X-Git-Url: http://review.tizen.org/git/?a=blobdiff_plain;f=isl_tab.c;h=e4cc386679d8760504af441f0741f9241120f479;hb=19596bc4e5cd282b2e75d17077b1aaaeacbfd6f9;hp=b697024357d42a2aee1a3b24f92eb1be626156ca;hpb=cca53b75cba3b0f730f18bfec8b912eb236eaf4f;p=platform%2Fupstream%2Fisl.git

diff --git a/isl_tab.c b/isl_tab.c
index b697024..e4cc386 100644
--- a/isl_tab.c
+++ b/isl_tab.c
@@ -1,7 +1,20 @@
-#include "isl_mat.h"
+/*
+ * Copyright 2008-2009 Katholieke Universiteit Leuven
+ * Copyright 2013      Ecole Normale Superieure
+ *
+ * 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_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
@@ -55,27 +68,41 @@ struct isl_tab *isl_tab_alloc(struct isl_ctx *ctx,
 	tab->n_div = 0;
 	tab->n_dead = 0;
 	tab->n_redundant = 0;
+	tab->strict_redundant = 0;
 	tab->need_undo = 0;
 	tab->rational = 0;
 	tab->empty = 0;
 	tab->in_undo = 0;
 	tab->M = M;
+	tab->cone = 0;
 	tab->bottom.type = isl_tab_undo_bottom;
 	tab->bottom.next = NULL;
 	tab->top = &tab->bottom;
+
+	tab->n_zero = 0;
+	tab->n_unbounded = 0;
+	tab->basis = NULL;
+
 	return tab;
 error:
 	isl_tab_free(tab);
 	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;
 
@@ -153,13 +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;
 }
@@ -171,13 +209,15 @@ void isl_tab_free(struct isl_tab *tab)
 	free_undo(tab);
 	isl_mat_free(tab->mat);
 	isl_vec_free(tab->dual);
-	isl_basic_set_free(tab->bset);
+	isl_basic_map_free(tab->bmap);
 	free(tab->var);
 	free(tab->con);
 	free(tab->row_var);
 	free(tab->col_var);
 	free(tab->row_sign);
 	isl_mat_free(tab->samples);
+	free(tab->sample_index);
+	isl_mat_free(tab->basis);
 	free(tab);
 }
 
@@ -191,34 +231,34 @@ struct isl_tab *isl_tab_dup(struct isl_tab *tab)
 		return NULL;
 
 	off = 2 + tab->M;
-	dup = isl_calloc_type(tab->ctx, struct isl_tab);
+	dup = isl_calloc_type(tab->mat->ctx, struct isl_tab);
 	if (!dup)
 		return NULL;
 	dup->mat = isl_mat_dup(tab->mat);
 	if (!dup->mat)
 		goto error;
-	dup->var = isl_alloc_array(tab->ctx, struct isl_tab_var, tab->max_var);
+	dup->var = isl_alloc_array(tab->mat->ctx, struct isl_tab_var, tab->max_var);
 	if (!dup->var)
 		goto error;
 	for (i = 0; i < tab->n_var; ++i)
 		dup->var[i] = tab->var[i];
-	dup->con = isl_alloc_array(tab->ctx, struct isl_tab_var, tab->max_con);
+	dup->con = isl_alloc_array(tab->mat->ctx, struct isl_tab_var, tab->max_con);
 	if (!dup->con)
 		goto error;
 	for (i = 0; i < tab->n_con; ++i)
 		dup->con[i] = tab->con[i];
-	dup->col_var = isl_alloc_array(tab->ctx, int, tab->mat->n_col - off);
+	dup->col_var = isl_alloc_array(tab->mat->ctx, int, tab->mat->n_col - off);
 	if (!dup->col_var)
 		goto error;
 	for (i = 0; i < tab->n_col; ++i)
 		dup->col_var[i] = tab->col_var[i];
-	dup->row_var = isl_alloc_array(tab->ctx, int, tab->mat->n_row);
+	dup->row_var = isl_alloc_array(tab->mat->ctx, int, tab->mat->n_row);
 	if (!dup->row_var)
 		goto error;
 	for (i = 0; i < tab->n_row; ++i)
 		dup->row_var[i] = tab->row_var[i];
 	if (tab->row_sign) {
-		dup->row_sign = isl_alloc_array(tab->ctx, enum isl_tab_row_sign,
+		dup->row_sign = isl_alloc_array(tab->mat->ctx, enum isl_tab_row_sign,
 						tab->mat->n_row);
 		if (!dup->row_sign)
 			goto error;
@@ -229,6 +269,10 @@ struct isl_tab *isl_tab_dup(struct isl_tab *tab)
 		dup->samples = isl_mat_dup(tab->samples);
 		if (!dup->samples)
 			goto error;
+		dup->sample_index = isl_alloc_array(tab->mat->ctx, int,
+							tab->samples->n_row);
+		if (!dup->sample_index)
+			goto error;
 		dup->n_sample = tab->n_sample;
 		dup->n_outside = tab->n_outside;
 	}
@@ -245,12 +289,19 @@ struct isl_tab *isl_tab_dup(struct isl_tab *tab)
 	dup->n_redundant = tab->n_redundant;
 	dup->rational = tab->rational;
 	dup->empty = tab->empty;
+	dup->strict_redundant = 0;
 	dup->need_undo = 0;
 	dup->in_undo = 0;
 	dup->M = tab->M;
+	tab->cone = tab->cone;
 	dup->bottom.type = isl_tab_undo_bottom;
 	dup->bottom.next = NULL;
 	dup->top = &dup->bottom;
+
+	dup->n_zero = tab->n_zero;
+	dup->n_unbounded = tab->n_unbounded;
+	dup->basis = isl_mat_dup(tab->basis);
+
 	return dup;
 error:
 	isl_tab_free(dup);
@@ -281,6 +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) {
@@ -391,6 +444,7 @@ struct isl_tab *isl_tab_product(struct isl_tab *tab1, struct isl_tab *tab2)
 
 	isl_assert(tab1->mat->ctx, tab1->M == tab2->M, return NULL);
 	isl_assert(tab1->mat->ctx, tab1->rational == tab2->rational, return NULL);
+	isl_assert(tab1->mat->ctx, tab1->cone == tab2->cone, return NULL);
 	isl_assert(tab1->mat->ctx, !tab1->row_sign, return NULL);
 	isl_assert(tab1->mat->ctx, !tab2->row_sign, return NULL);
 	isl_assert(tab1->mat->ctx, tab1->n_param == 0, return NULL);
@@ -474,6 +528,7 @@ struct isl_tab *isl_tab_product(struct isl_tab *tab1, struct isl_tab *tab2)
 		prod->row_var[pos] = t;
 	}
 	prod->samples = NULL;
+	prod->sample_index = NULL;
 	prod->n_row = tab1->n_row + tab2->n_row;
 	prod->n_con = tab1->n_con + tab2->n_con;
 	prod->n_eq = 0;
@@ -487,12 +542,19 @@ struct isl_tab *isl_tab_product(struct isl_tab *tab1, struct isl_tab *tab2)
 	prod->n_redundant = tab1->n_redundant + tab2->n_redundant;
 	prod->rational = tab1->rational;
 	prod->empty = tab1->empty || tab2->empty;
+	prod->strict_redundant = tab1->strict_redundant || tab2->strict_redundant;
 	prod->need_undo = 0;
 	prod->in_undo = 0;
 	prod->M = tab1->M;
+	prod->cone = tab1->cone;
 	prod->bottom.type = isl_tab_undo_bottom;
 	prod->bottom.next = NULL;
 	prod->top = &prod->bottom;
+
+	prod->n_zero = 0;
+	prod->n_unbounded = 0;
+	prod->basis = NULL;
+
 	return prod;
 error:
 	isl_tab_free(prod);
@@ -676,7 +738,7 @@ static void find_pivot(struct isl_tab *tab,
  * This means
  *	- it represents an inequality or a variable
  *	- that is the sum of a non-negative sample value and a positive
- *	  combination of zero or more non-negative variables.
+ *	  combination of zero or more non-negative constraints.
  */
 int isl_tab_row_is_redundant(struct isl_tab *tab, int row)
 {
@@ -688,12 +750,16 @@ int isl_tab_row_is_redundant(struct isl_tab *tab, int row)
 
