int *eq)
 	}
 	var->is_nonneg = 1;
 	if (to_col(tab, var) < 0)
-		goto error;
+		return -1;
 	var->is_nonneg = 0;
 	if (isl_tab_kill_col(tab, var->index) < 0)
-		goto error;
+		return -1;
 
-	return tab;
-error:
-	isl_tab_free(tab);
-	return NULL;
+	return 0;
 }
 
 static int add_zero_row(struct isl_tab *tab)
@@ -2056,7 +2131,35 @@ error:
 	return -1;
 }
 
-/* Add an extra div, prescrived by "div" to the tableau and
+/* Check whether the div described by "div" is obviously non-negative.
+ * If we are using a big parameter, then we will encode the div
+ * as div' = M + div, which is always non-negative.
+ * Otherwise, we check whether div is a non-negative affine combination
+ * of non-negative variables.
+ */
+static int div_is_nonneg(struct isl_tab *tab, __isl_keep isl_vec *div)
+{
+	int i;
+
+	if (tab->M)
+		return 1;
+
+	if (isl_int_is_neg(div->el[1]))
+		return 0;
+
+	for (i = 0; i < tab->n_var; ++i) {
+		if (isl_int_is_neg(div->el[2 + i]))
+			return 0;
+		if (isl_int_is_zero(div->el[2 + i]))
+			continue;
+		if (!tab->var[i].is_nonneg)
+			return 0;
+	}
+
+	return 1;
+}
+
+/* Add an extra div, prescribed by "div" to the tableau and
  * the associated bmap (which is assumed to be non-NULL).
  *
  * If add_ineq is not NULL, then this function is used instead
@@ -2068,7 +2171,6 @@ error:
 int isl_tab_add_div(struct isl_tab *tab, __isl_keep isl_vec *div,
 	int (*add_ineq)(void *user, isl_int *), void *user)
 {
-	int i;
 	int r;
 	int k;
 	int nonneg;
@@ -2078,15 +2180,7 @@ int isl_tab_add_div(struct isl_tab *tab, __isl_keep isl_vec *div,
 
 	isl_assert(tab->mat->ctx, tab->bmap, return -1);
 
-	for (i = 0; i < tab->n_var; ++i) {
-		if (isl_int_is_neg(div->el[2 + i]))
-			break;
-		if (isl_int_is_zero(div->el[2 + i]))
-			continue;
-		if (!tab->var[i].is_nonneg)
-			break;
-	}
-	nonneg = i == tab->n_var && !isl_int_is_neg(div->el[1]);
+	nonneg = div_is_nonneg(tab, div);
 
 	if (isl_tab_extend_cons(tab, 3) < 0)
 		return -1;
@@ -2099,8 +2193,8 @@ int isl_tab_add_div(struct isl_tab *tab, __isl_keep isl_vec *div,
 	if (nonneg)
 		tab->var[r].is_nonneg = 1;
 
-	tab->bmap = isl_basic_map_extend_dim(tab->bmap,
-		isl_basic_map_get_dim(tab->bmap), 1, 0, 2);
+	tab->bmap = isl_basic_map_extend_space(tab->bmap,
+		isl_basic_map_get_space(tab->bmap), 1, 0, 2);
 	k = isl_basic_map_alloc_div(tab->bmap);
 	if (k < 0)
 		return -1;
@@ -2114,7 +2208,13 @@ int isl_tab_add_div(struct isl_tab *tab, __isl_keep isl_vec *div,
 	return r;
 }
 
