text: /*
   * Copyright 2008-2009 Katholieke Universiteit Leuven
   * Copyright 2010      INRIA Saclay
   * Copyright 2012-2013 Ecole Normale Superieure
   * Copyright 2014      INRIA Rocquencourt
   * Copyright 2016      Sven Verdoolaege
   *
   * Use of this software is governed by the MIT license
   *
   * Written by Sven Verdoolaege, K.U.Leuven, Departement
   * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
   * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
   * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France 
   * and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
   * and Inria Paris - Rocquencourt, Domaine de Voluceau - Rocquencourt,
   * B.P. 105 - 78153 Le Chesnay, France
   */
  
  #include <isl_ctx_private.h>
  #include "isl_map_private.h"
  #include <isl_seq.h>
  #include <isl/options.h>
  #include "isl_tab.h"
  #include <isl_mat_private.h>
  #include <isl_local_space_private.h>
  #include <isl_vec_private.h>
  #include <isl_aff_private.h>
  #include <isl_equalities.h>
  
  #define STATUS_ERROR		-1
  #define STATUS_REDUNDANT	 1
  #define STATUS_VALID	 	 2
  #define STATUS_SEPARATE	 	 3
  #define STATUS_CUT	 	 4
  #define STATUS_ADJ_EQ	 	 5
  #define STATUS_ADJ_INEQ	 	 6
  
  static int status_in(isl_int *ineq, struct isl_tab *tab)
  {
  	enum isl_ineq_type type = isl_tab_ineq_type(tab, ineq);
  	switch (type) {
  	default:
  	case isl_ineq_error:		return STATUS_ERROR;
  	case isl_ineq_redundant:	return STATUS_VALID;
  	case isl_ineq_separate:		return STATUS_SEPARATE;
  	case isl_ineq_cut:		return STATUS_CUT;
  	case isl_ineq_adj_eq:		return STATUS_ADJ_EQ;
  	case isl_ineq_adj_ineq:		return STATUS_ADJ_INEQ;
  	}
  }
  
  /* Compute the position of the equalities of basic map "bmap_i"
   * with respect to the basic map represented by "tab_j".
   * The resulting array has twice as many entries as the number
   * of equalities corresponding to the two inequalties to which
   * each equality corresponds.
   */
  static int *eq_status_in(__isl_keep isl_basic_map *bmap_i,
  	struct isl_tab *tab_j)
  {
  	int k, l;
  	int *eq = isl_calloc_array(bmap_i->ctx, int, 2 * bmap_i->n_eq);
  	unsigned dim;
  
  	if (!eq)
  		return NULL;
  
  	dim = isl_basic_map_total_dim(bmap_i);
  	for (k = 0; k < bmap_i->n_eq; ++k) {
  		for (l = 0; l < 2; ++l) {
  			isl_seq_neg(bmap_i->eq[k], bmap_i->eq[k], 1+dim);
  			eq[2 * k + l] = status_in(bmap_i->eq[k], tab_j);
  			if (eq[2 * k + l] == STATUS_ERROR)
  				goto error;
  		}
  		if (eq[2 * k] == STATUS_SEPARATE ||
  		    eq[2 * k + 1] == STATUS_SEPARATE)
  			break;
  	}
  
  	return eq;
  error:
  	free(eq);
  	return NULL;
  }
  
  /* Compute the position of the inequalities of basic map "bmap_i"
   * (also represented by "tab_i", if not NULL) with respect to the basic map
   * represented by "tab_j".
   */
  static int *ineq_status_in(__isl_keep isl_basic_map *bmap_i,
  	struct isl_tab *tab_i, struct isl_tab *tab_j)
  {
  	int k;
  	unsigned n_eq = bmap_i->n_eq;
  	int *ineq = isl_calloc_array(bmap_i->ctx, int, bmap_i->n_ineq);
  
  	if (!ineq)
  		return NULL;
  
  	for (k = 0; k < bmap_i->n_ineq; ++k) {
  		if (tab_i && isl_tab_is_redundant(tab_i, n_eq + k)) {
  			ineq[k] = STATUS_REDUNDANT;
  			continue;
  		}
  		ineq[k] = status_in(bmap_i->ineq[k], tab_j);
  		if (ineq[k] == STATUS_ERROR)
  			goto error;
  		if (ineq[k] == STATUS_SEPARATE)
  			break;
  	}
  
  	return ineq;
  error:
  	free(ineq);
  	return NULL;
  }
  
  static int any(int *con, unsigned len, int status)
  {
  	int i;
  
  	for (i = 0; i < len ; ++i)
  		if (con[i] == status)
  			return 1;
  	return 0;
  }
  
  static int count(int *con, unsigned len, int status)
  {
  	int i;
  	int c = 0;
  
  	for (i = 0; i < len ; ++i)
  		if (con[i] == status)
  			c++;
  	return c;
  }
  
  static int all(int *con, unsigned len, int status)
  {
  	int i;
  
  	for (i = 0; i < len ; ++i) {
  		if (con[i] == STATUS_REDUNDANT)
  			continue;
  		if (con[i] != status)
  			return 0;
  	}
  	return 1;
  }
  
  /* Internal information associated to a basic map in a map
   * that is to be coalesced by isl_map_coalesce.
   *
   * "bmap" is the basic map itself (or NULL if "removed" is set)
   * "tab" is the corresponding tableau (or NULL if "removed" is set)
   * "hull_hash" identifies the affine space in which "bmap" lives.
   * "removed" is set if this basic map has been removed from the map
   * "simplify" is set if this basic map may have some unknown integer
   * divisions that were not present in the input basic maps.  The basic
   * map should then be simplified such that we may be able to find
   * a definition among the constraints.
   *
   * "eq" and "ineq" are only set if we are currently trying to coalesce
   * this basic map with another basic map, in which case they represent
   * the position of the inequalities of this basic map with respect to
   * the other basic map.  The number of elements in the "eq" array
   * is twice the number of equalities in the "bmap", corresponding
   * to the two inequalities that make up each equality.
   */
  struct isl_coalesce_info {
  	isl_basic_map *bmap;
  	struct isl_tab *tab;
  	uint32_t hull_hash;
  	int removed;
  	int simplify;
  	int *eq;
  	int *ineq;
  };
  
  /* Are all non-redundant constraints of the basic map represented by "info"
   * either valid or cut constraints with respect to the other basic map?
   */
  static int all_valid_or_cut(struct isl_coalesce_info *info)
  {
  	int i;
  
  	for (i = 0; i < 2 * info->bmap->n_eq; ++i) {
  		if (info->eq[i] == STATUS_REDUNDANT)
  			continue;
  		if (info->eq[i] == STATUS_VALID)
  			continue;
  		if (info->eq[i] == STATUS_CUT)
  			continue;
  		return 0;
  	}
  
  	for (i = 0; i < info->bmap->n_ineq; ++i) {
  		if (info->ineq[i] == STATUS_REDUNDANT)
  			continue;
  		if (info->ineq[i] == STATUS_VALID)
  			continue;
  		if (info->ineq[i] == STATUS_CUT)
  			continue;
  		return 0;
  	}
  
  	return 1;
  }
  
  /* Compute the hash of the (apparent) affine hull of info->bmap (with
   * the existentially quantified variables removed) and store it
   * in info->hash.
   */
  static int coalesce_info_set_hull_hash(struct isl_coalesce_info *info)
  {
  	isl_basic_map *hull;
  	unsigned n_div;
  
  	hull = isl_basic_map_copy(info->bmap);
  	hull = isl_basic_map_plain_affine_hull(hull);
  	n_div = isl_basic_map_dim(hull, isl_dim_div);
  	hull = isl_basic_map_drop_constraints_involving_dims(hull,
  							isl_dim_div, 0, n_div);
  	info->hull_hash = isl_basic_map_get_hash(hull);
  	isl_basic_map_free(hull);
  
  	return hull ? 0 : -1;
  }
  
  /* Free all the allocated memory in an array
   * of "n" isl_coalesce_info elements.
   */
  static void clear_coalesce_info(int n, struct isl_coalesce_info *info)
  {
  	int i;
  
  	if (!info)
  		return;
  
  	for (i = 0; i < n; ++i) {
  		isl_basic_map_free(info[i].bmap);
  		isl_tab_free(info[i].tab);
  	}
  
  	free(info);
  }
  
  /* Drop the basic map represented by "info".
   * That is, clear the memory associated to the entry and
   * mark it as having been removed.
   */
  static void drop(struct isl_coalesce_info *info)
  {
  	info->bmap = isl_basic_map_free(info->bmap);
  	isl_tab_free(info->tab);
  	info->tab = NULL;
  	info->removed = 1;
  }
  
  /* Exchange the information in "info1" with that in "info2".
   */
  static void exchange(struct isl_coalesce_info *info1,
  	struct isl_coalesce_info *info2)
  {
  	struct isl_coalesce_info info;
  
  	info = *info1;
  	*info1 = *info2;
  	*info2 = info;
  }
  
  /* This type represents the kind of change that has been performed
   * while trying to coalesce two basic maps.
   *
   * isl_change_none: nothing was changed
   * isl_change_drop_first: the first basic map was removed
   * isl_change_drop_second: the second basic map was removed
   * isl_change_fuse: the two basic maps were replaced by a new basic map.
   */
  enum isl_change {
  	isl_change_error = -1,
  	isl_change_none = 0,
  	isl_change_drop_first,
  	isl_change_drop_second,
  	isl_change_fuse,
  };
  
  /* Update "change" based on an interchange of the first and the second
   * basic map.  That is, interchange isl_change_drop_first and
   * isl_change_drop_second.
   */
  static enum isl_change invert_change(enum isl_change change)
  {
  	switch (change) {
  	case isl_change_error:
  		return isl_change_error;
  	case isl_change_none:
  		return isl_change_none;
  	case isl_change_drop_first:
  		return isl_change_drop_second;
  	case isl_change_drop_second:
  		return isl_change_drop_first;
  	case isl_change_fuse:
  		return isl_change_fuse;
  	}
  
  	return isl_change_error;
  }
  
  /* Add the valid constraints of the basic map represented by "info"
   * to "bmap".  "len" is the size of the constraints.
   * If only one of the pair of inequalities that make up an equality
   * is valid, then add that inequality.
   */
  static __isl_give isl_basic_map *add_valid_constraints(
  	__isl_take isl_basic_map *bmap, struct isl_coalesce_info *info,
  	unsigned len)
  {
  	int k, l;
  
  	if (!bmap)
  		return NULL;
  
  	for (k = 0; k < info->bmap->n_eq; ++k) {
  		if (info->eq[2 * k] == STATUS_VALID &&
  		    info->eq[2 * k + 1] == STATUS_VALID) {
  			l = isl_basic_map_alloc_equality(bmap);
  			if (l < 0)
  				return isl_basic_map_free(bmap);
  			isl_seq_cpy(bmap->eq[l], info->bmap->eq[k], len);
  		} else if (info->eq[2 * k] == STATUS_VALID) {
  			l = isl_basic_map_alloc_inequality(bmap);
  			if (l < 0)
  				return isl_basic_map_free(bmap);
  			isl_seq_neg(bmap->ineq[l], info->bmap->eq[k], len);
  		} else if (info->eq[2 * k + 1] == STATUS_VALID) {
  			l = isl_basic_map_alloc_inequality(bmap);
  			if (l < 0)
  				return isl_basic_map_free(bmap);
  			isl_seq_cpy(bmap->ineq[l], info->bmap->eq[k], len);
  		}
  	}
  
  	for (k = 0; k < info->bmap->n_ineq; ++k) {
  		if (info->ineq[k] != STATUS_VALID)
  			continue;
  		l = isl_basic_map_alloc_inequality(bmap);
  		if (l < 0)
  			return isl_basic_map_free(bmap);
  		isl_seq_cpy(bmap->ineq[l], info->bmap->ineq[k], len);
  	}
  
  	return bmap;
  }
  
  /* Is "bmap" defined by a number of (non-redundant) constraints that
   * is greater than the number of constraints of basic maps i and j combined?
   * Equalities are counted as two inequalities.
   */
  static int number_of_constraints_increases(int i, int j,
  	struct isl_coalesce_info *info,
  	__isl_keep isl_basic_map *bmap, struct isl_tab *tab)
  {
  	int k, n_old, n_new;
  
  	n_old = 2 * info[i].bmap->n_eq + info[i].bmap->n_ineq;
  	n_old += 2 * info[j].bmap->n_eq + info[j].bmap->n_ineq;
  
  	n_new = 2 * bmap->n_eq;
  	for (k = 0; k < bmap->n_ineq; ++k)
  		if (!isl_tab_is_redundant(tab, bmap->n_eq + k))
  			++n_new;
  
  	return n_new > n_old;
  }
  
  /* Replace the pair of basic maps i and j by the basic map bounded
   * by the valid constraints in both basic maps and the constraints
   * in extra (if not NULL).
   * Place the fused basic map in the position that is the smallest of i and j.
   *
   * If "detect_equalities" is set, then look for equalities encoded
   * as pairs of inequalities.
   * If "check_number" is set, then the original basic maps are only
   * replaced if the total number of constraints does not increase.
   * While the number of integer divisions in the two basic maps
   * is assumed to be the same, the actual definitions may be different.
   * We only copy the definition from one of the basic map if it is
   * the same as that of the other basic map.  Otherwise, we mark
   * the integer division as unknown and simplify the basic map
   * in an attempt to recover the integer division definition.
   */
  static enum isl_change fuse(int i, int j, struct isl_coalesce_info *info,
  	__isl_keep isl_mat *extra, int detect_equalities, int check_number)
  {
  	int k, l;
  	struct isl_basic_map *fused = NULL;
  	struct isl_tab *fused_tab = NULL;
  	unsigned total = isl_basic_map_total_dim(info[i].bmap);
  	unsigned extra_rows = extra ? extra->n_row : 0;
  	unsigned n_eq, n_ineq;
  	int simplify = 0;
  
  	if (j < i)
  		return fuse(j, i, info, extra, detect_equalities, check_number);
  
  	n_eq = info[i].bmap->n_eq + info[j].bmap->n_eq;
  	n_ineq = info[i].bmap->n_ineq + info[j].bmap->n_ineq;
  	fused = isl_basic_map_alloc_space(isl_space_copy(info[i].bmap->dim),
  		    info[i].bmap->n_div, n_eq, n_eq + n_ineq + extra_rows);
  	fused = add_valid_constraints(fused, &info[i], 1 + total);
  	fused = add_valid_constraints(fused, &info[j], 1 + total);
  	if (!fused)
  		goto error;
  
  	for (k = 0; k < info[i].bmap->n_div; ++k) {
  		int l = isl_basic_map_alloc_div(fused);
  		if (l < 0)
  			goto error;
  		if (isl_seq_eq(info[i].bmap->div[k], info[j].bmap->div[k],
  				1 + 1 + total)) {
  			isl_seq_cpy(fused->div[l], info[i].bmap->div[k],
  				1 + 1 + total);
  		} else {
  			isl_int_set_si(fused->div[l][0], 0);
  			simplify = 1;
  		}
  	}
  
  	for (k = 0; k < extra_rows; ++k) {
  		l = isl_basic_map_alloc_inequality(fused);
  		if (l < 0)
  			goto error;
  		isl_seq_cpy(fused->ineq[l], extra->row[k], 1 + total);
  	}
  
  	if (detect_equalities)
  		fused = isl_basic_map_detect_inequality_pairs(fused, NULL);
  	fused = isl_basic_map_gauss(fused, NULL);
  	if (simplify || info[j].simplify) {
  		fused = isl_basic_map_simplify(fused);
  		info[i].simplify = 0;
  	}
  	fused = isl_basic_map_finalize(fused);
  	if (ISL_F_ISSET(info[i].bmap, ISL_BASIC_MAP_RATIONAL) &&
  	    ISL_F_ISSET(info[j].bmap, ISL_BASIC_MAP_RATIONAL))
  		ISL_F_SET(fused, ISL_BASIC_MAP_RATIONAL);
  
  	fused_tab = isl_tab_from_basic_map(fused, 0);
  	if (isl_tab_detect_redundant(fused_tab) < 0)
  		goto error;
  
  	if (check_number &&
  	    number_of_constraints_increases(i, j, info, fused, fused_tab)) {
  		isl_tab_free(fused_tab);
  		isl_basic_map_free(fused);
  		return isl_change_none;
  	}
  
  	isl_basic_map_free(info[i].bmap);
  	info[i].bmap = fused;
  	isl_tab_free(info[i].tab);
  	info[i].tab = fused_tab;
  	drop(&info[j]);
  
  	return isl_change_fuse;
  error:
  	isl_tab_free(fused_tab);
  	isl_basic_map_free(fused);
  	return isl_change_error;
  }
  
