text: /*
   * Copyright 2010-2011 INRIA Saclay
   * Copyright 2013-2014 Ecole Normale Superieure
   * Copyright 2014      INRIA Rocquencourt
   * Copyright 2016-2017 Sven Verdoolaege
   *
   * 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
   */
  
  #include <isl_map_private.h>
  #include <isl_union_map_private.h>
  #include <isl/ctx.h>
  #include <isl/hash.h>
  #include <isl_aff_private.h>
  #include <isl/map.h>
  #include <isl/set.h>
  #include <isl_space_private.h>
  #include <isl/union_set.h>
  #include <isl_maybe_map.h>
  #include <isl_id_private.h>
  
  #include <bset_from_bmap.c>
  #include <set_to_map.c>
  #include <set_from_map.c>
  #include <uset_to_umap.c>
  #include <uset_from_umap.c>
  #include <set_list_from_map_list_inl.c>
  
  /* Return the number of parameters of "umap", where "type"
   * is required to be set to isl_dim_param.
   */
  isl_size isl_union_map_dim(__isl_keep isl_union_map *umap,
  	enum isl_dim_type type)
  {
  	if (!umap)
  		return isl_size_error;
  
  	if (type != isl_dim_param)
  		isl_die(isl_union_map_get_ctx(umap), isl_error_invalid,
  			"can only reference parameters", return isl_size_error);
  
  	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.
   */
  isl_size 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?
   */
  isl_bool isl_union_set_is_params(__isl_keep isl_union_set *uset)
  {
  	isl_set *set;
  	isl_bool params;
  
  	if (!uset)
  		return isl_bool_error;
  	if (uset->table.n != 1)
  		return isl_bool_false;
  
  	set = isl_set_from_union_set(isl_union_set_copy(uset));
  	params = isl_set_is_params(set);
  	isl_set_free(set);
  	return params;
  }
  
  /* Is this union map actually a parameter domain?
   * Users should never call this function.  Outside of isl,
   * a union map can never be a parameter domain.
   */
  isl_bool isl_union_map_is_params(__isl_keep isl_union_map *umap)
  {
  	return isl_union_set_is_params(uset_from_umap(umap));
  }
  
  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;
  }
  
  /* Create an empty union map without specifying any parameters.
   */
  __isl_give isl_union_map *isl_union_map_empty_ctx(isl_ctx *ctx)
  {
  	return isl_union_map_empty_space(isl_space_unit(ctx));
  }
  
  __isl_give isl_union_map *isl_union_map_empty_space(__isl_take isl_space *space)
  {
  	return isl_union_map_alloc(space, 16);
  }
  
  /* This is an alternative name for the function above.
   */
  __isl_give isl_union_map *isl_union_map_empty(__isl_take isl_space *space)
  {
  	return isl_union_map_empty_space(space);
  }
  
  /* Create an empty union set without specifying any parameters.
   */
  __isl_give isl_union_set *isl_union_set_empty_ctx(isl_ctx *ctx)
  {
  	return uset_from_umap(isl_union_map_empty_ctx(ctx));
  }
  
  __isl_give isl_union_set *isl_union_set_empty_space(__isl_take isl_space *space)
  {
  	return uset_from_umap(isl_union_map_empty_space(space));
  }
  
  /* This is an alternative name for the function above.
   */
  __isl_give isl_union_set *isl_union_set_empty(__isl_take isl_space *space)
  {
  	return isl_union_set_empty_space(space);
  }
  
  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;
  }
  
  /* Return the space of "umap".
   */
  __isl_keep isl_space *isl_union_map_peek_space(__isl_keep isl_union_map *umap)
  {
  	return umap ? umap->dim : NULL;
  }
  
  /* Return the space of "uset".
   */
  __isl_keep isl_space *isl_union_set_peek_space(__isl_keep isl_union_set *uset)
  {
  	return isl_union_map_peek_space(uset_to_umap(uset));
  }
  
  __isl_give isl_space *isl_union_map_get_space(__isl_keep isl_union_map *umap)
  {
  	return isl_space_copy(isl_union_map_peek_space(umap));
  }
  
  /* 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 isl_stat free_umap_entry(void **entry, void *user)
  {
  	isl_map *map = *entry;
  	isl_map_free(map);
  	return isl_stat_ok;
  }
  
  static isl_stat 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 isl_stat_ok;
  }
  
  __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 isl_stat 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 isl_stat_ok;
  }
  
  /* 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 };
  	isl_bool equal_params;
  
  	if (!umap || !model)
  		goto error;
  
  	equal_params = isl_space_has_equal_params(umap->dim, model);
  	if (equal_params < 0)
  		goto error;
  	if (equal_params) {
  		isl_space_free(model);
  		return umap;
  	}
  
  	data.exp = isl_parameter_alignment_reordering(umap->dim, model);
  	if (!data.exp)
  		goto error;
  
  	data.res = isl_union_map_alloc(isl_reordering_get_space(data.exp),
  					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);
  }
  
  /* Do "umap" and "space" have the same parameters?
   */
  isl_bool isl_union_map_space_has_equal_params(__isl_keep isl_union_map *umap,
  	__isl_keep isl_space *space)
  {
  	isl_space *umap_space;
  
  	umap_space = isl_union_map_peek_space(umap);
  	return isl_space_has_equal_params(umap_space, space);
  }
  
  /* Do "uset" and "space" have the same parameters?
   */
  isl_bool isl_union_set_space_has_equal_params(__isl_keep isl_union_set *uset,
  	__isl_keep isl_space *space)
  {
  	return isl_union_map_space_has_equal_params(uset_to_umap(uset), space);
  }
  
  static isl_bool has_space(const void *entry, const void *val)
  {
  	isl_map *map = (isl_map *)entry;
  	isl_space *space = (isl_space *) val;
  
  	return isl_space_is_equal(map->dim, space);
  }
  
  __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;
  	isl_bool aligned;
  
  	if (!map || !umap)
  		goto error;
  
  	if (isl_map_plain_is_empty(map)) {
  		isl_map_free(map);
  		return umap;
  	}
  
  	aligned = isl_map_space_has_equal_params(map, umap->dim);
  	if (aligned < 0)
  		goto error;
  	if (!aligned) {
  		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_space, 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, set_to_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(set_to_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
  {
  	isl_stat (*fn)(__isl_take isl_map *map, void *user);
  	void *user;
  };
  
  static isl_stat 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);
  }
  
  isl_size isl_union_map_n_map(__isl_keep isl_union_map *umap)
  {
  	return umap ? umap->table.n : isl_size_error;
  }
  
  isl_size isl_union_set_n_set(__isl_keep isl_union_set *uset)
  {
  	return uset ? uset->table.n : isl_size_error;
  }
  
  isl_stat isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
  	isl_stat (*fn)(__isl_take isl_map *map, void *user), void *user)
  {
  	struct isl_union_map_foreach_data data = { fn, user };
  
  	if (!umap)
  		return isl_stat_error;
  
  	return isl_hash_table_foreach(umap->dim->ctx, &umap->table,
  				      &call_on_copy, &data);
  }
  
  /* Internal data structure for isl_union_map_every_map.
   *
   * "test" is the user-specified callback function.
   * "user" is the user-specified callback function argument.
   *
   * "failed" is initialized to 0 and set to 1 if "test" fails
   * on any map.
   */
  struct isl_union_map_every_data {
  	isl_bool (*test)(__isl_keep isl_map *map, void *user);
  	void *user;
  	int failed;
  };
  
  /* Call data->test on "map".
   * If this fails, then set data->failed and abort.
   */
  static isl_stat call_every(void **entry, void *user)
  {
  	isl_map *map = *entry;
  	struct isl_union_map_every_data *data = user;
  	isl_bool r;
  
  	r = data->test(map, data->user);
  	if (r < 0)
  		return isl_stat_error;
  	if (r)
  		return isl_stat_ok;
  	data->failed = 1;
  	return isl_stat_error;
  }
  
  /* Does "test" succeed on every map in "umap"?
   */
  isl_bool isl_union_map_every_map(__isl_keep isl_union_map *umap,
  	isl_bool (*test)(__isl_keep isl_map *map, void *user), void *user)
  {
  	struct isl_union_map_every_data data = { test, user, 0 };
  	isl_stat r;
  
  	if (!umap)
  		return isl_bool_error;
  
  	r = isl_hash_table_foreach(isl_union_map_get_ctx(umap), &umap->table,
  				      &call_every, &data);
  	if (r >= 0)
  		return isl_bool_true;
  	if (data.failed)
  		return isl_bool_false;
  	return isl_bool_error;
  }
  
  /* Add "map" to "list".
   */
  static isl_stat add_list_map(__isl_take isl_map *map, void *user)
  {
  	isl_map_list **list = user;
  