-struct isl_tab *isl_tab_from_basic_map(struct isl_basic_map *bmap)
+/* If "track" is set, then we want to keep track of all constraints in tab
+ * in its bmap field.  This field is initialized from a copy of "bmap",
+ * so we need to make sure that all constraints in "bmap" also appear
+ * in the constructed tab.
+ */
+__isl_give struct isl_tab *isl_tab_from_basic_map(
+	__isl_keep isl_basic_map *bmap, int track)
 {
 	int i;
 	struct isl_tab *tab;
@@ -2126,11 +2226,12 @@ struct isl_tab *isl_tab_from_basic_map(struct isl_basic_map *bmap)
 			    isl_basic_map_total_dim(bmap), 0);
 	if (!tab)
 		return NULL;
+	tab->preserve = track;
 	tab->rational = ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL);
 	if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY)) {
 		if (isl_tab_mark_empty(tab) < 0)
 			goto error;
-		return tab;
+		goto done;
 	}
 	for (i = 0; i < bmap->n_eq; ++i) {
 		tab = add_eq(tab, bmap->eq[i]);
@@ -2141,17 +2242,21 @@ struct isl_tab *isl_tab_from_basic_map(struct isl_basic_map *bmap)
 		if (isl_tab_add_ineq(tab, bmap->ineq[i]) < 0)
 			goto error;
 		if (tab->empty)
-			return tab;
+			goto done;
 	}
+done:
+	if (track && isl_tab_track_bmap(tab, isl_basic_map_copy(bmap)) < 0)
+		goto error;
 	return tab;
 error:
 	isl_tab_free(tab);
 	return NULL;
 }
 
-struct isl_tab *isl_tab_from_basic_set(struct isl_basic_set *bset)
+__isl_give struct isl_tab *isl_tab_from_basic_set(
+	__isl_keep isl_basic_set *bset, int track)
 {
-	return isl_tab_from_basic_map((struct isl_basic_map *)bset);
+	return isl_tab_from_basic_map(bset, track);
 }
 
 /* Construct a tableau corresponding to the recession cone of "bset".
@@ -2460,6 +2565,13 @@ struct isl_tab *isl_tab_relax(struct isl_tab *tab, int con)
 
 	var = &tab->con[con];
 
+	if (var->is_row && (var->index < 0 || var->index < tab->n_redundant))
+		isl_die(tab->mat->ctx, isl_error_invalid,
+			"cannot relax redundant constraint", goto error);
+	if (!var->is_row && (var->index < 0 || var->index < tab->n_dead))
+		isl_die(tab->mat->ctx, isl_error_invalid,
+			"cannot relax dead constraint", goto error);
+
 	if (!var->is_row && !max_is_manifestly_unbounded(tab, var))
 		if (to_row(tab, var, 1) < 0)
 			goto error;
@@ -2493,6 +2605,29 @@ error:
 	return NULL;
 }
 
+/* Remove the sign constraint from constraint "con".
+ *
+ * If the constraint variable was originally marked non-negative,
+ * then we make sure we mark it non-negative again during rollback.
+ */
+int isl_tab_unrestrict(struct isl_tab *tab, int con)
+{
+	struct isl_tab_var *var;
+
+	if (!tab)
+		return -1;
+
+	var = &tab->con[con];
+	if (!var->is_nonneg)
+		return 0;
+
+	var->is_nonneg = 0;
+	if (isl_tab_push_var(tab, isl_tab_undo_unrestrict, var) < 0)
+		return -1;
+
+	return 0;
+}
+
 int isl_tab_select_facet(struct isl_tab *tab, int con)
 {
 	if (!tab)
@@ -2503,7 +2638,6 @@ int isl_tab_select_facet(struct isl_tab *tab, int con)
 
 static int may_be_equality(struct isl_tab *tab, int row)
 {
-	unsigned off = 2 + tab->M;
 	return tab->rational ? isl_int_is_zero(tab->mat->row[row][1])
 			     : isl_int_lt(tab->mat->row[row][1],
 					    tab->mat->row[row][0]);
@@ -2595,6 +2729,106 @@ int isl_tab_detect_implicit_equalities(struct isl_tab *tab)
 	return 0;
 }
 
