isl_space.c

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/*
 * Copyright 2008-2009 Katholieke Universiteit Leuven
 * Copyright 2010      INRIA Saclay
 * Copyright 2013-2014 Ecole Normale Superieure
 * Copyright 2018-2019 Cerebras Systems
 *
 * Use of this software is governed by the MIT license
 *
 * Written by Sven Verdoolaege, K.U.Leuven, Departement
 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
 * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
 * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France 
 * and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
 * and Cerebras Systems, 175 S San Antonio Rd, Los Altos, CA, USA
 */
 
#include <stdlib.h>
#include <string.h>
#include <isl_space_private.h>
#include <isl_id_private.h>
#include <isl_reordering.h>
 
isl_ctx *isl_space_get_ctx(__isl_keep isl_space *space)
{
  return space ? space->ctx : NULL;
}
 
__isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
      unsigned nparam, unsigned n_in, unsigned n_out)
{
  isl_space *space;
 
  space = isl_alloc_type(ctx, struct isl_space);
  if (!space)
    return NULL;
 
  space->ctx = ctx;
  isl_ctx_ref(ctx);
  space->ref = 1;
  space->nparam = nparam;
  space->n_in = n_in;
  space->n_out = n_out;
 
  space->tuple_id[0] = NULL;
  space->tuple_id[1] = NULL;
 
  space->nested[0] = NULL;
  space->nested[1] = NULL;
 
  space->n_id = 0;
  space->ids = NULL;
 
  return space;
}
 
/* Mark the space as being that of a set, by setting the domain tuple
 * to isl_id_none.
 */
static __isl_give isl_space *mark_as_set(__isl_take isl_space *space)
{
  space = isl_space_cow(space);
  if (!space)
    return NULL;
  space = isl_space_set_tuple_id(space, isl_dim_in, &isl_id_none);
  return space;
}
 
/* Is the space that of a set?
 */
isl_bool isl_space_is_set(__isl_keep isl_space *space)
{
  if (!space)
    return isl_bool_error;
  if (space->n_in != 0 || space->nested[0])
    return isl_bool_false;
  if (space->tuple_id[0] != &isl_id_none)
    return isl_bool_false;
  return isl_bool_true;
}
 
/* Check that "space" is a set space.
 */
isl_stat isl_space_check_is_set(__isl_keep isl_space *space)
{
  isl_bool is_set;
 
  is_set = isl_space_is_set(space);
  if (is_set < 0)
    return isl_stat_error;
  if (!is_set)
    isl_die(isl_space_get_ctx(space), isl_error_invalid,
      "space is not a set", return isl_stat_error);
  return isl_stat_ok;
}
 
/* Is the given space that of a map?
 */
isl_bool isl_space_is_map(__isl_keep isl_space *space)
{
  int r;
 
  if (!space)
    return isl_bool_error;
  r = space->tuple_id[0] != &isl_id_none &&
      space->tuple_id[1] != &isl_id_none;
  return isl_bool_ok(r);
}
 
/* Check that "space" is the space of a map.
 */
static isl_stat isl_space_check_is_map(__isl_keep isl_space *space)
{
  isl_bool is_space;
 
  is_space = isl_space_is_map(space);
  if (is_space < 0)
    return isl_stat_error;
  if (!is_space)
    isl_die(isl_space_get_ctx(space), isl_error_invalid,
      "expecting map space", return isl_stat_error);
  return isl_stat_ok;
}
 
/* Check that "space" is the space of a map
 * where the domain is a wrapped map space.
 */
isl_stat isl_space_check_domain_is_wrapping(__isl_keep isl_space *space)
{
  isl_bool wrapping;
 
  wrapping = isl_space_domain_is_wrapping(space);
  if (wrapping < 0)
    return isl_stat_error;
  if (!wrapping)
    isl_die(isl_space_get_ctx(space), isl_error_invalid,
      "domain not a product", return isl_stat_error);
  return isl_stat_ok;
}
 
/* Check that "space" is the space of a map
 * where the range is a wrapped map space.
 */
isl_stat isl_space_check_range_is_wrapping(__isl_keep isl_space *space)
{
  isl_bool wrapping;
 
  wrapping = isl_space_range_is_wrapping(space);
  if (wrapping < 0)
    return isl_stat_error;
  if (!wrapping)
    isl_die(isl_space_get_ctx(space), isl_error_invalid,
      "range not a product", return isl_stat_error);
  return isl_stat_ok;
}
 
__isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
      unsigned nparam, unsigned dim)
{
  isl_space *space;
  space = isl_space_alloc(ctx, nparam, 0, dim);
  space = mark_as_set(space);
  return space;
}
 
/* Mark the space as being that of a parameter domain, by setting
 * both tuples to isl_id_none.
 */
static __isl_give isl_space *mark_as_params(isl_space *space)
{
  if (!space)
    return NULL;
  space = isl_space_set_tuple_id(space, isl_dim_in, &isl_id_none);
  space = isl_space_set_tuple_id(space, isl_dim_out, &isl_id_none);
  return space;
}
 
/* Is the space that of a parameter domain?
 */
isl_bool isl_space_is_params(__isl_keep isl_space *space)
{
  if (!space)
    return isl_bool_error;
  if (space->n_in != 0 || space->nested[0] ||
      space->n_out != 0 || space->nested[1])
    return isl_bool_false;
  if (space->tuple_id[0] != &isl_id_none)
    return isl_bool_false;
  if (space->tuple_id[1] != &isl_id_none)
    return isl_bool_false;
  return isl_bool_true;
}
 
/* Create a space for a parameter domain.
 */
__isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx, unsigned nparam)
{
  isl_space *space;
  space = isl_space_alloc(ctx, nparam, 0, 0);
  space = mark_as_params(space);
  return space;
}
 
/* Create a space for a parameter domain, without any parameters.
 */
__isl_give isl_space *isl_space_unit(isl_ctx *ctx)
{
  return isl_space_params_alloc(ctx, 0);
}
 
static isl_size global_pos(__isl_keep isl_space *space,
         enum isl_dim_type type, unsigned pos)
{
  if (isl_space_check_range(space, type, pos, 1) < 0)
    return isl_size_error;
 
  switch (type) {
  case isl_dim_param:
    return pos;
  case isl_dim_in:
    return pos + space->nparam;
  case isl_dim_out:
    return pos + space->nparam + space->n_in;
  default:
    isl_assert(isl_space_get_ctx(space), 0, return isl_size_error);
  }
  return isl_size_error;
}
 
/* Extend length of ids array to the total number of dimensions.
 */
static __isl_give isl_space *extend_ids(__isl_take isl_space *space)
{
  isl_id **ids;
  int i;
  isl_size dim;
 
  dim = isl_space_dim(space, isl_dim_all);
  if (dim < 0)
    return isl_space_free(space);
  if (dim <= space->n_id)
    return space;
 
  if (!space->ids) {
    space->ids = isl_calloc_array(space->ctx, isl_id *, dim);
    if (!space->ids)
      goto error;
  } else {
    ids = isl_realloc_array(space->ctx, space->ids, isl_id *, dim);
    if (!ids)
      goto error;
    space->ids = ids;
    for (i = space->n_id; i < dim; ++i)
      space->ids[i] = NULL;
  }
 
  space->n_id = dim;
 
  return space;
error:
  isl_space_free(space);
  return NULL;
}
 
static __isl_give isl_space *set_id(__isl_take isl_space *space,
  enum isl_dim_type type, unsigned pos, __isl_take isl_id *id)
{
  isl_size gpos;
 
  space = isl_space_cow(space);
 
  gpos = global_pos(space, type, pos);
  if (gpos < 0)
    goto error;
 
  if (gpos >= space->n_id) {
    if (!id)
      return space;
    space = extend_ids(space);
    if (!space)
      goto error;
  }
 
  space->ids[gpos] = id;
 
  return space;
error:
  isl_id_free(id);
  isl_space_free(space);
  return NULL;
}
 
static __isl_keep isl_id *get_id(__isl_keep isl_space *space,
         enum isl_dim_type type, unsigned pos)
{
  isl_size gpos;
 
  gpos = global_pos(space, type, pos);
  if (gpos < 0)
    return NULL;
  if (gpos >= space->n_id)
    return NULL;
  return space->ids[gpos];
}
 
