X-Git-Url: http://review.tizen.org/git/?a=blobdiff_plain;f=isl_tab.c;h=e4cc386679d8760504af441f0741f9241120f479;hb=761e8797207a4953b2da4ddaf83b987b09fa366f;hp=da644532ef07d111b6a497bef0eccd320be02eae;hpb=77217749765eda514eb091e6986549152cd8e624;p=platform%2Fupstream%2Fisl.git

diff --git a/isl_tab.c b/isl_tab.c
index da64453..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
@@ -64,6 +68,7 @@ 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;
@@ -84,13 +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;
 
@@ -168,13 +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;
 }
@@ -208,34 +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;
@@ -266,6 +289,7 @@ 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;
@@ -308,6 +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) {
@@ -516,6 +542,7 @@ 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;
@@ -723,6 +750,8 @@ 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;
 
@@ -742,6 +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;
@@ -751,9 +782,9 @@ 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 int push_union(struct isl_tab *tab,
@@ -763,6 +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;
 
@@ -915,7 +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)
@@ -1072,6 +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) {
@@ -1159,6 +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;
@@ -1171,11 +1214,13 @@ static void check_table(struct isl_tab *tab)
 		if (!var->is_nonneg)
 			continue;
 		if (tab->M) {
-			assert(!isl_int_is_neg(tab->mat->row[i][2]));
+			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;
 		}
-		assert(!isl_int_is_neg(tab->mat->row[i][1]));
+		isl_assert(tab->mat->ctx, !isl_int_is_neg(tab->mat->row[i][1]),
+				abort());
 	}
 }
 
@@ -1210,6 +1255,20 @@ static int sign_of_max(struct isl_tab *tab, struct isl_tab_var *var)
 	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)
@@ -1361,7 +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)
@@ -1396,8 +1456,11 @@ 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);
@@ -1486,6 +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
@@ -1507,15 +1607,21 @@ static int close_row(struct isl_tab *tab, struct isl_tab_var *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 -1);
-		if (isl_tab_kill_col(tab, j))
+		recheck = isl_tab_kill_col(tab, j);
+		if (recheck < 0)
+			return -1;
+		if (recheck)
 			--j;
 	}
 	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;
 }
 
@@ -1595,6 +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)
 {
@@ -1639,7 +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;
 }
@@ -1798,24 +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])) {
@@ -1825,15 +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)
@@ -1855,7 +1961,7 @@ static int add_zero_row(struct isl_tab *tab)
 /* 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;
@@ -1865,8 +1971,8 @@ struct isl_tab *isl_tab_add_eq(struct isl_tab *tab, isl_int *eq)
 	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);
@@ -1881,32 +1987,32 @@ struct isl_tab *isl_tab_add_eq(struct isl_tab *tab, isl_int *eq)
 		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;
 	}
 
 	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;
+			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)
-			goto error;
+			return -1;
 		if (!tab->bmap)
-			goto error;
+			return -1;
 		if (add_zero_row(tab) < 0)
-			goto error;
+			return -1;
 	}
 
 	sgn = isl_int_sgn(tab->mat->row[row][1]);
@@ -1921,25 +2027,22 @@ struct isl_tab *isl_tab_add_eq(struct isl_tab *tab, isl_int *eq)
 	if (sgn < 0) {
 		sgn = sign_of_max(tab, var);
 		if (sgn < -1)
-			goto error;
+			return -1;
 		if (sgn < 0) {
 			if (isl_tab_mark_empty(tab) < 0)
-				goto error;
-			return tab;
+				return -1;
+			return 0;
 		}
 	}
 
 	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;
 }
 
 /* Construct and return an inequality that expresses an upper bound
@@ -2028,7 +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
@@ -2040,7 +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;
@@ -2050,15 +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;
@@ -2071,8 +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;
@@ -2086,7 +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;
@@ -2098,11 +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]);
@@ -2113,31 +2242,39 @@ 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".
  */
-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);
@@ -2145,17 +2282,21 @@ struct isl_tab *isl_tab_from_recession_cone(struct isl_basic_set *bset)
 
 	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;
@@ -2338,8 +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;
@@ -2347,12 +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);
-	isl_assert(tab->mat->ctx, var->is_nonneg, 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;
@@ -2378,27 +2518,24 @@ static struct isl_tab *cut_to_hyperplane(struct isl_tab *tab,
 	tab->n_row++;
 	tab->n_con++;
 	if (isl_tab_push_var(tab, isl_tab_undo_allocate, &tab->con[r]) < 0)
-		goto error;
+		return -1;
 
 	sgn = sign_of_max(tab, &tab->con[r]);
 	if (sgn < -1)
-		goto error;
+		return -1;
 	if (sgn < 0) {
 		if (isl_tab_mark_empty(tab) < 0)
-			goto error;
-		return tab;
+			return -1;
+		return 0;
 	}
 	tab->con[r].is_nonneg = 1;
 	if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0)
-		goto error;
+		return -1;
 	/* sgn == 0 */
 	if (close_row(tab, &tab->con[r]) < 0)
-		goto error;
+		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,
@@ -2428,6 +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;
@@ -2461,22 +2605,42 @@ error:
 	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 -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 NULL;
+		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.
@@ -2495,17 +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) {
@@ -2542,12 +2706,13 @@ struct isl_tab *isl_tab_detect_implicit_equalities(struct isl_tab *tab)
 		n_marked--;
 		sgn = sign_of_max(tab, var);
 		if (sgn < 0)
-			goto error;
+			return -1;
 		if (sgn == 0) {
 			if (close_row(tab, var) < 0)
-				goto error;
+				return -1;
 		} else if (!tab->rational && !at_least_one(tab, var)) {
-			tab = cut_to_hyperplane(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) {
@@ -2561,10 +2726,107 @@ struct isl_tab *isl_tab_detect_implicit_equalities(struct isl_tab *tab)
 		}
 	}
 
-	return tab;
-error:
-	isl_tab_free(tab);
-	return NULL;
+	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)
@@ -2680,16 +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,
@@ -2700,6 +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;
 
@@ -2708,8 +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);
@@ -2722,6 +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;
 
@@ -2813,17 +3079,33 @@ 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;
 	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;
@@ -2854,6 +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;
@@ -2909,11 +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;
 }
 
@@ -2952,6 +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);
@@ -2997,11 +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;
@@ -3016,9 +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)
 {
@@ -3030,15 +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(
@@ -3108,12 +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;
 
@@ -3136,7 +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;
@@ -3205,9 +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);
 }