  /* Given a pair of basic maps i and j such that all constraints are either
   * "valid" or "cut", check if the facets corresponding to the "cut"
   * constraints of i lie entirely within basic map j.
   * If so, replace the pair by the basic map consisting of the valid
   * constraints in both basic maps.
   * Checking whether the facet lies entirely within basic map j
   * is performed by checking whether the constraints of basic map j
   * are valid for the facet.  These tests are performed on a rational
   * tableau to avoid the theoretical possibility that a constraint
   * that was considered to be a cut constraint for the entire basic map i
   * happens to be considered to be a valid constraint for the facet,
   * even though it cuts off the same rational points.
   *
   * To see that we are not introducing any extra points, call the
   * two basic maps A and B and the resulting map U and let x
   * be an element of U \setminus ( A \cup B ).
   * A line connecting x with an element of A \cup B meets a facet F
   * of either A or B.  Assume it is a facet of B and let c_1 be
   * the corresponding facet constraint.  We have c_1(x) < 0 and
   * so c_1 is a cut constraint.  This implies that there is some
   * (possibly rational) point x' satisfying the constraints of A
   * and the opposite of c_1 as otherwise c_1 would have been marked
   * valid for A.  The line connecting x and x' meets a facet of A
   * in a (possibly rational) point that also violates c_1, but this
   * is impossible since all cut constraints of B are valid for all
   * cut facets of A.
   * In case F is a facet of A rather than B, then we can apply the
   * above reasoning to find a facet of B separating x from A \cup B first.
   */
  static enum isl_change check_facets(int i, int j,
  	struct isl_coalesce_info *info)
  {
  	int k, l;
  	struct isl_tab_undo *snap, *snap2;
  	unsigned n_eq = info[i].bmap->n_eq;
  
  	snap = isl_tab_snap(info[i].tab);
  	if (isl_tab_mark_rational(info[i].tab) < 0)
  		return isl_change_error;
  	snap2 = isl_tab_snap(info[i].tab);
  
  	for (k = 0; k < info[i].bmap->n_ineq; ++k) {
  		if (info[i].ineq[k] != STATUS_CUT)
  			continue;
  		if (isl_tab_select_facet(info[i].tab, n_eq + k) < 0)
  			return isl_change_error;
  		for (l = 0; l < info[j].bmap->n_ineq; ++l) {
  			int stat;
  			if (info[j].ineq[l] != STATUS_CUT)
  				continue;
  			stat = status_in(info[j].bmap->ineq[l], info[i].tab);
  			if (stat < 0)
  				return isl_change_error;
  			if (stat != STATUS_VALID)
  				break;
  		}
  		if (isl_tab_rollback(info[i].tab, snap2) < 0)
  			return isl_change_error;
  		if (l < info[j].bmap->n_ineq)
  			break;
  	}
  
  	if (k < info[i].bmap->n_ineq) {
  		if (isl_tab_rollback(info[i].tab, snap) < 0)
  			return isl_change_error;
  		return isl_change_none;
  	}
  	return fuse(i, j, info, NULL, 0, 0);
  }
  
  /* Check if info->bmap contains the basic map represented
   * by the tableau "tab".
   * For each equality, we check both the constraint itself
   * (as an inequality) and its negation.  Make sure the
   * equality is returned to its original state before returning.
   */
  static int contains(struct isl_coalesce_info *info, struct isl_tab *tab)
  {
  	int k;
  	unsigned dim;
  	isl_basic_map *bmap = info->bmap;
  
  	dim = isl_basic_map_total_dim(bmap);
  	for (k = 0; k < bmap->n_eq; ++k) {
  		int stat;
  		isl_seq_neg(bmap->eq[k], bmap->eq[k], 1 + dim);
  		stat = status_in(bmap->eq[k], tab);
  		isl_seq_neg(bmap->eq[k], bmap->eq[k], 1 + dim);
  		if (stat < 0)
  			return -1;
  		if (stat != STATUS_VALID)
  			return 0;
  		stat = status_in(bmap->eq[k], tab);
  		if (stat < 0)
  			return -1;
  		if (stat != STATUS_VALID)
  			return 0;
  	}
  
  	for (k = 0; k < bmap->n_ineq; ++k) {
  		int stat;
  		if (info->ineq[k] == STATUS_REDUNDANT)
  			continue;
  		stat = status_in(bmap->ineq[k], tab);
  		if (stat < 0)
  			return -1;
  		if (stat != STATUS_VALID)
  			return 0;
  	}
  	return 1;
  }
  
  /* Basic map "i" has an inequality (say "k") that is adjacent
   * to some inequality of basic map "j".  All the other inequalities
   * are valid for "j".
   * Check if basic map "j" forms an extension of basic map "i".
   *
   * Note that this function is only called if some of the equalities or
   * inequalities of basic map "j" do cut basic map "i".  The function is
   * correct even if there are no such cut constraints, but in that case
   * the additional checks performed by this function are overkill.
   *
   * In particular, we replace constraint k, say f >= 0, by constraint
   * f <= -1, add the inequalities of "j" that are valid for "i"
   * and check if the result is a subset of basic map "j".
   * If so, then we know that this result is exactly equal to basic map "j"
   * since all its constraints are valid for basic map "j".
   * By combining the valid constraints of "i" (all equalities and all
   * inequalities except "k") and the valid constraints of "j" we therefore
   * obtain a basic map that is equal to their union.
   * In this case, there is no need to perform a rollback of the tableau
   * since it is going to be destroyed in fuse().
   *
   *
   *	|\__			|\__
   *	|   \__			|   \__
   *	|      \_	=>	|      \__
   *	|_______| _		|_________\
   *
   *
   *	|\			|\
   *	| \			| \
   *	|  \			|  \
   *	|  |			|   \
   *	|  ||\		=>      |    \
   *	|  || \			|     \
   *	|  ||  |		|      |
   *	|__||_/			|_____/
   */
  static enum isl_change is_adj_ineq_extension(int i, int j,
  	struct isl_coalesce_info *info)
  {
  	int k;
  	struct isl_tab_undo *snap;
  	unsigned n_eq = info[i].bmap->n_eq;
  	unsigned total = isl_basic_map_total_dim(info[i].bmap);
  	int r;
  	int super;
  
  	if (isl_tab_extend_cons(info[i].tab, 1 + info[j].bmap->n_ineq) < 0)
  		return isl_change_error;
  
  	for (k = 0; k < info[i].bmap->n_ineq; ++k)
  		if (info[i].ineq[k] == STATUS_ADJ_INEQ)
  			break;
  	if (k >= info[i].bmap->n_ineq)
  		isl_die(isl_basic_map_get_ctx(info[i].bmap), isl_error_internal,
  			"info[i].ineq should have exactly one STATUS_ADJ_INEQ",
  			return isl_change_error);
  
  	snap = isl_tab_snap(info[i].tab);
  
  	if (isl_tab_unrestrict(info[i].tab, n_eq + k) < 0)
  		return isl_change_error;
  
  	isl_seq_neg(info[i].bmap->ineq[k], info[i].bmap->ineq[k], 1 + total);
  	isl_int_sub_ui(info[i].bmap->ineq[k][0], info[i].bmap->ineq[k][0], 1);
  	r = isl_tab_add_ineq(info[i].tab, info[i].bmap->ineq[k]);
  	isl_seq_neg(info[i].bmap->ineq[k], info[i].bmap->ineq[k], 1 + total);
  	isl_int_sub_ui(info[i].bmap->ineq[k][0], info[i].bmap->ineq[k][0], 1);
  	if (r < 0)
  		return isl_change_error;
  
  	for (k = 0; k < info[j].bmap->n_ineq; ++k) {
  		if (info[j].ineq[k] != STATUS_VALID)
  			continue;
  		if (isl_tab_add_ineq(info[i].tab, info[j].bmap->ineq[k]) < 0)
  			return isl_change_error;
  	}
  
  	super = contains(&info[j], info[i].tab);
  	if (super < 0)
  		return isl_change_error;
  	if (super)
  		return fuse(i, j, info, NULL, 0, 0);
  
  	if (isl_tab_rollback(info[i].tab, snap) < 0)
  		return isl_change_error;
  
  	return isl_change_none;
  }
  
  
  /* Both basic maps have at least one inequality with and adjacent
   * (but opposite) inequality in the other basic map.
   * Check that there are no cut constraints and that there is only
   * a single pair of adjacent inequalities.
   * If so, we can replace the pair by a single basic map described
   * by all but the pair of adjacent inequalities.
   * Any additional points introduced lie strictly between the two
   * adjacent hyperplanes and can therefore be integral.
   *
   *        ____			  _____
   *       /    ||\		 /     \
   *      /     || \		/       \
   *      \     ||  \	=>	\        \
   *       \    ||  /		 \       /
   *        \___||_/		  \_____/
   *
   * The test for a single pair of adjancent inequalities is important
   * for avoiding the combination of two basic maps like the following
   *
   *       /|
   *      / |
   *     /__|
   *         _____
   *         |   |
   *         |   |
   *         |___|
   *
   * If there are some cut constraints on one side, then we may
   * still be able to fuse the two basic maps, but we need to perform
   * some additional checks in is_adj_ineq_extension.
   */
  static enum isl_change check_adj_ineq(int i, int j,
  	struct isl_coalesce_info *info)
  {
  	int count_i, count_j;
  	int cut_i, cut_j;
  
  	count_i = count(info[i].ineq, info[i].bmap->n_ineq, STATUS_ADJ_INEQ);
  	count_j = count(info[j].ineq, info[j].bmap->n_ineq, STATUS_ADJ_INEQ);
  
  	if (count_i != 1 && count_j != 1)
  		return isl_change_none;
  
  	cut_i = any(info[i].eq, 2 * info[i].bmap->n_eq, STATUS_CUT) ||
  		any(info[i].ineq, info[i].bmap->n_ineq, STATUS_CUT);
  	cut_j = any(info[j].eq, 2 * info[j].bmap->n_eq, STATUS_CUT) ||
  		any(info[j].ineq, info[j].bmap->n_ineq, STATUS_CUT);
  
  	if (!cut_i && !cut_j && count_i == 1 && count_j == 1)
  		return fuse(i, j, info, NULL, 0, 0);
  
  	if (count_i == 1 && !cut_i)
  		return is_adj_ineq_extension(i, j, info);
  
  	if (count_j == 1 && !cut_j)
  		return is_adj_ineq_extension(j, i, info);
  
  	return isl_change_none;
  }
  
  /* Given an affine transformation matrix "T", does row "row" represent
   * anything other than a unit vector (possibly shifted by a constant)
   * that is not involved in any of the other rows?
   *
   * That is, if a constraint involves the variable corresponding to
   * the row, then could its preimage by "T" have any coefficients
   * that are different from those in the original constraint?
   */
  static int not_unique_unit_row(__isl_keep isl_mat *T, int row)
  {
  	int i, j;
  	int len = T->n_col - 1;
  
  	i = isl_seq_first_non_zero(T->row[row] + 1, len);
  	if (i < 0)
  		return 1;
  	if (!isl_int_is_one(T->row[row][1 + i]) &&
  	    !isl_int_is_negone(T->row[row][1 + i]))
  		return 1;
  
  	j = isl_seq_first_non_zero(T->row[row] + 1 + i + 1, len - (i + 1));
  	if (j >= 0)
  		return 1;
  
  	for (j = 1; j < T->n_row; ++j) {
  		if (j == row)
  			continue;
  		if (!isl_int_is_zero(T->row[j][1 + i]))
  			return 1;
  	}
  
  	return 0;
  }
  
  /* Does inequality constraint "ineq" of "bmap" involve any of
   * the variables marked in "affected"?
   * "total" is the total number of variables, i.e., the number
   * of entries in "affected".
   */
  static int is_affected(__isl_keep isl_basic_map *bmap, int ineq, int *affected,
  	int total)
  {
  	int i;
  
  	for (i = 0; i < total; ++i) {
  		if (!affected[i])
  			continue;
  		if (!isl_int_is_zero(bmap->ineq[ineq][1 + i]))
  			return 1;
  	}
  
  	return 0;
  }
  
  /* Given the compressed version of inequality constraint "ineq"
   * of info->bmap in "v", check if the constraint can be tightened,
   * where the compression is based on an equality constraint valid
   * for info->tab.
   * If so, add the tightened version of the inequality constraint
   * to info->tab.  "v" may be modified by this function.
   *
   * That is, if the compressed constraint is of the form
   *
   *	m f() + c >= 0
   *
   * with 0 < c < m, then it is equivalent to
   *
   *	f() >= 0
   *
   * This means that c can also be subtracted from the original,
   * uncompressed constraint without affecting the integer points
   * in info->tab.  Add this tightened constraint as an extra row
   * to info->tab to make this information explicitly available.
   */
  static __isl_give isl_vec *try_tightening(struct isl_coalesce_info *info,
  	int ineq, __isl_take isl_vec *v)
  {
  	isl_ctx *ctx;
  	int r;
  
  	if (!v)
  		return NULL;
  
