text: /*
   * Copyright 2010-2011 INRIA Saclay
   * Copyright 2013-2014 Ecole Normale Superieure
   * Copyright 2014      INRIA Rocquencourt
   *
   * Use of this software is governed by the MIT license
   *
   * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
   * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
   * 91893 Orsay, France 
   * and Inria Paris - Rocquencourt, Domaine de Voluceau - Rocquencourt,
   * B.P. 105 - 78153 Le Chesnay, France
   */
  
  #define ISL_DIM_H
  #include <isl_map_private.h>
  #include <isl_union_map_private.h>
  #include <isl/ctx.h>
  #include <isl/hash.h>
  #include <isl/aff.h>
  #include <isl/map.h>
  #include <isl/set.h>
  #include <isl_space_private.h>
  #include <isl/union_set.h>
  #include <isl/deprecated/union_map_int.h>
  
  /* Return the number of parameters of "umap", where "type"
   * is required to be set to isl_dim_param.
   */
  unsigned isl_union_map_dim(__isl_keep isl_union_map *umap,
  	enum isl_dim_type type)
  {
  	if (!umap)
  		return 0;
  
  	if (type != isl_dim_param)
  		isl_die(isl_union_map_get_ctx(umap), isl_error_invalid,
  			"can only reference parameters", return 0);
  
  	return isl_space_dim(umap->dim, type);
  }
  
  /* Return the number of parameters of "uset", where "type"
   * is required to be set to isl_dim_param.
   */
  unsigned isl_union_set_dim(__isl_keep isl_union_set *uset,
  	enum isl_dim_type type)
  {
  	return isl_union_map_dim(uset, type);
  }
  
  /* Return the id of the specified dimension.
   */
  __isl_give isl_id *isl_union_map_get_dim_id(__isl_keep isl_union_map *umap,
  	enum isl_dim_type type, unsigned pos)
  {
  	if (!umap)
  		return NULL;
  
  	if (type != isl_dim_param)
  		isl_die(isl_union_map_get_ctx(umap), isl_error_invalid,
  			"can only reference parameters", return NULL);
  
  	return isl_space_get_dim_id(umap->dim, type, pos);
  }
  
  /* Is this union set a parameter domain?
   */
  int isl_union_set_is_params(__isl_keep isl_union_set *uset)
  {
  	isl_set *set;
  	int params;
  
  	if (!uset)
  		return -1;
  	if (uset->table.n != 1)
  		return 0;
  
  	set = isl_set_from_union_set(isl_union_set_copy(uset));
  	params = isl_set_is_params(set);
  	isl_set_free(set);
  	return params;
  }
  
  static __isl_give isl_union_map *isl_union_map_alloc(
  	__isl_take isl_space *space, int size)
  {
  	isl_union_map *umap;
  
  	space = isl_space_params(space);
  	if (!space)
  		return NULL;
  
  	umap = isl_calloc_type(space->ctx, isl_union_map);
  	if (!umap) {
  		isl_space_free(space);
  		return NULL;
  	}
  
  	umap->ref = 1;
  	umap->dim = space;
  	if (isl_hash_table_init(space->ctx, &umap->table, size) < 0)
  		return isl_union_map_free(umap);
  
  	return umap;
  }
  
  __isl_give isl_union_map *isl_union_map_empty(__isl_take isl_space *dim)
  {
  	return isl_union_map_alloc(dim, 16);
  }
  
  __isl_give isl_union_set *isl_union_set_empty(__isl_take isl_space *dim)
  {
  	return isl_union_map_empty(dim);
  }
  
  isl_ctx *isl_union_map_get_ctx(__isl_keep isl_union_map *umap)
  {
  	return umap ? umap->dim->ctx : NULL;
  }
  
  isl_ctx *isl_union_set_get_ctx(__isl_keep isl_union_set *uset)
  {
  	return uset ? uset->dim->ctx : NULL;
  }
  
  __isl_give isl_space *isl_union_map_get_space(__isl_keep isl_union_map *umap)
  {
  	if (!umap)
  		return NULL;
  	return isl_space_copy(umap->dim);
  }
  
  /* Return the position of the parameter with the given name
   * in "umap".
   * Return -1 if no such dimension can be found.
   */
  int isl_union_map_find_dim_by_name(__isl_keep isl_union_map *umap,
  	enum isl_dim_type type, const char *name)
  {
  	if (!umap)
  		return -1;
  	return isl_space_find_dim_by_name(umap->dim, type, name);
  }
  
  __isl_give isl_space *isl_union_set_get_space(__isl_keep isl_union_set *uset)
  {
  	return isl_union_map_get_space(uset);
  }
  
  static int free_umap_entry(void **entry, void *user)
  {
  	isl_map *map = *entry;
  	isl_map_free(map);
  	return 0;
  }
  
  static int add_map(__isl_take isl_map *map, void *user)
  {
  	isl_union_map **umap = (isl_union_map **)user;
  
  	*umap = isl_union_map_add_map(*umap, map);
  
  	return 0;
  }
  
  __isl_give isl_union_map *isl_union_map_dup(__isl_keep isl_union_map *umap)
  {
  	isl_union_map *dup;
  
  	if (!umap)
  		return NULL;
  
  	dup = isl_union_map_empty(isl_space_copy(umap->dim));
  	if (isl_union_map_foreach_map(umap, &add_map, &dup) < 0)
  		goto error;
  	return dup;
  error:
  	isl_union_map_free(dup);
  	return NULL;
  }
  
  __isl_give isl_union_map *isl_union_map_cow(__isl_take isl_union_map *umap)
  {
  	if (!umap)
  		return NULL;
  
  	if (umap->ref == 1)
  		return umap;
  	umap->ref--;
  	return isl_union_map_dup(umap);
  }
  
  struct isl_union_align {
  	isl_reordering *exp;
  	isl_union_map *res;
  };
  
  static int align_entry(void **entry, void *user)
  {
  	isl_map *map = *entry;
  	isl_reordering *exp;
  	struct isl_union_align *data = user;
  
  	exp = isl_reordering_extend_space(isl_reordering_copy(data->exp),
  				    isl_map_get_space(map));
  
  	data->res = isl_union_map_add_map(data->res,
  					isl_map_realign(isl_map_copy(map), exp));
  
  	return 0;
  }
  
  /* Align the parameters of umap along those of model.
   * The result has the parameters of model first, in the same order
   * as they appear in model, followed by any remaining parameters of
   * umap that do not appear in model.
   */
  __isl_give isl_union_map *isl_union_map_align_params(
  	__isl_take isl_union_map *umap, __isl_take isl_space *model)
  {
  	struct isl_union_align data = { NULL, NULL };
  
  	if (!umap || !model)
  		goto error;
  
  	if (isl_space_match(umap->dim, isl_dim_param, model, isl_dim_param)) {
  		isl_space_free(model);
  		return umap;
  	}
  
  	model = isl_space_params(model);
  	data.exp = isl_parameter_alignment_reordering(umap->dim, model);
  	if (!data.exp)
  		goto error;
  
  	data.res = isl_union_map_alloc(isl_space_copy(data.exp->dim),
  					umap->table.n);
  	if (isl_hash_table_foreach(umap->dim->ctx, &umap->table,
  					&align_entry, &data) < 0)
  		goto error;
  
  	isl_reordering_free(data.exp);
  	isl_union_map_free(umap);
  	isl_space_free(model);
  	return data.res;
  error:
  	isl_reordering_free(data.exp);
  	isl_union_map_free(umap);
  	isl_union_map_free(data.res);
  	isl_space_free(model);
  	return NULL;
  }
  
  __isl_give isl_union_set *isl_union_set_align_params(
  	__isl_take isl_union_set *uset, __isl_take isl_space *model)
  {
  	return isl_union_map_align_params(uset, model);
  }
  
  __isl_give isl_union_map *isl_union_map_union(__isl_take isl_union_map *umap1,
  	__isl_take isl_union_map *umap2)
  {
  	umap1 = isl_union_map_align_params(umap1, isl_union_map_get_space(umap2));
  	umap2 = isl_union_map_align_params(umap2, isl_union_map_get_space(umap1));
  
  	umap1 = isl_union_map_cow(umap1);
  
  	if (!umap1 || !umap2)
  		goto error;
  
  	if (isl_union_map_foreach_map(umap2, &add_map, &umap1) < 0)
  		goto error;
  
  	isl_union_map_free(umap2);
  
  	return umap1;
  error:
  	isl_union_map_free(umap1);
  	isl_union_map_free(umap2);
  	return NULL;
  }
  
  __isl_give isl_union_set *isl_union_set_union(__isl_take isl_union_set *uset1,
  	__isl_take isl_union_set *uset2)
  {
  	return isl_union_map_union(uset1, uset2);
  }
  
  __isl_give isl_union_map *isl_union_map_copy(__isl_keep isl_union_map *umap)
  {
  	if (!umap)
  		return NULL;
  
  	umap->ref++;
  	return umap;
  }
  
  __isl_give isl_union_set *isl_union_set_copy(__isl_keep isl_union_set *uset)
  {
  	return isl_union_map_copy(uset);
  }
  
  __isl_null isl_union_map *isl_union_map_free(__isl_take isl_union_map *umap)
  {
  	if (!umap)
  		return NULL;
  
  	if (--umap->ref > 0)
  		return NULL;
  
  	isl_hash_table_foreach(umap->dim->ctx, &umap->table,
  			       &free_umap_entry, NULL);
  	isl_hash_table_clear(&umap->table);
  	isl_space_free(umap->dim);
  	free(umap);
  	return NULL;
  }
  
  __isl_null isl_union_set *isl_union_set_free(__isl_take isl_union_set *uset)
  {
  	return isl_union_map_free(uset);
  }
  
  static int has_dim(const void *entry, const void *val)
  {
  	isl_map *map = (isl_map *)entry;
  	isl_space *dim = (isl_space *)val;
  
  	return isl_space_is_equal(map->dim, dim);
  }
  
  __isl_give isl_union_map *isl_union_map_add_map(__isl_take isl_union_map *umap,
  	__isl_take isl_map *map)
  {
  	uint32_t hash;
  	struct isl_hash_table_entry *entry;
  
  	if (!map || !umap)
  		goto error;
  
  	if (isl_map_plain_is_empty(map)) {
  		isl_map_free(map);
  		return umap;
  	}
  
  	if (!isl_space_match(map->dim, isl_dim_param, umap->dim, isl_dim_param)) {
  		umap = isl_union_map_align_params(umap, isl_map_get_space(map));
  		map = isl_map_align_params(map, isl_union_map_get_space(umap));
  	}
  
  	umap = isl_union_map_cow(umap);
  
  	if (!map || !umap)
  		goto error;
  
  	hash = isl_space_get_hash(map->dim);
  	entry = isl_hash_table_find(umap->dim->ctx, &umap->table, hash,
  				    &has_dim, map->dim, 1);
  	if (!entry)
  		goto error;
  
  	if (!entry->data)
  		entry->data = map;
  	else {
  		entry->data = isl_map_union(entry->data, isl_map_copy(map));
  		if (!entry->data)
  			goto error;
  		isl_map_free(map);
  	}
  
  	return umap;
  error:
  	isl_map_free(map);
  	isl_union_map_free(umap);
  	return NULL;
  }
  
  __isl_give isl_union_set *isl_union_set_add_set(__isl_take isl_union_set *uset,
  	__isl_take isl_set *set)
  {
  	return isl_union_map_add_map(uset, (isl_map *)set);
  }
  
  __isl_give isl_union_map *isl_union_map_from_map(__isl_take isl_map *map)
  {
  	isl_space *dim;
  	isl_union_map *umap;
  
  	if (!map)
  		return NULL;
  
  	dim = isl_map_get_space(map);
  	dim = isl_space_params(dim);
  	umap = isl_union_map_empty(dim);
  	umap = isl_union_map_add_map(umap, map);
  
  	return umap;
  }
  
  __isl_give isl_union_set *isl_union_set_from_set(__isl_take isl_set *set)
  {
  	return isl_union_map_from_map((isl_map *)set);
  }
  
  __isl_give isl_union_map *isl_union_map_from_basic_map(
  	__isl_take isl_basic_map *bmap)
  {
  	return isl_union_map_from_map(isl_map_from_basic_map(bmap));
  }
  
  __isl_give isl_union_set *isl_union_set_from_basic_set(
  	__isl_take isl_basic_set *bset)
  {
  	return isl_union_map_from_basic_map(bset);
  }
  
  struct isl_union_map_foreach_data
  {
  	int (*fn)(__isl_take isl_map *map, void *user);
  	void *user;
  };
  
  static int call_on_copy(void **entry, void *user)
  {
  	isl_map *map = *entry;
  	struct isl_union_map_foreach_data *data;
  	data = (struct isl_union_map_foreach_data *)user;
  
  	return data->fn(isl_map_copy(map), data->user);
  }
  
  int isl_union_map_n_map(__isl_keep isl_union_map *umap)
  {
  	return umap ? umap->table.n : 0;
  }
  
  int isl_union_set_n_set(__isl_keep isl_union_set *uset)
  {
  	return uset ? uset->table.n : 0;
  }
  
  int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
  	int (*fn)(__isl_take isl_map *map, void *user), void *user)
  {
  	struct isl_union_map_foreach_data data = { fn, user };
  
  	if (!umap)
  		return -1;
  
  	return isl_hash_table_foreach(umap->dim->ctx, &umap->table,
  				      &call_on_copy, &data);
  }
  
  static int copy_map(void **entry, void *user)
  {
  	isl_map *map = *entry;
  	isl_map **map_p = user;
  
  	*map_p = isl_map_copy(map);
  
  	return -1;
  }
  
  __isl_give isl_map *isl_map_from_union_map(__isl_take isl_union_map *umap)
  {
  	isl_ctx *ctx;
  	isl_map *map = NULL;
  
  	if (!umap)
  		return NULL;
  	ctx = isl_union_map_get_ctx(umap);
  	if (umap->table.n != 1)
  		isl_die(ctx, isl_error_invalid,
  			"union map needs to contain elements in exactly "
  			"one space", goto error);
  
  	isl_hash_table_foreach(ctx, &umap->table, &copy_map, &map);
  
  	isl_union_map_free(umap);
  
  	return map;
  error:
  	isl_union_map_free(umap);
  	return NULL;
  }
  
  __isl_give isl_set *isl_set_from_union_set(__isl_take isl_union_set *uset)
  {
  	return isl_map_from_union_map(uset);
  }
  
  /* Extract the map in "umap" that lives in the given space (ignoring
   * parameters).
   */
  __isl_give isl_map *isl_union_map_extract_map(__isl_keep isl_union_map *umap,
  	__isl_take isl_space *space)
  {
  	uint32_t hash;
  	struct isl_hash_table_entry *entry;
  
  	space = isl_space_drop_dims(space, isl_dim_param,
  					0, isl_space_dim(space, isl_dim_param));
  	space = isl_space_align_params(space, isl_union_map_get_space(umap));
  	if (!umap || !space)
  		goto error;
  
  	hash = isl_space_get_hash(space);
  	entry = isl_hash_table_find(umap->dim->ctx, &umap->table, hash,
  				    &has_dim, space, 0);
  	if (!entry)
  		return isl_map_empty(space);
  	isl_space_free(space);
  	return isl_map_copy(entry->data);
  error:
  	isl_space_free(space);
  	return NULL;
  }
  
