X-Git-Url: http://review.tizen.org/git/?a=blobdiff_plain;f=isl_tab_pip.c;h=412e8eea67432fcc53d85ef31475061321f23d40;hb=ac6f74dd43d400a61b57c7cfbf34e201c7c5f1fa;hp=7f7db31f4a9a4f2911fb25157e5bd4670f1e32ba;hpb=d5cbda10655caf8a2b1bbd4532d6c7d78de7d29b;p=platform%2Fupstream%2Fisl.git

diff --git a/isl_tab_pip.c b/isl_tab_pip.c
index 7f7db31..412e8ee 100644
--- a/isl_tab_pip.c
+++ b/isl_tab_pip.c
@@ -1,7 +1,23 @@
+/*
+ * Copyright 2008-2009 Katholieke Universiteit Leuven
+ * Copyright 2010      INRIA Saclay
+ *
+ * Use of this software is governed by the GNU LGPLv2.1 license
+ *
+ * Written by Sven Verdoolaege, K.U.Leuven, Departement
+ * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
+ * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
+ * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France 
+ */
+
+#include <isl_ctx_private.h>
 #include "isl_map_private.h"
-#include "isl_seq.h"
+#include <isl/seq.h>
 #include "isl_tab.h"
 #include "isl_sample.h"
+#include <isl_mat_private.h>
+#include <isl_aff_private.h>
+#include <isl_config.h>
 
 /*
  * The implementation of parametric integer linear programming in this file
@@ -12,7 +28,7 @@
  * The strategy used for obtaining a feasible solution is different
  * from the one used in isl_tab.c.  In particular, in isl_tab.c,
  * upon finding a constraint that is not yet satisfied, we pivot
- * in a row that increases the constant term of row holding the
+ * in a row that increases the constant term of the row holding the
  * constraint, making sure the sample solution remains feasible
  * for all the constraints it already satisfied.
  * Here, we always pivot in the row holding the constraint,
@@ -26,10 +42,10 @@
  * then the initial sample value may be chosen equal to zero.
  * However, we will not make this assumption.  Instead, we apply
  * the "big parameter" trick.  Any variable x is then not directly
- * used in the tableau, but instead it its represented by another
+ * used in the tableau, but instead it is represented by another
  * variable x' = M + x, where M is an arbitrarily large (positive)
  * value.  x' is therefore always non-negative, whatever the value of x.
- * Taking as initial smaple value x' = 0 corresponds to x = -M,
+ * Taking as initial sample value x' = 0 corresponds to x = -M,
  * which is always smaller than any possible value of x.
  *
  * The big parameter trick is used in the main tableau and
@@ -71,9 +87,8 @@ struct isl_context_op {
 	/* return index of a div that corresponds to "div" */
 	int (*get_div)(struct isl_context *context, struct isl_tab *tab,
 			struct isl_vec *div);
-	/* add div "div" to context and return index and non-negativity */
-	int (*add_div)(struct isl_context *context, struct isl_vec *div,
-			int *nonneg);
+	/* add div "div" to context and return non-negativity */
+	int (*add_div)(struct isl_context *context, struct isl_vec *div);
 	int (*detect_equalities)(struct isl_context *context,
 			struct isl_tab *tab);
 	/* return row index of "best" split */
@@ -101,6 +116,20 @@ struct isl_context_lex {
 	struct isl_tab *tab;
 };
 
+struct isl_partial_sol {
+	int level;
+	struct isl_basic_set *dom;
+	struct isl_mat *M;
+
+	struct isl_partial_sol *next;
+};
+
+struct isl_sol;
+struct isl_sol_callback {
+	struct isl_tab_callback callback;
+	struct isl_sol *sol;
+};
+
 /* isl_sol is an interface for constructing a solution to
  * a parametric integer linear programming problem.
  * Every time the algorithm reaches a state where a solution
@@ -118,57 +147,225 @@ struct isl_context_lex {
  * the solution.
  */
 struct isl_sol {
+	int error;
+	int rational;
+	int level;
+	int max;
+	int n_out;
 	struct isl_context *context;
-	struct isl_sol *(*add)(struct isl_sol *sol, struct isl_tab *tab);
+	struct isl_partial_sol *partial;
+	void (*add)(struct isl_sol *sol,
+			    struct isl_basic_set *dom, struct isl_mat *M);
+	void (*add_empty)(struct isl_sol *sol, struct isl_basic_set *bset);
 	void (*free)(struct isl_sol *sol);
+	struct isl_sol_callback	dec_level;
 };
 
 static void sol_free(struct isl_sol *sol)
 {
+	struct isl_partial_sol *partial, *next;
 	if (!sol)
 		return;
+	for (partial = sol->partial; partial; partial = next) {
+		next = partial->next;
+		isl_basic_set_free(partial->dom);
+		isl_mat_free(partial->M);
+		free(partial);
+	}
 	sol->free(sol);
 }
 
-struct isl_sol_map {
-	struct isl_sol	sol;
-	struct isl_map	*map;
-	struct isl_set	*empty;
-	int		max;
-};
-
-static void sol_map_free(struct isl_sol_map *sol_map)
+/* Push a partial solution represented by a domain and mapping M
+ * onto the stack of partial solutions.
+ */
+static void sol_push_sol(struct isl_sol *sol,
+	struct isl_basic_set *dom, struct isl_mat *M)
 {
-	if (sol_map->sol.context)
-		sol_map->sol.context->op->free(sol_map->sol.context);
-	isl_map_free(sol_map->map);
-	isl_set_free(sol_map->empty);
-	free(sol_map);
+	struct isl_partial_sol *partial;
+
+	if (sol->error || !dom)
+		goto error;
+
+	partial = isl_alloc_type(dom->ctx, struct isl_partial_sol);
+	if (!partial)
+		goto error;
+
+	partial->level = sol->level;
+	partial->dom = dom;
+	partial->M = M;
+	partial->next = sol->partial;
+
+	sol->partial = partial;
+
+	return;
+error:
+	isl_basic_set_free(dom);
+	sol->error = 1;
 }
 
-static void sol_map_free_wrap(struct isl_sol *sol)
+/* Pop one partial solution from the partial solution stack and
+ * pass it on to sol->add or sol->add_empty.
+ */
+static void sol_pop_one(struct isl_sol *sol)
 {
-	sol_map_free((struct isl_sol_map *)sol);
+	struct isl_partial_sol *partial;
+
+	partial = sol->partial;
+	sol->partial = partial->next;
+
+	if (partial->M)
+		sol->add(sol, partial->dom, partial->M);
+	else
+		sol->add_empty(sol, partial->dom);
+	free(partial);
 }
 
-static struct isl_sol_map *add_empty(struct isl_sol_map *sol)
+/* Return a fresh copy of the domain represented by the context tableau.
+ */
+static struct isl_basic_set *sol_domain(struct isl_sol *sol)
 {
 	struct isl_basic_set *bset;
 
-	if (!sol->empty)
-		return sol;
-	sol->empty = isl_set_grow(sol->empty, 1);
-	bset = sol->sol.context->op->peek_basic_set(sol->sol.context);
-	bset = isl_basic_set_copy(bset);
-	bset = isl_basic_set_simplify(bset);
-	bset = isl_basic_set_finalize(bset);
-	sol->empty = isl_set_add(sol->empty, bset);
-	if (!sol->empty)
-		goto error;
-	return sol;
-error:
-	sol_map_free(sol);
-	return NULL;
+	if (sol->error)
+		return NULL;
+
+	bset = isl_basic_set_dup(sol->context->op->peek_basic_set(sol->context));
+	bset = isl_basic_set_update_from_tab(bset,
+			sol->context->op->peek_tab(sol->context));
+
+	return bset;
+}
+
+/* Check whether two partial solutions have the same mapping, where n_div
+ * is the number of divs that the two partial solutions have in common.
+ */
+static int same_solution(struct isl_partial_sol *s1, struct isl_partial_sol *s2,
+	unsigned n_div)
+{
+	int i;
+	unsigned dim;
+
+	if (!s1->M != !s2->M)
+		return 0;
+	if (!s1->M)
+		return 1;
+
+	dim = isl_basic_set_total_dim(s1->dom) - s1->dom->n_div;
+
+	for (i = 0; i < s1->M->n_row; ++i) {
+		if (isl_seq_first_non_zero(s1->M->row[i]+1+dim+n_div,
+					    s1->M->n_col-1-dim-n_div) != -1)
+			return 0;
+		if (isl_seq_first_non_zero(s2->M->row[i]+1+dim+n_div,
+					    s2->M->n_col-1-dim-n_div) != -1)
+			return 0;
+		if (!isl_seq_eq(s1->M->row[i], s2->M->row[i], 1+dim+n_div))
+			return 0;
+	}
+	return 1;
+}
+
+/* Pop all solutions from the partial solution stack that were pushed onto
+ * the stack at levels that are deeper than the current level.
+ * If the two topmost elements on the stack have the same level
+ * and represent the same solution, then their domains are combined.
+ * This combined domain is the same as the current context domain
+ * as sol_pop is called each time we move back to a higher level.
+ */
+static void sol_pop(struct isl_sol *sol)
+{
+	struct isl_partial_sol *partial;
+	unsigned n_div;
+
+	if (sol->error)
+		return;
+
+	if (sol->level == 0) {
+		for (partial = sol->partial; partial; partial = sol->partial)
+			sol_pop_one(sol);
+		return;
+	}
+
+	partial = sol->partial;
+	if (!partial)
+		return;
+
+	if (partial->level <= sol->level)
+		return;
+
+	if (partial->next && partial->next->level == partial->level) {
+		n_div = isl_basic_set_dim(
+				sol->context->op->peek_basic_set(sol->context),
+				isl_dim_div);
+
+		if (!same_solution(partial, partial->next, n_div)) {
+			sol_pop_one(sol);
+			sol_pop_one(sol);
+		} else {
+			struct isl_basic_set *bset;
+
+			bset = sol_domain(sol);
+
+			isl_basic_set_free(partial->next->dom);
+			partial->next->dom = bset;
+			partial->next->level = sol->level;
+
+			sol->partial = partial->next;
+			isl_basic_set_free(partial->dom);
+			isl_mat_free(partial->M);
+			free(partial);
+		}
+	} else
+		sol_pop_one(sol);
+}
+
+static void sol_dec_level(struct isl_sol *sol)
+{
+	if (sol->error)
+		return;
+
+	sol->level--;
+
+	sol_pop(sol);
+}
+
+static int sol_dec_level_wrap(struct isl_tab_callback *cb)
+{
+	struct isl_sol_callback *callback = (struct isl_sol_callback *)cb;
+
+	sol_dec_level(callback->sol);
+
+	return callback->sol->error ? -1 : 0;
+}
+
+/* Move down to next level and push callback onto context tableau
+ * to decrease the level again when it gets rolled back across
+ * the current state.  That is, dec_level will be called with
+ * the context tableau in the same state as it is when inc_level
+ * is called.
+ */
+static void sol_inc_level(struct isl_sol *sol)
+{
+	struct isl_tab *tab;
+
+	if (sol->error)
+		return;
+
+	sol->level++;
+	tab = sol->context->op->peek_tab(sol->context);
+	if (isl_tab_push_callback(tab, &sol->dec_level.callback) < 0)
+		sol->error = 1;
+}
+
+static void scale_rows(struct isl_mat *mat, isl_int m, int n_row)
+{
+	int i;
+
+	if (isl_int_is_one(m))
+		return;
+
+	for (i = 0; i < n_row; ++i)
+		isl_seq_scale(mat->row[i], mat->row[i], m, mat->n_col);
 }
 
 /* Add the solution identified by the tableau and the context tableau.
@@ -184,23 +381,23 @@ error:
  *			dimensions in the input map
  *	tab->n_div is equal to the number of divs in the context
  *
- * If there is no solution, then the basic set corresponding to the
- * context tableau is added to the set "empty".
+ * If there is no solution, then call add_empty with a basic set
+ * that corresponds to the context tableau.  (If add_empty is NULL,
+ * then do nothing).
  *
- * Otherwise, a basic map is constructed with the same parameters
- * and divs as the context, the dimensions of the context as input
- * dimensions and a number of output dimensions that is equal to
- * the number of output dimensions in the input map.
+ * If there is a solution, then first construct a matrix that maps
+ * all dimensions of the context to the output variables, i.e.,
+ * the output dimensions in the input map.
  * The divs in the input map (if any) that do not correspond to any
  * div in the context do not appear in the solution.
  * The algorithm will make sure that they have an integer value,
  * but these values themselves are of no interest.
+ * We have to be careful not to drop or rearrange any divs in the
+ * context because that would change the meaning of the matrix.
  *
- * The constraints and divs of the context are simply copied
- * fron context_tab->bset.
  * To extract the value of the output variables, it should be noted
- * that we always use a big parameter M and so the variable stored
- * in the tableau is not an output variable x itself, but
+ * that we always use a big parameter M in the main tableau and so
+ * the variable stored in this tableau is not an output variable x itself, but
  *	x' = M + x (in case of minimization)
  * or
  *	x' = M - x (in case of maximization)
@@ -211,140 +408,252 @@ error:
  * are bounded, so this cannot occur.
  * Similarly, when x' appears in a row, then the coefficient of M in that
  * row is necessarily 1.
- * If the row represents
+ * If the row in the tableau represents
  *	d x' = c + d M + e(y)
- * then, in case of minimization, an equality
- *	c + e(y) - d x' = 0
- * is added, and in case of maximization,
- *	c + e(y) + d x' = 0
+ * then, in case of minimization, the corresponding row in the matrix
+ * will be
+ *	a c + a e(y)
+ * with a d = m, the (updated) common denominator of the matrix.
+ * In case of maximization, the row will be
+ *	-a c - a e(y)
  */
-static struct isl_sol_map *sol_map_add(struct isl_sol_map *sol,
-	struct isl_tab *tab)
+static void sol_add(struct isl_sol *sol, struct isl_tab *tab)
+{
+	struct isl_basic_set *bset = NULL;
+	struct isl_mat *mat = NULL;
+	unsigned off;
+	int row;
+	isl_int m;
+
+	if (sol->error || !tab)
+		goto error;
+
+	if (tab->empty && !sol->add_empty)
+		return;
+
+	bset = sol_domain(sol);
+
+	if (tab->empty) {
+		sol_push_sol(sol, bset, NULL);
+		return;
+	}
+
+	off = 2 + tab->M;
+
+	mat = isl_mat_alloc(tab->mat->ctx, 1 + sol->n_out,
+					    1 + tab->n_param + tab->n_div);
+	if (!mat)
+		goto error;
+
+	isl_int_init(m);
+
+	isl_seq_clr(mat->row[0] + 1, mat->n_col - 1);
+	isl_int_set_si(mat->row[0][0], 1);
+	for (row = 0; row < sol->n_out; ++row) {
+		int i = tab->n_param + row;
+		int r, j;
+
+		isl_seq_clr(mat->row[1 + row], mat->n_col);
+		if (!tab->var[i].is_row) {
+			if (tab->M)
+				isl_die(mat->ctx, isl_error_invalid,
+					"unbounded optimum", goto error2);
+			continue;
+		}
+
+		r = tab->var[i].index;
+		if (tab->M &&
+		    isl_int_ne(tab->mat->row[r][2], tab->mat->row[r][0]))
+			isl_die(mat->ctx, isl_error_invalid,
+				"unbounded optimum", goto error2);
+		isl_int_gcd(m, mat->row[0][0], tab->mat->row[r][0]);
+		isl_int_divexact(m, tab->mat->row[r][0], m);
+		scale_rows(mat, m, 1 + row);
+		isl_int_divexact(m, mat->row[0][0], tab->mat->row[r][0]);
+		isl_int_mul(mat->row[1 + row][0], m, tab->mat->row[r][1]);
+		for (j = 0; j < tab->n_param; ++j) {
+			int col;
+			if (tab->var[j].is_row)
+				continue;
+			col = tab->var[j].index;
+			isl_int_mul(mat->row[1 + row][1 + j], m,
+				    tab->mat->row[r][off + col]);
+		}
+		for (j = 0; j < tab->n_div; ++j) {
+			int col;
+			if (tab->var[tab->n_var - tab->n_div+j].is_row)
+				continue;
+			col = tab->var[tab->n_var - tab->n_div+j].index;
+			isl_int_mul(mat->row[1 + row][1 + tab->n_param + j], m,
+				    tab->mat->row[r][off + col]);
+		}
+		if (sol->max)
+			isl_seq_neg(mat->row[1 + row], mat->row[1 + row],
+				    mat->n_col);
+	}
+
+	isl_int_clear(m);
+
+	sol_push_sol(sol, bset, mat);
+	return;
+error2:
+	isl_int_clear(m);
+error:
+	isl_basic_set_free(bset);
+	isl_mat_free(mat);
+	sol->error = 1;
+}
+
+struct isl_sol_map {
+	struct isl_sol	sol;
+	struct isl_map	*map;
+	struct isl_set	*empty;
+};
+
+static void sol_map_free(struct isl_sol_map *sol_map)
+{
+	if (!sol_map)
+		return;
+	if (sol_map->sol.context)
+		sol_map->sol.context->op->free(sol_map->sol.context);
+	isl_map_free(sol_map->map);
+	isl_set_free(sol_map->empty);
+	free(sol_map);
+}
+
+static void sol_map_free_wrap(struct isl_sol *sol)
+{
+	sol_map_free((struct isl_sol_map *)sol);
+}
+
+/* This function is called for parts of the context where there is
+ * no solution, with "bset" corresponding to the context tableau.
+ * Simply add the basic set to the set "empty".
+ */
+static void sol_map_add_empty(struct isl_sol_map *sol,
+	struct isl_basic_set *bset)
+{
+	if (!bset)
+		goto error;
+	isl_assert(bset->ctx, sol->empty, goto error);
+
+	sol->empty = isl_set_grow(sol->empty, 1);
+	bset = isl_basic_set_simplify(bset);
+	bset = isl_basic_set_finalize(bset);
+	sol->empty = isl_set_add_basic_set(sol->empty, isl_basic_set_copy(bset));
+	if (!sol->empty)
+		goto error;
+	isl_basic_set_free(bset);
+	return;
+error:
+	isl_basic_set_free(bset);
+	sol->sol.error = 1;
+}
+
+static void sol_map_add_empty_wrap(struct isl_sol *sol,
+	struct isl_basic_set *bset)
+{
+	sol_map_add_empty((struct isl_sol_map *)sol, bset);
+}
+
+/* Given a basic map "dom" that represents the context and an affine
+ * matrix "M" that maps the dimensions of the context to the
+ * output variables, construct a basic map with the same parameters
+ * and divs as the context, the dimensions of the context as input
+ * dimensions and a number of output dimensions that is equal to
+ * the number of output dimensions in the input map.
+ *
+ * The constraints and divs of the context are simply copied
+ * from "dom".  For each row
+ *	x = c + e(y)
+ * an equality
+ *	c + e(y) - d x = 0
+ * is added, with d the common denominator of M.
+ */
+static void sol_map_add(struct isl_sol_map *sol,
+	struct isl_basic_set *dom, struct isl_mat *M)
 {
 	int i;
 	struct isl_basic_map *bmap = NULL;
-	isl_basic_set *context_bset;
 	unsigned n_eq;
 	unsigned n_ineq;
 	unsigned nparam;
 	unsigned total;
 	unsigned n_div;
 	unsigned n_out;
-	unsigned off;
 
-	if (!sol || !tab)
+	if (sol->sol.error || !dom || !M)
 		goto error;
 