  	*list = isl_map_list_add(*list, map);
  
  	if (!*list)
  		return isl_stat_error;
  	return isl_stat_ok;
  }
  
  /* Return the maps in "umap" as a list.
   *
   * First construct a list of the appropriate size and then add all the
   * elements.
   */
  __isl_give isl_map_list *isl_union_map_get_map_list(
  	__isl_keep isl_union_map *umap)
  {
  	isl_size n_maps;
  	isl_ctx *ctx;
  	isl_map_list *list;
  
  	n_maps = isl_union_map_n_map(umap);
  	if (n_maps < 0)
  		return NULL;
  	ctx = isl_union_map_get_ctx(umap);
  	list = isl_map_list_alloc(ctx, n_maps);
  
  	if (isl_union_map_foreach_map(umap, &add_list_map, &list) < 0)
  		list = isl_map_list_free(list);
  
  	return list;
  }
  
  /* Return the sets in "uset" as a list.
   */
  __isl_give isl_set_list *isl_union_set_get_set_list(
  	__isl_keep isl_union_set *uset)
  {
  	return set_list_from_map_list(
  		isl_union_map_get_map_list(uset_to_umap(uset)));
  }
  
  /* Can "umap" be converted to an isl_map?
   * That is, does it contain elements in exactly one space?
   */
  isl_bool isl_union_map_isa_map(__isl_keep isl_union_map *umap)
  {
  	isl_size n;
  
  	n = isl_union_map_n_map(umap);
  	if (n < 0)
  		return isl_bool_error;
  	return isl_bool_ok(n == 1);
  }
  
  /* Can "uset" be converted to an isl_set?
   * That is, does it contain elements in exactly one space?
   */
  isl_bool isl_union_set_isa_set(__isl_keep isl_union_set *uset)
  {
  	return isl_union_map_isa_map(uset_to_umap(uset));
  }
  
  static isl_stat copy_map(void **entry, void *user)
  {
  	isl_map *map = *entry;
  	isl_map **map_p = user;
  
  	*map_p = isl_map_copy(map);
  
  	return isl_stat_error;
  }
  
  __isl_give isl_map *isl_map_from_union_map(__isl_take isl_union_map *umap)
  {
  	isl_bool is_map;
  	isl_ctx *ctx;
  	isl_map *map = NULL;
  
  	is_map = isl_union_map_isa_map(umap);
  	if (is_map < 0)
  		goto error;
  	ctx = isl_union_map_get_ctx(umap);
  	if (!is_map)
  		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_all_params(space);
  	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_space, space, 0);
  	if (!entry)
  		goto error;
  	if (entry == isl_hash_table_entry_none)
  		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 set_from_map(isl_union_map_extract_map(uset, dim));
  }
  
  /* Check if umap contains a map in the given space.
   */
  isl_bool isl_union_map_contains(__isl_keep isl_union_map *umap,
  	__isl_keep isl_space *space)
  {
  	uint32_t hash;
  	struct isl_hash_table_entry *entry;
  
  	if (!umap || !space)
  		return isl_bool_error;
  
  	hash = isl_space_get_hash(space);
  	entry = isl_hash_table_find(umap->dim->ctx, &umap->table, hash,
  				    &has_space, space, 0);
  	if (!entry)
  		return isl_bool_error;
  	return isl_bool_ok(entry != isl_hash_table_entry_none);
  }
  
  isl_bool isl_union_set_contains(__isl_keep isl_union_set *uset,
  	__isl_keep isl_space *space)
  {
  	return isl_union_map_contains(uset, space);
  }
  
  isl_stat isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
  	isl_stat (*fn)(__isl_take isl_set *set, void *user), void *user)
  {
  	return isl_union_map_foreach_map(uset,
  		(isl_stat(*)(__isl_take isl_map *, void*))fn, user);
  }
  
  /* Internal data structure for isl_union_set_every_set.
   *
   * "test" is the user-specified callback function.
   * "user" is the user-specified callback function argument.
   */
  struct isl_test_set_from_map_data {
  	isl_bool (*test)(__isl_keep isl_set *set, void *user);
  	void *user;
  };
  
  /* Call data->test on "map", which is part of an isl_union_set and
   * therefore known to be an isl_set.
   */
  static isl_bool test_set_from_map(__isl_keep isl_map *map, void *user)
  {
  	struct isl_test_set_from_map_data *data = user;
  
  	return data->test(set_from_map(map), data->user);
  }
  
  /* Does "test" succeed on every set in "uset"?
   */
  isl_bool isl_union_set_every_set(__isl_keep isl_union_set *uset,
  	isl_bool (*test)(__isl_keep isl_set *set, void *user), void *user)
  {
  	struct isl_test_set_from_map_data data = { test, user };
  
  	return isl_union_map_every_map(uset_to_umap(uset),
  					&test_set_from_map, &data);
  }
  
  struct isl_union_set_foreach_point_data {
  	isl_stat (*fn)(__isl_take isl_point *pnt, void *user);
  	void *user;
  };
  
  static isl_stat foreach_point(__isl_take isl_set *set, void *user)
  {
  	struct isl_union_set_foreach_point_data *data = user;
  	isl_stat r;
  
  	r = isl_set_foreach_point(set, data->fn, data->user);
  	isl_set_free(set);
  
  	return r;
  }
  
  isl_stat isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
  	isl_stat (*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);
  }
  
  /* Data structure that specifies how gen_bin_op should
   * construct results from the inputs.
   *
   * If "subtract" is set, then a map in the first input is copied to the result
   * if there is no corresponding map in the second input.
   * Otherwise, a map in the first input with no corresponding map
   * in the second input is ignored.
   * If "filter" is not NULL, then it specifies which maps in the first
   * input may have a matching map in the second input.
   * In particular, it makes sure that "match_space" can be called
   * on the space of the map.
   * "match_space" specifies how to transform the space of a map
   * in the first input to the space of the corresponding map
   * in the second input.
   * "fn_map" specifies how the matching maps, one from each input,
   * should be combined to form a map in the result.
   */
  struct isl_bin_op_control {
  	int subtract;
  	isl_bool (*filter)(__isl_keep isl_map *map);
  	__isl_give isl_space *(*match_space)(__isl_take isl_space *space);
  	__isl_give isl_map *(*fn_map)(__isl_take isl_map *map1,
  		__isl_take isl_map *map2);
  };
  
  /* Internal data structure for gen_bin_op.
   * "control" specifies how the maps in the result should be constructed.
   * "umap2" is a pointer to the second argument.
   * "res" collects the results.
   */
  struct isl_union_map_gen_bin_data {
  	struct isl_bin_op_control *control;
  	isl_union_map *umap2;
  	isl_union_map *res;
  };
  
  /* Add a copy of "map" to "res" and return the result.
   */
  static __isl_give isl_union_map *bin_add_map(__isl_take isl_union_map *res,
  	__isl_keep isl_map *map)
  {
  	return isl_union_map_add_map(res, isl_map_copy(map));
  }
  
  /* Combine "map1" and "map2", add the result to "res" and return the result.
   * Check whether the result is empty before adding it to "res".
   */
  static __isl_give isl_union_map *bin_add_pair(__isl_take isl_union_map *res,
  	__isl_keep isl_map *map1, __isl_keep isl_map *map2,
  	struct isl_union_map_gen_bin_data *data)
  {
  	isl_bool empty;
  	isl_map *map;
  
  	map = data->control->fn_map(isl_map_copy(map1), isl_map_copy(map2));
  	empty = isl_map_is_empty(map);
  	if (empty < 0 || empty) {
  		isl_map_free(map);
  		if (empty < 0)
  			return isl_union_map_free(res);
  		return res;
  	}
  	return isl_union_map_add_map(res, map);
  }
  
  /* Dummy match_space function that simply returns the input space.
   */
  static __isl_give isl_space *identity(__isl_take isl_space *space)
  {
  	return space;
  }
  
  /* Look for the map in data->umap2 that corresponds to "map", if any.
   * Return (isl_bool_true, matching map) if there is one,
   * (isl_bool_false, NULL) if there is no matching map and
   * (isl_bool_error, NULL) on error.
   *
   * If not NULL, then data->control->filter specifies whether "map"
   * can have any matching map.  If so,
   * data->control->match_space specifies which map in data->umap2
   * corresponds to "map".
   */
  static __isl_keep isl_maybe_isl_map bin_try_get_match(
  	struct isl_union_map_gen_bin_data *data, __isl_keep isl_map *map)
  {
  	uint32_t hash;
  	struct isl_hash_table_entry *entry2;
  	isl_space *space;
  	isl_maybe_isl_map res = { isl_bool_error, NULL };
  
  	if (data->control->filter) {
  		res.valid = data->control->filter(map);
  		if (res.valid < 0 || !res.valid)
  			return res;
  		res.valid = isl_bool_error;
  	}
  
  	space = isl_map_get_space(map);
  	if (data->control->match_space != &identity)
  		space = data->control->match_space(space);
  	if (!space)
  		return res;
  	hash = isl_space_get_hash(space);
  	entry2 = isl_hash_table_find(isl_union_map_get_ctx(data->umap2),
  				     &data->umap2->table, hash,
  				     &has_space, space, 0);
  	isl_space_free(space);
  	if (entry2)
  		res.valid = isl_bool_ok(entry2 != isl_hash_table_entry_none);
  	if (res.valid >= 0 && res.valid)
  		res.value = entry2->data;
  