 	if (isl_int_is_neg(tab->mat->row[row][1]))
 		return 0;
+	if (tab->strict_redundant && isl_int_is_zero(tab->mat->row[row][1]))
+		return 0;
 	if (tab->M && isl_int_is_neg(tab->mat->row[row][2]))
 		return 0;
 
 	for (i = tab->n_dead; i < tab->n_col; ++i) {
 		if (isl_int_is_zero(tab->mat->row[row][off + i]))
 			continue;
+		if (tab->col_var[i] >= 0)
+			return 0;
 		if (isl_int_is_neg(tab->mat->row[row][off + i]))
 			return 0;
 		if (!var_from_col(tab, i)->is_nonneg)
@@ -705,6 +771,8 @@ int isl_tab_row_is_redundant(struct isl_tab *tab, int row)
 static void swap_rows(struct isl_tab *tab, int row1, int row2)
 {
 	int t;
+	enum isl_tab_row_sign s;
+
 	t = tab->row_var[row1];
 	tab->row_var[row1] = tab->row_var[row2];
 	tab->row_var[row2] = t;
@@ -714,32 +782,35 @@ static void swap_rows(struct isl_tab *tab, int row1, int row2)
 
 	if (!tab->row_sign)
 		return;
-	t = tab->row_sign[row1];
+	s = tab->row_sign[row1];
 	tab->row_sign[row1] = tab->row_sign[row2];
-	tab->row_sign[row2] = t;
+	tab->row_sign[row2] = s;
 }
 
-static void push_union(struct isl_tab *tab,
+static int push_union(struct isl_tab *tab,
+	enum isl_tab_undo_type type, union isl_tab_undo_val u) WARN_UNUSED;
+static int push_union(struct isl_tab *tab,
 	enum isl_tab_undo_type type, union isl_tab_undo_val u)
 {
 	struct isl_tab_undo *undo;
 
+	if (!tab)
+		return -1;
 	if (!tab->need_undo)
-		return;
+		return 0;
 
 	undo = isl_alloc_type(tab->mat->ctx, struct isl_tab_undo);
-	if (!undo) {
-		free_undo(tab);
-		tab->top = NULL;
-		return;
-	}
+	if (!undo)
+		return -1;
 	undo->type = type;
 	undo->u = u;
 	undo->next = tab->top;
 	tab->top = undo;
+
+	return 0;
 }
 
-void isl_tab_push_var(struct isl_tab *tab,
+int isl_tab_push_var(struct isl_tab *tab,
 	enum isl_tab_undo_type type, struct isl_tab_var *var)
 {
 	union isl_tab_undo_val u;
@@ -747,32 +818,117 @@ void isl_tab_push_var(struct isl_tab *tab,
 		u.var_index = tab->row_var[var->index];
 	else
 		u.var_index = tab->col_var[var->index];
-	push_union(tab, type, u);
+	return push_union(tab, type, u);
 }
 
-void isl_tab_push(struct isl_tab *tab, enum isl_tab_undo_type type)
+int isl_tab_push(struct isl_tab *tab, enum isl_tab_undo_type type)
 {
 	union isl_tab_undo_val u = { 0 };
-	push_union(tab, type, u);
+	return push_union(tab, type, u);
 }
 
 /* Push a record on the undo stack describing the current basic
  * variables, so that the this state can be restored during rollback.
  */
-void isl_tab_push_basis(struct isl_tab *tab)
+int isl_tab_push_basis(struct isl_tab *tab)
 {
 	int i;
 	union isl_tab_undo_val u;
 
 	u.col_var = isl_alloc_array(tab->mat->ctx, int, tab->n_col);
-	if (!u.col_var) {
-		free_undo(tab);
-		tab->top = NULL;
-		return;
-	}
+	if (!u.col_var)
+		return -1;
 	for (i = 0; i < tab->n_col; ++i)
 		u.col_var[i] = tab->col_var[i];
-	push_union(tab, isl_tab_undo_saved_basis, u);
+	return push_union(tab, isl_tab_undo_saved_basis, u);
+}
+
+int isl_tab_push_callback(struct isl_tab *tab, struct isl_tab_callback *callback)
+{
+	union isl_tab_undo_val u;
+	u.callback = callback;
+	return push_union(tab, isl_tab_undo_callback, u);
+}
+
+struct isl_tab *isl_tab_init_samples(struct isl_tab *tab)
+{
+	if (!tab)
+		return NULL;
+
+	tab->n_sample = 0;
+	tab->n_outside = 0;
+	tab->samples = isl_mat_alloc(tab->mat->ctx, 1, 1 + tab->n_var);
+	if (!tab->samples)
+		goto error;
+	tab->sample_index = isl_alloc_array(tab->mat->ctx, int, 1);
+	if (!tab->sample_index)
+		goto error;
+	return tab;
+error:
+	isl_tab_free(tab);
+	return NULL;
+}
+
+struct isl_tab *isl_tab_add_sample(struct isl_tab *tab,
+	__isl_take isl_vec *sample)
+{
+	if (!tab || !sample)
+		goto error;
+
+	if (tab->n_sample + 1 > tab->samples->n_row) {
+		int *t = isl_realloc_array(tab->mat->ctx,
+			    tab->sample_index, int, tab->n_sample + 1);
+		if (!t)
+			goto error;
+		tab->sample_index = t;
+	}
+
+	tab->samples = isl_mat_extend(tab->samples,
+				tab->n_sample + 1, tab->samples->n_col);
+	if (!tab->samples)
+		goto error;
+
+	isl_seq_cpy(tab->samples->row[tab->n_sample], sample->el, sample->size);
+	isl_vec_free(sample);
+	tab->sample_index[tab->n_sample] = tab->n_sample;
+	tab->n_sample++;
+
+	return tab;
+error:
+	isl_vec_free(sample);
+	isl_tab_free(tab);
+	return NULL;
+}
+
+struct isl_tab *isl_tab_drop_sample(struct isl_tab *tab, int s)
+{
+	if (s != tab->n_outside) {
+		int t = tab->sample_index[tab->n_outside];
+		tab->sample_index[tab->n_outside] = tab->sample_index[s];
+		tab->sample_index[s] = t;
+		isl_mat_swap_rows(tab->samples, tab->n_outside, s);
+	}
+	tab->n_outside++;
+	if (isl_tab_push(tab, isl_tab_undo_drop_sample) < 0) {
+		isl_tab_free(tab);
+		return NULL;
+	}
+
+	return tab;
+}
+
+/* Record the current number of samples so that we can remove newer
+ * samples during a rollback.
+ */
+int isl_tab_save_samples(struct isl_tab *tab)
+{
+	union isl_tab_undo_val u;
+
+	if (!tab)
+		return -1;
+
+	u.n = tab->n_sample;
+	return push_union(tab, isl_tab_undo_saved_samples, u);
 }
 
 /* Mark row with index "row" as being redundant.
@@ -792,16 +948,16 @@ 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;
-			isl_tab_push_var(tab, isl_tab_undo_nonneg, var);
+			if (isl_tab_push_var(tab, isl_tab_undo_nonneg, var) < 0)
+				return -1;
 		}
 		if (row != tab->n_redundant)
 			swap_rows(tab, row, tab->n_redundant);
-		isl_tab_push_var(tab, isl_tab_undo_redundant, var);
 		tab->n_redundant++;
-		return 0;
+		return isl_tab_push_var(tab, isl_tab_undo_redundant, var);
 	} else {
 		if (row != tab->n_row - 1)
 			swap_rows(tab, row, tab->n_row - 1);
@@ -811,12 +967,35 @@ int isl_tab_mark_redundant(struct isl_tab *tab, int row)
 	}
 }
 
-struct isl_tab *isl_tab_mark_empty(struct isl_tab *tab)
+int isl_tab_mark_empty(struct isl_tab *tab)
 {
+	if (!tab)
+		return -1;
 	if (!tab->empty && tab->need_undo)
-		isl_tab_push(tab, isl_tab_undo_empty);
+		if (isl_tab_push(tab, isl_tab_undo_empty) < 0)
+			return -1;
 	tab->empty = 1;
-	return tab;
+	return 0;
+}
+
+int isl_tab_freeze_constraint(struct isl_tab *tab, int con)
+{
+	struct isl_tab_var *var;
+
+	if (!tab)
+		return -1;
+
+	var = &tab->con[con];
+	if (var->frozen)
+		return 0;
+	if (var->index < 0)
+		return 0;
+	var->frozen = 1;
+
+	if (tab->need_undo)
+		return isl_tab_push_var(tab, isl_tab_undo_freeze, var);
+
+	return 0;
 }
 