-	if (tab->empty)
-		return add_empty(sol);
-
-	context_bset = sol->sol.context->op->peek_basic_set(sol->sol.context);
-	off = 2 + tab->M;
-	n_out = isl_map_dim(sol->map, isl_dim_out);
-	n_eq = context_bset->n_eq + n_out;
-	n_ineq = context_bset->n_ineq;
-	nparam = tab->n_param;
+	n_out = sol->sol.n_out;
+	n_eq = dom->n_eq + n_out;
+	n_ineq = dom->n_ineq;
+	n_div = dom->n_div;
+	nparam = isl_basic_set_total_dim(dom) - n_div;
 	total = isl_map_dim(sol->map, isl_dim_all);
-	bmap = isl_basic_map_alloc_dim(isl_map_get_dim(sol->map),
-				    tab->n_div, n_eq, 2 * tab->n_div + n_ineq);
+	bmap = isl_basic_map_alloc_space(isl_map_get_space(sol->map),
+					n_div, n_eq, 2 * n_div + n_ineq);
 	if (!bmap)
 		goto error;
-	n_div = tab->n_div;
-	if (tab->rational)
+	if (sol->sol.rational)
 		ISL_F_SET(bmap, ISL_BASIC_MAP_RATIONAL);
-	for (i = 0; i < context_bset->n_div; ++i) {
+	for (i = 0; i < dom->n_div; ++i) {
 		int k = isl_basic_map_alloc_div(bmap);
 		if (k < 0)
 			goto error;
-		isl_seq_cpy(bmap->div[k],
-			    context_bset->div[i], 1 + 1 + nparam);
+		isl_seq_cpy(bmap->div[k], dom->div[i], 1 + 1 + nparam);
 		isl_seq_clr(bmap->div[k] + 1 + 1 + nparam, total - nparam);
 		isl_seq_cpy(bmap->div[k] + 1 + 1 + total,
-			    context_bset->div[i] + 1 + 1 + nparam, i);
+			    dom->div[i] + 1 + 1 + nparam, i);
 	}
-	for (i = 0; i < context_bset->n_eq; ++i) {
+	for (i = 0; i < dom->n_eq; ++i) {
 		int k = isl_basic_map_alloc_equality(bmap);
 		if (k < 0)
 			goto error;
-		isl_seq_cpy(bmap->eq[k], context_bset->eq[i], 1 + nparam);
+		isl_seq_cpy(bmap->eq[k], dom->eq[i], 1 + nparam);
 		isl_seq_clr(bmap->eq[k] + 1 + nparam, total - nparam);
 		isl_seq_cpy(bmap->eq[k] + 1 + total,
-			    context_bset->eq[i] + 1 + nparam, n_div);
+			    dom->eq[i] + 1 + nparam, n_div);
 	}
-	for (i = 0; i < context_bset->n_ineq; ++i) {
+	for (i = 0; i < dom->n_ineq; ++i) {
 		int k = isl_basic_map_alloc_inequality(bmap);
 		if (k < 0)
 			goto error;
-		isl_seq_cpy(bmap->ineq[k],
-			context_bset->ineq[i], 1 + nparam);
+		isl_seq_cpy(bmap->ineq[k], dom->ineq[i], 1 + nparam);
 		isl_seq_clr(bmap->ineq[k] + 1 + nparam, total - nparam);
 		isl_seq_cpy(bmap->ineq[k] + 1 + total,
-			context_bset->ineq[i] + 1 + nparam, n_div);
+			dom->ineq[i] + 1 + nparam, n_div);
 	}
-	for (i = tab->n_param; i < total; ++i) {
+	for (i = 0; i < M->n_row - 1; ++i) {
 		int k = isl_basic_map_alloc_equality(bmap);
 		if (k < 0)
 			goto error;
-		isl_seq_clr(bmap->eq[k] + 1, isl_basic_map_total_dim(bmap));
-		if (!tab->var[i].is_row) {
-			/* no unbounded */
-			isl_assert(bmap->ctx, !tab->M, goto error);
-			isl_int_set_si(bmap->eq[k][0], 0);
-			if (sol->max)
-				isl_int_set_si(bmap->eq[k][1 + i], 1);
-			else
-				isl_int_set_si(bmap->eq[k][1 + i], -1);
-		} else {
-			int row, j;
-			row = tab->var[i].index;
-			/* no unbounded */
-			if (tab->M)
-				isl_assert(bmap->ctx,
-					isl_int_eq(tab->mat->row[row][2],
-						   tab->mat->row[row][0]),
-					goto error);
-			isl_int_set(bmap->eq[k][0], tab->mat->row[row][1]);
-			for (j = 0; j < tab->n_param; ++j) {
-				int col;
-				if (tab->var[j].is_row)
-					continue;
-				col = tab->var[j].index;
-				isl_int_set(bmap->eq[k][1 + j],
-					    tab->mat->row[row][off + col]);
-			}
-			for (j = 0; j < tab->n_div; ++j) {
-				int col;
-				if (tab->var[tab->n_var - tab->n_div+j].is_row)
-					continue;
-				col = tab->var[tab->n_var - tab->n_div+j].index;
-				isl_int_set(bmap->eq[k][1 + total + j],
-					    tab->mat->row[row][off + col]);
-			}
-			if (sol->max)
-				isl_int_set(bmap->eq[k][1 + i],
-					    tab->mat->row[row][0]);
-			else
-				isl_int_neg(bmap->eq[k][1 + i],
-					    tab->mat->row[row][0]);
-		}
+		isl_seq_cpy(bmap->eq[k], M->row[1 + i], 1 + nparam);
+		isl_seq_clr(bmap->eq[k] + 1 + nparam, n_out);
+		isl_int_neg(bmap->eq[k][1 + nparam + i], M->row[0][0]);
+		isl_seq_cpy(bmap->eq[k] + 1 + nparam + n_out,
+			    M->row[1 + i] + 1 + nparam, n_div);
 	}
 	bmap = isl_basic_map_simplify(bmap);
 	bmap = isl_basic_map_finalize(bmap);
 	sol->map = isl_map_grow(sol->map, 1);
-	sol->map = isl_map_add(sol->map, bmap);
+	sol->map = isl_map_add_basic_map(sol->map, bmap);
+	isl_basic_set_free(dom);
+	isl_mat_free(M);
 	if (!sol->map)
-		goto error;
-	return sol;
+		sol->sol.error = 1;
+	return;
 error:
+	isl_basic_set_free(dom);
+	isl_mat_free(M);
 	isl_basic_map_free(bmap);
-	sol_free(&sol->sol);
-	return NULL;
+	sol->sol.error = 1;
 }
 
-static struct isl_sol *sol_map_add_wrap(struct isl_sol *sol,
-	struct isl_tab *tab)
+static void sol_map_add_wrap(struct isl_sol *sol,
+	struct isl_basic_set *dom, struct isl_mat *M)
 {
-	return (struct isl_sol *)sol_map_add((struct isl_sol_map *)sol, tab);
+	sol_map_add((struct isl_sol_map *)sol, dom, M);
 }
 
 
@@ -757,7 +1066,7 @@ error:
 }
 
 /* Return the first known violated constraint, i.e., a non-negative
- * contraint that currently has an either obviously negative value
+ * constraint that currently has an either obviously negative value
  * or a previously determined to be negative value.
  *
  * If any constraint has a negative coefficient for the big parameter,
@@ -771,8 +1080,11 @@ static int first_neg(struct isl_tab *tab)
 		for (row = tab->n_redundant; row < tab->n_row; ++row) {
 			if (!isl_tab_var_from_row(tab, row)->is_nonneg)
 				continue;
-			if (isl_int_is_neg(tab->mat->row[row][2]))
-				return row;
+			if (!isl_int_is_neg(tab->mat->row[row][2]))
+				continue;
+			if (tab->row_sign)
+				tab->row_sign[row] = isl_tab_row_neg;
+			return row;
 		}
 	for (row = tab->n_redundant; row < tab->n_row; ++row) {
 		if (!isl_tab_var_from_row(tab, row)->is_nonneg)
@@ -790,32 +1102,117 @@ static int first_neg(struct isl_tab *tab)
 	return -1;
 }
 
-/* Resolve all known or obviously violated constraints through pivoting.
- * In particular, as long as we can find any violated constraint, we
- * look for a pivoting column that would result in the lexicographicallly
- * smallest increment in the sample point.  If there is no such column
- * then the tableau is infeasible.
+/* Check whether the invariant that all columns are lexico-positive
+ * is satisfied.  This function is not called from the current code
+ * but is useful during debugging.
  */
-static struct isl_tab *restore_lexmin(struct isl_tab *tab)
+static void check_lexpos(struct isl_tab *tab) __attribute__ ((unused));
+static void check_lexpos(struct isl_tab *tab)
 {
-	int row, col;
+	unsigned off = 2 + tab->M;
+	int col;
+	int var;
+	int row;
 
-	if (!tab)
-		return NULL;
+	for (col = tab->n_dead; col < tab->n_col; ++col) {
+		if (tab->col_var[col] >= 0 &&
+		    (tab->col_var[col] < tab->n_param ||
+		     tab->col_var[col] >= tab->n_var - tab->n_div))
+			continue;
+		for (var = tab->n_param; var < tab->n_var - tab->n_div; ++var) {
+			if (!tab->var[var].is_row) {
+				if (tab->var[var].index == col)
+					break;
+				else
+					continue;
+			}
+			row = tab->var[var].index;
+			if (isl_int_is_zero(tab->mat->row[row][off + col]))
+				continue;
+			if (isl_int_is_pos(tab->mat->row[row][off + col]))
+				break;
+			fprintf(stderr, "lexneg column %d (row %d)\n",
+				col, row);
+		}
+		if (var >= tab->n_var - tab->n_div)
+			fprintf(stderr, "zero column %d\n", col);
+	}
+}
+
+/* Report to the caller that the given constraint is part of an encountered
+ * conflict.
+ */
+static int report_conflicting_constraint(struct isl_tab *tab, int con)
+{
+	return tab->conflict(con, tab->conflict_user);
+}
+
+/* Given a conflicting row in the tableau, report all constraints
+ * involved in the row to the caller.  That is, the row itself
+ * (if represents a constraint) and all constraint columns with
+ * non-zero (and therefore negative) coefficient.
+ */
+static int report_conflict(struct isl_tab *tab, int row)
+{
+	int j;
+	isl_int *tr;
+
+	if (!tab->conflict)
+		return 0;
+
+	if (tab->row_var[row] < 0 &&
+	    report_conflicting_constraint(tab, ~tab->row_var[row]) < 0)
+		return -1;
+
+	tr = tab->mat->row[row] + 2 + tab->M;
+
+	for (j = tab->n_dead; j < tab->n_col; ++j) {
+		if (tab->col_var[j] >= 0 &&
+		    (tab->col_var[j] < tab->n_param  ||
+		    tab->col_var[j] >= tab->n_var - tab->n_div))
+			continue;
+
+		if (!isl_int_is_neg(tr[j]))
+			continue;
+
+		if (tab->col_var[j] < 0 &&
+		    report_conflicting_constraint(tab, ~tab->col_var[j]) < 0)
+			return -1;
+	}
+
+	return 0;
+}
+
+/* Resolve all known or obviously violated constraints through pivoting.
+ * In particular, as long as we can find any violated constraint, we
+ * look for a pivoting column that would result in the lexicographically
+ * smallest increment in the sample point.  If there is no such column
+ * then the tableau is infeasible.
+ */
+static int restore_lexmin(struct isl_tab *tab) WARN_UNUSED;
+static int restore_lexmin(struct isl_tab *tab)
+{
+	int row, col;
+
+	if (!tab)
+		return -1;
 	if (tab->empty)
-		return tab;
+		return 0;
 	while ((row = first_neg(tab)) != -1) {
 		col = lexmin_pivot_col(tab, row);
-		if (col >= tab->n_col)
-			return isl_tab_mark_empty(tab);
+		if (col >= tab->n_col) {
+			if (report_conflict(tab, row) < 0)
+				return -1;
+			if (isl_tab_mark_empty(tab) < 0)
+				return -1;
+			return 0;
+		}
 		if (col < 0)
-			goto error;
-		isl_tab_pivot(tab, row, col);
+			return -1;
+		if (isl_tab_pivot(tab, row, col) < 0)
+			return -1;
 	}
-	return tab;
-error:
-	isl_tab_free(tab);
-	return NULL;
+	return 0;
 }
 
 /* Given a row that represents an equality, look for an appropriate
@@ -884,19 +1281,21 @@ static struct isl_tab *add_lexmin_valid_eq(struct isl_tab *tab, isl_int *eq)
 	i = last_var_col_or_int_par_col(tab, r);
 	if (i < 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)
+			goto error;
 		isl_seq_neg(eq, eq, 1 + tab->n_var);
 		r = isl_tab_add_row(tab, eq);
 		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;
 	} else {
-		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++;
-
-		tab = restore_lexmin(tab);
 	}
 
 	return tab;
@@ -924,78 +1323,77 @@ static int is_constant(struct isl_tab *tab, int row)
  * In the end we try to use one of the two constraints to eliminate
  * a column.
  */
-static struct isl_tab *add_lexmin_eq(struct isl_tab *tab, isl_int *eq)
+static int add_lexmin_eq(struct isl_tab *tab, isl_int *eq) WARN_UNUSED;
+static int add_lexmin_eq(struct isl_tab *tab, isl_int *eq)
 {
 	int r1, r2;
 	int row;
 	struct isl_tab_undo *snap;
 
 	if (!tab)
-		return NULL;
+		return -1;
 	snap = isl_tab_snap(tab);
 	r1 = isl_tab_add_row(tab, eq);
 	if (r1 < 0)
-		goto error;
+		return -1;
 	tab->con[r1].is_nonneg = 1;
-	isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r1]);
+	if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r1]) < 0)
+		return -1;
 
 	row = tab->con[r1].index;
 	if (is_constant(tab, row)) {
 		if (!isl_int_is_zero(tab->mat->row[row][1]) ||
-		    (tab->M && !isl_int_is_zero(tab->mat->row[row][2])))
-			return isl_tab_mark_empty(tab);
+		    (tab->M && !isl_int_is_zero(tab->mat->row[row][2]))) {
+			if (isl_tab_mark_empty(tab) < 0)
+				return -1;
+			return 0;
+		}
 		if (isl_tab_rollback(tab, snap) < 0)
-			goto error;
-		return tab;
+			return -1;
+		return 0;
 	}
 
-	tab = restore_lexmin(tab);
-	if (!tab || tab->empty)
-		return tab;
+	if (restore_lexmin(tab) < 0)
+		return -1;
+	if (tab->empty)
+		return 0;
 
 	isl_seq_neg(eq, eq, 1 + tab->n_var);
 
 	r2 = isl_tab_add_row(tab, eq);
 	if (r2 < 0)
-		goto error;
+		return -1;
 	tab->con[r2].is_nonneg = 1;
-	isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r2]);
+	if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r2]) < 0)
+		return -1;
 
-	tab = restore_lexmin(tab);
-	if (!tab || tab->empty)
-		return tab;
+	if (restore_lexmin(tab) < 0)
+		return -1;
+	if (tab->empty)
+		return 0;
 
-	if (!tab->con[r1].is_row)
-		isl_tab_kill_col(tab, tab->con[r1].index);
-	else if (!tab->con[r2].is_row)
-		isl_tab_kill_col(tab, tab->con[r2].index);
-	else if (isl_int_is_zero(tab->mat->row[tab->con[r1].index][1])) {
-		unsigned off = 2 + tab->M;
-		int i;
-		int row = tab->con[r1].index;
-		i = isl_seq_first_non_zero(tab->mat->row[row]+off+tab->n_dead,
-						tab->n_col - tab->n_dead);
-		if (i != -1) {
-			isl_tab_pivot(tab, row, tab->n_dead + i);
-			isl_tab_kill_col(tab, tab->n_dead + i);
-		}
+	if (!tab->con[r1].is_row) {
+		if (isl_tab_kill_col(tab, tab->con[r1].index) < 0)
+			return -1;
+	} else if (!tab->con[r2].is_row) {
+		if (isl_tab_kill_col(tab, tab->con[r2].index) < 0)
+			return -1;
 	}
 
-	if (tab->bset) {
-		tab->bset = isl_basic_set_add_ineq(tab->bset, eq);
-		isl_tab_push(tab, isl_tab_undo_bset_ineq);
+	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->bset = isl_basic_set_add_ineq(tab->bset, eq);
+		tab->bmap = isl_basic_map_add_ineq(tab->bmap, eq);
 		isl_seq_neg(eq, eq, 1 + tab->n_var);
-		isl_tab_push(tab, isl_tab_undo_bset_ineq);
-		if (!tab->bset)
-			goto error;
+		if (isl_tab_push(tab, isl_tab_undo_bmap_ineq) < 0)
+			return -1;
+		if (!tab->bmap)
+			return -1;
 	}
 
-	return tab;
-error:
-	isl_tab_free(tab);
-	return NULL;
+	return 0;
 }
 
 /* Add an inequality to the tableau, resolving violations using
@@ -1007,26 +1405,31 @@ static struct isl_tab *add_lexmin_ineq(struct isl_tab *tab, isl_int *ineq)
 
 	if (!tab)
 		return NULL;
-	if (tab->bset) {
-		tab->bset = isl_basic_set_add_ineq(tab->bset, ineq);
-		isl_tab_push(tab, isl_tab_undo_bset_ineq);
-		if (!tab->bset)
+	if (tab->bmap) {
+		tab->bmap = isl_basic_map_add_ineq(tab->bmap, ineq);
+		if (isl_tab_push(tab, isl_tab_undo_bmap_ineq) < 0)
+			goto error;
+		if (!tab->bmap)
 			goto error;
 	}
 	r = isl_tab_add_row(tab, ineq);
 	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;
 	if (isl_tab_row_is_redundant(tab, tab->con[r].index)) {
-		isl_tab_mark_redundant(tab, tab->con[r].index);
+		if (isl_tab_mark_redundant(tab, tab->con[r].index) < 0)
+			goto error;
 		return tab;
 	}
 
-	tab = restore_lexmin(tab);
-	if (tab && !tab->empty && tab->con[r].is_row &&
+	if (restore_lexmin(tab) < 0)
+		goto error;
+	if (!tab->empty && tab->con[r].is_row &&
 		 isl_tab_row_is_redundant(tab, tab->con[r].index))
-		isl_tab_mark_redundant(tab, tab->con[r].index);
+		if (isl_tab_mark_redundant(tab, tab->con[r].index) < 0)
+			goto error;
 	return tab;
 error:
 	isl_tab_free(tab);
@@ -1068,7 +1471,7 @@ static int integer_variable(struct isl_tab *tab, int row)
 	int i;
 	unsigned off = 2 + tab->M;
 
-	for (i = 0; i < tab->n_col; ++i) {
+	for (i = tab->n_dead; i < tab->n_col; ++i) {
 		if (tab->col_var[i] >= 0 &&
 		    (tab->col_var[i] < tab->n_param ||
 		     tab->col_var[i] >= tab->n_var - tab->n_div))
@@ -1092,8 +1495,9 @@ static int integer_constant(struct isl_tab *tab, int row)
 #define I_PAR	1 << 1
 #define I_VAR	1 << 2
 
-/* Check for first (non-parameter) variable that is non-integer and
- * therefore requires a cut.
+/* Check for next (non-parameter) variable after "var" (first if var == -1)
+ * that is non-integer and therefore requires a cut and return
+ * the index of the variable.
  * For parametric tableaus, there are three parts in a row,
  * the constant, the coefficients of the parameters and the rest.
  * For each part, we check whether the coefficients in that part
@@ -1102,16 +1506,16 @@ static int integer_constant(struct isl_tab *tab, int row)
  * current sample value is integral and no cut is required
  * (irrespective of whether the variable part is integral).
  */
-static int first_non_integer(struct isl_tab *tab, int *f)
+static int next_non_integer_var(struct isl_tab *tab, int var, int *f)
 {
-	int i;
+	var = var < 0 ? tab->n_param : var + 1;
 