  __isl_give isl_set *isl_union_set_extract_set(__isl_keep isl_union_set *uset,
  	__isl_take isl_space *dim)
  {
  	return (isl_set *)isl_union_map_extract_map(uset, dim);
  }
  
  /* Check if umap contains a map in the given space.
   */
  __isl_give int isl_union_map_contains(__isl_keep isl_union_map *umap,
  	__isl_keep isl_space *dim)
  {
  	uint32_t hash;
  	struct isl_hash_table_entry *entry;
  
  	if (!umap || !dim)
  		return -1;
  
  	hash = isl_space_get_hash(dim);
  	entry = isl_hash_table_find(umap->dim->ctx, &umap->table, hash,
  				    &has_dim, dim, 0);
  	return !!entry;
  }
  
  __isl_give int isl_union_set_contains(__isl_keep isl_union_set *uset,
  	__isl_keep isl_space *dim)
  {
  	return isl_union_map_contains(uset, dim);
  }
  
  int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
  	int (*fn)(__isl_take isl_set *set, void *user), void *user)
  {
  	return isl_union_map_foreach_map(uset,
  		(int(*)(__isl_take isl_map *, void*))fn, user);
  }
  
  struct isl_union_set_foreach_point_data {
  	int (*fn)(__isl_take isl_point *pnt, void *user);
  	void *user;
  };
  
  static int foreach_point(__isl_take isl_set *set, void *user)
  {
  	struct isl_union_set_foreach_point_data *data = user;
  	int r;
  
  	r = isl_set_foreach_point(set, data->fn, data->user);
  	isl_set_free(set);
  
  	return r;
  }
  
  int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
  	int (*fn)(__isl_take isl_point *pnt, void *user), void *user)
  {
  	struct isl_union_set_foreach_point_data data = { fn, user };
  	return isl_union_set_foreach_set(uset, &foreach_point, &data);
  }
  
  struct isl_union_map_gen_bin_data {
  	isl_union_map *umap2;
  	isl_union_map *res;
  };
  
  static int subtract_entry(void **entry, void *user)
  {
  	struct isl_union_map_gen_bin_data *data = user;
  	uint32_t hash;
  	struct isl_hash_table_entry *entry2;
  	isl_map *map = *entry;
  
  	hash = isl_space_get_hash(map->dim);
  	entry2 = isl_hash_table_find(data->umap2->dim->ctx, &data->umap2->table,
  				     hash, &has_dim, map->dim, 0);
  	map = isl_map_copy(map);
  	if (entry2) {
  		int empty;
  		map = isl_map_subtract(map, isl_map_copy(entry2->data));
  
  		empty = isl_map_is_empty(map);
  		if (empty < 0) {
  			isl_map_free(map);
  			return -1;
  		}
  		if (empty) {
  			isl_map_free(map);
  			return 0;
  		}
  	}
  	data->res = isl_union_map_add_map(data->res, map);
  
  	return 0;
  }
  
  static __isl_give isl_union_map *gen_bin_op(__isl_take isl_union_map *umap1,
  	__isl_take isl_union_map *umap2, int (*fn)(void **, void *))
  {
  	struct isl_union_map_gen_bin_data data = { NULL, NULL };
  
  	umap1 = isl_union_map_align_params(umap1, isl_union_map_get_space(umap2));
  	umap2 = isl_union_map_align_params(umap2, isl_union_map_get_space(umap1));
  
  	if (!umap1 || !umap2)
  		goto error;
  
  	data.umap2 = umap2;
  	data.res = isl_union_map_alloc(isl_space_copy(umap1->dim),
  				       umap1->table.n);
  	if (isl_hash_table_foreach(umap1->dim->ctx, &umap1->table,
  				   fn, &data) < 0)
  		goto error;
  
  	isl_union_map_free(umap1);
  	isl_union_map_free(umap2);
  	return data.res;
  error:
  	isl_union_map_free(umap1);
  	isl_union_map_free(umap2);
  	isl_union_map_free(data.res);
  	return NULL;
  }
  
  __isl_give isl_union_map *isl_union_map_subtract(
  	__isl_take isl_union_map *umap1, __isl_take isl_union_map *umap2)
  {
  	return gen_bin_op(umap1, umap2, &subtract_entry);
  }
  
  __isl_give isl_union_set *isl_union_set_subtract(
  	__isl_take isl_union_set *uset1, __isl_take isl_union_set *uset2)
  {
  	return isl_union_map_subtract(uset1, uset2);
  }
  
  struct isl_union_map_gen_bin_set_data {
  	isl_set *set;
  	isl_union_map *res;
  };
  
  static int intersect_params_entry(void **entry, void *user)
  {
  	struct isl_union_map_gen_bin_set_data *data = user;
  	isl_map *map = *entry;
  	int empty;
  
  	map = isl_map_copy(map);
  	map = isl_map_intersect_params(map, isl_set_copy(data->set));
  
  	empty = isl_map_is_empty(map);
  	if (empty < 0) {
  		isl_map_free(map);
  		return -1;
  	}
  
  	data->res = isl_union_map_add_map(data->res, map);
  
  	return 0;
  }
  
  static __isl_give isl_union_map *gen_bin_set_op(__isl_take isl_union_map *umap,
  	__isl_take isl_set *set, int (*fn)(void **, void *))
  {
  	struct isl_union_map_gen_bin_set_data data = { NULL, NULL };
  
  	umap = isl_union_map_align_params(umap, isl_set_get_space(set));
  	set = isl_set_align_params(set, isl_union_map_get_space(umap));
  
  	if (!umap || !set)
  		goto error;
  
  	data.set = set;
  	data.res = isl_union_map_alloc(isl_space_copy(umap->dim),
  				       umap->table.n);
  	if (isl_hash_table_foreach(umap->dim->ctx, &umap->table,
  				   fn, &data) < 0)
  		goto error;
  
  	isl_union_map_free(umap);
  	isl_set_free(set);
  	return data.res;
  error:
  	isl_union_map_free(umap);
  	isl_set_free(set);
  	isl_union_map_free(data.res);
  	return NULL;
  }
  
  /* Intersect "umap" with the parameter domain "set".
   *
   * If "set" does not have any constraints, then we can return immediately.
   */
  __isl_give isl_union_map *isl_union_map_intersect_params(
  	__isl_take isl_union_map *umap, __isl_take isl_set *set)
  {
  	int is_universe;
  
  	is_universe = isl_set_plain_is_universe(set);
  	if (is_universe < 0)
  		goto error;
  	if (is_universe) {
  		isl_set_free(set);
  		return umap;
  	}
  
  	return gen_bin_set_op(umap, set, &intersect_params_entry);
  error:
  	isl_union_map_free(umap);
  	isl_set_free(set);
  	return NULL;
  }
  
  __isl_give isl_union_set *isl_union_set_intersect_params(
  	__isl_take isl_union_set *uset, __isl_take isl_set *set)
  {
  	return isl_union_map_intersect_params(uset, set);
  }
  
  static __isl_give isl_union_map *union_map_intersect_params(
  	__isl_take isl_union_map *umap, __isl_take isl_union_set *uset)
  {
  	return isl_union_map_intersect_params(umap,
  						isl_set_from_union_set(uset));
  }
  
  static __isl_give isl_union_map *union_map_gist_params(
  	__isl_take isl_union_map *umap, __isl_take isl_union_set *uset)
  {
  	return isl_union_map_gist_params(umap, isl_set_from_union_set(uset));
  }
  
  struct isl_union_map_match_bin_data {
  	isl_union_map *umap2;
  	isl_union_map *res;
  	__isl_give isl_map *(*fn)(__isl_take isl_map*, __isl_take isl_map*);
  };
  
  static int match_bin_entry(void **entry, void *user)
  {
  	struct isl_union_map_match_bin_data *data = user;
  	uint32_t hash;
  	struct isl_hash_table_entry *entry2;
  	isl_map *map = *entry;
  	int empty;
  
  	hash = isl_space_get_hash(map->dim);
  	entry2 = isl_hash_table_find(data->umap2->dim->ctx, &data->umap2->table,
  				     hash, &has_dim, map->dim, 0);
  	if (!entry2)
  		return 0;
  
  	map = isl_map_copy(map);
  	map = data->fn(map, isl_map_copy(entry2->data));
  
  	empty = isl_map_is_empty(map);
  	if (empty < 0) {
  		isl_map_free(map);
  		return -1;
  	}
  	if (empty) {
  		isl_map_free(map);
  		return 0;
  	}
  
  	data->res = isl_union_map_add_map(data->res, map);
  
  	return 0;
  }
  
  static __isl_give isl_union_map *match_bin_op(__isl_take isl_union_map *umap1,
  	__isl_take isl_union_map *umap2,
  	__isl_give isl_map *(*fn)(__isl_take isl_map*, __isl_take isl_map*))
  {
  	struct isl_union_map_match_bin_data data = { NULL, NULL, fn };
  
  	umap1 = isl_union_map_align_params(umap1, isl_union_map_get_space(umap2));
  	umap2 = isl_union_map_align_params(umap2, isl_union_map_get_space(umap1));
  
  	if (!umap1 || !umap2)
  		goto error;
  
  	data.umap2 = umap2;
  	data.res = isl_union_map_alloc(isl_space_copy(umap1->dim),
  				       umap1->table.n);
  	if (isl_hash_table_foreach(umap1->dim->ctx, &umap1->table,
  				   &match_bin_entry, &data) < 0)
  		goto error;
  
  	isl_union_map_free(umap1);
  	isl_union_map_free(umap2);
  	return data.res;
  error:
  	isl_union_map_free(umap1);
  	isl_union_map_free(umap2);
  	isl_union_map_free(data.res);
  	return NULL;
  }
  
  __isl_give isl_union_map *isl_union_map_intersect(
  	__isl_take isl_union_map *umap1, __isl_take isl_union_map *umap2)
  {
  	return match_bin_op(umap1, umap2, &isl_map_intersect);
  }
  
  /* Compute the intersection of the two union_sets.
   * As a special case, if exactly one of the two union_sets
   * is a parameter domain, then intersect the parameter domain
   * of the other one with this set.
   */
  __isl_give isl_union_set *isl_union_set_intersect(
  	__isl_take isl_union_set *uset1, __isl_take isl_union_set *uset2)
  {
  	int p1, p2;
  
  	p1 = isl_union_set_is_params(uset1);
  	p2 = isl_union_set_is_params(uset2);
  	if (p1 < 0 || p2 < 0)
  		goto error;
  	if (!p1 && p2)
  		return union_map_intersect_params(uset1, uset2);
  	if (p1 && !p2)
  		return union_map_intersect_params(uset2, uset1);
  	return isl_union_map_intersect(uset1, uset2);
  error:
  	isl_union_set_free(uset1);
  	isl_union_set_free(uset2);
  	return NULL;
  }
  
  static int gist_params_entry(void **entry, void *user)
  {
  	struct isl_union_map_gen_bin_set_data *data = user;
  	isl_map *map = *entry;
  	int empty;
  
  	map = isl_map_copy(map);
  	map = isl_map_gist_params(map, isl_set_copy(data->set));
  
  	empty = isl_map_is_empty(map);
  	if (empty < 0) {
  		isl_map_free(map);
  		return -1;
  	}
  
  	data->res = isl_union_map_add_map(data->res, map);
  
  	return 0;
  }
  
  __isl_give isl_union_map *isl_union_map_gist_params(
  	__isl_take isl_union_map *umap, __isl_take isl_set *set)
  {
  	return gen_bin_set_op(umap, set, &gist_params_entry);
  }
  
  __isl_give isl_union_set *isl_union_set_gist_params(
  	__isl_take isl_union_set *uset, __isl_take isl_set *set)
  {
  	return isl_union_map_gist_params(uset, set);
  }
  
  __isl_give isl_union_map *isl_union_map_gist(__isl_take isl_union_map *umap,
  	__isl_take isl_union_map *context)
  {
  	return match_bin_op(umap, context, &isl_map_gist);
  }
  
  __isl_give isl_union_set *isl_union_set_gist(__isl_take isl_union_set *uset,
  	__isl_take isl_union_set *context)
  {
  	if (isl_union_set_is_params(context))
  		return union_map_gist_params(uset, context);
  	return isl_union_map_gist(uset, context);
  }
  
  static __isl_give isl_map *lex_le_set(__isl_take isl_map *set1,
  	__isl_take isl_map *set2)
  {
  	return isl_set_lex_le_set((isl_set *)set1, (isl_set *)set2);
  }
  
  static __isl_give isl_map *lex_lt_set(__isl_take isl_map *set1,
  	__isl_take isl_map *set2)
  {
  	return isl_set_lex_lt_set((isl_set *)set1, (isl_set *)set2);
  }
  
  __isl_give isl_union_map *isl_union_set_lex_lt_union_set(
  	__isl_take isl_union_set *uset1, __isl_take isl_union_set *uset2)
  {
  	return match_bin_op(uset1, uset2, &lex_lt_set);
  }
  
  __isl_give isl_union_map *isl_union_set_lex_le_union_set(
  	__isl_take isl_union_set *uset1, __isl_take isl_union_set *uset2)
  {
  	return match_bin_op(uset1, uset2, &lex_le_set);
  }
  
  __isl_give isl_union_map *isl_union_set_lex_gt_union_set(
  	__isl_take isl_union_set *uset1, __isl_take isl_union_set *uset2)
  {
  	return isl_union_map_reverse(isl_union_set_lex_lt_union_set(uset2, uset1));
  }
  
  __isl_give isl_union_map *isl_union_set_lex_ge_union_set(
  	__isl_take isl_union_set *uset1, __isl_take isl_union_set *uset2)
  {
  	return isl_union_map_reverse(isl_union_set_lex_le_union_set(uset2, uset1));
  }
  
  __isl_give isl_union_map *isl_union_map_lex_gt_union_map(
  	__isl_take isl_union_map *umap1, __isl_take isl_union_map *umap2)
  {
  	return isl_union_map_reverse(isl_union_map_lex_lt_union_map(umap2, umap1));
  }
  
