X-Git-Url: http://review.tizen.org/git/?a=blobdiff_plain;f=isl_tab_pip.c;h=00efda46ee17bffe4dfb1ad335463f516ca81e7b;hb=f87b09b28f9398fd91d4aa5a87925520bf4e808e;hp=5886fd7ec2896b94bd08640782a13658a2d514e7;hpb=79d277b08490900bd698114586a63160a3da5d01;p=platform%2Fupstream%2Fisl.git

diff --git a/isl_tab_pip.c b/isl_tab_pip.c
index 5886fd7..00efda4 100644
--- a/isl_tab_pip.c
+++ b/isl_tab_pip.c
@@ -1,6 +1,21 @@
+/*
+ * Copyright 2008-2009 Katholieke Universiteit Leuven
+ * Copyright 2010      INRIA Saclay
+ *
+ * Use of this software is governed by the GNU LGPLv2.1 license
+ *
+ * Written by Sven Verdoolaege, K.U.Leuven, Departement
+ * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
+ * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
+ * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France 
+ */
+
+#include <isl_ctx_private.h>
 #include "isl_map_private.h"
-#include "isl_seq.h"
+#include <isl/seq.h>
 #include "isl_tab.h"
+#include "isl_sample.h"
+#include <isl_mat_private.h>
 
 /*
  * The implementation of parametric integer linear programming in this file
@@ -11,7 +26,7 @@
  * The strategy used for obtaining a feasible solution is different
  * from the one used in isl_tab.c.  In particular, in isl_tab.c,
  * upon finding a constraint that is not yet satisfied, we pivot
- * in a row that increases the constant term of row holding the
+ * in a row that increases the constant term of the row holding the
  * constraint, making sure the sample solution remains feasible
  * for all the constraints it already satisfied.
  * Here, we always pivot in the row holding the constraint,
@@ -25,19 +40,94 @@
  * 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.
  *
- * We use the big parameter trick both in the main tableau and
- * the context tableau, each of course having its own big parameter.
+ * The big parameter trick is used in the main tableau and
+ * also in the context tableau if isl_context_lex is used.
+ * In this case, each tableaus has its own big parameter.
  * Before doing any real work, we check if all the parameters
  * happen to be non-negative.  If so, we drop the column corresponding
  * to M from the initial context tableau.
+ * If isl_context_gbr is used, then the big parameter trick is only
+ * used in the main tableau.
  */
 
+struct isl_context;
+struct isl_context_op {
+	/* detect nonnegative parameters in context and mark them in tab */
+	struct isl_tab *(*detect_nonnegative_parameters)(
+			struct isl_context *context, struct isl_tab *tab);
+	/* return temporary reference to basic set representation of context */
+	struct isl_basic_set *(*peek_basic_set)(struct isl_context *context);
+	/* return temporary reference to tableau representation of context */
+	struct isl_tab *(*peek_tab)(struct isl_context *context);
+	/* add equality; check is 1 if eq may not be valid;
+	 * update is 1 if we may want to call ineq_sign on context later.
+	 */
+	void (*add_eq)(struct isl_context *context, isl_int *eq,
+			int check, int update);
+	/* add inequality; check is 1 if ineq may not be valid;
+	 * update is 1 if we may want to call ineq_sign on context later.
+	 */
+	void (*add_ineq)(struct isl_context *context, isl_int *ineq,
+			int check, int update);
+	/* check sign of ineq based on previous information.
+	 * strict is 1 if saturation should be treated as a positive sign.
+	 */
+	enum isl_tab_row_sign (*ineq_sign)(struct isl_context *context,
+			isl_int *ineq, int strict);
+	/* check if inequality maintains feasibility */
+	int (*test_ineq)(struct isl_context *context, isl_int *ineq);
+	/* 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 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 */
+	int (*best_split)(struct isl_context *context, struct isl_tab *tab);
+	/* check if context has already been determined to be empty */
+	int (*is_empty)(struct isl_context *context);
+	/* check if context is still usable */
+	int (*is_ok)(struct isl_context *context);
+	/* save a copy/snapshot of context */
+	void *(*save)(struct isl_context *context);
+	/* restore saved context */
+	void (*restore)(struct isl_context *context, void *);
+	/* invalidate context */
+	void (*invalidate)(struct isl_context *context);
+	/* free context */
+	void (*free)(struct isl_context *context);
+};
+
+struct isl_context {
+	struct isl_context_op *op;
+};
+
+struct isl_context_lex {
+	struct isl_context context;
+	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
@@ -55,55 +145,225 @@
  * the solution.
  */
 struct isl_sol {
-	struct isl_tab *context_tab;
-	struct isl_sol *(*add)(struct isl_sol *sol, struct isl_tab *tab);
+	int error;
+	int rational;
+	int level;
+	int max;
+	int n_out;
+	struct isl_context *context;
+	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)
 {
-	isl_tab_free(sol_map->sol.context_tab);
-	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 = isl_basic_set_copy(sol->sol.context_tab->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.
@@ -119,23 +379,23 @@ 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)
@@ -146,140 +406,264 @@ 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);
+}
+
+/* Add bset to sol's empty, but only if we are actually collecting
+ * the empty set.
+ */
+static void sol_map_add_empty_if_needed(struct isl_sol_map *sol,
+	struct isl_basic_set *bset)
+{
+	if (sol->empty)
+		sol_map_add_empty(sol, bset);
+	else
+		isl_basic_set_free(bset);
+}
+
+/* Given a basic map "dom" that represents the context and an affine
+ * matrix "M" that maps the dimensions of the context to the
+ * output variables, construct a basic map with the same parameters
+ * 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;
-	struct isl_tab *context_tab;
 	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_tab = sol->sol.context_tab;
-	off = 2 + tab->M;
-	n_out = isl_map_dim(sol->map, isl_dim_out);
-	n_eq = context_tab->bset->n_eq + n_out;
-	n_ineq = context_tab->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);
+					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_tab->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_tab->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_tab->bset->div[i] + 1 + 1 + nparam, i);
+			    dom->div[i] + 1 + 1 + nparam, i);
 	}
-	for (i = 0; i < context_tab->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_tab->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_tab->bset->eq[i] + 1 + nparam, n_div);
+			    dom->eq[i] + 1 + nparam, n_div);
 	}
-	for (i = 0; i < context_tab->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_tab->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_tab->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);
 	if (!sol->map)
 		goto error;
-	return sol;
+	isl_basic_set_free(dom);
+	isl_mat_free(M);
+	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);
 }
 
 
@@ -438,6 +822,9 @@ static struct isl_vec *ineq_for_div(struct isl_basic_set *bset, unsigned div)
 	unsigned div_pos;
 	struct isl_vec *ineq;
 
+	if (!bset)
+		return NULL;
+
 	total = isl_basic_set_total_dim(bset);
 	div_pos = 1 + total - bset->n_div + div;
 
@@ -465,19 +852,25 @@ static struct isl_vec *ineq_for_div(struct isl_basic_set *bset, unsigned div)
  */
 static struct isl_tab *set_row_cst_to_div(struct isl_tab *tab, int row, int div)
 {
-	int col;
-	unsigned off = 2 + tab->M;
-
 	isl_seq_fdiv_q(tab->mat->row[row] + 1, tab->mat->row[row] + 1,
 			tab->mat->row[row][0], 1 + tab->M + tab->n_col);
 
 	isl_int_set_si(tab->mat->row[row][0], 1);
 
-	isl_assert(tab->mat->ctx,
-		!tab->var[tab->n_var - tab->n_div + div].is_row, goto error);
+	if (tab->var[tab->n_var - tab->n_div + div].is_row) {
+		int drow = tab->var[tab->n_var - tab->n_div + div].index;
+
+		isl_assert(tab->mat->ctx,
+			isl_int_is_one(tab->mat->row[drow][0]), goto error);
+		isl_seq_combine(tab->mat->row[row] + 1,
+			tab->mat->ctx->one, tab->mat->row[row] + 1,
+			tab->mat->ctx->one, tab->mat->row[drow] + 1,
+			1 + tab->M + tab->n_col);
+	} else {
+		int dcol = tab->var[tab->n_var - tab->n_div + div].index;
 
-	col = tab->var[tab->n_var - tab->n_div + div].index;
-	isl_int_set_si(tab->mat->row[row][off + col], 1);
+		isl_int_set_si(tab->mat->row[row][2 + tab->M + dcol], 1);
+	}
 
 	return tab;
 error:
@@ -683,7 +1076,7 @@ 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,
@@ -697,8 +1090,11 @@ 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)
@@ -716,32 +1112,116 @@ static int first_neg(struct isl_tab *tab)
 	return -1;
 }
 
+/* Check whether the invariant that all columns are lexico-positive
+ * is satisfied.  This function is not called from the current code
+ * but is useful during debugging.
+ */
+static void check_lexpos(struct isl_tab *tab)
+{
+	unsigned off = 2 + tab->M;
+	int col;
+	int var;
+	int row;
+
+	for (col = tab->n_dead; col < tab->n_col; ++col) {
+		if (tab->col_var[col] >= 0 &&
+		    (tab->col_var[col] < tab->n_param ||
+		     tab->col_var[col] >= tab->n_var - tab->n_div))
+			continue;
+		for (var = tab->n_param; var < tab->n_var - tab->n_div; ++var) {
+			if (!tab->var[var].is_row) {
+				if (tab->var[var].index == col)
+					break;
+				else
+					continue;
+			}
+			row = tab->var[var].index;
+			if (isl_int_is_zero(tab->mat->row[row][off + col]))
+				continue;
+			if (isl_int_is_pos(tab->mat->row[row][off + col]))
+				break;
+			fprintf(stderr, "lexneg column %d (row %d)\n",
+				col, row);
+		}
+		if (var >= tab->n_var - tab->n_div)
+			fprintf(stderr, "zero column %d\n", col);
+	}
+}
+
+/* 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 lexicographicallly
+ * look for a pivoting column that would result in the lexicographically
  * smallest increment in the sample point.  If there is no such column
  * then the tableau is infeasible.
  */
-static struct isl_tab *restore_lexmin(struct isl_tab *tab)
+static int restore_lexmin(struct isl_tab *tab) WARN_UNUSED;
+static int restore_lexmin(struct isl_tab *tab)
 {
 	int row, col;
 
 	if (!tab)
-		return NULL;
+		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
@@ -810,19 +1290,21 @@ 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;
@@ -850,78 +1332,77 @@ 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
@@ -933,26 +1414,31 @@ 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);
@@ -994,7 +1480,7 @@ 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))
@@ -1018,8 +1504,9 @@ 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
@@ -1028,16 +1515,16 @@ 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))
@@ -1047,11 +1534,28 @@ 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.
  *
@@ -1099,7 +1603,8 @@ 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;
 
@@ -1110,15 +1615,17 @@ 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;
 
@@ -1127,14 +1634,21 @@ 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;
@@ -1155,7 +1669,7 @@ 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);
 
@@ -1203,30 +1717,28 @@ static int sample_is_finite(struct isl_tab *tab)
 }
 
 /* Check if the context tableau of sol has any integer points.
- * Returns -1 if an error occurred.
+ * Leave tab in empty state if no integer point can be found.
  * If an integer point can be found and if moreover it is finite,
  * then it is added to the list of sample values.
  *
  * This function is only called when none of the currently active sample
  * values satisfies the most recently added constraint.
  */
-static int context_is_feasible(struct isl_sol *sol)
+static struct isl_tab *check_integer_feasible(struct isl_tab *tab)
 {
 	struct isl_tab_undo *snap;
-	struct isl_tab *tab;
-	int feasible;
 
-	if (!sol || !sol->context_tab)
-		return -1;
+	if (!tab)
+		return NULL;
 
-	snap = isl_tab_snap(sol->context_tab);
-	isl_tab_push_basis(sol->context_tab);
+	snap = isl_tab_snap(tab);
+	if (isl_tab_push_basis(tab) < 0)
+		goto error;
 
-	sol->context_tab = cut_to_integer_lexmin(sol->context_tab);
-	if (!sol->context_tab)
+	tab = cut_to_integer_lexmin(tab);
+	if (!tab)
 		goto error;
 
-	tab = sol->context_tab;
 	if (!tab->empty && sample_is_finite(tab)) {
 		struct isl_vec *sample;
 
@@ -1235,33 +1747,27 @@ static int context_is_feasible(struct isl_sol *sol)
 		tab = isl_tab_add_sample(tab, sample);
 	}
 