+/* Update the element of row_var or col_var that corresponds to
+ * constraint tab->con[i] to a move from position "old" to position "i".
+ */
+static int update_con_after_move(struct isl_tab *tab, int i, int old)
+{
+	int *p;
+	int index;
+
+	index = tab->con[i].index;
+	if (index == -1)
+		return 0;
+	p = tab->con[i].is_row ? tab->row_var : tab->col_var;
+	if (p[index] != ~old)
+		isl_die(tab->mat->ctx, isl_error_internal,
+			"broken internal state", return -1);
+	p[index] = ~i;
+
+	return 0;
+}
+
+/* Rotate the "n" constraints starting at "first" to the right,
+ * putting the last constraint in the position of the first constraint.
+ */
+static int rotate_constraints(struct isl_tab *tab, int first, int n)
+{
+	int i, last;
+	struct isl_tab_var var;
+
+	if (n <= 1)
+		return 0;
+
+	last = first + n - 1;
+	var = tab->con[last];
+	for (i = last; i > first; --i) {
+		tab->con[i] = tab->con[i - 1];
+		if (update_con_after_move(tab, i, i - 1) < 0)
+			return -1;
+	}
+	tab->con[first] = var;
+	if (update_con_after_move(tab, first, last) < 0)
+		return -1;
+
+	return 0;
+}
+
+/* Make the equalities that are implicit in "bmap" but that have been
+ * detected in the corresponding "tab" explicit in "bmap" and update
+ * "tab" to reflect the new order of the constraints.
+ *
+ * In particular, if inequality i is an implicit equality then
+ * isl_basic_map_inequality_to_equality will move the inequality
+ * in front of the other equality and it will move the last inequality
+ * in the position of inequality i.
+ * In the tableau, the inequalities of "bmap" are stored after the equalities
+ * and so the original order
+ *
+ *		E E E E E A A A I B B B B L
+ *
+ * is changed into
+ *
+ *		I E E E E E A A A L B B B B
+ *
+ * where I is the implicit equality, the E are equalities,
+ * the A inequalities before I, the B inequalities after I and
+ * L the last inequality.
+ * We therefore need to rotate to the right two sets of constraints,
+ * those up to and including I and those after I.
+ *
+ * If "tab" contains any constraints that are not in "bmap" then they
+ * appear after those in "bmap" and they should be left untouched.
+ *
+ * Note that this function leaves "bmap" in a temporary state
+ * as it does not call isl_basic_map_gauss.  Calling this function
+ * is the responsibility of the caller.
+ */
+__isl_give isl_basic_map *isl_tab_make_equalities_explicit(struct isl_tab *tab,
+	__isl_take isl_basic_map *bmap)
+{
+	int i;
+
+	if (!tab || !bmap)
+		return isl_basic_map_free(bmap);
+	if (tab->empty)
+		return bmap;
+
+	for (i = bmap->n_ineq - 1; i >= 0; --i) {
+		if (!isl_tab_is_equality(tab, bmap->n_eq + i))
+			continue;
+		isl_basic_map_inequality_to_equality(bmap, i);
+		if (rotate_constraints(tab, 0, tab->n_eq + i + 1) < 0)
+			return isl_basic_map_free(bmap);
+		if (rotate_constraints(tab, tab->n_eq + i + 1,
+					bmap->n_ineq - i) < 0)
+			return isl_basic_map_free(bmap);
+		tab->n_eq++;
+	}
+
+	return bmap;
+}
+
 static int con_is_redundant(struct isl_tab *tab, struct isl_tab_var *var)
 {
 	if (!tab)
@@ -2708,16 +2942,17 @@ int isl_tab_is_equality(struct isl_tab *tab, int con)
 
 	off = 2 + tab->M;
 	return isl_int_is_zero(tab->mat->row[row][1]) &&
-		isl_seq_first_non_zero(tab->mat->row[row] + 2 + tab->n_dead,
+		(!tab->M || isl_int_is_zero(tab->mat->row[row][2])) &&
+		isl_seq_first_non_zero(tab->mat->row[row] + off + tab->n_dead,
 					tab->n_col - tab->n_dead) == -1;
 }
 
-/* Return the minimial value of the affine expression "f" with denominator
+/* Return the minimal value of the affine expression "f" with denominator
  * "denom" in *opt, *opt_denom, assuming the tableau is not empty and
  * the expression cannot attain arbitrarily small values.
  * If opt_denom is NULL, then *opt is rounded up to the nearest integer.
  * The return value reflects the nature of the result (empty, unbounded,
- * minmimal value returned in *opt).
+ * minimal value returned in *opt).
  */
 enum isl_lp_result isl_tab_min(struct isl_tab *tab,
 	isl_int *f, isl_int denom, isl_int *opt, isl_int *opt_denom,
@@ -2728,6 +2963,9 @@ enum isl_lp_result isl_tab_min(struct isl_tab *tab,
 	struct isl_tab_var *var;
 	struct isl_tab_undo *snap;
 