  __isl_give isl_union_map *isl_union_map_lex_ge_union_map(
  	__isl_take isl_union_map *umap1, __isl_take isl_union_map *umap2)
  {
  	return isl_union_map_reverse(isl_union_map_lex_le_union_map(umap2, umap1));
  }
  
  static int intersect_domain_entry(void **entry, void *user)
  {
  	struct isl_union_map_gen_bin_data *data = user;
  	uint32_t hash;
  	struct isl_hash_table_entry *entry2;
  	isl_space *dim;
  	isl_map *map = *entry;
  	int empty;
  
  	dim = isl_map_get_space(map);
  	dim = isl_space_domain(dim);
  	hash = isl_space_get_hash(dim);
  	entry2 = isl_hash_table_find(data->umap2->dim->ctx, &data->umap2->table,
  				     hash, &has_dim, dim, 0);
  	isl_space_free(dim);
  	if (!entry2)
  		return 0;
  
  	map = isl_map_copy(map);
  	map = isl_map_intersect_domain(map, isl_set_copy(entry2->data));
  
  	empty = isl_map_is_empty(map);
  	if (empty < 0) {
  		isl_map_free(map);
  		return -1;
  	}
  	if (empty) {
  		isl_map_free(map);
  		return 0;
  	}
  
  	data->res = isl_union_map_add_map(data->res, map);
  
  	return 0;
  }
  
  /* Intersect the domain of "umap" with "uset".
   * If "uset" is a parameters domain, then intersect the parameter
   * domain of "umap" with this set.
   */
  __isl_give isl_union_map *isl_union_map_intersect_domain(
  	__isl_take isl_union_map *umap, __isl_take isl_union_set *uset)
  {
  	if (isl_union_set_is_params(uset))
  		return union_map_intersect_params(umap, uset);
  	return gen_bin_op(umap, uset, &intersect_domain_entry);
  }
  
  /* Remove the elements of data->umap2 from the domain of *entry
   * and add the result to data->res.
   */
  static int subtract_domain_entry(void **entry, void *user)
  {
  	struct isl_union_map_gen_bin_data *data = user;
  	uint32_t hash;
  	struct isl_hash_table_entry *entry2;
  	isl_space *dim;
  	isl_map *map = *entry;
  	int empty;
  
  	dim = isl_map_get_space(map);
  	dim = isl_space_domain(dim);
  	hash = isl_space_get_hash(dim);
  	entry2 = isl_hash_table_find(data->umap2->dim->ctx, &data->umap2->table,
  				     hash, &has_dim, dim, 0);
  	isl_space_free(dim);
  
  	map = isl_map_copy(map);
  
  	if (!entry2) {
  		data->res = isl_union_map_add_map(data->res, map);
  		return 0;
  	}
  
  	map = isl_map_subtract_domain(map, isl_set_copy(entry2->data));
  
  	empty = isl_map_is_empty(map);
  	if (empty < 0) {
  		isl_map_free(map);
  		return -1;
  	}
  	if (empty) {
  		isl_map_free(map);
  		return 0;
  	}
  
  	data->res = isl_union_map_add_map(data->res, map);
  
  	return 0;
  }
  
  /* Remove the elements of "uset" from the domain of "umap".
   */
  __isl_give isl_union_map *isl_union_map_subtract_domain(
  	__isl_take isl_union_map *umap, __isl_take isl_union_set *dom)
  {
  	return gen_bin_op(umap, dom, &subtract_domain_entry);
  }
  
  /* Remove the elements of data->umap2 from the range of *entry
   * and add the result to data->res.
   */
  static int subtract_range_entry(void **entry, void *user)
  {
  	struct isl_union_map_gen_bin_data *data = user;
  	uint32_t hash;
  	struct isl_hash_table_entry *entry2;
  	isl_space *space;
  	isl_map *map = *entry;
  	int empty;
  
  	space = isl_map_get_space(map);
  	space = isl_space_range(space);
  	hash = isl_space_get_hash(space);
  	entry2 = isl_hash_table_find(data->umap2->dim->ctx, &data->umap2->table,
  				     hash, &has_dim, space, 0);
  	isl_space_free(space);
  
  	map = isl_map_copy(map);
  
  	if (!entry2) {
  		data->res = isl_union_map_add_map(data->res, map);
  		return 0;
  	}
  
  	map = isl_map_subtract_range(map, isl_set_copy(entry2->data));
  
  	empty = isl_map_is_empty(map);
  	if (empty < 0) {
  		isl_map_free(map);
  		return -1;
  	}
  	if (empty) {
  		isl_map_free(map);
  		return 0;
  	}
  
  	data->res = isl_union_map_add_map(data->res, map);
  
  	return 0;
  }
  
  /* Remove the elements of "uset" from the range of "umap".
   */
  __isl_give isl_union_map *isl_union_map_subtract_range(
  	__isl_take isl_union_map *umap, __isl_take isl_union_set *dom)
  {
  	return gen_bin_op(umap, dom, &subtract_range_entry);
  }
  
  static int gist_domain_entry(void **entry, void *user)
  {
  	struct isl_union_map_gen_bin_data *data = user;
  	uint32_t hash;
  	struct isl_hash_table_entry *entry2;
  	isl_space *dim;
  	isl_map *map = *entry;
  	int empty;
  
  	dim = isl_map_get_space(map);
  	dim = isl_space_domain(dim);
  	hash = isl_space_get_hash(dim);
  	entry2 = isl_hash_table_find(data->umap2->dim->ctx, &data->umap2->table,
  				     hash, &has_dim, dim, 0);
  	isl_space_free(dim);
  	if (!entry2)
  		return 0;
  
  	map = isl_map_copy(map);
  	map = isl_map_gist_domain(map, isl_set_copy(entry2->data));
  
  	empty = isl_map_is_empty(map);
  	if (empty < 0) {
  		isl_map_free(map);
  		return -1;
  	}
  
  	data->res = isl_union_map_add_map(data->res, map);
  
  	return 0;
  }
  
  /* Compute the gist of "umap" with respect to the domain "uset".
   * If "uset" is a parameters domain, then compute the gist
   * with respect to this parameter domain.
   */
  __isl_give isl_union_map *isl_union_map_gist_domain(
  	__isl_take isl_union_map *umap, __isl_take isl_union_set *uset)
  {
  	if (isl_union_set_is_params(uset))
  		return union_map_gist_params(umap, uset);
  	return gen_bin_op(umap, uset, &gist_domain_entry);
  }
  
  static int gist_range_entry(void **entry, void *user)
  {
  	struct isl_union_map_gen_bin_data *data = user;
  	uint32_t hash;
  	struct isl_hash_table_entry *entry2;
  	isl_space *space;
  	isl_map *map = *entry;
  	int empty;
  
  	space = isl_map_get_space(map);
  	space = isl_space_range(space);
  	hash = isl_space_get_hash(space);
  	entry2 = isl_hash_table_find(data->umap2->dim->ctx, &data->umap2->table,
  				     hash, &has_dim, space, 0);
  	isl_space_free(space);
  	if (!entry2)
  		return 0;
  
  	map = isl_map_copy(map);
  	map = isl_map_gist_range(map, isl_set_copy(entry2->data));
  
  	empty = isl_map_is_empty(map);
  	if (empty < 0) {
  		isl_map_free(map);
  		return -1;
  	}
  
  	data->res = isl_union_map_add_map(data->res, map);
  
  	return 0;
  }
  
  /* Compute the gist of "umap" with respect to the range "uset".
   */
  __isl_give isl_union_map *isl_union_map_gist_range(
  	__isl_take isl_union_map *umap, __isl_take isl_union_set *uset)
  {
  	return gen_bin_op(umap, uset, &gist_range_entry);
  }
  
  static int intersect_range_entry(void **entry, void *user)
  {
  	struct isl_union_map_gen_bin_data *data = user;
  	uint32_t hash;
  	struct isl_hash_table_entry *entry2;
  	isl_space *dim;
  	isl_map *map = *entry;
  	int empty;
  
  	dim = isl_map_get_space(map);
  	dim = isl_space_range(dim);
  	hash = isl_space_get_hash(dim);
  	entry2 = isl_hash_table_find(data->umap2->dim->ctx, &data->umap2->table,
  				     hash, &has_dim, dim, 0);
  	isl_space_free(dim);
  	if (!entry2)
  		return 0;
  
  	map = isl_map_copy(map);
  	map = isl_map_intersect_range(map, isl_set_copy(entry2->data));
  
  	empty = isl_map_is_empty(map);
  	if (empty < 0) {
  		isl_map_free(map);
  		return -1;
  	}
  	if (empty) {
  		isl_map_free(map);
  		return 0;
  	}
  
  	data->res = isl_union_map_add_map(data->res, map);
  
  	return 0;
  }
  
  __isl_give isl_union_map *isl_union_map_intersect_range(
  	__isl_take isl_union_map *umap, __isl_take isl_union_set *uset)
  {
  	return gen_bin_op(umap, uset, &intersect_range_entry);
  }
  
  struct isl_union_map_bin_data {
  	isl_union_map *umap2;
  	isl_union_map *res;
  	isl_map *map;
  	int (*fn)(void **entry, void *user);
  };
  
  static int apply_range_entry(void **entry, void *user)
  {
  	struct isl_union_map_bin_data *data = user;
  	isl_map *map2 = *entry;
  	int empty;
  
  	if (!isl_space_tuple_is_equal(data->map->dim, isl_dim_out,
  				 map2->dim, isl_dim_in))
  		return 0;
  
  	map2 = isl_map_apply_range(isl_map_copy(data->map), isl_map_copy(map2));
  
  	empty = isl_map_is_empty(map2);
  	if (empty < 0) {
  		isl_map_free(map2);
  		return -1;
  	}
  	if (empty) {
  		isl_map_free(map2);
  		return 0;
  	}
  
  	data->res = isl_union_map_add_map(data->res, map2);
  
  	return 0;
  }
  
  static int bin_entry(void **entry, void *user)
  {
  	struct isl_union_map_bin_data *data = user;
  	isl_map *map = *entry;
  
  	data->map = map;
  	if (isl_hash_table_foreach(data->umap2->dim->ctx, &data->umap2->table,
  				   data->fn, data) < 0)
  		return -1;
  
  	return 0;
  }
  
  static __isl_give isl_union_map *bin_op(__isl_take isl_union_map *umap1,
  	__isl_take isl_union_map *umap2, int (*fn)(void **entry, void *user))
  {
  	struct isl_union_map_bin_data data = { NULL, NULL, NULL, fn };
  
  	umap1 = isl_union_map_align_params(umap1, isl_union_map_get_space(umap2));
  	umap2 = isl_union_map_align_params(umap2, isl_union_map_get_space(umap1));
  
  	if (!umap1 || !umap2)
  		goto error;
  
  	data.umap2 = umap2;
  	data.res = isl_union_map_alloc(isl_space_copy(umap1->dim),
  				       umap1->table.n);
  	if (isl_hash_table_foreach(umap1->dim->ctx, &umap1->table,
  				   &bin_entry, &data) < 0)
  		goto error;
  
  	isl_union_map_free(umap1);
  	isl_union_map_free(umap2);
  	return data.res;
  error:
  	isl_union_map_free(umap1);
  	isl_union_map_free(umap2);
  	isl_union_map_free(data.res);
  	return NULL;
  }
  
  __isl_give isl_union_map *isl_union_map_apply_range(
  	__isl_take isl_union_map *umap1, __isl_take isl_union_map *umap2)
  {
  	return bin_op(umap1, umap2, &apply_range_entry);
  }
  
  __isl_give isl_union_map *isl_union_map_apply_domain(
  	__isl_take isl_union_map *umap1, __isl_take isl_union_map *umap2)
  {
  	umap1 = isl_union_map_reverse(umap1);
  	umap1 = isl_union_map_apply_range(umap1, umap2);
  	return isl_union_map_reverse(umap1);
  }
  
  __isl_give isl_union_set *isl_union_set_apply(
  	__isl_take isl_union_set *uset, __isl_take isl_union_map *umap)
  {
  	return isl_union_map_apply_range(uset, umap);
  }
  
  static int map_lex_lt_entry(void **entry, void *user)
  {
  	struct isl_union_map_bin_data *data = user;
  	isl_map *map2 = *entry;
  
  	if (!isl_space_tuple_is_equal(data->map->dim, isl_dim_out,
  				 map2->dim, isl_dim_out))
  		return 0;
  
  	map2 = isl_map_lex_lt_map(isl_map_copy(data->map), isl_map_copy(map2));
  
  	data->res = isl_union_map_add_map(data->res, map2);
  
  	return 0;
  }
  
  __isl_give isl_union_map *isl_union_map_lex_lt_union_map(
  	__isl_take isl_union_map *umap1, __isl_take isl_union_map *umap2)
  {
  	return bin_op(umap1, umap2, &map_lex_lt_entry);
  }
  
  static int map_lex_le_entry(void **entry, void *user)
  {
  	struct isl_union_map_bin_data *data = user;
  	isl_map *map2 = *entry;
  
  	if (!isl_space_tuple_is_equal(data->map->dim, isl_dim_out,
  				 map2->dim, isl_dim_out))
  		return 0;
  
  	map2 = isl_map_lex_le_map(isl_map_copy(data->map), isl_map_copy(map2));
  
  	data->res = isl_union_map_add_map(data->res, map2);
  
  	return 0;
  }
  
  __isl_give isl_union_map *isl_union_map_lex_le_union_map(
  	__isl_take isl_union_map *umap1, __isl_take isl_union_map *umap2)
  {
  	return bin_op(umap1, umap2, &map_lex_le_entry);
  }
  
  static int product_entry(void **entry, void *user)
  {
  	struct isl_union_map_bin_data *data = user;
  	isl_map *map2 = *entry;
  
  	map2 = isl_map_product(isl_map_copy(data->map), isl_map_copy(map2));
  
  	data->res = isl_union_map_add_map(data->res, map2);
  
  	return 0;
  }
  
  __isl_give isl_union_map *isl_union_map_product(__isl_take isl_union_map *umap1,
  	__isl_take isl_union_map *umap2)
  {
  	return bin_op(umap1, umap2, &product_entry);
  }
  
  static int set_product_entry(void **entry, void *user)
  {
  	struct isl_union_map_bin_data *data = user;
  	isl_set *set2 = *entry;
  
  	set2 = isl_set_product(isl_set_copy(data->map), isl_set_copy(set2));
  
  	data->res = isl_union_set_add_set(data->res, set2);
  
  	return 0;
  }
  
  __isl_give isl_union_set *isl_union_set_product(__isl_take isl_union_set *uset1,
  	__isl_take isl_union_set *uset2)
  {
  	return bin_op(uset1, uset2, &set_product_entry);
  }
  
  static int domain_product_entry(void **entry, void *user)
  {
  	struct isl_union_map_bin_data *data = user;
  	isl_map *map2 = *entry;
  
  	if (!isl_space_tuple_is_equal(data->map->dim, isl_dim_out,
  				 map2->dim, isl_dim_out))
  		return 0;
  
  	map2 = isl_map_domain_product(isl_map_copy(data->map),
  				     isl_map_copy(map2));
  
  	data->res = isl_union_map_add_map(data->res, map2);
  
  	return 0;
  }
  
  /* Given two maps A -> B and C -> D, construct a map [A -> C] -> (B * D)
   */
  __isl_give isl_union_map *isl_union_map_domain_product(
  	__isl_take isl_union_map *umap1, __isl_take isl_union_map *umap2)
  {
  	return bin_op(umap1, umap2, &domain_product_entry);
  }
  
  static int range_product_entry(void **entry, void *user)
  {
  	struct isl_union_map_bin_data *data = user;
  	isl_map *map2 = *entry;
  
  	if (!isl_space_tuple_is_equal(data->map->dim, isl_dim_in,
  				 map2->dim, isl_dim_in))
  		return 0;
  
  	map2 = isl_map_range_product(isl_map_copy(data->map),
  				     isl_map_copy(map2));
  
  	data->res = isl_union_map_add_map(data->res, map2);
  
  	return 0;
  }
  
  __isl_give isl_union_map *isl_union_map_range_product(
  	__isl_take isl_union_map *umap1, __isl_take isl_union_map *umap2)
  {
  	return bin_op(umap1, umap2, &range_product_entry);
  }
  