-	feasible = !sol->context_tab->empty;
-	if (isl_tab_rollback(sol->context_tab, snap) < 0)
+	if (!tab->empty && isl_tab_rollback(tab, snap) < 0)
 		goto error;
 
-	return feasible;
+	return tab;
 error:
-	isl_tab_free(sol->context_tab);
-	sol->context_tab = NULL;
-	return -1;
+	isl_tab_free(tab);
+	return NULL;
 }
 
-/* First check if any of the currently active sample values satisfies
+/* Check if any of the currently active sample values satisfies
  * the inequality "ineq" (an equality if eq is set).
- * If not, continue with check_integer_feasible.
  */
-static int context_valid_sample_or_feasible(struct isl_sol *sol,
-	isl_int *ineq, int eq)
+static int tab_has_valid_sample(struct isl_tab *tab, isl_int *ineq, int eq)
 {
 	int i;
 	isl_int v;
-	struct isl_tab *tab;
 
-	if (!sol || !sol->context_tab)
+	if (!tab)
 		return -1;
 
-	tab = sol->context_tab;
-	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);
 
@@ -1276,51 +1782,39 @@ static int context_valid_sample_or_feasible(struct isl_sol *sol,
 	}
 	isl_int_clear(v);
 
-	if (i < tab->n_sample)
-		return 1;
-
-	return context_is_feasible(sol);
+	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
+/* Add a div specified by "div" to the tableau "tab" and return
+ * 1 if the div is obviously non-negative.
  */
-static struct isl_tab *add_div_constraints(struct isl_tab *tab, unsigned div)
+static int context_tab_add_div(struct isl_tab *tab, struct isl_vec *div,
+	int (*add_ineq)(void *user, isl_int *), void *user)
 {
-	unsigned total;
-	unsigned div_pos;
-	struct isl_vec *ineq;
-
-	if (!tab)
-		return NULL;
-
-	total = isl_basic_set_total_dim(tab->bset);
-	div_pos = 1 + total - tab->bset->n_div + div;
-
-	ineq = ineq_for_div(tab->bset, div);
-	if (!ineq)
-		goto error;
-
-	tab = add_lexmin_ineq(tab, ineq->el);
+	int i;
+	int r;
+	struct isl_mat *samples;
+	int nonneg;
 
-	isl_seq_neg(ineq->el, tab->bset->div[div] + 1, 1 + total);
-	isl_int_set(ineq->el[div_pos], tab->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);
-	tab = add_lexmin_ineq(tab, ineq->el);
+	r = isl_tab_add_div(tab, div, add_ineq, user);
+	if (r < 0)
+		return -1;
+	nonneg = tab->var[r].is_nonneg;
+	tab->var[r].frozen = 1;
 
-	isl_vec_free(ineq);
+	samples = isl_mat_extend(tab->samples,
+			tab->n_sample, 1 + tab->n_var);
+	tab->samples = samples;
+	if (!samples)
+		return -1;
+	for (i = tab->n_outside; i < samples->n_row; ++i) {
+		isl_seq_inner_product(div->el + 1, samples->row[i],
+			div->size - 1, &samples->row[i][samples->n_col - 1]);
+		isl_int_fdiv_q(samples->row[i][samples->n_col - 1],
+			       samples->row[i][samples->n_col - 1], div->el[0]);
+	}
 
-	return tab;
-error:
-	isl_tab_free(tab);
-	return NULL;
+	return nonneg;
 }
 
 /* Add a div specified by "div" to both the main tableau and
@@ -1329,43 +1823,16 @@ error:
  * need to express the meaning of the div.
  * Return the index of the div or -1 if anything went wrong.
  */
-static int add_div(struct isl_tab *tab, struct isl_tab **context_tab,
+static int add_div(struct isl_tab *tab, struct isl_context *context,
 	struct isl_vec *div)
 {
-	int i;
 	int r;
-	int k;
-	struct isl_mat *samples;
-
-	if (isl_tab_extend_vars(*context_tab, 1) < 0)
-		goto error;
-	r = isl_tab_allocate_var(*context_tab);
-	if (r < 0)
-		goto error;
-	(*context_tab)->var[r].is_nonneg = 1;
-	(*context_tab)->var[r].frozen = 1;
+	int nonneg;
 
-	samples = isl_mat_extend((*context_tab)->samples,
-			(*context_tab)->n_sample, 1 + (*context_tab)->n_var);
-	(*context_tab)->samples = samples;
-	if (!samples)
+	if ((nonneg = context->op->add_div(context, div)) < 0)
 		goto error;
-	for (i = (*context_tab)->n_outside; i < samples->n_row; ++i) {
-		isl_seq_inner_product(div->el + 1, samples->row[i],
-			div->size - 1, &samples->row[i][samples->n_col - 1]);
-		isl_int_fdiv_q(samples->row[i][samples->n_col - 1],
-			       samples->row[i][samples->n_col - 1], div->el[0]);
-	}
 
-	(*context_tab)->bset = isl_basic_set_extend_dim((*context_tab)->bset,
-		isl_basic_set_get_dim((*context_tab)->bset), 1, 0, 2);
-	k = isl_basic_set_alloc_div((*context_tab)->bset);
-	if (k < 0)
-		goto error;
-	isl_seq_cpy((*context_tab)->bset->div[k], div->el, div->size);
-	isl_tab_push((*context_tab), isl_tab_undo_bset_div);
-	*context_tab = add_div_constraints(*context_tab, k);
-	if (!*context_tab)
+	if (!context->op->is_ok(context))
 		goto error;
 
 	if (isl_tab_extend_vars(tab, 1) < 0)
@@ -1373,27 +1840,26 @@ static int add_div(struct isl_tab *tab, struct isl_tab **context_tab,
 	r = isl_tab_allocate_var(tab);
 	if (r < 0)
 		goto error;
-	if (!(*context_tab)->M)
+	if (nonneg)
 		tab->var[r].is_nonneg = 1;
 	tab->var[r].frozen = 1;
 	tab->n_div++;
 
 	return tab->n_div - 1;
 error:
-	isl_tab_free(*context_tab);
-	*context_tab = NULL;
+	context->op->invalidate(context);
 	return -1;
 }
 
 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;
 	}
@@ -1403,16 +1869,20 @@ static int find_div(struct isl_tab *tab, isl_int *div, isl_int denom)
 /* Return the index of a div that corresponds to "div".
  * We first check if we already have such a div and if not, we create one.
  */
-static int get_div(struct isl_tab *tab, struct isl_tab **context_tab,
+static int get_div(struct isl_tab *tab, struct isl_context *context,
 	struct isl_vec *div)
 {
 	int d;
+	struct isl_tab *context_tab = context->op->peek_tab(context);
+
+	if (!context_tab)
+		return -1;
 
-	d = find_div(*context_tab, div->el + 1, div->el[0]);
+	d = find_div(context_tab, div->el + 1, div->el[0]);
 	if (d != -1)
 		return d;
 
-	return add_div(tab, context_tab, div);
+	return add_div(tab, context, div);
 }
 
 /* Add a parametric cut to cut away the non-integral sample value
@@ -1439,7 +1909,7 @@ static int get_div(struct isl_tab *tab, struct isl_tab **context_tab,
  * Return the row of the cut or -1.
  */
 static int add_parametric_cut(struct isl_tab *tab, int row,
-	struct isl_tab **context_tab)
+	struct isl_context *context)
 {
 	struct isl_vec *div;
 	int d;
@@ -1447,21 +1917,20 @@ static int add_parametric_cut(struct isl_tab *tab, int row,
 	int r;
 	isl_int *r_row;
 	int col;
+	int n;
 	unsigned off = 2 + tab->M;
 
-	if (!*context_tab)
-		goto error;
-
-	if (isl_tab_extend_cons(*context_tab, 3) < 0)
-		goto error;
+	if (!context)
+		return -1;
 
 	div = get_row_parameter_div(tab, row);
 	if (!div)
 		return -1;
 
-	d = get_div(tab, context_tab, div);
+	n = tab->n_div;
+	d = context->op->get_div(context, tab, div);
 	if (d < 0)
-		goto error;
+		return -1;
 
 	if (isl_tab_extend_cons(tab, 1) < 0)
 		return -1;
@@ -1520,17 +1989,19 @@ 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;
 
 	isl_vec_free(div);
 
-	return tab->con[r].index;
-error:
-	isl_tab_free(*context_tab);
-	*context_tab = NULL;
-	return -1;
+	row = tab->con[r].index;
+
+	if (d >= n && context->op->detect_equalities(context, tab) < 0)
+		return -1;
+
+	return row;
 }
 
 /* Construct a tableau for bmap that can be used for computing
@@ -1565,8 +2036,11 @@ 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;
@@ -1585,6 +2059,8 @@ 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,
@@ -1604,23 +2080,1204 @@ error:
 	return NULL;
 }
 
-static struct isl_tab *context_tab_for_lexmin(struct isl_basic_set *bset)
+/* Given a main tableau where more than one row requires a split,
+ * determine and return the "best" row to split on.
+ *
+ * Given two rows in the main tableau, if the inequality corresponding
+ * to the first row is redundant with respect to that of the second row
+ * in the current tableau, then it is better to split on the second row,
+ * since in the positive part, both row will be positive.
+ * (In the negative part a pivot will have to be performed and just about
+ * anything can happen to the sign of the other row.)
+ *
+ * As a simple heuristic, we therefore select the row that makes the most
+ * of the other rows redundant.
+ *
+ * Perhaps it would also be useful to look at the number of constraints
+ * that conflict with any given constraint.
+ */
+static int best_split(struct isl_tab *tab, struct isl_tab *context_tab)
 {
-	struct isl_tab *tab;
+	struct isl_tab_undo *snap;
+	int split;
+	int row;
+	int best = -1;
+	int best_r;
 