-	for (i = tab->n_param; i < tab->n_var - tab->n_div; ++i) {
+	for (; var < tab->n_var - tab->n_div; ++var) {
 		int flags = 0;
 		int row;
-		if (!tab->var[i].is_row)
+		if (!tab->var[var].is_row)
 			continue;
-		row = tab->var[i].index;
+		row = tab->var[var].index;
 		if (integer_constant(tab, row))
 			ISL_FL_SET(flags, I_CST);
 		if (integer_parameter(tab, row))
@@ -1121,11 +1525,28 @@ static int first_non_integer(struct isl_tab *tab, int *f)
 		if (integer_variable(tab, row))
 			ISL_FL_SET(flags, I_VAR);
 		*f = flags;
-		return row;
+		return var;
 	}
 	return -1;
 }
 
+/* Check for first (non-parameter) variable that is non-integer and
+ * therefore requires a cut and return the corresponding row.
+ * For parametric tableaus, there are three parts in a row,
+ * the constant, the coefficients of the parameters and the rest.
+ * For each part, we check whether the coefficients in that part
+ * are all integral and if so, set the corresponding flag in *f.
+ * If the constant and the parameter part are integral, then the
+ * current sample value is integral and no cut is required
+ * (irrespective of whether the variable part is integral).
+ */
+static int first_non_integer_row(struct isl_tab *tab, int *f)
+{
+	int var = next_non_integer_var(tab, -1, f);
+
+	return var < 0 ? -1 : tab->var[var].index;
+}
+
 /* Add a (non-parametric) cut to cut away the non-integral sample
  * value of the given row.
  *
@@ -1173,7 +1594,8 @@ static int add_cut(struct isl_tab *tab, int row)
 			tab->mat->row[row][off + i], tab->mat->row[row][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;
 	if (tab->row_sign)
 		tab->row_sign[tab->con[r].index] = isl_tab_row_neg;
 
@@ -1184,15 +1606,17 @@ static int add_cut(struct isl_tab *tab, int row)
  * sample point is obtained or until the tableau is determined
  * to be integer infeasible.
  * As long as there is any non-integer value in the sample point,
- * we add an appropriate cut, if possible and resolve the violated
- * cut constraint using restore_lexmin.
+ * we add appropriate cuts, if possible, for each of these
+ * non-integer values and then resolve the violated
+ * cut constraints using restore_lexmin.
  * If one of the corresponding rows is equal to an integral
  * combination of variables/constraints plus a non-integral constant,
- * then there is no way to obtain an integer point an we return
+ * then there is no way to obtain an integer point and we return
  * a tableau that is marked empty.
  */
 static struct isl_tab *cut_to_integer_lexmin(struct isl_tab *tab)
 {
+	int var;
 	int row;
 	int flags;
 
@@ -1201,14 +1625,21 @@ static struct isl_tab *cut_to_integer_lexmin(struct isl_tab *tab)
 	if (tab->empty)
 		return tab;
 
-	while ((row = first_non_integer(tab, &flags)) != -1) {
-		if (ISL_FL_ISSET(flags, I_VAR))
-			return isl_tab_mark_empty(tab);
-		row = add_cut(tab, row);
-		if (row < 0)
+	while ((var = next_non_integer_var(tab, -1, &flags)) != -1) {
+		do {
+			if (ISL_FL_ISSET(flags, I_VAR)) {
+				if (isl_tab_mark_empty(tab) < 0)
+					goto error;
+				return tab;
+			}
+			row = tab->var[var].index;
+			row = add_cut(tab, row);
+			if (row < 0)
+				goto error;
+		} while ((var = next_non_integer_var(tab, var, &flags)) != -1);
+		if (restore_lexmin(tab) < 0)
 			goto error;
-		tab = restore_lexmin(tab);
-		if (!tab || tab->empty)
+		if (tab->empty)
 			break;
 	}
 	return tab;
@@ -1229,7 +1660,7 @@ static struct isl_tab *check_samples(struct isl_tab *tab, isl_int *ineq, int eq)
 	if (!tab)
 		return NULL;
 
-	isl_assert(tab->mat->ctx, tab->bset, goto error);
+	isl_assert(tab->mat->ctx, tab->bmap, goto error);
 	isl_assert(tab->mat->ctx, tab->samples, goto error);
 	isl_assert(tab->mat->ctx, tab->samples->n_col == 1 + tab->n_var, goto error);
 
@@ -1287,13 +1718,13 @@ static int sample_is_finite(struct isl_tab *tab)
 static struct isl_tab *check_integer_feasible(struct isl_tab *tab)
 {
 	struct isl_tab_undo *snap;
-	int feasible;
 
 	if (!tab)
 		return NULL;
 
 	snap = isl_tab_snap(tab);
-	isl_tab_push_basis(tab);
+	if (isl_tab_push_basis(tab) < 0)
+		goto error;
 
 	tab = cut_to_integer_lexmin(tab);
 	if (!tab)
@@ -1327,7 +1758,7 @@ static int tab_has_valid_sample(struct isl_tab *tab, isl_int *ineq, int eq)
 	if (!tab)
 		return -1;
 
-	isl_assert(tab->mat->ctx, tab->bset, return -1);
+	isl_assert(tab->mat->ctx, tab->bmap, return -1);
 	isl_assert(tab->mat->ctx, tab->samples, return -1);
 	isl_assert(tab->mat->ctx, tab->samples->n_col == 1 + tab->n_var, return -1);
 
@@ -1345,78 +1776,21 @@ static int tab_has_valid_sample(struct isl_tab *tab, isl_int *ineq, int eq)
 	return i < tab->n_sample;
 }
 
-/* For a div d = floor(f/m), add the constraints
- *
- *		f - m d >= 0
- *		-(f-(m-1)) + m d >= 0
- *
- * Note that the second constraint is the negation of
- *
- *		f - m d >= m
- */
-static void add_div_constraints(struct isl_context *context, unsigned div)
-{
-	unsigned total;
-	unsigned div_pos;
-	struct isl_vec *ineq;
-	struct isl_basic_set *bset;
-
-	bset = context->op->peek_basic_set(context);
-	if (!bset)
-		goto error;
-
-	total = isl_basic_set_total_dim(bset);
-	div_pos = 1 + total - bset->n_div + div;
-
-	ineq = ineq_for_div(bset, div);
-	if (!ineq)
-		goto error;
-
-	context->op->add_ineq(context, ineq->el, 0, 0);
-
-	isl_seq_neg(ineq->el, bset->div[div] + 1, 1 + total);
-	isl_int_set(ineq->el[div_pos], bset->div[div][0]);
-	isl_int_add(ineq->el[0], ineq->el[0], ineq->el[div_pos]);
-	isl_int_sub_ui(ineq->el[0], ineq->el[0], 1);
-
-	context->op->add_ineq(context, ineq->el, 0, 0);
-
-	isl_vec_free(ineq);
-
-	return;
-error:
-	context->op->invalidate(context);
-}
-
-/* Add a div specifed by "div" to the tableau "tab" and return
- * the index of the new div.  *nonneg is set to 1 if the div
- * is obviously non-negative.
+/* Add a div specified by "div" to the tableau "tab" and return
+ * 1 if the div is obviously non-negative.
  */
 static int context_tab_add_div(struct isl_tab *tab, struct isl_vec *div,
-	int *nonneg)
+	int (*add_ineq)(void *user, isl_int *), void *user)
 {
 	int i;
 	int r;
-	int k;
 	struct isl_mat *samples;
+	int nonneg;
 
-	for (i = 0; i < tab->n_var; ++i) {
-		if (isl_int_is_zero(div->el[2 + i]))
-			continue;
-		if (!tab->var[i].is_nonneg)
-			break;
-	}
-	*nonneg = i == tab->n_var;
-
-	if (isl_tab_extend_cons(tab, 3) < 0)
-		return -1;
-	if (isl_tab_extend_vars(tab, 1) < 0)
-		return -1;
-	r = isl_tab_allocate_var(tab);
+	r = isl_tab_add_div(tab, div, add_ineq, user);
 	if (r < 0)
 		return -1;
-	if (*nonneg)
-		tab->var[r].is_nonneg = 1;
+	nonneg = tab->var[r].is_nonneg;
 	tab->var[r].frozen = 1;
 
 	samples = isl_mat_extend(tab->samples,
@@ -1431,15 +1805,7 @@ static int context_tab_add_div(struct isl_tab *tab, struct isl_vec *div,
 			       samples->row[i][samples->n_col - 1], div->el[0]);
 	}
 
-	tab->bset = isl_basic_set_extend_dim(tab->bset,
-		isl_basic_set_get_dim(tab->bset), 1, 0, 2);
-	k = isl_basic_set_alloc_div(tab->bset);
-	if (k < 0)
-		return -1;
-	isl_seq_cpy(tab->bset->div[k], div->el, div->size);
-	isl_tab_push(tab, isl_tab_undo_bset_div);
-
-	return k;
+	return nonneg;
 }
 
 /* Add a div specified by "div" to both the main tableau and
@@ -1452,14 +1818,11 @@ static int add_div(struct isl_tab *tab, struct isl_context *context,
 	struct isl_vec *div)
 {
 	int r;
-	int k;
 	int nonneg;
 
-	k = context->op->add_div(context, div, &nonneg);
-	if (k < 0)
+	if ((nonneg = context->op->add_div(context, div)) < 0)
 		goto error;
 
-	add_div_constraints(context, k);
 	if (!context->op->is_ok(context))
 		goto error;
 
@@ -1482,12 +1845,12 @@ error:
 static int find_div(struct isl_tab *tab, isl_int *div, isl_int denom)
 {
 	int i;
-	unsigned total = isl_basic_set_total_dim(tab->bset);
+	unsigned total = isl_basic_map_total_dim(tab->bmap);
 
-	for (i = 0; i < tab->bset->n_div; ++i) {
-		if (isl_int_ne(tab->bset->div[i][0], denom))
+	for (i = 0; i < tab->bmap->n_div; ++i) {
+		if (isl_int_ne(tab->bmap->div[i][0], denom))
 			continue;
-		if (!isl_seq_eq(tab->bset->div[i] + 1, div, total))
+		if (!isl_seq_eq(tab->bmap->div[i] + 1, div, 1 + total))
 			continue;
 		return i;
 	}
@@ -1617,7 +1980,8 @@ static int add_parametric_cut(struct isl_tab *tab, int row,
 	}
 
 	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 (tab->row_sign)
 		tab->row_sign[tab->con[r].index] = isl_tab_row_neg;
 
@@ -1663,8 +2027,11 @@ static struct isl_tab *tab_for_lexmin(struct isl_basic_map *bmap,
 		if (!tab->row_sign)
 			goto error;
 	}
-	if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
-		return isl_tab_mark_empty(tab);
+	if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY)) {
+		if (isl_tab_mark_empty(tab) < 0)
+			goto error;
+		return tab;
+	}
 
 	for (i = tab->n_param; i < tab->n_var - tab->n_div; ++i) {
 		tab->var[i].is_nonneg = 1;
@@ -1683,6 +2050,8 @@ static struct isl_tab *tab_for_lexmin(struct isl_basic_map *bmap,
 		if (!tab || tab->empty)
 			return tab;
 	}
+	if (bmap->n_eq && restore_lexmin(tab) < 0)
+		goto error;
 	for (i = 0; i < bmap->n_ineq; ++i) {
 		if (max)
 			isl_seq_neg(bmap->ineq[i] + 1 + tab->n_param,
@@ -1735,6 +2104,7 @@ static int best_split(struct isl_tab *tab, struct isl_tab *context_tab)
 		struct isl_tab_undo *snap2;
 		struct isl_vec *ineq = NULL;
 		int r = 0;
+		int ok;
 
 		if (!isl_tab_var_from_row(tab, split)->is_nonneg)
 			continue;
@@ -1744,8 +2114,10 @@ static int best_split(struct isl_tab *tab, struct isl_tab *context_tab)
 		ineq = get_row_parameter_ineq(tab, split);
 		if (!ineq)
 			return -1;
-		context_tab = isl_tab_add_ineq(context_tab, ineq->el);
+		ok = isl_tab_add_ineq(context_tab, ineq->el) >= 0;
 		isl_vec_free(ineq);
+		if (!ok)
+			return -1;
 
 		snap2 = isl_tab_snap(context_tab);
 
@@ -1762,8 +2134,10 @@ static int best_split(struct isl_tab *tab, struct isl_tab *context_tab)
 			ineq = get_row_parameter_ineq(tab, row);
 			if (!ineq)
 				return -1;
-			context_tab = isl_tab_add_ineq(context_tab, ineq->el);
+			ok = isl_tab_add_ineq(context_tab, ineq->el) >= 0;
 			isl_vec_free(ineq);
+			if (!ok)
+				return -1;
 			var = &context_tab->con[context_tab->n_con - 1];
 			if (!context_tab->empty &&
 			    !isl_tab_min_at_most_neg_one(context_tab, var))
@@ -1788,7 +2162,7 @@ static struct isl_basic_set *context_lex_peek_basic_set(
 	struct isl_context_lex *clex = (struct isl_context_lex *)context;
 	if (!clex->tab)
 		return NULL;
-	return clex->tab->bset;
+	return isl_tab_peek_bset(clex->tab);
 }
 
 static struct isl_tab *context_lex_peek_tab(struct isl_context *context)
@@ -1797,24 +2171,14 @@ static struct isl_tab *context_lex_peek_tab(struct isl_context *context)
 	return clex->tab;
 }
 
-static void context_lex_extend(struct isl_context *context, int n)
-{
-	struct isl_context_lex *clex = (struct isl_context_lex *)context;
-	if (!clex->tab)
-		return;
-	if (isl_tab_extend_cons(clex->tab, n) >= 0)
-		return;
-	isl_tab_free(clex->tab);
-	clex->tab = NULL;
-}
-
 static void context_lex_add_eq(struct isl_context *context, isl_int *eq,
 		int check, int update)
 {
 	struct isl_context_lex *clex = (struct isl_context_lex *)context;
 	if (isl_tab_extend_cons(clex->tab, 2) < 0)
 		goto error;
-	clex->tab = add_lexmin_eq(clex->tab, eq);
+	if (add_lexmin_eq(clex->tab, eq) < 0)
+		goto error;
 	if (check) {
 		int v = tab_has_valid_sample(clex->tab, eq, 1);
 		if (v < 0)
@@ -1852,6 +2216,13 @@ error:
 	clex->tab = NULL;
 }
 
+static int context_lex_add_ineq_wrap(void *user, isl_int *ineq)
+{
+	struct isl_context *context = (struct isl_context *)user;
+	context_lex_add_ineq(context, ineq, 0, 0);
+	return context->op->is_ok(context) ? 0 : -1;
+}
+
 /* Check which signs can be obtained by "ineq" on all the currently
  * active sample values.  See row_sign for more information.
  */
@@ -1861,10 +2232,11 @@ static enum isl_tab_row_sign tab_ineq_sign(struct isl_tab *tab, isl_int *ineq,
 	int i;
 	int sgn;
 	isl_int tmp;
-	int res = isl_tab_row_unknown;
+	enum isl_tab_row_sign res = isl_tab_row_unknown;
 
-	isl_assert(tab->mat->ctx, tab->samples, return 0);
-	isl_assert(tab->mat->ctx, tab->samples->n_col == 1 + tab->n_var, return 0);
+	isl_assert(tab->mat->ctx, tab->samples, return isl_tab_row_unknown);
+	isl_assert(tab->mat->ctx, tab->samples->n_col == 1 + tab->n_var,
+			return isl_tab_row_unknown);
 
 	isl_int_init(tmp);
 	for (i = tab->n_outside; i < tab->n_sample; ++i) {
@@ -1914,7 +2286,8 @@ static int context_lex_test_ineq(struct isl_context *context, isl_int *ineq)
 		return -1;
 
 	snap = isl_tab_snap(clex->tab);
-	isl_tab_push_basis(clex->tab);
+	if (isl_tab_push_basis(clex->tab) < 0)
+		return -1;
 	clex->tab = add_lexmin_ineq(clex->tab, ineq);
 	clex->tab = check_integer_feasible(clex->tab);
 	if (!clex->tab)
@@ -1932,11 +2305,25 @@ static int context_lex_get_div(struct isl_context *context, struct isl_tab *tab,
 	return get_div(tab, context, div);
 }
 
-static int context_lex_add_div(struct isl_context *context, struct isl_vec *div,
-	int *nonneg)
+/* Add a div specified by "div" to the context tableau and return
+ * 1 if the div is obviously non-negative.
+ * context_tab_add_div will always return 1, because all variables
+ * in a isl_context_lex tableau are non-negative.
+ * However, if we are using a big parameter in the context, then this only
+ * reflects the non-negativity of the variable used to _encode_ the
+ * div, i.e., div' = M + div, so we can't draw any conclusions.
+ */
+static int context_lex_add_div(struct isl_context *context, struct isl_vec *div)
 {
 	struct isl_context_lex *clex = (struct isl_context_lex *)context;
-	return context_tab_add_div(clex->tab, div, nonneg);
+	int nonneg;
+	nonneg = context_tab_add_div(clex->tab, div,
+					context_lex_add_ineq_wrap, context);
+	if (nonneg < 0)
+		return -1;
+	if (clex->tab->M)
+		return 0;
+	return nonneg;
 }
 
 static int context_lex_detect_equalities(struct isl_context *context,
@@ -1953,10 +2340,11 @@ static int context_lex_best_split(struct isl_context *context,
 	int r;
 
 	snap = isl_tab_snap(clex->tab);
-	isl_tab_push_basis(clex->tab);
+	if (isl_tab_push_basis(clex->tab) < 0)
+		return -1;
 	r = best_split(tab, clex->tab);
 
-	if (isl_tab_rollback(clex->tab, snap) < 0)
+	if (r >= 0 && isl_tab_rollback(clex->tab, snap) < 0)
 		return -1;
 
 	return r;
@@ -1976,8 +2364,10 @@ static void *context_lex_save(struct isl_context *context)
 	struct isl_tab_undo *snap;
 
 	snap = isl_tab_snap(clex->tab);
-	isl_tab_push_basis(clex->tab);
-	isl_tab_save_samples(clex->tab);
+	if (isl_tab_push_basis(clex->tab) < 0)
+		return NULL;
+	if (isl_tab_save_samples(clex->tab) < 0)
+		return NULL;
 
 	return snap;
 }
@@ -2027,7 +2417,8 @@ static struct isl_tab *tab_detect_nonnegative_parameters(struct isl_tab *tab,
 	isl_seq_clr(ineq->el, ineq->size);
 	for (i = 0; i < context_tab->n_var; ++i) {
 		isl_int_set_si(ineq->el[1 + i], 1);
-		context_tab = isl_tab_add_ineq(context_tab, ineq->el);
+		if (isl_tab_add_ineq(context_tab, ineq->el) < 0)
+			goto error;
 		var = &context_tab->con[context_tab->n_con - 1];
 		if (!context_tab->empty &&
 		    !isl_tab_min_at_most_neg_one(context_tab, var)) {
@@ -2061,8 +2452,12 @@ static struct isl_tab *context_lex_detect_nonnegative_parameters(
 	struct isl_context_lex *clex = (struct isl_context_lex *)context;
 	struct isl_tab_undo *snap;
 
+	if (!tab)
+		return NULL;
+
 	snap = isl_tab_snap(clex->tab);
-	isl_tab_push_basis(clex->tab);
+	if (isl_tab_push_basis(clex->tab) < 0)
+		goto error;
 
 	tab = tab_detect_nonnegative_parameters(tab, clex->tab);
 