  /* If data->map A -> B and "map2" C -> D have the same range space,
   * then add (A, C) -> (B * D) to data->res.
   */
  static int flat_domain_product_entry(void **entry, void *user)
  {
  	struct isl_union_map_bin_data *data = user;
  	isl_map *map2 = *entry;
  
  	if (!isl_space_tuple_is_equal(data->map->dim, isl_dim_out,
  				 map2->dim, isl_dim_out))
  		return 0;
  
  	map2 = isl_map_flat_domain_product(isl_map_copy(data->map),
  					  isl_map_copy(map2));
  
  	data->res = isl_union_map_add_map(data->res, map2);
  
  	return 0;
  }
  
  /* Given two maps A -> B and C -> D, construct a map (A, C) -> (B * D).
   */
  __isl_give isl_union_map *isl_union_map_flat_domain_product(
  	__isl_take isl_union_map *umap1, __isl_take isl_union_map *umap2)
  {
  	return bin_op(umap1, umap2, &flat_domain_product_entry);
  }
  
  static int flat_range_product_entry(void **entry, void *user)
  {
  	struct isl_union_map_bin_data *data = user;
  	isl_map *map2 = *entry;
  
  	if (!isl_space_tuple_is_equal(data->map->dim, isl_dim_in,
  				 map2->dim, isl_dim_in))
  		return 0;
  
  	map2 = isl_map_flat_range_product(isl_map_copy(data->map),
  					  isl_map_copy(map2));
  
  	data->res = isl_union_map_add_map(data->res, map2);
  
  	return 0;
  }
  
  __isl_give isl_union_map *isl_union_map_flat_range_product(
  	__isl_take isl_union_map *umap1, __isl_take isl_union_map *umap2)
  {
  	return bin_op(umap1, umap2, &flat_range_product_entry);
  }
  
  static __isl_give isl_union_set *cond_un_op(__isl_take isl_union_map *umap,
  	int (*fn)(void **, void *))
  {
  	isl_union_set *res;
  
  	if (!umap)
  		return NULL;
  
  	res = isl_union_map_alloc(isl_space_copy(umap->dim), umap->table.n);
  	if (isl_hash_table_foreach(umap->dim->ctx, &umap->table, fn, &res) < 0)
  		goto error;
  
  	isl_union_map_free(umap);
  	return res;
  error:
  	isl_union_map_free(umap);
  	isl_union_set_free(res);
  	return NULL;
  }
  
  static int from_range_entry(void **entry, void *user)
  {
  	isl_map *set = *entry;
  	isl_union_set **res = user;
  
  	*res = isl_union_map_add_map(*res,
  					isl_map_from_range(isl_set_copy(set)));
  
  	return 0;
  }
  
  __isl_give isl_union_map *isl_union_map_from_range(
  	__isl_take isl_union_set *uset)
  {
  	return cond_un_op(uset, &from_range_entry);
  }
  
  __isl_give isl_union_map *isl_union_map_from_domain(
  	__isl_take isl_union_set *uset)
  {
  	return isl_union_map_reverse(isl_union_map_from_range(uset));
  }
  
  __isl_give isl_union_map *isl_union_map_from_domain_and_range(
  	__isl_take isl_union_set *domain, __isl_take isl_union_set *range)
  {
  	return isl_union_map_apply_range(isl_union_map_from_domain(domain),
  				         isl_union_map_from_range(range));
  }
  
  static __isl_give isl_union_map *un_op(__isl_take isl_union_map *umap,
  	int (*fn)(void **, void *))
  {
  	umap = isl_union_map_cow(umap);
  	if (!umap)
  		return NULL;
  
  	if (isl_hash_table_foreach(umap->dim->ctx, &umap->table, fn, NULL) < 0)
  		goto error;
  
  	return umap;
  error:
  	isl_union_map_free(umap);
  	return NULL;
  }
  
  static int affine_entry(void **entry, void *user)
  {
  	isl_map **map = (isl_map **)entry;
  
  	*map = isl_map_from_basic_map(isl_map_affine_hull(*map));
  
  	return *map ? 0 : -1;
  }
  
  __isl_give isl_union_map *isl_union_map_affine_hull(
  	__isl_take isl_union_map *umap)
  {
  	return un_op(umap, &affine_entry);
  }
  
  __isl_give isl_union_set *isl_union_set_affine_hull(
  	__isl_take isl_union_set *uset)
  {
  	return isl_union_map_affine_hull(uset);
  }
  
  static int polyhedral_entry(void **entry, void *user)
  {
  	isl_map **map = (isl_map **)entry;
  
  	*map = isl_map_from_basic_map(isl_map_polyhedral_hull(*map));
  
  	return *map ? 0 : -1;
  }
  
  __isl_give isl_union_map *isl_union_map_polyhedral_hull(
  	__isl_take isl_union_map *umap)
  {
  	return un_op(umap, &polyhedral_entry);
  }
  
  __isl_give isl_union_set *isl_union_set_polyhedral_hull(
  	__isl_take isl_union_set *uset)
  {
  	return isl_union_map_polyhedral_hull(uset);
  }
  
  static int simple_entry(void **entry, void *user)
  {
  	isl_map **map = (isl_map **)entry;
  
  	*map = isl_map_from_basic_map(isl_map_simple_hull(*map));
  
  	return *map ? 0 : -1;
  }
  
  __isl_give isl_union_map *isl_union_map_simple_hull(
  	__isl_take isl_union_map *umap)
  {
  	return un_op(umap, &simple_entry);
  }
  
  __isl_give isl_union_set *isl_union_set_simple_hull(
  	__isl_take isl_union_set *uset)
  {
  	return isl_union_map_simple_hull(uset);
  }
  
  static int inplace_entry(void **entry, void *user)
  {
  	__isl_give isl_map *(*fn)(__isl_take isl_map *);
  	isl_map **map = (isl_map **)entry;
  	isl_map *copy;
  
  	fn = *(__isl_give isl_map *(**)(__isl_take isl_map *)) user;
  	copy = fn(isl_map_copy(*map));
  	if (!copy)
  		return -1;
  
  	isl_map_free(*map);
  	*map = copy;
  
  	return 0;
  }
  
  static __isl_give isl_union_map *inplace(__isl_take isl_union_map *umap,
  	__isl_give isl_map *(*fn)(__isl_take isl_map *))
  {
  	if (!umap)
  		return NULL;
  
  	if (isl_hash_table_foreach(umap->dim->ctx, &umap->table,
  				    &inplace_entry, &fn) < 0)
  		goto error;
  
  	return umap;
  error:
  	isl_union_map_free(umap);
  	return NULL;
  }
  
  /* Remove redundant constraints in each of the basic maps of "umap".
   * Since removing redundant constraints does not change the meaning
   * or the space, the operation can be performed in-place.
   */
  __isl_give isl_union_map *isl_union_map_remove_redundancies(
  	__isl_take isl_union_map *umap)
  {
  	return inplace(umap, &isl_map_remove_redundancies);
  }
  
  /* Remove redundant constraints in each of the basic sets of "uset".
   */
  __isl_give isl_union_set *isl_union_set_remove_redundancies(
  	__isl_take isl_union_set *uset)
  {
  	return isl_union_map_remove_redundancies(uset);
  }
  
  __isl_give isl_union_map *isl_union_map_coalesce(
  	__isl_take isl_union_map *umap)
  {
  	return inplace(umap, &isl_map_coalesce);
  }
  
  __isl_give isl_union_set *isl_union_set_coalesce(
  	__isl_take isl_union_set *uset)
  {
  	return isl_union_map_coalesce(uset);
  }
  
  __isl_give isl_union_map *isl_union_map_detect_equalities(
  	__isl_take isl_union_map *umap)
  {
  	return inplace(umap, &isl_map_detect_equalities);
  }
  
  __isl_give isl_union_set *isl_union_set_detect_equalities(
  	__isl_take isl_union_set *uset)
  {
  	return isl_union_map_detect_equalities(uset);
  }
  
  __isl_give isl_union_map *isl_union_map_compute_divs(
  	__isl_take isl_union_map *umap)
  {
  	return inplace(umap, &isl_map_compute_divs);
  }
  
  __isl_give isl_union_set *isl_union_set_compute_divs(
  	__isl_take isl_union_set *uset)
  {
  	return isl_union_map_compute_divs(uset);
  }
  
  static int lexmin_entry(void **entry, void *user)
  {
  	isl_map **map = (isl_map **)entry;
  
  	*map = isl_map_lexmin(*map);
  
  	return *map ? 0 : -1;
  }
  
  __isl_give isl_union_map *isl_union_map_lexmin(
  	__isl_take isl_union_map *umap)
  {
  	return un_op(umap, &lexmin_entry);
  }
  
  __isl_give isl_union_set *isl_union_set_lexmin(
  	__isl_take isl_union_set *uset)
  {
  	return isl_union_map_lexmin(uset);
  }
  
  static int lexmax_entry(void **entry, void *user)
  {
  	isl_map **map = (isl_map **)entry;
  
  	*map = isl_map_lexmax(*map);
  
  	return *map ? 0 : -1;
  }
  
  __isl_give isl_union_map *isl_union_map_lexmax(
  	__isl_take isl_union_map *umap)
  {
  	return un_op(umap, &lexmax_entry);
  }
  
  __isl_give isl_union_set *isl_union_set_lexmax(
  	__isl_take isl_union_set *uset)
  {
  	return isl_union_map_lexmax(uset);
  }
  
  static int universe_entry(void **entry, void *user)
  {
  	isl_map *map = *entry;
  	isl_union_map **res = user;
  
  	map = isl_map_universe(isl_map_get_space(map));
  	*res = isl_union_map_add_map(*res, map);
  
  	return 0;
  }
  
  __isl_give isl_union_map *isl_union_map_universe(__isl_take isl_union_map *umap)
  {
  	return cond_un_op(umap, &universe_entry);
  }
  
  __isl_give isl_union_set *isl_union_set_universe(__isl_take isl_union_set *uset)
  {
  	return isl_union_map_universe(uset);
  }
  
  static int reverse_entry(void **entry, void *user)
  {
  	isl_map *map = *entry;
  	isl_union_map **res = user;
  
  	*res = isl_union_map_add_map(*res, isl_map_reverse(isl_map_copy(map)));
  
  	return 0;
  }
  
  __isl_give isl_union_map *isl_union_map_reverse(__isl_take isl_union_map *umap)
  {
  	return cond_un_op(umap, &reverse_entry);
  }
  
  static int params_entry(void **entry, void *user)
  {
  	isl_map *map = *entry;
  	isl_union_set **res = user;
  
  	*res = isl_union_set_add_set(*res, isl_map_params(isl_map_copy(map)));
  
  	return 0;
  }
  
  /* Compute the parameter domain of the given union map.
   */
  __isl_give isl_set *isl_union_map_params(__isl_take isl_union_map *umap)
  {
  	int empty;
  
  	empty = isl_union_map_is_empty(umap);
  	if (empty < 0)
  		goto error;
  	if (empty) {
  		isl_space *space;
  		space = isl_union_map_get_space(umap);
  		isl_union_map_free(umap);
  		return isl_set_empty(space);
  	}
  	return isl_set_from_union_set(cond_un_op(umap, &params_entry));
  error:
  	isl_union_map_free(umap);
  	return NULL;
  }
  
  /* Compute the parameter domain of the given union set.
   */
  __isl_give isl_set *isl_union_set_params(__isl_take isl_union_set *uset)
  {
  	return isl_union_map_params(uset);
  }
  
  static int domain_entry(void **entry, void *user)
  {
  	isl_map *map = *entry;
  	isl_union_set **res = user;
  
  	*res = isl_union_set_add_set(*res, isl_map_domain(isl_map_copy(map)));
  
  	return 0;
  }
  
  __isl_give isl_union_set *isl_union_map_domain(__isl_take isl_union_map *umap)
  {
  	return cond_un_op(umap, &domain_entry);
  }
  
  static int range_entry(void **entry, void *user)
  {
  	isl_map *map = *entry;
  	isl_union_set **res = user;
  
  	*res = isl_union_set_add_set(*res, isl_map_range(isl_map_copy(map)));
  
  	return 0;
  }
  
  __isl_give isl_union_set *isl_union_map_range(__isl_take isl_union_map *umap)
  {
  	return cond_un_op(umap, &range_entry);
  }
  
  static int domain_map_entry(void **entry, void *user)
  {
  	isl_map *map = *entry;
  	isl_union_set **res = user;
  
  	*res = isl_union_map_add_map(*res,
  					isl_map_domain_map(isl_map_copy(map)));
  
  	return 0;
  }
  
  __isl_give isl_union_map *isl_union_map_domain_map(
  	__isl_take isl_union_map *umap)
  {
  	return cond_un_op(umap, &domain_map_entry);
  }
  
  /* Construct an isl_pw_multi_aff that maps "map" to its domain and
   * add the result to "res".
   */
  static int domain_map_upma(__isl_take isl_map *map, void *user)
  {
  	isl_union_pw_multi_aff **res = user;
  	isl_multi_aff *ma;
  	isl_pw_multi_aff *pma;
  
  	ma = isl_multi_aff_domain_map(isl_map_get_space(map));
  	pma = isl_pw_multi_aff_alloc(isl_map_wrap(map), ma);
  	*res = isl_union_pw_multi_aff_add_pw_multi_aff(*res, pma);
  
  	return *res ? 0 : -1;
  
  }
  
  /* Return an isl_union_pw_multi_aff that maps a wrapped copy of "umap"
   * to its domain.
   */
  __isl_give isl_union_pw_multi_aff *isl_union_map_domain_map_union_pw_multi_aff(
  	__isl_take isl_union_map *umap)
  {
  	isl_union_pw_multi_aff *res;
  
  	res = isl_union_pw_multi_aff_empty(isl_union_map_get_space(umap));
  	if (isl_union_map_foreach_map(umap, &domain_map_upma, &res) < 0)
  		res = isl_union_pw_multi_aff_free(res);
  
  	isl_union_map_free(umap);
  	return res;
  }
  
  static int range_map_entry(void **entry, void *user)
  {
  	isl_map *map = *entry;
  	isl_union_set **res = user;
  
  	*res = isl_union_map_add_map(*res,
  					isl_map_range_map(isl_map_copy(map)));
  
  	return 0;
  }
  
  __isl_give isl_union_map *isl_union_map_range_map(
  	__isl_take isl_union_map *umap)
  {
  	return cond_un_op(umap, &range_map_entry);
  }
  