  	ctx = isl_vec_get_ctx(v);
  	isl_seq_gcd(v->el + 1, v->size - 1, &ctx->normalize_gcd);
  	if (isl_int_is_zero(ctx->normalize_gcd) ||
  	    isl_int_is_one(ctx->normalize_gcd)) {
  		return v;
  	}
  
  	v = isl_vec_cow(v);
  	if (!v)
  		return NULL;
  
  	isl_int_fdiv_r(v->el[0], v->el[0], ctx->normalize_gcd);
  	if (isl_int_is_zero(v->el[0]))
  		return v;
  
  	if (isl_tab_extend_cons(info->tab, 1) < 0)
  		return isl_vec_free(v);
  
  	isl_int_sub(info->bmap->ineq[ineq][0],
  		    info->bmap->ineq[ineq][0], v->el[0]);
  	r = isl_tab_add_ineq(info->tab, info->bmap->ineq[ineq]);
  	isl_int_add(info->bmap->ineq[ineq][0],
  		    info->bmap->ineq[ineq][0], v->el[0]);
  
  	if (r < 0)
  		return isl_vec_free(v);
  
  	return v;
  }
  
  /* Tighten the constraints on the facet represented by info->tab.
   * In particular, on input, info->tab represents the result
   * of replacing constraint k of info->bmap, i.e., f_k >= 0,
   * by the adjacent equality, i.e., f_k + 1 = 0.
   *
   * Compute a variable compression from the equality constraint f_k + 1 = 0
   * and use it to tighten the other constraints of info->bmap,
   * updating info->tab (and leaving info->bmap untouched).
   * The compression handles essentially two cases, one where a variable
   * is assigned a fixed value and can therefore be eliminated, and one
   * where one variable is a shifted multiple of some other variable and
   * can therefore be replaced by that multiple.
   * Gaussian elimination would also work for the first case, but for
   * the second case, the effectiveness would depend on the order
   * of the variables.
   * After compression, some of the constraints may have coefficients
   * with a common divisor.  If this divisor does not divide the constant
   * term, then the constraint can be tightened.
   * The tightening is performed on the tableau info->tab by introducing
   * extra (temporary) constraints.
   *
   * Only constraints that are possibly affected by the compression are
   * considered.  In particular, if the constraint only involves variables
   * that are directly mapped to a distinct set of other variables, then
   * no common divisor can be introduced and no tightening can occur.
   */
  static isl_stat tighten_on_relaxed_facet(struct isl_coalesce_info *info,
  	int k)
  {
  	unsigned total;
  	isl_ctx *ctx;
  	isl_vec *v = NULL;
  	isl_mat *T;
  	int i;
  	int *affected;
  
  	ctx = isl_basic_map_get_ctx(info->bmap);
  	total = isl_basic_map_total_dim(info->bmap);
  	isl_int_add_ui(info->bmap->ineq[k][0], info->bmap->ineq[k][0], 1);
  	T = isl_mat_sub_alloc6(ctx, info->bmap->ineq, k, 1, 0, 1 + total);
  	T = isl_mat_variable_compression(T, NULL);
  	isl_int_sub_ui(info->bmap->ineq[k][0], info->bmap->ineq[k][0], 1);
  	if (!T)
  		return isl_stat_error;
  	if (T->n_col == 0) {
  		isl_mat_free(T);
  		return isl_stat_ok;
  	}
  
  	affected = isl_alloc_array(ctx, int, total);
  	if (!affected)
  		goto error;
  
  	for (i = 0; i < total; ++i)
  		affected[i] = not_unique_unit_row(T, 1 + i);
  
  	for (i = 0; i < info->bmap->n_ineq; ++i) {
  		if (i == k)
  			continue;
  		if (!is_affected(info->bmap, i, affected, total))
  			continue;
  		v = isl_vec_alloc(ctx, 1 + total);
  		if (!v)
  			goto error;
  		isl_seq_cpy(v->el, info->bmap->ineq[i], 1 + total);
  		v = isl_vec_mat_product(v, isl_mat_copy(T));
  		v = try_tightening(info, i, v);
  		isl_vec_free(v);
  		if (!v)
  			goto error;
  	}
  
  	isl_mat_free(T);
  	free(affected);
  	return isl_stat_ok;
  error:
  	isl_mat_free(T);
  	free(affected);
  	return isl_stat_error;
  }
  
  /* Basic map "i" has an inequality "k" that is adjacent to some equality
   * of basic map "j".  All the other inequalities are valid for "j".
   * Check if basic map "j" forms an extension of basic map "i".
   *
   * In particular, we relax constraint "k", compute the corresponding
   * facet and check whether it is included in the other basic map.
   * Before testing for inclusion, the constraints on the facet
   * are tightened to increase the chance of an inclusion being detected.
   * If the facet is included, we know that relaxing the constraint extends
   * the basic map with exactly the other basic map (we already know that this
   * other basic map is included in the extension, because there
   * were no "cut" inequalities in "i") and we can replace the
   * two basic maps by this extension.
   * Each integer division that does not have exactly the same
   * definition in "i" and "j" is marked unknown and the basic map
   * is scheduled to be simplified in an attempt to recover
   * the integer division definition.
   * Place this extension in the position that is the smallest of i and j.
   *        ____			  _____
   *       /    || 		 /     |
   *      /     ||  		/      |
   *      \     ||   	=>	\      |
   *       \    ||		 \     |
   *        \___||		  \____|
   */
  static enum isl_change is_adj_eq_extension(int i, int j, int k,
  	struct isl_coalesce_info *info)
  {
  	int change = isl_change_none;
  	int super;
  	struct isl_tab_undo *snap, *snap2;
  	unsigned n_eq = info[i].bmap->n_eq;
  
  	if (isl_tab_is_equality(info[i].tab, n_eq + k))
  		return isl_change_none;
  
  	snap = isl_tab_snap(info[i].tab);
  	if (isl_tab_relax(info[i].tab, n_eq + k) < 0)
  		return isl_change_error;
  	snap2 = isl_tab_snap(info[i].tab);
  	if (isl_tab_select_facet(info[i].tab, n_eq + k) < 0)
  		return isl_change_error;
  	if (tighten_on_relaxed_facet(&info[i], k) < 0)
  		return isl_change_error;
  	super = contains(&info[j], info[i].tab);
  	if (super < 0)
  		return isl_change_error;
  	if (super) {
  		int l;
  		unsigned total;
  
  		if (isl_tab_rollback(info[i].tab, snap2) < 0)
  			return isl_change_error;
  		info[i].bmap = isl_basic_map_cow(info[i].bmap);
  		if (!info[i].bmap)
  			return isl_change_error;
  		total = isl_basic_map_total_dim(info[i].bmap);
  		for (l = 0; l < info[i].bmap->n_div; ++l)
  			if (!isl_seq_eq(info[i].bmap->div[l],
  					info[j].bmap->div[l], 1 + 1 + total)) {
  				isl_int_set_si(info[i].bmap->div[l][0], 0);
  				info[i].simplify = 1;
  			}
  		isl_int_add_ui(info[i].bmap->ineq[k][0],
  				info[i].bmap->ineq[k][0], 1);
  		ISL_F_SET(info[i].bmap, ISL_BASIC_MAP_FINAL);
  		drop(&info[j]);
  		if (j < i)
  			exchange(&info[i], &info[j]);
  		change = isl_change_fuse;
  	} else
  		if (isl_tab_rollback(info[i].tab, snap) < 0)
  			return isl_change_error;
  
  	return change;
  }
  
  /* Data structure that keeps track of the wrapping constraints
   * and of information to bound the coefficients of those constraints.
   *
   * bound is set if we want to apply a bound on the coefficients
   * mat contains the wrapping constraints
   * max is the bound on the coefficients (if bound is set)
   */
  struct isl_wraps {
  	int bound;
  	isl_mat *mat;
  	isl_int max;
  };
  
  /* Update wraps->max to be greater than or equal to the coefficients
   * in the equalities and inequalities of info->bmap that can be removed
   * if we end up applying wrapping.
   */
  static void wraps_update_max(struct isl_wraps *wraps,
  	struct isl_coalesce_info *info)
  {
  	int k;
  	isl_int max_k;
  	unsigned total = isl_basic_map_total_dim(info->bmap);
  
  	isl_int_init(max_k);
  
  	for (k = 0; k < info->bmap->n_eq; ++k) {
  		if (info->eq[2 * k] == STATUS_VALID &&
  		    info->eq[2 * k + 1] == STATUS_VALID)
  			continue;
  		isl_seq_abs_max(info->bmap->eq[k] + 1, total, &max_k);
  		if (isl_int_abs_gt(max_k, wraps->max))
  			isl_int_set(wraps->max, max_k);
  	}
  
  	for (k = 0; k < info->bmap->n_ineq; ++k) {
  		if (info->ineq[k] == STATUS_VALID ||
  		    info->ineq[k] == STATUS_REDUNDANT)
  			continue;
  		isl_seq_abs_max(info->bmap->ineq[k] + 1, total, &max_k);
  		if (isl_int_abs_gt(max_k, wraps->max))
  			isl_int_set(wraps->max, max_k);
  	}
  
  	isl_int_clear(max_k);
  }
  
  /* Initialize the isl_wraps data structure.
   * If we want to bound the coefficients of the wrapping constraints,
   * we set wraps->max to the largest coefficient
   * in the equalities and inequalities that can be removed if we end up
   * applying wrapping.
   */
  static void wraps_init(struct isl_wraps *wraps, __isl_take isl_mat *mat,
  	struct isl_coalesce_info *info, int i, int j)
  {
  	isl_ctx *ctx;
  
  	wraps->bound = 0;
  	wraps->mat = mat;
  	if (!mat)
  		return;
  	ctx = isl_mat_get_ctx(mat);
  	wraps->bound = isl_options_get_coalesce_bounded_wrapping(ctx);
  	if (!wraps->bound)
  		return;
  	isl_int_init(wraps->max);
  	isl_int_set_si(wraps->max, 0);
  	wraps_update_max(wraps, &info[i]);
  	wraps_update_max(wraps, &info[j]);
  }
  
  /* Free the contents of the isl_wraps data structure.
   */
  static void wraps_free(struct isl_wraps *wraps)
  {
  	isl_mat_free(wraps->mat);
  	if (wraps->bound)
  		isl_int_clear(wraps->max);
  }
  
  /* Is the wrapping constraint in row "row" allowed?
   *
   * If wraps->bound is set, we check that none of the coefficients
   * is greater than wraps->max.
   */
  static int allow_wrap(struct isl_wraps *wraps, int row)
  {
  	int i;
  
  	if (!wraps->bound)
  		return 1;
  
  	for (i = 1; i < wraps->mat->n_col; ++i)
  		if (isl_int_abs_gt(wraps->mat->row[row][i], wraps->max))
  			return 0;
  
  	return 1;
  }
  
  /* Wrap "ineq" (or its opposite if "negate" is set) around "bound"
   * to include "set" and add the result in position "w" of "wraps".
   * "len" is the total number of coefficients in "bound" and "ineq".
   * Return 1 on success, 0 on failure and -1 on error.
   * Wrapping can fail if the result of wrapping is equal to "bound"
   * or if we want to bound the sizes of the coefficients and
   * the wrapped constraint does not satisfy this bound.
   */
  static int add_wrap(struct isl_wraps *wraps, int w, isl_int *bound,
  	isl_int *ineq, unsigned len, __isl_keep isl_set *set, int negate)
  {
  	isl_seq_cpy(wraps->mat->row[w], bound, len);
  	if (negate) {
  		isl_seq_neg(wraps->mat->row[w + 1], ineq, len);
  		ineq = wraps->mat->row[w + 1];
  	}
  	if (!isl_set_wrap_facet(set, wraps->mat->row[w], ineq))
  		return -1;
  	if (isl_seq_eq(wraps->mat->row[w], bound, len))
  		return 0;
  	if (!allow_wrap(wraps, w))
  		return 0;
  	return 1;
  }
  
  /* For each constraint in info->bmap that is not redundant (as determined
   * by info->tab) and that is not a valid constraint for the other basic map,
   * wrap the constraint around "bound" such that it includes the whole
   * set "set" and append the resulting constraint to "wraps".
   * Note that the constraints that are valid for the other basic map
   * will be added to the combined basic map by default, so there is
   * no need to wrap them.
   * The caller wrap_in_facets even relies on this function not wrapping
   * any constraints that are already valid.
   * "wraps" is assumed to have been pre-allocated to the appropriate size.
   * wraps->n_row is the number of actual wrapped constraints that have
   * been added.
   * If any of the wrapping problems results in a constraint that is
   * identical to "bound", then this means that "set" is unbounded in such
   * way that no wrapping is possible.  If this happens then wraps->n_row
   * is reset to zero.
   * Similarly, if we want to bound the coefficients of the wrapping
   * constraints and a newly added wrapping constraint does not
   * satisfy the bound, then wraps->n_row is also reset to zero.
   */
  static int add_wraps(struct isl_wraps *wraps, struct isl_coalesce_info *info,
  	isl_int *bound, __isl_keep isl_set *set)
  {
  	int l, m;
  	int w;
  	int added;
  	isl_basic_map *bmap = info->bmap;
  	unsigned len = 1 + isl_basic_map_total_dim(bmap);
  
  	w = wraps->mat->n_row;
  
  	for (l = 0; l < bmap->n_ineq; ++l) {
  		if (info->ineq[l] == STATUS_VALID ||
  		    info->ineq[l] == STATUS_REDUNDANT)
  			continue;
  		if (isl_seq_is_neg(bound, bmap->ineq[l], len))
  			continue;
  		if (isl_seq_eq(bound, bmap->ineq[l], len))
  			continue;
  		if (isl_tab_is_redundant(info->tab, bmap->n_eq + l))
  			continue;
  
  		added = add_wrap(wraps, w, bound, bmap->ineq[l], len, set, 0);
  		if (added < 0)
  			return -1;
  		if (!added)
  			goto unbounded;
  		++w;
  	}
  	for (l = 0; l < bmap->n_eq; ++l) {
  		if (isl_seq_is_neg(bound, bmap->eq[l], len))
  			continue;
  		if (isl_seq_eq(bound, bmap->eq[l], len))
  			continue;
  
  		for (m = 0; m < 2; ++m) {
  			if (info->eq[2 * l + m] == STATUS_VALID)
  				continue;
  			added = add_wrap(wraps, w, bound, bmap->eq[l], len,
  					set, !m);
  			if (added < 0)
  				return -1;
  			if (!added)
  				goto unbounded;
  			++w;
  		}
  	}
  
  	wraps->mat->n_row = w;
  	return 0;
  unbounded:
  	wraps->mat->n_row = 0;
  	return 0;
  }
  