-	bset = isl_basic_set_cow(bset);
-	if (!bset)
-		return NULL;
-	tab = tab_for_lexmin((struct isl_basic_map *)bset, NULL, 1, 0);
-	if (!tab)
-		goto error;
-	tab->bset = bset;
-	tab = isl_tab_init_samples(tab);
-	return tab;
-error:
-	isl_basic_set_free(bset);
-	return NULL;
-}
+	if (isl_tab_extend_cons(context_tab, 2) < 0)
+		return -1;
+
+	snap = isl_tab_snap(context_tab);
+
+	for (split = tab->n_redundant; split < tab->n_row; ++split) {
+		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;
+		if (tab->row_sign[split] != isl_tab_row_any)
+			continue;
+
+		ineq = get_row_parameter_ineq(tab, split);
+		if (!ineq)
+			return -1;
+		ok = isl_tab_add_ineq(context_tab, ineq->el) >= 0;
+		isl_vec_free(ineq);
+		if (!ok)
+			return -1;
+
+		snap2 = isl_tab_snap(context_tab);
+
+		for (row = tab->n_redundant; row < tab->n_row; ++row) {
+			struct isl_tab_var *var;
+
+			if (row == split)
+				continue;
+			if (!isl_tab_var_from_row(tab, row)->is_nonneg)
+				continue;
+			if (tab->row_sign[row] != isl_tab_row_any)
+				continue;
+
+			ineq = get_row_parameter_ineq(tab, row);
+			if (!ineq)
+				return -1;
+			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))
+				r++;
+			if (isl_tab_rollback(context_tab, snap2) < 0)
+				return -1;
+		}
+		if (best == -1 || r > best_r) {
+			best = split;
+			best_r = r;
+		}
+		if (isl_tab_rollback(context_tab, snap) < 0)
+			return -1;
+	}
+
+	return best;
+}
+
+static struct isl_basic_set *context_lex_peek_basic_set(
+	struct isl_context *context)
+{
+	struct isl_context_lex *clex = (struct isl_context_lex *)context;
+	if (!clex->tab)
+		return NULL;
+	return isl_tab_peek_bset(clex->tab);
+}
+
+static struct isl_tab *context_lex_peek_tab(struct isl_context *context)
+{
+	struct isl_context_lex *clex = (struct isl_context_lex *)context;
+	return clex->tab;
+}
+
+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;
+	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)
+			goto error;
+		if (!v)
+			clex->tab = check_integer_feasible(clex->tab);
+	}
+	if (update)
+		clex->tab = check_samples(clex->tab, eq, 1);
+	return;
+error:
+	isl_tab_free(clex->tab);
+	clex->tab = NULL;
+}
+
+static void context_lex_add_ineq(struct isl_context *context, isl_int *ineq,
+		int check, int update)
+{
+	struct isl_context_lex *clex = (struct isl_context_lex *)context;
+	if (isl_tab_extend_cons(clex->tab, 1) < 0)
+		goto error;
+	clex->tab = add_lexmin_ineq(clex->tab, ineq);
+	if (check) {
+		int v = tab_has_valid_sample(clex->tab, ineq, 0);
+		if (v < 0)
+			goto error;
+		if (!v)
+			clex->tab = check_integer_feasible(clex->tab);
+	}
+	if (update)
+		clex->tab = check_samples(clex->tab, ineq, 0);
+	return;
+error:
+	isl_tab_free(clex->tab);
+	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.
+ */
+static enum isl_tab_row_sign tab_ineq_sign(struct isl_tab *tab, isl_int *ineq,
+	int strict)
+{
+	int i;
+	int sgn;
+	isl_int tmp;
+	enum isl_tab_row_sign res = isl_tab_row_unknown;
+
+	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) {
+		isl_seq_inner_product(tab->samples->row[i], ineq,
+					1 + tab->n_var, &tmp);
+		sgn = isl_int_sgn(tmp);
+		if (sgn > 0 || (sgn == 0 && strict)) {
+			if (res == isl_tab_row_unknown)
+				res = isl_tab_row_pos;
+			if (res == isl_tab_row_neg)
+				res = isl_tab_row_any;
+		}
+		if (sgn < 0) {
+			if (res == isl_tab_row_unknown)
+				res = isl_tab_row_neg;
+			if (res == isl_tab_row_pos)
+				res = isl_tab_row_any;
+		}
+		if (res == isl_tab_row_any)
+			break;
+	}
+	isl_int_clear(tmp);
+
+	return res;
+}
+
+static enum isl_tab_row_sign context_lex_ineq_sign(struct isl_context *context,
+			isl_int *ineq, int strict)
+{
+	struct isl_context_lex *clex = (struct isl_context_lex *)context;
+	return tab_ineq_sign(clex->tab, ineq, strict);
+}
+
+/* Check whether "ineq" can be added to the tableau without rendering
+ * it infeasible.
+ */
+static int context_lex_test_ineq(struct isl_context *context, isl_int *ineq)
+{
+	struct isl_context_lex *clex = (struct isl_context_lex *)context;
+	struct isl_tab_undo *snap;
+	int feasible;
+
+	if (!clex->tab)
+		return -1;
+
+	if (isl_tab_extend_cons(clex->tab, 1) < 0)
+		return -1;
+
+	snap = isl_tab_snap(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)
+		return -1;
+	feasible = !clex->tab->empty;
+	if (isl_tab_rollback(clex->tab, snap) < 0)
+		return -1;
+
+	return feasible;
+}
+
+static int context_lex_get_div(struct isl_context *context, struct isl_tab *tab,
+		struct isl_vec *div)
+{
+	return get_div(tab, context, div);
+}
+
+/* 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;
+	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,
+		struct isl_tab *tab)
+{
+	return 0;
+}
+
+static int context_lex_best_split(struct isl_context *context,
+		struct isl_tab *tab)
+{
+	struct isl_context_lex *clex = (struct isl_context_lex *)context;
+	struct isl_tab_undo *snap;
+	int r;
+
+	snap = isl_tab_snap(clex->tab);
+	if (isl_tab_push_basis(clex->tab) < 0)
+		return -1;
+	r = best_split(tab, clex->tab);
+
+	if (r >= 0 && isl_tab_rollback(clex->tab, snap) < 0)
+		return -1;
+
+	return r;
+}
+
+static int context_lex_is_empty(struct isl_context *context)
+{
+	struct isl_context_lex *clex = (struct isl_context_lex *)context;
+	if (!clex->tab)
+		return -1;
+	return clex->tab->empty;
+}
+
+static void *context_lex_save(struct isl_context *context)
+{
+	struct isl_context_lex *clex = (struct isl_context_lex *)context;
+	struct isl_tab_undo *snap;
+
+	snap = isl_tab_snap(clex->tab);
+	if (isl_tab_push_basis(clex->tab) < 0)
+		return NULL;
+	if (isl_tab_save_samples(clex->tab) < 0)
+		return NULL;
+
+	return snap;
+}
+
+static void context_lex_restore(struct isl_context *context, void *save)
+{
+	struct isl_context_lex *clex = (struct isl_context_lex *)context;
+	if (isl_tab_rollback(clex->tab, (struct isl_tab_undo *)save) < 0) {
+		isl_tab_free(clex->tab);
+		clex->tab = NULL;
+	}
+}
+
+static int context_lex_is_ok(struct isl_context *context)
+{
+	struct isl_context_lex *clex = (struct isl_context_lex *)context;
+	return !!clex->tab;
+}
+
+/* For each variable in the context tableau, check if the variable can
+ * only attain non-negative values.  If so, mark the parameter as non-negative
+ * in the main tableau.  This allows for a more direct identification of some
+ * cases of violated constraints.
+ */
+static struct isl_tab *tab_detect_nonnegative_parameters(struct isl_tab *tab,
+	struct isl_tab *context_tab)
+{
+	int i;
+	struct isl_tab_undo *snap;
+	struct isl_vec *ineq = NULL;
+	struct isl_tab_var *var;
+	int n;
+
+	if (context_tab->n_var == 0)
+		return tab;
+
+	ineq = isl_vec_alloc(tab->mat->ctx, 1 + context_tab->n_var);
+	if (!ineq)
+		goto error;
+
+	if (isl_tab_extend_cons(context_tab, 1) < 0)
+		goto error;
+
+	snap = isl_tab_snap(context_tab);
+
+	n = 0;
+	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);
+		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)) {
+			int j = i;
+			if (i >= tab->n_param)
+				j = i - tab->n_param + tab->n_var - tab->n_div;
+			tab->var[j].is_nonneg = 1;
+			n++;
+		}
+		isl_int_set_si(ineq->el[1 + i], 0);
+		if (isl_tab_rollback(context_tab, snap) < 0)
+			goto error;
+	}
+
+	if (context_tab->M && n == context_tab->n_var) {
+		context_tab->mat = isl_mat_drop_cols(context_tab->mat, 2, 1);
+		context_tab->M = 0;
+	}
+
+	isl_vec_free(ineq);
+	return tab;
+error:
+	isl_vec_free(ineq);
+	isl_tab_free(tab);
+	return NULL;
+}
+
+static struct isl_tab *context_lex_detect_nonnegative_parameters(
+	struct isl_context *context, struct isl_tab *tab)
+{
+	struct isl_context_lex *clex = (struct isl_context_lex *)context;
+	struct isl_tab_undo *snap;
+
+	if (!tab)
+		return NULL;
+
+	snap = isl_tab_snap(clex->tab);
+	if (isl_tab_push_basis(clex->tab) < 0)
+		goto error;
+
+	tab = tab_detect_nonnegative_parameters(tab, clex->tab);
+
+	if (isl_tab_rollback(clex->tab, snap) < 0)
+		goto error;
+
+	return tab;
+error:
+	isl_tab_free(tab);
+	return NULL;
+}
+
+static void context_lex_invalidate(struct isl_context *context)
+{
+	struct isl_context_lex *clex = (struct isl_context_lex *)context;
+	isl_tab_free(clex->tab);
+	clex->tab = NULL;
+}
+
+static void context_lex_free(struct isl_context *context)
+{
+	struct isl_context_lex *clex = (struct isl_context_lex *)context;
+	isl_tab_free(clex->tab);
+	free(clex);
+}
+
+struct isl_context_op isl_context_lex_op = {
+	context_lex_detect_nonnegative_parameters,
+	context_lex_peek_basic_set,
+	context_lex_peek_tab,
+	context_lex_add_eq,
+	context_lex_add_ineq,
+	context_lex_ineq_sign,
+	context_lex_test_ineq,
+	context_lex_get_div,
+	context_lex_add_div,
+	context_lex_detect_equalities,
+	context_lex_best_split,
+	context_lex_is_empty,
+	context_lex_is_ok,
+	context_lex_save,
+	context_lex_restore,
+	context_lex_invalidate,
+	context_lex_free,
+};
+
+static struct isl_tab *context_tab_for_lexmin(struct isl_basic_set *bset)
+{
+	struct isl_tab *tab;
+
+	bset = isl_basic_set_cow(bset);
+	if (!bset)
+		return NULL;
+	tab = tab_for_lexmin((struct isl_basic_map *)bset, NULL, 1, 0);
+	if (!tab)
+		goto error;
+	if (isl_tab_track_bset(tab, bset) < 0)
+		goto error;
+	tab = isl_tab_init_samples(tab);
+	return tab;
+error:
+	isl_basic_set_free(bset);
+	return NULL;
+}
+
+static struct isl_context *isl_context_lex_alloc(struct isl_basic_set *dom)
+{
+	struct isl_context_lex *clex;
+
+	if (!dom)
+		return NULL;
+
+	clex = isl_alloc_type(dom->ctx, struct isl_context_lex);
+	if (!clex)
+		return NULL;
+
+	clex->context.op = &isl_context_lex_op;
+
+	clex->tab = context_tab_for_lexmin(isl_basic_set_copy(dom));
+	if (restore_lexmin(clex->tab) < 0)
+		goto error;
+	clex->tab = check_integer_feasible(clex->tab);
+	if (!clex->tab)
+		goto error;
+
+	return &clex->context;
+error:
+	clex->context.op->free(&clex->context);
+	return NULL;
+}
+
+struct isl_context_gbr {
+	struct isl_context context;
+	struct isl_tab *tab;
+	struct isl_tab *shifted;
+	struct isl_tab *cone;
+};
+
+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);
+}
+
+static struct isl_basic_set *context_gbr_peek_basic_set(
+	struct isl_context *context)
+{
+	struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
+	if (!cgbr->tab)
+		return NULL;
+	return isl_tab_peek_bset(cgbr->tab);
+}
+
+static struct isl_tab *context_gbr_peek_tab(struct isl_context *context)
+{
+	struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
+	return cgbr->tab;
+}
+
+/* Initialize the "shifted" tableau of the context, which
+ * contains the constraints of the original tableau shifted
+ * by the sum of all negative coefficients.  This ensures
+ * that any rational point in the shifted tableau can
+ * be rounded up to yield an integer point in the original tableau.
+ */
+static void gbr_init_shifted(struct isl_context_gbr *cgbr)
+{
+	int i, j;
+	struct isl_vec *cst;
+	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);
+	if (!cst)
+		return;
+
+	for (i = 0; i < bset->n_ineq; ++i) {
+		isl_int_set(cst->el[i], bset->ineq[i][0]);
+		for (j = 0; j < dim; ++j) {
+			if (!isl_int_is_neg(bset->ineq[i][1 + j]))
+				continue;
+			isl_int_add(bset->ineq[i][0], bset->ineq[i][0],
+				    bset->ineq[i][1 + j]);
+		}
+	}
+
+	cgbr->shifted = isl_tab_from_basic_set(bset);
+
+	for (i = 0; i < bset->n_ineq; ++i)
+		isl_int_set(bset->ineq[i][0], cst->el[i]);
+
+	isl_vec_free(cst);
+}
+
+/* Check if the shifted tableau is non-empty, and if so
+ * use the sample point to construct an integer point
+ * of the context tableau.
+ */
+static struct isl_vec *gbr_get_shifted_sample(struct isl_context_gbr *cgbr)
+{
+	struct isl_vec *sample;
+
+	if (!cgbr->shifted)
+		gbr_init_shifted(cgbr);
+	if (!cgbr->shifted)
+		return NULL;
+	if (cgbr->shifted->empty)
+		return isl_vec_alloc(cgbr->tab->mat->ctx, 0);
+
+	sample = isl_tab_get_sample_value(cgbr->shifted);
+	sample = isl_vec_ceil(sample);
+
+	return sample;
+}
+
+static struct isl_basic_set *drop_constant_terms(struct isl_basic_set *bset)
+{
+	int i;
+
+	if (!bset)
+		return NULL;
+
+	for (i = 0; i < bset->n_eq; ++i)
+		isl_int_set_si(bset->eq[i][0], 0);
+
+	for (i = 0; i < bset->n_ineq; ++i)
+		isl_int_set_si(bset->ineq[i][0], 0);
+
+	return bset;
+}
+
+static int use_shifted(struct isl_context_gbr *cgbr)
+{
+	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)
+{
+	struct isl_basic_set *bset;
+	struct isl_basic_set *cone;
+
+	if (isl_tab_sample_is_integer(cgbr->tab))
+		return isl_tab_get_sample_value(cgbr->tab);
+
+	if (use_shifted(cgbr)) {
+		struct isl_vec *sample;
+