/* Return the nested space at the given position.
 */
static __isl_keep isl_space *isl_space_peek_nested(__isl_keep isl_space *space,
  int pos)
{
  if (!space)
    return NULL;
  if (!space->nested[pos])
    isl_die(isl_space_get_ctx(space), isl_error_invalid,
      "no nested space", return NULL);
  return space->nested[pos];
}
 
static unsigned offset(__isl_keep isl_space *space, enum isl_dim_type type)
{
  switch (type) {
  case isl_dim_param: return 0;
  case isl_dim_in:  return space->nparam;
  case isl_dim_out: return space->nparam + space->n_in;
  default:    return 0;
  }
}
 
static unsigned n(__isl_keep isl_space *space, enum isl_dim_type type)
{
  switch (type) {
  case isl_dim_param: return space->nparam;
  case isl_dim_in:  return space->n_in;
  case isl_dim_out: return space->n_out;
  case isl_dim_all:
    return space->nparam + space->n_in + space->n_out;
  default:    return 0;
  }
}
 
isl_size isl_space_dim(__isl_keep isl_space *space, enum isl_dim_type type)
{
  if (!space)
    return isl_size_error;
  return n(space, type);
}
 
/* Return the dimensionality of tuple "inner" within the wrapped relation
 * inside tuple "outer".
 */
isl_size isl_space_wrapped_dim(__isl_keep isl_space *space,
  enum isl_dim_type outer, enum isl_dim_type inner)
{
  int pos;
 
  if (!space)
    return isl_size_error;
  if (outer != isl_dim_in && outer != isl_dim_out)
    isl_die(isl_space_get_ctx(space), isl_error_invalid,
      "only input, output and set tuples "
      "can have nested relations", return isl_size_error);
  pos = outer - isl_dim_in;
  return isl_space_dim(isl_space_peek_nested(space, pos), inner);
}
 
unsigned isl_space_offset(__isl_keep isl_space *space, enum isl_dim_type type)
{
  if (!space)
    return 0;
  return offset(space, type);
}
 
static __isl_give isl_space *copy_ids(__isl_take isl_space *dst,
  enum isl_dim_type dst_type, unsigned offset, __isl_keep isl_space *src,
  enum isl_dim_type src_type)
{
  int i;
  isl_id *id;
 
  if (!dst)
    return NULL;
 
  for (i = 0; i < n(src, src_type); ++i) {
    id = get_id(src, src_type, i);
    if (!id)
      continue;
    dst = set_id(dst, dst_type, offset + i, isl_id_copy(id));
    if (!dst)
      return NULL;
  }
  return dst;
}
 
__isl_give isl_space *isl_space_dup(__isl_keep isl_space *space)
{
  isl_space *dup;
  if (!space)
    return NULL;
  dup = isl_space_alloc(space->ctx,
        space->nparam, space->n_in, space->n_out);
  if (!dup)
    return NULL;
  if (space->tuple_id[0] &&
      !(dup->tuple_id[0] = isl_id_copy(space->tuple_id[0])))
    goto error;
  if (space->tuple_id[1] &&
      !(dup->tuple_id[1] = isl_id_copy(space->tuple_id[1])))
    goto error;
  if (space->nested[0] &&
      !(dup->nested[0] = isl_space_copy(space->nested[0])))
    goto error;
  if (space->nested[1] &&
      !(dup->nested[1] = isl_space_copy(space->nested[1])))
    goto error;
  if (!space->ids)
    return dup;
  dup = copy_ids(dup, isl_dim_param, 0, space, isl_dim_param);
  dup = copy_ids(dup, isl_dim_in, 0, space, isl_dim_in);
  dup = copy_ids(dup, isl_dim_out, 0, space, isl_dim_out);
  return dup;
error:
  isl_space_free(dup);
  return NULL;
}
 
__isl_give isl_space *isl_space_cow(__isl_take isl_space *space)
{
  if (!space)
    return NULL;
 
  if (space->ref == 1)
    return space;
  space->ref--;
  return isl_space_dup(space);
}
 