+	if (!tab)
+		return isl_lp_error;
+
 	if (tab->empty)
 		return isl_lp_empty;
 
@@ -2736,8 +2974,6 @@ enum isl_lp_result isl_tab_min(struct isl_tab *tab,
 	if (r < 0)
 		return isl_lp_error;
 	var = &tab->con[r];
-	isl_int_mul(tab->mat->row[var->index][0],
-		    tab->mat->row[var->index][0], denom);
 	for (;;) {
 		int row, col;
 		find_pivot(tab, var, var, -1, &row, &col);
@@ -2750,6 +2986,8 @@ enum isl_lp_result isl_tab_min(struct isl_tab *tab,
 		if (isl_tab_pivot(tab, row, col) < 0)
 			return isl_lp_error;
 	}
+	isl_int_mul(tab->mat->row[var->index][0],
+		    tab->mat->row[var->index][0], denom);
 	if (ISL_FL_ISSET(flags, ISL_TAB_SAVE_DUAL)) {
 		int i;
 
@@ -2841,11 +3079,26 @@ static int unrelax(struct isl_tab *tab, struct isl_tab_var *var)
 	return 0;
 }
 
+/* Undo the operation performed by isl_tab_unrestrict.
+ *
+ * In particular, mark the variable as being non-negative and make
+ * sure the sample value respects this constraint.
+ */
+static int ununrestrict(struct isl_tab *tab, struct isl_tab_var *var)
+{
+	var->is_nonneg = 1;
+
+	if (var->is_row && restore_row(tab, var) < -1)
+		return -1;
+
+	return 0;
+}
+
 static int perform_undo_var(struct isl_tab *tab, struct isl_tab_undo *undo) WARN_UNUSED;
 static int perform_undo_var(struct isl_tab *tab, struct isl_tab_undo *undo)
 {
 	struct isl_tab_var *var = var_from_index(tab, undo->u.var_index);
-	switch(undo->type) {
+	switch (undo->type) {
 	case isl_tab_undo_nonneg:
 		var->is_nonneg = 0;
 		break;
@@ -2883,6 +3136,12 @@ static int perform_undo_var(struct isl_tab *tab, struct isl_tab_undo *undo)
 		break;
 	case isl_tab_undo_relax:
 		return unrelax(tab, var);
+	case isl_tab_undo_unrestrict:
+		return ununrestrict(tab, var);
+	default:
+		isl_die(tab->mat->ctx, isl_error_internal,
+			"perform_undo_var called on invalid undo record",
+			return -1);
 	}
 
 	return 0;
@@ -2938,11 +3197,9 @@ static int restore_basis(struct isl_tab *tab, int *col_var)
 	}
 
 	free(extra);
-	free(col_var);
 	return 0;
 error:
 	free(extra);
-	free(col_var);
 	return -1;
 }
 