+		sample = gbr_get_shifted_sample(cgbr);
+		if (!sample || sample->size > 0)
+			return sample;
+
+		isl_vec_free(sample);
+	}
+
+	if (!cgbr->cone) {
+		bset = isl_tab_peek_bset(cgbr->tab);
+		cgbr->cone = isl_tab_from_recession_cone(bset, 0);
+		if (!cgbr->cone)
+			return NULL;
+		if (isl_tab_track_bset(cgbr->cone, isl_basic_set_dup(bset)) < 0)
+			return NULL;
+	}
+	if (isl_tab_detect_implicit_equalities(cgbr->cone) < 0)
+		return NULL;
+
+	if (cgbr->cone->n_dead == cgbr->cone->n_col) {
+		struct isl_vec *sample;
+		struct isl_tab_undo *snap;
+
+		if (cgbr->tab->basis) {
+			if (cgbr->tab->basis->n_col != 1 + cgbr->tab->n_var) {
+				isl_mat_free(cgbr->tab->basis);
+				cgbr->tab->basis = NULL;
+			}
+			cgbr->tab->n_zero = 0;
+			cgbr->tab->n_unbounded = 0;
+		}
+
+		snap = isl_tab_snap(cgbr->tab);
+
+		sample = isl_tab_sample(cgbr->tab);
+
+		if (isl_tab_rollback(cgbr->tab, snap) < 0) {
+			isl_vec_free(sample);
+			return NULL;
+		}
+
+		return sample;
+	}
+
+	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(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);
+
+	return isl_basic_set_sample_with_cone(bset, cone);
+}
+
+static void check_gbr_integer_feasible(struct isl_context_gbr *cgbr)
+{
+	struct isl_vec *sample;
+
+	if (!cgbr->tab)
+		return;
+
+	if (cgbr->tab->empty)
+		return;
+
+	sample = gbr_get_sample(cgbr);
+	if (!sample)
+		goto error;
+
+	if (sample->size == 0) {
+		isl_vec_free(sample);
+		if (isl_tab_mark_empty(cgbr->tab) < 0)
+			goto error;
+		return;
+	}
+
+	cgbr->tab = isl_tab_add_sample(cgbr->tab, sample);
+
+	return;
+error:
+	isl_tab_free(cgbr->tab);
+	cgbr->tab = NULL;
+}
+
+static struct isl_tab *add_gbr_eq(struct isl_tab *tab, isl_int *eq)
+{
+	if (!tab)
+		return NULL;
+
+	if (isl_tab_extend_cons(tab, 2) < 0)
+		goto error;
+
+	if (isl_tab_add_eq(tab, eq) < 0)
+		goto error;
+
+	return tab;
+error:
+	isl_tab_free(tab);
+	return NULL;
+}
+
+static void context_gbr_add_eq(struct isl_context *context, isl_int *eq,
+		int check, int update)
+{
+	struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
+
+	cgbr->tab = add_gbr_eq(cgbr->tab, eq);
+
+	if (cgbr->cone && cgbr->cone->n_col != cgbr->cone->n_dead) {
+		if (isl_tab_extend_cons(cgbr->cone, 2) < 0)
+			goto error;
+		if (isl_tab_add_eq(cgbr->cone, eq) < 0)
+			goto error;
+	}
+
+	if (check) {
+		int v = tab_has_valid_sample(cgbr->tab, eq, 1);
+		if (v < 0)
+			goto error;
+		if (!v)
+			check_gbr_integer_feasible(cgbr);
+	}
+	if (update)
+		cgbr->tab = check_samples(cgbr->tab, eq, 1);
+	return;
+error:
+	isl_tab_free(cgbr->tab);
+	cgbr->tab = NULL;
+}
+
+static void add_gbr_ineq(struct isl_context_gbr *cgbr, isl_int *ineq)
+{
+	if (!cgbr->tab)
+		return;
+
+	if (isl_tab_extend_cons(cgbr->tab, 1) < 0)
+		goto error;
+
+	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_map_total_dim(cgbr->tab->bmap);
+
+		if (isl_tab_extend_cons(cgbr->shifted, 1) < 0)
+			goto error;
+
+		for (i = 0; i < dim; ++i) {
+			if (!isl_int_is_neg(ineq[1 + i]))
+				continue;
+			isl_int_add(ineq[0], ineq[0], ineq[1 + i]);
+		}
+
+		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]))
+				continue;
+			isl_int_sub(ineq[0], ineq[0], ineq[1 + i]);
+		}
+	}
+
+	if (cgbr->cone && cgbr->cone->n_col != cgbr->cone->n_dead) {
+		if (isl_tab_extend_cons(cgbr->cone, 1) < 0)
+			goto error;
+		if (isl_tab_add_ineq(cgbr->cone, ineq) < 0)
+			goto error;
+	}
+
+	return;
+error:
+	isl_tab_free(cgbr->tab);
+	cgbr->tab = NULL;
+}
+
+static void context_gbr_add_ineq(struct isl_context *context, isl_int *ineq,
+		int check, int update)
+{
+	struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
+
+	add_gbr_ineq(cgbr, ineq);
+	if (!cgbr->tab)
+		return;
+
+	if (check) {
+		int v = tab_has_valid_sample(cgbr->tab, ineq, 0);
+		if (v < 0)
+			goto error;
+		if (!v)
+			check_gbr_integer_feasible(cgbr);
+	}
+	if (update)
+		cgbr->tab = check_samples(cgbr->tab, ineq, 0);
+	return;
+error:
+	isl_tab_free(cgbr->tab);
+	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)
+{
+	struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
+	return tab_ineq_sign(cgbr->tab, ineq, strict);
+}
+
+/* Check whether "ineq" can be added to the tableau without rendering
+ * it infeasible.
+ */
+static int context_gbr_test_ineq(struct isl_context *context, isl_int *ineq)
+{
+	struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
+	struct isl_tab_undo *snap;
+	struct isl_tab_undo *shifted_snap = NULL;
+	struct isl_tab_undo *cone_snap = NULL;
+	int feasible;
+
+	if (!cgbr->tab)
+		return -1;
+
+	if (isl_tab_extend_cons(cgbr->tab, 1) < 0)
+		return -1;
+
+	snap = isl_tab_snap(cgbr->tab);
+	if (cgbr->shifted)
+		shifted_snap = isl_tab_snap(cgbr->shifted);
+	if (cgbr->cone)
+		cone_snap = isl_tab_snap(cgbr->cone);
+	add_gbr_ineq(cgbr, ineq);
+	check_gbr_integer_feasible(cgbr);
+	if (!cgbr->tab)
+		return -1;
+	feasible = !cgbr->tab->empty;
+	if (isl_tab_rollback(cgbr->tab, snap) < 0)
+		return -1;
+	if (shifted_snap) {
+		if (isl_tab_rollback(cgbr->shifted, shifted_snap))
+			return -1;
+	} else if (cgbr->shifted) {
+		isl_tab_free(cgbr->shifted);
+		cgbr->shifted = NULL;
+	}
+	if (cone_snap) {
+		if (isl_tab_rollback(cgbr->cone, cone_snap))
+			return -1;
+	} else if (cgbr->cone) {
+		isl_tab_free(cgbr->cone);
+		cgbr->cone = NULL;
+	}
+
+	return feasible;
+}
+
+/* Return the column of the last of the variables associated to
+ * a column that has a non-zero coefficient.
+ * This function is called in a context where only coefficients
+ * of parameters or divs can be non-zero.
+ */
+static int last_non_zero_var_col(struct isl_tab *tab, isl_int *p)
+{
+	int i;
+	int col;
+
+	if (tab->n_var == 0)
+		return -1;
+
+	for (i = tab->n_var - 1; i >= 0; --i) {
+		if (i >= tab->n_param && i < tab->n_var - tab->n_div)
+			continue;
+		if (tab->var[i].is_row)
+			continue;
+		col = tab->var[i].index;
+		if (!isl_int_is_zero(p[col]))
+			return col;
+	}
+
+	return -1;
+}
+
+/* Look through all the recently added equalities in the context
+ * to see if we can propagate any of them to the main tableau.
+ *
+ * The newly added equalities in the context are encoded as pairs
+ * of inequalities starting at inequality "first".
+ *
+ * We tentatively add each of these equalities to the main tableau
+ * and if this happens to result in a row with a final coefficient
+ * that is one or negative one, we use it to kill a column
+ * in the main tableau.  Otherwise, we discard the tentatively
+ * added row.
+ */
+static void propagate_equalities(struct isl_context_gbr *cgbr,
+	struct isl_tab *tab, unsigned first)
+{
+	int i;
+	struct isl_vec *eq = NULL;
+
+	eq = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_var);
+	if (!eq)
+		goto error;
+
+	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->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->bmap->ineq[i], 1 + tab->n_param);
+		isl_seq_cpy(eq->el + 1 + tab->n_var - tab->n_div,
+			    cgbr->tab->bmap->ineq[i] + 1 + tab->n_param,
+			    tab->n_div);
+
+		r = isl_tab_add_row(tab, eq->el);
+		if (r < 0)
+			goto error;
+		r = tab->con[r].index;
+		j = last_non_zero_var_col(tab, tab->mat->row[r] + 2 + tab->M);
+		if (j < 0 || j < tab->n_dead ||
+		    !isl_int_is_one(tab->mat->row[r][0]) ||
+		    (!isl_int_is_one(tab->mat->row[r][2 + tab->M + j]) &&
+		     !isl_int_is_negone(tab->mat->row[r][2 + tab->M + j]))) {
+			if (isl_tab_rollback(tab, snap) < 0)
+				goto error;
+			continue;
+		}
+		if (isl_tab_pivot(tab, r, j) < 0)
+			goto error;
+		if (isl_tab_kill_col(tab, j) < 0)
+			goto error;
+
+		if (restore_lexmin(tab) < 0)
+			goto error;
+	}
+
+	isl_vec_free(eq);
+
+	return;
+error:
+	isl_vec_free(eq);
+	isl_tab_free(cgbr->tab);
+	cgbr->tab = NULL;
+}
+
+static int context_gbr_detect_equalities(struct isl_context *context,
+	struct isl_tab *tab)
+{
+	struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
+	struct isl_ctx *ctx;
+	unsigned n_ineq;
+
+	ctx = cgbr->tab->mat->ctx;
+
+	if (!cgbr->cone) {
+		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;
+		if (isl_tab_track_bset(cgbr->cone, isl_basic_set_dup(bset)) < 0)
+			goto error;
+	}
+	if (isl_tab_detect_implicit_equalities(cgbr->cone) < 0)
+		goto error;
+
+	n_ineq = cgbr->tab->bmap->n_ineq;
+	cgbr->tab = isl_tab_detect_equalities(cgbr->tab, cgbr->cone);
+	if (cgbr->tab && cgbr->tab->bmap->n_ineq > n_ineq)
+		propagate_equalities(cgbr, tab, n_ineq);
+
+	return 0;
+error:
+	isl_tab_free(cgbr->tab);
+	cgbr->tab = NULL;
+	return -1;
+}
+
+static int context_gbr_get_div(struct isl_context *context, struct isl_tab *tab,
+		struct isl_vec *div)
+{
+	return get_div(tab, context, div);
+}
+
+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) {
+		int k;
+
+		if (isl_tab_extend_cons(cgbr->cone, 3) < 0)
+			return -1;
+		if (isl_tab_extend_vars(cgbr->cone, 1) < 0)
+			return -1;
+		if (isl_tab_allocate_var(cgbr->cone) <0)
+			return -1;
+
+		cgbr->cone->bmap = isl_basic_map_extend_dim(cgbr->cone->bmap,
+			isl_basic_map_get_dim(cgbr->cone->bmap), 1, 0, 2);
+		k = isl_basic_map_alloc_div(cgbr->cone->bmap);
+		if (k < 0)
+			return -1;
+		isl_seq_cpy(cgbr->cone->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,
+					context_gbr_add_ineq_wrap, context);
+}
+
+static int context_gbr_best_split(struct isl_context *context,
+		struct isl_tab *tab)
+{
+	struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
+	struct isl_tab_undo *snap;
+	int r;
+
+	snap = isl_tab_snap(cgbr->tab);
+	r = best_split(tab, cgbr->tab);
+
+	if (r >= 0 && isl_tab_rollback(cgbr->tab, snap) < 0)
+		return -1;
+
+	return r;
+}
+
+static int context_gbr_is_empty(struct isl_context *context)
+{
+	struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
+	if (!cgbr->tab)
+		return -1;
+	return cgbr->tab->empty;
+}
+
+struct isl_gbr_tab_undo {
+	struct isl_tab_undo *tab_snap;
+	struct isl_tab_undo *shifted_snap;
+	struct isl_tab_undo *cone_snap;
+};
+
+static void *context_gbr_save(struct isl_context *context)
+{
+	struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
+	struct isl_gbr_tab_undo *snap;
+
+	snap = isl_alloc_type(cgbr->tab->mat->ctx, struct isl_gbr_tab_undo);
+	if (!snap)
+		return NULL;
+
+	snap->tab_snap = isl_tab_snap(cgbr->tab);
+	if (isl_tab_save_samples(cgbr->tab) < 0)
+		goto error;
+
+	if (cgbr->shifted)
+		snap->shifted_snap = isl_tab_snap(cgbr->shifted);
+	else
+		snap->shifted_snap = NULL;
+
+	if (cgbr->cone)
+		snap->cone_snap = isl_tab_snap(cgbr->cone);
+	else
+		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) {
+		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) {
+		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);
+
+	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;
+}
+
+static void context_gbr_invalidate(struct isl_context *context)
+{
+	struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
+	isl_tab_free(cgbr->tab);
+	cgbr->tab = NULL;
+}
+
+static void context_gbr_free(struct isl_context *context)
+{
+	struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
+	isl_tab_free(cgbr->tab);
+	isl_tab_free(cgbr->shifted);
+	isl_tab_free(cgbr->cone);
+	free(cgbr);
+}
+
+struct isl_context_op isl_context_gbr_op = {
+	context_gbr_detect_nonnegative_parameters,
+	context_gbr_peek_basic_set,
+	context_gbr_peek_tab,
+	context_gbr_add_eq,
+	context_gbr_add_ineq,
+	context_gbr_ineq_sign,
+	context_gbr_test_ineq,
+	context_gbr_get_div,
+	context_gbr_add_div,
+	context_gbr_detect_equalities,
+	context_gbr_best_split,
+	context_gbr_is_empty,
+	context_gbr_is_ok,
+	context_gbr_save,
+	context_gbr_restore,
+	context_gbr_invalidate,
+	context_gbr_free,
+};
+
+static struct isl_context *isl_context_gbr_alloc(struct isl_basic_set *dom)
+{
+	struct isl_context_gbr *cgbr;
+
+	if (!dom)
+		return NULL;
+
+	cgbr = isl_calloc_type(dom->ctx, struct isl_context_gbr);
+	if (!cgbr)
+		return NULL;
+
+	cgbr->context.op = &isl_context_gbr_op;
+
+	cgbr->shifted = NULL;
+	cgbr->cone = NULL;
+	cgbr->tab = isl_tab_from_basic_set(dom);
+	cgbr->tab = isl_tab_init_samples(cgbr->tab);
+	if (!cgbr->tab)
+		goto error;
+	if (isl_tab_track_bset(cgbr->tab,
+				isl_basic_set_cow(isl_basic_set_copy(dom))) < 0)
+		goto error;
+	check_gbr_integer_feasible(cgbr);
+
+	return &cgbr->context;
+error:
+	cgbr->context.op->free(&cgbr->context);
+	return NULL;
+}
+
+static struct isl_context *isl_context_alloc(struct isl_basic_set *dom)
+{
+	if (!dom)
+		return NULL;
+
+	if (dom->ctx->opt->context == ISL_CONTEXT_LEXMIN)
+		return isl_context_lex_alloc(dom);
+	else
+		return isl_context_gbr_alloc(dom);
+}
 