  	return res;
  }
  
  /* isl_hash_table_foreach callback for gen_bin_op.
   * Look for the map in data->umap2 that corresponds
   * to the map that "entry" points to, apply the binary operation and
   * add the result to data->res.
   *
   * If no corresponding map can be found, then the effect depends
   * on data->control->subtract.  If it is set, then the current map
   * is added directly to the result.  Otherwise, it is ignored.
   */
  static isl_stat gen_bin_entry(void **entry, void *user)
  {
  	struct isl_union_map_gen_bin_data *data = user;
  	isl_map *map = *entry;
  	isl_maybe_isl_map m;
  
  	m = bin_try_get_match(data, map);
  	if (m.valid < 0)
  		return isl_stat_error;
  	if (!m.valid && !data->control->subtract)
  		return isl_stat_ok;
  
  	if (!m.valid)
  		data->res = bin_add_map(data->res, map);
  	else
  		data->res = bin_add_pair(data->res, map, m.value, data);
  	if (!data->res)
  		return isl_stat_error;
  
  	return isl_stat_ok;
  }
  
  /* Apply a binary operation to "umap1" and "umap2" based on "control".
   * Run over all maps in "umap1" and look for the corresponding map in "umap2"
   * in gen_bin_entry.
   */
  static __isl_give isl_union_map *gen_bin_op(__isl_take isl_union_map *umap1,
  	__isl_take isl_union_map *umap2, struct isl_bin_op_control *control)
  {
  	struct isl_union_map_gen_bin_data data = { control, 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,
  				   &gen_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_subtract(
  	__isl_take isl_union_map *umap1, __isl_take isl_union_map *umap2)
  {
  	struct isl_bin_op_control control = {
  		.subtract = 1,
  		.match_space = &identity,
  		.fn_map = &isl_map_subtract,
  	};
  
  	return gen_bin_op(umap1, umap2, &control);
  }
  
  __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 isl_stat 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 isl_stat_error;
  	}
  
  	data->res = isl_union_map_add_map(data->res, map);
  
  	return isl_stat_ok;
  }
  
  static __isl_give isl_union_map *gen_bin_set_op(__isl_take isl_union_map *umap,
  	__isl_take isl_set *set, isl_stat (*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 isl_stat 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_space, map->dim, 0);
  	if (!entry2)
  		return isl_stat_error;
  	if (entry2 == isl_hash_table_entry_none)
  		return isl_stat_ok;
  
  	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 isl_stat_error;
  	}
  	if (empty) {
  		isl_map_free(map);
  		return isl_stat_ok;
  	}
  
  	data->res = isl_union_map_add_map(data->res, map);
  
  	return isl_stat_ok;
  }
  
  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 isl_stat 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 isl_stat_error;
  	}
  
  	data->res = isl_union_map_add_map(data->res, map);
  
  	return isl_stat_ok;
  }
  
  __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);
  }
  
  /* For each map in "umap", remove the constraints in the corresponding map
   * of "context".
   * Each map in "context" is assumed to consist of a single disjunct and
   * to have explicit representations for all local variables.
   */
  __isl_give isl_union_map *isl_union_map_plain_gist(
  	__isl_take isl_union_map *umap, __isl_take isl_union_map *context)
  {
  	return match_bin_op(umap, context, &isl_map_plain_gist);
  }
  
  /* For each set in "uset", remove the constraints in the corresponding set
   * of "context".
   * Each set in "context" is assumed to consist of a single disjunct and
   * to have explicit representations for all local variables.
   */
  __isl_give isl_union_set *isl_union_set_plain_gist(
  	__isl_take isl_union_set *uset, __isl_take isl_union_set *context)
  {
  	return isl_union_map_plain_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(set_from_map(set1), set_from_map(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(set_from_map(set1), set_from_map(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));
  }
  
  /* Intersect the domain of "umap" with "uset".
   */
  static __isl_give isl_union_map *union_map_intersect_domain(
  	__isl_take isl_union_map *umap, __isl_take isl_union_set *uset)
  {
  	struct isl_bin_op_control control = {
  		.match_space = &isl_space_domain,
  		.fn_map = &isl_map_intersect_domain,
  	};
  
  	return gen_bin_op(umap, uset, &control);
  }
  
  /* 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);
  	else
  		return union_map_intersect_domain(umap, uset);
  }
  
  /* 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)
  {
  	struct isl_bin_op_control control = {
  		.subtract = 1,
  		.match_space = &isl_space_domain,
  		.fn_map = &isl_map_subtract_domain,
  	};
  
  	return gen_bin_op(umap, dom, &control);
  }
  
  /* 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)
  {
  	struct isl_bin_op_control control = {
  		.subtract = 1,
  		.match_space = &isl_space_range,
  		.fn_map = &isl_map_subtract_range,
  	};
  
  	return gen_bin_op(umap, dom, &control);
  }
  
  /* Compute the gist of "umap" with respect to the domain "uset".
   */
  static __isl_give isl_union_map *union_map_gist_domain(
  	__isl_take isl_union_map *umap, __isl_take isl_union_set *uset)
  {
  	struct isl_bin_op_control control = {
  		.match_space = &isl_space_domain,
  		.fn_map = &isl_map_gist_domain,
  	};
  
  	return gen_bin_op(umap, uset, &control);
  }
  
  /* 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);
  	else
  		return union_map_gist_domain(umap, uset);
  }
  
  /* 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)
  {
  	struct isl_bin_op_control control = {
  		.match_space = &isl_space_range,
  		.fn_map = &isl_map_gist_range,
  	};
  
  	return gen_bin_op(umap, uset, &control);
  }
  
  __isl_give isl_union_map *isl_union_map_intersect_range(
  	__isl_take isl_union_map *umap, __isl_take isl_union_set *uset)
  {
  	struct isl_bin_op_control control = {
  		.match_space = &isl_space_range,
  		.fn_map = &isl_map_intersect_range,
  	};
  
  	return gen_bin_op(umap, uset, &control);
  }
  
  /* Intersect each map in "umap" in a space [A -> B] -> C
   * with the corresponding map in "factor" in the space B -> C and
   * collect the results.
   */
  __isl_give isl_union_map *isl_union_map_intersect_domain_factor_range(
  	__isl_take isl_union_map *umap, __isl_take isl_union_map *factor)
  {
  	struct isl_bin_op_control control = {
  		.filter = &isl_map_domain_is_wrapping,
  		.match_space = &isl_space_domain_factor_range,
  		.fn_map = &isl_map_intersect_domain_factor_range,
  	};
  
  	return gen_bin_op(umap, factor, &control);
  }
  
  /* Intersect each map in "umap" in a space A -> [B -> C]
   * with the corresponding map in "factor" in the space A -> B and
   * collect the results.
   */
  __isl_give isl_union_map *isl_union_map_intersect_range_factor_domain(
  	__isl_take isl_union_map *umap, __isl_take isl_union_map *factor)
  {
  	struct isl_bin_op_control control = {
  		.filter = &isl_map_range_is_wrapping,
  		.match_space = &isl_space_range_factor_domain,
  		.fn_map = &isl_map_intersect_range_factor_domain,
  	};
  
  	return gen_bin_op(umap, factor, &control);
  }
  
  /* Intersect each map in "umap" in a space A -> [B -> C]
   * with the corresponding map in "factor" in the space A -> C and
   * collect the results.
   */
  __isl_give isl_union_map *isl_union_map_intersect_range_factor_range(
  	__isl_take isl_union_map *umap, __isl_take isl_union_map *factor)
  {
  	struct isl_bin_op_control control = {
  		.filter = &isl_map_range_is_wrapping,
  		.match_space = &isl_space_range_factor_range,
  		.fn_map = &isl_map_intersect_range_factor_range,
  	};
  
  	return gen_bin_op(umap, factor, &control);
  }
  
  struct isl_union_map_bin_data {
  	isl_union_map *umap2;
  	isl_union_map *res;
  	isl_map *map;
  	isl_stat (*fn)(void **entry, void *user);
  };
  
  static isl_stat apply_range_entry(void **entry, void *user)
  {
  	struct isl_union_map_bin_data *data = user;
  	isl_map *map2 = *entry;
  	isl_bool empty;
  
  	if (!isl_space_tuple_is_equal(data->map->dim, isl_dim_out,
  				 map2->dim, isl_dim_in))
  		return isl_stat_ok;
  
  	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 isl_stat_error;
  	}
  	if (empty) {
  		isl_map_free(map2);
  		return isl_stat_ok;
  	}
  
  	data->res = isl_union_map_add_map(data->res, map2);
  
  	return isl_stat_ok;
  }
  
  static isl_stat 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 isl_stat_error;
  
  	return isl_stat_ok;
  }
  
  static __isl_give isl_union_map *bin_op(__isl_take isl_union_map *umap1,
  	__isl_take isl_union_map *umap2,
  	isl_stat (*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 isl_stat 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 isl_stat_ok;
  
  	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 isl_stat_ok;
  }
  
  __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 isl_stat 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 isl_stat_ok;
  
  	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 isl_stat_ok;
  }
  
  __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 isl_stat 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 isl_stat_ok;
  }
  
  __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 isl_stat 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 isl_stat_ok;
  }
  
  __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 isl_stat 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 isl_stat_ok;
  