@@ -2119,7 +2514,8 @@ static struct isl_tab *context_tab_for_lexmin(struct isl_basic_set *bset)
 	tab = tab_for_lexmin((struct isl_basic_map *)bset, NULL, 1, 0);
 	if (!tab)
 		goto error;
-	tab->bset = bset;
+	if (isl_tab_track_bset(tab, bset) < 0)
+		goto error;
 	tab = isl_tab_init_samples(tab);
 	return tab;
 error:
@@ -2141,7 +2537,8 @@ static struct isl_context *isl_context_lex_alloc(struct isl_basic_set *dom)
 	clex->context.op = &isl_context_lex_op;
 
 	clex->tab = context_tab_for_lexmin(isl_basic_set_copy(dom));
-	clex->tab = restore_lexmin(clex->tab);
+	if (restore_lexmin(clex->tab) < 0)
+		goto error;
 	clex->tab = check_integer_feasible(clex->tab);
 	if (!clex->tab)
 		goto error;
@@ -2163,6 +2560,8 @@ static struct isl_tab *context_gbr_detect_nonnegative_parameters(
 	struct isl_context *context, struct isl_tab *tab)
 {
 	struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
+	if (!tab)
+		return NULL;
 	return tab_detect_nonnegative_parameters(tab, cgbr->tab);
 }
 
@@ -2172,7 +2571,7 @@ static struct isl_basic_set *context_gbr_peek_basic_set(
 	struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
 	if (!cgbr->tab)
 		return NULL;
-	return cgbr->tab->bset;
+	return isl_tab_peek_bset(cgbr->tab);
 }
 
 static struct isl_tab *context_gbr_peek_tab(struct isl_context *context)
@@ -2191,7 +2590,7 @@ static void gbr_init_shifted(struct isl_context_gbr *cgbr)
 {
 	int i, j;
 	struct isl_vec *cst;
-	struct isl_basic_set *bset = cgbr->tab->bset;
+	struct isl_basic_set *bset = isl_tab_peek_bset(cgbr->tab);
 	unsigned dim = isl_basic_set_total_dim(bset);
 
 	cst = isl_vec_alloc(cgbr->tab->mat->ctx, bset->n_ineq);
@@ -2255,7 +2654,7 @@ static struct isl_basic_set *drop_constant_terms(struct isl_basic_set *bset)
 
 static int use_shifted(struct isl_context_gbr *cgbr)
 {
-	return cgbr->tab->bset->n_eq == 0 && cgbr->tab->bset->n_div == 0;
+	return cgbr->tab->bmap->n_eq == 0 && cgbr->tab->bmap->n_div == 0;
 }
 
 static struct isl_vec *gbr_get_sample(struct isl_context_gbr *cgbr)
@@ -2277,13 +2676,14 @@ static struct isl_vec *gbr_get_sample(struct isl_context_gbr *cgbr)
 	}
 
 	if (!cgbr->cone) {
-		cgbr->cone = isl_tab_from_recession_cone(cgbr->tab->bset);
+		bset = isl_tab_peek_bset(cgbr->tab);
+		cgbr->cone = isl_tab_from_recession_cone(bset, 0);
 		if (!cgbr->cone)
 			return NULL;
-		cgbr->cone->bset = isl_basic_set_dup(cgbr->tab->bset);
+		if (isl_tab_track_bset(cgbr->cone, isl_basic_set_dup(bset)) < 0)
+			return NULL;
 	}
-	cgbr->cone = isl_tab_detect_implicit_equalities(cgbr->cone);
-	if (!cgbr->cone)
+	if (isl_tab_detect_implicit_equalities(cgbr->cone) < 0)
 		return NULL;
 
 	if (cgbr->cone->n_dead == cgbr->cone->n_col) {
@@ -2294,10 +2694,9 @@ static struct isl_vec *gbr_get_sample(struct isl_context_gbr *cgbr)
 			if (cgbr->tab->basis->n_col != 1 + cgbr->tab->n_var) {
 				isl_mat_free(cgbr->tab->basis);
 				cgbr->tab->basis = NULL;
-			} else {
-				cgbr->tab->n_zero = 0;
-				cgbr->tab->n_unbounded = 0;
 			}
+			cgbr->tab->n_zero = 0;
+			cgbr->tab->n_unbounded = 0;
 		}
 
 		snap = isl_tab_snap(cgbr->tab);
@@ -2312,13 +2711,13 @@ static struct isl_vec *gbr_get_sample(struct isl_context_gbr *cgbr)
 		return sample;
 	}
 
-	cone = isl_basic_set_dup(cgbr->cone->bset);
+	cone = isl_basic_set_dup(isl_tab_peek_bset(cgbr->cone));
 	cone = drop_constant_terms(cone);
 	cone = isl_basic_set_update_from_tab(cone, cgbr->cone);
 	cone = isl_basic_set_underlying_set(cone);
 	cone = isl_basic_set_gauss(cone, NULL);
 
-	bset = isl_basic_set_dup(cgbr->tab->bset);
+	bset = isl_basic_set_dup(isl_tab_peek_bset(cgbr->tab));
 	bset = isl_basic_set_update_from_tab(bset, cgbr->tab);
 	bset = isl_basic_set_underlying_set(bset);
 	bset = isl_basic_set_gauss(bset, NULL);
@@ -2342,7 +2741,8 @@ static void check_gbr_integer_feasible(struct isl_context_gbr *cgbr)
 
 	if (sample->size == 0) {
 		isl_vec_free(sample);
-		cgbr->tab = isl_tab_mark_empty(cgbr->tab);
+		if (isl_tab_mark_empty(cgbr->tab) < 0)
+			goto error;
 		return;
 	}
 
@@ -2356,15 +2756,14 @@ error:
 
 static struct isl_tab *add_gbr_eq(struct isl_tab *tab, isl_int *eq)
 {
-	int r;
-
 	if (!tab)
 		return NULL;
 
 	if (isl_tab_extend_cons(tab, 2) < 0)
 		goto error;
 
-	tab = isl_tab_add_eq(tab, eq);
+	if (isl_tab_add_eq(tab, eq) < 0)
+		goto error;
 
 	return tab;
 error:
@@ -2382,7 +2781,8 @@ static void context_gbr_add_eq(struct isl_context *context, isl_int *eq,
 	if (cgbr->cone && cgbr->cone->n_col != cgbr->cone->n_dead) {
 		if (isl_tab_extend_cons(cgbr->cone, 2) < 0)
 			goto error;
-		cgbr->cone = isl_tab_add_eq(cgbr->cone, eq);
+		if (isl_tab_add_eq(cgbr->cone, eq) < 0)
+			goto error;
 	}
 
 	if (check) {
@@ -2408,12 +2808,13 @@ static void add_gbr_ineq(struct isl_context_gbr *cgbr, isl_int *ineq)
 	if (isl_tab_extend_cons(cgbr->tab, 1) < 0)
 		goto error;
 
-	cgbr->tab = isl_tab_add_ineq(cgbr->tab, ineq);
+	if (isl_tab_add_ineq(cgbr->tab, ineq) < 0)
+		goto error;
 
 	if (cgbr->shifted && !cgbr->shifted->empty && use_shifted(cgbr)) {
 		int i;
 		unsigned dim;
-		dim = isl_basic_set_total_dim(cgbr->tab->bset);
+		dim = isl_basic_map_total_dim(cgbr->tab->bmap);
 
 		if (isl_tab_extend_cons(cgbr->shifted, 1) < 0)
 			goto error;
@@ -2424,7 +2825,8 @@ static void add_gbr_ineq(struct isl_context_gbr *cgbr, isl_int *ineq)
 			isl_int_add(ineq[0], ineq[0], ineq[1 + i]);
 		}
 
-		cgbr->shifted = isl_tab_add_ineq(cgbr->shifted, ineq);
+		if (isl_tab_add_ineq(cgbr->shifted, ineq) < 0)
+			goto error;
 
 		for (i = 0; i < dim; ++i) {
 			if (!isl_int_is_neg(ineq[1 + i]))
@@ -2436,7 +2838,8 @@ static void add_gbr_ineq(struct isl_context_gbr *cgbr, isl_int *ineq)
 	if (cgbr->cone && cgbr->cone->n_col != cgbr->cone->n_dead) {
 		if (isl_tab_extend_cons(cgbr->cone, 1) < 0)
 			goto error;
-		cgbr->cone = isl_tab_add_ineq(cgbr->cone, ineq);
+		if (isl_tab_add_ineq(cgbr->cone, ineq) < 0)
+			goto error;
 	}
 
 	return;
@@ -2469,6 +2872,13 @@ error:
 	cgbr->tab = NULL;
 }
 
+static int context_gbr_add_ineq_wrap(void *user, isl_int *ineq)
+{
+	struct isl_context *context = (struct isl_context *)user;
+	context_gbr_add_ineq(context, ineq, 0, 0);
+	return context->op->is_ok(context) ? 0 : -1;
+}
+
 static enum isl_tab_row_sign context_gbr_ineq_sign(struct isl_context *context,
 			isl_int *ineq, int strict)
 {
@@ -2532,7 +2942,6 @@ static int last_non_zero_var_col(struct isl_tab *tab, isl_int *p)
 {
 	int i;
 	int col;
-	unsigned dim = tab->n_var - tab->n_param - tab->n_div;
 
 	if (tab->n_var == 0)
 		return -1;
@@ -2572,20 +2981,20 @@ static void propagate_equalities(struct isl_context_gbr *cgbr,
 	if (!eq)
 		goto error;
 
-	if (isl_tab_extend_cons(tab, (cgbr->tab->bset->n_ineq - first)/2) < 0)
+	if (isl_tab_extend_cons(tab, (cgbr->tab->bmap->n_ineq - first)/2) < 0)
 		goto error;
 
 	isl_seq_clr(eq->el + 1 + tab->n_param,
 		    tab->n_var - tab->n_param - tab->n_div);
-	for (i = first; i < cgbr->tab->bset->n_ineq; i += 2) {
+	for (i = first; i < cgbr->tab->bmap->n_ineq; i += 2) {
 		int j;
 		int r;
 		struct isl_tab_undo *snap;
 		snap = isl_tab_snap(tab);
 
-		isl_seq_cpy(eq->el, cgbr->tab->bset->ineq[i], 1 + tab->n_param);
+		isl_seq_cpy(eq->el, cgbr->tab->bmap->ineq[i], 1 + tab->n_param);
 		isl_seq_cpy(eq->el + 1 + tab->n_var - tab->n_div,
-			    cgbr->tab->bset->ineq[i] + 1 + tab->n_param,
+			    cgbr->tab->bmap->ineq[i] + 1 + tab->n_param,
 			    tab->n_div);
 
 		r = isl_tab_add_row(tab, eq->el);
@@ -2601,10 +3010,13 @@ static void propagate_equalities(struct isl_context_gbr *cgbr,
 				goto error;
 			continue;
 		}
-		isl_tab_pivot(tab, r, j);
-		isl_tab_kill_col(tab, j);
+		if (isl_tab_pivot(tab, r, j) < 0)
+			goto error;
+		if (isl_tab_kill_col(tab, j) < 0)
+			goto error;
 
-		tab = restore_lexmin(tab);
+		if (restore_lexmin(tab) < 0)
+			goto error;
 	}
 
 	isl_vec_free(eq);
@@ -2621,23 +3033,24 @@ static int context_gbr_detect_equalities(struct isl_context *context,
 {
 	struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
 	struct isl_ctx *ctx;
-	int i;
-	enum isl_lp_result res;
 	unsigned n_ineq;
 
 	ctx = cgbr->tab->mat->ctx;
 
 	if (!cgbr->cone) {
-		cgbr->cone = isl_tab_from_recession_cone(cgbr->tab->bset);
+		struct isl_basic_set *bset = isl_tab_peek_bset(cgbr->tab);
+		cgbr->cone = isl_tab_from_recession_cone(bset, 0);
 		if (!cgbr->cone)
 			goto error;
-		cgbr->cone->bset = isl_basic_set_dup(cgbr->tab->bset);
+		if (isl_tab_track_bset(cgbr->cone, isl_basic_set_dup(bset)) < 0)
+			goto error;
 	}
-	cgbr->cone = isl_tab_detect_implicit_equalities(cgbr->cone);
+	if (isl_tab_detect_implicit_equalities(cgbr->cone) < 0)
+		goto error;
 
-	n_ineq = cgbr->tab->bset->n_ineq;
+	n_ineq = cgbr->tab->bmap->n_ineq;
 	cgbr->tab = isl_tab_detect_equalities(cgbr->tab, cgbr->cone);
-	if (cgbr->tab && cgbr->tab->bset->n_ineq > n_ineq)
+	if (cgbr->tab && cgbr->tab->bmap->n_ineq > n_ineq)
 		propagate_equalities(cgbr, tab, n_ineq);
 
 	return 0;
@@ -2653,8 +3066,7 @@ static int context_gbr_get_div(struct isl_context *context, struct isl_tab *tab,
 	return get_div(tab, context, div);
 }
 
-static int context_gbr_add_div(struct isl_context *context, struct isl_vec *div,
-	int *nonneg)
+static int context_gbr_add_div(struct isl_context *context, struct isl_vec *div)
 {
 	struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
 	if (cgbr->cone) {
@@ -2667,15 +3079,17 @@ static int context_gbr_add_div(struct isl_context *context, struct isl_vec *div,
 		if (isl_tab_allocate_var(cgbr->cone) <0)
 			return -1;
 
-		cgbr->cone->bset = isl_basic_set_extend_dim(cgbr->cone->bset,
-			isl_basic_set_get_dim(cgbr->cone->bset), 1, 0, 2);
-		k = isl_basic_set_alloc_div(cgbr->cone->bset);
+		cgbr->cone->bmap = isl_basic_map_extend_space(cgbr->cone->bmap,
+			isl_basic_map_get_space(cgbr->cone->bmap), 1, 0, 2);
+		k = isl_basic_map_alloc_div(cgbr->cone->bmap);
 		if (k < 0)
 			return -1;
-		isl_seq_cpy(cgbr->cone->bset->div[k], div->el, div->size);
-		isl_tab_push(cgbr->cone, isl_tab_undo_bset_div);
+		isl_seq_cpy(cgbr->cone->bmap->div[k], div->el, div->size);
+		if (isl_tab_push(cgbr->cone, isl_tab_undo_bmap_div) < 0)
+			return -1;
 	}
-	return context_tab_add_div(cgbr->tab, div, nonneg);
+	return context_tab_add_div(cgbr->tab, div,
+					context_gbr_add_ineq_wrap, context);
 }
 
 static int context_gbr_best_split(struct isl_context *context,
@@ -2688,7 +3102,7 @@ static int context_gbr_best_split(struct isl_context *context,
 	snap = isl_tab_snap(cgbr->tab);
 	r = best_split(tab, cgbr->tab);
 
-	if (isl_tab_rollback(cgbr->tab, snap) < 0)
+	if (r >= 0 && isl_tab_rollback(cgbr->tab, snap) < 0)
 		return -1;
 
 	return r;
@@ -2718,7 +3132,8 @@ static void *context_gbr_save(struct isl_context *context)
 		return NULL;
 
 	snap->tab_snap = isl_tab_snap(cgbr->tab);
-	isl_tab_save_samples(cgbr->tab);
+	if (isl_tab_save_samples(cgbr->tab) < 0)
+		goto error;
 
 	if (cgbr->shifted)
 		snap->shifted_snap = isl_tab_snap(cgbr->shifted);
@@ -2731,36 +3146,49 @@ static void *context_gbr_save(struct isl_context *context)
 		snap->cone_snap = NULL;
 
 	return snap;
+error:
+	free(snap);
+	return NULL;
 }
 
 static void context_gbr_restore(struct isl_context *context, void *save)
 {
 	struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
 	struct isl_gbr_tab_undo *snap = (struct isl_gbr_tab_undo *)save;
+	if (!snap)
+		goto error;
 	if (isl_tab_rollback(cgbr->tab, snap->tab_snap) < 0) {
 		isl_tab_free(cgbr->tab);
 		cgbr->tab = NULL;
 	}
 
-	if (snap->shifted_snap)
-		isl_tab_rollback(cgbr->shifted, snap->shifted_snap);
-	else if (cgbr->shifted) {
+	if (snap->shifted_snap) {
+		if (isl_tab_rollback(cgbr->shifted, snap->shifted_snap) < 0)
+			goto error;
+	} else if (cgbr->shifted) {
 		isl_tab_free(cgbr->shifted);
 		cgbr->shifted = NULL;
 	}
 
-	if (snap->cone_snap)
-		isl_tab_rollback(cgbr->cone, snap->cone_snap);
-	else if (cgbr->cone) {
+	if (snap->cone_snap) {
+		if (isl_tab_rollback(cgbr->cone, snap->cone_snap) < 0)
+			goto error;
+	} else if (cgbr->cone) {
 		isl_tab_free(cgbr->cone);
 		cgbr->cone = NULL;
 	}
 
 	free(snap);
-}
 
-static int context_gbr_is_ok(struct isl_context *context)
-{
+	return;
+error:
+	free(snap);
+	isl_tab_free(cgbr->tab);
+	cgbr->tab = NULL;
+}
+
+static int context_gbr_is_ok(struct isl_context *context)
+{
 	struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
 	return !!cgbr->tab;
 }
@@ -2820,8 +3248,8 @@ static struct isl_context *isl_context_gbr_alloc(struct isl_basic_set *dom)
 	cgbr->tab = isl_tab_init_samples(cgbr->tab);
 	if (!cgbr->tab)
 		goto error;
-	cgbr->tab->bset = isl_basic_set_cow(isl_basic_set_copy(dom));
-	if (!cgbr->tab->bset)
+	if (isl_tab_track_bset(cgbr->tab,
+				isl_basic_set_cow(isl_basic_set_copy(dom))) < 0)
 		goto error;
 	check_gbr_integer_feasible(cgbr);
 
@@ -2836,7 +3264,7 @@ static struct isl_context *isl_context_alloc(struct isl_basic_set *dom)
 	if (!dom)
 		return NULL;
 
-	if (dom->ctx->context == ISL_CONTEXT_LEXMIN)
+	if (dom->ctx->opt->context == ISL_CONTEXT_LEXMIN)
 		return isl_context_lex_alloc(dom);
 	else
 		return isl_context_gbr_alloc(dom);
@@ -2849,19 +3277,27 @@ static struct isl_context *isl_context_alloc(struct isl_basic_set *dom)
  * a minimization problem, which means that the variables in the
  * tableau have value "M - x" rather than "M + x".
  */
-static struct isl_sol_map *sol_map_init(struct isl_basic_map *bmap,
+static struct isl_sol *sol_map_init(struct isl_basic_map *bmap,
 	struct isl_basic_set *dom, int track_empty, int max)
 {
-	struct isl_sol_map *sol_map;
+	struct isl_sol_map *sol_map = NULL;
+
+	if (!bmap)
+		goto error;
 
-	sol_map = isl_calloc_type(bset->ctx, struct isl_sol_map);
+	sol_map = isl_calloc_type(bmap->ctx, struct isl_sol_map);
 	if (!sol_map)
 		goto error;
 