 /* Update the rows signs after a pivot of "row" and "col", with "row_sgn"
@@ -917,7 +1096,7 @@ static void update_row_sign(struct isl_tab *tab, int row, int col, int row_sgn)
  * s(n_rc)d_r n_jc/(|n_rc| d_j)	(n_ji |n_rc| - s(n_rc)n_jc n_ri)/(|n_rc| d_j)
  *
  */
-void isl_tab_pivot(struct isl_tab *tab, int row, int col)
+int isl_tab_pivot(struct isl_tab *tab, int row, int col)
 {
 	int i, j;
 	int sgn;
@@ -926,6 +1105,11 @@ void 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) {
@@ -969,15 +1153,20 @@ void isl_tab_pivot(struct isl_tab *tab, int row, int col)
 	var->index = col;
 	update_row_sign(tab, row, col, sgn);
 	if (tab->in_undo)
-		return;
+		return 0;
 	for (i = tab->n_redundant; i < tab->n_row; ++i) {
 		if (isl_int_is_zero(mat->row[i][off + col]))
 			continue;
 		if (!isl_tab_var_from_row(tab, i)->frozen &&
-		    isl_tab_row_is_redundant(tab, i))
-			if (isl_tab_mark_redundant(tab, i))
+		    isl_tab_row_is_redundant(tab, i)) {
+			int redo = isl_tab_mark_redundant(tab, i);
+			if (redo < 0)
+				return -1;
+			if (redo)
 				--i;
+		}
 	}
+	return 0;
 }
 
 /* If "var" represents a column variable, then pivot is up (sgn > 0)
@@ -986,37 +1175,52 @@ void isl_tab_pivot(struct isl_tab *tab, int row, int col)
  * If sgn = 0, then the variable is unbounded in both directions,
  * and we pivot with any row we can find.
  */
-static void to_row(struct isl_tab *tab, struct isl_tab_var *var, int sign)
+static int to_row(struct isl_tab *tab, struct isl_tab_var *var, int sign) WARN_UNUSED;
+static int to_row(struct isl_tab *tab, struct isl_tab_var *var, int sign)
 {
 	int r;
 	unsigned off = 2 + tab->M;
 
 	if (var->is_row)
-		return;
+		return 0;
 
 	if (sign == 0) {
 		for (r = tab->n_redundant; r < tab->n_row; ++r)
 			if (!isl_int_is_zero(tab->mat->row[r][off+var->index]))
 				break;
-		isl_assert(tab->mat->ctx, r < tab->n_row, return);
+		isl_assert(tab->mat->ctx, r < tab->n_row, return -1);
 	} else {
 		r = pivot_row(tab, NULL, sign, var->index);
-		isl_assert(tab->mat->ctx, r >= 0, return);
+		isl_assert(tab->mat->ctx, r >= 0, return -1);
 	}
 
-	isl_tab_pivot(tab, r, var->index);
+	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;
 
 	if (tab->empty)
 		return;
-	for (i = 0; i < tab->n_row; ++i) {
-		if (!isl_tab_var_from_row(tab, i)->is_nonneg)
+	for (i = tab->n_redundant; i < tab->n_row; ++i) {
+		struct isl_tab_var *var;
+		var = isl_tab_var_from_row(tab, i);
+		if (!var->is_nonneg)
 			continue;
-		assert(!isl_int_is_neg(tab->mat->row[i][1]));
+		if (tab->M) {
+			isl_assert(tab->mat->ctx,
+				!isl_int_is_neg(tab->mat->row[i][2]), abort());
+			if (isl_int_is_pos(tab->mat->row[i][2]))
+				continue;
+		}
+		isl_assert(tab->mat->ctx, !isl_int_is_neg(tab->mat->row[i][1]),
+				abort());
 	}
 }
 
@@ -1037,18 +1241,34 @@ static int sign_of_max(struct isl_tab *tab, struct isl_tab_var *var)
 
 	if (max_is_manifestly_unbounded(tab, var))
 		return 1;
-	to_row(tab, var, 1);
+	if (to_row(tab, var, 1) < 0)
+		return -2;
 	while (!isl_int_is_pos(tab->mat->row[var->index][1])) {
 		find_pivot(tab, var, var, 1, &row, &col);
 		if (row == -1)
 			return isl_int_sgn(tab->mat->row[var->index][1]);
-		isl_tab_pivot(tab, row, col);
+		if (isl_tab_pivot(tab, row, col) < 0)
+			return -2;
 		if (!var->is_row) /* manifestly unbounded */
 			return 1;
 	}
 	return 1;
 }
 
+int isl_tab_sign_of_max(struct isl_tab *tab, int con)
+{
+	struct isl_tab_var *var;
+
+	if (!tab)
+		return -2;
+
+	var = &tab->con[con];
+	isl_assert(tab->mat->ctx, !var->is_redundant, return -2);
+	isl_assert(tab->mat->ctx, !var->is_zero, return -2);
+
+	return sign_of_max(tab, var);
+}
+
 static int row_is_neg(struct isl_tab *tab, int row)
 {
 	if (!tab->M)
@@ -1083,7 +1303,8 @@ static int restore_row(struct isl_tab *tab, struct isl_tab_var *var)
 		find_pivot(tab, var, var, 1, &row, &col);
 		if (row == -1)
 			break;
-		isl_tab_pivot(tab, row, col);
+		if (isl_tab_pivot(tab, row, col) < 0)
+			return -2;
 		if (!var->is_row) /* manifestly unbounded */
 			return 1;
 	}
@@ -1105,7 +1326,8 @@ static int at_least_zero(struct isl_tab *tab, struct isl_tab_var *var)
 			break;
 		if (row == var->index) /* manifestly unbounded */
 			return 1;
-		isl_tab_pivot(tab, row, col);
+		if (isl_tab_pivot(tab, row, col) < 0)
+			return -1;
 	}
 	return !isl_int_is_neg(tab->mat->row[var->index][1]);
 }
@@ -1138,16 +1360,19 @@ static int sign_of_min(struct isl_tab *tab, struct isl_tab_var *var)
 		col = var->index;
 		row = pivot_row(tab, NULL, -1, col);
 		pivot_var = var_from_col(tab, col);
-		isl_tab_pivot(tab, row, col);
+		if (isl_tab_pivot(tab, row, col) < 0)
+			return -2;
 		if (var->is_redundant)
 			return 0;
 		if (isl_int_is_neg(tab->mat->row[var->index][1])) {
 			if (var->is_nonneg) {
 				if (!pivot_var->is_redundant &&
-				    pivot_var->index == row)
-					isl_tab_pivot(tab, row, col);
-				else
-					restore_row(tab, var);
+				    pivot_var->index == row) {
+					if (isl_tab_pivot(tab, row, col) < 0)
+						return -2;
+				} else
+					if (restore_row(tab, var) < -1)
+						return -2;
 			}
 			return -1;
 		}
@@ -1161,16 +1386,19 @@ static int sign_of_min(struct isl_tab *tab, struct isl_tab_var *var)
 		if (row == -1)
 			return isl_int_sgn(tab->mat->row[var->index][1]);
 		pivot_var = var_from_col(tab, col);
-		isl_tab_pivot(tab, row, col);
+		if (isl_tab_pivot(tab, row, col) < 0)
+			return -2;
 		if (var->is_redundant)
 			return 0;
 	}
 	if (pivot_var && var->is_nonneg) {
 		/* pivot back to non-negative value */
-		if (!pivot_var->is_redundant && pivot_var->index == row)
-			isl_tab_pivot(tab, row, col);
-		else
-			restore_row(tab, var);
+		if (!pivot_var->is_redundant && pivot_var->index == row) {
+			if (isl_tab_pivot(tab, row, col) < 0)
+				return -2;
+		} else
+			if (restore_row(tab, var) < -1)
+				return -2;
 	}
 	return -1;
 }
@@ -1192,7 +1420,8 @@ static int row_at_most_neg_one(struct isl_tab *tab, int row)
  * Return 0 otherwise.
  *
  * The sample value of "var" is assumed to be non-negative when the
- * the function is called and will be made non-negative again before
+ * the function is called.  If 1 is returned then the constraint
+ * is not redundant and the sample value is made non-negative again before
  * the function returns.
  */
 int isl_tab_min_at_most_neg_one(struct isl_tab *tab, struct isl_tab_var *var)
@@ -1206,16 +1435,19 @@ int isl_tab_min_at_most_neg_one(struct isl_tab *tab, struct isl_tab_var *var)
 		col = var->index;
 		row = pivot_row(tab, NULL, -1, col);
 		pivot_var = var_from_col(tab, col);
-		isl_tab_pivot(tab, row, col);
+		if (isl_tab_pivot(tab, row, col) < 0)
+			return -1;
 		if (var->is_redundant)
 			return 0;
 		if (row_at_most_neg_one(tab, var->index)) {
 			if (var->is_nonneg) {
 				if (!pivot_var->is_redundant &&
-				    pivot_var->index == row)
-					isl_tab_pivot(tab, row, col);
-				else
-					restore_row(tab, var);
+				    pivot_var->index == row) {
+					if (isl_tab_pivot(tab, row, col) < 0)
+						return -1;
+				} else
+					if (restore_row(tab, var) < -1)
+						return -1;
 			}
 			return 1;
 		}
@@ -1224,20 +1456,26 @@ int isl_tab_min_at_most_neg_one(struct isl_tab *tab, struct isl_tab_var *var)
 		return 0;
 	do {
 		find_pivot(tab, var, var, -1, &row, &col);
-		if (row == var->index)
+		if (row == var->index) {
+			if (restore_row(tab, var) < -1)
+				return -1;
 			return 1;
+		}
 		if (row == -1)
 			return 0;
 		pivot_var = var_from_col(tab, col);
-		isl_tab_pivot(tab, row, col);
+		if (isl_tab_pivot(tab, row, col) < 0)
+			return -1;
 		if (var->is_redundant)
 			return 0;
 	} while (!row_at_most_neg_one(tab, var->index));
 	if (var->is_nonneg) {
 		/* pivot back to non-negative value */
 		if (!pivot_var->is_redundant && pivot_var->index == row)
-			isl_tab_pivot(tab, row, col);
-		restore_row(tab, var);
+			if (isl_tab_pivot(tab, row, col) < 0)
+				return -1;
+		if (restore_row(tab, var) < -1)
+			return -1;
 	}
 	return 1;
 }
@@ -1252,7 +1490,8 @@ static int at_least_one(struct isl_tab *tab, struct isl_tab_var *var)
 