  	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 isl_stat_ok;
  }
  
  /* 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 isl_stat 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 isl_stat_ok;
  
  	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 isl_stat_ok;
  }
  
  __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 isl_stat 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 isl_stat_ok;
  
  	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 isl_stat_ok;
  }
  
  /* 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 isl_stat 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 isl_stat_ok;
  
  	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 isl_stat_ok;
  }
  
  __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);
  }
  
  /* Data structure that specifies how un_op should modify
   * the maps in the union map.
   *
   * If "inplace" is set, then the maps in the input union map
   * are modified in place.  This means that "fn_map" should not
   * change the meaning of the map or that the union map only
   * has a single reference.
   * If "total" is set, then all maps need to be modified and
   * the results need to live in the same space.
   * Otherwise, a new union map is constructed to store the results.
   * If "filter" is not NULL, then only the input maps that satisfy "filter"
   * are taken into account.  "filter_user" is passed as the second argument
   * to "filter".  No filter can be set if "inplace" or
   * "total" is set.
   * Exactly one of "fn_map" or "fn_map2" should be set, specifying
   * how the maps (selected by "filter") should be transformed.
   * If "fn_map2" is set, then "fn_map2_user" is passed as the second argument.
   */
  struct isl_un_op_control {
  	int inplace;
  	int total;
  	isl_bool (*filter)(__isl_keep isl_map *map, void *user);
  	void *filter_user;
  	__isl_give isl_map *(*fn_map)(__isl_take isl_map *map);
  	__isl_give isl_map *(*fn_map2)(__isl_take isl_map *map, void *user);
  	void *fn_map2_user;
  };
  
  /* Data structure for wrapping the data for un_op_filter_drop_user.
   * "filter" is the function that is being wrapped.
   */
  struct isl_un_op_drop_user_data {
  	isl_bool (*filter)(__isl_keep isl_map *map);
  };
  
  /* Wrapper for isl_un_op_control filters that do not require
   * a second argument.
   * Simply call data->filter without the second argument.
   */
  static isl_bool un_op_filter_drop_user(__isl_keep isl_map *map, void *user)
  {
  	struct isl_un_op_drop_user_data *data = user;
  	return data->filter(map);
  }
  
  /* Internal data structure for "un_op".
   * "control" specifies how the maps in the union map should be modified.
   * "res" collects the results.
   */
  struct isl_union_map_un_data {
  	struct isl_un_op_control *control;
  	isl_union_map *res;
  };
  
  /* isl_hash_table_foreach callback for un_op.
   * Handle the map that "entry" points to.
   *
   * If control->filter is set, then check if this map satisfies the filter.
   * If so (or if control->filter is not set), modify the map
   * by calling control->fn_map or control->fn_map2 and
   * either add the result to data->res or
   * replace the original entry by the result (if control->inplace is set).
   */
  static isl_stat un_entry(void **entry, void *user)
  {
  	struct isl_union_map_un_data *data = user;
  	struct isl_un_op_control *control = data->control;
  	isl_map *map = *entry;
  
  	if (control->filter) {
  		isl_bool ok;
  
  		ok = control->filter(map, control->filter_user);
  		if (ok < 0)
  			return isl_stat_error;
  		if (!ok)
  			return isl_stat_ok;
  	}
  
  	map = isl_map_copy(map);
  	if (control->fn_map2 != NULL)
  		map = control->fn_map2(map, control->fn_map2_user);
  	else
  		map = control->fn_map(map);
  	if (!map)
  		return isl_stat_error;
  	if (control->inplace) {
  		isl_map_free(*entry);
  		*entry = map;
  	} else {
  		data->res = isl_union_map_add_map(data->res, map);
  		if (!data->res)
  			return isl_stat_error;
  	}
  
  	return isl_stat_ok;
  }
  
  /* Modify the maps in "umap" based on "control".
   * If control->inplace is set, then modify the maps in "umap" in-place.
   * Otherwise, create a new union map to hold the results.
   * If control->total is set, then perform an inplace computation
   * if "umap" is only referenced once.  Otherwise, create a new union map
   * to store the results.
   */
  static __isl_give isl_union_map *un_op(__isl_take isl_union_map *umap,
  	struct isl_un_op_control *control)
  {
  	struct isl_union_map_un_data data = { control };
  
  	if (!umap)
  		return NULL;
  	if (!!control->fn_map == !!control->fn_map2)
  		isl_die(isl_union_map_get_ctx(umap), isl_error_internal,
  			"exactly one mapping function should be specified",
  			return isl_union_map_free(umap));
  	if ((control->inplace || control->total) && control->filter)
  		isl_die(isl_union_map_get_ctx(umap), isl_error_invalid,
  			"inplace/total modification cannot be filtered",
  			return isl_union_map_free(umap));
  
  	if (control->total && umap->ref == 1)
  		control->inplace = 1;
  	if (control->inplace) {
  		data.res = umap;
  	} else {
  		isl_space *space;
  
  		space = isl_union_map_get_space(umap);
  		data.res = isl_union_map_alloc(space, umap->table.n);
  	}
  	if (isl_hash_table_foreach(isl_union_map_get_ctx(umap),
  				    &umap->table, &un_entry, &data) < 0)
  		data.res = isl_union_map_free(data.res);
  
  	if (control->inplace)
  		return data.res;
  	isl_union_map_free(umap);
  	return data.res;
  }
  
  __isl_give isl_union_map *isl_union_map_from_range(
  	__isl_take isl_union_set *uset)
  {
  	struct isl_un_op_control control = {
  		.fn_map = &isl_map_from_range,
  	};
  	return un_op(uset, &control);
  }
  
  __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));
  }
  
  /* Modify the maps in "umap" by applying "fn" on them.
   * "fn" should apply to all maps in "umap" and should not modify the space.
   */
  static __isl_give isl_union_map *total(__isl_take isl_union_map *umap,
  	__isl_give isl_map *(*fn)(__isl_take isl_map *))
  {
  	struct isl_un_op_control control = {
  		.total = 1,
  		.fn_map = fn,
  	};
  
  	return un_op(umap, &control);
  }
  
  /* Compute the affine hull of "map" and return the result as an isl_map.
   */
  static __isl_give isl_map *isl_map_affine_hull_map(__isl_take isl_map *map)
  {
  	return isl_map_from_basic_map(isl_map_affine_hull(map));
  }
  
  __isl_give isl_union_map *isl_union_map_affine_hull(
  	__isl_take isl_union_map *umap)
  {
  	return total(umap, &isl_map_affine_hull_map);
  }
  
  __isl_give isl_union_set *isl_union_set_affine_hull(
  	__isl_take isl_union_set *uset)
  {
  	return isl_union_map_affine_hull(uset);
  }
  
  /* Wrapper around isl_set_combined_lineality_space
   * that returns the combined lineality space in the form of an isl_set
   * instead of an isl_basic_set.
   */
  static __isl_give isl_set *combined_lineality_space(__isl_take isl_set *set)
  {
  	return isl_set_from_basic_set(isl_set_combined_lineality_space(set));
  }
  
  /* For each set in "uset", compute the (linear) hull
   * of the lineality spaces of its basic sets and
   * collect and return the results.
   */
  __isl_give isl_union_set *isl_union_set_combined_lineality_space(
  	__isl_take isl_union_set *uset)
  {
  	struct isl_un_op_control control = {
  		.fn_map = &combined_lineality_space,
  	};
  	return un_op(uset, &control);
  }
  
  /* Compute the polyhedral hull of "map" and return the result as an isl_map.
   */
  static __isl_give isl_map *isl_map_polyhedral_hull_map(__isl_take isl_map *map)
  {
  	return isl_map_from_basic_map(isl_map_polyhedral_hull(map));
  }
  
  __isl_give isl_union_map *isl_union_map_polyhedral_hull(
  	__isl_take isl_union_map *umap)
  {
  	return total(umap, &isl_map_polyhedral_hull_map);
  }
  
  __isl_give isl_union_set *isl_union_set_polyhedral_hull(
  	__isl_take isl_union_set *uset)
  {
  	return isl_union_map_polyhedral_hull(uset);
  }
  
  /* Compute a superset of the convex hull of "map" that is described
   * by only translates of the constraints in the constituents of "map" and
   * return the result as an isl_map.
   */
  static __isl_give isl_map *isl_map_simple_hull_map(__isl_take isl_map *map)
  {
  	return isl_map_from_basic_map(isl_map_simple_hull(map));
  }
  
  __isl_give isl_union_map *isl_union_map_simple_hull(
  	__isl_take isl_union_map *umap)
  {
  	return total(umap, &isl_map_simple_hull_map);
  }
  
  __isl_give isl_union_set *isl_union_set_simple_hull(
  	__isl_take isl_union_set *uset)
  {
  	return isl_union_map_simple_hull(uset);
  }
  
  static __isl_give isl_union_map *inplace(__isl_take isl_union_map *umap,
  	__isl_give isl_map *(*fn)(__isl_take isl_map *))
  {
  	struct isl_un_op_control control = {
  		.inplace = 1,
  		.fn_map = fn,
  	};
  
  	return un_op(umap, &control);
  }
  
  /* 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);
  }
  
  __isl_give isl_union_map *isl_union_map_lexmin(
  	__isl_take isl_union_map *umap)
  {
  	return total(umap, &isl_map_lexmin);
  }
  