-	sol_map->max = max;
+	sol_map->sol.rational = ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL);
+	sol_map->sol.dec_level.callback.run = &sol_dec_level_wrap;
+	sol_map->sol.dec_level.sol = &sol_map->sol;
+	sol_map->sol.max = max;
+	sol_map->sol.n_out = isl_basic_map_dim(bmap, isl_dim_out);
 	sol_map->sol.add = &sol_map_add_wrap;
+	sol_map->sol.add_empty = track_empty ? &sol_map_add_empty_wrap : NULL;
 	sol_map->sol.free = &sol_map_free_wrap;
-	sol_map->map = isl_map_alloc_dim(isl_basic_map_get_dim(bmap), 1,
+	sol_map->map = isl_map_alloc_space(isl_basic_map_get_space(bmap), 1,
 					    ISL_MAP_DISJOINT);
 	if (!sol_map->map)
 		goto error;
@@ -2871,14 +3307,14 @@ static struct isl_sol_map *sol_map_init(struct isl_basic_map *bmap,
 		goto error;
 
 	if (track_empty) {
-		sol_map->empty = isl_set_alloc_dim(isl_basic_set_get_dim(dom),
+		sol_map->empty = isl_set_alloc_space(isl_basic_set_get_space(dom),
 							1, ISL_SET_DISJOINT);
 		if (!sol_map->empty)
 			goto error;
 	}
 
 	isl_basic_set_free(dom);
-	return sol_map;
+	return &sol_map->sol;
 error:
 	isl_basic_set_free(dom);
 	sol_map_free(sol_map);
@@ -2989,7 +3425,7 @@ static enum isl_tab_row_sign row_sign(struct isl_tab *tab,
 	struct isl_sol *sol, int row)
 {
 	struct isl_vec *ineq = NULL;
-	int res = isl_tab_row_unknown;
+	enum isl_tab_row_sign res = isl_tab_row_unknown;
 	int critical;
 	int strict;
 	int row2;
@@ -3053,10 +3489,10 @@ static enum isl_tab_row_sign row_sign(struct isl_tab *tab,
 	return res;
 error:
 	isl_vec_free(ineq);
-	return 0;
+	return isl_tab_row_unknown;
 }
 
-static struct isl_sol *find_solutions(struct isl_sol *sol, struct isl_tab *tab);
+static void find_solutions(struct isl_sol *sol, struct isl_tab *tab);
 
 /* Find solutions for values of the parameters that satisfy the given
  * inequality.
@@ -3072,8 +3508,7 @@ static struct isl_sol *find_solutions(struct isl_sol *sol, struct isl_tab *tab);
  * and that we need to do this before saving the current basis
  * such that the basis has been restore before we restore the row signs.
  */
-static struct isl_sol *find_in_pos(struct isl_sol *sol,
-	struct isl_tab *tab, isl_int *ineq)
+static void find_in_pos(struct isl_sol *sol, struct isl_tab *tab, isl_int *ineq)
 {
 	void *saved;
 
@@ -3087,25 +3522,25 @@ static struct isl_sol *find_in_pos(struct isl_sol *sol,
 
 	sol->context->op->add_ineq(sol->context, ineq, 0, 1);
 
-	sol = find_solutions(sol, tab);
+	find_solutions(sol, tab);
 
-	sol->context->op->restore(sol->context, saved);
-	return sol;
+	if (!sol->error)
+		sol->context->op->restore(sol->context, saved);
+	return;
 error:
-	sol_free(sol);
-	return NULL;
+	sol->error = 1;
 }
 
 /* Record the absence of solutions for those values of the parameters
  * that do not satisfy the given inequality with equality.
  */
-static struct isl_sol *no_sol_in_strict(struct isl_sol *sol,
+static void no_sol_in_strict(struct isl_sol *sol,
 	struct isl_tab *tab, struct isl_vec *ineq)
 {
 	int empty;
 	void *saved;
 
-	if (!sol->context)
+	if (!sol->context || sol->error)
 		goto error;
 	saved = sol->context->op->save(sol->context);
 
@@ -3117,16 +3552,15 @@ static struct isl_sol *no_sol_in_strict(struct isl_sol *sol,
 
 	empty = tab->empty;
 	tab->empty = 1;
-	sol = sol->add(sol, tab);
+	sol_add(sol, tab);
 	tab->empty = empty;
 
 	isl_int_add_ui(ineq->el[0], ineq->el[0], 1);
 
 	sol->context->op->restore(sol->context, saved);
-	return sol;
+	return;
 error:
-	sol_free(sol);
-	return NULL;
+	sol->error = 1;
 }
 
 /* Compute the lexicographic minimum of the set represented by the main
@@ -3203,7 +3637,7 @@ error:
  * coefficient are integral, then there is nothing that can be done
  * and the tableau has no integral solution.
  * If, on the other hand, one or more of the other columns have rational
- * coeffcients, but the parameter coefficients are all integral, then
+ * coefficients, but the parameter coefficients are all integral, then
  * we can perform a regular (non-parametric) cut.
  * Finally, if there is any parameter coefficient that is non-integral,
  * then we need to involve the context tableau.  There are two cases here.
@@ -3223,11 +3657,12 @@ error:
  * In the part of the context where this inequality does not hold, the
  * main tableau is marked as being empty.
  */
-static struct isl_sol *find_solutions(struct isl_sol *sol, struct isl_tab *tab)
+static void find_solutions(struct isl_sol *sol, struct isl_tab *tab)
 {
 	struct isl_context *context;
+	int r;
 
-	if (!tab || !sol)
+	if (!tab || sol->error)
 		goto error;
 
 	context = sol->context;
@@ -3237,10 +3672,10 @@ static struct isl_sol *find_solutions(struct isl_sol *sol, struct isl_tab *tab)
 	if (context->op->is_empty(context))
 		goto done;
 
-	for (; tab && !tab->empty; tab = restore_lexmin(tab)) {
+	for (r = 0; r >= 0 && tab && !tab->empty; r = restore_lexmin(tab)) {
 		int flags;
 		int row;
-		int sgn;
+		enum isl_tab_row_sign sgn;
 		int split = -1;
 		int n_split = 0;
 
@@ -3277,25 +3712,28 @@ static struct isl_sol *find_solutions(struct isl_sol *sol, struct isl_tab *tab)
 					tab->row_sign[row] = isl_tab_row_unknown;
 			}
 			tab->row_sign[split] = isl_tab_row_pos;
-			sol = find_in_pos(sol, tab, ineq->el);
+			sol_inc_level(sol);
+			find_in_pos(sol, tab, ineq->el);
 			tab->row_sign[split] = isl_tab_row_neg;
 			row = split;
 			isl_seq_neg(ineq->el, ineq->el, ineq->size);
 			isl_int_sub_ui(ineq->el[0], ineq->el[0], 1);
-			context->op->add_ineq(context, ineq->el, 0, 1);
+			if (!sol->error)
+				context->op->add_ineq(context, ineq->el, 0, 1);
 			isl_vec_free(ineq);
-			if (!sol)
+			if (sol->error)
 				goto error;
 			continue;
 		}
 		if (tab->rational)
 			break;
-		row = first_non_integer(tab, &flags);
+		row = first_non_integer_row(tab, &flags);
 		if (row < 0)
 			break;
 		if (ISL_FL_ISSET(flags, I_PAR)) {
 			if (ISL_FL_ISSET(flags, I_VAR)) {
-				tab = isl_tab_mark_empty(tab);
+				if (isl_tab_mark_empty(tab) < 0)
+					goto error;
 				break;
 			}
 			row = add_cut(tab, row);
@@ -3311,26 +3749,32 @@ static struct isl_sol *find_solutions(struct isl_sol *sol, struct isl_tab *tab)
 			if (d < 0)
 				goto error;
 			ineq = ineq_for_div(context->op->peek_basic_set(context), d);
-			sol = no_sol_in_strict(sol, tab, ineq);
+			if (!ineq)
+				goto error;
+			sol_inc_level(sol);
+			no_sol_in_strict(sol, tab, ineq);
 			isl_seq_neg(ineq->el, ineq->el, ineq->size);
 			context->op->add_ineq(context, ineq->el, 1, 1);
 			isl_vec_free(ineq);
-			if (!sol || !context->op->is_ok(context))
+			if (sol->error || !context->op->is_ok(context))
 				goto error;
 			tab = set_row_cst_to_div(tab, row, d);
+			if (context->op->is_empty(context))
+				break;
 		} else
 			row = add_parametric_cut(tab, row, context);
 		if (row < 0)
 			goto error;
 	}
+	if (r < 0)
+		goto error;
 done:
-	sol = sol->add(sol, tab);
+	sol_add(sol, tab);
 	isl_tab_free(tab);
-	return sol;
+	return;
 error:
 	isl_tab_free(tab);
-	sol_free(sol);
-	return NULL;
+	sol->error = 1;
 }
 
 /* Compute the lexicographic minimum of the set represented by the main
@@ -3344,11 +3788,15 @@ error:
  * In parts of the context where the added equality does not hold,
  * the main tableau is marked as being empty.
  */
-static struct isl_sol *find_solutions_main(struct isl_sol *sol,
-	struct isl_tab *tab)
+static void find_solutions_main(struct isl_sol *sol, struct isl_tab *tab)
 {
 	int row;
 
+	if (!tab)
+		goto error;
+
+	sol->level = 0;
+
 	for (row = tab->n_redundant; row < tab->n_row; ++row) {
 		int p;
 		struct isl_vec *eq;
@@ -3365,21 +3813,26 @@ static struct isl_sol *find_solutions_main(struct isl_sol *sol,
 				+ tab->n_param - (tab->n_var - tab->n_div);
 
 		eq = isl_vec_alloc(tab->mat->ctx, 1+tab->n_param+tab->n_div);
+		if (!eq)
+			goto error;
 		get_row_parameter_line(tab, row, eq->el);
 		isl_int_neg(eq->el[1 + p], tab->mat->row[row][0]);
 		eq = isl_vec_normalize(eq);
 
-		sol = no_sol_in_strict(sol, tab, eq);
+		sol_inc_level(sol);
+		no_sol_in_strict(sol, tab, eq);
 
 		isl_seq_neg(eq->el, eq->el, eq->size);
-		sol = no_sol_in_strict(sol, tab, eq);
+		sol_inc_level(sol);
+		no_sol_in_strict(sol, tab, eq);
 		isl_seq_neg(eq->el, eq->el, eq->size);
 
 		sol->context->op->add_eq(sol->context, eq->el, 1, 1);
 
 		isl_vec_free(eq);
 
-		isl_tab_mark_redundant(tab, row);
+		if (isl_tab_mark_redundant(tab, row) < 0)
+			goto error;
 
 		if (sol->context->op->is_empty(sol->context))
 			break;
@@ -3387,17 +3840,15 @@ static struct isl_sol *find_solutions_main(struct isl_sol *sol,
 		row = tab->n_redundant - 1;
 	}
 
-	return find_solutions(sol, tab);
+	find_solutions(sol, tab);
+
+	sol->level = 0;
+	sol_pop(sol);
+
+	return;
 error:
 	isl_tab_free(tab);
-	sol_free(sol);
-	return NULL;
-}
-
-static struct isl_sol_map *sol_map_find_solutions(struct isl_sol_map *sol_map,
-	struct isl_tab *tab)
-{
-	return (struct isl_sol_map *)find_solutions_main(&sol_map->sol, tab);
+	sol->error = 1;
 }
 
 /* Check if integer division "div" of "dom" also occurs in "bmap".
@@ -3408,8 +3859,8 @@ static int find_context_div(struct isl_basic_map *bmap,
 	struct isl_basic_set *dom, unsigned div)
 {
 	int i;
-	unsigned b_dim = isl_dim_total(bmap->dim);
-	unsigned d_dim = isl_dim_total(dom->dim);
+	unsigned b_dim = isl_space_dim(bmap->dim, isl_dim_all);
+	unsigned d_dim = isl_space_dim(dom->dim, isl_dim_all);
 
 	if (isl_int_is_zero(dom->div[div][0]))
 		return -1;
@@ -3454,7 +3905,7 @@ static struct isl_basic_map *align_context_divs(struct isl_basic_map *bmap,
 			common++;
 	other = bmap->n_div - common;
 	if (dom->n_div - common > 0) {
-		bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim),
+		bmap = isl_basic_map_extend_space(bmap, isl_space_copy(bmap->dim),
 				dom->n_div - common, 0, 0);
 		if (!bmap)
 			return NULL;
@@ -3476,280 +3927,1611 @@ error:
 	return NULL;
 }
 
-/* Compute the lexicographic minimum (or maximum if "max" is set)
- * of "bmap" over the domain "dom" and return the result as a map.
- * If "empty" is not NULL, then *empty is assigned a set that
- * contains those parts of the domain where there is no solution.
- * If "bmap" is marked as rational (ISL_BASIC_MAP_RATIONAL),
- * then we compute the rational optimum.  Otherwise, we compute
- * the integral optimum.
+/* Base case of isl_tab_basic_map_partial_lexopt, after removing
+ * some obvious symmetries.
  *
- * We perform some preprocessing.  As the PILP solver does not
- * handle implicit equalities very well, we first make sure all
- * the equalities are explicitly available.
- * We also make sure the divs in the domain are properly order,
+ * We make sure the divs in the domain are properly ordered,
  * because they will be added one by one in the given order
  * during the construction of the solution map.
  */
-struct isl_map *isl_tab_basic_map_partial_lexopt(
-		struct isl_basic_map *bmap, struct isl_basic_set *dom,
-		struct isl_set **empty, int max)
+static struct isl_sol *basic_map_partial_lexopt_base(
+	__isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
+	__isl_give isl_set **empty, int max,
+	struct isl_sol *(*init)(__isl_keep isl_basic_map *bmap,
+		    __isl_take isl_basic_set *dom, int track_empty, int max))
 {
 	struct isl_tab *tab;
-	struct isl_map *result = NULL;
-	struct isl_sol_map *sol_map = NULL;
+	struct isl_sol *sol = NULL;
 	struct isl_context *context;
 
-	if (empty)
-		*empty = NULL;
-	if (!bmap || !dom)
-		goto error;
-
-	isl_assert(bmap->ctx,
-	    isl_basic_map_compatible_domain(bmap, dom), goto error);
-
-	bmap = isl_basic_map_detect_equalities(bmap);
-
 	if (dom->n_div) {
 		dom = isl_basic_set_order_divs(dom);
 		bmap = align_context_divs(bmap, dom);
 	}
-	sol_map = sol_map_init(bmap, dom, !!empty, max);
-	if (!sol_map)
+	sol = init(bmap, dom, !!empty, max);
+	if (!sol)
 		goto error;
 
-	context = sol_map->sol.context;
-	if (isl_basic_set_fast_is_empty(context->op->peek_basic_set(context)))
+	context = sol->context;
+	if (isl_basic_set_plain_is_empty(context->op->peek_basic_set(context)))
 		/* nothing */;
-	else if (isl_basic_map_fast_is_empty(bmap))
-		sol_map = add_empty(sol_map);
-	else {
+	else if (isl_basic_map_plain_is_empty(bmap)) {
+		if (sol->add_empty)
+			sol->add_empty(sol,
+		    isl_basic_set_copy(context->op->peek_basic_set(context)));
+	} else {
 		tab = tab_for_lexmin(bmap,
 				    context->op->peek_basic_set(context), 1, max);
 		tab = context->op->detect_nonnegative_parameters(context, tab);
-		sol_map = sol_map_find_solutions(sol_map, tab);
-		if (!sol_map)
-			goto error;
+		find_solutions_main(sol, tab);
 	}
+	if (sol->error)
+		goto error;
 
-	result = isl_map_copy(sol_map->map);
-	if (empty)
-		*empty = isl_set_copy(sol_map->empty);
-	sol_map_free(sol_map);
 	isl_basic_map_free(bmap);
-	return result;
+	return sol;
 error:
-	sol_map_free(sol_map);
+	sol_free(sol);
 	isl_basic_map_free(bmap);
 	return NULL;
 }
 
-struct isl_sol_for {
-	struct isl_sol	sol;
-	int		(*fn)(__isl_take isl_basic_set *dom,
-				__isl_take isl_mat *map, void *user);
-	void		*user;
-	int		max;
-};
-
-static void sol_for_free(struct isl_sol_for *sol_for)
+/* Base case of isl_tab_basic_map_partial_lexopt, after removing
+ * some obvious symmetries.
+ *
+ * We call basic_map_partial_lexopt_base and extract the results.
+ */
+static __isl_give isl_map *basic_map_partial_lexopt_base_map(
+	__isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
+	__isl_give isl_set **empty, int max)
 {
-	if (sol_for->sol.context)
-		sol_for->sol.context->op->free(sol_for->sol.context);
-	free(sol_for);
+	isl_map *result = NULL;
+	struct isl_sol *sol;
+	struct isl_sol_map *sol_map;
+
+	sol = basic_map_partial_lexopt_base(bmap, dom, empty, max,
+					    &sol_map_init);
+	if (!sol)
+		return NULL;
+	sol_map = (struct isl_sol_map *) sol;
+
+	result = isl_map_copy(sol_map->map);
+	if (empty)
+		*empty = isl_set_copy(sol_map->empty);
+	sol_free(&sol_map->sol);
+	return result;
 }
 
-static void sol_for_free_wrap(struct isl_sol *sol)
+/* Structure used during detection of parallel constraints.
+ * n_in: number of "input" variables: isl_dim_param + isl_dim_in
+ * n_out: number of "output" variables: isl_dim_out + isl_dim_div
+ * val: the coefficients of the output variables
+ */
+struct isl_constraint_equal_info {
+	isl_basic_map *bmap;
+	unsigned n_in;
+	unsigned n_out;
+	isl_int *val;
+};
+
+/* Check whether the coefficients of the output variables
+ * of the constraint in "entry" are equal to info->val.
+ */
+static int constraint_equal(const void *entry, const void *val)
 {
-	sol_for_free((struct isl_sol_for *)sol);
+	isl_int **row = (isl_int **)entry;
+	const struct isl_constraint_equal_info *info = val;
+
+	return isl_seq_eq((*row) + 1 + info->n_in, info->val, info->n_out);
 }
 
-/* Add the solution identified by the tableau and the context tableau.
- *
- * See documentation of sol_map_add for more details.
- *
- * Instead of constructing a basic map, this function calls a user
- * defined function with the current context as a basic set and
- * an affine matrix reprenting the relation between the input and output.
- * The number of rows in this matrix is equal to one plus the number
- * of output variables.  The number of columns is equal to one plus
- * the total dimension of the context, i.e., the number of parameters,
- * input variables and divs.  Since some of the columns in the matrix
- * may refer to the divs, the basic set is not simplified.
- * (Simplification may reorder or remove divs.)
- */
-static struct isl_sol_for *sol_for_add(struct isl_sol_for *sol,
-	struct isl_tab *tab)
+/* Check whether "bmap" has a pair of constraints that have
+ * the same coefficients for the output variables.
+ * Note that the coefficients of the existentially quantified
+ * variables need to be zero since the existentially quantified
+ * of the result are usually not the same as those of the input.
+ * the isl_dim_out and isl_dim_div dimensions.
+ * If so, return 1 and return the row indices of the two constraints
+ * in *first and *second.
+ */
+static int parallel_constraints(__isl_keep isl_basic_map *bmap,
+	int *first, int *second)
 {
-	struct isl_basic_set *bset;
-	struct isl_mat *mat = NULL;
+	int i;
+	isl_ctx *ctx = isl_basic_map_get_ctx(bmap);
+	struct isl_hash_table *table = NULL;
+	struct isl_hash_table_entry *entry;
+	struct isl_constraint_equal_info info;
 	unsigned n_out;
-	unsigned off;
-	int row, i;
+	unsigned n_div;
 
-	if (!sol || !tab)
+	ctx = isl_basic_map_get_ctx(bmap);
+	table = isl_hash_table_alloc(ctx, bmap->n_ineq);
+	if (!table)
 		goto error;
 
-	if (tab->empty)
-		return sol;
+	info.n_in = isl_basic_map_dim(bmap, isl_dim_param) +
+		    isl_basic_map_dim(bmap, isl_dim_in);
+	info.bmap = bmap;
+	n_out = isl_basic_map_dim(bmap, isl_dim_out);
+	n_div = isl_basic_map_dim(bmap, isl_dim_div);
+	info.n_out = n_out + n_div;
+	for (i = 0; i < bmap->n_ineq; ++i) {
+		uint32_t hash;
 