 	if (max_is_manifestly_unbounded(tab, var))
 		return 1;
-	to_row(tab, var, 1);
+	if (to_row(tab, var, 1) < 0)
+		return -1;
 	r = tab->mat->row[var->index];
 	while (isl_int_lt(r[1], r[0])) {
 		find_pivot(tab, var, var, 1, &row, &col);
@@ -1260,7 +1499,8 @@ static int at_least_one(struct isl_tab *tab, struct isl_tab_var *var)
 			return isl_int_ge(r[1], r[0]);
 		if (row == var->index) /* manifestly unbounded */
 			return 1;
-		isl_tab_pivot(tab, row, col);
+		if (isl_tab_pivot(tab, row, col) < 0)
+			return -1;
 	}
 	return 1;
 }
@@ -1293,7 +1533,9 @@ int isl_tab_kill_col(struct isl_tab *tab, int col)
 {
 	var_from_col(tab, col)->is_zero = 1;
 	if (tab->need_undo) {
-		isl_tab_push_var(tab, isl_tab_undo_zero, var_from_col(tab, col));
+		if (isl_tab_push_var(tab, isl_tab_undo_zero,
+					    var_from_col(tab, col)) < 0)
+			return -1;
 		if (col != tab->n_dead)
 			swap_cols(tab, col, tab->n_dead);
 		tab->n_dead++;
@@ -1307,6 +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
@@ -1315,25 +1594,35 @@ int isl_tab_kill_col(struct isl_tab *tab, int col)
  * then also be written as the negative sum of non-negative variables
  * and must therefore also be zero.
  */
-static void close_row(struct isl_tab *tab, struct isl_tab_var *var)
+static int close_row(struct isl_tab *tab, struct isl_tab_var *var) WARN_UNUSED;
+static int close_row(struct isl_tab *tab, struct isl_tab_var *var)
 {
 	int j;
 	struct isl_mat *mat = tab->mat;
 	unsigned off = 2 + tab->M;
 
-	isl_assert(tab->mat->ctx, var->is_nonneg, return);
+	isl_assert(tab->mat->ctx, var->is_nonneg, return -1);
 	var->is_zero = 1;
 	if (tab->need_undo)
-		isl_tab_push_var(tab, isl_tab_undo_zero, var);
+		if (isl_tab_push_var(tab, isl_tab_undo_zero, var) < 0)
+			return -1;
 	for (j = tab->n_dead; j < tab->n_col; ++j) {
+		int recheck;
 		if (isl_int_is_zero(mat->row[var->index][off + j]))
 			continue;
 		isl_assert(tab->mat->ctx,
-			isl_int_is_neg(mat->row[var->index][off + j]), return);
-		if (isl_tab_kill_col(tab, j))
+		    isl_int_is_neg(mat->row[var->index][off + j]), return -1);
+		recheck = isl_tab_kill_col(tab, j);
+		if (recheck < 0)
+			return -1;
+		if (recheck)
 			--j;
 	}
-	isl_tab_mark_redundant(tab, var->index);
+	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;
 }
 
 /* Add a constraint to the tableau and allocate a row for it.
@@ -1358,7 +1647,8 @@ int isl_tab_allocate_con(struct isl_tab *tab)
 
 	tab->n_row++;
 	tab->n_con++;
-	isl_tab_push_var(tab, isl_tab_undo_allocate, &tab->con[r]);
+	if (isl_tab_push_var(tab, isl_tab_undo_allocate, &tab->con[r]) < 0)
+		return -1;
 
 	return r;
 }
@@ -1390,7 +1680,8 @@ int isl_tab_allocate_var(struct isl_tab *tab)
 
 	tab->n_var++;
 	tab->n_col++;
-	isl_tab_push_var(tab, isl_tab_undo_allocate, &tab->var[r]);
+	if (isl_tab_push_var(tab, isl_tab_undo_allocate, &tab->var[r]) < 0)
+		return -1;
 
 	return r;
 }
@@ -1410,6 +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)
 {
@@ -1454,7 +1748,7 @@ int isl_tab_add_row(struct isl_tab *tab, isl_int *line)
 	isl_int_clear(b);
 
 	if (tab->row_sign)
-		tab->row_sign[tab->con[r].index] = 0;
+		tab->row_sign[tab->con[r].index] = isl_tab_row_unknown;
 
 	return r;
 }
@@ -1482,37 +1776,61 @@ static int drop_col(struct isl_tab *tab, int col)
 /* Add inequality "ineq" and check if it conflicts with the
  * previously added constraints or if it is obviously redundant.
  */
-struct isl_tab *isl_tab_add_ineq(struct isl_tab *tab, isl_int *ineq)
+int isl_tab_add_ineq(struct isl_tab *tab, isl_int *ineq)
 {
 	int r;
 	int sgn;
+	isl_int cst;
 
 	if (!tab)
-		return NULL;
+		return -1;
+	if (tab->bmap) {
+		struct isl_basic_map *bmap = tab->bmap;
+
+		isl_assert(tab->mat->ctx, tab->n_eq == bmap->n_eq, return -1);
+		isl_assert(tab->mat->ctx,
+			    tab->n_con == bmap->n_eq + bmap->n_ineq, return -1);
+		tab->bmap = isl_basic_map_add_ineq(tab->bmap, ineq);
+		if (isl_tab_push(tab, isl_tab_undo_bmap_ineq) < 0)
+			return -1;
+		if (!tab->bmap)
+			return -1;
+	}
+	if (tab->cone) {
+		isl_int_init(cst);
+		isl_int_swap(ineq[0], cst);
+	}
 	r = isl_tab_add_row(tab, ineq);
+	if (tab->cone) {
+		isl_int_swap(ineq[0], cst);
+		isl_int_clear(cst);
+	}
 	if (r < 0)
-		goto error;
+		return -1;
 	tab->con[r].is_nonneg = 1;
-	isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]);
+	if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0)
+		return -1;
 	if (isl_tab_row_is_redundant(tab, tab->con[r].index)) {
-		isl_tab_mark_redundant(tab, tab->con[r].index);
-		return tab;
+		if (isl_tab_mark_redundant(tab, tab->con[r].index) < 0)
+			return -1;
+		return 0;
 	}
 
 	sgn = restore_row(tab, &tab->con[r]);
+	if (sgn < -1)
+		return -1;
 	if (sgn < 0)
 		return isl_tab_mark_empty(tab);
 	if (tab->con[r].is_row && isl_tab_row_is_redundant(tab, tab->con[r].index))
-		isl_tab_mark_redundant(tab, tab->con[r].index);
-	return tab;
-error:
-	isl_tab_free(tab);
-	return NULL;
+		if (isl_tab_mark_redundant(tab, tab->con[r].index) < 0)
+			return -1;
+	return 0;
 }
 