  /* Check if "set" is of the form A[B -> C].
   * If so, add A[B -> C] -> B to "res".
   */
  static int wrapped_domain_map_entry(void **entry, void *user)
  {
  	isl_set *set = *entry;
  	isl_union_set **res = user;
  	int wrapping;
  
  	wrapping = isl_set_is_wrapping(set);
  	if (wrapping < 0)
  		return -1;
  	if (!wrapping)
  		return 0;
  
  	*res = isl_union_map_add_map(*res,
  				isl_set_wrapped_domain_map(isl_set_copy(set)));
  
  	return 0;
  }
  
  /* Given a collection of wrapped maps of the form A[B -> C],
   * return the collection of maps A[B -> C] -> B.
   */
  __isl_give isl_union_map *isl_union_set_wrapped_domain_map(
  	__isl_take isl_union_set *uset)
  {
  	return cond_un_op(uset, &wrapped_domain_map_entry);
  }
  
  static int deltas_entry(void **entry, void *user)
  {
  	isl_map *map = *entry;
  	isl_union_set **res = user;
  
  	if (!isl_space_tuple_is_equal(map->dim, isl_dim_in,
  					map->dim, isl_dim_out))
  		return 0;
  
  	*res = isl_union_set_add_set(*res, isl_map_deltas(isl_map_copy(map)));
  
  	return 0;
  }
  
  __isl_give isl_union_set *isl_union_map_deltas(__isl_take isl_union_map *umap)
  {
  	return cond_un_op(umap, &deltas_entry);
  }
  
  static int deltas_map_entry(void **entry, void *user)
  {
  	isl_map *map = *entry;
  	isl_union_map **res = user;
  
  	if (!isl_space_tuple_is_equal(map->dim, isl_dim_in,
  					map->dim, isl_dim_out))
  		return 0;
  
  	*res = isl_union_map_add_map(*res,
  				     isl_map_deltas_map(isl_map_copy(map)));
  
  	return 0;
  }
  
  __isl_give isl_union_map *isl_union_map_deltas_map(
  	__isl_take isl_union_map *umap)
  {
  	return cond_un_op(umap, &deltas_map_entry);
  }
  
  static int identity_entry(void **entry, void *user)
  {
  	isl_set *set = *entry;
  	isl_union_map **res = user;
  
  	*res = isl_union_map_add_map(*res, isl_set_identity(isl_set_copy(set)));
  
  	return 0;
  }
  
  __isl_give isl_union_map *isl_union_set_identity(__isl_take isl_union_set *uset)
  {
  	return cond_un_op(uset, &identity_entry);
  }
  
  /* Construct an identity isl_pw_multi_aff on "set" and add it to *res.
   */
  static int identity_upma(__isl_take isl_set *set, void *user)
  {
  	isl_union_pw_multi_aff **res = user;
  	isl_space *space;
  	isl_pw_multi_aff *pma;
  
  	space = isl_space_map_from_set(isl_set_get_space(set));
  	pma = isl_pw_multi_aff_identity(space);
  	pma = isl_pw_multi_aff_intersect_domain(pma, set);
  	*res = isl_union_pw_multi_aff_add_pw_multi_aff(*res, pma);
  
  	return *res ? 0 : -1;
  }
  
  /* Return an identity function on "uset" in the form
   * of an isl_union_pw_multi_aff.
   */
  __isl_give isl_union_pw_multi_aff *isl_union_set_identity_union_pw_multi_aff(
  	__isl_take isl_union_set *uset)
  {
  	isl_union_pw_multi_aff *res;
  
  	res = isl_union_pw_multi_aff_empty(isl_union_set_get_space(uset));
  	if (isl_union_set_foreach_set(uset, &identity_upma, &res) < 0)
  		res = isl_union_pw_multi_aff_free(res);
  
  	isl_union_set_free(uset);
  	return res;
  }
  
  /* If "map" is of the form [A -> B] -> C, then add A -> C to "res".
   */
  static int domain_factor_domain_entry(void **entry, void *user)
  {
  	isl_map *map = *entry;
  	isl_union_map **res = user;
  
  	if (!isl_map_domain_is_wrapping(map))
  		return 0;
  
  	*res = isl_union_map_add_map(*res,
  			    isl_map_domain_factor_domain(isl_map_copy(map)));
  
  	return *res ? 0 : -1;
  }
  
  /* For each map in "umap" of the form [A -> B] -> C,
   * construct the map A -> C and collect the results.
   */
  __isl_give isl_union_map *isl_union_map_domain_factor_domain(
  	__isl_take isl_union_map *umap)
  {
  	return cond_un_op(umap, &domain_factor_domain_entry);
  }
  
  /* If "map" is of the form [A -> B] -> C, then add B -> C to "res".
   */
  static int domain_factor_range_entry(void **entry, void *user)
  {
  	isl_map *map = *entry;
  	isl_union_map **res = user;
  
  	if (!isl_map_domain_is_wrapping(map))
  		return 0;
  
  	*res = isl_union_map_add_map(*res,
  				isl_map_domain_factor_range(isl_map_copy(map)));
  
  	return *res ? 0 : -1;
  }
  
  /* For each map in "umap" of the form [A -> B] -> C,
   * construct the map B -> C and collect the results.
   */
  __isl_give isl_union_map *isl_union_map_domain_factor_range(
  	__isl_take isl_union_map *umap)
  {
  	return cond_un_op(umap, &domain_factor_range_entry);
  }
  
  /* If "map" is of the form A -> [B -> C], then add A -> C to "res".
   */
  static int range_factor_range_entry(void **entry, void *user)
  {
  	isl_map *map = *entry;
  	isl_union_map **res = user;
  
  	if (!isl_map_range_is_wrapping(map))
  		return 0;
  
  	*res = isl_union_map_add_map(*res,
  				isl_map_range_factor_range(isl_map_copy(map)));
  
  	return *res ? 0 : -1;
  }
  
  /* For each map in "umap" of the form A -> [B -> C],
   * construct the map A -> C and collect the results.
   */
  __isl_give isl_union_map *isl_union_map_range_factor_range(
  	__isl_take isl_union_map *umap)
  {
  	return cond_un_op(umap, &range_factor_range_entry);
  }
  
  /* If "map" is of the form [A -> B] -> [C -> D], then add A -> C to "res".
   */
  static int factor_domain_entry(void **entry, void *user)
  {
  	isl_map *map = *entry;
  	isl_union_map **res = user;
  
  	if (!isl_map_domain_is_wrapping(map) || !isl_map_range_is_wrapping(map))
  		return 0;
  
  	*res = isl_union_map_add_map(*res,
  				isl_map_factor_domain(isl_map_copy(map)));
  
  	return *res ? 0 : -1;
  }
  
  /* For each map in "umap" of the form [A -> B] -> [C -> D],
   * construct the map A -> C and collect the results.
   */
  __isl_give isl_union_map *isl_union_map_factor_domain(
  	__isl_take isl_union_map *umap)
  {
  	return cond_un_op(umap, &factor_domain_entry);
  }
  
  /* If "map" is of the form [A -> B] -> [C -> D], then add B -> D to "res".
   */
  static int factor_range_entry(void **entry, void *user)
  {
  	isl_map *map = *entry;
  	isl_union_map **res = user;
  
  	if (!isl_map_domain_is_wrapping(map) || !isl_map_range_is_wrapping(map))
  		return 0;
  
  	*res = isl_union_map_add_map(*res,
  				isl_map_factor_range(isl_map_copy(map)));
  
  	return *res ? 0 : -1;
  }
  
  /* For each map in "umap" of the form [A -> B] -> [C -> D],
   * construct the map B -> D and collect the results.
   */
  __isl_give isl_union_map *isl_union_map_factor_range(
  	__isl_take isl_union_map *umap)
  {
  	return cond_un_op(umap, &factor_range_entry);
  }
  
  static int unwrap_entry(void **entry, void *user)
  {
  	isl_set *set = *entry;
  	isl_union_set **res = user;
  
  	if (!isl_set_is_wrapping(set))
  		return 0;
  
  	*res = isl_union_map_add_map(*res, isl_set_unwrap(isl_set_copy(set)));
  
  	return 0;
  }
  
  __isl_give isl_union_map *isl_union_set_unwrap(__isl_take isl_union_set *uset)
  {
  	return cond_un_op(uset, &unwrap_entry);
  }
  
  static int wrap_entry(void **entry, void *user)
  {
  	isl_map *map = *entry;
  	isl_union_set **res = user;
  
  	*res = isl_union_set_add_set(*res, isl_map_wrap(isl_map_copy(map)));
  
  	return 0;
  }
  
  __isl_give isl_union_set *isl_union_map_wrap(__isl_take isl_union_map *umap)
  {
  	return cond_un_op(umap, &wrap_entry);
  }
  
  struct isl_union_map_is_subset_data {
  	isl_union_map *umap2;
  	int is_subset;
  };
  
  static int is_subset_entry(void **entry, void *user)
  {
  	struct isl_union_map_is_subset_data *data = user;
  	uint32_t hash;
  	struct isl_hash_table_entry *entry2;
  	isl_map *map = *entry;
  
  	hash = isl_space_get_hash(map->dim);
  	entry2 = isl_hash_table_find(data->umap2->dim->ctx, &data->umap2->table,
  				     hash, &has_dim, map->dim, 0);
  	if (!entry2) {
  		int empty = isl_map_is_empty(map);
  		if (empty < 0)
  			return -1;
  		if (empty)
  			return 0;
  		data->is_subset = 0;
  		return -1;
  	}
  
  	data->is_subset = isl_map_is_subset(map, entry2->data);
  	if (data->is_subset < 0 || !data->is_subset)
  		return -1;
  
  	return 0;
  }
  
  int isl_union_map_is_subset(__isl_keep isl_union_map *umap1,
  	__isl_keep isl_union_map *umap2)
  {
  	struct isl_union_map_is_subset_data data = { NULL, 1 };
  
  	umap1 = isl_union_map_copy(umap1);
  	umap2 = isl_union_map_copy(umap2);
  	umap1 = isl_union_map_align_params(umap1, isl_union_map_get_space(umap2));
  	umap2 = isl_union_map_align_params(umap2, isl_union_map_get_space(umap1));
  
  	if (!umap1 || !umap2)
  		goto error;
  
  	data.umap2 = umap2;
  	if (isl_hash_table_foreach(umap1->dim->ctx, &umap1->table,
  				   &is_subset_entry, &data) < 0 &&
  	    data.is_subset)
  		goto error;
  
  	isl_union_map_free(umap1);
  	isl_union_map_free(umap2);
  
  	return data.is_subset;
  error:
  	isl_union_map_free(umap1);
  	isl_union_map_free(umap2);
  	return -1;
  }
  
  int isl_union_set_is_subset(__isl_keep isl_union_set *uset1,
  	__isl_keep isl_union_set *uset2)
  {
  	return isl_union_map_is_subset(uset1, uset2);
  }
  
  int isl_union_map_is_equal(__isl_keep isl_union_map *umap1,
  	__isl_keep isl_union_map *umap2)
  {
  	int is_subset;
  
  	if (!umap1 || !umap2)
  		return -1;
  	is_subset = isl_union_map_is_subset(umap1, umap2);
  	if (is_subset != 1)
  		return is_subset;
  	is_subset = isl_union_map_is_subset(umap2, umap1);
  	return is_subset;
  }
  
  int isl_union_set_is_equal(__isl_keep isl_union_set *uset1,
  	__isl_keep isl_union_set *uset2)
  {
  	return isl_union_map_is_equal(uset1, uset2);
  }
  
  int isl_union_map_is_strict_subset(__isl_keep isl_union_map *umap1,
  	__isl_keep isl_union_map *umap2)
  {
  	int is_subset;
  
  	if (!umap1 || !umap2)
  		return -1;
  	is_subset = isl_union_map_is_subset(umap1, umap2);
  	if (is_subset != 1)
  		return is_subset;
  	is_subset = isl_union_map_is_subset(umap2, umap1);
  	if (is_subset == -1)
  		return is_subset;
  	return !is_subset;
  }
  
  int isl_union_set_is_strict_subset(__isl_keep isl_union_set *uset1,
  	__isl_keep isl_union_set *uset2)
  {
  	return isl_union_map_is_strict_subset(uset1, uset2);
  }
  
  /* Internal data structure for isl_union_map_is_disjoint.
   * umap2 is the union map with which we are comparing.
   * is_disjoint is initialized to 1 and is set to 0 as soon
   * as the union maps turn out not to be disjoint.
   */
  struct isl_union_map_is_disjoint_data {
  	isl_union_map *umap2;
  	int is_disjoint;
  };
  
  /* Check if "map" is disjoint from data->umap2 and abort
   * the search if it is not.
   */
  static int is_disjoint_entry(void **entry, void *user)
  {
  	struct isl_union_map_is_disjoint_data *data = user;
  	uint32_t hash;
  	struct isl_hash_table_entry *entry2;
  	isl_map *map = *entry;
  
  	hash = isl_space_get_hash(map->dim);
  	entry2 = isl_hash_table_find(data->umap2->dim->ctx, &data->umap2->table,
  				     hash, &has_dim, map->dim, 0);
  	if (!entry2)
  		return 0;
  
  	data->is_disjoint = isl_map_is_disjoint(map, entry2->data);
  	if (data->is_disjoint < 0 || !data->is_disjoint)
  		return -1;
  
  	return 0;
  }
  
  /* Are "umap1" and "umap2" disjoint?
   */
  int isl_union_map_is_disjoint(__isl_keep isl_union_map *umap1,
  	__isl_keep isl_union_map *umap2)
  {
  	struct isl_union_map_is_disjoint_data data = { NULL, 1 };
  
  	umap1 = isl_union_map_copy(umap1);
  	umap2 = isl_union_map_copy(umap2);
  	umap1 = isl_union_map_align_params(umap1,
  						isl_union_map_get_space(umap2));
  	umap2 = isl_union_map_align_params(umap2,
  						isl_union_map_get_space(umap1));
  
  	if (!umap1 || !umap2)
  		goto error;
  
  	data.umap2 = umap2;
  	if (isl_hash_table_foreach(umap1->dim->ctx, &umap1->table,
  				   &is_disjoint_entry, &data) < 0 &&
  	    data.is_disjoint)
  		goto error;
  
  	isl_union_map_free(umap1);
  	isl_union_map_free(umap2);
  
  	return data.is_disjoint;
  error:
  	isl_union_map_free(umap1);
  	isl_union_map_free(umap2);
  	return -1;
  }
  
  /* Are "uset1" and "uset2" disjoint?
   */
  int isl_union_set_is_disjoint(__isl_keep isl_union_set *uset1,
  	__isl_keep isl_union_set *uset2)
  {
  	return isl_union_map_is_disjoint(uset1, uset2);
  }
  
  static int sample_entry(void **entry, void *user)
  {
  	isl_basic_map **sample = (isl_basic_map **)user;
  	isl_map *map = *entry;
  
  	*sample = isl_map_sample(isl_map_copy(map));
  	if (!*sample)
  		return -1;
  	if (!isl_basic_map_plain_is_empty(*sample))
  		return -1;
  	return 0;
  }
  