-	off = 2 + tab->M;
+		info.val = bmap->ineq[i] + 1 + info.n_in;
+		if (isl_seq_first_non_zero(info.val, n_out) < 0)
+			continue;
+		if (isl_seq_first_non_zero(info.val + n_out, n_div) >= 0)
+			continue;
+		hash = isl_seq_get_hash(info.val, info.n_out);
+		entry = isl_hash_table_find(ctx, table, hash,
+					    constraint_equal, &info, 1);
+		if (!entry)
+			goto error;
+		if (entry->data)
+			break;
+		entry->data = &bmap->ineq[i];
+	}
 
-	n_out = tab->n_var - tab->n_param - tab->n_div;
-	mat = isl_mat_alloc(tab->mat->ctx, 1 + n_out, 1 + tab->n_param + tab->n_div);
-	if (!mat)
-		goto error;
+	if (i < bmap->n_ineq) {
+		*first = ((isl_int **)entry->data) - bmap->ineq; 
+		*second = i;
+	}
 
-	isl_seq_clr(mat->row[0] + 1, mat->n_col - 1);
-	isl_int_set_si(mat->row[0][0], 1);
-	for (row = 0; row < n_out; ++row) {
-		int i = tab->n_param + row;
-		int r, j;
+	isl_hash_table_free(ctx, table);
 
-		isl_seq_clr(mat->row[1 + row], mat->n_col);
-		if (!tab->var[i].is_row)
-			continue;
+	return i < bmap->n_ineq;
+error:
+	isl_hash_table_free(ctx, table);
+	return -1;
+}
 
-		r = tab->var[i].index;
-		/* no unbounded */
-		if (tab->M)
-			isl_assert(mat->ctx, isl_int_eq(tab->mat->row[r][2],
-					                tab->mat->row[r][0]),
-				    goto error);
-		isl_int_set(mat->row[1 + row][0], tab->mat->row[r][1]);
-		for (j = 0; j < tab->n_param; ++j) {
-			int col;
-			if (tab->var[j].is_row)
-				continue;
-			col = tab->var[j].index;
-			isl_int_set(mat->row[1 + row][1 + j],
-				    tab->mat->row[r][off + col]);
-		}
-		for (j = 0; j < tab->n_div; ++j) {
-			int col;
-			if (tab->var[tab->n_var - tab->n_div+j].is_row)
-				continue;
-			col = tab->var[tab->n_var - tab->n_div+j].index;
-			isl_int_set(mat->row[1 + row][1 + tab->n_param + j],
-				    tab->mat->row[r][off + col]);
-		}
-		if (!isl_int_is_one(tab->mat->row[r][0]))
-			isl_seq_scale_down(mat->row[1 + row], mat->row[1 + row],
-					    tab->mat->row[r][0], mat->n_col);
-		if (sol->max)
-			isl_seq_neg(mat->row[1 + row], mat->row[1 + row],
-				    mat->n_col);
+/* Given a set of upper bounds in "var", add constraints to "bset"
+ * that make the i-th bound smallest.
+ *
+ * In particular, if there are n bounds b_i, then add the constraints
+ *
+ *	b_i <= b_j	for j > i
+ *	b_i <  b_j	for j < i
+ */
+static __isl_give isl_basic_set *select_minimum(__isl_take isl_basic_set *bset,
+	__isl_keep isl_mat *var, int i)
+{
+	isl_ctx *ctx;
+	int j, k;
+
+	ctx = isl_mat_get_ctx(var);
+
+	for (j = 0; j < var->n_row; ++j) {
+		if (j == i)
+			continue;
+		k = isl_basic_set_alloc_inequality(bset);
+		if (k < 0)
+			goto error;
+		isl_seq_combine(bset->ineq[k], ctx->one, var->row[j],
+				ctx->negone, var->row[i], var->n_col);
+		isl_int_set_si(bset->ineq[k][var->n_col], 0);
+		if (j < i)
+			isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
 	}
 
-	bset = sol->sol.context->op->peek_basic_set(sol->sol.context);
-	bset = isl_basic_set_dup(bset);
 	bset = isl_basic_set_finalize(bset);
 
-	if (sol->fn(bset, isl_mat_copy(mat), sol->user) < 0)
-		goto error;
-
-	isl_mat_free(mat);
-	return sol;
+	return bset;
 error:
-	isl_mat_free(mat);
-	sol_free(&sol->sol);
+	isl_basic_set_free(bset);
 	return NULL;
 }
 
-static struct isl_sol *sol_for_add_wrap(struct isl_sol *sol,
-	struct isl_tab *tab)
-{
-	return (struct isl_sol *)sol_for_add((struct isl_sol_for *)sol, tab);
-}
-
-static struct isl_sol_for *sol_for_init(struct isl_basic_map *bmap, int max,
-	int (*fn)(__isl_take isl_basic_set *dom, __isl_take isl_mat *map,
-		  void *user),
-	void *user)
+/* Given a set of upper bounds on the last "input" variable m,
+ * construct a set that assigns the minimal upper bound to m, i.e.,
+ * construct a set that divides the space into cells where one
+ * of the upper bounds is smaller than all the others and assign
+ * this upper bound to m.
+ *
+ * In particular, if there are n bounds b_i, then the result
+ * consists of n basic sets, each one of the form
+ *
+ *	m = b_i
+ *	b_i <= b_j	for j > i
+ *	b_i <  b_j	for j < i
+ */
+static __isl_give isl_set *set_minimum(__isl_take isl_space *dim,
+	__isl_take isl_mat *var)
 {
-	struct isl_sol_for *sol_for = NULL;
-	struct isl_dim *dom_dim;
-	struct isl_basic_set *dom = NULL;
+	int i, k;
+	isl_basic_set *bset = NULL;
+	isl_ctx *ctx;
+	isl_set *set = NULL;
 
-	sol_for = isl_calloc_type(bset->ctx, struct isl_sol_for);
-	if (!sol_for)
+	if (!dim || !var)
 		goto error;
 
-	dom_dim = isl_dim_domain(isl_dim_copy(bmap->dim));
-	dom = isl_basic_set_universe(dom_dim);
-
-	sol_for->fn = fn;
-	sol_for->user = user;
-	sol_for->max = max;
-	sol_for->sol.add = &sol_for_add_wrap;
-	sol_for->sol.free = &sol_for_free_wrap;
+	ctx = isl_space_get_ctx(dim);
+	set = isl_set_alloc_space(isl_space_copy(dim),
+				var->n_row, ISL_SET_DISJOINT);
 
-	sol_for->sol.context = isl_context_alloc(dom);
-	if (!sol_for->sol.context)
-		goto error;
+	for (i = 0; i < var->n_row; ++i) {
+		bset = isl_basic_set_alloc_space(isl_space_copy(dim), 0,
+					       1, var->n_row - 1);
+		k = isl_basic_set_alloc_equality(bset);
+		if (k < 0)
+			goto error;
+		isl_seq_cpy(bset->eq[k], var->row[i], var->n_col);
+		isl_int_set_si(bset->eq[k][var->n_col], -1);
+		bset = select_minimum(bset, var, i);
+		set = isl_set_add_basic_set(set, bset);
+	}
 
-	isl_basic_set_free(dom);
-	return sol_for;
+	isl_space_free(dim);
+	isl_mat_free(var);
+	return set;
 error:
-	isl_basic_set_free(dom);
-	sol_for_free(sol_for);
+	isl_basic_set_free(bset);
+	isl_set_free(set);
+	isl_space_free(dim);
+	isl_mat_free(var);
 	return NULL;
 }
 
-static struct isl_sol_for *sol_for_find_solutions(struct isl_sol_for *sol_for,
-	struct isl_tab *tab)
+/* Given that the last input variable of "bmap" represents the minimum
+ * of the bounds in "cst", check whether we need to split the domain
+ * based on which bound attains the minimum.
+ *
+ * A split is needed when the minimum appears in an integer division
+ * or in an equality.  Otherwise, it is only needed if it appears in
+ * an upper bound that is different from the upper bounds on which it
+ * is defined.
+ */
+static int need_split_basic_map(__isl_keep isl_basic_map *bmap,
+	__isl_keep isl_mat *cst)
 {
-	return (struct isl_sol_for *)find_solutions_main(&sol_for->sol, tab);
-}
+	int i, j;
+	unsigned total;
+	unsigned pos;
 
-int isl_basic_map_foreach_lexopt(__isl_keep isl_basic_map *bmap, int max,
-	int (*fn)(__isl_take isl_basic_set *dom, __isl_take isl_mat *map,
-		  void *user),
-	void *user)
-{
-	struct isl_sol_for *sol_for = NULL;
+	pos = cst->n_col - 1;
+	total = isl_basic_map_dim(bmap, isl_dim_all);
 
-	bmap = isl_basic_map_copy(bmap);
-	if (!bmap)
-		return -1;
+	for (i = 0; i < bmap->n_div; ++i)
+		if (!isl_int_is_zero(bmap->div[i][2 + pos]))
+			return 1;
 
-	bmap = isl_basic_map_detect_equalities(bmap);
-	sol_for = sol_for_init(bmap, max, fn, user);
+	for (i = 0; i < bmap->n_eq; ++i)
+		if (!isl_int_is_zero(bmap->eq[i][1 + pos]))
+			return 1;
 
-	if (isl_basic_map_fast_is_empty(bmap))
-		/* nothing */;
-	else {
-		struct isl_tab *tab;
-		struct isl_context *context = sol_for->sol.context;
-		tab = tab_for_lexmin(bmap,
-				context->op->peek_basic_set(context), 1, max);
-		tab = context->op->detect_nonnegative_parameters(context, tab);
-		sol_for = sol_for_find_solutions(sol_for, tab);
-		if (!sol_for)
-			goto error;
+	for (i = 0; i < bmap->n_ineq; ++i) {
+		if (isl_int_is_nonneg(bmap->ineq[i][1 + pos]))
+			continue;
+		if (!isl_int_is_negone(bmap->ineq[i][1 + pos]))
+			return 1;
+		if (isl_seq_first_non_zero(bmap->ineq[i] + 1 + pos + 1,
+					   total - pos - 1) >= 0)
+			return 1;
+
+		for (j = 0; j < cst->n_row; ++j)
+			if (isl_seq_eq(bmap->ineq[i], cst->row[j], cst->n_col))
+				break;
+		if (j >= cst->n_row)
+			return 1;
 	}
 
-	sol_for_free(sol_for);
-	isl_basic_map_free(bmap);
 	return 0;
-error:
-	sol_for_free(sol_for);
-	isl_basic_map_free(bmap);
-	return -1;
 }
 