  /* Check if the constraints in "wraps" from "first" until the last
   * are all valid for the basic set represented by "tab".
   * If not, wraps->n_row is set to zero.
   */
  static int check_wraps(__isl_keep isl_mat *wraps, int first,
  	struct isl_tab *tab)
  {
  	int i;
  
  	for (i = first; i < wraps->n_row; ++i) {
  		enum isl_ineq_type type;
  		type = isl_tab_ineq_type(tab, wraps->row[i]);
  		if (type == isl_ineq_error)
  			return -1;
  		if (type == isl_ineq_redundant)
  			continue;
  		wraps->n_row = 0;
  		return 0;
  	}
  
  	return 0;
  }
  
  /* Return a set that corresponds to the non-redundant constraints
   * (as recorded in tab) of bmap.
   *
   * It's important to remove the redundant constraints as some
   * of the other constraints may have been modified after the
   * constraints were marked redundant.
   * In particular, a constraint may have been relaxed.
   * Redundant constraints are ignored when a constraint is relaxed
   * and should therefore continue to be ignored ever after.
   * Otherwise, the relaxation might be thwarted by some of
   * these constraints.
   *
   * Update the underlying set to ensure that the dimension doesn't change.
   * Otherwise the integer divisions could get dropped if the tab
   * turns out to be empty.
   */
  static __isl_give isl_set *set_from_updated_bmap(__isl_keep isl_basic_map *bmap,
  	struct isl_tab *tab)
  {
  	isl_basic_set *bset;
  
  	bmap = isl_basic_map_copy(bmap);
  	bset = isl_basic_map_underlying_set(bmap);
  	bset = isl_basic_set_cow(bset);
  	bset = isl_basic_set_update_from_tab(bset, tab);
  	return isl_set_from_basic_set(bset);
  }
  
  /* Wrap the constraints of info->bmap that bound the facet defined
   * by inequality "k" around (the opposite of) this inequality to
   * include "set".  "bound" may be used to store the negated inequality.
   * Since the wrapped constraints are not guaranteed to contain the whole
   * of info->bmap, we check them in check_wraps.
   * If any of the wrapped constraints turn out to be invalid, then
   * check_wraps will reset wrap->n_row to zero.
   */
  static int add_wraps_around_facet(struct isl_wraps *wraps,
  	struct isl_coalesce_info *info, int k, isl_int *bound,
  	__isl_keep isl_set *set)
  {
  	struct isl_tab_undo *snap;
  	int n;
  	unsigned total = isl_basic_map_total_dim(info->bmap);
  
  	snap = isl_tab_snap(info->tab);
  
  	if (isl_tab_select_facet(info->tab, info->bmap->n_eq + k) < 0)
  		return -1;
  	if (isl_tab_detect_redundant(info->tab) < 0)
  		return -1;
  
  	isl_seq_neg(bound, info->bmap->ineq[k], 1 + total);
  
  	n = wraps->mat->n_row;
  	if (add_wraps(wraps, info, bound, set) < 0)
  		return -1;
  
  	if (isl_tab_rollback(info->tab, snap) < 0)
  		return -1;
  	if (check_wraps(wraps->mat, n, info->tab) < 0)
  		return -1;
  
  	return 0;
  }
  
  /* Given a basic set i with a constraint k that is adjacent to
   * basic set j, check if we can wrap
   * both the facet corresponding to k (if "wrap_facet" is set) and basic map j
   * (always) around their ridges to include the other set.
   * If so, replace the pair of basic sets by their union.
   *
   * All constraints of i (except k) are assumed to be valid or
   * cut constraints for j.
   * Wrapping the cut constraints to include basic map j may result
   * in constraints that are no longer valid of basic map i
   * we have to check that the resulting wrapping constraints are valid for i.
   * If "wrap_facet" is not set, then all constraints of i (except k)
   * are assumed to be valid for j.
   *        ____			  _____
   *       /    | 		 /     \
   *      /     ||  		/      |
   *      \     ||   	=>	\      |
   *       \    ||		 \     |
   *        \___||		  \____|
   *
   */
  static enum isl_change can_wrap_in_facet(int i, int j, int k,
  	struct isl_coalesce_info *info, int wrap_facet)
  {
  	enum isl_change change = isl_change_none;
  	struct isl_wraps wraps;
  	isl_ctx *ctx;
  	isl_mat *mat;
  	struct isl_set *set_i = NULL;
  	struct isl_set *set_j = NULL;
  	struct isl_vec *bound = NULL;
  	unsigned total = isl_basic_map_total_dim(info[i].bmap);
  
  	set_i = set_from_updated_bmap(info[i].bmap, info[i].tab);
  	set_j = set_from_updated_bmap(info[j].bmap, info[j].tab);
  	ctx = isl_basic_map_get_ctx(info[i].bmap);
  	mat = isl_mat_alloc(ctx, 2 * (info[i].bmap->n_eq + info[j].bmap->n_eq) +
  				    info[i].bmap->n_ineq + info[j].bmap->n_ineq,
  				    1 + total);
  	wraps_init(&wraps, mat, info, i, j);
  	bound = isl_vec_alloc(ctx, 1 + total);
  	if (!set_i || !set_j || !wraps.mat || !bound)
  		goto error;
  
  	isl_seq_cpy(bound->el, info[i].bmap->ineq[k], 1 + total);
  	isl_int_add_ui(bound->el[0], bound->el[0], 1);
  
  	isl_seq_cpy(wraps.mat->row[0], bound->el, 1 + total);
  	wraps.mat->n_row = 1;
  
  	if (add_wraps(&wraps, &info[j], bound->el, set_i) < 0)
  		goto error;
  	if (!wraps.mat->n_row)
  		goto unbounded;
  
  	if (wrap_facet) {
  		if (add_wraps_around_facet(&wraps, &info[i], k,
  					    bound->el, set_j) < 0)
  			goto error;
  		if (!wraps.mat->n_row)
  			goto unbounded;
  	}
  
  	change = fuse(i, j, info, wraps.mat, 0, 0);
  
  unbounded:
  	wraps_free(&wraps);
  
  	isl_set_free(set_i);
  	isl_set_free(set_j);
  
  	isl_vec_free(bound);
  
  	return change;
  error:
  	wraps_free(&wraps);
  	isl_vec_free(bound);
  	isl_set_free(set_i);
  	isl_set_free(set_j);
  	return isl_change_error;
  }
  
  /* Given a cut constraint t(x) >= 0 of basic map i, stored in row "w"
   * of wrap.mat, replace it by its relaxed version t(x) + 1 >= 0, and
   * add wrapping constraints to wrap.mat for all constraints
   * of basic map j that bound the part of basic map j that sticks out
   * of the cut constraint.
   * "set_i" is the underlying set of basic map i.
   * If any wrapping fails, then wraps->mat.n_row is reset to zero.
   *
   * In particular, we first intersect basic map j with t(x) + 1 = 0.
   * If the result is empty, then t(x) >= 0 was actually a valid constraint
   * (with respect to the integer points), so we add t(x) >= 0 instead.
   * Otherwise, we wrap the constraints of basic map j that are not
   * redundant in this intersection and that are not already valid
   * for basic map i over basic map i.
   * Note that it is sufficient to wrap the constraints to include
   * basic map i, because we will only wrap the constraints that do
   * not include basic map i already.  The wrapped constraint will
   * therefore be more relaxed compared to the original constraint.
   * Since the original constraint is valid for basic map j, so is
   * the wrapped constraint.
   */
  static isl_stat wrap_in_facet(struct isl_wraps *wraps, int w,
  	struct isl_coalesce_info *info_j, __isl_keep isl_set *set_i,
  	struct isl_tab_undo *snap)
  {
  	isl_int_add_ui(wraps->mat->row[w][0], wraps->mat->row[w][0], 1);
  	if (isl_tab_add_eq(info_j->tab, wraps->mat->row[w]) < 0)
  		return isl_stat_error;
  	if (isl_tab_detect_redundant(info_j->tab) < 0)
  		return isl_stat_error;
  
  	if (info_j->tab->empty)
  		isl_int_sub_ui(wraps->mat->row[w][0], wraps->mat->row[w][0], 1);
  	else if (add_wraps(wraps, info_j, wraps->mat->row[w], set_i) < 0)
  		return isl_stat_error;
  
  	if (isl_tab_rollback(info_j->tab, snap) < 0)
  		return isl_stat_error;
  
  	return isl_stat_ok;
  }
  
  /* Given a pair of basic maps i and j such that j sticks out
   * of i at n cut constraints, each time by at most one,
   * try to compute wrapping constraints and replace the two
   * basic maps by a single basic map.
   * The other constraints of i are assumed to be valid for j.
   * "set_i" is the underlying set of basic map i.
   * "wraps" has been initialized to be of the right size.
   *
   * For each cut constraint t(x) >= 0 of i, we add the relaxed version
   * t(x) + 1 >= 0, along with wrapping constraints for all constraints
   * of basic map j that bound the part of basic map j that sticks out
   * of the cut constraint.
   *
   * If any wrapping fails, i.e., if we cannot wrap to touch
   * the union, then we give up.
   * Otherwise, the pair of basic maps is replaced by their union.
   */
  static enum isl_change try_wrap_in_facets(int i, int j,
  	struct isl_coalesce_info *info, struct isl_wraps *wraps,
  	__isl_keep isl_set *set_i)
  {
  	int k, l, w;
  	unsigned total;
  	struct isl_tab_undo *snap;
  
  	total = isl_basic_map_total_dim(info[i].bmap);
  
  	snap = isl_tab_snap(info[j].tab);
  
  	wraps->mat->n_row = 0;
  
  	for (k = 0; k < info[i].bmap->n_eq; ++k) {
  		for (l = 0; l < 2; ++l) {
  			if (info[i].eq[2 * k + l] != STATUS_CUT)
  				continue;
  			w = wraps->mat->n_row++;
  			if (l == 0)
  				isl_seq_neg(wraps->mat->row[w],
  					    info[i].bmap->eq[k], 1 + total);
  			else
  				isl_seq_cpy(wraps->mat->row[w],
  					    info[i].bmap->eq[k], 1 + total);
  			if (wrap_in_facet(wraps, w, &info[j], set_i, snap) < 0)
  				return isl_change_error;
  
  			if (!wraps->mat->n_row)
  				return isl_change_none;
  		}
  	}
  
  	for (k = 0; k < info[i].bmap->n_ineq; ++k) {
  		if (info[i].ineq[k] != STATUS_CUT)
  			continue;
  		w = wraps->mat->n_row++;
  		isl_seq_cpy(wraps->mat->row[w],
  			    info[i].bmap->ineq[k], 1 + total);
  		if (wrap_in_facet(wraps, w, &info[j], set_i, snap) < 0)
  			return isl_change_error;
  
  		if (!wraps->mat->n_row)
  			return isl_change_none;
  	}
  
  	return fuse(i, j, info, wraps->mat, 0, 1);
  }
  
  /* Given a pair of basic maps i and j such that j sticks out
   * of i at n cut constraints, each time by at most one,
   * try to compute wrapping constraints and replace the two
   * basic maps by a single basic map.
   * The other constraints of i are assumed to be valid for j.
   *
   * The core computation is performed by try_wrap_in_facets.
   * This function simply extracts an underlying set representation
   * of basic map i and initializes the data structure for keeping
   * track of wrapping constraints.
   */
  static enum isl_change wrap_in_facets(int i, int j, int n,
  	struct isl_coalesce_info *info)
  {
  	enum isl_change change = isl_change_none;
  	struct isl_wraps wraps;
  	isl_ctx *ctx;
  	isl_mat *mat;
  	isl_set *set_i = NULL;
  	unsigned total = isl_basic_map_total_dim(info[i].bmap);
  	int max_wrap;
  
  	if (isl_tab_extend_cons(info[j].tab, 1) < 0)
  		return isl_change_error;
  
  	max_wrap = 1 + 2 * info[j].bmap->n_eq + info[j].bmap->n_ineq;
  	max_wrap *= n;
  
  	set_i = set_from_updated_bmap(info[i].bmap, info[i].tab);
  	ctx = isl_basic_map_get_ctx(info[i].bmap);
  	mat = isl_mat_alloc(ctx, max_wrap, 1 + total);
  	wraps_init(&wraps, mat, info, i, j);
  	if (!set_i || !wraps.mat)
  		goto error;
  
  	change = try_wrap_in_facets(i, j, info, &wraps, set_i);
  
  	wraps_free(&wraps);
  	isl_set_free(set_i);
  
  	return change;
  error:
  	wraps_free(&wraps);
  	isl_set_free(set_i);
  	return isl_change_error;
  }
  
  /* Return the effect of inequality "ineq" on the tableau "tab",
   * after relaxing the constant term of "ineq" by one.
   */
  static enum isl_ineq_type type_of_relaxed(struct isl_tab *tab, isl_int *ineq)
  {
  	enum isl_ineq_type type;
  
  	isl_int_add_ui(ineq[0], ineq[0], 1);
  	type = isl_tab_ineq_type(tab, ineq);
  	isl_int_sub_ui(ineq[0], ineq[0], 1);
  
  	return type;
  }
  
  /* Given two basic sets i and j,
   * check if relaxing all the cut constraints of i by one turns
   * them into valid constraint for j and check if we can wrap in
   * the bits that are sticking out.
   * If so, replace the pair by their union.
   *
   * We first check if all relaxed cut inequalities of i are valid for j
   * and then try to wrap in the intersections of the relaxed cut inequalities
   * with j.
   *
   * During this wrapping, we consider the points of j that lie at a distance
   * of exactly 1 from i.  In particular, we ignore the points that lie in
   * between this lower-dimensional space and the basic map i.
   * We can therefore only apply this to integer maps.
   *        ____			  _____
   *       / ___|_		 /     \
   *      / |    |  		/      |
   *      \ |    |   	=>	\      |
   *       \|____|		 \     |
   *        \___| 		  \____/
   *
   *	 _____			 ______
   *	| ____|_		|      \
   *	| |     |		|       |
   *	| |	|	=>	|       |
   *	|_|     |		|       |
   *	  |_____|		 \______|
   *
   *	 _______
   *	|       |
   *	|  |\   |
   *	|  | \  |
   *	|  |  \ |
   *	|  |   \|
   *	|  |    \
   *	|  |_____\
   *	|       |
   *	|_______|
   *
   * Wrapping can fail if the result of wrapping one of the facets
   * around its edges does not produce any new facet constraint.
   * In particular, this happens when we try to wrap in unbounded sets.
   *
   *	 _______________________________________________________________________
   *	|
   *	|  ___
   *	| |   |
   *	|_|   |_________________________________________________________________
   *	  |___|
   *
   * The following is not an acceptable result of coalescing the above two
   * sets as it includes extra integer points.
   *	 _______________________________________________________________________
   *	|
   *	|     
   *	|      
   *	|
   *	 \______________________________________________________________________
   */
  static enum isl_change can_wrap_in_set(int i, int j,
  	struct isl_coalesce_info *info)
  {
  	int k, l;
  	int n;
  	unsigned total;
  