 /* Construct an isl_sol_map structure for accumulating the solution.
  * If track_empty is set, then we also keep track of the parts
@@ -1632,27 +3289,30 @@ error:
 static struct isl_sol_map *sol_map_init(struct isl_basic_map *bmap,
 	struct isl_basic_set *dom, int track_empty, int max)
 {
-	struct isl_sol_map *sol_map;
-	struct isl_tab *context_tab;
-	int f;
+	struct isl_sol_map *sol_map = NULL;
 
-	sol_map = isl_calloc_type(bset->ctx, struct isl_sol_map);
+	if (!bmap)
+		goto error;
+
+	sol_map = isl_calloc_type(bmap->ctx, struct isl_sol_map);
 	if (!sol_map)
 		goto error;
 
-	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,
 					    ISL_MAP_DISJOINT);
 	if (!sol_map->map)
 		goto error;
 
-	context_tab = context_tab_for_lexmin(isl_basic_set_copy(dom));
-	context_tab = restore_lexmin(context_tab);
-	sol_map->sol.context_tab = context_tab;
-	f = context_is_feasible(&sol_map->sol);
-	if (f < 0)
+	sol_map->sol.context = isl_context_alloc(dom);
+	if (!sol_map->sol.context)
 		goto error;
 
 	if (track_empty) {
@@ -1670,70 +3330,6 @@ error:
 	return NULL;
 }
 
-/* For each variable in the context tableau, check if the variable can
- * only attain non-negative values.  If so, mark the parameter as non-negative
- * in the main tableau.  This allows for a more direct identification of some
- * cases of violated constraints.
- */
-static struct isl_tab *tab_detect_nonnegative_parameters(struct isl_tab *tab,
-	struct isl_tab *context_tab)
-{
-	int i;
-	struct isl_tab_undo *snap, *snap2;
-	struct isl_vec *ineq = NULL;
-	struct isl_tab_var *var;
-	int n;
-
-	if (context_tab->n_var == 0)
-		return tab;
-
-	ineq = isl_vec_alloc(tab->mat->ctx, 1 + context_tab->n_var);
-	if (!ineq)
-		goto error;
-
-	if (isl_tab_extend_cons(context_tab, 1) < 0)
-		goto error;
-
-	snap = isl_tab_snap(context_tab);
-	isl_tab_push_basis(context_tab);
-
-	snap2 = isl_tab_snap(context_tab);
-
-	n = 0;
-	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);
-		var = &context_tab->con[context_tab->n_con - 1];
-		if (!context_tab->empty &&
-		    !isl_tab_min_at_most_neg_one(context_tab, var)) {
-			int j = i;
-			if (i >= tab->n_param)
-				j = i - tab->n_param + tab->n_var - tab->n_div;
-			tab->var[j].is_nonneg = 1;
-			n++;
-		}
-		isl_int_set_si(ineq->el[1 + i], 0);
-		if (isl_tab_rollback(context_tab, snap2) < 0)
-			goto error;
-	}
-
-	if (isl_tab_rollback(context_tab, snap) < 0)
-		goto error;
-
-	if (n == context_tab->n_var) {
-		context_tab->mat = isl_mat_drop_cols(context_tab->mat, 2, 1);
-		context_tab->M = 0;
-	}
-
-	isl_vec_free(ineq);
-	return tab;
-error:
-	isl_vec_free(ineq);
-	isl_tab_free(tab);
-	return NULL;
-}
-
 /* Check whether all coefficients of (non-parameter) variables
  * are non-positive, meaning that no pivots can be performed on the row.
  */
@@ -1834,18 +3430,14 @@ static int is_strict(struct isl_vec *vec)
  *	>=0 ?	     Y      N
  *		    any    neg
  */
-static int row_sign(struct isl_tab *tab, struct isl_sol *sol, int row)
+static enum isl_tab_row_sign row_sign(struct isl_tab *tab,
+	struct isl_sol *sol, int row)
 {
-	int i;
-	struct isl_tab_undo *snap = NULL;
 	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 sgn;
 	int row2;
-	isl_int tmp;
-	struct isl_tab *context_tab = sol->context_tab;
 
 	if (tab->row_sign[row] != isl_tab_row_unknown)
 		return tab->row_sign[row];
@@ -1860,44 +3452,14 @@ static int row_sign(struct isl_tab *tab, struct isl_sol *sol, int row)
 
 	critical = is_critical(tab, row);
 
-	isl_assert(tab->mat->ctx, context_tab->samples, goto error);
-	isl_assert(tab->mat->ctx, context_tab->samples->n_col == 1 + context_tab->n_var, goto error);
-
 	ineq = get_row_parameter_ineq(tab, row);
 	if (!ineq)
 		goto error;
 
 	strict = is_strict(ineq);
 
-	isl_int_init(tmp);
-	for (i = context_tab->n_outside; i < context_tab->n_sample; ++i) {
-		isl_seq_inner_product(context_tab->samples->row[i], ineq->el,
-					ineq->size, &tmp);
-		sgn = isl_int_sgn(tmp);
-		if (sgn > 0 || (sgn == 0 && (critical || strict))) {
-			if (res == isl_tab_row_unknown)
-				res = isl_tab_row_pos;
-			if (res == isl_tab_row_neg)
-				res = isl_tab_row_any;
-		}
-		if (sgn < 0) {
-			if (res == isl_tab_row_unknown)
-				res = isl_tab_row_neg;
-			if (res == isl_tab_row_pos)
-				res = isl_tab_row_any;
-		}
-		if (res == isl_tab_row_any)
-			break;
-	}
-	isl_int_clear(tmp);
-
-	if (res != isl_tab_row_any) {
-		if (isl_tab_extend_cons(context_tab, 1) < 0)
-			goto error;
-
-		snap = isl_tab_snap(context_tab);
-		isl_tab_push_basis(context_tab);
-	}
+	res = sol->context->op->ineq_sign(sol->context, ineq->el,
+					  critical || strict);
 
 	if (res == isl_tab_row_unknown || res == isl_tab_row_pos) {
 		/* test for negative values */
@@ -1905,20 +3467,14 @@ static int row_sign(struct isl_tab *tab, struct isl_sol *sol, int row)
 		isl_seq_neg(ineq->el, ineq->el, ineq->size);
 		isl_int_sub_ui(ineq->el[0], ineq->el[0], 1);
 
-		isl_tab_push_basis(context_tab);
-		sol->context_tab = add_lexmin_ineq(sol->context_tab, ineq->el);
-		feasible = context_is_feasible(sol);
+		feasible = sol->context->op->test_ineq(sol->context, ineq->el);
 		if (feasible < 0)
 			goto error;
-		context_tab = sol->context_tab;
 		if (!feasible)
 			res = isl_tab_row_pos;
 		else
 			res = (res == isl_tab_row_unknown) ? isl_tab_row_neg
 							   : isl_tab_row_any;
-		if (isl_tab_rollback(context_tab, snap) < 0)
-			goto error;
-
 		if (res == isl_tab_row_neg) {
 			isl_seq_neg(ineq->el, ineq->el, ineq->size);
 			isl_int_sub_ui(ineq->el[0], ineq->el[0], 1);
@@ -1931,26 +3487,21 @@ static int row_sign(struct isl_tab *tab, struct isl_sol *sol, int row)
 		if (!critical && !strict)
 			isl_int_sub_ui(ineq->el[0], ineq->el[0], 1);
 
-		isl_tab_push_basis(context_tab);
-		sol->context_tab = add_lexmin_ineq(sol->context_tab, ineq->el);
-		feasible = context_is_feasible(sol);
+		feasible = sol->context->op->test_ineq(sol->context, ineq->el);
 		if (feasible < 0)
 			goto error;
-		context_tab = sol->context_tab;
 		if (feasible)
 			res = isl_tab_row_any;
-		if (isl_tab_rollback(context_tab, snap) < 0)
-			goto error;
 	}
 
 	isl_vec_free(ineq);
 	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.
@@ -1966,154 +3517,59 @@ 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)
 {
-	struct isl_tab_undo *snap;
+	void *saved;
 
-	snap = isl_tab_snap(sol->context_tab);
-	isl_tab_push_basis(sol->context_tab);
-	isl_tab_save_samples(sol->context_tab);
-	if (isl_tab_extend_cons(sol->context_tab, 1) < 0)
+	if (!sol->context)
 		goto error;
+	saved = sol->context->op->save(sol->context);
 
 	tab = isl_tab_dup(tab);
 	if (!tab)
 		goto error;
 
-	sol->context_tab = add_lexmin_ineq(sol->context_tab, ineq);
-	sol->context_tab = check_samples(sol->context_tab, ineq, 0);
+	sol->context->op->add_ineq(sol->context, ineq, 0, 1);
 
-	sol = find_solutions(sol, tab);
+	find_solutions(sol, tab);
 