 /* Pivot a non-negative variable down until it reaches the value zero
  * and then pivot the variable into a column position.
  */
+static int to_col(struct isl_tab *tab, struct isl_tab_var *var) WARN_UNUSED;
 static int to_col(struct isl_tab *tab, struct isl_tab_var *var)
 {
 	int i;
@@ -1525,7 +1843,8 @@ static int to_col(struct isl_tab *tab, struct isl_tab_var *var)
 	while (isl_int_is_pos(tab->mat->row[var->index][1])) {
 		find_pivot(tab, var, NULL, -1, &row, &col);
 		isl_assert(tab->mat->ctx, row != -1, return -1);
-		isl_tab_pivot(tab, row, col);
+		if (isl_tab_pivot(tab, row, col) < 0)
+			return -1;
 		if (!var->is_row)
 			return 0;
 	}
@@ -1535,7 +1854,8 @@ static int to_col(struct isl_tab *tab, struct isl_tab_var *var)
 			break;
 
 	isl_assert(tab->mat->ctx, i < tab->n_col, return -1);
-	isl_tab_pivot(tab, var->index, i);
+	if (isl_tab_pivot(tab, var->index, i) < 0)
+		return -1;
 
 	return 0;
 }
@@ -1561,8 +1881,10 @@ static struct isl_tab *add_eq(struct isl_tab *tab, isl_int *eq)
 					tab->n_col - tab->n_dead);
 	isl_assert(tab->mat->ctx, i >= 0, goto error);
 	i += tab->n_dead;
-	isl_tab_pivot(tab, r, i);
-	isl_tab_kill_col(tab, i);
+	if (isl_tab_pivot(tab, r, i) < 0)
+		goto error;
+	if (isl_tab_kill_col(tab, i) < 0)
+		goto error;
 	tab->n_eq++;
 
 	return tab;
@@ -1585,23 +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;
-		isl_tab_mark_redundant(tab, r);
-		return tab;
+		if (isl_tab_mark_redundant(tab, r) < 0)
+			return -1;
+		return 0;
 	}
 
 	if (isl_int_is_neg(tab->mat->row[r][1])) {
@@ -1611,50 +1934,88 @@ 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;
-	isl_tab_kill_col(tab, var->index);
+	if (isl_tab_kill_col(tab, var->index) < 0)
+		return -1;
 
-	return tab;
-error:
-	isl_tab_free(tab);
-	return NULL;
+	return 0;
+}
+
+static int add_zero_row(struct isl_tab *tab)
+{
+	int r;
+	isl_int *row;
+
+	r = isl_tab_allocate_con(tab);
+	if (r < 0)
+		return -1;
+
+	row = tab->mat->row[tab->con[r].index];
+	isl_seq_clr(row + 1, 1 + tab->M + tab->n_col);
+	isl_int_set_si(row[0], 1);
+
+	return r;
 }
 
 /* Add equality "eq" and check if it conflicts with the
  * previously added constraints or if it is obviously redundant.
  */
-struct isl_tab *isl_tab_add_eq(struct isl_tab *tab, isl_int *eq)
+int isl_tab_add_eq(struct isl_tab *tab, isl_int *eq)
 {
 	struct isl_tab_undo *snap = NULL;
 	struct isl_tab_var *var;
 	int r;
 	int row;
 	int sgn;
+	isl_int cst;
 
 	if (!tab)
-		return NULL;
-	isl_assert(tab->mat->ctx, !tab->M, goto error);
+		return -1;
+	isl_assert(tab->mat->ctx, !tab->M, return -1);
 
 	if (tab->need_undo)
 		snap = isl_tab_snap(tab);
 
+	if (tab->cone) {
+		isl_int_init(cst);
+		isl_int_swap(eq[0], cst);
+	}
 	r = isl_tab_add_row(tab, eq);
+	if (tab->cone) {
+		isl_int_swap(eq[0], cst);
+		isl_int_clear(cst);
+	}
 	if (r < 0)
-		goto error;
+		return -1;
 
 	var = &tab->con[r];
 	row = var->index;
 	if (row_is_manifestly_zero(tab, row)) {
 		if (snap) {
 			if (isl_tab_rollback(tab, snap) < 0)
-				goto error;
+				return -1;
 		} else
 			drop_row(tab, row);
-		return tab;
+		return 0;
 	}
 
-	sgn = isl_int_sgn(tab->mat->row[row][1]);
+	if (tab->bmap) {
+		tab->bmap = isl_basic_map_add_ineq(tab->bmap, eq);
+		if (isl_tab_push(tab, isl_tab_undo_bmap_ineq) < 0)
+			return -1;
+		isl_seq_neg(eq, eq, 1 + tab->n_var);
+		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_bmap_ineq) < 0)
+			return -1;
+		if (!tab->bmap)
+			return -1;
+		if (add_zero_row(tab) < 0)
+			return -1;
+	}
+
+	sgn = isl_int_sgn(tab->mat->row[row][1]);
 
 	if (sgn > 0) {
 		isl_seq_neg(tab->mat->row[row] + 1, tab->mat->row[row] + 1,
@@ -1663,22 +2024,197 @@ struct isl_tab *isl_tab_add_eq(struct isl_tab *tab, isl_int *eq)
 		sgn = -1;
 	}
 
-	if (sgn < 0 && sign_of_max(tab, var) < 0)
-		return isl_tab_mark_empty(tab);
+	if (sgn < 0) {
+		sgn = sign_of_max(tab, var);
+		if (sgn < -1)
+			return -1;
+		if (sgn < 0) {
+			if (isl_tab_mark_empty(tab) < 0)
+				return -1;
+			return 0;
+		}
+	}
 
 	var->is_nonneg = 1;
 	if (to_col(tab, var) < 0)
-		goto error;
+		return -1;
 	var->is_nonneg = 0;
-	isl_tab_kill_col(tab, var->index);
+	if (isl_tab_kill_col(tab, var->index) < 0)
+		return -1;
 