  	if (ISL_F_ISSET(info[i].bmap, ISL_BASIC_MAP_RATIONAL) ||
  	    ISL_F_ISSET(info[j].bmap, ISL_BASIC_MAP_RATIONAL))
  		return isl_change_none;
  
  	n = count(info[i].eq, 2 * info[i].bmap->n_eq, STATUS_CUT);
  	n += count(info[i].ineq, info[i].bmap->n_ineq, STATUS_CUT);
  	if (n == 0)
  		return isl_change_none;
  
  	total = isl_basic_map_total_dim(info[i].bmap);
  	for (k = 0; k < info[i].bmap->n_eq; ++k) {
  		for (l = 0; l < 2; ++l) {
  			enum isl_ineq_type type;
  
  			if (info[i].eq[2 * k + l] != STATUS_CUT)
  				continue;
  
  			if (l == 0)
  				isl_seq_neg(info[i].bmap->eq[k],
  					    info[i].bmap->eq[k], 1 + total);
  			type = type_of_relaxed(info[j].tab,
  					    info[i].bmap->eq[k]);
  			if (l == 0)
  				isl_seq_neg(info[i].bmap->eq[k],
  					    info[i].bmap->eq[k], 1 + total);
  			if (type == isl_ineq_error)
  				return isl_change_error;
  			if (type != isl_ineq_redundant)
  				return isl_change_none;
  		}
  	}
  
  	for (k = 0; k < info[i].bmap->n_ineq; ++k) {
  		enum isl_ineq_type type;
  
  		if (info[i].ineq[k] != STATUS_CUT)
  			continue;
  
  		type = type_of_relaxed(info[j].tab, info[i].bmap->ineq[k]);
  		if (type == isl_ineq_error)
  			return isl_change_error;
  		if (type != isl_ineq_redundant)
  			return isl_change_none;
  	}
  
  	return wrap_in_facets(i, j, n, info);
  }
  
  /* Check if either i or j has only cut constraints that can
   * be used to wrap in (a facet of) the other basic set.
   * if so, replace the pair by their union.
   */
  static enum isl_change check_wrap(int i, int j, struct isl_coalesce_info *info)
  {
  	enum isl_change change = isl_change_none;
  
  	change = can_wrap_in_set(i, j, info);
  	if (change != isl_change_none)
  		return change;
  
  	change = can_wrap_in_set(j, i, info);
  	return change;
  }
  
  /* At least one of the basic maps has an equality that is adjacent
   * to inequality.  Make sure that only one of the basic maps has
   * such an equality and that the other basic map has exactly one
   * inequality adjacent to an equality.
   * If the other basic map does not have such an inequality, then
   * check if all its constraints are either valid or cut constraints
   * and, if so, try wrapping in the first map into the second.
   *
   * We call the basic map that has the inequality "i" and the basic
   * map that has the equality "j".
   * If "i" has any "cut" (in)equality, then relaxing the inequality
   * by one would not result in a basic map that contains the other
   * basic map.  However, it may still be possible to wrap in the other
   * basic map.
   */
  static enum isl_change check_adj_eq(int i, int j,
  	struct isl_coalesce_info *info)
  {
  	enum isl_change change = isl_change_none;
  	int k;
  	int any_cut;
  
  	if (any(info[i].eq, 2 * info[i].bmap->n_eq, STATUS_ADJ_INEQ) &&
  	    any(info[j].eq, 2 * info[j].bmap->n_eq, STATUS_ADJ_INEQ))
  		/* ADJ EQ TOO MANY */
  		return isl_change_none;
  
  	if (any(info[i].eq, 2 * info[i].bmap->n_eq, STATUS_ADJ_INEQ))
  		return check_adj_eq(j, i, info);
  
  	/* j has an equality adjacent to an inequality in i */
  
  	if (count(info[i].ineq, info[i].bmap->n_ineq, STATUS_ADJ_EQ) != 1) {
  		if (all_valid_or_cut(&info[i]))
  			return can_wrap_in_set(i, j, info);
  		return isl_change_none;
  	}
  	if (any(info[i].eq, 2 * info[i].bmap->n_eq, STATUS_CUT))
  		return isl_change_none;
  	any_cut = any(info[i].ineq, info[i].bmap->n_ineq, STATUS_CUT);
  	if (any(info[j].ineq, info[j].bmap->n_ineq, STATUS_ADJ_EQ) ||
  	    any(info[i].ineq, info[i].bmap->n_ineq, STATUS_ADJ_INEQ) ||
  	    any(info[j].ineq, info[j].bmap->n_ineq, STATUS_ADJ_INEQ))
  		/* ADJ EQ TOO MANY */
  		return isl_change_none;
  
  	for (k = 0; k < info[i].bmap->n_ineq; ++k)
  		if (info[i].ineq[k] == STATUS_ADJ_EQ)
  			break;
  
  	if (!any_cut) {
  		change = is_adj_eq_extension(i, j, k, info);
  		if (change != isl_change_none)
  			return change;
  	}
  
  	change = can_wrap_in_facet(i, j, k, info, any_cut);
  
  	return change;
  }
  
  /* The two basic maps lie on adjacent hyperplanes.  In particular,
   * basic map "i" has an equality that lies parallel to basic map "j".
   * Check if we can wrap the facets around the parallel hyperplanes
   * to include the other set.
   *
   * We perform basically the same operations as can_wrap_in_facet,
   * except that we don't need to select a facet of one of the sets.
   *				_
   *	\\			\\
   *	 \\		=>	 \\
   *	  \			  \|
   *
   * If there is more than one equality of "i" adjacent to an equality of "j",
   * then the result will satisfy one or more equalities that are a linear
   * combination of these equalities.  These will be encoded as pairs
   * of inequalities in the wrapping constraints and need to be made
   * explicit.
   */
  static enum isl_change check_eq_adj_eq(int i, int j,
  	struct isl_coalesce_info *info)
  {
  	int k;
  	enum isl_change change = isl_change_none;
  	int detect_equalities = 0;
  	struct isl_wraps wraps;
  	isl_ctx *ctx;
  	isl_mat *mat;
  	struct isl_set *set_i = NULL;
  	struct isl_set *set_j = NULL;
  	struct isl_vec *bound = NULL;
  	unsigned total = isl_basic_map_total_dim(info[i].bmap);
  
  	if (count(info[i].eq, 2 * info[i].bmap->n_eq, STATUS_ADJ_EQ) != 1)
  		detect_equalities = 1;
  
  	for (k = 0; k < 2 * info[i].bmap->n_eq ; ++k)
  		if (info[i].eq[k] == STATUS_ADJ_EQ)
  			break;
  
  	set_i = set_from_updated_bmap(info[i].bmap, info[i].tab);
  	set_j = set_from_updated_bmap(info[j].bmap, info[j].tab);
  	ctx = isl_basic_map_get_ctx(info[i].bmap);
  	mat = isl_mat_alloc(ctx, 2 * (info[i].bmap->n_eq + info[j].bmap->n_eq) +
  				    info[i].bmap->n_ineq + info[j].bmap->n_ineq,
  				    1 + total);
  	wraps_init(&wraps, mat, info, i, j);
  	bound = isl_vec_alloc(ctx, 1 + total);
  	if (!set_i || !set_j || !wraps.mat || !bound)
  		goto error;
  
  	if (k % 2 == 0)
  		isl_seq_neg(bound->el, info[i].bmap->eq[k / 2], 1 + total);
  	else
  		isl_seq_cpy(bound->el, info[i].bmap->eq[k / 2], 1 + total);
  	isl_int_add_ui(bound->el[0], bound->el[0], 1);
  
  	isl_seq_cpy(wraps.mat->row[0], bound->el, 1 + total);
  	wraps.mat->n_row = 1;
  
  	if (add_wraps(&wraps, &info[j], bound->el, set_i) < 0)
  		goto error;
  	if (!wraps.mat->n_row)
  		goto unbounded;
  
  	isl_int_sub_ui(bound->el[0], bound->el[0], 1);
  	isl_seq_neg(bound->el, bound->el, 1 + total);
  
  	isl_seq_cpy(wraps.mat->row[wraps.mat->n_row], bound->el, 1 + total);
  	wraps.mat->n_row++;
  
  	if (add_wraps(&wraps, &info[i], bound->el, set_j) < 0)
  		goto error;
  	if (!wraps.mat->n_row)
  		goto unbounded;
  
  	change = fuse(i, j, info, wraps.mat, detect_equalities, 0);
  
  	if (0) {
  error:		change = isl_change_error;
  	}
  unbounded:
  
  	wraps_free(&wraps);
  	isl_set_free(set_i);
  	isl_set_free(set_j);
  	isl_vec_free(bound);
  
  	return change;
  }
  
  /* Initialize the "eq" and "ineq" fields of "info".
   */
  static void init_status(struct isl_coalesce_info *info)
  {
  	info->eq = info->ineq = NULL;
  }
  
  /* Set info->eq to the positions of the equalities of info->bmap
   * with respect to the basic map represented by "tab".
   * If info->eq has already been computed, then do not compute it again.
   */
  static void set_eq_status_in(struct isl_coalesce_info *info,
  	struct isl_tab *tab)
  {
  	if (info->eq)
  		return;
  	info->eq = eq_status_in(info->bmap, tab);
  }
  
  /* Set info->ineq to the positions of the inequalities of info->bmap
   * with respect to the basic map represented by "tab".
   * If info->ineq has already been computed, then do not compute it again.
   */
  static void set_ineq_status_in(struct isl_coalesce_info *info,
  	struct isl_tab *tab)
  {
  	if (info->ineq)
  		return;
  	info->ineq = ineq_status_in(info->bmap, info->tab, tab);
  }
  
  /* Free the memory allocated by the "eq" and "ineq" fields of "info".
   * This function assumes that init_status has been called on "info" first,
   * after which the "eq" and "ineq" fields may or may not have been
   * assigned a newly allocated array.
   */
  static void clear_status(struct isl_coalesce_info *info)
  {
  	free(info->eq);
  	free(info->ineq);
  }
  
  /* Check if the union of the given pair of basic maps
   * can be represented by a single basic map.
   * If so, replace the pair by the single basic map and return
   * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
   * Otherwise, return isl_change_none.
   * The two basic maps are assumed to live in the same local space.
   * The "eq" and "ineq" fields of info[i] and info[j] are assumed
   * to have been initialized by the caller, either to NULL or
   * to valid information.
   *
   * We first check the effect of each constraint of one basic map
   * on the other basic map.
   * The constraint may be
   *	redundant	the constraint is redundant in its own
   *			basic map and should be ignore and removed
   *			in the end
   *	valid		all (integer) points of the other basic map
   *			satisfy the constraint
   *	separate	no (integer) point of the other basic map
   *			satisfies the constraint
   *	cut		some but not all points of the other basic map
   *			satisfy the constraint
   *	adj_eq		the given constraint is adjacent (on the outside)
   *			to an equality of the other basic map
   *	adj_ineq	the given constraint is adjacent (on the outside)
   *			to an inequality of the other basic map
   *
   * We consider seven cases in which we can replace the pair by a single
   * basic map.  We ignore all "redundant" constraints.
   *
   *	1. all constraints of one basic map are valid
   *		=> the other basic map is a subset and can be removed
   *
   *	2. all constraints of both basic maps are either "valid" or "cut"
   *	   and the facets corresponding to the "cut" constraints
   *	   of one of the basic maps lies entirely inside the other basic map
   *		=> the pair can be replaced by a basic map consisting
   *		   of the valid constraints in both basic maps
   *
   *	3. there is a single pair of adjacent inequalities
   *	   (all other constraints are "valid")
   *		=> the pair can be replaced by a basic map consisting
   *		   of the valid constraints in both basic maps
   *
   *	4. one basic map has a single adjacent inequality, while the other
   *	   constraints are "valid".  The other basic map has some
   *	   "cut" constraints, but replacing the adjacent inequality by
   *	   its opposite and adding the valid constraints of the other
   *	   basic map results in a subset of the other basic map
   *		=> the pair can be replaced by a basic map consisting
   *		   of the valid constraints in both basic maps
   *
   *	5. there is a single adjacent pair of an inequality and an equality,
   *	   the other constraints of the basic map containing the inequality are
   *	   "valid".  Moreover, if the inequality the basic map is relaxed
   *	   and then turned into an equality, then resulting facet lies
   *	   entirely inside the other basic map
   *		=> the pair can be replaced by the basic map containing
   *		   the inequality, with the inequality relaxed.
   *
   *	6. there is a single adjacent pair of an inequality and an equality,
   *	   the other constraints of the basic map containing the inequality are
   *	   "valid".  Moreover, the facets corresponding to both
   *	   the inequality and the equality can be wrapped around their
   *	   ridges to include the other basic map
   *		=> the pair can be replaced by a basic map consisting
   *		   of the valid constraints in both basic maps together
   *		   with all wrapping constraints
   *
   *	7. one of the basic maps extends beyond the other by at most one.
   *	   Moreover, the facets corresponding to the cut constraints and
   *	   the pieces of the other basic map at offset one from these cut
   *	   constraints can be wrapped around their ridges to include
   *	   the union of the two basic maps
   *		=> the pair can be replaced by a basic map consisting
   *		   of the valid constraints in both basic maps together
   *		   with all wrapping constraints
   *
   *	8. the two basic maps live in adjacent hyperplanes.  In principle
   *	   such sets can always be combined through wrapping, but we impose
   *	   that there is only one such pair, to avoid overeager coalescing.
   *
   * Throughout the computation, we maintain a collection of tableaus
   * corresponding to the basic maps.  When the basic maps are dropped
   * or combined, the tableaus are modified accordingly.
   */
  static enum isl_change coalesce_local_pair_reuse(int i, int j,
  	struct isl_coalesce_info *info)
  {
  	enum isl_change change = isl_change_none;
  
  	set_eq_status_in(&info[i], info[j].tab);
  	if (info[i].bmap->n_eq && !info[i].eq)
  		goto error;
  	if (any(info[i].eq, 2 * info[i].bmap->n_eq, STATUS_ERROR))
  		goto error;
  	if (any(info[i].eq, 2 * info[i].bmap->n_eq, STATUS_SEPARATE))
  		goto done;
  
  	set_eq_status_in(&info[j], info[i].tab);
  	if (info[j].bmap->n_eq && !info[j].eq)
  		goto error;
  	if (any(info[j].eq, 2 * info[j].bmap->n_eq, STATUS_ERROR))
  		goto error;
  	if (any(info[j].eq, 2 * info[j].bmap->n_eq, STATUS_SEPARATE))
  		goto done;
  
  	set_ineq_status_in(&info[i], info[j].tab);
  	if (info[i].bmap->n_ineq && !info[i].ineq)
  		goto error;
  	if (any(info[i].ineq, info[i].bmap->n_ineq, STATUS_ERROR))
  		goto error;
  	if (any(info[i].ineq, info[i].bmap->n_ineq, STATUS_SEPARATE))
  		goto done;
  