-	isl_tab_rollback(sol->context_tab, snap);
-	return sol;
+	if (!sol->error)
+		sol->context->op->restore(sol->context, saved);
+	return;
 error:
-	isl_tab_rollback(sol->context_tab, snap);
-	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;
-	int f;
-	struct isl_tab_undo *snap;
-	snap = isl_tab_snap(sol->context_tab);
-	isl_tab_push_basis(sol->context_tab);
-	isl_tab_save_samples(sol->context_tab);
-	if (isl_tab_extend_cons(sol->context_tab, 1) < 0)
+	void *saved;
+
+	if (!sol->context || sol->error)
 		goto error;
+	saved = sol->context->op->save(sol->context);
 
 	isl_int_sub_ui(ineq->el[0], ineq->el[0], 1);
 
-	sol->context_tab = add_lexmin_ineq(sol->context_tab, ineq->el);
-	f = context_valid_sample_or_feasible(sol, ineq->el, 0);
-	if (f < 0)
+	sol->context->op->add_ineq(sol->context, ineq->el, 1, 0);
+	if (!sol->context)
 		goto error;
 
 	empty = tab->empty;
-	tab->empty = 1;
-	sol = sol->add(sol, tab);
-	tab->empty = empty;
-
-	isl_int_add_ui(ineq->el[0], ineq->el[0], 1);
-
-	if (isl_tab_rollback(sol->context_tab, snap) < 0)
-		goto error;
-	return sol;
-error:
-	sol_free(sol);
-	return NULL;
-}
-
-/* Given a main tableau where more than one row requires a split,
- * determine and return the "best" row to split on.
- *
- * Given two rows in the main tableau, if the inequality corresponding
- * to the first row is redundant with respect to that of the second row
- * in the current tableau, then it is better to split on the second row,
- * since in the positive part, both row will be positive.
- * (In the negative part a pivot will have to be performed and just about
- * anything can happen to the sign of the other row.)
- *
- * As a simple heuristic, we therefore select the row that makes the most
- * of the other rows redundant.
- *
- * Perhaps it would also be useful to look at the number of constraints
- * that conflict with any given constraint.
- */
-static int best_split(struct isl_tab *tab, struct isl_tab *context_tab)
-{
-	struct isl_tab_undo *snap, *snap2;
-	int split;
-	int row;
-	int best = -1;
-	int best_r;
-
-	if (isl_tab_extend_cons(context_tab, 2) < 0)
-		return -1;
-
-	snap = isl_tab_snap(context_tab);
-	isl_tab_push_basis(context_tab);
-	snap2 = isl_tab_snap(context_tab);
-
-	for (split = tab->n_redundant; split < tab->n_row; ++split) {
-		struct isl_tab_undo *snap3;
-		struct isl_vec *ineq = NULL;
-		int r = 0;
-
-		if (!isl_tab_var_from_row(tab, split)->is_nonneg)
-			continue;
-		if (tab->row_sign[split] != isl_tab_row_any)
-			continue;
-
-		ineq = get_row_parameter_ineq(tab, split);
-		if (!ineq)
-			return -1;
-		context_tab = isl_tab_add_ineq(context_tab, ineq->el);
-		isl_vec_free(ineq);
-
-		snap3 = isl_tab_snap(context_tab);
-
-		for (row = tab->n_redundant; row < tab->n_row; ++row) {
-			struct isl_tab_var *var;
-
-			if (row == split)
-				continue;
-			if (!isl_tab_var_from_row(tab, row)->is_nonneg)
-				continue;
-			if (tab->row_sign[row] != isl_tab_row_any)
-				continue;
-
-			ineq = get_row_parameter_ineq(tab, row);
-			if (!ineq)
-				return -1;
-			context_tab = isl_tab_add_ineq(context_tab, ineq->el);
-			isl_vec_free(ineq);
-			var = &context_tab->con[context_tab->n_con - 1];
-			if (!context_tab->empty &&
-			    !isl_tab_min_at_most_neg_one(context_tab, var))
-				r++;
-			if (isl_tab_rollback(context_tab, snap3) < 0)
-				return -1;
-		}
-		if (best == -1 || r > best_r) {
-			best = split;
-			best_r = r;
-		}
-		if (isl_tab_rollback(context_tab, snap2) < 0)
-			return -1;
-	}
+	tab->empty = 1;
+	sol_add(sol, tab);
+	tab->empty = empty;
 
-	if (isl_tab_rollback(context_tab, snap) < 0)
-		return -1;
+	isl_int_add_ui(ineq->el[0], ineq->el[0], 1);
 
-	return best;
+	sol->context->op->restore(sol->context, saved);
+	return;
+error:
+	sol->error = 1;
 }
 
 /* Compute the lexicographic minimum of the set represented by the main
@@ -2190,7 +3646,7 @@ static int best_split(struct isl_tab *tab, struct isl_tab *context_tab)
  * 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.
@@ -2210,24 +3666,25 @@ static int best_split(struct isl_tab *tab, struct isl_tab *context_tab)
  * 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_tab **context_tab;
+	struct isl_context *context;
+	int r;
 
-	if (!tab || !sol)
+	if (!tab || sol->error)
 		goto error;
 
-	context_tab = &sol->context_tab;
+	context = sol->context;
 
 	if (tab->empty)
 		goto done;
-	if ((*context_tab)->empty)
+	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;
 
@@ -2250,7 +3707,7 @@ static struct isl_sol *find_solutions(struct isl_sol *sol, struct isl_tab *tab)
 		if (split != -1) {
 			struct isl_vec *ineq;
 			if (n_split != 1)
-				split = best_split(tab, *context_tab);
+				split = context->op->best_split(context, tab);
 			if (split < 0)
 				goto error;
 			ineq = get_row_parameter_ineq(tab, split);
@@ -2264,26 +3721,28 @@ 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_tab = add_lexmin_ineq(*context_tab, ineq->el);
-			*context_tab = check_samples(*context_tab, ineq->el, 0);
+			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);
@@ -2291,37 +3750,40 @@ static struct isl_sol *find_solutions(struct isl_sol *sol, struct isl_tab *tab)
 			struct isl_vec *div;
 			struct isl_vec *ineq;
 			int d;
-			if (isl_tab_extend_cons(*context_tab, 3) < 0)
-				goto error;
 			div = get_row_split_div(tab, row);
 			if (!div)
 				goto error;
-			d = get_div(tab, context_tab, div);
+			d = context->op->get_div(context, tab, div);
 			isl_vec_free(div);
 			if (d < 0)
 				goto error;
-			ineq = ineq_for_div((*context_tab)->bset, d);
-			sol = no_sol_in_strict(sol, tab, ineq);
+			ineq = ineq_for_div(context->op->peek_basic_set(context), d);
+			if (!ineq)
+				goto error;
+			sol_inc_level(sol);
+			no_sol_in_strict(sol, tab, ineq);
 			isl_seq_neg(ineq->el, ineq->el, ineq->size);
-			*context_tab = add_lexmin_ineq(*context_tab, ineq->el);
-			*context_tab = check_samples(*context_tab, ineq->el, 0);
+			context->op->add_ineq(context, ineq->el, 1, 1);
 			isl_vec_free(ineq);
-			if (!sol)
+			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_tab);
+			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
@@ -2335,11 +3797,15 @@ 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;
@@ -2355,47 +3821,49 @@ static struct isl_sol *find_solutions_main(struct isl_sol *sol,
 			p = tab->row_var[row]
 				+ tab->n_param - (tab->n_var - tab->n_div);
 
-		if (isl_tab_extend_cons(sol->context_tab, 2) < 0)
-			goto error;
-
 		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_tab = add_lexmin_eq(sol->context_tab, eq->el);
-		context_valid_sample_or_feasible(sol, eq->el, 1);
-		sol->context_tab = check_samples(sol->context_tab, eq->el, 1);
+		sol->context->op->add_eq(sol->context, eq->el, 1, 1);
 
 		isl_vec_free(eq);
 
-		isl_tab_mark_redundant(tab, row);
-
-		if (!sol->context_tab)
+		if (isl_tab_mark_redundant(tab, row) < 0)
 			goto error;
-		if (sol->context_tab->empty)
+
+		if (sol->context->op->is_empty(sol->context))
 			break;
 
 		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;
+	sol->error = 1;
 }
 
-static struct isl_sol_map *sol_map_find_solutions(struct isl_sol_map *sol_map,
+static void 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);
+	find_solutions_main(&sol_map->sol, tab);
 }
 
 /* Check if integer division "div" of "dom" also occurs in "bmap".
@@ -2426,50 +3894,566 @@ static int find_context_div(struct isl_basic_map *bmap,
 	return -1;
 }
 