  __isl_give isl_basic_map *isl_union_map_sample(__isl_take isl_union_map *umap)
  {
  	isl_basic_map *sample = NULL;
  
  	if (!umap)
  		return NULL;
  
  	if (isl_hash_table_foreach(umap->dim->ctx, &umap->table,
  				   &sample_entry, &sample) < 0 &&
  	    !sample)
  		goto error;
  
  	if (!sample)
  		sample = isl_basic_map_empty(isl_union_map_get_space(umap));
  
  	isl_union_map_free(umap);
  
  	return sample;
  error:
  	isl_union_map_free(umap);
  	return NULL;
  }
  
  __isl_give isl_basic_set *isl_union_set_sample(__isl_take isl_union_set *uset)
  {
  	return (isl_basic_set *)isl_union_map_sample(uset);
  }
  
  struct isl_forall_data {
  	int res;
  	int (*fn)(__isl_keep isl_map *map);
  };
  
  static int forall_entry(void **entry, void *user)
  {
  	struct isl_forall_data *data = user;
  	isl_map *map = *entry;
  
  	data->res = data->fn(map);
  	if (data->res < 0)
  		return -1;
  
  	if (!data->res)
  		return -1;
  
  	return 0;
  }
  
  static int union_map_forall(__isl_keep isl_union_map *umap,
  	int (*fn)(__isl_keep isl_map *map))
  {
  	struct isl_forall_data data = { 1, fn };
  
  	if (!umap)
  		return -1;
  
  	if (isl_hash_table_foreach(umap->dim->ctx, &umap->table,
  				   &forall_entry, &data) < 0 && data.res)
  		return -1;
  
  	return data.res;
  }
  
  struct isl_forall_user_data {
  	int res;
  	int (*fn)(__isl_keep isl_map *map, void *user);
  	void *user;
  };
  
  static int forall_user_entry(void **entry, void *user)
  {
  	struct isl_forall_user_data *data = user;
  	isl_map *map = *entry;
  
  	data->res = data->fn(map, data->user);
  	if (data->res < 0)
  		return -1;
  
  	if (!data->res)
  		return -1;
  
  	return 0;
  }
  
  /* Check if fn(map, user) returns true for all maps "map" in umap.
   */
  static int union_map_forall_user(__isl_keep isl_union_map *umap,
  	int (*fn)(__isl_keep isl_map *map, void *user), void *user)
  {
  	struct isl_forall_user_data data = { 1, fn, user };
  
  	if (!umap)
  		return -1;
  
  	if (isl_hash_table_foreach(umap->dim->ctx, &umap->table,
  				   &forall_user_entry, &data) < 0 && data.res)
  		return -1;
  
  	return data.res;
  }
  
  int isl_union_map_is_empty(__isl_keep isl_union_map *umap)
  {
  	return union_map_forall(umap, &isl_map_is_empty);
  }
  
  int isl_union_set_is_empty(__isl_keep isl_union_set *uset)
  {
  	return isl_union_map_is_empty(uset);
  }
  
  static int is_subset_of_identity(__isl_keep isl_map *map)
  {
  	int is_subset;
  	isl_space *dim;
  	isl_map *id;
  
  	if (!map)
  		return -1;
  
  	if (!isl_space_tuple_is_equal(map->dim, isl_dim_in,
  					map->dim, isl_dim_out))
  		return 0;
  
  	dim = isl_map_get_space(map);
  	id = isl_map_identity(dim);
  
  	is_subset = isl_map_is_subset(map, id);
  
  	isl_map_free(id);
  
  	return is_subset;
  }
  
  /* Given an isl_union_map that consists of a single map, check
   * if it is single-valued.
   */
  static int single_map_is_single_valued(__isl_keep isl_union_map *umap)
  {
  	isl_map *map;
  	int sv;
  
  	umap = isl_union_map_copy(umap);
  	map = isl_map_from_union_map(umap);
  	sv = isl_map_is_single_valued(map);
  	isl_map_free(map);
  
  	return sv;
  }
  
  /* Internal data structure for single_valued_on_domain.
   *
   * "umap" is the union map to be tested.
   * "sv" is set to 1 as long as "umap" may still be single-valued.
   */
  struct isl_union_map_is_sv_data {
  	isl_union_map *umap;
  	int sv;
  };
  
  /* Check if the data->umap is single-valued on "set".
   *
   * If data->umap consists of a single map on "set", then test it
   * as an isl_map.
   *
   * Otherwise, compute
   *
   *	M \circ M^-1
   *
   * check if the result is a subset of the identity mapping and
   * store the result in data->sv.
   *
   * Terminate as soon as data->umap has been determined not to
   * be single-valued.
   */
  static int single_valued_on_domain(__isl_take isl_set *set, void *user)
  {
  	struct isl_union_map_is_sv_data *data = user;
  	isl_union_map *umap, *test;
  
  	umap = isl_union_map_copy(data->umap);
  	umap = isl_union_map_intersect_domain(umap,
  						isl_union_set_from_set(set));
  
  	if (isl_union_map_n_map(umap) == 1) {
  		data->sv = single_map_is_single_valued(umap);
  		isl_union_map_free(umap);
  	} else {
  		test = isl_union_map_reverse(isl_union_map_copy(umap));
  		test = isl_union_map_apply_range(test, umap);
  
  		data->sv = union_map_forall(test, &is_subset_of_identity);
  
  		isl_union_map_free(test);
  	}
  
  	if (data->sv < 0 || !data->sv)
  		return -1;
  	return 0;
  }
  
  /* Check if the given map is single-valued.
   *
   * If the union map consists of a single map, then test it as an isl_map.
   * Otherwise, check if the union map is single-valued on each of its
   * domain spaces.
   */
  int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap)
  {
  	isl_union_map *universe;
  	isl_union_set *domain;
  	struct isl_union_map_is_sv_data data;
  
  	if (isl_union_map_n_map(umap) == 1)
  		return single_map_is_single_valued(umap);
  
  	universe = isl_union_map_universe(isl_union_map_copy(umap));
  	domain = isl_union_map_domain(universe);
  
  	data.sv = 1;
  	data.umap = umap;
  	if (isl_union_set_foreach_set(domain,
  			    &single_valued_on_domain, &data) < 0 && data.sv)
  		data.sv = -1;
  	isl_union_set_free(domain);
  
  	return data.sv;
  }
  
  int isl_union_map_is_injective(__isl_keep isl_union_map *umap)
  {
  	int in;
  
  	umap = isl_union_map_copy(umap);
  	umap = isl_union_map_reverse(umap);
  	in = isl_union_map_is_single_valued(umap);
  	isl_union_map_free(umap);
  
  	return in;
  }
  
  /* Represents a map that has a fixed value (v) for one of its
   * range dimensions.
   * The map in this structure is not reference counted, so it
   * is only valid while the isl_union_map from which it was
   * obtained is still alive.
   */
  struct isl_fixed_map {
  	isl_int v;
  	isl_map *map;
  };
  
  static struct isl_fixed_map *alloc_isl_fixed_map_array(isl_ctx *ctx,
  	int n)
  {
  	int i;
  	struct isl_fixed_map *v;
  
  	v = isl_calloc_array(ctx, struct isl_fixed_map, n);
  	if (!v)
  		return NULL;
  	for (i = 0; i < n; ++i)
  		isl_int_init(v[i].v);
  	return v;
  }
  
  static void free_isl_fixed_map_array(struct isl_fixed_map *v, int n)
  {
  	int i;
  
  	if (!v)
  		return;
  	for (i = 0; i < n; ++i)
  		isl_int_clear(v[i].v);
  	free(v);
  }
  
  /* Compare the "v" field of two isl_fixed_map structs.
   */
  static int qsort_fixed_map_cmp(const void *p1, const void *p2)
  {
  	const struct isl_fixed_map *e1 = (const struct isl_fixed_map *) p1;
  	const struct isl_fixed_map *e2 = (const struct isl_fixed_map *) p2;
  
  	return isl_int_cmp(e1->v, e2->v);
  }
  
  /* Internal data structure used while checking whether all maps
   * in a union_map have a fixed value for a given output dimension.
   * v is the list of maps, with the fixed value for the dimension
   * n is the number of maps considered so far
   * pos is the output dimension under investigation
   */
  struct isl_fixed_dim_data {
  	struct isl_fixed_map *v;
  	int n;
  	int pos;
  };
  
  static int fixed_at_pos(__isl_keep isl_map *map, void *user)
  {
  	struct isl_fixed_dim_data *data = user;
  
  	data->v[data->n].map = map;
  	return isl_map_plain_is_fixed(map, isl_dim_out, data->pos,
  				      &data->v[data->n++].v);
  }
  
  static int plain_injective_on_range(__isl_take isl_union_map *umap,
  	int first, int n_range);
  
  /* Given a list of the maps, with their fixed values at output dimension "pos",
   * check whether the ranges of the maps form an obvious partition.
   *
   * We first sort the maps according to their fixed values.
   * If all maps have a different value, then we know the ranges form
   * a partition.
   * Otherwise, we collect the maps with the same fixed value and
   * check whether each such collection is obviously injective
   * based on later dimensions.
   */
  static int separates(struct isl_fixed_map *v, int n,
  	__isl_take isl_space *dim, int pos, int n_range)
  {
  	int i;
  
  	if (!v)
  		goto error;
  
  	qsort(v, n, sizeof(*v), &qsort_fixed_map_cmp);
  
  	for (i = 0; i + 1 < n; ++i) {
  		int j, k;
  		isl_union_map *part;
  		int injective;
  
  		for (j = i + 1; j < n; ++j)
  			if (isl_int_ne(v[i].v, v[j].v))
  				break;
  
  		if (j == i + 1)
  			continue;
  
  		part = isl_union_map_alloc(isl_space_copy(dim), j - i);
  		for (k = i; k < j; ++k)
  			part = isl_union_map_add_map(part,
  						     isl_map_copy(v[k].map));
  
  		injective = plain_injective_on_range(part, pos + 1, n_range);
  		if (injective < 0)
  			goto error;
  		if (!injective)
  			break;
  
  		i = j - 1;
  	}
  
  	isl_space_free(dim);
  	free_isl_fixed_map_array(v, n);
  	return i + 1 >= n;
  error:
  	isl_space_free(dim);
  	free_isl_fixed_map_array(v, n);
  	return -1;
  }
  
  /* Check whether the maps in umap have obviously distinct ranges.
   * In particular, check for an output dimension in the range
   * [first,n_range) for which all maps have a fixed value
   * and then check if these values, possibly along with fixed values
   * at later dimensions, entail distinct ranges.
   */
  static int plain_injective_on_range(__isl_take isl_union_map *umap,
  	int first, int n_range)
  {
  	isl_ctx *ctx;
  	int n;
  	struct isl_fixed_dim_data data = { NULL };
  
  	ctx = isl_union_map_get_ctx(umap);
  
  	n = isl_union_map_n_map(umap);
  	if (!umap)
  		goto error;
  
  	if (n <= 1) {
  		isl_union_map_free(umap);
  		return 1;
  	}
  
  	if (first >= n_range) {
  		isl_union_map_free(umap);
  		return 0;
  	}
  
  	data.v = alloc_isl_fixed_map_array(ctx, n);
  	if (!data.v)
  		goto error;
  
  	for (data.pos = first; data.pos < n_range; ++data.pos) {
  		int fixed;
  		int injective;
  		isl_space *dim;
  
  		data.n = 0;
  		fixed = union_map_forall_user(umap, &fixed_at_pos, &data);
  		if (fixed < 0)
  			goto error;
  		if (!fixed)
  			continue;
  		dim = isl_union_map_get_space(umap);
  		injective = separates(data.v, n, dim, data.pos, n_range);
  		isl_union_map_free(umap);
  		return injective;
  	}
  
  	free_isl_fixed_map_array(data.v, n);
  	isl_union_map_free(umap);
  
  	return 0;
  error:
  	free_isl_fixed_map_array(data.v, n);
  	isl_union_map_free(umap);
  	return -1;
  }
  
  /* Check whether the maps in umap that map to subsets of "ran"
   * have obviously distinct ranges.
   */
  static int plain_injective_on_range_wrap(__isl_keep isl_set *ran, void *user)
  {
  	isl_union_map *umap = user;
  
  	umap = isl_union_map_copy(umap);
  	umap = isl_union_map_intersect_range(umap,
  			isl_union_set_from_set(isl_set_copy(ran)));
  	return plain_injective_on_range(umap, 0, isl_set_dim(ran, isl_dim_set));
  }
  
  /* Check if the given union_map is obviously injective.
   *
   * In particular, we first check if all individual maps are obviously
   * injective and then check if all the ranges of these maps are
   * obviously disjoint.
   */
  int isl_union_map_plain_is_injective(__isl_keep isl_union_map *umap)
  {
  	int in;
  	isl_union_map *univ;
  	isl_union_set *ran;
  
  	in = union_map_forall(umap, &isl_map_plain_is_injective);
  	if (in < 0)
  		return -1;
  	if (!in)
  		return 0;
  
  	univ = isl_union_map_universe(isl_union_map_copy(umap));
  	ran = isl_union_map_range(univ);
  
  	in = union_map_forall_user(ran, &plain_injective_on_range_wrap, umap);
  
  	isl_union_set_free(ran);
  
  	return in;
  }
  
  int isl_union_map_is_bijective(__isl_keep isl_union_map *umap)
  {
  	int sv;
  
  	sv = isl_union_map_is_single_valued(umap);
  	if (sv < 0 || !sv)
  		return sv;
  
  	return isl_union_map_is_injective(umap);
  }
  
  static int zip_entry(void **entry, void *user)
  {
  	isl_map *map = *entry;
  	isl_union_map **res = user;
  
  	if (!isl_map_can_zip(map))
  		return 0;
  
  	*res = isl_union_map_add_map(*res, isl_map_zip(isl_map_copy(map)));
  
  	return 0;
  }
  
  __isl_give isl_union_map *isl_union_map_zip(__isl_take isl_union_map *umap)
  {
  	return cond_un_op(umap, &zip_entry);
  }
  
  static int uncurry_entry(void **entry, void *user)
  {
  	isl_map *map = *entry;
  	isl_union_map **res = user;
  
  	if (!isl_map_can_uncurry(map))
  		return 0;
  
  	*res = isl_union_map_add_map(*res, isl_map_uncurry(isl_map_copy(map)));
  
  	return 0;
  }
  
  /* Given a union map, take the maps of the form A -> (B -> C) and
   * return the union of the corresponding maps (A -> B) -> C.
   */
  __isl_give isl_union_map *isl_union_map_uncurry(__isl_take isl_union_map *umap)
  {
  	return cond_un_op(umap, &uncurry_entry);
  }
  
  static int curry_entry(void **entry, void *user)
  {
  	isl_map *map = *entry;
  	isl_union_map **res = user;
  
  	if (!isl_map_can_curry(map))
  		return 0;
  
  	*res = isl_union_map_add_map(*res, isl_map_curry(isl_map_copy(map)));
  
  	return 0;
  }
  
  /* Given a union map, take the maps of the form (A -> B) -> C and
   * return the union of the corresponding maps A -> (B -> C).
   */
  __isl_give isl_union_map *isl_union_map_curry(__isl_take isl_union_map *umap)
  {
  	return cond_un_op(umap, &curry_entry);
  }
  
  static int lift_entry(void **entry, void *user)
  {
  	isl_set *set = *entry;
  	isl_union_set **res = user;
  