  __isl_give isl_union_set *isl_union_set_lexmin(
  	__isl_take isl_union_set *uset)
  {
  	return isl_union_map_lexmin(uset);
  }
  
  __isl_give isl_union_map *isl_union_map_lexmax(
  	__isl_take isl_union_map *umap)
  {
  	return total(umap, &isl_map_lexmax);
  }
  
  __isl_give isl_union_set *isl_union_set_lexmax(
  	__isl_take isl_union_set *uset)
  {
  	return isl_union_map_lexmax(uset);
  }
  
  /* Return the universe in the space of "map".
   */
  static __isl_give isl_map *universe(__isl_take isl_map *map)
  {
  	isl_space *space;
  
  	space = isl_map_get_space(map);
  	isl_map_free(map);
  	return isl_map_universe(space);
  }
  
  __isl_give isl_union_map *isl_union_map_universe(__isl_take isl_union_map *umap)
  {
  	struct isl_un_op_control control = {
  		.fn_map = &universe,
  	};
  	return un_op(umap, &control);
  }
  
  __isl_give isl_union_set *isl_union_set_universe(__isl_take isl_union_set *uset)
  {
  	return isl_union_map_universe(uset);
  }
  
  __isl_give isl_union_map *isl_union_map_reverse(__isl_take isl_union_map *umap)
  {
  	struct isl_un_op_control control = {
  		.fn_map = &isl_map_reverse,
  	};
  	return un_op(umap, &control);
  }
  
  /* Given a union map, take the maps of the form A -> (B -> C) and
   * return the union of the corresponding maps A -> (C -> B).
   */
  __isl_give isl_union_map *isl_union_map_range_reverse(
  	__isl_take isl_union_map *umap)
  {
  	struct isl_un_op_drop_user_data data = { &isl_map_range_is_wrapping };
  	struct isl_un_op_control control = {
  		.filter = &un_op_filter_drop_user,
  		.filter_user = &data,
  		.fn_map = &isl_map_range_reverse,
  	};
  	return un_op(umap, &control);
  }
  
  /* Compute the parameter domain of the given union map.
   */
  __isl_give isl_set *isl_union_map_params(__isl_take isl_union_map *umap)
  {
  	struct isl_un_op_control control = {
  		.fn_map = &isl_map_params,
  	};
  	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(un_op(umap, &control));
  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);
  }
  
  __isl_give isl_union_set *isl_union_map_domain(__isl_take isl_union_map *umap)
  {
  	struct isl_un_op_control control = {
  		.fn_map = &isl_map_domain,
  	};
  	return un_op(umap, &control);
  }
  
  __isl_give isl_union_set *isl_union_map_range(__isl_take isl_union_map *umap)
  {
  	struct isl_un_op_control control = {
  		.fn_map = &isl_map_range,
  	};
  	return un_op(umap, &control);
  }
  
  __isl_give isl_union_map *isl_union_map_domain_map(
  	__isl_take isl_union_map *umap)
  {
  	struct isl_un_op_control control = {
  		.fn_map = &isl_map_domain_map,
  	};
  	return un_op(umap, &control);
  }
  
  /* Construct an isl_pw_multi_aff that maps "map" to its domain and
   * add the result to "res".
   */
  static isl_stat 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 ? isl_stat_ok : isl_stat_error;
  
  }
  
  /* 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;
  }
  
  __isl_give isl_union_map *isl_union_map_range_map(
  	__isl_take isl_union_map *umap)
  {
  	struct isl_un_op_control control = {
  		.fn_map = &isl_map_range_map,
  	};
  	return un_op(umap, &control);
  }
  
  /* 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)
  {
  	struct isl_un_op_drop_user_data data = { &isl_set_is_wrapping };
  	struct isl_un_op_control control = {
  		.filter = &un_op_filter_drop_user,
  		.filter_user = &data,
  		.fn_map = &isl_set_wrapped_domain_map,
  	};
  	return un_op(uset, &control);
  }
  
  /* Does "map" relate elements from the same space?
   */
  static isl_bool equal_tuples(__isl_keep isl_map *map, void *user)
  {
  	return isl_space_tuple_is_equal(map->dim, isl_dim_in,
  					map->dim, isl_dim_out);
  }
  
  __isl_give isl_union_set *isl_union_map_deltas(__isl_take isl_union_map *umap)
  {
  	struct isl_un_op_control control = {
  		.filter = &equal_tuples,
  		.fn_map = &isl_map_deltas,
  	};
  	return un_op(umap, &control);
  }
  
  __isl_give isl_union_map *isl_union_map_deltas_map(
  	__isl_take isl_union_map *umap)
  {
  	struct isl_un_op_control control = {
  		.filter = &equal_tuples,
  		.fn_map = &isl_map_deltas_map,
  	};
  	return un_op(umap, &control);
  }
  
  __isl_give isl_union_map *isl_union_set_identity(__isl_take isl_union_set *uset)
  {
  	struct isl_un_op_control control = {
  		.fn_map = &isl_set_identity,
  	};
  	return un_op(uset, &control);
  }
  
  /* Construct an identity isl_pw_multi_aff on "set" and add it to *res.
   */
  static isl_stat 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 ? isl_stat_ok : isl_stat_error;
  }
  
  /* 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;
  }
  
  /* 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)
  {
  	struct isl_un_op_drop_user_data data = { &isl_map_domain_is_wrapping };
  	struct isl_un_op_control control = {
  		.filter = &un_op_filter_drop_user,
  		.filter_user = &data,
  		.fn_map = &isl_map_domain_factor_domain,
  	};
  	return un_op(umap, &control);
  }
  
  /* 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)
  {
  	struct isl_un_op_drop_user_data data = { &isl_map_domain_is_wrapping };
  	struct isl_un_op_control control = {
  		.filter = &un_op_filter_drop_user,
  		.filter_user = &data,
  		.fn_map = &isl_map_domain_factor_range,
  	};
  	return un_op(umap, &control);
  }
  
  /* For each map in "umap" of the form A -> [B -> C],
   * construct the map A -> B and collect the results.
   */
  __isl_give isl_union_map *isl_union_map_range_factor_domain(
  	__isl_take isl_union_map *umap)
  {
  	struct isl_un_op_drop_user_data data = { &isl_map_range_is_wrapping };
  	struct isl_un_op_control control = {
  		.filter = &un_op_filter_drop_user,
  		.filter_user = &data,
  		.fn_map = &isl_map_range_factor_domain,
  	};
  	return un_op(umap, &control);
  }
  
  /* 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)
  {
  	struct isl_un_op_drop_user_data data = { &isl_map_range_is_wrapping };
  	struct isl_un_op_control control = {
  		.filter = &un_op_filter_drop_user,
  		.filter_user = &data,
  		.fn_map = &isl_map_range_factor_range,
  	};
  	return un_op(umap, &control);
  }
  
  /* 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)
  {
  	struct isl_un_op_drop_user_data data = { &isl_map_is_product };
  	struct isl_un_op_control control = {
  		.filter = &un_op_filter_drop_user,
  		.filter_user = &data,
  		.fn_map = &isl_map_factor_domain,
  	};
  	return un_op(umap, &control);
  }
  
  /* 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)
  {
  	struct isl_un_op_drop_user_data data = { &isl_map_is_product };
  	struct isl_un_op_control control = {
  		.filter = &un_op_filter_drop_user,
  		.filter_user = &data,
  		.fn_map = &isl_map_factor_range,
  	};
  	return un_op(umap, &control);
  }
  
  __isl_give isl_union_map *isl_union_set_unwrap(__isl_take isl_union_set *uset)
  {
  	struct isl_un_op_drop_user_data data = { &isl_set_is_wrapping };
  	struct isl_un_op_control control = {
  		.filter = &un_op_filter_drop_user,
  		.filter_user = &data,
  		.fn_map = &isl_set_unwrap,
  	};
  	return un_op(uset, &control);
  }
  
  __isl_give isl_union_set *isl_union_map_wrap(__isl_take isl_union_map *umap)
  {
  	struct isl_un_op_control control = {
  		.fn_map = &isl_map_wrap,
  	};
  	return un_op(umap, &control);
  }
  
  struct isl_union_map_is_subset_data {
  	isl_union_map *umap2;
  	isl_bool is_subset;
  };
  
  static isl_stat 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_space, map->dim, 0);
  	if (!entry2)
  		return isl_stat_error;
  	if (entry2 == isl_hash_table_entry_none) {
  		int empty = isl_map_is_empty(map);
  		if (empty < 0)
  			return isl_stat_error;
  		if (empty)
  			return isl_stat_ok;
  		data->is_subset = isl_bool_false;
  		return isl_stat_error;
  	}
  
  	data->is_subset = isl_map_is_subset(map, entry2->data);
  	if (data->is_subset < 0 || !data->is_subset)
  		return isl_stat_error;
  
  	return isl_stat_ok;
  }
  
  isl_bool 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, isl_bool_true };
  