  	set_ineq_status_in(&info[j], info[i].tab);
  	if (info[j].bmap->n_ineq && !info[j].ineq)
  		goto error;
  	if (any(info[j].ineq, info[j].bmap->n_ineq, STATUS_ERROR))
  		goto error;
  	if (any(info[j].ineq, info[j].bmap->n_ineq, STATUS_SEPARATE))
  		goto done;
  
  	if (all(info[i].eq, 2 * info[i].bmap->n_eq, STATUS_VALID) &&
  	    all(info[i].ineq, info[i].bmap->n_ineq, STATUS_VALID)) {
  		drop(&info[j]);
  		change = isl_change_drop_second;
  	} else if (all(info[j].eq, 2 * info[j].bmap->n_eq, STATUS_VALID) &&
  		   all(info[j].ineq, info[j].bmap->n_ineq, STATUS_VALID)) {
  		drop(&info[i]);
  		change = isl_change_drop_first;
  	} else if (any(info[i].eq, 2 * info[i].bmap->n_eq, STATUS_ADJ_EQ)) {
  		change = check_eq_adj_eq(i, j, info);
  	} else if (any(info[j].eq, 2 * info[j].bmap->n_eq, STATUS_ADJ_EQ)) {
  		change = check_eq_adj_eq(j, i, info);
  	} else if (any(info[i].eq, 2 * info[i].bmap->n_eq, STATUS_ADJ_INEQ) ||
  		   any(info[j].eq, 2 * info[j].bmap->n_eq, STATUS_ADJ_INEQ)) {
  		change = check_adj_eq(i, j, info);
  	} else if (any(info[i].ineq, info[i].bmap->n_ineq, STATUS_ADJ_EQ) ||
  		   any(info[j].ineq, info[j].bmap->n_ineq, STATUS_ADJ_EQ)) {
  		/* Can't happen */
  		/* BAD ADJ INEQ */
  	} else if (any(info[i].ineq, info[i].bmap->n_ineq, STATUS_ADJ_INEQ) ||
  		   any(info[j].ineq, info[j].bmap->n_ineq, STATUS_ADJ_INEQ)) {
  		change = check_adj_ineq(i, j, info);
  	} else {
  		if (!any(info[i].eq, 2 * info[i].bmap->n_eq, STATUS_CUT) &&
  		    !any(info[j].eq, 2 * info[j].bmap->n_eq, STATUS_CUT))
  			change = check_facets(i, j, info);
  		if (change == isl_change_none)
  			change = check_wrap(i, j, info);
  	}
  
  done:
  	clear_status(&info[i]);
  	clear_status(&info[j]);
  	return change;
  error:
  	clear_status(&info[i]);
  	clear_status(&info[j]);
  	return isl_change_error;
  }
  
  /* Check if the union of the given pair of basic maps
   * can be represented by a single basic map.
   * If so, replace the pair by the single basic map and return
   * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
   * Otherwise, return isl_change_none.
   * The two basic maps are assumed to live in the same local space.
   */
  static enum isl_change coalesce_local_pair(int i, int j,
  	struct isl_coalesce_info *info)
  {
  	init_status(&info[i]);
  	init_status(&info[j]);
  	return coalesce_local_pair_reuse(i, j, info);
  }
  
  /* Shift the integer division at position "div" of the basic map
   * represented by "info" by "shift".
   *
   * That is, if the integer division has the form
   *
   *	floor(f(x)/d)
   *
   * then replace it by
   *
   *	floor((f(x) + shift * d)/d) - shift
   */
  static int shift_div(struct isl_coalesce_info *info, int div, isl_int shift)
  {
  	unsigned total;
  
  	info->bmap = isl_basic_map_shift_div(info->bmap, div, 0, shift);
  	if (!info->bmap)
  		return -1;
  
  	total = isl_basic_map_dim(info->bmap, isl_dim_all);
  	total -= isl_basic_map_dim(info->bmap, isl_dim_div);
  	if (isl_tab_shift_var(info->tab, total + div, shift) < 0)
  		return -1;
  
  	return 0;
  }
  
  /* Check if some of the divs in the basic map represented by "info1"
   * are shifts of the corresponding divs in the basic map represented
   * by "info2".  If so, align them with those of "info2".
   * Only do this if "info1" and "info2" have the same number
   * of integer divisions.
   *
   * An integer division is considered to be a shift of another integer
   * division if one is equal to the other plus a constant.
   *
   * In particular, for each pair of integer divisions, if both are known,
   * have identical coefficients (apart from the constant term) and
   * if the difference between the constant terms (taking into account
   * the denominator) is an integer, then move the difference outside.
   * That is, if one integer division is of the form
   *
   *	floor((f(x) + c_1)/d)
   *
   * while the other is of the form
   *
   *	floor((f(x) + c_2)/d)
   *
   * and n = (c_2 - c_1)/d is an integer, then replace the first
   * integer division by
   *
   *	floor((f(x) + c_1 + n * d)/d) - n = floor((f(x) + c_2)/d) - n
   */
  static int harmonize_divs(struct isl_coalesce_info *info1,
  	struct isl_coalesce_info *info2)
  {
  	int i;
  	int total;
  
  	if (!info1->bmap || !info2->bmap)
  		return -1;
  
  	if (info1->bmap->n_div != info2->bmap->n_div)
  		return 0;
  	if (info1->bmap->n_div == 0)
  		return 0;
  
  	total = isl_basic_map_total_dim(info1->bmap);
  	for (i = 0; i < info1->bmap->n_div; ++i) {
  		isl_int d;
  		int r = 0;
  
  		if (isl_int_is_zero(info1->bmap->div[i][0]) ||
  		    isl_int_is_zero(info2->bmap->div[i][0]))
  			continue;
  		if (isl_int_ne(info1->bmap->div[i][0], info2->bmap->div[i][0]))
  			continue;
  		if (isl_int_eq(info1->bmap->div[i][1], info2->bmap->div[i][1]))
  			continue;
  		if (!isl_seq_eq(info1->bmap->div[i] + 2,
  				info2->bmap->div[i] + 2, total))
  			continue;
  		isl_int_init(d);
  		isl_int_sub(d, info2->bmap->div[i][1], info1->bmap->div[i][1]);
  		if (isl_int_is_divisible_by(d, info1->bmap->div[i][0])) {
  			isl_int_divexact(d, d, info1->bmap->div[i][0]);
  			r = shift_div(info1, i, d);
  		}
  		isl_int_clear(d);
  		if (r < 0)
  			return -1;
  	}
  
  	return 0;
  }
  
  /* Do the two basic maps live in the same local space, i.e.,
   * do they have the same (known) divs?
   * If either basic map has any unknown divs, then we can only assume
   * that they do not live in the same local space.
   */
  static int same_divs(__isl_keep isl_basic_map *bmap1,
  	__isl_keep isl_basic_map *bmap2)
  {
  	int i;
  	int known;
  	int total;
  
  	if (!bmap1 || !bmap2)
  		return -1;
  	if (bmap1->n_div != bmap2->n_div)
  		return 0;
  
  	if (bmap1->n_div == 0)
  		return 1;
  
  	known = isl_basic_map_divs_known(bmap1);
  	if (known < 0 || !known)
  		return known;
  	known = isl_basic_map_divs_known(bmap2);
  	if (known < 0 || !known)
  		return known;
  
  	total = isl_basic_map_total_dim(bmap1);
  	for (i = 0; i < bmap1->n_div; ++i)
  		if (!isl_seq_eq(bmap1->div[i], bmap2->div[i], 2 + total))
  			return 0;
  
  	return 1;
  }
  
  /* Expand info->tab in the same way info->bmap was expanded in
   * isl_basic_map_expand_divs using the expansion "exp" and
   * update info->ineq with respect to the redundant constraints
   * in the resulting tableau.
   * In particular, introduce extra variables corresponding
   * to the extra integer divisions and add the div constraints
   * that were added to info->bmap after info->tab was created
   * from the original info->bmap.
   * info->ineq was computed without a tableau and therefore
   * does not take into account the redundant constraints
   * in the tableau.  Mark them here.
   */
  static isl_stat expand_tab(struct isl_coalesce_info *info, int *exp)
  {
  	unsigned total, pos, n_div;
  	int extra_var;
  	int i, n, j, n_ineq;
  	unsigned n_eq;
  
  	total = isl_basic_map_dim(info->bmap, isl_dim_all);
  	n_div = isl_basic_map_dim(info->bmap, isl_dim_div);
  	pos = total - n_div;
  	extra_var = total - info->tab->n_var;
  	n = n_div - extra_var;
  
  	if (isl_tab_extend_vars(info->tab, extra_var) < 0)
  		return isl_stat_error;
  	if (isl_tab_extend_cons(info->tab, 2 * extra_var) < 0)
  		return isl_stat_error;
  
  	i = 0;
  	for (j = 0; j < n_div; ++j) {
  		if (i < n && exp[i] == j) {
  			++i;
  			continue;
  		}
  		if (isl_tab_insert_var(info->tab, pos + j) < 0)
  			return isl_stat_error;
  	}
  
  	n_ineq = info->tab->n_con - info->tab->n_eq;
  	for (i = n_ineq; i < info->bmap->n_ineq; ++i)
  		if (isl_tab_add_ineq(info->tab, info->bmap->ineq[i]) < 0)
  			return isl_stat_error;
  
  	n_eq = info->bmap->n_eq;
  	for (i = 0; i < info->bmap->n_ineq; ++i) {
  		if (isl_tab_is_redundant(info->tab, n_eq + i))
  			info->ineq[i] = STATUS_REDUNDANT;
  	}
  
  	return isl_stat_ok;
  }
  
  /* Check if the union of the basic maps represented by info[i] and info[j]
   * can be represented by a single basic map,
   * after expanding the divs of info[i] to match those of info[j].
   * If so, replace the pair by the single basic map and return
   * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
   * Otherwise, return isl_change_none.
   *
   * The caller has already checked for info[j] being a subset of info[i].
   * If some of the divs of info[j] are unknown, then the expanded info[i]
   * will not have the corresponding div constraints.  The other patterns
   * therefore cannot apply.  Skip the computation in this case.
   *
   * The expansion is performed using the divs "div" and expansion "exp"
   * computed by the caller.
   * info[i].bmap has already been expanded and the result is passed in
   * as "bmap".
   * The "eq" and "ineq" fields of info[i] reflect the status of
   * the constraints of the expanded "bmap" with respect to info[j].tab.
   * However, inequality constraints that are redundant in info[i].tab
   * have not yet been marked as such because no tableau was available.
   *
   * Replace info[i].bmap by "bmap" and expand info[i].tab as well,
   * updating info[i].ineq with respect to the redundant constraints.
   * Then try and coalesce the expanded info[i] with info[j],
   * reusing the information in info[i].eq and info[i].ineq.
   * If this does not result in any coalescing or if it results in info[j]
   * getting dropped (which should not happen in practice, since the case
   * of info[j] being a subset of info[i] has already been checked by
   * the caller), then revert info[i] to its original state.
   */
  static enum isl_change coalesce_expand_tab_divs(__isl_take isl_basic_map *bmap,
  	int i, int j, struct isl_coalesce_info *info, __isl_keep isl_mat *div,
  	int *exp)
  {
  	isl_bool known;
  	isl_basic_map *bmap_i;
  	struct isl_tab_undo *snap;
  	enum isl_change change = isl_change_none;
  
  	known = isl_basic_map_divs_known(info[j].bmap);
  	if (known < 0 || !known) {
  		clear_status(&info[i]);
  		isl_basic_map_free(bmap);
  		return known < 0 ? isl_change_error : isl_change_none;
  	}
  
  	bmap_i = info[i].bmap;
  	info[i].bmap = isl_basic_map_copy(bmap);
  	snap = isl_tab_snap(info[i].tab);
  	if (!info[i].bmap || expand_tab(&info[i], exp) < 0)
  		change = isl_change_error;
  
  	init_status(&info[j]);
  	if (change == isl_change_none)
  		change = coalesce_local_pair_reuse(i, j, info);
  	else
  		clear_status(&info[i]);
  	if (change != isl_change_none && change != isl_change_drop_second) {
  		isl_basic_map_free(bmap_i);
  	} else {
  		isl_basic_map_free(info[i].bmap);
  		info[i].bmap = bmap_i;
  
  		if (isl_tab_rollback(info[i].tab, snap) < 0)
  			change = isl_change_error;
  	}
  
  	isl_basic_map_free(bmap);
  	return change;
  }
  
  /* Check if the union of "bmap" and the basic map represented by info[j]
   * can be represented by a single basic map,
   * after expanding the divs of "bmap" to match those of info[j].
   * If so, replace the pair by the single basic map and return
   * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
   * Otherwise, return isl_change_none.
   *
   * In particular, check if the expanded "bmap" contains the basic map
   * represented by the tableau info[j].tab.
   * The expansion is performed using the divs "div" and expansion "exp"
   * computed by the caller.
   * Then we check if all constraints of the expanded "bmap" are valid for
   * info[j].tab.
   *
   * If "i" is not equal to -1, then "bmap" is equal to info[i].bmap.
   * In this case, the positions of the constraints of info[i].bmap
   * with respect to the basic map represented by info[j] are stored
   * in info[i].
   *
   * If the expanded "bmap" does not contain the basic map
   * represented by the tableau info[j].tab and if "i" is not -1,
   * i.e., if the original "bmap" is info[i].bmap, then expand info[i].tab
   * as well and check if that results in coalescing.
   */
  static enum isl_change coalesce_with_expanded_divs(
  	__isl_keep isl_basic_map *bmap, int i, int j,
  	struct isl_coalesce_info *info, __isl_keep isl_mat *div, int *exp)
  {
  	enum isl_change change = isl_change_none;
  	struct isl_coalesce_info info_local, *info_i;
  
  	info_i = i >= 0 ? &info[i] : &info_local;
  	init_status(info_i);
  	bmap = isl_basic_map_copy(bmap);
  	bmap = isl_basic_map_expand_divs(bmap, isl_mat_copy(div), exp);
  
  	if (!bmap)
  		goto error;
  
  	info_i->eq = eq_status_in(bmap, info[j].tab);
  	if (bmap->n_eq && !info_i->eq)
  		goto error;
  	if (any(info_i->eq, 2 * bmap->n_eq, STATUS_ERROR))
  		goto error;
  	if (any(info_i->eq, 2 * bmap->n_eq, STATUS_SEPARATE))
  		goto done;
  
  	info_i->ineq = ineq_status_in(bmap, NULL, info[j].tab);
  	if (bmap->n_ineq && !info_i->ineq)
  		goto error;
  	if (any(info_i->ineq, bmap->n_ineq, STATUS_ERROR))
  		goto error;
  	if (any(info_i->ineq, bmap->n_ineq, STATUS_SEPARATE))
  		goto done;
  
  	if (all(info_i->eq, 2 * bmap->n_eq, STATUS_VALID) &&
  	    all(info_i->ineq, bmap->n_ineq, STATUS_VALID)) {
  		drop(&info[j]);
  		change = isl_change_drop_second;
  	}
  
  	if (change == isl_change_none && i != -1)
  		return coalesce_expand_tab_divs(bmap, i, j, info, div, exp);
  
  done:
  	isl_basic_map_free(bmap);
  	clear_status(info_i);
  	return change;
  error:
  	isl_basic_map_free(bmap);
  	clear_status(info_i);
  	return isl_change_error;
  }
  