-/* The correspondence between the variables in the main tableau,
- * the context tableau, and the input map and domain is as follows.
- * The first n_param and the last n_div variables of the main tableau
- * form the variables of the context tableau.
- * In the basic map, these n_param variables correspond to the
- * parameters and the input dimensions.  In the domain, they correspond
- * to the parameters and the set dimensions.
- * The n_div variables correspond to the integer divisions in the domain.
- * To ensure that everything lines up, we may need to copy some of the
- * integer divisions of the domain to the map.  These have to be placed
- * in the same order as those in the context and they have to be placed
- * after any other integer divisions that the map may have.
- * This function performs the required reordering.
+/* The correspondence between the variables in the main tableau,
+ * the context tableau, and the input map and domain is as follows.
+ * The first n_param and the last n_div variables of the main tableau
+ * form the variables of the context tableau.
+ * In the basic map, these n_param variables correspond to the
+ * parameters and the input dimensions.  In the domain, they correspond
+ * to the parameters and the set dimensions.
+ * The n_div variables correspond to the integer divisions in the domain.
+ * To ensure that everything lines up, we may need to copy some of the
+ * integer divisions of the domain to the map.  These have to be placed
+ * in the same order as those in the context and they have to be placed
+ * after any other integer divisions that the map may have.
+ * This function performs the required reordering.
+ */
+static struct isl_basic_map *align_context_divs(struct isl_basic_map *bmap,
+	struct isl_basic_set *dom)
+{
+	int i;
+	int common = 0;
+	int other;
+
+	for (i = 0; i < dom->n_div; ++i)
+		if (find_context_div(bmap, dom, i) != -1)
+			common++;
+	other = bmap->n_div - common;
+	if (dom->n_div - common > 0) {
+		bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim),
+				dom->n_div - common, 0, 0);
+		if (!bmap)
+			return NULL;
+	}
+	for (i = 0; i < dom->n_div; ++i) {
+		int pos = find_context_div(bmap, dom, i);
+		if (pos < 0) {
+			pos = isl_basic_map_alloc_div(bmap);
+			if (pos < 0)
+				goto error;
+			isl_int_set_si(bmap->div[pos][0], 0);
+		}
+		if (pos != other + i)
+			isl_basic_map_swap_div(bmap, pos, other + i);
+	}
+	return bmap;
+error:
+	isl_basic_map_free(bmap);
+	return NULL;
+}
+
+/* Base case of isl_tab_basic_map_partial_lexopt, after removing
+ * some obvious symmetries.
+ *
+ * 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.
+ */
+static __isl_give isl_map *basic_map_partial_lexopt_base(
+	__isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
+	__isl_give isl_set **empty, int max)
+{
+	isl_map *result = NULL;
+	struct isl_tab *tab;
+	struct isl_sol_map *sol_map = NULL;
+	struct isl_context *context;
+
+	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)
+		goto error;
+
+	context = sol_map->sol.context;
+	if (isl_basic_set_plain_is_empty(context->op->peek_basic_set(context)))
+		/* nothing */;
+	else if (isl_basic_map_plain_is_empty(bmap))
+		sol_map_add_empty_if_needed(sol_map,
+		    isl_basic_set_copy(context->op->peek_basic_set(context)));
+	else {
+		tab = tab_for_lexmin(bmap,
+				    context->op->peek_basic_set(context), 1, max);
+		tab = context->op->detect_nonnegative_parameters(context, tab);
+		sol_map_find_solutions(sol_map, tab);
+	}
+	if (sol_map->sol.error)
+		goto error;
+
+	result = isl_map_copy(sol_map->map);
+	if (empty)
+		*empty = isl_set_copy(sol_map->empty);
+	sol_free(&sol_map->sol);
+	isl_basic_map_free(bmap);
+	return result;
+error:
+	sol_free(&sol_map->sol);
+	isl_basic_map_free(bmap);
+	return NULL;
+}
+
+/* Structure used during detection of parallel constraints.
+ * n_in: number of "input" variables: isl_dim_param + isl_dim_in
+ * n_out: number of "output" variables: isl_dim_out + isl_dim_div
+ * val: the coefficients of the output variables
+ */
+struct isl_constraint_equal_info {
+	isl_basic_map *bmap;
+	unsigned n_in;
+	unsigned n_out;
+	isl_int *val;
+};
+
+/* Check whether the coefficients of the output variables
+ * of the constraint in "entry" are equal to info->val.
+ */
+static int constraint_equal(const void *entry, const void *val)
+{
+	isl_int **row = (isl_int **)entry;
+	const struct isl_constraint_equal_info *info = val;
+
+	return isl_seq_eq((*row) + 1 + info->n_in, info->val, info->n_out);
+}
+
+/* Check whether "bmap" has a pair of constraints that have
+ * the same coefficients for the output variables.
+ * Note that the coefficients of the existentially quantified
+ * variables need to be zero since the existentially quantified
+ * of the result are usually not the same as those of the input.
+ * the isl_dim_out and isl_dim_div dimensions.
+ * If so, return 1 and return the row indices of the two constraints
+ * in *first and *second.
+ */
+static int parallel_constraints(__isl_keep isl_basic_map *bmap,
+	int *first, int *second)
+{
+	int i;
+	isl_ctx *ctx = isl_basic_map_get_ctx(bmap);
+	struct isl_hash_table *table = NULL;
+	struct isl_hash_table_entry *entry;
+	struct isl_constraint_equal_info info;
+	unsigned n_out;
+	unsigned n_div;
+
+	ctx = isl_basic_map_get_ctx(bmap);
+	table = isl_hash_table_alloc(ctx, bmap->n_ineq);
+	if (!table)
+		goto error;
+
+	info.n_in = isl_basic_map_dim(bmap, isl_dim_param) +
+		    isl_basic_map_dim(bmap, isl_dim_in);
+	info.bmap = bmap;
+	n_out = isl_basic_map_dim(bmap, isl_dim_out);
+	n_div = isl_basic_map_dim(bmap, isl_dim_div);
+	info.n_out = n_out + n_div;
+	for (i = 0; i < bmap->n_ineq; ++i) {
+		uint32_t hash;
+
+		info.val = bmap->ineq[i] + 1 + info.n_in;
+		if (isl_seq_first_non_zero(info.val, n_out) < 0)
+			continue;
+		if (isl_seq_first_non_zero(info.val + n_out, n_div) >= 0)
+			continue;
+		hash = isl_seq_get_hash(info.val, info.n_out);
+		entry = isl_hash_table_find(ctx, table, hash,
+					    constraint_equal, &info, 1);
+		if (!entry)
+			goto error;
+		if (entry->data)
+			break;
+		entry->data = &bmap->ineq[i];
+	}
+
+	if (i < bmap->n_ineq) {
+		*first = ((isl_int **)entry->data) - bmap->ineq; 
+		*second = i;
+	}
+
+	isl_hash_table_free(ctx, table);
+
+	return i < bmap->n_ineq;
+error:
+	isl_hash_table_free(ctx, table);
+	return -1;
+}
+
+/* Given a set of upper bounds on the last "input" variable m,
+ * construct a set that assigns the minimal upper bound to m, i.e.,
+ * construct a set that divides the space into cells where one
+ * of the upper bounds is smaller than all the others and assign
+ * this upper bound to m.
+ *
+ * In particular, if there are n bounds b_i, then the result
+ * consists of n basic sets, each one of the form
+ *
+ *	m = b_i
+ *	b_i <= b_j	for j > i
+ *	b_i <  b_j	for j < i
+ */
+static __isl_give isl_set *set_minimum(__isl_take isl_dim *dim,
+	__isl_take isl_mat *var)
+{
+	int i, j, k;
+	isl_basic_set *bset = NULL;
+	isl_ctx *ctx;
+	isl_set *set = NULL;
+
+	if (!dim || !var)
+		goto error;
+
+	ctx = isl_dim_get_ctx(dim);
+	set = isl_set_alloc_dim(isl_dim_copy(dim),
+				var->n_row, ISL_SET_DISJOINT);
+
+	for (i = 0; i < var->n_row; ++i) {
+		bset = isl_basic_set_alloc_dim(isl_dim_copy(dim), 0,
+					       1, var->n_row - 1);
+		k = isl_basic_set_alloc_equality(bset);
+		if (k < 0)
+			goto error;
+		isl_seq_cpy(bset->eq[k], var->row[i], var->n_col);
+		isl_int_set_si(bset->eq[k][var->n_col], -1);
+		for (j = 0; j < var->n_row; ++j) {
+			if (j == i)
+				continue;
+			k = isl_basic_set_alloc_inequality(bset);
+			if (k < 0)
+				goto error;
+			isl_seq_combine(bset->ineq[k], ctx->one, var->row[j],
+					ctx->negone, var->row[i],
+					var->n_col);
+			isl_int_set_si(bset->ineq[k][var->n_col], 0);
+			if (j < i)
+				isl_int_sub_ui(bset->ineq[k][0],
+					       bset->ineq[k][0], 1);
+		}
+		bset = isl_basic_set_finalize(bset);
+		set = isl_set_add_basic_set(set, bset);
+	}
+
+	isl_dim_free(dim);
+	isl_mat_free(var);
+	return set;
+error:
+	isl_basic_set_free(bset);
+	isl_set_free(set);
+	isl_dim_free(dim);
+	isl_mat_free(var);
+	return NULL;
+}
+
+/* Given that the last input variable of "bmap" represents the minimum
+ * of the bounds in "cst", check whether we need to split the domain
+ * based on which bound attains the minimum.
+ *
+ * A split is needed when the minimum appears in an integer division
+ * or in an equality.  Otherwise, it is only needed if it appears in
+ * an upper bound that is different from the upper bounds on which it
+ * is defined.
+ */
+static int need_split_map(__isl_keep isl_basic_map *bmap,
+	__isl_keep isl_mat *cst)
+{
+	int i, j;
+	unsigned total;
+	unsigned pos;
+
+	pos = cst->n_col - 1;
+	total = isl_basic_map_dim(bmap, isl_dim_all);
+
+	for (i = 0; i < bmap->n_div; ++i)
+		if (!isl_int_is_zero(bmap->div[i][2 + pos]))
+			return 1;
+
+	for (i = 0; i < bmap->n_eq; ++i)
+		if (!isl_int_is_zero(bmap->eq[i][1 + pos]))
+			return 1;
+
+	for (i = 0; i < bmap->n_ineq; ++i) {
+		if (isl_int_is_nonneg(bmap->ineq[i][1 + pos]))
+			continue;
+		if (!isl_int_is_negone(bmap->ineq[i][1 + pos]))
+			return 1;
+		if (isl_seq_first_non_zero(bmap->ineq[i] + 1 + pos + 1,
+					   total - pos - 1) >= 0)
+			return 1;
+
+		for (j = 0; j < cst->n_row; ++j)
+			if (isl_seq_eq(bmap->ineq[i], cst->row[j], cst->n_col))
+				break;
+		if (j >= cst->n_row)
+			return 1;
+	}
+
+	return 0;
+}
+
+static int need_split_set(__isl_keep isl_basic_set *bset,
+	__isl_keep isl_mat *cst)
+{
+	return need_split_map((isl_basic_map *)bset, cst);
+}
+
+/* Given a set of which the last set variable is the minimum
+ * of the bounds in "cst", split each basic set in the set
+ * in pieces where one of the bounds is (strictly) smaller than the others.
+ * This subdivision is given in "min_expr".
+ * The variable is subsequently projected out.
+ *
+ * We only do the split when it is needed.
+ * For example if the last input variable m = min(a,b) and the only
+ * constraints in the given basic set are lower bounds on m,
+ * i.e., l <= m = min(a,b), then we can simply project out m
+ * to obtain l <= a and l <= b, without having to split on whether
+ * m is equal to a or b.
+ */
+static __isl_give isl_set *split(__isl_take isl_set *empty,
+	__isl_take isl_set *min_expr, __isl_take isl_mat *cst)
+{
+	int n_in;
+	int i;
+	isl_dim *dim;
+	isl_set *res;
+
+	if (!empty || !min_expr || !cst)
+		goto error;
+
+	n_in = isl_set_dim(empty, isl_dim_set);
+	dim = isl_set_get_dim(empty);
+	dim = isl_dim_drop(dim, isl_dim_set, n_in - 1, 1);
+	res = isl_set_empty(dim);
+
+	for (i = 0; i < empty->n; ++i) {
+		isl_set *set;
+
+		set = isl_set_from_basic_set(isl_basic_set_copy(empty->p[i]));
+		if (need_split_set(empty->p[i], cst))
+			set = isl_set_intersect(set, isl_set_copy(min_expr));
+		set = isl_set_remove_dims(set, isl_dim_set, n_in - 1, 1);
+
+		res = isl_set_union_disjoint(res, set);
+	}
+
+	isl_set_free(empty);
+	isl_set_free(min_expr);
+	isl_mat_free(cst);
+	return res;
+error:
+	isl_set_free(empty);
+	isl_set_free(min_expr);
+	isl_mat_free(cst);
+	return NULL;
+}
+
+/* Given a map of which the last input variable is the minimum
+ * of the bounds in "cst", split each basic set in the set
+ * in pieces where one of the bounds is (strictly) smaller than the others.
+ * This subdivision is given in "min_expr".
+ * The variable is subsequently projected out.
+ *
+ * The implementation is essentially the same as that of "split".
+ */
+static __isl_give isl_map *split_domain(__isl_take isl_map *opt,
+	__isl_take isl_set *min_expr, __isl_take isl_mat *cst)
+{
+	int n_in;
+	int i;
+	isl_dim *dim;
+	isl_map *res;
+
+	if (!opt || !min_expr || !cst)
+		goto error;
+
+	n_in = isl_map_dim(opt, isl_dim_in);
+	dim = isl_map_get_dim(opt);
+	dim = isl_dim_drop(dim, isl_dim_in, n_in - 1, 1);
+	res = isl_map_empty(dim);
+
+	for (i = 0; i < opt->n; ++i) {
+		isl_map *map;
+
+		map = isl_map_from_basic_map(isl_basic_map_copy(opt->p[i]));
+		if (need_split_map(opt->p[i], cst))
+			map = isl_map_intersect_domain(map,
+						       isl_set_copy(min_expr));
+		map = isl_map_remove_dims(map, isl_dim_in, n_in - 1, 1);
+
+		res = isl_map_union_disjoint(res, map);
+	}
+
+	isl_map_free(opt);
+	isl_set_free(min_expr);
+	isl_mat_free(cst);
+	return res;
+error:
+	isl_map_free(opt);
+	isl_set_free(min_expr);
+	isl_mat_free(cst);
+	return NULL;
+}
+
+static __isl_give isl_map *basic_map_partial_lexopt(
+	__isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
+	__isl_give isl_set **empty, int max);
+
+/* Given a basic map with at least two parallel constraints (as found
+ * by the function parallel_constraints), first look for more constraints
+ * parallel to the two constraint and replace the found list of parallel
+ * constraints by a single constraint with as "input" part the minimum
+ * of the input parts of the list of constraints.  Then, recursively call
+ * basic_map_partial_lexopt (possibly finding more parallel constraints)
+ * and plug in the definition of the minimum in the result.
+ *
+ * More specifically, given a set of constraints
+ *
+ *	a x + b_i(p) >= 0
+ *
+ * Replace this set by a single constraint
+ *
+ *	a x + u >= 0
+ *
+ * with u a new parameter with constraints
+ *
+ *	u <= b_i(p)
+ *
+ * Any solution to the new system is also a solution for the original system
+ * since
+ *
+ *	a x >= -u >= -b_i(p)
+ *
+ * Moreover, m = min_i(b_i(p)) satisfies the constraints on u and can
+ * therefore be plugged into the solution.
+ */
+static __isl_give isl_map *basic_map_partial_lexopt_symm(
+	__isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
+	__isl_give isl_set **empty, int max, int first, int second)
+{
+	int i, n, k;
+	int *list = NULL;
+	unsigned n_in, n_out, n_div;
+	isl_ctx *ctx;
+	isl_vec *var = NULL;
+	isl_mat *cst = NULL;
+	isl_map *opt;
+	isl_set *min_expr;
+	isl_dim *map_dim, *set_dim;
+
+	map_dim = isl_basic_map_get_dim(bmap);
+	set_dim = empty ? isl_basic_set_get_dim(dom) : NULL;
+
+	n_in = isl_basic_map_dim(bmap, isl_dim_param) +
+	       isl_basic_map_dim(bmap, isl_dim_in);
+	n_out = isl_basic_map_dim(bmap, isl_dim_all) - n_in;
+
+	ctx = isl_basic_map_get_ctx(bmap);
+	list = isl_alloc_array(ctx, int, bmap->n_ineq);
+	var = isl_vec_alloc(ctx, n_out);
+	if (!list || !var)
+		goto error;
+
+	list[0] = first;
+	list[1] = second;
+	isl_seq_cpy(var->el, bmap->ineq[first] + 1 + n_in, n_out);
+	for (i = second + 1, n = 2; i < bmap->n_ineq; ++i) {
+		if (isl_seq_eq(var->el, bmap->ineq[i] + 1 + n_in, n_out))
+			list[n++] = i;
+	}
+
+	cst = isl_mat_alloc(ctx, n, 1 + n_in);
+	if (!cst)
+		goto error;
+
+	for (i = 0; i < n; ++i)
+		isl_seq_cpy(cst->row[i], bmap->ineq[list[i]], 1 + n_in);
+
+	bmap = isl_basic_map_cow(bmap);
+	if (!bmap)
+		goto error;
+	for (i = n - 1; i >= 0; --i)
+		if (isl_basic_map_drop_inequality(bmap, list[i]) < 0)
+			goto error;
+
+	bmap = isl_basic_map_add(bmap, isl_dim_in, 1);
+	bmap = isl_basic_map_extend_constraints(bmap, 0, 1);
+	k = isl_basic_map_alloc_inequality(bmap);
+	if (k < 0)
+		goto error;
+	isl_seq_clr(bmap->ineq[k], 1 + n_in);
+	isl_int_set_si(bmap->ineq[k][1 + n_in], 1);
+	isl_seq_cpy(bmap->ineq[k] + 1 + n_in + 1, var->el, n_out);
+	bmap = isl_basic_map_finalize(bmap);
+
+	n_div = isl_basic_set_dim(dom, isl_dim_div);
+	dom = isl_basic_set_add(dom, isl_dim_set, 1);
+	dom = isl_basic_set_extend_constraints(dom, 0, n);
+	for (i = 0; i < n; ++i) {
+		k = isl_basic_set_alloc_inequality(dom);
+		if (k < 0)
+			goto error;
+		isl_seq_cpy(dom->ineq[k], cst->row[i], 1 + n_in);
+		isl_int_set_si(dom->ineq[k][1 + n_in], -1);
+		isl_seq_clr(dom->ineq[k] + 1 + n_in + 1, n_div);
+	}
+
+	min_expr = set_minimum(isl_basic_set_get_dim(dom), isl_mat_copy(cst));
+
+	isl_vec_free(var);
+	free(list);
+
+	opt = basic_map_partial_lexopt(bmap, dom, empty, max);
+
+	if (empty) {
+		*empty = split(*empty,
+			       isl_set_copy(min_expr), isl_mat_copy(cst));
+		*empty = isl_set_reset_dim(*empty, set_dim);
+	}
+
+	opt = split_domain(opt, min_expr, cst);
+	opt = isl_map_reset_dim(opt, map_dim);
+
+	return opt;
+error:
+	isl_dim_free(map_dim);
+	isl_dim_free(set_dim);
+	isl_mat_free(cst);
+	isl_vec_free(var);
+	free(list);
+	isl_basic_set_free(dom);
+	isl_basic_map_free(bmap);
+	return NULL;
+}
+
+/* Recursive part of isl_tab_basic_map_partial_lexopt, after detecting
+ * equalities and removing redundant constraints.
+ *
+ * We first check if there are any parallel constraints (left).
+ * If not, we are in the base case.
+ * If there are parallel constraints, we replace them by a single
+ * constraint in basic_map_partial_lexopt_symm and then call
+ * this function recursively to look for more parallel constraints.
  */
-static struct isl_basic_map *align_context_divs(struct isl_basic_map *bmap,
-	struct isl_basic_set *dom)
+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 i;
-	int common = 0;
-	int other;
+	int par = 0;
+	int first, second;
 