__isl_give isl_space *isl_space_copy(__isl_keep isl_space *space)
{
  if (!space)
    return NULL;
 
  space->ref++;
  return space;
}
 
__isl_null isl_space *isl_space_free(__isl_take isl_space *space)
{
  int i;
 
  if (!space)
    return NULL;
 
  if (--space->ref > 0)
    return NULL;
 
  isl_id_free(space->tuple_id[0]);
  isl_id_free(space->tuple_id[1]);
 
  isl_space_free(space->nested[0]);
  isl_space_free(space->nested[1]);
 
  for (i = 0; i < space->n_id; ++i)
    isl_id_free(space->ids[i]);
  free(space->ids);
  isl_ctx_deref(space->ctx);
  
  free(space);
 
  return NULL;
}
 
/* Check if "s" is a valid dimension or tuple name.
 * We currently only forbid names that look like a number.
 *
 * s is assumed to be non-NULL.
 */
static int name_ok(isl_ctx *ctx, const char *s)
{
  char *p;
 
  strtol(s, &p, 0);
  if (p != s)
    isl_die(ctx, isl_error_invalid, "name looks like a number",
      return 0);
 
  return 1;
}
 
/* Return a copy of the nested space at the given position.
 */
static __isl_keep isl_space *isl_space_get_nested(__isl_keep isl_space *space,
  int pos)
{
  return isl_space_copy(isl_space_peek_nested(space, pos));
}
 
/* Return the nested space at the given position.
 * This may be either a copy or the nested space itself
 * if there is only one reference to "space".
 * This allows the nested space to be modified inplace
 * if both "space" and the nested space have only a single reference.
 * The caller is not allowed to modify "space" between this call and
 * a subsequent call to isl_space_restore_nested.
 * The only exception is that isl_space_free can be called instead.
 */
static __isl_give isl_space *isl_space_take_nested(__isl_keep isl_space *space,
  int pos)
{
  isl_space *nested;
 
  if (!space)
    return NULL;
  if (space->ref != 1)
    return isl_space_get_nested(space, pos);
  nested = space->nested[pos];
  space->nested[pos] = NULL;
  return nested;
}
 
/* Replace the nested space at the given position by "nested",
 * where this nested space of "space" may be missing
 * due to a preceding call to isl_space_take_nested.
 * However, in this case, "space" only has a single reference and
 * then the call to isl_space_cow has no effect.
 */
static __isl_give isl_space *isl_space_restore_nested(
  __isl_take isl_space *space, int pos, __isl_take isl_space *nested)
{
  if (!space || !nested)
    goto error;
 
  if (space->nested[pos] == nested) {
    isl_space_free(nested);
    return space;
  }
 
  space = isl_space_cow(space);
  if (!space)
    goto error;
  isl_space_free(space->nested[pos]);
  space->nested[pos] = nested;
 
  return space;
error:
  isl_space_free(space);
  isl_space_free(nested);
  return NULL;
}
 
/* Is it possible for the given dimension type to have a tuple id?
 */
static int space_can_have_id(__isl_keep isl_space *space,
  enum isl_dim_type type)
{
  if (!space)
    return 0;
  if (isl_space_is_params(space))
    isl_die(space->ctx, isl_error_invalid,
      "parameter spaces don't have tuple ids", return 0);
  if (isl_space_is_set(space) && type != isl_dim_set)
    isl_die(space->ctx, isl_error_invalid,
      "set spaces can only have a set id", return 0);
  if (type != isl_dim_in && type != isl_dim_out)
    isl_die(space->ctx, isl_error_invalid,
      "only input, output and set tuples can have ids",
      return 0);
 
  return 1;
}
 
/* Does the tuple have an id?
 */
isl_bool isl_space_has_tuple_id(__isl_keep isl_space *space,
  enum isl_dim_type type)
{
  if (!space_can_have_id(space, type))
    return isl_bool_error;
  return isl_bool_ok(space->tuple_id[type - isl_dim_in] != NULL);
}
 
/* Does the domain tuple of the map space "space" have an identifier?
 */
isl_bool isl_space_has_domain_tuple_id(__isl_keep isl_space *space)
{
  if (isl_space_check_is_map(space) < 0)
    return isl_bool_error;
  return isl_space_has_tuple_id(space, isl_dim_in);
}
 
/* Does the range tuple of the map space "space" have an identifier?
 */
isl_bool isl_space_has_range_tuple_id(__isl_keep isl_space *space)
{
  if (isl_space_check_is_map(space) < 0)
    return isl_bool_error;
  return isl_space_has_tuple_id(space, isl_dim_out);
}
 
__isl_give isl_id *isl_space_get_tuple_id(__isl_keep isl_space *space,
  enum isl_dim_type type)
{
  int has_id;
 
  if (!space)
    return NULL;
  has_id = isl_space_has_tuple_id(space, type);
  if (has_id < 0)
    return NULL;
  if (!has_id)
    isl_die(space->ctx, isl_error_invalid,
      "tuple has no id", return NULL);
  return isl_id_copy(space->tuple_id[type - isl_dim_in]);
}
 