  	*res = isl_union_set_add_set(*res, isl_set_lift(isl_set_copy(set)));
  
  	return 0;
  }
  
  __isl_give isl_union_set *isl_union_set_lift(__isl_take isl_union_set *uset)
  {
  	return cond_un_op(uset, &lift_entry);
  }
  
  static int coefficients_entry(void **entry, void *user)
  {
  	isl_set *set = *entry;
  	isl_union_set **res = user;
  
  	set = isl_set_copy(set);
  	set = isl_set_from_basic_set(isl_set_coefficients(set));
  	*res = isl_union_set_add_set(*res, set);
  
  	return 0;
  }
  
  __isl_give isl_union_set *isl_union_set_coefficients(
  	__isl_take isl_union_set *uset)
  {
  	isl_ctx *ctx;
  	isl_space *dim;
  	isl_union_set *res;
  
  	if (!uset)
  		return NULL;
  
  	ctx = isl_union_set_get_ctx(uset);
  	dim = isl_space_set_alloc(ctx, 0, 0);
  	res = isl_union_map_alloc(dim, uset->table.n);
  	if (isl_hash_table_foreach(uset->dim->ctx, &uset->table,
  				   &coefficients_entry, &res) < 0)
  		goto error;
  
  	isl_union_set_free(uset);
  	return res;
  error:
  	isl_union_set_free(uset);
  	isl_union_set_free(res);
  	return NULL;
  }
  
  static int solutions_entry(void **entry, void *user)
  {
  	isl_set *set = *entry;
  	isl_union_set **res = user;
  
  	set = isl_set_copy(set);
  	set = isl_set_from_basic_set(isl_set_solutions(set));
  	if (!*res)
  		*res = isl_union_set_from_set(set);
  	else
  		*res = isl_union_set_add_set(*res, set);
  
  	if (!*res)
  		return -1;
  
  	return 0;
  }
  
  __isl_give isl_union_set *isl_union_set_solutions(
  	__isl_take isl_union_set *uset)
  {
  	isl_union_set *res = NULL;
  
  	if (!uset)
  		return NULL;
  
  	if (uset->table.n == 0) {
  		res = isl_union_set_empty(isl_union_set_get_space(uset));
  		isl_union_set_free(uset);
  		return res;
  	}
  
  	if (isl_hash_table_foreach(uset->dim->ctx, &uset->table,
  				   &solutions_entry, &res) < 0)
  		goto error;
  
  	isl_union_set_free(uset);
  	return res;
  error:
  	isl_union_set_free(uset);
  	isl_union_set_free(res);
  	return NULL;
  }
  
  /* Is the domain space of "map" equal to "space"?
   */
  static int domain_match(__isl_keep isl_map *map, __isl_keep isl_space *space)
  {
  	return isl_space_tuple_is_equal(map->dim, isl_dim_in,
  					space, isl_dim_out);
  }
  
  /* Is the range space of "map" equal to "space"?
   */
  static int range_match(__isl_keep isl_map *map, __isl_keep isl_space *space)
  {
  	return isl_space_tuple_is_equal(map->dim, isl_dim_out,
  					space, isl_dim_out);
  }
  
  /* Is the set space of "map" equal to "space"?
   */
  static int set_match(__isl_keep isl_map *map, __isl_keep isl_space *space)
  {
  	return isl_space_tuple_is_equal(map->dim, isl_dim_set,
  					space, isl_dim_out);
  }
  
  /* Internal data structure for preimage_pw_multi_aff.
   *
   * "pma" is the function under which the preimage should be taken.
   * "space" is the space of "pma".
   * "res" collects the results.
   * "fn" computes the preimage for a given map.
   * "match" returns true if "fn" can be called.
   */
  struct isl_union_map_preimage_data {
  	isl_space *space;
  	isl_pw_multi_aff *pma;
  	isl_union_map *res;
  	int (*match)(__isl_keep isl_map *map, __isl_keep isl_space *space);
  	__isl_give isl_map *(*fn)(__isl_take isl_map *map,
  		__isl_take isl_pw_multi_aff *pma);
  };
  
  /* Call data->fn to compute the preimage of the domain or range of *entry
   * under the function represented by data->pma, provided the domain/range
   * space of *entry matches the target space of data->pma
   * (as given by data->match), and add the result to data->res.
   */
  static int preimage_entry(void **entry, void *user)
  {
  	int m;
  	isl_map *map = *entry;
  	struct isl_union_map_preimage_data *data = user;
  	int empty;
  
  	m = data->match(map, data->space);
  	if (m < 0)
  		return -1;
  	if (!m)
  		return 0;
  
  	map = isl_map_copy(map);
  	map = data->fn(map, isl_pw_multi_aff_copy(data->pma));
  
  	empty = isl_map_is_empty(map);
  	if (empty < 0 || empty) {
  		isl_map_free(map);
  		return empty < 0 ? -1 : 0;
  	}
  
  	data->res = isl_union_map_add_map(data->res, map);
  
  	return 0;
  }
  
  /* Compute the preimage of the domain or range of "umap" under the function
   * represented by "pma".
   * In other words, plug in "pma" in the domain or range of "umap".
   * The function "fn" performs the actual preimage computation on a map,
   * while "match" determines to which maps the function should be applied.
   */
  static __isl_give isl_union_map *preimage_pw_multi_aff(
  	__isl_take isl_union_map *umap, __isl_take isl_pw_multi_aff *pma,
  	int (*match)(__isl_keep isl_map *map, __isl_keep isl_space *space),
  	__isl_give isl_map *(*fn)(__isl_take isl_map *map,
  		__isl_take isl_pw_multi_aff *pma))
  {
  	isl_ctx *ctx;
  	isl_space *space;
  	struct isl_union_map_preimage_data data;
  
  	umap = isl_union_map_align_params(umap,
  					    isl_pw_multi_aff_get_space(pma));
  	pma = isl_pw_multi_aff_align_params(pma, isl_union_map_get_space(umap));
  
  	if (!umap || !pma)
  		goto error;
  
  	ctx = isl_union_map_get_ctx(umap);
  	space = isl_union_map_get_space(umap);
  	data.space = isl_pw_multi_aff_get_space(pma);
  	data.pma = pma;
  	data.res = isl_union_map_alloc(space, umap->table.n);
  	data.match = match;
  	data.fn = fn;
  	if (isl_hash_table_foreach(ctx, &umap->table, &preimage_entry,
  					&data) < 0)
  		data.res = isl_union_map_free(data.res);
  
  	isl_space_free(data.space);
  	isl_union_map_free(umap);
  	isl_pw_multi_aff_free(pma);
  	return data.res;
  error:
  	isl_union_map_free(umap);
  	isl_pw_multi_aff_free(pma);
  	return NULL;
  }
  
  /* Compute the preimage of the domain of "umap" under the function
   * represented by "pma".
   * In other words, plug in "pma" in the domain of "umap".
   * The result contains maps that live in the same spaces as the maps of "umap"
   * with domain space equal to the target space of "pma",
   * except that the domain has been replaced by the domain space of "pma".
   */
  __isl_give isl_union_map *isl_union_map_preimage_domain_pw_multi_aff(
  	__isl_take isl_union_map *umap, __isl_take isl_pw_multi_aff *pma)
  {
  	return preimage_pw_multi_aff(umap, pma, &domain_match,
  					&isl_map_preimage_domain_pw_multi_aff);
  }
  
  /* Compute the preimage of the range of "umap" under the function
   * represented by "pma".
   * In other words, plug in "pma" in the range of "umap".
   * The result contains maps that live in the same spaces as the maps of "umap"
   * with range space equal to the target space of "pma",
   * except that the range has been replaced by the domain space of "pma".
   */
  __isl_give isl_union_map *isl_union_map_preimage_range_pw_multi_aff(
  	__isl_take isl_union_map *umap, __isl_take isl_pw_multi_aff *pma)
  {
  	return preimage_pw_multi_aff(umap, pma, &range_match,
  					&isl_map_preimage_range_pw_multi_aff);
  }
  
  /* Compute the preimage of "uset" under the function represented by "pma".
   * In other words, plug in "pma" in "uset".
   * The result contains sets that live in the same spaces as the sets of "uset"
   * with space equal to the target space of "pma",
   * except that the space has been replaced by the domain space of "pma".
   */
  __isl_give isl_union_set *isl_union_set_preimage_pw_multi_aff(
  	__isl_take isl_union_set *uset, __isl_take isl_pw_multi_aff *pma)
  {
  	return preimage_pw_multi_aff(uset, pma, &set_match,
  					&isl_set_preimage_pw_multi_aff);
  }
  
  /* Compute the preimage of the domain of "umap" under the function
   * represented by "ma".
   * In other words, plug in "ma" in the domain of "umap".
   * The result contains maps that live in the same spaces as the maps of "umap"
   * with domain space equal to the target space of "ma",
   * except that the domain has been replaced by the domain space of "ma".
   */
  __isl_give isl_union_map *isl_union_map_preimage_domain_multi_aff(
  	__isl_take isl_union_map *umap, __isl_take isl_multi_aff *ma)
  {
  	return isl_union_map_preimage_domain_pw_multi_aff(umap,
  					isl_pw_multi_aff_from_multi_aff(ma));
  }
  
  /* Compute the preimage of the range of "umap" under the function
   * represented by "ma".
   * In other words, plug in "ma" in the range of "umap".
   * The result contains maps that live in the same spaces as the maps of "umap"
   * with range space equal to the target space of "ma",
   * except that the range has been replaced by the domain space of "ma".
   */
  __isl_give isl_union_map *isl_union_map_preimage_range_multi_aff(
  	__isl_take isl_union_map *umap, __isl_take isl_multi_aff *ma)
  {
  	return isl_union_map_preimage_range_pw_multi_aff(umap,
  					isl_pw_multi_aff_from_multi_aff(ma));
  }
  
  /* Compute the preimage of "uset" under the function represented by "ma".
   * In other words, plug in "ma" in "uset".
   * The result contains sets that live in the same spaces as the sets of "uset"
   * with space equal to the target space of "ma",
   * except that the space has been replaced by the domain space of "ma".
   */
  __isl_give isl_union_map *isl_union_set_preimage_multi_aff(
  	__isl_take isl_union_set *uset, __isl_take isl_multi_aff *ma)
  {
  	return isl_union_set_preimage_pw_multi_aff(uset,
  					isl_pw_multi_aff_from_multi_aff(ma));
  }
  
  /* Internal data structure for preimage_multi_pw_aff.
   *
   * "mpa" is the function under which the preimage should be taken.
   * "space" is the space of "mpa".
   * "res" collects the results.
   * "fn" computes the preimage for a given map.
   * "match" returns true if "fn" can be called.
   */
  struct isl_union_map_preimage_mpa_data {
  	isl_space *space;
  	isl_multi_pw_aff *mpa;
  	isl_union_map *res;
  	int (*match)(__isl_keep isl_map *map, __isl_keep isl_space *space);
  	__isl_give isl_map *(*fn)(__isl_take isl_map *map,
  		__isl_take isl_multi_pw_aff *mpa);
  };
  
  /* Call data->fn to compute the preimage of the domain or range of *entry
   * under the function represented by data->mpa, provided the domain/range
   * space of *entry matches the target space of data->mpa
   * (as given by data->match), and add the result to data->res.
   */
  static int preimage_mpa_entry(void **entry, void *user)
  {
  	int m;
  	isl_map *map = *entry;
  	struct isl_union_map_preimage_mpa_data *data = user;
  	int empty;
  
  	m = data->match(map, data->space);
  	if (m < 0)
  		return -1;
  	if (!m)
  		return 0;
  
  	map = isl_map_copy(map);
  	map = data->fn(map, isl_multi_pw_aff_copy(data->mpa));
  
  	empty = isl_map_is_empty(map);
  	if (empty < 0 || empty) {
  		isl_map_free(map);
  		return empty < 0 ? -1 : 0;
  	}
  
  	data->res = isl_union_map_add_map(data->res, map);
  
  	return 0;
  }
  
  /* Compute the preimage of the domain or range of "umap" under the function
   * represented by "mpa".
   * In other words, plug in "mpa" in the domain or range of "umap".
   * The function "fn" performs the actual preimage computation on a map,
   * while "match" determines to which maps the function should be applied.
   */
  static __isl_give isl_union_map *preimage_multi_pw_aff(
  	__isl_take isl_union_map *umap, __isl_take isl_multi_pw_aff *mpa,
  	int (*match)(__isl_keep isl_map *map, __isl_keep isl_space *space),
  	__isl_give isl_map *(*fn)(__isl_take isl_map *map,
  		__isl_take isl_multi_pw_aff *mpa))
  {
  	isl_ctx *ctx;
  	isl_space *space;
  	struct isl_union_map_preimage_mpa_data data;
  
  	umap = isl_union_map_align_params(umap,
  					    isl_multi_pw_aff_get_space(mpa));
  	mpa = isl_multi_pw_aff_align_params(mpa, isl_union_map_get_space(umap));
  
  	if (!umap || !mpa)
  		goto error;
  
  	ctx = isl_union_map_get_ctx(umap);
  	space = isl_union_map_get_space(umap);
  	data.space = isl_multi_pw_aff_get_space(mpa);
  	data.mpa = mpa;
  	data.res = isl_union_map_alloc(space, umap->table.n);
  	data.match = match;
  	data.fn = fn;
  	if (isl_hash_table_foreach(ctx, &umap->table, &preimage_mpa_entry,
  					&data) < 0)
  		data.res = isl_union_map_free(data.res);
  
  	isl_space_free(data.space);
  	isl_union_map_free(umap);
  	isl_multi_pw_aff_free(mpa);
  	return data.res;
  error:
  	isl_union_map_free(umap);
  	isl_multi_pw_aff_free(mpa);
  	return NULL;
  }
  
  /* Compute the preimage of the domain of "umap" under the function
   * represented by "mpa".
   * In other words, plug in "mpa" in the domain of "umap".
   * The result contains maps that live in the same spaces as the maps of "umap"
   * with domain space equal to the target space of "mpa",
   * except that the domain has been replaced by the domain space of "mpa".
   */
  __isl_give isl_union_map *isl_union_map_preimage_domain_multi_pw_aff(
  	__isl_take isl_union_map *umap, __isl_take isl_multi_pw_aff *mpa)
  {
  	return preimage_multi_pw_aff(umap, mpa, &domain_match,
  					&isl_map_preimage_domain_multi_pw_aff);
  }
  
  /* Internal data structure for preimage_upma.
   *
   * "umap" is the map of which the preimage should be computed.
   * "res" collects the results.
   * "fn" computes the preimage for a given piecewise multi-affine function.
   */
  struct isl_union_map_preimage_upma_data {
  	isl_union_map *umap;
  	isl_union_map *res;
  	__isl_give isl_union_map *(*fn)(__isl_take isl_union_map *umap,
  		__isl_take isl_pw_multi_aff *pma);
  };
  