-	for (i = 0; i < dom->n_div; ++i)
-		if (find_context_div(bmap, dom, i) != -1)
-			common++;
-	other = bmap->n_div - common;
-	if (dom->n_div - common > 0) {
-		bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim),
-				dom->n_div - common, 0, 0);
-		if (!bmap)
-			return NULL;
-	}
-	for (i = 0; i < dom->n_div; ++i) {
-		int pos = find_context_div(bmap, dom, i);
-		if (pos < 0) {
-			pos = isl_basic_map_alloc_div(bmap);
-			if (pos < 0)
-				goto error;
-			isl_int_set_si(bmap->div[pos][0], 0);
-		}
-		if (pos != other + i)
-			isl_basic_map_swap_div(bmap, pos, other + i);
-	}
-	return bmap;
+	if (!bmap)
+		goto error;
+
+	if (bmap->ctx->opt->pip_symmetry)
+		par = parallel_constraints(bmap, &first, &second);
+	if (par < 0)
+		goto error;
+	if (!par)
+		return basic_map_partial_lexopt_base(bmap, dom, empty, max);
+	
+	return basic_map_partial_lexopt_symm(bmap, dom, empty, max,
+					     first, second);
 error:
+	isl_basic_set_free(dom);
 	isl_basic_map_free(bmap);
 	return NULL;
 }
@@ -2485,18 +4469,17 @@ error:
  * 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,
- * because they will be added one by one in the given order
- * during the construction of the solution map.
+ *
+ * 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)
 {
-	struct isl_tab *tab;
-	struct isl_map *result = NULL;
-	struct isl_sol_map *sol_map = NULL;
-
 	if (empty)
 		*empty = NULL;
 	if (!bmap || !dom)
@@ -2505,38 +4488,16 @@ struct isl_map *isl_tab_basic_map_partial_lexopt(
 	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)
-		goto error;
+	if (isl_basic_set_dim(dom, isl_dim_all) == 0)
+		return basic_map_partial_lexopt(bmap, dom, empty, max);
 
-	if (isl_basic_set_fast_is_empty(sol_map->sol.context_tab->bset))
-		/* nothing */;
-	else if (isl_basic_map_fast_is_empty(bmap))
-		sol_map = add_empty(sol_map);
-	else {
-		tab = tab_for_lexmin(bmap,
-					sol_map->sol.context_tab->bset, 1, max);
-		tab = tab_detect_nonnegative_parameters(tab,
-						sol_map->sol.context_tab);
-		sol_map = sol_map_find_solutions(sol_map, tab);
-		if (!sol_map)
-			goto error;
-	}
+	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);
 
-	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 basic_map_partial_lexopt(bmap, dom, empty, max);
 error:
-	sol_map_free(sol_map);
+	isl_basic_set_free(dom);
 	isl_basic_map_free(bmap);
 	return NULL;
 }
@@ -2546,12 +4507,12 @@ struct isl_sol_for {
 	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)
 {
-	isl_tab_free(sol_for->sol.context_tab);
+	if (sol_for->sol.context)
+		sol_for->sol.context->op->free(sol_for->sol.context);
 	free(sol_for);
 }
 
@@ -2562,11 +4523,11 @@ static void sol_for_free_wrap(struct isl_sol *sol)
 
 /* Add the solution identified by the tableau and the context tableau.
  *
- * See documentation of sol_map_add for more details.
+ * 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
- * an affine matrix reprenting the relation between the input and output.
+ * an affine matrix representing the relation between the input and output.
  * The number of rows in this matrix is equal to one plus the number
  * of output variables.  The number of columns is equal to one plus
  * the total dimension of the context, i.e., the number of parameters,
@@ -2574,89 +4535,30 @@ static void sol_for_free_wrap(struct isl_sol *sol)
  * 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)
+static void sol_for_add(struct isl_sol_for *sol,
+	struct isl_basic_set *dom, struct isl_mat *M)
 {
-	struct isl_tab *context_tab;
-	struct isl_basic_set *bset;
-	struct isl_mat *mat = NULL;
-	unsigned n_out;
-	unsigned off;
-	int row, i;
-
-	if (!sol || !tab)
-		goto error;
-
-	if (tab->empty)
-		return sol;
-
-	off = 2 + tab->M;
-	context_tab = sol->sol.context_tab;
-
-	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)
+	if (sol->sol.error || !dom || !M)
 		goto error;
 
-	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_seq_clr(mat->row[1 + row], mat->n_col);
-		if (!tab->var[i].is_row)
-			continue;
-
-		r = tab->var[i].index;
-		/* no unbounded */
-		if (tab->M)
-			isl_assert(mat->ctx, isl_int_eq(tab->mat->row[r][2],
-					                tab->mat->row[r][0]),
-				    goto 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);
-	}
-
-	bset = isl_basic_set_dup(context_tab->bset);
-	bset = isl_basic_set_finalize(bset);
+	dom = isl_basic_set_finalize(dom);
 
-	if (sol->fn(bset, isl_mat_copy(mat), sol->user) < 0)
+	if (sol->fn(isl_basic_set_copy(dom), isl_mat_copy(M), sol->user) < 0)
 		goto error;
 
-	isl_mat_free(mat);
-	return sol;
+	isl_basic_set_free(dom);
+	isl_mat_free(M);
+	return;
 error:
-	isl_mat_free(mat);
-	sol_free(&sol->sol);
-	return NULL;
+	isl_basic_set_free(dom);
+	isl_mat_free(M);
+	sol->sol.error = 1;
 }
 
-static struct isl_sol *sol_for_add_wrap(struct isl_sol *sol,
-	struct isl_tab *tab)
+static void sol_for_add_wrap(struct isl_sol *sol,
+	struct isl_basic_set *dom, struct isl_mat *M)
 {
-	return (struct isl_sol *)sol_for_add((struct isl_sol_for *)sol, tab);
+	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,
@@ -2667,27 +4569,27 @@ static struct isl_sol_for *sol_for_init(struct isl_basic_map *bmap, int max,
 	struct isl_sol_for *sol_for = NULL;
 	struct isl_dim *dom_dim;
 	struct isl_basic_set *dom = NULL;
-	struct isl_tab *context_tab;
-	int f;
 
-	sol_for = isl_calloc_type(bset->ctx, struct isl_sol_for);
+	sol_for = isl_calloc_type(bmap->ctx, struct isl_sol_for);
 	if (!sol_for)
 		goto error;
 
 	dom_dim = isl_dim_domain(isl_dim_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->max = max;
+	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;
 
-	context_tab = context_tab_for_lexmin(isl_basic_set_copy(dom));
-	context_tab = restore_lexmin(context_tab);
-	sol_for->sol.context_tab = context_tab;
-	f = context_is_feasible(&sol_for->sol);
-	if (f < 0)
+	sol_for->sol.context = isl_context_alloc(dom);
+	if (!sol_for->sol.context)
 		goto error;
 
 	isl_basic_set_free(dom);
@@ -2698,10 +4600,10 @@ error:
 	return NULL;
 }
 
-static struct isl_sol_for *sol_for_find_solutions(struct isl_sol_for *sol_for,
+static void sol_for_find_solutions(struct isl_sol_for *sol_for,
 	struct isl_tab *tab)
 {
-	return (struct isl_sol_for *)find_solutions_main(&sol_for->sol, tab);
+	find_solutions_main(&sol_for->sol, tab);
 }
 
 int isl_basic_map_foreach_lexopt(__isl_keep isl_basic_map *bmap, int max,
@@ -2718,24 +4620,24 @@ int isl_basic_map_foreach_lexopt(__isl_keep isl_basic_map *bmap, int max,
 	bmap = isl_basic_map_detect_equalities(bmap);
 	sol_for = sol_for_init(bmap, max, fn, user);
 
-	if (isl_basic_map_fast_is_empty(bmap))
+	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,
-					sol_for->sol.context_tab->bset, 1, max);
-		tab = tab_detect_nonnegative_parameters(tab,
-						sol_for->sol.context_tab);
-		sol_for = sol_for_find_solutions(sol_for, tab);
-		if (!sol_for)
+				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_for_free(sol_for);
+	sol_free(&sol_for->sol);
 	isl_basic_map_free(bmap);
 	return 0;
 error:
-	sol_for_free(sol_for);
+	sol_free(&sol_for->sol);
 	isl_basic_map_free(bmap);
 	return -1;
 }
@@ -2755,3 +4657,308 @@ int isl_basic_map_foreach_lexmax(__isl_keep isl_basic_map *bmap,
 {
 	return isl_basic_map_foreach_lexopt(bmap, 1, 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(isl_basic_map_from_range(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(isl_basic_map_from_range(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;
+}