@@ -2981,6 +3238,7 @@ static int perform_undo(struct isl_tab *tab, struct isl_tab_undo *undo)
 	case isl_tab_undo_zero:
 	case isl_tab_undo_allocate:
 	case isl_tab_undo_relax:
+	case isl_tab_undo_unrestrict:
 		return perform_undo_var(tab, undo);
 	case isl_tab_undo_bmap_eq:
 		return isl_basic_map_free_equality(tab->bmap, 1);
@@ -3026,11 +3284,12 @@ int isl_tab_rollback(struct isl_tab *tab, struct isl_tab_undo *snap)
 		if (undo == snap)
 			break;
 		if (perform_undo(tab, undo) < 0) {
+			tab->top = undo;
 			free_undo(tab);
 			tab->in_undo = 0;
 			return -1;
 		}
-		free(undo);
+		free_undo_record(undo);
 	}
 	tab->in_undo = 0;
 	tab->top = undo;
@@ -3045,9 +3304,9 @@ int isl_tab_rollback(struct isl_tab *tab, struct isl_tab_undo *snap)
  * In particular, if the row has been reduced to the constant -1,
  * then we know the inequality is adjacent (but opposite) to
  * an equality in the tableau.
- * If the row has been reduced to r = -1 -r', with r' an inequality
- * of the tableau, then the inequality is adjacent (but opposite)
- * to the inequality r'.
+ * If the row has been reduced to r = c*(-1 -r'), with r' an inequality
+ * of the tableau and c a positive constant, then the inequality
+ * is adjacent (but opposite) to the inequality r'.
  */
 static enum isl_ineq_type separation_type(struct isl_tab *tab, unsigned row)
 {
@@ -3059,15 +3318,18 @@ static enum isl_ineq_type separation_type(struct isl_tab *tab, unsigned row)
 
 	if (!isl_int_is_one(tab->mat->row[row][0]))
 		return isl_ineq_separate;
-	if (!isl_int_is_negone(tab->mat->row[row][1]))
-		return isl_ineq_separate;
 
 	pos = isl_seq_first_non_zero(tab->mat->row[row] + off + tab->n_dead,
 					tab->n_col - tab->n_dead);
-	if (pos == -1)
-		return isl_ineq_adj_eq;
+	if (pos == -1) {
+		if (isl_int_is_negone(tab->mat->row[row][1]))
+			return isl_ineq_adj_eq;
+		else
+			return isl_ineq_separate;
+	}
 
-	if (!isl_int_is_negone(tab->mat->row[row][off + tab->n_dead + pos]))
+	if (!isl_int_eq(tab->mat->row[row][1],
+			tab->mat->row[row][off + tab->n_dead + pos]))
 		return isl_ineq_separate;
 
 	pos = isl_seq_first_non_zero(
@@ -3137,12 +3399,21 @@ error:
 
 int isl_tab_track_bmap(struct isl_tab *tab, __isl_take isl_basic_map *bmap)
 {
+	bmap = isl_basic_map_cow(bmap);
 	if (!tab || !bmap)
 		goto error;
 
-	isl_assert(tab->mat->ctx, tab->n_eq == bmap->n_eq, return -1);
+	if (tab->empty) {
+		bmap = isl_basic_map_set_to_empty(bmap);
+		if (!bmap)
+			goto error;
+		tab->bmap = bmap;
+		return 0;
+	}
+
+	isl_assert(tab->mat->ctx, tab->n_eq == bmap->n_eq, goto error);
 	isl_assert(tab->mat->ctx,
-		    tab->n_con == bmap->n_eq + bmap->n_ineq, return -1);
+		    tab->n_con == bmap->n_eq + bmap->n_ineq, goto error);
 
 	tab->bmap = bmap;
 
@@ -3165,7 +3436,8 @@ __isl_keep isl_basic_set *isl_tab_peek_bset(struct isl_tab *tab)
 	return (isl_basic_set *)tab->bmap;
 }
 
-void isl_tab_dump(struct isl_tab *tab, FILE *out, int indent)
+static void isl_tab_print_internal(__isl_keep struct isl_tab *tab,
+	FILE *out, int indent)
 {
 	unsigned r, c;
 	int i;
@@ -3234,9 +3506,14 @@ void isl_tab_dump(struct isl_tab *tab, FILE *out, int indent)
 	tab->mat->n_row = tab->n_row;
 	c = tab->mat->n_col;
 	tab->mat->n_col = 2 + tab->M + tab->n_col;
-	isl_mat_dump(tab->mat, out, indent);
+	isl_mat_print_internal(tab->mat, out, indent);
 	tab->mat->n_row = r;
 	tab->mat->n_col = c;
 	if (tab->bmap)
-		isl_basic_map_dump(tab->bmap, out, indent);
+		isl_basic_map_print_internal(tab->bmap, out, indent);
+}
+
+void isl_tab_dump(__isl_keep struct isl_tab *tab)
+{
+	isl_tab_print_internal(tab, stderr, 0);
 }