-	return tab;
+	return 0;
+}
+
+/* Construct and return an inequality that expresses an upper bound
+ * on the given div.
+ * In particular, if the div is given by
+ *
+ *	d = floor(e/m)
+ *
+ * then the inequality expresses
+ *
+ *	m d <= e
+ */
+static struct isl_vec *ineq_for_div(struct isl_basic_map *bmap, unsigned div)
+{
+	unsigned total;
+	unsigned div_pos;
+	struct isl_vec *ineq;
+
+	if (!bmap)
+		return NULL;
+
+	total = isl_basic_map_total_dim(bmap);
+	div_pos = 1 + total - bmap->n_div + div;
+
+	ineq = isl_vec_alloc(bmap->ctx, 1 + total);
+	if (!ineq)
+		return NULL;
+
+	isl_seq_cpy(ineq->el, bmap->div[div] + 1, 1 + total);
+	isl_int_neg(ineq->el[div_pos], bmap->div[div][0]);
+	return ineq;
+}
+
+/* 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
+ *
+ * If add_ineq is not NULL, then this function is used
+ * instead of isl_tab_add_ineq to effectively add the inequalities.
+ */
+static int add_div_constraints(struct isl_tab *tab, unsigned div,
+	int (*add_ineq)(void *user, isl_int *), void *user)
+{
+	unsigned total;
+	unsigned div_pos;
+	struct isl_vec *ineq;
+
+	total = isl_basic_map_total_dim(tab->bmap);
+	div_pos = 1 + total - tab->bmap->n_div + div;
+
+	ineq = ineq_for_div(tab->bmap, div);
+	if (!ineq)
+		goto error;
+
+	if (add_ineq) {
+		if (add_ineq(user, ineq->el) < 0)
+			goto error;
+	} else {
+		if (isl_tab_add_ineq(tab, ineq->el) < 0)
+			goto error;
+	}
+
+	isl_seq_neg(ineq->el, tab->bmap->div[div] + 1, 1 + total);
+	isl_int_set(ineq->el[div_pos], tab->bmap->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);
+
+	if (add_ineq) {
+		if (add_ineq(user, ineq->el) < 0)
+			goto error;
+	} else {
+		if (isl_tab_add_ineq(tab, ineq->el) < 0)
+			goto error;
+	}
+
+	isl_vec_free(ineq);
+
+	return 0;
 error:
-	isl_tab_free(tab);
-	return NULL;
+	isl_vec_free(ineq);
+	return -1;
+}
+
+/* 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
+ * of isl_tab_add_ineq to add the div constraints.
+ * This complication is needed because the code in isl_tab_pip
+ * wants to perform some extra processing when an inequality
+ * is added to the tableau.
+ */
+int isl_tab_add_div(struct isl_tab *tab, __isl_keep isl_vec *div,
+	int (*add_ineq)(void *user, isl_int *), void *user)
+{
+	int r;
+	int k;
+	int nonneg;
+
+	if (!tab || !div)
+		return -1;
+
+	isl_assert(tab->mat->ctx, tab->bmap, return -1);
+
+	nonneg = div_is_nonneg(tab, div);
+
+	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);
+	if (r < 0)
+		return -1;
+
+	if (nonneg)
+		tab->var[r].is_nonneg = 1;
+
+	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;
+	isl_seq_cpy(tab->bmap->div[k], div->el, div->size);
+	if (isl_tab_push(tab, isl_tab_undo_bmap_div) < 0)
+		return -1;
+
+	if (add_div_constraints(tab, k, add_ineq, user) < 0)
+		return -1;
+
+	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;
@@ -1690,60 +2226,82 @@ 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))
-		return isl_tab_mark_empty(tab);
+	if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY)) {
+		if (isl_tab_mark_empty(tab) < 0)
+			goto error;
+		goto done;
+	}
 	for (i = 0; i < bmap->n_eq; ++i) {
 		tab = add_eq(tab, bmap->eq[i]);
 		if (!tab)
 			return tab;
 	}
 	for (i = 0; i < bmap->n_ineq; ++i) {
-		tab = isl_tab_add_ineq(tab, bmap->ineq[i]);
-		if (!tab || tab->empty)
-			return tab;
+		if (isl_tab_add_ineq(tab, bmap->ineq[i]) < 0)
+			goto error;
+		if (tab->empty)
+			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".
  */
-struct isl_tab *isl_tab_from_recession_cone(struct isl_basic_set *bset)
+struct isl_tab *isl_tab_from_recession_cone(__isl_keep isl_basic_set *bset,
+	int parametric)
 {
 	isl_int cst;
 	int i;
 	struct isl_tab *tab;
+	unsigned offset = 0;
 
 	if (!bset)
 		return NULL;
+	if (parametric)
+		offset = isl_basic_set_dim(bset, isl_dim_param);
 	tab = isl_tab_alloc(bset->ctx, bset->n_eq + bset->n_ineq,
-				isl_basic_set_total_dim(bset), 0);
+				isl_basic_set_total_dim(bset) - offset, 0);
 	if (!tab)
 		return NULL;
 	tab->rational = ISL_F_ISSET(bset, ISL_BASIC_SET_RATIONAL);
+	tab->cone = 1;
 
 	isl_int_init(cst);
 	for (i = 0; i < bset->n_eq; ++i) {
-		isl_int_swap(bset->eq[i][0], cst);
-		tab = add_eq(tab, bset->eq[i]);
-		isl_int_swap(bset->eq[i][0], cst);
+		isl_int_swap(bset->eq[i][offset], cst);
+		if (offset > 0) {
+			if (isl_tab_add_eq(tab, bset->eq[i] + offset) < 0)
+				goto error;
+		} else
+			tab = add_eq(tab, bset->eq[i]);
+		isl_int_swap(bset->eq[i][offset], cst);
 		if (!tab)
 			goto done;
 	}
 	for (i = 0; i < bset->n_ineq; ++i) {
 		int r;
-		isl_int_swap(bset->ineq[i][0], cst);
-		r = isl_tab_add_row(tab, bset->ineq[i]);
-		isl_int_swap(bset->ineq[i][0], cst);
+		isl_int_swap(bset->ineq[i][offset], cst);
+		r = isl_tab_add_row(tab, bset->ineq[i] + offset);
+		isl_int_swap(bset->ineq[i][offset], cst);
 		if (r < 0)
 			goto error;
 		tab->con[r].is_nonneg = 1;
-		isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]);
+		if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0)
+			goto error;
 	}
 done:
 	isl_int_clear(cst);
@@ -1771,12 +2329,17 @@ int isl_tab_cone_is_bounded(struct isl_tab *tab)
 	for (;;) {
 		for (i = tab->n_redundant; i < tab->n_row; ++i) {
 			struct isl_tab_var *var;
+			int sgn;
 			var = isl_tab_var_from_row(tab, i);
 			if (!var->is_nonneg)
 				continue;
-			if (sign_of_max(tab, var) != 0)
+			sgn = sign_of_max(tab, var);
+			if (sgn < -1)
+				return -1;
+			if (sgn != 0)
 				return 0;
-			close_row(tab, var);
+			if (close_row(tab, var) < 0)
+				return -1;
 			break;
 		}
 		if (tab->n_dead == tab->n_col)
@@ -1892,6 +2455,8 @@ struct isl_basic_map *isl_basic_map_update_from_tab(struct isl_basic_map *bmap,
 			else if (isl_tab_is_redundant(tab, n_eq + i))
 				isl_basic_map_drop_inequality(bmap, i);
 		}
+	if (bmap->n_eq != n_eq)
+		isl_basic_map_gauss(bmap, NULL);
 	if (!tab->rational &&
 	    !bmap->sample && isl_tab_sample_is_integer(tab))
 		bmap->sample = extract_integer_sample(tab);
@@ -1914,8 +2479,7 @@ struct isl_basic_set *isl_basic_set_update_from_tab(struct isl_basic_set *bset,
  * the resulting tableau is empty.
  * Otherwise, we know the value will be zero and we close the row.
  */
-static struct isl_tab *cut_to_hyperplane(struct isl_tab *tab,
-	struct isl_tab_var *var)
+static int cut_to_hyperplane(struct isl_tab *tab, struct isl_tab_var *var)
 {
 	unsigned r;
 	isl_int *row;
@@ -1923,11 +2487,12 @@ static struct isl_tab *cut_to_hyperplane(struct isl_tab *tab,
 	unsigned off = 2 + tab->M;
 
 	if (var->is_zero)
-		return tab;
-	isl_assert(tab->mat->ctx, !var->is_redundant, goto error);
+		return 0;
+	isl_assert(tab->mat->ctx, !var->is_redundant, return -1);
+	isl_assert(tab->mat->ctx, var->is_nonneg, return -1);
 
 	if (isl_tab_extend_cons(tab, 1) < 0)
-		goto error;
+		return -1;
 
 	r = tab->n_con;
 	tab->con[r].index = tab->n_row;
@@ -1952,20 +2517,25 @@ static struct isl_tab *cut_to_hyperplane(struct isl_tab *tab,
 
 	tab->n_row++;
 	tab->n_con++;
-	isl_tab_push_var(tab, isl_tab_undo_allocate, &tab->con[r]);
+	if (isl_tab_push_var(tab, isl_tab_undo_allocate, &tab->con[r]) < 0)
+		return -1;
 
 	sgn = sign_of_max(tab, &tab->con[r]);
-	if (sgn < 0)
-		return isl_tab_mark_empty(tab);
+	if (sgn < -1)
+		return -1;
+	if (sgn < 0) {
+		if (isl_tab_mark_empty(tab) < 0)
+			return -1;
+		return 0;
+	}
 	tab->con[r].is_nonneg = 1;
-	isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]);
+	if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0)
+		return -1;
 	/* sgn == 0 */
-	close_row(tab, &tab->con[r]);
+	if (close_row(tab, &tab->con[r]) < 0)
+		return -1;
 