-int isl_basic_map_foreach_lexmin(__isl_keep isl_basic_map *bmap,
-	int (*fn)(__isl_take isl_basic_set *dom, __isl_take isl_mat *map,
+/* Given that the last set variable of "bset" represents the minimum
+ * of the bounds in "cst", check whether we need to split the domain
+ * based on which bound attains the minimum.
+ *
+ * We simply call need_split_basic_map here.  This is safe because
+ * the position of the minimum is computed from "cst" and not
+ * from "bmap".
+ */
+static int need_split_basic_set(__isl_keep isl_basic_set *bset,
+	__isl_keep isl_mat *cst)
+{
+	return need_split_basic_map((isl_basic_map *)bset, cst);
+}
+
+/* Given that the last set variable of "set" represents the minimum
+ * of the bounds in "cst", check whether we need to split the domain
+ * based on which bound attains the minimum.
+ */
+static int need_split_set(__isl_keep isl_set *set, __isl_keep isl_mat *cst)
+{
+	int i;
+
+	for (i = 0; i < set->n; ++i)
+		if (need_split_basic_set(set->p[i], cst))
+			return 1;
+
+	return 0;
+}
+
+/* Given a set of which the last set variable is the minimum
+ * of the bounds in "cst", split each basic set in the set
+ * in pieces where one of the bounds is (strictly) smaller than the others.
+ * This subdivision is given in "min_expr".
+ * The variable is subsequently projected out.
+ *
+ * We only do the split when it is needed.
+ * For example if the last input variable m = min(a,b) and the only
+ * constraints in the given basic set are lower bounds on m,
+ * i.e., l <= m = min(a,b), then we can simply project out m
+ * to obtain l <= a and l <= b, without having to split on whether
+ * m is equal to a or b.
+ */
+static __isl_give isl_set *split(__isl_take isl_set *empty,
+	__isl_take isl_set *min_expr, __isl_take isl_mat *cst)
+{
+	int n_in;
+	int i;
+	isl_space *dim;
+	isl_set *res;
+
+	if (!empty || !min_expr || !cst)
+		goto error;
+
+	n_in = isl_set_dim(empty, isl_dim_set);
+	dim = isl_set_get_space(empty);
+	dim = isl_space_drop_dims(dim, isl_dim_set, n_in - 1, 1);
+	res = isl_set_empty(dim);
+
+	for (i = 0; i < empty->n; ++i) {
+		isl_set *set;
+
+		set = isl_set_from_basic_set(isl_basic_set_copy(empty->p[i]));
+		if (need_split_basic_set(empty->p[i], cst))
+			set = isl_set_intersect(set, isl_set_copy(min_expr));
+		set = isl_set_remove_dims(set, isl_dim_set, n_in - 1, 1);
+
+		res = isl_set_union_disjoint(res, set);
+	}
+
+	isl_set_free(empty);
+	isl_set_free(min_expr);
+	isl_mat_free(cst);
+	return res;
+error:
+	isl_set_free(empty);
+	isl_set_free(min_expr);
+	isl_mat_free(cst);
+	return NULL;
+}
+
+/* Given a map of which the last input variable is the minimum
+ * of the bounds in "cst", split each basic set in the set
+ * in pieces where one of the bounds is (strictly) smaller than the others.
+ * This subdivision is given in "min_expr".
+ * The variable is subsequently projected out.
+ *
+ * The implementation is essentially the same as that of "split".
+ */
+static __isl_give isl_map *split_domain(__isl_take isl_map *opt,
+	__isl_take isl_set *min_expr, __isl_take isl_mat *cst)
+{
+	int n_in;
+	int i;
+	isl_space *dim;
+	isl_map *res;
+
+	if (!opt || !min_expr || !cst)
+		goto error;
+
+	n_in = isl_map_dim(opt, isl_dim_in);
+	dim = isl_map_get_space(opt);
+	dim = isl_space_drop_dims(dim, isl_dim_in, n_in - 1, 1);
+	res = isl_map_empty(dim);
+
+	for (i = 0; i < opt->n; ++i) {
+		isl_map *map;
+
+		map = isl_map_from_basic_map(isl_basic_map_copy(opt->p[i]));
+		if (need_split_basic_map(opt->p[i], cst))
+			map = isl_map_intersect_domain(map,
+						       isl_set_copy(min_expr));
+		map = isl_map_remove_dims(map, isl_dim_in, n_in - 1, 1);
+
+		res = isl_map_union_disjoint(res, map);
+	}
+
+	isl_map_free(opt);
+	isl_set_free(min_expr);
+	isl_mat_free(cst);
+	return res;
+error:
+	isl_map_free(opt);
+	isl_set_free(min_expr);
+	isl_mat_free(cst);
+	return NULL;
+}
+
+static __isl_give isl_map *basic_map_partial_lexopt(
+	__isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
+	__isl_give isl_set **empty, int max);
+
+union isl_lex_res {
+	void *p;
+	isl_map *map;
+	isl_pw_multi_aff *pma;
+};
+
+/* This function is called from basic_map_partial_lexopt_symm.
+ * The last variable of "bmap" and "dom" corresponds to the minimum
+ * of the bounds in "cst".  "map_space" is the space of the original
+ * input relation (of basic_map_partial_lexopt_symm) and "set_space"
+ * is the space of the original domain.
+ *
+ * We recursively call basic_map_partial_lexopt and then plug in
+ * the definition of the minimum in the result.
+ */
+static __isl_give union isl_lex_res basic_map_partial_lexopt_symm_map_core(
+	__isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
+	__isl_give isl_set **empty, int max, __isl_take isl_mat *cst,
+	__isl_take isl_space *map_space, __isl_take isl_space *set_space)
+{
+	isl_map *opt;
+	isl_set *min_expr;
+	union isl_lex_res res;
+
+	min_expr = set_minimum(isl_basic_set_get_space(dom), isl_mat_copy(cst));
+
+	opt = basic_map_partial_lexopt(bmap, dom, empty, max);
+
+	if (empty) {
+		*empty = split(*empty,
+			       isl_set_copy(min_expr), isl_mat_copy(cst));
+		*empty = isl_set_reset_space(*empty, set_space);
+	}
+
+	opt = split_domain(opt, min_expr, cst);
+	opt = isl_map_reset_space(opt, map_space);
+
+	res.map = opt;
+	return res;
+}
+
+/* Given a basic map with at least two parallel constraints (as found
+ * by the function parallel_constraints), first look for more constraints
+ * parallel to the two constraint and replace the found list of parallel
+ * constraints by a single constraint with as "input" part the minimum
+ * of the input parts of the list of constraints.  Then, recursively call
+ * basic_map_partial_lexopt (possibly finding more parallel constraints)
+ * and plug in the definition of the minimum in the result.
+ *
+ * More specifically, given a set of constraints
+ *
+ *	a x + b_i(p) >= 0
+ *
+ * Replace this set by a single constraint
+ *
+ *	a x + u >= 0
+ *
+ * with u a new parameter with constraints
+ *
+ *	u <= b_i(p)
+ *
+ * Any solution to the new system is also a solution for the original system
+ * since
+ *
+ *	a x >= -u >= -b_i(p)
+ *
+ * Moreover, m = min_i(b_i(p)) satisfies the constraints on u and can
+ * therefore be plugged into the solution.
+ */
+static union isl_lex_res basic_map_partial_lexopt_symm(
+	__isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
+	__isl_give isl_set **empty, int max, int first, int second,
+	__isl_give union isl_lex_res (*core)(__isl_take isl_basic_map *bmap,
+					    __isl_take isl_basic_set *dom,
+					    __isl_give isl_set **empty,
+					    int max, __isl_take isl_mat *cst,
+					    __isl_take isl_space *map_space,
+					    __isl_take isl_space *set_space))
+{
+	int i, n, k;
+	int *list = NULL;
+	unsigned n_in, n_out, n_div;
+	isl_ctx *ctx;
+	isl_vec *var = NULL;
+	isl_mat *cst = NULL;
+	isl_space *map_space, *set_space;
+	union isl_lex_res res;
+
+	map_space = isl_basic_map_get_space(bmap);
+	set_space = empty ? isl_basic_set_get_space(dom) : NULL;
+
+	n_in = isl_basic_map_dim(bmap, isl_dim_param) +
+	       isl_basic_map_dim(bmap, isl_dim_in);
+	n_out = isl_basic_map_dim(bmap, isl_dim_all) - n_in;
+
+	ctx = isl_basic_map_get_ctx(bmap);
+	list = isl_alloc_array(ctx, int, bmap->n_ineq);
+	var = isl_vec_alloc(ctx, n_out);
+	if (!list || !var)
+		goto error;
+
+	list[0] = first;
+	list[1] = second;
+	isl_seq_cpy(var->el, bmap->ineq[first] + 1 + n_in, n_out);
+	for (i = second + 1, n = 2; i < bmap->n_ineq; ++i) {
+		if (isl_seq_eq(var->el, bmap->ineq[i] + 1 + n_in, n_out))
+			list[n++] = i;
+	}
+
+	cst = isl_mat_alloc(ctx, n, 1 + n_in);
+	if (!cst)
+		goto error;
+
+	for (i = 0; i < n; ++i)
+		isl_seq_cpy(cst->row[i], bmap->ineq[list[i]], 1 + n_in);
+
+	bmap = isl_basic_map_cow(bmap);
+	if (!bmap)
+		goto error;
+	for (i = n - 1; i >= 0; --i)
+		if (isl_basic_map_drop_inequality(bmap, list[i]) < 0)
+			goto error;
+
+	bmap = isl_basic_map_add(bmap, isl_dim_in, 1);
+	bmap = isl_basic_map_extend_constraints(bmap, 0, 1);
+	k = isl_basic_map_alloc_inequality(bmap);
+	if (k < 0)
+		goto error;
+	isl_seq_clr(bmap->ineq[k], 1 + n_in);
+	isl_int_set_si(bmap->ineq[k][1 + n_in], 1);
+	isl_seq_cpy(bmap->ineq[k] + 1 + n_in + 1, var->el, n_out);
+	bmap = isl_basic_map_finalize(bmap);
+
+	n_div = isl_basic_set_dim(dom, isl_dim_div);
+	dom = isl_basic_set_add(dom, isl_dim_set, 1);
+	dom = isl_basic_set_extend_constraints(dom, 0, n);
+	for (i = 0; i < n; ++i) {
+		k = isl_basic_set_alloc_inequality(dom);
+		if (k < 0)
+			goto error;
+		isl_seq_cpy(dom->ineq[k], cst->row[i], 1 + n_in);
+		isl_int_set_si(dom->ineq[k][1 + n_in], -1);
+		isl_seq_clr(dom->ineq[k] + 1 + n_in + 1, n_div);
+	}
+
+	isl_vec_free(var);
+	free(list);
+
+	return core(bmap, dom, empty, max, cst, map_space, set_space);
+error:
+	isl_space_free(map_space);
+	isl_space_free(set_space);
+	isl_mat_free(cst);
+	isl_vec_free(var);
+	free(list);
+	isl_basic_set_free(dom);
+	isl_basic_map_free(bmap);
+	res.p = NULL;
+	return res;
+}
+
+static __isl_give isl_map *basic_map_partial_lexopt_symm_map(
+	__isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
+	__isl_give isl_set **empty, int max, int first, int second)
+{
+	return basic_map_partial_lexopt_symm(bmap, dom, empty, max,
+		    first, second, &basic_map_partial_lexopt_symm_map_core).map;
+}
+
+/* Recursive part of isl_tab_basic_map_partial_lexopt, after detecting
+ * equalities and removing redundant constraints.
+ *
+ * We first check if there are any parallel constraints (left).
+ * If not, we are in the base case.
+ * If there are parallel constraints, we replace them by a single
+ * constraint in basic_map_partial_lexopt_symm and then call
+ * this function recursively to look for more parallel constraints.
+ */
+static __isl_give isl_map *basic_map_partial_lexopt(
+	__isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
+	__isl_give isl_set **empty, int max)
+{
+	int par = 0;
+	int first, second;
+
+	if (!bmap)
+		goto error;
+
+	if (bmap->ctx->opt->pip_symmetry)
+		par = parallel_constraints(bmap, &first, &second);
+	if (par < 0)
+		goto error;
+	if (!par)
+		return basic_map_partial_lexopt_base_map(bmap, dom, empty, max);
+	
+	return basic_map_partial_lexopt_symm_map(bmap, dom, empty, max,
+						 first, second);
+error:
+	isl_basic_set_free(dom);
+	isl_basic_map_free(bmap);
+	return NULL;
+}
+
+/* Compute the lexicographic minimum (or maximum if "max" is set)
+ * of "bmap" over the domain "dom" and return the result as a map.
+ * If "empty" is not NULL, then *empty is assigned a set that
+ * contains those parts of the domain where there is no solution.
+ * If "bmap" is marked as rational (ISL_BASIC_MAP_RATIONAL),
+ * then we compute the rational optimum.  Otherwise, we compute
+ * the integral optimum.
+ *
+ * We perform some preprocessing.  As the PILP solver does not
+ * handle implicit equalities very well, we first make sure all
+ * the equalities are explicitly available.
+ *
+ * We also add context constraints to the basic map and remove
+ * redundant constraints.  This is only needed because of the
+ * way we handle simple symmetries.  In particular, we currently look
+ * for symmetries on the constraints, before we set up the main tableau.
+ * It is then no good to look for symmetries on possibly redundant constraints.
+ */
+struct isl_map *isl_tab_basic_map_partial_lexopt(
+		struct isl_basic_map *bmap, struct isl_basic_set *dom,
+		struct isl_set **empty, int max)
+{
+	if (empty)
+		*empty = NULL;
+	if (!bmap || !dom)
+		goto error;
+
+	isl_assert(bmap->ctx,
+	    isl_basic_map_compatible_domain(bmap, dom), goto error);
+
+	if (isl_basic_set_dim(dom, isl_dim_all) == 0)
+		return basic_map_partial_lexopt(bmap, dom, empty, max);
+
+	bmap = isl_basic_map_intersect_domain(bmap, isl_basic_set_copy(dom));
+	bmap = isl_basic_map_detect_equalities(bmap);
+	bmap = isl_basic_map_remove_redundancies(bmap);
+
+	return basic_map_partial_lexopt(bmap, dom, empty, max);
+error:
+	isl_basic_set_free(dom);
+	isl_basic_map_free(bmap);
+	return NULL;
+}
+
+struct isl_sol_for {
+	struct isl_sol	sol;
+	int		(*fn)(__isl_take isl_basic_set *dom,
+				__isl_take isl_aff_list *list, void *user);
+	void		*user;
+};
+
+static void sol_for_free(struct isl_sol_for *sol_for)
+{
+	if (sol_for->sol.context)
+		sol_for->sol.context->op->free(sol_for->sol.context);
+	free(sol_for);
+}
+
+static void sol_for_free_wrap(struct isl_sol *sol)
+{
+	sol_for_free((struct isl_sol_for *)sol);
+}
+
+/* Add the solution identified by the tableau and the context tableau.
+ *
+ * See documentation of sol_add for more details.
+ *
+ * Instead of constructing a basic map, this function calls a user
+ * defined function with the current context as a basic set and
+ * a list of affine expressions representing the relation between
+ * the input and output.  The space over which the affine expressions
+ * are defined is the same as that of the domain.  The number of
+ * affine expressions in the list is equal to the number of output variables.
+ */
+static void sol_for_add(struct isl_sol_for *sol,
+	struct isl_basic_set *dom, struct isl_mat *M)
+{
+	int i;
+	isl_ctx *ctx;
+	isl_local_space *ls;
+	isl_aff *aff;
+	isl_aff_list *list;
+
+	if (sol->sol.error || !dom || !M)
+		goto error;
+
+	ctx = isl_basic_set_get_ctx(dom);
+	ls = isl_basic_set_get_local_space(dom);
+	list = isl_aff_list_alloc(ctx, M->n_row - 1);
+	for (i = 1; i < M->n_row; ++i) {
+		aff = isl_aff_alloc(isl_local_space_copy(ls));
+		if (aff) {
+			isl_int_set(aff->v->el[0], M->row[0][0]);
+			isl_seq_cpy(aff->v->el + 1, M->row[i], M->n_col);
+		}
+		list = isl_aff_list_add(list, aff);
+	}
+	isl_local_space_free(ls);
+
+	dom = isl_basic_set_finalize(dom);
+
+	if (sol->fn(isl_basic_set_copy(dom), list, sol->user) < 0)
+		goto error;
+
+	isl_basic_set_free(dom);
+	isl_mat_free(M);
+	return;
+error:
+	isl_basic_set_free(dom);
+	isl_mat_free(M);
+	sol->sol.error = 1;
+}
+
+static void sol_for_add_wrap(struct isl_sol *sol,
+	struct isl_basic_set *dom, struct isl_mat *M)
+{
+	sol_for_add((struct isl_sol_for *)sol, dom, M);
+}
+
+static struct isl_sol_for *sol_for_init(struct isl_basic_map *bmap, int max,
+	int (*fn)(__isl_take isl_basic_set *dom, __isl_take isl_aff_list *list,
 		  void *user),
 	void *user)
 {
-	return isl_basic_map_foreach_lexopt(bmap, 0, fn, user);
+	struct isl_sol_for *sol_for = NULL;
+	isl_space *dom_dim;
+	struct isl_basic_set *dom = NULL;
+
+	sol_for = isl_calloc_type(bmap->ctx, struct isl_sol_for);
+	if (!sol_for)
+		goto error;
+
+	dom_dim = isl_space_domain(isl_space_copy(bmap->dim));
+	dom = isl_basic_set_universe(dom_dim);
+
+	sol_for->sol.rational = ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL);
+	sol_for->sol.dec_level.callback.run = &sol_dec_level_wrap;
+	sol_for->sol.dec_level.sol = &sol_for->sol;
+	sol_for->fn = fn;
+	sol_for->user = user;
+	sol_for->sol.max = max;
+	sol_for->sol.n_out = isl_basic_map_dim(bmap, isl_dim_out);
+	sol_for->sol.add = &sol_for_add_wrap;
+	sol_for->sol.add_empty = NULL;
+	sol_for->sol.free = &sol_for_free_wrap;
+
+	sol_for->sol.context = isl_context_alloc(dom);
+	if (!sol_for->sol.context)
+		goto error;
+
+	isl_basic_set_free(dom);
+	return sol_for;
+error:
+	isl_basic_set_free(dom);
+	sol_for_free(sol_for);
+	return NULL;
 }
 