  /* Call data->fn to compute the preimage of the domain or range of data->umap
   * under the function represented by pma and add the result to data->res.
   */
  static int preimage_upma(__isl_take isl_pw_multi_aff *pma, void *user)
  {
  	struct isl_union_map_preimage_upma_data *data = user;
  	isl_union_map *umap;
  
  	umap = isl_union_map_copy(data->umap);
  	umap = data->fn(umap, pma);
  	data->res = isl_union_map_union(data->res, umap);
  
  	return data->res ? 0 : -1;
  }
  
  /* Compute the preimage of the domain or range of "umap" under the function
   * represented by "upma".
   * In other words, plug in "upma" in the domain or range of "umap".
   * The function "fn" performs the actual preimage computation
   * on a piecewise multi-affine function.
   */
  static __isl_give isl_union_map *preimage_union_pw_multi_aff(
  	__isl_take isl_union_map *umap,
  	__isl_take isl_union_pw_multi_aff *upma,
  	__isl_give isl_union_map *(*fn)(__isl_take isl_union_map *umap,
  		__isl_take isl_pw_multi_aff *pma))
  {
  	struct isl_union_map_preimage_upma_data data;
  
  	data.umap = umap;
  	data.res = isl_union_map_empty(isl_union_map_get_space(umap));
  	data.fn = fn;
  	if (isl_union_pw_multi_aff_foreach_pw_multi_aff(upma,
  						    &preimage_upma, &data) < 0)
  		data.res = isl_union_map_free(data.res);
  
  	isl_union_map_free(umap);
  	isl_union_pw_multi_aff_free(upma);
  
  	return data.res;
  }
  
  /* Compute the preimage of the domain of "umap" under the function
   * represented by "upma".
   * In other words, plug in "upma" in the domain of "umap".
   * The result contains maps that live in the same spaces as the maps of "umap"
   * with domain space equal to one of the target spaces of "upma",
   * except that the domain has been replaced by one of the the domain spaces that
   * corresponds to that target space of "upma".
   */
  __isl_give isl_union_map *isl_union_map_preimage_domain_union_pw_multi_aff(
  	__isl_take isl_union_map *umap,
  	__isl_take isl_union_pw_multi_aff *upma)
  {
  	return preimage_union_pw_multi_aff(umap, upma,
  				&isl_union_map_preimage_domain_pw_multi_aff);
  }
  
  /* Compute the preimage of the range of "umap" under the function
   * represented by "upma".
   * In other words, plug in "upma" in the range of "umap".
   * The result contains maps that live in the same spaces as the maps of "umap"
   * with range space equal to one of the target spaces of "upma",
   * except that the range has been replaced by one of the the domain spaces that
   * corresponds to that target space of "upma".
   */
  __isl_give isl_union_map *isl_union_map_preimage_range_union_pw_multi_aff(
  	__isl_take isl_union_map *umap,
  	__isl_take isl_union_pw_multi_aff *upma)
  {
  	return preimage_union_pw_multi_aff(umap, upma,
  				&isl_union_map_preimage_range_pw_multi_aff);
  }
  
  /* Compute the preimage of "uset" under the function represented by "upma".
   * In other words, plug in "upma" in the range of "uset".
   * The result contains sets that live in the same spaces as the sets of "uset"
   * with space equal to one of the target spaces of "upma",
   * except that the space has been replaced by one of the the domain spaces that
   * corresponds to that target space of "upma".
   */
  __isl_give isl_union_set *isl_union_set_preimage_union_pw_multi_aff(
  	__isl_take isl_union_set *uset,
  	__isl_take isl_union_pw_multi_aff *upma)
  {
  	return preimage_union_pw_multi_aff(uset, upma,
  					&isl_union_set_preimage_pw_multi_aff);
  }
  
  /* Reset the user pointer on all identifiers of parameters and tuples
   * of the space of *entry.
   */
  static int reset_user(void **entry, void *user)
  {
  	isl_map **map = (isl_map **)entry;
  
  	*map = isl_map_reset_user(*map);
  
  	return *map ? 0 : -1;
  }
  
  /* Reset the user pointer on all identifiers of parameters and tuples
   * of the spaces of "umap".
   */
  __isl_give isl_union_map *isl_union_map_reset_user(
  	__isl_take isl_union_map *umap)
  {
  	umap = isl_union_map_cow(umap);
  	if (!umap)
  		return NULL;
  	umap->dim = isl_space_reset_user(umap->dim);
  	if (!umap->dim)
  		return isl_union_map_free(umap);
  	umap = un_op(umap, &reset_user);
  
  	return umap;
  }
  
  /* Reset the user pointer on all identifiers of parameters and tuples
   * of the spaces of "uset".
   */
  __isl_give isl_union_set *isl_union_set_reset_user(
  	__isl_take isl_union_set *uset)
  {
  	return isl_union_map_reset_user(uset);
  }
  
  /* Internal data structure for isl_union_map_project_out.
   * "type", "first" and "n" are the arguments for the isl_map_project_out
   * call.
   * "res" collects the results.
   */
  struct isl_union_map_project_out_data {
  	enum isl_dim_type type;
  	unsigned first;
  	unsigned n;
  
  	isl_union_map *res;
  };
  
  /* Turn the data->n dimensions of type data->type, starting at data->first
   * into existentially quantified variables and add the result to data->res.
   */
  static int project_out(__isl_take isl_map *map, void *user)
  {
  	struct isl_union_map_project_out_data *data = user;
  
  	map = isl_map_project_out(map, data->type, data->first, data->n);
  	data->res = isl_union_map_add_map(data->res, map);
  
  	return 0;
  }
  
  /* Turn the "n" dimensions of type "type", starting at "first"
   * into existentially quantified variables.
   * Since the space of an isl_union_map only contains parameters,
   * type is required to be equal to isl_dim_param.
   */
  __isl_give isl_union_map *isl_union_map_project_out(
  	__isl_take isl_union_map *umap,
  	enum isl_dim_type type, unsigned first, unsigned n)
  {
  	isl_space *space;
  	struct isl_union_map_project_out_data data = { type, first, n };
  
  	if (!umap)
  		return NULL;
  
  	if (type != isl_dim_param)
  		isl_die(isl_union_map_get_ctx(umap), isl_error_invalid,
  			"can only project out parameters",
  			return isl_union_map_free(umap));
  
  	space = isl_union_map_get_space(umap);
  	space = isl_space_drop_dims(space, type, first, n);
  	data.res = isl_union_map_empty(space);
  	if (isl_union_map_foreach_map(umap, &project_out, &data) < 0)
  		data.res = isl_union_map_free(data.res);
  
  	isl_union_map_free(umap);
  
  	return data.res;
  }
  
  /* Turn the "n" dimensions of type "type", starting at "first"
   * into existentially quantified variables.
   * Since the space of an isl_union_set only contains parameters,
   * "type" is required to be equal to isl_dim_param.
   */
  __isl_give isl_union_set *isl_union_set_project_out(
  	__isl_take isl_union_set *uset,
  	enum isl_dim_type type, unsigned first, unsigned n)
  {
  	return isl_union_map_project_out(uset, type, first, n);
  }
  
  /* Internal data structure for isl_union_map_involves_dims.
   * "first" and "n" are the arguments for the isl_map_involves_dims calls.
   */
  struct isl_union_map_involves_dims_data {
  	unsigned first;
  	unsigned n;
  };
  
  /* Does "map" _not_ involve the data->n parameters starting at data->first?
   */
  static int map_excludes(__isl_keep isl_map *map, void *user)
  {
  	struct isl_union_map_involves_dims_data *data = user;
  	int involves;
  
  	involves = isl_map_involves_dims(map,
  					isl_dim_param, data->first, data->n);
  	if (involves < 0)
  		return -1;
  	return !involves;
  }
  
  /* Does "umap" involve any of the n parameters starting at first?
   * "type" is required to be set to isl_dim_param.
   *
   * "umap" involves any of those parameters if any of its maps
   * involve the parameters.  In other words, "umap" does not
   * involve any of the parameters if all its maps to not
   * involve the parameters.
   */
  int isl_union_map_involves_dims(__isl_keep isl_union_map *umap,
  	enum isl_dim_type type, unsigned first, unsigned n)
  {
  	struct isl_union_map_involves_dims_data data = { first, n };
  	int excludes;
  
  	if (type != isl_dim_param)
  		isl_die(isl_union_map_get_ctx(umap), isl_error_invalid,
  			"can only reference parameters", return 0);
  
  	excludes = union_map_forall_user(umap, &map_excludes, &data);
  
  	if (excludes < 0)
  		return -1;
  
  	return !excludes;
  }
  
  /* Internal data structure for isl_union_map_reset_range_space.
   * "range" is the space from which to set the range space.
   * "res" collects the results.
   */
  struct isl_union_map_reset_range_space_data {
  	isl_space *range;
  	isl_union_map *res;
  };
  
  /* Replace the range space of "map" by the range space of data->range and
   * add the result to data->res.
   */
  static int reset_range_space(__isl_take isl_map *map, void *user)
  {
  	struct isl_union_map_reset_range_space_data *data = user;
  	isl_space *space;
  
  	space = isl_map_get_space(map);
  	space = isl_space_domain(space);
  	space = isl_space_extend_domain_with_range(space,
  						isl_space_copy(data->range));
  	map = isl_map_reset_space(map, space);
  	data->res = isl_union_map_add_map(data->res, map);
  
  	return data->res ? 0 : -1;
  }
  
  /* Replace the range space of all the maps in "umap" by
   * the range space of "space".
   *
   * This assumes that all maps have the same output dimension.
   * This function should therefore not be made publicly available.
   *
   * Since the spaces of the maps change, so do their hash value.
   * We therefore need to create a new isl_union_map.
   */
  __isl_give isl_union_map *isl_union_map_reset_range_space(
  	__isl_take isl_union_map *umap, __isl_take isl_space *space)
  {
  	struct isl_union_map_reset_range_space_data data = { space };
  
  	data.res = isl_union_map_empty(isl_union_map_get_space(umap));
  	if (isl_union_map_foreach_map(umap, &reset_range_space, &data) < 0)
  		data.res = isl_union_map_free(data.res);
  
  	isl_space_free(space);
  	isl_union_map_free(umap);
  	return data.res;
  }
  
  /* Internal data structure for isl_union_map_order_at_multi_union_pw_aff.
   * "mupa" is the function from which the isl_multi_pw_affs are extracted.
   * "order" is applied to the extracted isl_multi_pw_affs that correspond
   * to the domain and the range of each map.
   * "res" collects the results.
   */
  struct isl_union_order_at_data {
  	isl_multi_union_pw_aff *mupa;
  	__isl_give isl_map *(*order)(__isl_take isl_multi_pw_aff *mpa1,
  		__isl_take isl_multi_pw_aff *mpa2);
  	isl_union_map *res;
  };
  
  /* Intersect "map" with the result of applying data->order to
   * the functions in data->mupa that apply to the domain and the range
   * of "map" and add the result to data->res.
   */
  static int order_at(__isl_take isl_map *map, void *user)
  {
  	struct isl_union_order_at_data *data = user;
  	isl_space *space;
  	isl_multi_pw_aff *mpa1, *mpa2;
  	isl_map *order;
  
  	space = isl_space_domain(isl_map_get_space(map));
  	mpa1 = isl_multi_union_pw_aff_extract_multi_pw_aff(data->mupa, space);
  	space = isl_space_range(isl_map_get_space(map));
  	mpa2 = isl_multi_union_pw_aff_extract_multi_pw_aff(data->mupa, space);
  	order = data->order(mpa1, mpa2);
  	map = isl_map_intersect(map, order);
  	data->res = isl_union_map_add_map(data->res, map);
  
  	return data->res ? 0 : -1;
  }
  
  /* Intersect each map in "umap" with the result of calling "order"
   * on the functions is "mupa" that apply to the domain and the range
   * of the map.
   */
  static __isl_give isl_union_map *isl_union_map_order_at_multi_union_pw_aff(
  	__isl_take isl_union_map *umap, __isl_take isl_multi_union_pw_aff *mupa,
  	__isl_give isl_map *(*order)(__isl_take isl_multi_pw_aff *mpa1,
  		__isl_take isl_multi_pw_aff *mpa2))
  {
  	struct isl_union_order_at_data data;
  
  	umap = isl_union_map_align_params(umap,
  				isl_multi_union_pw_aff_get_space(mupa));
  	mupa = isl_multi_union_pw_aff_align_params(mupa,
  				isl_union_map_get_space(umap));
  	data.mupa = mupa;
  	data.order = order;
  	data.res = isl_union_map_empty(isl_union_map_get_space(umap));
  	if (isl_union_map_foreach_map(umap, &order_at, &data) < 0)
  		data.res = isl_union_map_free(data.res);
  
  	isl_multi_union_pw_aff_free(mupa);
  	isl_union_map_free(umap);
  	return data.res;
  }
  
  /* Return the subset of "umap" where the domain and the range
   * have equal "mupa" values.
   */
  __isl_give isl_union_map *isl_union_map_eq_at_multi_union_pw_aff(
  	__isl_take isl_union_map *umap,
  	__isl_take isl_multi_union_pw_aff *mupa)
  {
  	return isl_union_map_order_at_multi_union_pw_aff(umap, mupa,
  						&isl_multi_pw_aff_eq_map);
  }
  
  /* Return the subset of "umap" where the domain has a lexicographically
   * smaller "mupa" value than the range.
   */
  __isl_give isl_union_map *isl_union_map_lex_lt_at_multi_union_pw_aff(
  	__isl_take isl_union_map *umap,
  	__isl_take isl_multi_union_pw_aff *mupa)
  {
  	return isl_union_map_order_at_multi_union_pw_aff(umap, mupa,
  						&isl_multi_pw_aff_lex_lt_map);
  }
  
  /* Return the subset of "umap" where the domain has a lexicographically
   * greater "mupa" value than the range.
   */
  __isl_give isl_union_map *isl_union_map_lex_gt_at_multi_union_pw_aff(
  	__isl_take isl_union_map *umap,
  	__isl_take isl_multi_union_pw_aff *mupa)
  {
  	return isl_union_map_order_at_multi_union_pw_aff(umap, mupa,
  						&isl_multi_pw_aff_lex_gt_map);
  }
  
  /* Return the union of the elements in the list "list".
   */
  __isl_give isl_union_set *isl_union_set_list_union(
  	__isl_take isl_union_set_list *list)
  {
  	int i, n;
  	isl_ctx *ctx;
  	isl_space *space;
  	isl_union_set *res;
  
  	if (!list)
  		return NULL;
  
  	ctx = isl_union_set_list_get_ctx(list);
  	space = isl_space_params_alloc(ctx, 0);
  	res = isl_union_set_empty(space);
  
  	n = isl_union_set_list_n_union_set(list);
  	for (i = 0; i < n; ++i) {
  		isl_union_set *uset_i;
  
  		uset_i = isl_union_set_list_get_union_set(list, i);
  		res = isl_union_set_union(res, uset_i);
  	}
  
  	isl_union_set_list_free(list);
  	return res;
  }
  