  	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 isl_bool_error;
  }
  
  isl_bool 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);
  }
  
  isl_bool isl_union_map_is_equal(__isl_keep isl_union_map *umap1,
  	__isl_keep isl_union_map *umap2)
  {
  	isl_bool is_subset;
  
  	if (!umap1 || !umap2)
  		return isl_bool_error;
  	is_subset = isl_union_map_is_subset(umap1, umap2);
  	if (is_subset != isl_bool_true)
  		return is_subset;
  	is_subset = isl_union_map_is_subset(umap2, umap1);
  	return is_subset;
  }
  
  isl_bool 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);
  }
  
  isl_bool isl_union_map_is_strict_subset(__isl_keep isl_union_map *umap1,
  	__isl_keep isl_union_map *umap2)
  {
  	isl_bool is_subset;
  
  	if (!umap1 || !umap2)
  		return isl_bool_error;
  	is_subset = isl_union_map_is_subset(umap1, umap2);
  	if (is_subset != isl_bool_true)
  		return is_subset;
  	is_subset = isl_union_map_is_subset(umap2, umap1);
  	return isl_bool_not(is_subset);
  }
  
  isl_bool 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;
  	isl_bool is_disjoint;
  };
  
  /* Check if "map" is disjoint from data->umap2 and abort
   * the search if it is not.
   */
  static isl_stat 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_space, map->dim, 0);
  	if (!entry2)
  		return isl_stat_error;
  	if (entry2 == isl_hash_table_entry_none)
  		return isl_stat_ok;
  
  	data->is_disjoint = isl_map_is_disjoint(map, entry2->data);
  	if (data->is_disjoint < 0 || !data->is_disjoint)
  		return isl_stat_error;
  
  	return isl_stat_ok;
  }
  
  /* Are "umap1" and "umap2" disjoint?
   */
  isl_bool 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, isl_bool_true };
  
  	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 isl_bool_error;
  }
  
  /* Are "uset1" and "uset2" disjoint?
   */
  isl_bool 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 isl_stat 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 isl_stat_error;
  	if (!isl_basic_map_plain_is_empty(*sample))
  		return isl_stat_error;
  	return isl_stat_ok;
  }
  
  __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 bset_from_bmap(isl_union_map_sample(uset));
  }
  
  /* Return an element in "uset" in the form of an isl_point.
   * Return a void isl_point if "uset" is empty.
   */
  __isl_give isl_point *isl_union_set_sample_point(__isl_take isl_union_set *uset)
  {
  	return isl_basic_set_sample_point(isl_union_set_sample(uset));
  }
  
  struct isl_forall_data {
  	isl_bool res;
  	isl_bool (*fn)(__isl_keep isl_map *map);
  };
  
  static isl_stat 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 isl_stat_error;
  
  	if (!data->res)
  		return isl_stat_error;
  
  	return isl_stat_ok;
  }
  
  static isl_bool union_map_forall(__isl_keep isl_union_map *umap,
  	isl_bool (*fn)(__isl_keep isl_map *map))
  {
  	struct isl_forall_data data = { isl_bool_true, fn };
  
  	if (!umap)
  		return isl_bool_error;
  
  	if (isl_hash_table_foreach(umap->dim->ctx, &umap->table,
  				   &forall_entry, &data) < 0 && data.res)
  		return isl_bool_error;
  
  	return data.res;
  }
  
  struct isl_forall_user_data {
  	isl_bool res;
  	isl_bool (*fn)(__isl_keep isl_map *map, void *user);
  	void *user;
  };
  
  static isl_stat 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 isl_stat_error;
  
  	if (!data->res)
  		return isl_stat_error;
  
  	return isl_stat_ok;
  }
  
  /* Check if fn(map, user) returns true for all maps "map" in umap.
   */
  static isl_bool union_map_forall_user(__isl_keep isl_union_map *umap,
  	isl_bool (*fn)(__isl_keep isl_map *map, void *user), void *user)
  {
  	struct isl_forall_user_data data = { isl_bool_true, fn, user };
  
  	if (!umap)
  		return isl_bool_error;
  
  	if (isl_hash_table_foreach(umap->dim->ctx, &umap->table,
  				   &forall_user_entry, &data) < 0 && data.res)
  		return isl_bool_error;
  
  	return data.res;
  }
  
  /* Is "umap" obviously empty?
   */
  isl_bool isl_union_map_plain_is_empty(__isl_keep isl_union_map *umap)
  {
  	isl_size n;
  
  	n = isl_union_map_n_map(umap);
  	if (n < 0)
  		return isl_bool_error;
  	return n == 0;
  }
  
  isl_bool isl_union_map_is_empty(__isl_keep isl_union_map *umap)
  {
  	return union_map_forall(umap, &isl_map_is_empty);
  }
  
  isl_bool isl_union_set_is_empty(__isl_keep isl_union_set *uset)
  {
  	return isl_union_map_is_empty(uset);
  }
  
  static isl_bool is_subset_of_identity(__isl_keep isl_map *map)
  {
  	isl_bool is_subset;
  	isl_space *dim;
  	isl_map *id;
  
  	if (!map)
  		return isl_bool_error;
  
  	if (!isl_space_tuple_is_equal(map->dim, isl_dim_in,
  					map->dim, isl_dim_out))
  		return isl_bool_false;
  
  	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 isl_bool single_map_is_single_valued(__isl_keep isl_union_map *umap)
  {
  	isl_map *map;
  	isl_bool 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;
  	isl_bool 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 isl_stat 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;
  	isl_size n;
  
  	umap = isl_union_map_copy(data->umap);
  	umap = isl_union_map_intersect_domain(umap,
  						isl_union_set_from_set(set));
  
  	n = isl_union_map_n_map(umap);
  	if (n < 0) {
  		data->sv = isl_bool_error;
  	} else if (n == 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 isl_stat_error;
  	return isl_stat_ok;
  }
  
  /* 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.
   */
  isl_bool 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;
  	isl_size n;
  
  	n = isl_union_map_n_map(umap);
  	if (n < 0)
  		return isl_bool_error;
  	if (n == 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 = isl_bool_true;
  	data.umap = umap;
  	if (isl_union_set_foreach_set(domain,
  			    &single_valued_on_domain, &data) < 0 && data.sv)
  		data.sv = isl_bool_error;
  	isl_union_set_free(domain);
  
  	return data.sv;
  }
  
  isl_bool isl_union_map_is_injective(__isl_keep isl_union_map *umap)
  {
  	isl_bool 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;
  }
  
  /* Is "map" obviously not an identity relation because
   * it maps elements from one space to another space?
   * Update *non_identity accordingly.
   *
   * In particular, if the domain and range spaces are the same,
   * then the map is not considered to obviously not be an identity relation.
   * Otherwise, the map is considered to obviously not be an identity relation
   * if it is is non-empty.
   *
   * If "map" is determined to obviously not be an identity relation,
   * then the search is aborted.
   */
  static isl_stat map_plain_is_not_identity(__isl_take isl_map *map, void *user)
  {
  	isl_bool *non_identity = user;
  	isl_bool equal;
  	isl_space *space;
  
  	space = isl_map_get_space(map);
  	equal = isl_space_tuple_is_equal(space, isl_dim_in, space, isl_dim_out);
  	if (equal >= 0 && !equal)
  		*non_identity = isl_bool_not(isl_map_is_empty(map));
  	else
  		*non_identity = isl_bool_not(equal);
  	isl_space_free(space);
  	isl_map_free(map);
  
  	if (*non_identity < 0 || *non_identity)
  		return isl_stat_error;
  
  	return isl_stat_ok;
  }
  
  /* Is "umap" obviously not an identity relation because
   * it maps elements from one space to another space?
   *
   * As soon as a map has been found that maps elements to a different space,
   * non_identity is changed and the search is aborted.
   */
  static isl_bool isl_union_map_plain_is_not_identity(
  	__isl_keep isl_union_map *umap)
  {
  	isl_bool non_identity;
  
  	non_identity = isl_bool_false;
  	if (isl_union_map_foreach_map(umap, &map_plain_is_not_identity,
  					&non_identity) < 0 &&
  	    non_identity == isl_bool_false)
  		return isl_bool_error;
  
  	return non_identity;
  }
  
  /* Does "map" only map elements to themselves?
   * Update *identity accordingly.
   *
   * If "map" is determined not to be an identity relation,
   * then the search is aborted.
   */
  static isl_stat map_is_identity(__isl_take isl_map *map, void *user)
  {
  	isl_bool *identity = user;
  