-int isl_basic_map_foreach_lexmax(__isl_keep isl_basic_map *bmap,
-	int (*fn)(__isl_take isl_basic_set *dom, __isl_take isl_mat *map,
+static void sol_for_find_solutions(struct isl_sol_for *sol_for,
+	struct isl_tab *tab)
+{
+	find_solutions_main(&sol_for->sol, tab);
+}
+
+int isl_basic_map_foreach_lexopt(__isl_keep isl_basic_map *bmap, int max,
+	int (*fn)(__isl_take isl_basic_set *dom, __isl_take isl_aff_list *list,
 		  void *user),
 	void *user)
 {
-	return isl_basic_map_foreach_lexopt(bmap, 1, fn, user);
+	struct isl_sol_for *sol_for = NULL;
+
+	bmap = isl_basic_map_copy(bmap);
+	if (!bmap)
+		return -1;
+
+	bmap = isl_basic_map_detect_equalities(bmap);
+	sol_for = sol_for_init(bmap, max, fn, user);
+
+	if (isl_basic_map_plain_is_empty(bmap))
+		/* nothing */;
+	else {
+		struct isl_tab *tab;
+		struct isl_context *context = sol_for->sol.context;
+		tab = tab_for_lexmin(bmap,
+				context->op->peek_basic_set(context), 1, max);
+		tab = context->op->detect_nonnegative_parameters(context, tab);
+		sol_for_find_solutions(sol_for, tab);
+		if (sol_for->sol.error)
+			goto error;
+	}
+
+	sol_free(&sol_for->sol);
+	isl_basic_map_free(bmap);
+	return 0;
+error:
+	sol_free(&sol_for->sol);
+	isl_basic_map_free(bmap);
+	return -1;
+}
+
+int isl_basic_set_foreach_lexopt(__isl_keep isl_basic_set *bset, int max,
+	int (*fn)(__isl_take isl_basic_set *dom, __isl_take isl_aff_list *list,
+		  void *user),
+	void *user)
+{
+	return isl_basic_map_foreach_lexopt(bset, max, fn, user);
+}
+
+int isl_basic_map_foreach_lexmin(__isl_keep isl_basic_map *bmap,
+	int (*fn)(__isl_take isl_basic_set *dom, __isl_take isl_aff_list *list,
+		  void *user),
+	void *user)
+{
+	return isl_basic_map_foreach_lexopt(bmap, 0, fn, user);
+}
+
+int isl_basic_map_foreach_lexmax(__isl_keep isl_basic_map *bmap,
+	int (*fn)(__isl_take isl_basic_set *dom, __isl_take isl_aff_list *list,
+		  void *user),
+	void *user)
+{
+	return isl_basic_map_foreach_lexopt(bmap, 1, fn, user);
+}
+
+int isl_basic_set_foreach_lexmax(__isl_keep isl_basic_set *bset,
+	int (*fn)(__isl_take isl_basic_set *dom, __isl_take isl_aff_list *list,
+		  void *user),
+	void *user)
+{
+	return isl_basic_map_foreach_lexmax(bset, fn, user);
+}
+
+/* Check if the given sequence of len variables starting at pos
+ * represents a trivial (i.e., zero) solution.
+ * The variables are assumed to be non-negative and to come in pairs,
+ * with each pair representing a variable of unrestricted sign.
+ * The solution is trivial if each such pair in the sequence consists
+ * of two identical values, meaning that the variable being represented
+ * has value zero.
+ */
+static int region_is_trivial(struct isl_tab *tab, int pos, int len)
+{
+	int i;
+
+	if (len == 0)
+		return 0;
+
+	for (i = 0; i < len; i +=  2) {
+		int neg_row;
+		int pos_row;
+
+		neg_row = tab->var[pos + i].is_row ?
+				tab->var[pos + i].index : -1;
+		pos_row = tab->var[pos + i + 1].is_row ?
+				tab->var[pos + i + 1].index : -1;
+
+		if ((neg_row < 0 ||
+		     isl_int_is_zero(tab->mat->row[neg_row][1])) &&
+		    (pos_row < 0 ||
+		     isl_int_is_zero(tab->mat->row[pos_row][1])))
+			continue;
+
+		if (neg_row < 0 || pos_row < 0)
+			return 0;
+		if (isl_int_ne(tab->mat->row[neg_row][1],
+			       tab->mat->row[pos_row][1]))
+			return 0;
+	}
+
+	return 1;
+}
+
+/* Return the index of the first trivial region or -1 if all regions
+ * are non-trivial.
+ */
+static int first_trivial_region(struct isl_tab *tab,
+	int n_region, struct isl_region *region)
+{
+	int i;
+
+	for (i = 0; i < n_region; ++i) {
+		if (region_is_trivial(tab, region[i].pos, region[i].len))
+			return i;
+	}
+
+	return -1;
+}
+
+/* Check if the solution is optimal, i.e., whether the first
+ * n_op entries are zero.
+ */
+static int is_optimal(__isl_keep isl_vec *sol, int n_op)
+{
+	int i;
+
+	for (i = 0; i < n_op; ++i)
+		if (!isl_int_is_zero(sol->el[1 + i]))
+			return 0;
+	return 1;
+}
+
+/* Add constraints to "tab" that ensure that any solution is significantly
+ * better that that represented by "sol".  That is, find the first
+ * relevant (within first n_op) non-zero coefficient and force it (along
+ * with all previous coefficients) to be zero.
+ * If the solution is already optimal (all relevant coefficients are zero),
+ * then just mark the table as empty.
+ */
+static int force_better_solution(struct isl_tab *tab,
+	__isl_keep isl_vec *sol, int n_op)
+{
+	int i;
+	isl_ctx *ctx;
+	isl_vec *v = NULL;
+
+	if (!sol)
+		return -1;
+
+	for (i = 0; i < n_op; ++i)
+		if (!isl_int_is_zero(sol->el[1 + i]))
+			break;
+
+	if (i == n_op) {
+		if (isl_tab_mark_empty(tab) < 0)
+			return -1;
+		return 0;
+	}
+
+	ctx = isl_vec_get_ctx(sol);
+	v = isl_vec_alloc(ctx, 1 + tab->n_var);
+	if (!v)
+		return -1;
+
+	for (; i >= 0; --i) {
+		v = isl_vec_clr(v);
+		isl_int_set_si(v->el[1 + i], -1);
+		if (add_lexmin_eq(tab, v->el) < 0)
+			goto error;
+	}
+
+	isl_vec_free(v);
+	return 0;
+error:
+	isl_vec_free(v);
+	return -1;
+}
+
+struct isl_trivial {
+	int update;
+	int region;
+	int side;
+	struct isl_tab_undo *snap;
+};
+
+/* Return the lexicographically smallest non-trivial solution of the
+ * given ILP problem.
+ *
+ * All variables are assumed to be non-negative.
+ *
+ * n_op is the number of initial coordinates to optimize.
+ * That is, once a solution has been found, we will only continue looking
+ * for solution that result in significantly better values for those
+ * initial coordinates.  That is, we only continue looking for solutions
+ * that increase the number of initial zeros in this sequence.
+ *
+ * A solution is non-trivial, if it is non-trivial on each of the
+ * specified regions.  Each region represents a sequence of pairs
+ * of variables.  A solution is non-trivial on such a region if
+ * at least one of these pairs consists of different values, i.e.,
+ * such that the non-negative variable represented by the pair is non-zero.
+ *
+ * Whenever a conflict is encountered, all constraints involved are
+ * reported to the caller through a call to "conflict".
+ *
+ * We perform a simple branch-and-bound backtracking search.
+ * Each level in the search represents initially trivial region that is forced
+ * to be non-trivial.
+ * At each level we consider n cases, where n is the length of the region.
+ * In terms of the n/2 variables of unrestricted signs being encoded by
+ * the region, we consider the cases
+ *	x_0 >= 1
+ *	x_0 <= -1
+ *	x_0 = 0 and x_1 >= 1
+ *	x_0 = 0 and x_1 <= -1
+ *	x_0 = 0 and x_1 = 0 and x_2 >= 1
+ *	x_0 = 0 and x_1 = 0 and x_2 <= -1
+ *	...
+ * The cases are considered in this order, assuming that each pair
+ * x_i_a x_i_b represents the value x_i_b - x_i_a.
+ * That is, x_0 >= 1 is enforced by adding the constraint
+ *	x_0_b - x_0_a >= 1
+ */
+__isl_give isl_vec *isl_tab_basic_set_non_trivial_lexmin(
+	__isl_take isl_basic_set *bset, int n_op, int n_region,
+	struct isl_region *region,
+	int (*conflict)(int con, void *user), void *user)
+{
+	int i, j;
+	int r;
+	isl_ctx *ctx = isl_basic_set_get_ctx(bset);
+	isl_vec *v = NULL;
+	isl_vec *sol = isl_vec_alloc(ctx, 0);
+	struct isl_tab *tab;
+	struct isl_trivial *triv = NULL;
+	int level, init;
+
+	tab = tab_for_lexmin(bset, NULL, 0, 0);
+	if (!tab)
+		goto error;
+	tab->conflict = conflict;
+	tab->conflict_user = user;
+
+	v = isl_vec_alloc(ctx, 1 + tab->n_var);
+	triv = isl_calloc_array(ctx, struct isl_trivial, n_region);
+	if (!v || !triv)
+		goto error;
+
+	level = 0;
+	init = 1;
+
+	while (level >= 0) {
+		int side, base;
+
+		if (init) {
+			tab = cut_to_integer_lexmin(tab);
+			if (!tab)
+				goto error;
+			if (tab->empty)
+				goto backtrack;
+			r = first_trivial_region(tab, n_region, region);
+			if (r < 0) {
+				for (i = 0; i < level; ++i)
+					triv[i].update = 1;
+				isl_vec_free(sol);
+				sol = isl_tab_get_sample_value(tab);
+				if (!sol)
+					goto error;
+				if (is_optimal(sol, n_op))
+					break;
+				goto backtrack;
+			}
+			if (level >= n_region)
+				isl_die(ctx, isl_error_internal,
+					"nesting level too deep", goto error);
+			if (isl_tab_extend_cons(tab,
+					    2 * region[r].len + 2 * n_op) < 0)
+				goto error;
+			triv[level].region = r;
+			triv[level].side = 0;
+		}
+
+		r = triv[level].region;
+		side = triv[level].side;
+		base = 2 * (side/2);
+
+		if (side >= region[r].len) {
+backtrack:
+			level--;
+			init = 0;
+			if (level >= 0)
+				if (isl_tab_rollback(tab, triv[level].snap) < 0)
+					goto error;
+			continue;
+		}
+
+		if (triv[level].update) {
+			if (force_better_solution(tab, sol, n_op) < 0)
+				goto error;
+			triv[level].update = 0;
+		}
+
+		if (side == base && base >= 2) {
+			for (j = base - 2; j < base; ++j) {
+				v = isl_vec_clr(v);
+				isl_int_set_si(v->el[1 + region[r].pos + j], 1);
+				if (add_lexmin_eq(tab, v->el) < 0)
+					goto error;
+			}
+		}
+
+		triv[level].snap = isl_tab_snap(tab);
+		if (isl_tab_push_basis(tab) < 0)
+			goto error;
+
+		v = isl_vec_clr(v);
+		isl_int_set_si(v->el[0], -1);
+		isl_int_set_si(v->el[1 + region[r].pos + side], -1);
+		isl_int_set_si(v->el[1 + region[r].pos + (side ^ 1)], 1);
+		tab = add_lexmin_ineq(tab, v->el);
+
+		triv[level].side++;
+		level++;
+		init = 1;
+	}
+
+	free(triv);
+	isl_vec_free(v);
+	isl_tab_free(tab);
+	isl_basic_set_free(bset);
+
+	return sol;
+error:
+	free(triv);
+	isl_vec_free(v);
+	isl_tab_free(tab);
+	isl_basic_set_free(bset);
+	isl_vec_free(sol);
+	return NULL;
+}
+
+/* Return the lexicographically smallest rational point in "bset",
+ * assuming that all variables are non-negative.
+ * If "bset" is empty, then return a zero-length vector.
+ */
+__isl_give isl_vec *isl_tab_basic_set_non_neg_lexmin(
+	__isl_take isl_basic_set *bset)
+{
+	struct isl_tab *tab;
+	isl_ctx *ctx = isl_basic_set_get_ctx(bset);
+	isl_vec *sol;
+
+	tab = tab_for_lexmin(bset, NULL, 0, 0);
+	if (!tab)
+		goto error;
+	if (tab->empty)
+		sol = isl_vec_alloc(ctx, 0);
+	else
+		sol = isl_tab_get_sample_value(tab);
+	isl_tab_free(tab);
+	isl_basic_set_free(bset);
+	return sol;
+error:
+	isl_tab_free(tab);
+	isl_basic_set_free(bset);
+	return NULL;
+}
+
+struct isl_sol_pma {
+	struct isl_sol	sol;
+	isl_pw_multi_aff *pma;
+	isl_set *empty;
+};
+
+static void sol_pma_free(struct isl_sol_pma *sol_pma)
+{
+	if (!sol_pma)
+		return;
+	if (sol_pma->sol.context)
+		sol_pma->sol.context->op->free(sol_pma->sol.context);
+	isl_pw_multi_aff_free(sol_pma->pma);
+	isl_set_free(sol_pma->empty);
+	free(sol_pma);
+}
+
+/* This function is called for parts of the context where there is
+ * no solution, with "bset" corresponding to the context tableau.
+ * Simply add the basic set to the set "empty".
+ */
+static void sol_pma_add_empty(struct isl_sol_pma *sol,
+	__isl_take isl_basic_set *bset)
+{
+	if (!bset)
+		goto error;
+	isl_assert(bset->ctx, sol->empty, goto error);
+
+	sol->empty = isl_set_grow(sol->empty, 1);
+	bset = isl_basic_set_simplify(bset);
+	bset = isl_basic_set_finalize(bset);
+	sol->empty = isl_set_add_basic_set(sol->empty, bset);
+	if (!sol->empty)
+		sol->sol.error = 1;
+	return;
+error:
+	isl_basic_set_free(bset);
+	sol->sol.error = 1;
+}
+
+/* Given a basic map "dom" that represents the context and an affine
+ * matrix "M" that maps the dimensions of the context to the
+ * output variables, construct an isl_pw_multi_aff with a single
+ * cell corresponding to "dom" and affine expressions copied from "M".
+ */
+static void sol_pma_add(struct isl_sol_pma *sol,
+	__isl_take isl_basic_set *dom, __isl_take isl_mat *M)
+{
+	int i;
+	isl_local_space *ls;
+	isl_aff *aff;
+	isl_multi_aff *maff;
+	isl_pw_multi_aff *pma;
+
+	maff = isl_multi_aff_alloc(isl_pw_multi_aff_get_space(sol->pma));
+	ls = isl_basic_set_get_local_space(dom);
+	for (i = 1; i < M->n_row; ++i) {
+		aff = isl_aff_alloc(isl_local_space_copy(ls));
+		if (aff) {
+			isl_int_set(aff->v->el[0], M->row[0][0]);
+			isl_seq_cpy(aff->v->el + 1, M->row[i], M->n_col);
+		}
+		aff = isl_aff_normalize(aff);
+		maff = isl_multi_aff_set_aff(maff, i - 1, aff);
+	}
+	isl_local_space_free(ls);
+	isl_mat_free(M);
+	dom = isl_basic_set_simplify(dom);
+	pma = isl_pw_multi_aff_alloc(isl_set_from_basic_set(dom), maff);
+	sol->pma = isl_pw_multi_aff_add_disjoint(sol->pma, pma);
+	if (!sol->pma)
+		sol->sol.error = 1;
+}
+
+static void sol_pma_free_wrap(struct isl_sol *sol)
+{
+	sol_pma_free((struct isl_sol_pma *)sol);
+}
+
+static void sol_pma_add_empty_wrap(struct isl_sol *sol,
+	__isl_take isl_basic_set *bset)
+{
+	sol_pma_add_empty((struct isl_sol_pma *)sol, bset);
+}
+
+static void sol_pma_add_wrap(struct isl_sol *sol,
+	__isl_take isl_basic_set *dom, __isl_take isl_mat *M)
+{
+	sol_pma_add((struct isl_sol_pma *)sol, dom, M);
+}
+
+/* Construct an isl_sol_pma structure for accumulating the solution.
+ * If track_empty is set, then we also keep track of the parts
+ * of the context where there is no solution.
+ * If max is set, then we are solving a maximization, rather than
+ * a minimization problem, which means that the variables in the
+ * tableau have value "M - x" rather than "M + x".
+ */
+static struct isl_sol *sol_pma_init(__isl_keep isl_basic_map *bmap,
+	__isl_take isl_basic_set *dom, int track_empty, int max)
+{
+	struct isl_sol_pma *sol_pma = NULL;
+
+	if (!bmap)
+		goto error;
+
+	sol_pma = isl_calloc_type(bmap->ctx, struct isl_sol_pma);
+	if (!sol_pma)
+		goto error;
+
+	sol_pma->sol.rational = ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL);
+	sol_pma->sol.dec_level.callback.run = &sol_dec_level_wrap;
+	sol_pma->sol.dec_level.sol = &sol_pma->sol;
+	sol_pma->sol.max = max;
+	sol_pma->sol.n_out = isl_basic_map_dim(bmap, isl_dim_out);
+	sol_pma->sol.add = &sol_pma_add_wrap;
+	sol_pma->sol.add_empty = track_empty ? &sol_pma_add_empty_wrap : NULL;
+	sol_pma->sol.free = &sol_pma_free_wrap;
+	sol_pma->pma = isl_pw_multi_aff_empty(isl_basic_map_get_space(bmap));
+	if (!sol_pma->pma)
+		goto error;
+
+	sol_pma->sol.context = isl_context_alloc(dom);
+	if (!sol_pma->sol.context)
+		goto error;
+
+	if (track_empty) {
+		sol_pma->empty = isl_set_alloc_space(isl_basic_set_get_space(dom),
+							1, ISL_SET_DISJOINT);
+		if (!sol_pma->empty)
+			goto error;
+	}
+
+	isl_basic_set_free(dom);
+	return &sol_pma->sol;
+error:
+	isl_basic_set_free(dom);
+	sol_pma_free(sol_pma);
+	return NULL;
+}
+
+/* Base case of isl_tab_basic_map_partial_lexopt, after removing
+ * some obvious symmetries.
+ *
+ * We call basic_map_partial_lexopt_base and extract the results.
+ */
+static __isl_give isl_pw_multi_aff *basic_map_partial_lexopt_base_pma(
+	__isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
+	__isl_give isl_set **empty, int max)
+{
+	isl_pw_multi_aff *result = NULL;
+	struct isl_sol *sol;
+	struct isl_sol_pma *sol_pma;
+
+	sol = basic_map_partial_lexopt_base(bmap, dom, empty, max,
+					    &sol_pma_init);
+	if (!sol)
+		return NULL;
+	sol_pma = (struct isl_sol_pma *) sol;
+
+	result = isl_pw_multi_aff_copy(sol_pma->pma);
+	if (empty)
+		*empty = isl_set_copy(sol_pma->empty);
+	sol_free(&sol_pma->sol);
+	return result;
+}
+
+/* Given that the last input variable of "maff" represents the minimum
+ * of some bounds, check whether we need to plug in the expression
+ * of the minimum.
+ *
+ * In particular, check if the last input variable appears in any
+ * of the expressions in "maff".
+ */
+static int need_substitution(__isl_keep isl_multi_aff *maff)
+{
+	int i;
+	unsigned pos;
+
+	pos = isl_multi_aff_dim(maff, isl_dim_in) - 1;
+
+	for (i = 0; i < maff->n; ++i)
+		if (isl_aff_involves_dims(maff->p[i], isl_dim_in, pos, 1))
+			return 1;
+
+	return 0;
+}
+
+/* Given a set of upper bounds on the last "input" variable m,
+ * construct a piecewise affine expression that selects
+ * the minimal upper bound to m, i.e.,
+ * divide the space into cells where one
+ * of the upper bounds is smaller than all the others and select
+ * this upper bound on that cell.
+ *
+ * In particular, if there are n bounds b_i, then the result
+ * consists of n cell, each one of the form
+ *
+ *	b_i <= b_j	for j > i
+ *	b_i <  b_j	for j < i
+ *
+ * The affine expression on this cell is
+ *
+ *	b_i
+ */
+static __isl_give isl_pw_aff *set_minimum_pa(__isl_take isl_space *space,
+	__isl_take isl_mat *var)
+{
+	int i;
+	isl_aff *aff = NULL;
+	isl_basic_set *bset = NULL;
+	isl_ctx *ctx;
+	isl_pw_aff *paff = NULL;
+	isl_space *pw_space;
+	isl_local_space *ls = NULL;
+
+	if (!space || !var)
+		goto error;
+
+	ctx = isl_space_get_ctx(space);
+	ls = isl_local_space_from_space(isl_space_copy(space));
+	pw_space = isl_space_copy(space);
+	pw_space = isl_space_from_domain(pw_space);
+	pw_space = isl_space_add_dims(pw_space, isl_dim_out, 1);
+	paff = isl_pw_aff_alloc_size(pw_space, var->n_row);
+
+	for (i = 0; i < var->n_row; ++i) {
+		isl_pw_aff *paff_i;
+
+		aff = isl_aff_alloc(isl_local_space_copy(ls));
+		bset = isl_basic_set_alloc_space(isl_space_copy(space), 0,
+					       0, var->n_row - 1);
+		if (!aff || !bset)
+			goto error;
+		isl_int_set_si(aff->v->el[0], 1);
+		isl_seq_cpy(aff->v->el + 1, var->row[i], var->n_col);
+		isl_int_set_si(aff->v->el[1 + var->n_col], 0);
+		bset = select_minimum(bset, var, i);
+		paff_i = isl_pw_aff_alloc(isl_set_from_basic_set(bset), aff);
+		paff = isl_pw_aff_add_disjoint(paff, paff_i);
+	}
+
+	isl_local_space_free(ls);
+	isl_space_free(space);
+	isl_mat_free(var);
+	return paff;
+error:
+	isl_aff_free(aff);
+	isl_basic_set_free(bset);
+	isl_pw_aff_free(paff);
+	isl_local_space_free(ls);
+	isl_space_free(space);
+	isl_mat_free(var);
+	return NULL;
+}
+
+/* Given a piecewise multi-affine expression of which the last input variable
+ * is the minimum of the bounds in "cst", plug in the value of the minimum.
+ * This minimum expression is given in "min_expr_pa".
+ * The set "min_expr" contains the same information, but in the form of a set.
+ * The variable is subsequently projected out.
+ *
+ * The implementation is similar to those of "split" and "split_domain".
+ * If the variable appears in a given expression, then minimum expression
+ * is plugged in.  Otherwise, if the variable appears in the constraints
+ * and a split is required, then the domain is split.  Otherwise, no split
+ * is performed.
+ */
+static __isl_give isl_pw_multi_aff *split_domain_pma(
+	__isl_take isl_pw_multi_aff *opt, __isl_take isl_pw_aff *min_expr_pa,
+	__isl_take isl_set *min_expr, __isl_take isl_mat *cst)
+{
+	int n_in;
+	int i;
+	isl_space *space;
+	isl_pw_multi_aff *res;
+
+	if (!opt || !min_expr || !cst)
+		goto error;
+
+	n_in = isl_pw_multi_aff_dim(opt, isl_dim_in);
+	space = isl_pw_multi_aff_get_space(opt);
+	space = isl_space_drop_dims(space, isl_dim_in, n_in - 1, 1);
+	res = isl_pw_multi_aff_empty(space);
+
+	for (i = 0; i < opt->n; ++i) {
+		isl_pw_multi_aff *pma;
+
+		pma = isl_pw_multi_aff_alloc(isl_set_copy(opt->p[i].set),
+					 isl_multi_aff_copy(opt->p[i].maff));
+		if (need_substitution(opt->p[i].maff))
+			pma = isl_pw_multi_aff_substitute(pma,
+					isl_dim_in, n_in - 1, min_expr_pa);
+		else if (need_split_set(opt->p[i].set, cst))
+			pma = isl_pw_multi_aff_intersect_domain(pma,
+						       isl_set_copy(min_expr));
+		pma = isl_pw_multi_aff_project_out(pma,
+						    isl_dim_in, n_in - 1, 1);
+
+		res = isl_pw_multi_aff_add_disjoint(res, pma);
+	}
+
+	isl_pw_multi_aff_free(opt);
+	isl_pw_aff_free(min_expr_pa);
+	isl_set_free(min_expr);
+	isl_mat_free(cst);
+	return res;
+error:
+	isl_pw_multi_aff_free(opt);
+	isl_pw_aff_free(min_expr_pa);
+	isl_set_free(min_expr);
+	isl_mat_free(cst);
+	return NULL;
+}
+
+static __isl_give isl_pw_multi_aff *basic_map_partial_lexopt_pma(
+	__isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
+	__isl_give isl_set **empty, int max);
+
+/* This function is called from basic_map_partial_lexopt_symm.
+ * The last variable of "bmap" and "dom" corresponds to the minimum
+ * of the bounds in "cst".  "map_space" is the space of the original
+ * input relation (of basic_map_partial_lexopt_symm) and "set_space"
+ * is the space of the original domain.
+ *
+ * We recursively call basic_map_partial_lexopt and then plug in
+ * the definition of the minimum in the result.
+ */
+static __isl_give union isl_lex_res basic_map_partial_lexopt_symm_pma_core(
+	__isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
+	__isl_give isl_set **empty, int max, __isl_take isl_mat *cst,
+	__isl_take isl_space *map_space, __isl_take isl_space *set_space)
+{
+	isl_pw_multi_aff *opt;
+	isl_pw_aff *min_expr_pa;
+	isl_set *min_expr;
+	union isl_lex_res res;
+
+	min_expr = set_minimum(isl_basic_set_get_space(dom), isl_mat_copy(cst));
+	min_expr_pa = set_minimum_pa(isl_basic_set_get_space(dom),
+					isl_mat_copy(cst));
+
+	opt = basic_map_partial_lexopt_pma(bmap, dom, empty, max);
+
+	if (empty) {
+		*empty = split(*empty,
+			       isl_set_copy(min_expr), isl_mat_copy(cst));
+		*empty = isl_set_reset_space(*empty, set_space);
+	}
+
+	opt = split_domain_pma(opt, min_expr_pa, min_expr, cst);
+	opt = isl_pw_multi_aff_reset_space(opt, map_space);
+
+	res.pma = opt;
+	return res;
+}
+
+static __isl_give isl_pw_multi_aff *basic_map_partial_lexopt_symm_pma(
+	__isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
+	__isl_give isl_set **empty, int max, int first, int second)
+{
+	return basic_map_partial_lexopt_symm(bmap, dom, empty, max,
+		    first, second, &basic_map_partial_lexopt_symm_pma_core).pma;
+}
+
+/* Recursive part of isl_basic_map_partial_lexopt_pw_multi_aff, after detecting
+ * equalities and removing redundant constraints.
+ *
+ * We first check if there are any parallel constraints (left).
+ * If not, we are in the base case.
+ * If there are parallel constraints, we replace them by a single
+ * constraint in basic_map_partial_lexopt_symm_pma and then call
+ * this function recursively to look for more parallel constraints.
+ */
+static __isl_give isl_pw_multi_aff *basic_map_partial_lexopt_pma(
+	__isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
+	__isl_give isl_set **empty, int max)
+{
+	int par = 0;
+	int first, second;
+
+	if (!bmap)
+		goto error;
+
+	if (bmap->ctx->opt->pip_symmetry)
+		par = parallel_constraints(bmap, &first, &second);
+	if (par < 0)
+		goto error;
+	if (!par)
+		return basic_map_partial_lexopt_base_pma(bmap, dom, empty, max);
+	
+	return basic_map_partial_lexopt_symm_pma(bmap, dom, empty, max,
+						 first, second);
+error:
+	isl_basic_set_free(dom);
+	isl_basic_map_free(bmap);
+	return NULL;
+}
+
+/* Compute the lexicographic minimum (or maximum if "max" is set)
+ * of "bmap" over the domain "dom" and return the result as a piecewise
+ * multi-affine expression.
+ * If "empty" is not NULL, then *empty is assigned a set that
+ * contains those parts of the domain where there is no solution.
+ * If "bmap" is marked as rational (ISL_BASIC_MAP_RATIONAL),
+ * then we compute the rational optimum.  Otherwise, we compute
+ * the integral optimum.
+ *
+ * We perform some preprocessing.  As the PILP solver does not
+ * handle implicit equalities very well, we first make sure all
+ * the equalities are explicitly available.
+ *
+ * We also add context constraints to the basic map and remove
+ * redundant constraints.  This is only needed because of the
+ * way we handle simple symmetries.  In particular, we currently look
+ * for symmetries on the constraints, before we set up the main tableau.
+ * It is then no good to look for symmetries on possibly redundant constraints.
+ */
+__isl_give isl_pw_multi_aff *isl_basic_map_partial_lexopt_pw_multi_aff(
+	__isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
+	__isl_give isl_set **empty, int max)
+{
+	if (empty)
+		*empty = NULL;
+	if (!bmap || !dom)
+		goto error;
+
+	isl_assert(bmap->ctx,
+	    isl_basic_map_compatible_domain(bmap, dom), goto error);
+
+	if (isl_basic_set_dim(dom, isl_dim_all) == 0)
+		return basic_map_partial_lexopt_pma(bmap, dom, empty, max);
+
+	bmap = isl_basic_map_intersect_domain(bmap, isl_basic_set_copy(dom));
+	bmap = isl_basic_map_detect_equalities(bmap);
+	bmap = isl_basic_map_remove_redundancies(bmap);
+
+	return basic_map_partial_lexopt_pma(bmap, dom, empty, max);
+error:
+	isl_basic_set_free(dom);
+	isl_basic_map_free(bmap);
+	return NULL;
 }