  /* Check if the union of "bmap_i" and the basic map represented by info[j]
   * can be represented by a single basic map,
   * after aligning the divs of "bmap_i" to match those of info[j].
   * If so, replace the pair by the single basic map and return
   * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
   * Otherwise, return isl_change_none.
   *
   * In particular, check if "bmap_i" contains the basic map represented by
   * info[j] after aligning the divs of "bmap_i" to those of info[j].
   * Note that this can only succeed if the number of divs of "bmap_i"
   * is smaller than (or equal to) the number of divs of info[j].
   *
   * We first check if the divs of "bmap_i" are all known and form a subset
   * of those of info[j].bmap.  If so, we pass control over to
   * coalesce_with_expanded_divs.
   *
   * If "i" is not equal to -1, then "bmap" is equal to info[i].bmap.
   */
  static enum isl_change coalesce_after_aligning_divs(
  	__isl_keep isl_basic_map *bmap_i, int i, int j,
  	struct isl_coalesce_info *info)
  {
  	int known;
  	isl_mat *div_i, *div_j, *div;
  	int *exp1 = NULL;
  	int *exp2 = NULL;
  	isl_ctx *ctx;
  	enum isl_change change;
  
  	known = isl_basic_map_divs_known(bmap_i);
  	if (known < 0 || !known)
  		return known;
  
  	ctx = isl_basic_map_get_ctx(bmap_i);
  
  	div_i = isl_basic_map_get_divs(bmap_i);
  	div_j = isl_basic_map_get_divs(info[j].bmap);
  
  	if (!div_i || !div_j)
  		goto error;
  
  	exp1 = isl_alloc_array(ctx, int, div_i->n_row);
  	exp2 = isl_alloc_array(ctx, int, div_j->n_row);
  	if ((div_i->n_row && !exp1) || (div_j->n_row && !exp2))
  		goto error;
  
  	div = isl_merge_divs(div_i, div_j, exp1, exp2);
  	if (!div)
  		goto error;
  
  	if (div->n_row == div_j->n_row)
  		change = coalesce_with_expanded_divs(bmap_i,
  							i, j, info, div, exp1);
  	else
  		change = isl_change_none;
  
  	isl_mat_free(div);
  
  	isl_mat_free(div_i);
  	isl_mat_free(div_j);
  
  	free(exp2);
  	free(exp1);
  
  	return change;
  error:
  	isl_mat_free(div_i);
  	isl_mat_free(div_j);
  	free(exp1);
  	free(exp2);
  	return isl_change_error;
  }
  
  /* Check if basic map "j" is a subset of basic map "i" after
   * exploiting the extra equalities of "j" to simplify the divs of "i".
   * If so, remove basic map "j" and return isl_change_drop_second.
   *
   * If "j" does not have any equalities or if they are the same
   * as those of "i", then we cannot exploit them to simplify the divs.
   * Similarly, if there are no divs in "i", then they cannot be simplified.
   * If, on the other hand, the affine hulls of "i" and "j" do not intersect,
   * then "j" cannot be a subset of "i".
   *
   * Otherwise, we intersect "i" with the affine hull of "j" and then
   * check if "j" is a subset of the result after aligning the divs.
   * If so, then "j" is definitely a subset of "i" and can be removed.
   * Note that if after intersection with the affine hull of "j".
   * "i" still has more divs than "j", then there is no way we can
   * align the divs of "i" to those of "j".
   */
  static enum isl_change coalesce_subset_with_equalities(int i, int j,
  	struct isl_coalesce_info *info)
  {
  	isl_basic_map *hull_i, *hull_j, *bmap_i;
  	int equal, empty;
  	enum isl_change change;
  
  	if (info[j].bmap->n_eq == 0)
  		return isl_change_none;
  	if (info[i].bmap->n_div == 0)
  		return isl_change_none;
  
  	hull_i = isl_basic_map_copy(info[i].bmap);
  	hull_i = isl_basic_map_plain_affine_hull(hull_i);
  	hull_j = isl_basic_map_copy(info[j].bmap);
  	hull_j = isl_basic_map_plain_affine_hull(hull_j);
  
  	hull_j = isl_basic_map_intersect(hull_j, isl_basic_map_copy(hull_i));
  	equal = isl_basic_map_plain_is_equal(hull_i, hull_j);
  	empty = isl_basic_map_plain_is_empty(hull_j);
  	isl_basic_map_free(hull_i);
  
  	if (equal < 0 || equal || empty < 0 || empty) {
  		isl_basic_map_free(hull_j);
  		if (equal < 0 || empty < 0)
  			return isl_change_error;
  		return isl_change_none;
  	}
  
  	bmap_i = isl_basic_map_copy(info[i].bmap);
  	bmap_i = isl_basic_map_intersect(bmap_i, hull_j);
  	if (!bmap_i)
  		return isl_change_error;
  
  	if (bmap_i->n_div > info[j].bmap->n_div) {
  		isl_basic_map_free(bmap_i);
  		return isl_change_none;
  	}
  
  	change = coalesce_after_aligning_divs(bmap_i, -1, j, info);
  
  	isl_basic_map_free(bmap_i);
  
  	return change;
  }
  
  /* Check if the union of and the basic maps represented by info[i] and info[j]
   * can be represented by a single basic map, by aligning or equating
   * their integer divisions.
   * If so, replace the pair by the single basic map and return
   * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
   * Otherwise, return isl_change_none.
   *
   * Note that we only perform any test if the number of divs is different
   * in the two basic maps.  In case the number of divs is the same,
   * we have already established that the divs are different
   * in the two basic maps.
   * In particular, if the number of divs of basic map i is smaller than
   * the number of divs of basic map j, then we check if j is a subset of i
   * and vice versa.
   */
  static enum isl_change coalesce_divs(int i, int j,
  	struct isl_coalesce_info *info)
  {
  	enum isl_change change = isl_change_none;
  
  	if (info[i].bmap->n_div < info[j].bmap->n_div)
  		change = coalesce_after_aligning_divs(info[i].bmap, i, j, info);
  	if (change != isl_change_none)
  		return change;
  
  	if (info[j].bmap->n_div < info[i].bmap->n_div)
  		change = coalesce_after_aligning_divs(info[j].bmap, j, i, info);
  	if (change != isl_change_none)
  		return invert_change(change);
  
  	change = coalesce_subset_with_equalities(i, j, info);
  	if (change != isl_change_none)
  		return change;
  
  	change = coalesce_subset_with_equalities(j, i, info);
  	if (change != isl_change_none)
  		return invert_change(change);
  
  	return isl_change_none;
  }
  
  /* Does "bmap" involve any divs that themselves refer to divs?
   */
  static int has_nested_div(__isl_keep isl_basic_map *bmap)
  {
  	int i;
  	unsigned total;
  	unsigned n_div;
  
  	total = isl_basic_map_dim(bmap, isl_dim_all);
  	n_div = isl_basic_map_dim(bmap, isl_dim_div);
  	total -= n_div;
  
  	for (i = 0; i < n_div; ++i)
  		if (isl_seq_first_non_zero(bmap->div[i] + 2 + total,
  					    n_div) != -1)
  			return 1;
  
  	return 0;
  }
  
  /* Return a list of affine expressions, one for each integer division
   * in "bmap_i".  For each integer division that also appears in "bmap_j",
   * the affine expression is set to NaN.  The number of NaNs in the list
   * is equal to the number of integer divisions in "bmap_j".
   * For the other integer divisions of "bmap_i", the corresponding
   * element in the list is a purely affine expression equal to the integer
   * division in "hull".
   * If no such list can be constructed, then the number of elements
   * in the returned list is smaller than the number of integer divisions
   * in "bmap_i".
   */
  static __isl_give isl_aff_list *set_up_substitutions(
  	__isl_keep isl_basic_map *bmap_i, __isl_keep isl_basic_map *bmap_j,
  	__isl_take isl_basic_map *hull)
  {
  	unsigned n_div_i, n_div_j, total;
  	isl_ctx *ctx;
  	isl_local_space *ls;
  	isl_basic_set *wrap_hull;
  	isl_aff *aff_nan;
  	isl_aff_list *list;
  	int i, j;
  
  	if (!hull)
  		return NULL;
  
  	ctx = isl_basic_map_get_ctx(hull);
  
  	n_div_i = isl_basic_map_dim(bmap_i, isl_dim_div);
  	n_div_j = isl_basic_map_dim(bmap_j, isl_dim_div);
  	total = isl_basic_map_total_dim(bmap_i) - n_div_i;
  
  	ls = isl_basic_map_get_local_space(bmap_i);
  	ls = isl_local_space_wrap(ls);
  	wrap_hull = isl_basic_map_wrap(hull);
  
  	aff_nan = isl_aff_nan_on_domain(isl_local_space_copy(ls));
  	list = isl_aff_list_alloc(ctx, n_div_i);
  
  	j = 0;
  	for (i = 0; i < n_div_i; ++i) {
  		isl_aff *aff;
  
  		if (j < n_div_j &&
  		    isl_seq_eq(bmap_i->div[i], bmap_j->div[j], 2 + total)) {
  			++j;
  			list = isl_aff_list_add(list, isl_aff_copy(aff_nan));
  			continue;
  		}
  		if (n_div_i - i <= n_div_j - j)
  			break;
  
  		aff = isl_local_space_get_div(ls, i);
  		aff = isl_aff_substitute_equalities(aff,
  						isl_basic_set_copy(wrap_hull));
  		aff = isl_aff_floor(aff);
  		if (!aff)
  			goto error;
  		if (isl_aff_dim(aff, isl_dim_div) != 0) {
  			isl_aff_free(aff);
  			break;
  		}
  
  		list = isl_aff_list_add(list, aff);
  	}
  
  	isl_aff_free(aff_nan);
  	isl_local_space_free(ls);
  	isl_basic_set_free(wrap_hull);
  
  	return list;
  error:
  	isl_aff_free(aff_nan);
  	isl_local_space_free(ls);
  	isl_basic_set_free(wrap_hull);
  	isl_aff_list_free(list);
  	return NULL;
  }
  
  /* Add variables to info->bmap and info->tab corresponding to the elements
   * in "list" that are not set to NaN.
   * "extra_var" is the number of these elements.
   * "dim" is the offset in the variables of "tab" where we should
   * start considering the elements in "list".
   * When this function returns, the total number of variables in "tab"
   * is equal to "dim" plus the number of elements in "list".
   *
   * The newly added existentially quantified variables are not given
   * an explicit representation because the corresponding div constraints
   * do not appear in info->bmap.  These constraints are not added
   * to info->bmap because for internal consistency, they would need to
   * be added to info->tab as well, where they could combine with the equality
   * that is added later to result in constraints that do not hold
   * in the original input.
   */
  static int add_sub_vars(struct isl_coalesce_info *info,
  	__isl_keep isl_aff_list *list, int dim, int extra_var)
  {
  	int i, j, n, d;
  	isl_space *space;
  
  	space = isl_basic_map_get_space(info->bmap);
  	info->bmap = isl_basic_map_cow(info->bmap);
  	info->bmap = isl_basic_map_extend_space(info->bmap, space,
  						extra_var, 0, 0);
  	if (!info->bmap)
  		return -1;
  	n = isl_aff_list_n_aff(list);
  	for (i = 0; i < n; ++i) {
  		int is_nan;
  		isl_aff *aff;
  
  		aff = isl_aff_list_get_aff(list, i);
  		is_nan = isl_aff_is_nan(aff);
  		isl_aff_free(aff);
  		if (is_nan < 0)
  			return -1;
  		if (is_nan)
  			continue;
  
  		if (isl_tab_insert_var(info->tab, dim + i) < 0)
  			return -1;
  		d = isl_basic_map_alloc_div(info->bmap);
  		if (d < 0)
  			return -1;
  		info->bmap = isl_basic_map_mark_div_unknown(info->bmap, d);
  		if (!info->bmap)
  			return -1;
  		for (j = d; j > i; --j)
  			isl_basic_map_swap_div(info->bmap, j - 1, j);
  	}
  
  	return 0;
  }
  
  /* For each element in "list" that is not set to NaN, fix the corresponding
   * variable in "tab" to the purely affine expression defined by the element.
   * "dim" is the offset in the variables of "tab" where we should
   * start considering the elements in "list".
   *
   * This function assumes that a sufficient number of rows and
   * elements in the constraint array are available in the tableau.
   */
  static int add_sub_equalities(struct isl_tab *tab,
  	__isl_keep isl_aff_list *list, int dim)
  {
  	int i, n;
  	isl_ctx *ctx;
  	isl_vec *sub;
  	isl_aff *aff;
  
  	n = isl_aff_list_n_aff(list);
  
  	ctx = isl_tab_get_ctx(tab);
  	sub = isl_vec_alloc(ctx, 1 + dim + n);
  	if (!sub)
  		return -1;
  	isl_seq_clr(sub->el + 1 + dim, n);
  
  	for (i = 0; i < n; ++i) {
  		aff = isl_aff_list_get_aff(list, i);
  		if (!aff)
  			goto error;
  		if (isl_aff_is_nan(aff)) {
  			isl_aff_free(aff);
  			continue;
  		}
  		isl_seq_cpy(sub->el, aff->v->el + 1, 1 + dim);
  		isl_int_neg(sub->el[1 + dim + i], aff->v->el[0]);
  		if (isl_tab_add_eq(tab, sub->el) < 0)
  			goto error;
  		isl_int_set_si(sub->el[1 + dim + i], 0);
  		isl_aff_free(aff);
  	}
  
  	isl_vec_free(sub);
  	return 0;
  error:
  	isl_aff_free(aff);
  	isl_vec_free(sub);
  	return -1;
  }
  