  	*identity = isl_map_is_identity(map);
  	isl_map_free(map);
  
  	if (*identity < 0 || !*identity)
  		return isl_stat_error;
  
  	return isl_stat_ok;
  }
  
  /* Does "umap" only map elements to themselves?
   *
   * First check if there are any maps that map elements to different spaces.
   * If not, then check that all the maps (between identical spaces)
   * are identity relations.
   */
  isl_bool isl_union_map_is_identity(__isl_keep isl_union_map *umap)
  {
  	isl_bool non_identity;
  	isl_bool identity;
  
  	non_identity = isl_union_map_plain_is_not_identity(umap);
  	if (non_identity < 0 || non_identity)
  		return isl_bool_not(non_identity);
  
  	identity = isl_bool_true;
  	if (isl_union_map_foreach_map(umap, &map_is_identity, &identity) < 0 &&
  	    identity == isl_bool_true)
  		return isl_bool_error;
  
  	return identity;
  }
  
  /* 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 isl_bool 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 isl_bool 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 isl_bool plain_injective_on_range(__isl_take isl_union_map *umap,
  	int first, int n_range)
  {
  	isl_ctx *ctx;
  	isl_size n;
  	struct isl_fixed_dim_data data = { NULL };
  
  	ctx = isl_union_map_get_ctx(umap);
  
  	n = isl_union_map_n_map(umap);
  	if (n < 0)
  		goto error;
  
  	if (n <= 1) {
  		isl_union_map_free(umap);
  		return isl_bool_true;
  	}
  
  	if (first >= n_range) {
  		isl_union_map_free(umap);
  		return isl_bool_false;
  	}
  
  	data.v = alloc_isl_fixed_map_array(ctx, n);
  	if (!data.v)
  		goto error;
  
  	for (data.pos = first; data.pos < n_range; ++data.pos) {
  		isl_bool 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 isl_bool_false;
  error:
  	free_isl_fixed_map_array(data.v, n);
  	isl_union_map_free(umap);
  	return isl_bool_error;
  }
  
  /* Check whether the maps in umap that map to subsets of "ran"
   * have obviously distinct ranges.
   */
  static isl_bool plain_injective_on_range_wrap(__isl_keep isl_set *ran,
  	void *user)
  {
  	isl_size dim;
  	isl_union_map *umap = user;
  
  	dim = isl_set_dim(ran, isl_dim_set);
  	if (dim < 0)
  		return isl_bool_error;
  
  	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, dim);
  }
  
  /* 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.
   */
  isl_bool isl_union_map_plain_is_injective(__isl_keep isl_union_map *umap)
  {
  	isl_bool in;
  	isl_union_map *univ;
  	isl_union_set *ran;
  
  	in = union_map_forall(umap, &isl_map_plain_is_injective);
  	if (in < 0)
  		return isl_bool_error;
  	if (!in)
  		return isl_bool_false;
  
  	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;
  }
  
  isl_bool isl_union_map_is_bijective(__isl_keep isl_union_map *umap)
  {
  	isl_bool sv;
  
  	sv = isl_union_map_is_single_valued(umap);
  	if (sv < 0 || !sv)
  		return sv;
  
  	return isl_union_map_is_injective(umap);
  }
  
  __isl_give isl_union_map *isl_union_map_zip(__isl_take isl_union_map *umap)
  {
  	struct isl_un_op_drop_user_data data = { &isl_map_can_zip };
  	struct isl_un_op_control control = {
  		.filter = &un_op_filter_drop_user,
  		.filter_user = &data,
  		.fn_map = &isl_map_zip,
  	};
  	return un_op(umap, &control);
  }
  
  /* 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)
  {
  	struct isl_un_op_drop_user_data data = { &isl_map_can_uncurry };
  	struct isl_un_op_control control = {
  		.filter = &un_op_filter_drop_user,
  		.filter_user = &data,
  		.fn_map = &isl_map_uncurry,
  	};
  	return un_op(umap, &control);
  }
  
  /* 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)
  {
  	struct isl_un_op_drop_user_data data = { &isl_map_can_curry };
  	struct isl_un_op_control control = {
  		.filter = &un_op_filter_drop_user,
  		.filter_user = &data,
  		.fn_map = &isl_map_curry,
  	};
  	return un_op(umap, &control);
  }
  
  /* Given a union map, take the maps of the form A -> ((B -> C) -> D) and
   * return the union of the corresponding maps A -> (B -> (C -> D)).
   */
  __isl_give isl_union_map *isl_union_map_range_curry(
  	__isl_take isl_union_map *umap)
  {
  	struct isl_un_op_drop_user_data data = { &isl_map_can_range_curry };
  	struct isl_un_op_control control = {
  		.filter = &un_op_filter_drop_user,
  		.filter_user = &data,
  		.fn_map = &isl_map_range_curry,
  	};
  	return un_op(umap, &control);
  }
  
  __isl_give isl_union_set *isl_union_set_lift(__isl_take isl_union_set *uset)
  {
  	struct isl_un_op_control control = {
  		.fn_map = &isl_set_lift,
  	};
  	return un_op(uset, &control);
  }
  
  static isl_stat 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 isl_stat_ok;
  }
  
  __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 isl_stat 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 isl_stat_error;
  
  	return isl_stat_ok;
  }
  
  __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 isl_stat preimage_entry(void **entry, void *user)
  {
  	int m;
  	isl_map *map = *entry;
  	struct isl_union_map_preimage_data *data = user;
  	isl_bool empty;
  
  	m = data->match(map, data->space);
  	if (m < 0)
  		return isl_stat_error;
  	if (!m)
  		return isl_stat_ok;
  
  	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 ? isl_stat_error : isl_stat_ok;
  	}
  
  	data->res = isl_union_map_add_map(data->res, map);
  
  	return isl_stat_ok;
  }
  
  /* 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 isl_stat preimage_mpa_entry(void **entry, void *user)
  {
  	int m;
  	isl_map *map = *entry;
  	struct isl_union_map_preimage_mpa_data *data = user;
  	isl_bool empty;
  
  	m = data->match(map, data->space);
  	if (m < 0)
  		return isl_stat_error;
  	if (!m)
  		return isl_stat_ok;
  
  	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 ? isl_stat_error : isl_stat_ok;
  	}
  
  	data->res = isl_union_map_add_map(data->res, map);
  
  	return isl_stat_ok;
  }
  
  /* 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 isl_stat 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 ? isl_stat_ok : isl_stat_error;
  }
  
  /* 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 domain spaces that
   * correspond 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 domain spaces that
   * correspond 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 domain spaces that
   * correspond 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 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);
  	return total(umap, &isl_map_reset_user);
  }
  
  /* 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);
  }
  
  /* Remove all existentially quantified variables and integer divisions
   * from "umap" using Fourier-Motzkin elimination.
   */
  __isl_give isl_union_map *isl_union_map_remove_divs(
  	__isl_take isl_union_map *umap)
  {
  	return total(umap, &isl_map_remove_divs);
  }
  
  /* Remove all existentially quantified variables and integer divisions
   * from "uset" using Fourier-Motzkin elimination.
   */
  __isl_give isl_union_set *isl_union_set_remove_divs(
  	__isl_take isl_union_set *uset)
  {
  	return isl_union_map_remove_divs(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 isl_stat 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 isl_stat_ok;
  }
  
  /* 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;
  }
  
  #undef TYPE
  #define TYPE	isl_union_map
  #include "isl_project_out_all_params_templ.c"
  
  /* 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);
  }
  
  /* Project out all parameters from "uset" by existentially quantifying
   * over them.
   */
  __isl_give isl_union_set *isl_union_set_project_out_all_params(
  	__isl_take isl_union_set *uset)
  {
  	return uset_from_umap(
  		    isl_union_map_project_out_all_params(uset_to_umap(uset)));
  }
  
  /* 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 isl_bool map_excludes(__isl_keep isl_map *map, void *user)
  {
  	struct isl_union_map_involves_dims_data *data = user;
  	isl_bool involves;
  
  	involves = isl_map_involves_dims(map,
  					isl_dim_param, data->first, data->n);
  	return isl_bool_not(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.
   */
  isl_bool 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 };
  	isl_bool excludes;
  
  	if (type != isl_dim_param)
  		isl_die(isl_union_map_get_ctx(umap), isl_error_invalid,
  			"can only reference parameters", return isl_bool_error);
  
  	excludes = union_map_forall_user(umap, &map_excludes, &data);
  
  	return isl_bool_not(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 isl_stat 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 ? isl_stat_ok : isl_stat_error;
  }
  
  /* 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;
  }
  
  /* Check that "umap" and "space" have the same number of parameters.
   */
  static isl_stat check_union_map_space_equal_dim(__isl_keep isl_union_map *umap,
  	__isl_keep isl_space *space)
  {
  	isl_size dim1, dim2;
  
  	dim1 = isl_union_map_dim(umap, isl_dim_param);
  	dim2 = isl_space_dim(space, isl_dim_param);
  	if (dim1 < 0 || dim2 < 0)
  		return isl_stat_error;
  	if (dim1 == dim2)
  		return isl_stat_ok;
  	isl_die(isl_union_map_get_ctx(umap), isl_error_invalid,
  		"number of parameters does not match", return isl_stat_error);
  }
  
  /* Internal data structure for isl_union_map_reset_equal_dim_space.
   * "space" is the target space.
   * "res" collects the results.
   */
  struct isl_union_map_reset_params_data {
  	isl_space *space;
  	isl_union_map *res;
  };
  