-	return tab;
-error:
-	isl_tab_free(tab);
-	return NULL;
+	return 0;
 }
 
 /* Given a tableau "tab" and an inequality constraint "con" of the tableau,
@@ -1976,6 +2546,14 @@ error:
  * If r is a column variable, then we need to modify each row that
  * refers to r = r' - 1 by substituting this equality, effectively
  * subtracting the coefficient of the column from the constant.
+ * We should only do this if the minimum is manifestly unbounded,
+ * however.  Otherwise, we may end up with negative sample values
+ * for non-negative variables.
+ * So, if r is a column variable with a minimum that is not
+ * manifestly unbounded, then we need to move it to a row.
+ * However, the sample value of this row may be negative,
+ * even after the relaxation, so we need to restore it.
+ * We therefore prefer to pivot a column up to a row, if possible.
  */
 struct isl_tab *isl_tab_relax(struct isl_tab *tab, int con)
 {
@@ -1987,13 +2565,26 @@ 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))
-		to_row(tab, var, 1);
+		if (to_row(tab, var, 1) < 0)
+			goto error;
+	if (!var->is_row && !min_is_manifestly_unbounded(tab, var))
+		if (to_row(tab, var, -1) < 0)
+			goto error;
 
-	if (var->is_row)
+	if (var->is_row) {
 		isl_int_add(tab->mat->row[var->index][1],
 		    tab->mat->row[var->index][1], tab->mat->row[var->index][0]);
-	else {
+		if (restore_row(tab, var) < 0)
+			goto error;
+	} else {
 		int i;
 
 		for (i = 0; i < tab->n_row; ++i) {
@@ -2005,27 +2596,51 @@ struct isl_tab *isl_tab_relax(struct isl_tab *tab, int con)
 
 	}
 
-	isl_tab_push_var(tab, isl_tab_undo_relax, var);
+	if (isl_tab_push_var(tab, isl_tab_undo_relax, var) < 0)
+		goto error;
 
 	return tab;
+error:
+	isl_tab_free(tab);
+	return NULL;
 }
 
-struct isl_tab *isl_tab_select_facet(struct isl_tab *tab, int con)
+/* 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 NULL;
+		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)
+		return -1;
 
 	return cut_to_hyperplane(tab, &tab->con[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])) &&
-		isl_seq_first_non_zero(tab->mat->row[row] + off + tab->n_dead,
-					tab->n_col - tab->n_dead) != -1;
+	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]);
 }
 
 /* Check for (near) equalities among the constraints.
@@ -2044,17 +2659,17 @@ static int may_be_equality(struct isl_tab *tab, int row)
  * tableau is integer), then we restrict the value to being zero
  * by adding an opposite non-negative variable.
  */
-struct isl_tab *isl_tab_detect_implicit_equalities(struct isl_tab *tab)
+int isl_tab_detect_implicit_equalities(struct isl_tab *tab)
 {
 	int i;
 	unsigned n_marked;
 
 	if (!tab)
-		return NULL;
+		return -1;
 	if (tab->empty)
-		return tab;
+		return 0;
 	if (tab->n_dead == tab->n_col)
-		return tab;
+		return 0;
 
 	n_marked = 0;
 	for (i = tab->n_redundant; i < tab->n_row; ++i) {
@@ -2072,6 +2687,7 @@ struct isl_tab *isl_tab_detect_implicit_equalities(struct isl_tab *tab)
 	}
 	while (n_marked) {
 		struct isl_tab_var *var;
+		int sgn;
 		for (i = tab->n_redundant; i < tab->n_row; ++i) {
 			var = isl_tab_var_from_row(tab, i);
 			if (var->marked)
@@ -2088,10 +2704,15 @@ struct isl_tab *isl_tab_detect_implicit_equalities(struct isl_tab *tab)
 		}
 		var->marked = 0;
 		n_marked--;
-		if (sign_of_max(tab, var) == 0)
-			close_row(tab, var);
-		else if (!tab->rational && !at_least_one(tab, var)) {
-			tab = cut_to_hyperplane(tab, var);
+		sgn = sign_of_max(tab, var);
+		if (sgn < 0)
+			return -1;
+		if (sgn == 0) {
+			if (close_row(tab, var) < 0)
+				return -1;
+		} else if (!tab->rational && !at_least_one(tab, var)) {
+			if (cut_to_hyperplane(tab, var) < 0)
+				return -1;
 			return isl_tab_detect_implicit_equalities(tab);
 		}
 		for (i = tab->n_redundant; i < tab->n_row; ++i) {
@@ -2105,7 +2726,124 @@ struct isl_tab *isl_tab_detect_implicit_equalities(struct isl_tab *tab)
 		}
 	}
 
-	return 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)
+		return -1;
+	if (tab->rational) {
+		int sgn = sign_of_min(tab, var);
+		if (sgn < -1)
+			return -1;
+		return sgn >= 0;
+	} else {
+		int irred = isl_tab_min_at_most_neg_one(tab, var);
+		if (irred < 0)
+			return -1;
+		return !irred;
+	}
 }
 
 /* Check for (near) redundant constraints.
@@ -2121,17 +2859,17 @@ struct isl_tab *isl_tab_detect_implicit_equalities(struct isl_tab *tab)
  * If not, we mark the row as being redundant (assuming it hasn't
  * been detected as being obviously redundant in the mean time).
  */
-struct isl_tab *isl_tab_detect_redundant(struct isl_tab *tab)
+int isl_tab_detect_redundant(struct isl_tab *tab)
 {
 	int i;
 	unsigned n_marked;
 
 	if (!tab)
-		return NULL;
+		return -1;
 	if (tab->empty)
-		return tab;
+		return 0;
 	if (tab->n_redundant == tab->n_row)
-		return tab;
+		return 0;
 
 	n_marked = 0;
 	for (i = tab->n_redundant; i < tab->n_row; ++i) {
@@ -2149,6 +2887,7 @@ struct isl_tab *isl_tab_detect_redundant(struct isl_tab *tab)
 	}
 	while (n_marked) {
 		struct isl_tab_var *var;
+		int red;
 		for (i = tab->n_redundant; i < tab->n_row; ++i) {
 			var = isl_tab_var_from_row(tab, i);
 			if (var->marked)
@@ -2165,10 +2904,12 @@ struct isl_tab *isl_tab_detect_redundant(struct isl_tab *tab)
 		}
 		var->marked = 0;
 		n_marked--;
-		if ((tab->rational ? (sign_of_min(tab, var) >= 0)
-				   : !isl_tab_min_at_most_neg_one(tab, var)) &&
-		    !var->is_redundant)
-			isl_tab_mark_redundant(tab, var->index);
+		red = con_is_redundant(tab, var);
+		if (red < 0)
+			return -1;
+		if (red && !var->is_redundant)
+			if (isl_tab_mark_redundant(tab, var->index) < 0)
+				return -1;
 		for (i = tab->n_dead; i < tab->n_col; ++i) {
 			var = var_from_col(tab, i);
 			if (!var->marked)
@@ -2180,7 +2921,7 @@ struct isl_tab *isl_tab_detect_redundant(struct isl_tab *tab)
 		}
 	}
 
-	return tab;
+	return 0;
 }
 
 int isl_tab_is_equality(struct isl_tab *tab, int con)
@@ -2201,16 +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,
@@ -2221,6 +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;
 
@@ -2229,8 +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);
@@ -2240,8 +2983,11 @@ enum isl_lp_result isl_tab_min(struct isl_tab *tab,
 		}
 		if (row == -1)
 			break;
-		isl_tab_pivot(tab, row, col);
+		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;
 
@@ -2302,17 +3048,23 @@ struct isl_tab_undo *isl_tab_snap(struct isl_tab *tab)
 
 /* Undo the operation performed by isl_tab_relax.
  */
-static void unrelax(struct isl_tab *tab, struct isl_tab_var *var)
+static int unrelax(struct isl_tab *tab, struct isl_tab_var *var) WARN_UNUSED;
+static int unrelax(struct isl_tab *tab, struct isl_tab_var *var)
 {
 	unsigned off = 2 + tab->M;
 
 	if (!var->is_row && !max_is_manifestly_unbounded(tab, var))
-		to_row(tab, var, 1);
+		if (to_row(tab, var, 1) < 0)
+			return -1;
 