  /* Add variables to info->tab and info->bmap corresponding to the elements
   * in "list" that are not set to NaN.  The value of the added variable
   * in info->tab is fixed to the purely affine expression defined by the element.
   * "dim" is the offset in the variables of info->tab where we should
   * start considering the elements in "list".
   * When this function returns, the total number of variables in info->tab
   * is equal to "dim" plus the number of elements in "list".
   */
  static int add_subs(struct isl_coalesce_info *info,
  	__isl_keep isl_aff_list *list, int dim)
  {
  	int extra_var;
  	int n;
  
  	if (!list)
  		return -1;
  
  	n = isl_aff_list_n_aff(list);
  	extra_var = n - (info->tab->n_var - dim);
  
  	if (isl_tab_extend_vars(info->tab, extra_var) < 0)
  		return -1;
  	if (isl_tab_extend_cons(info->tab, 2 * extra_var) < 0)
  		return -1;
  	if (add_sub_vars(info, list, dim, extra_var) < 0)
  		return -1;
  
  	return add_sub_equalities(info->tab, list, dim);
  }
  
  /* Coalesce basic map "j" into basic map "i" after adding the extra integer
   * divisions in "i" but not in "j" to basic map "j", with values
   * specified by "list".  The total number of elements in "list"
   * is equal to the number of integer divisions in "i", while the number
   * of NaN elements in the list is equal to the number of integer divisions
   * in "j".
   *
   * If no coalescing can be performed, then we need to revert basic map "j"
   * to its original state.  We do the same if basic map "i" gets dropped
   * during the coalescing, even though this should not happen in practice
   * since we have already checked for "j" being a subset of "i"
   * before we reach this stage.
   */
  static enum isl_change coalesce_with_subs(int i, int j,
  	struct isl_coalesce_info *info, __isl_keep isl_aff_list *list)
  {
  	isl_basic_map *bmap_j;
  	struct isl_tab_undo *snap;
  	unsigned dim;
  	enum isl_change change;
  
  	bmap_j = isl_basic_map_copy(info[j].bmap);
  	snap = isl_tab_snap(info[j].tab);
  
  	dim = isl_basic_map_dim(bmap_j, isl_dim_all);
  	dim -= isl_basic_map_dim(bmap_j, isl_dim_div);
  	if (add_subs(&info[j], list, dim) < 0)
  		goto error;
  
  	change = coalesce_local_pair(i, j, info);
  	if (change != isl_change_none && change != isl_change_drop_first) {
  		isl_basic_map_free(bmap_j);
  	} else {
  		isl_basic_map_free(info[j].bmap);
  		info[j].bmap = bmap_j;
  
  		if (isl_tab_rollback(info[j].tab, snap) < 0)
  			return isl_change_error;
  	}
  
  	return change;
  error:
  	isl_basic_map_free(bmap_j);
  	return isl_change_error;
  }
  
  /* Check if we can coalesce basic map "j" into basic map "i" after copying
   * those extra integer divisions in "i" that can be simplified away
   * using the extra equalities in "j".
   * All divs are assumed to be known and not contain any nested divs.
   *
   * We first check if there are any extra equalities in "j" that we
   * can exploit.  Then we check if every integer division in "i"
   * either already appears in "j" or can be simplified using the
   * extra equalities to a purely affine expression.
   * If these tests succeed, then we try to coalesce the two basic maps
   * by introducing extra dimensions in "j" corresponding to
   * the extra integer divsisions "i" fixed to the corresponding
   * purely affine expression.
   */
  static enum isl_change check_coalesce_into_eq(int i, int j,
  	struct isl_coalesce_info *info)
  {
  	unsigned n_div_i, n_div_j;
  	isl_basic_map *hull_i, *hull_j;
  	int equal, empty;
  	isl_aff_list *list;
  	enum isl_change change;
  
  	n_div_i = isl_basic_map_dim(info[i].bmap, isl_dim_div);
  	n_div_j = isl_basic_map_dim(info[j].bmap, isl_dim_div);
  	if (n_div_i <= n_div_j)
  		return isl_change_none;
  	if (info[j].bmap->n_eq == 0)
  		return isl_change_none;
  
  	hull_i = isl_basic_map_copy(info[i].bmap);
  	hull_i = isl_basic_map_plain_affine_hull(hull_i);
  	hull_j = isl_basic_map_copy(info[j].bmap);
  	hull_j = isl_basic_map_plain_affine_hull(hull_j);
  
  	hull_j = isl_basic_map_intersect(hull_j, isl_basic_map_copy(hull_i));
  	equal = isl_basic_map_plain_is_equal(hull_i, hull_j);
  	empty = isl_basic_map_plain_is_empty(hull_j);
  	isl_basic_map_free(hull_i);
  
  	if (equal < 0 || empty < 0)
  		goto error;
  	if (equal || empty) {
  		isl_basic_map_free(hull_j);
  		return isl_change_none;
  	}
  
  	list = set_up_substitutions(info[i].bmap, info[j].bmap, hull_j);
  	if (!list)
  		return isl_change_error;
  	if (isl_aff_list_n_aff(list) < n_div_i)
  		change = isl_change_none;
  	else
  		change = coalesce_with_subs(i, j, info, list);
  
  	isl_aff_list_free(list);
  
  	return change;
  error:
  	isl_basic_map_free(hull_j);
  	return isl_change_error;
  }
  
  /* Check if we can coalesce basic maps "i" and "j" after copying
   * those extra integer divisions in one of the basic maps that can
   * be simplified away using the extra equalities in the other basic map.
   * We require all divs to be known in both basic maps.
   * Furthermore, to simplify the comparison of div expressions,
   * we do not allow any nested integer divisions.
   */
  static enum isl_change check_coalesce_eq(int i, int j,
  	struct isl_coalesce_info *info)
  {
  	int known, nested;
  	enum isl_change change;
  
  	known = isl_basic_map_divs_known(info[i].bmap);
  	if (known < 0 || !known)
  		return known < 0 ? isl_change_error : isl_change_none;
  	known = isl_basic_map_divs_known(info[j].bmap);
  	if (known < 0 || !known)
  		return known < 0 ? isl_change_error : isl_change_none;
  	nested = has_nested_div(info[i].bmap);
  	if (nested < 0 || nested)
  		return nested < 0 ? isl_change_error : isl_change_none;
  	nested = has_nested_div(info[j].bmap);
  	if (nested < 0 || nested)
  		return nested < 0 ? isl_change_error : isl_change_none;
  
  	change = check_coalesce_into_eq(i, j, info);
  	if (change != isl_change_none)
  		return change;
  	change = check_coalesce_into_eq(j, i, info);
  	if (change != isl_change_none)
  		return invert_change(change);
  
  	return isl_change_none;
  }
  
  /* Check if the union of the given pair of basic maps
   * can be represented by a single basic map.
   * If so, replace the pair by the single basic map and return
   * isl_change_drop_first, isl_change_drop_second or isl_change_fuse.
   * Otherwise, return isl_change_none.
   *
   * We first check if the two basic maps live in the same local space,
   * after aligning the divs that differ by only an integer constant.
   * If so, we do the complete check.  Otherwise, we check if they have
   * the same number of integer divisions and can be coalesced, if one is
   * an obvious subset of the other or if the extra integer divisions
   * of one basic map can be simplified away using the extra equalities
   * of the other basic map.
   */
  static enum isl_change coalesce_pair(int i, int j,
  	struct isl_coalesce_info *info)
  {
  	int same;
  	enum isl_change change;
  
  	if (harmonize_divs(&info[i], &info[j]) < 0)
  		return isl_change_error;
  	same = same_divs(info[i].bmap, info[j].bmap);
  	if (same < 0)
  		return isl_change_error;
  	if (same)
  		return coalesce_local_pair(i, j, info);
  
  	if (info[i].bmap->n_div == info[j].bmap->n_div) {
  		change = coalesce_local_pair(i, j, info);
  		if (change != isl_change_none)
  			return change;
  	}
  
  	change = coalesce_divs(i, j, info);
  	if (change != isl_change_none)
  		return change;
  
  	return check_coalesce_eq(i, j, info);
  }
  
  /* Return the maximum of "a" and "b".
   */
  static int isl_max(int a, int b)
  {
  	return a > b ? a : b;
  }
  
  /* Pairwise coalesce the basic maps in the range [start1, end1[ of "info"
   * with those in the range [start2, end2[, skipping basic maps
   * that have been removed (either before or within this function).
   *
   * For each basic map i in the first range, we check if it can be coalesced
   * with respect to any previously considered basic map j in the second range.
   * If i gets dropped (because it was a subset of some j), then
   * we can move on to the next basic map.
   * If j gets dropped, we need to continue checking against the other
   * previously considered basic maps.
   * If the two basic maps got fused, then we recheck the fused basic map
   * against the previously considered basic maps, starting at i + 1
   * (even if start2 is greater than i + 1).
   */
  static int coalesce_range(isl_ctx *ctx, struct isl_coalesce_info *info,
  	int start1, int end1, int start2, int end2)
  {
  	int i, j;
  
  	for (i = end1 - 1; i >= start1; --i) {
  		if (info[i].removed)
  			continue;
  		for (j = isl_max(i + 1, start2); j < end2; ++j) {
  			enum isl_change changed;
  
  			if (info[j].removed)
  				continue;
  			if (info[i].removed)
  				isl_die(ctx, isl_error_internal,
  					"basic map unexpectedly removed",
  					return -1);
  			changed = coalesce_pair(i, j, info);
  			switch (changed) {
  			case isl_change_error:
  				return -1;
  			case isl_change_none:
  			case isl_change_drop_second:
  				continue;
  			case isl_change_drop_first:
  				j = end2;
  				break;
  			case isl_change_fuse:
  				j = i;
  				break;
  			}
  		}
  	}
  
  	return 0;
  }
  
  /* Pairwise coalesce the basic maps described by the "n" elements of "info".
   *
   * We consider groups of basic maps that live in the same apparent
   * affine hull and we first coalesce within such a group before we
   * coalesce the elements in the group with elements of previously
   * considered groups.  If a fuse happens during the second phase,
   * then we also reconsider the elements within the group.
   */
  static int coalesce(isl_ctx *ctx, int n, struct isl_coalesce_info *info)
  {
  	int start, end;
  
  	for (end = n; end > 0; end = start) {
  		start = end - 1;
  		while (start >= 1 &&
  		    info[start - 1].hull_hash == info[start].hull_hash)
  			start--;
  		if (coalesce_range(ctx, info, start, end, start, end) < 0)
  			return -1;
  		if (coalesce_range(ctx, info, start, end, end, n) < 0)
  			return -1;
  	}
  
  	return 0;
  }
  
  /* Update the basic maps in "map" based on the information in "info".
   * In particular, remove the basic maps that have been marked removed and
   * update the others based on the information in the corresponding tableau.
   * Since we detected implicit equalities without calling
   * isl_basic_map_gauss, we need to do it now.
   * Also call isl_basic_map_simplify if we may have lost the definition
   * of one or more integer divisions.
   */
  static __isl_give isl_map *update_basic_maps(__isl_take isl_map *map,
  	int n, struct isl_coalesce_info *info)
  {
  	int i;
  
  	if (!map)
  		return NULL;
  
  	for (i = n - 1; i >= 0; --i) {
  		if (info[i].removed) {
  			isl_basic_map_free(map->p[i]);
  			if (i != map->n - 1)
  				map->p[i] = map->p[map->n - 1];
  			map->n--;
  			continue;
  		}
  
  		info[i].bmap = isl_basic_map_update_from_tab(info[i].bmap,
  							info[i].tab);
  		info[i].bmap = isl_basic_map_gauss(info[i].bmap, NULL);
  		if (info[i].simplify)
  			info[i].bmap = isl_basic_map_simplify(info[i].bmap);
  		info[i].bmap = isl_basic_map_finalize(info[i].bmap);
  		if (!info[i].bmap)
  			return isl_map_free(map);
  		ISL_F_SET(info[i].bmap, ISL_BASIC_MAP_NO_IMPLICIT);
  		ISL_F_SET(info[i].bmap, ISL_BASIC_MAP_NO_REDUNDANT);
  		isl_basic_map_free(map->p[i]);
  		map->p[i] = info[i].bmap;
  		info[i].bmap = NULL;
  	}
  
  	return map;
  }
  
  /* For each pair of basic maps in the map, check if the union of the two
   * can be represented by a single basic map.
   * If so, replace the pair by the single basic map and start over.
   *
   * We factor out any (hidden) common factor from the constraint
   * coefficients to improve the detection of adjacent constraints.
   *
   * Since we are constructing the tableaus of the basic maps anyway,
   * we exploit them to detect implicit equalities and redundant constraints.
   * This also helps the coalescing as it can ignore the redundant constraints.
   * In order to avoid confusion, we make all implicit equalities explicit
   * in the basic maps.  We don't call isl_basic_map_gauss, though,
   * as that may affect the number of constraints.
   * This means that we have to call isl_basic_map_gauss at the end
   * of the computation (in update_basic_maps) to ensure that
   * the basic maps are not left in an unexpected state.
   * For each basic map, we also compute the hash of the apparent affine hull
   * for use in coalesce.
   */
  struct isl_map *isl_map_coalesce(struct isl_map *map)
  {
  	int i;
  	unsigned n;
  	isl_ctx *ctx;
  	struct isl_coalesce_info *info = NULL;
  
  	map = isl_map_remove_empty_parts(map);
  	if (!map)
  		return NULL;
  
  	if (map->n <= 1)
  		return map;
  
  	ctx = isl_map_get_ctx(map);
  	map = isl_map_sort_divs(map);
  	map = isl_map_cow(map);
  
  	if (!map)
  		return NULL;
  
  	n = map->n;
  
  	info = isl_calloc_array(map->ctx, struct isl_coalesce_info, n);
  	if (!info)
  		goto error;
  
  	for (i = 0; i < map->n; ++i) {
  		map->p[i] = isl_basic_map_reduce_coefficients(map->p[i]);
  		if (!map->p[i])
  			goto error;
  		info[i].bmap = isl_basic_map_copy(map->p[i]);
  		info[i].tab = isl_tab_from_basic_map(info[i].bmap, 0);
  		if (!info[i].tab)
  			goto error;
  		if (!ISL_F_ISSET(info[i].bmap, ISL_BASIC_MAP_NO_IMPLICIT))
  			if (isl_tab_detect_implicit_equalities(info[i].tab) < 0)
  				goto error;
  		info[i].bmap = isl_tab_make_equalities_explicit(info[i].tab,
  								info[i].bmap);
  		if (!info[i].bmap)
  			goto error;
  		if (!ISL_F_ISSET(info[i].bmap, ISL_BASIC_MAP_NO_REDUNDANT))
  			if (isl_tab_detect_redundant(info[i].tab) < 0)
  				goto error;
  		if (coalesce_info_set_hull_hash(&info[i]) < 0)
  			goto error;
  	}
  	for (i = map->n - 1; i >= 0; --i)
  		if (info[i].tab->empty)
  			drop(&info[i]);
  
  	if (coalesce(ctx, n, info) < 0)
  		goto error;
  
  	map = update_basic_maps(map, n, info);
  
  	clear_coalesce_info(n, info);
  
  	return map;
  error:
  	clear_coalesce_info(n, info);
  	isl_map_free(map);
  	return NULL;
  }
  
  /* For each pair of basic sets in the set, check if the union of the two
   * can be represented by a single basic set.
   * If so, replace the pair by the single basic set and start over.
   */
  struct isl_set *isl_set_coalesce(struct isl_set *set)
  {
  	return (struct isl_set *)isl_map_coalesce((struct isl_map *)set);
  }
  