  /* Replace the parameters of "map" by those of data->space and
   * add the result to data->res.
   */
  static isl_stat reset_params(__isl_take isl_map *map, void *user)
  {
  	struct isl_union_map_reset_params_data *data = user;
  	isl_space *space;
  
  	space = isl_map_get_space(map);
  	space = isl_space_replace_params(space, data->space);
  	map = isl_map_reset_equal_dim_space(map, space);
  	data->res = isl_union_map_add_map(data->res, map);
  
  	return data->res ? isl_stat_ok : isl_stat_error;
  }
  
  /* Replace the space of "umap" by "space", without modifying
   * the dimension of "umap", i.e., the number of parameters of "umap".
   *
   * Since the hash values of the maps in the union map depend
   * on the parameters, a new union map needs to be constructed.
   */
  __isl_give isl_union_map *isl_union_map_reset_equal_dim_space(
  	__isl_take isl_union_map *umap, __isl_take isl_space *space)
  {
  	struct isl_union_map_reset_params_data data = { space };
  	isl_bool equal;
  	isl_space *umap_space;
  
  	umap_space = isl_union_map_peek_space(umap);
  	equal = isl_space_is_equal(umap_space, space);
  	if (equal < 0)
  		goto error;
  	if (equal) {
  		isl_space_free(space);
  		return umap;
  	}
  	if (check_union_map_space_equal_dim(umap, space) < 0)
  		goto error;
  
  	data.res = isl_union_map_empty(isl_space_copy(space));
  	if (isl_union_map_foreach_map(umap, &reset_params, &data) < 0)
  		data.res = isl_union_map_free(data.res);
  
  	isl_space_free(space);
  	isl_union_map_free(umap);
  	return data.res;
  error:
  	isl_union_map_free(umap);
  	isl_space_free(space);
  	return NULL;
  }
  
  /* 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 isl_stat 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 ? isl_stat_ok : isl_stat_error;
  }
  
  /* If "mupa" has a non-trivial explicit domain, then intersect
   * domain and range of "umap" with this explicit domain.
   * If the explicit domain only describes constraints on the parameters,
   * then the intersection only needs to be performed once.
   */
  static __isl_give isl_union_map *intersect_explicit_domain(
  	__isl_take isl_union_map *umap, __isl_keep isl_multi_union_pw_aff *mupa)
  {
  	isl_bool non_trivial, is_params;
  	isl_union_set *dom;
  
  	non_trivial = isl_multi_union_pw_aff_has_non_trivial_domain(mupa);
  	if (non_trivial < 0)
  		return isl_union_map_free(umap);
  	if (!non_trivial)
  		return umap;
  	mupa = isl_multi_union_pw_aff_copy(mupa);
  	dom = isl_multi_union_pw_aff_domain(mupa);
  	is_params = isl_union_set_is_params(dom);
  	if (is_params < 0) {
  		isl_union_set_free(dom);
  		return isl_union_map_free(umap);
  	}
  	if (is_params) {
  		isl_set *set;
  
  		set = isl_union_set_params(dom);
  		umap = isl_union_map_intersect_params(umap, set);
  		return umap;
  	}
  	umap = isl_union_map_intersect_domain(umap, isl_union_set_copy(dom));
  	umap = isl_union_map_intersect_range(umap, dom);
  	return umap;
  }
  
  /* 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));
  	umap = intersect_explicit_domain(umap, mupa);
  	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;
  	isl_size n;
  	isl_ctx *ctx;
  	isl_space *space;
  	isl_union_set *res;
  
  	n = isl_union_set_list_n_union_set(list);
  	if (n < 0)
  		goto error;
  
  	ctx = isl_union_set_list_get_ctx(list);
  	space = isl_space_params_alloc(ctx, 0);
  	res = isl_union_set_empty(space);
  
  	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;
  error:
  	isl_union_set_list_free(list);
  	return NULL;
  }
  
  /* Update *hash with the hash value of "map".
   */
  static isl_stat add_hash(__isl_take isl_map *map, void *user)
  {
  	uint32_t *hash = user;
  	uint32_t map_hash;
  
  	map_hash = isl_map_get_hash(map);
  	isl_hash_hash(*hash, map_hash);
  
  	isl_map_free(map);
  	return isl_stat_ok;
  }
  
  /* Return a hash value that digests "umap".
   */
  uint32_t isl_union_map_get_hash(__isl_keep isl_union_map *umap)
  {
  	uint32_t hash;
  
  	if (!umap)
  		return 0;
  
  	hash = isl_hash_init();
  	if (isl_union_map_foreach_map(umap, &add_hash, &hash) < 0)
  		return 0;
  
  	return hash;
  }
  
  /* Return a hash value that digests "uset".
   */
  uint32_t isl_union_set_get_hash(__isl_keep isl_union_set *uset)
  {
  	return isl_union_map_get_hash(uset);
  }
  
  /* Add the number of basic sets in "set" to "n".
   */
  static isl_stat add_n(__isl_take isl_set *set, void *user)
  {
  	int *n = user;
  	isl_size set_n;
  
  	set_n = isl_set_n_basic_set(set);
  	*n += set_n;
  	isl_set_free(set);
  
  	return set_n < 0 ? isl_stat_error : isl_stat_ok;
  }
  
  /* Return the total number of basic sets in "uset".
   */
  int isl_union_set_n_basic_set(__isl_keep isl_union_set *uset)
  {
  	int n = 0;
  
  	if (isl_union_set_foreach_set(uset, &add_n, &n) < 0)
  		return -1;
  
  	return n;
  }
  
  /* Add the basic sets in "set" to "list".
   */
  static isl_stat add_list(__isl_take isl_set *set, void *user)
  {
  	isl_basic_set_list **list = user;
  	isl_basic_set_list *list_i;
  
  	list_i = isl_set_get_basic_set_list(set);
  	*list = isl_basic_set_list_concat(*list, list_i);
  	isl_set_free(set);
  
  	if (!*list)
  		return isl_stat_error;
  	return isl_stat_ok;
  }
  
  /* Return a list containing all the basic sets in "uset".
   *
   * First construct a list of the appropriate size and
   * then add all the elements.
   */
  __isl_give isl_basic_set_list *isl_union_set_get_basic_set_list(
  	__isl_keep isl_union_set *uset)
  {
  	int n;
  	isl_ctx *ctx;
  	isl_basic_set_list *list;
  
  	if (!uset)
  		return NULL;
  	ctx = isl_union_set_get_ctx(uset);
  	n = isl_union_set_n_basic_set(uset);
  	if (n < 0)
  		return NULL;
  	list = isl_basic_set_list_alloc(ctx, n);
  	if (isl_union_set_foreach_set(uset, &add_list, &list) < 0)
  		list = isl_basic_set_list_free(list);
  
  	return list;
  }
  
  /* Internal data structure for isl_union_map_remove_map_if.
   * "fn" and "user" are the arguments to isl_union_map_remove_map_if.
   */
  struct isl_union_map_remove_map_if_data {
  	isl_bool (*fn)(__isl_keep isl_map *map, void *user);
  	void *user;
  };
  
  /* isl_un_op_control filter that negates the result of data->fn
   * called on "map".
   */
  static isl_bool not(__isl_keep isl_map *map, void *user)
  {
  	struct isl_union_map_remove_map_if_data *data = user;
  
  	return isl_bool_not(data->fn(map, data->user));
  }
  
  /* Dummy isl_un_op_control transformation callback that
   * simply returns the input.
   */
  static __isl_give isl_map *map_id(__isl_take isl_map *map)
  {
  	return map;
  }
  
  /* Call "fn" on every map in "umap" and remove those maps
   * for which the callback returns true.
   *
   * Use un_op to keep only those maps that are not filtered out,
   * applying an identity transformation on them.
   */
  __isl_give isl_union_map *isl_union_map_remove_map_if(
  	__isl_take isl_union_map *umap,
  	isl_bool (*fn)(__isl_keep isl_map *map, void *user), void *user)
  {
  	struct isl_union_map_remove_map_if_data data = { fn, user };
  	struct isl_un_op_control control = {
  		.filter = &not,
  		.filter_user = &data,
  		.fn_map = &map_id,
  	};
  	return un_op(umap, &control);
  }
  
  /* Does "map" have "space" as range (ignoring parameters)?
   */
  static isl_bool has_range_space(__isl_keep isl_map *map, void *user)
  {
  	isl_space *space = user;
  
  	return isl_space_has_range_tuples(space, isl_map_peek_space(map));
  }
  
  /* Wrapper around isl_map_bind_range for use as a un_op callback.
   */
  static __isl_give isl_map *bind_range(__isl_take isl_map *map, void *user)
  {
  	isl_multi_id *tuple = user;
  
  	return isl_map_bind_range(map, isl_multi_id_copy(tuple));
  }
  
  /* Bind the output dimensions of "umap" to parameters with identifiers
   * specified by "tuple", living in the range space of "umap",
   * for those maps that have a matching range space.
   */
  __isl_give isl_union_set *isl_union_map_bind_range(
  	__isl_take isl_union_map *umap, __isl_take isl_multi_id *tuple)
  {
  	struct isl_un_op_control control = {
  		.filter = &has_range_space,
  		.filter_user = isl_multi_id_peek_space(tuple),
  		.fn_map2 = &bind_range,
  		.fn_map2_user = tuple,
  	};
  	isl_union_set *bound;
  
  	bound = uset_from_umap(un_op(umap, &control));
  	isl_multi_id_free(tuple);
  	return bound;
  }
  