-	if (var->is_row)
+	if (var->is_row) {
 		isl_int_sub(tab->mat->row[var->index][1],
 		    tab->mat->row[var->index][1], tab->mat->row[var->index][0]);
-	else {
+		if (var->is_nonneg) {
+			int sgn = restore_row(tab, var);
+			isl_assert(tab->mat->ctx, sgn >= 0, return -1);
+		}
+	} else {
 		int i;
 
 		for (i = 0; i < tab->n_row; ++i) {
@@ -2323,18 +3075,40 @@ static void unrelax(struct isl_tab *tab, struct isl_tab_var *var)
 		}
 
 	}
+
+	return 0;
 }
 
-static void perform_undo_var(struct isl_tab *tab, struct isl_tab_undo *undo)
+/* 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;
 	case isl_tab_undo_redundant:
 		var->is_redundant = 0;
 		tab->n_redundant--;
+		restore_row(tab, isl_tab_var_from_row(tab, tab->n_redundant));
+		break;
+	case isl_tab_undo_freeze:
+		var->frozen = 0;
 		break;
 	case isl_tab_undo_zero:
 		var->is_zero = 0;
@@ -2343,24 +3117,34 @@ static void perform_undo_var(struct isl_tab *tab, struct isl_tab_undo *undo)
 		break;
 	case isl_tab_undo_allocate:
 		if (undo->u.var_index >= 0) {
-			isl_assert(tab->mat->ctx, !var->is_row, return);
+			isl_assert(tab->mat->ctx, !var->is_row, return -1);
 			drop_col(tab, var->index);
 			break;
 		}
 		if (!var->is_row) {
-			if (!max_is_manifestly_unbounded(tab, var))
-				to_row(tab, var, 1);
-			else if (!min_is_manifestly_unbounded(tab, var))
-				to_row(tab, var, -1);
-			else
-				to_row(tab, var, 0);
+			if (!max_is_manifestly_unbounded(tab, var)) {
+				if (to_row(tab, var, 1) < 0)
+					return -1;
+			} else if (!min_is_manifestly_unbounded(tab, var)) {
+				if (to_row(tab, var, -1) < 0)
+					return -1;
+			} else
+				if (to_row(tab, var, 0) < 0)
+					return -1;
 		}
 		drop_row(tab, var->index);
 		break;
 	case isl_tab_undo_relax:
-		unrelax(tab, var);
-		break;
+		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;
 }
 
 /* Restore the tableau to the state where the basic variables
@@ -2407,19 +3191,41 @@ static int restore_basis(struct isl_tab *tab, int *col_var)
 			if (!isl_int_is_zero(tab->mat->row[row][off+extra[j]]))
 				break;
 		isl_assert(tab->mat->ctx, j < n_extra, goto error);
-		isl_tab_pivot(tab, row, extra[j]);
+		if (isl_tab_pivot(tab, row, extra[j]) < 0)
+			goto error;
 		extra[j] = extra[--n_extra];
 	}
 
 	free(extra);
-	free(col_var);
 	return 0;
 error:
 	free(extra);
-	free(col_var);
 	return -1;
 }
 
+/* Remove all samples with index n or greater, i.e., those samples
+ * that were added since we saved this number of samples in
+ * isl_tab_save_samples.
+ */
+static void drop_samples_since(struct isl_tab *tab, int n)
+{
+	int i;
+
+	for (i = tab->n_sample - 1; i >= 0 && tab->n_sample > n; --i) {
+		if (tab->sample_index[i] < n)
+			continue;
+
+		if (i != tab->n_sample - 1) {
+			int t = tab->sample_index[tab->n_sample-1];
+			tab->sample_index[tab->n_sample-1] = tab->sample_index[i];
+			tab->sample_index[i] = t;
+			isl_mat_swap_rows(tab->samples, tab->n_sample-1, i);
+		}
+		tab->n_sample--;
+	}
+}
+
+static int perform_undo(struct isl_tab *tab, struct isl_tab_undo *undo) WARN_UNUSED;
 static int perform_undo(struct isl_tab *tab, struct isl_tab_undo *undo)
 {
 	switch (undo->type) {
@@ -2428,19 +3234,19 @@ static int perform_undo(struct isl_tab *tab, struct isl_tab_undo *undo)
 		break;
 	case isl_tab_undo_nonneg:
 	case isl_tab_undo_redundant:
+	case isl_tab_undo_freeze:
 	case isl_tab_undo_zero:
 	case isl_tab_undo_allocate:
 	case isl_tab_undo_relax:
-		perform_undo_var(tab, undo);
-		break;
-	case isl_tab_undo_bset_eq:
-		isl_basic_set_free_equality(tab->bset, 1);
-		break;
-	case isl_tab_undo_bset_ineq:
-		isl_basic_set_free_inequality(tab->bset, 1);
-		break;
-	case isl_tab_undo_bset_div:
-		isl_basic_set_free_div(tab->bset, 1);
+	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);
+	case isl_tab_undo_bmap_ineq:
+		return isl_basic_map_free_inequality(tab->bmap, 1);
+	case isl_tab_undo_bmap_div:
+		if (isl_basic_map_free_div(tab->bmap, 1) < 0)
+			return -1;
 		if (tab->samples)
 			tab->samples->n_col--;
 		break;
@@ -2451,6 +3257,11 @@ static int perform_undo(struct isl_tab *tab, struct isl_tab_undo *undo)
 	case isl_tab_undo_drop_sample:
 		tab->n_outside--;
 		break;
+	case isl_tab_undo_saved_samples:
+		drop_samples_since(tab, undo->u.n);
+		break;
+	case isl_tab_undo_callback:
+		return undo->u.callback->run(undo->u.callback);
 	default:
 		isl_assert(tab->mat->ctx, 0, return -1);
 	}
@@ -2473,11 +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;
@@ -2492,9 +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)
 {
@@ -2506,15 +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(
@@ -2558,25 +3373,71 @@ enum isl_ineq_type isl_tab_ineq_type(struct isl_tab *tab, isl_int *ineq)
 		 (tab->rational ||
 		    isl_int_abs_ge(tab->mat->row[row][1],
 				   tab->mat->row[row][0]))) {
-		if (at_least_zero(tab, &tab->con[con]))
+		int nonneg = at_least_zero(tab, &tab->con[con]);
+		if (nonneg < 0)
+			goto error;
+		if (nonneg)
 			type = isl_ineq_cut;
 		else
 			type = separation_type(tab, row);
-	} else if (tab->rational ? (sign_of_min(tab, &tab->con[con]) < 0)
-			     : isl_tab_min_at_most_neg_one(tab, &tab->con[con]))
-		type = isl_ineq_cut;
-	else
-		type = isl_ineq_redundant;
+	} else {
+		int red = con_is_redundant(tab, &tab->con[con]);
+		if (red < 0)
+			goto error;
+		if (!red)
+			type = isl_ineq_cut;
+		else
+			type = isl_ineq_redundant;
+	}
 
 	if (isl_tab_rollback(tab, snap))
 		return isl_ineq_error;
 	return type;
 error:
-	isl_tab_rollback(tab, snap);
 	return isl_ineq_error;
 }
 
-void isl_tab_dump(struct isl_tab *tab, FILE *out, int indent)
+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;
+
+	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, goto error);
+
+	tab->bmap = bmap;
+
+	return 0;
+error:
+	isl_basic_map_free(bmap);
+	return -1;
+}
+
+int isl_tab_track_bset(struct isl_tab *tab, __isl_take isl_basic_set *bset)
+{
+	return isl_tab_track_bmap(tab, (isl_basic_map *)bset);
+}
+
+__isl_keep isl_basic_set *isl_tab_peek_bset(struct isl_tab *tab)
+{
+	if (!tab)
+		return NULL;
+
+	return (isl_basic_set *)tab->bmap;
+}
+
+static void isl_tab_print_internal(__isl_keep struct isl_tab *tab,
+	FILE *out, int indent)
 {
 	unsigned r, c;
 	int i;
@@ -2645,9 +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->bset)
-		isl_basic_set_dump(tab->bset, out, indent);
+	if (tab->bmap)
+		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);
 }