/* Return the identifier of the domain tuple of the map space "space",
 * assuming it has one.
 */
__isl_give isl_id *isl_space_get_domain_tuple_id(
  __isl_keep isl_space *space)
{
  if (isl_space_check_is_map(space) < 0)
    return NULL;
  return isl_space_get_tuple_id(space, isl_dim_in);
}
 
/* Return the identifier of the range tuple of the map space "space",
 * assuming it has one.
 */
__isl_give isl_id *isl_space_get_range_tuple_id(
  __isl_keep isl_space *space)
{
  if (isl_space_check_is_map(space) < 0)
    return NULL;
  return isl_space_get_tuple_id(space, isl_dim_out);
}
 
__isl_give isl_space *isl_space_set_tuple_id(__isl_take isl_space *space,
  enum isl_dim_type type, __isl_take isl_id *id)
{
  space = isl_space_cow(space);
  if (!space || !id)
    goto error;
  if (type != isl_dim_in && type != isl_dim_out)
    isl_die(space->ctx, isl_error_invalid,
      "only input, output and set tuples can have names",
      goto error);
 
  isl_id_free(space->tuple_id[type - isl_dim_in]);
  space->tuple_id[type - isl_dim_in] = id;
 
  return space;
error:
  isl_id_free(id);
  isl_space_free(space);
  return NULL;
}
 
/* Replace the identifier of the domain tuple of the map space "space"
 * by "id".
 */
__isl_give isl_space *isl_space_set_domain_tuple_id(
  __isl_take isl_space *space, __isl_take isl_id *id)
{
  if (isl_space_check_is_map(space) < 0)
    space = isl_space_free(space);
  return isl_space_set_tuple_id(space, isl_dim_in, id);
}
 
/* Replace the identifier of the range tuple of the map space "space"
 * by "id".
 */
__isl_give isl_space *isl_space_set_range_tuple_id(
  __isl_take isl_space *space, __isl_take isl_id *id)
{
  if (isl_space_check_is_map(space) < 0)
    space = isl_space_free(space);
  return isl_space_set_tuple_id(space, isl_dim_out, id);
}
 
__isl_give isl_space *isl_space_reset_tuple_id(__isl_take isl_space *space,
  enum isl_dim_type type)
{
  space = isl_space_cow(space);
  if (!space)
    return NULL;
  if (type != isl_dim_in && type != isl_dim_out)
    isl_die(space->ctx, isl_error_invalid,
      "only input, output and set tuples can have names",
      goto error);
 
  isl_id_free(space->tuple_id[type - isl_dim_in]);
  space->tuple_id[type - isl_dim_in] = NULL;
 
  return space;
error:
  isl_space_free(space);
  return NULL;
}
 
/* Set the id of the given dimension of "space" to "id".
 * If the dimension already has an id, then it is replaced.
 * If the dimension is a parameter, then we need to change it
 * in the nested spaces (if any) as well.
 */
__isl_give isl_space *isl_space_set_dim_id(__isl_take isl_space *space,
  enum isl_dim_type type, unsigned pos, __isl_take isl_id *id)
{
  space = isl_space_cow(space);
  if (!space || !id)
    goto error;
 
  if (type == isl_dim_param) {
    int i;
 
    for (i = 0; i < 2; ++i) {
      if (!space->nested[i])
        continue;
      space->nested[i] =
        isl_space_set_dim_id(space->nested[i],
            type, pos, isl_id_copy(id));
      if (!space->nested[i])
        goto error;
    }
  }
 
  isl_id_free(get_id(space, type, pos));
  return set_id(space, type, pos, id);
error:
  isl_id_free(id);
  isl_space_free(space);
  return NULL;
}
 
/* Reset the id of the given dimension of "space".
 * If the dimension already has an id, then it is removed.
 * If the dimension is a parameter, then we need to reset it
 * in the nested spaces (if any) as well.
 */
__isl_give isl_space *isl_space_reset_dim_id(__isl_take isl_space *space,
  enum isl_dim_type type, unsigned pos)
{
  space = isl_space_cow(space);
  if (!space)
    goto error;
 
  if (type == isl_dim_param) {
    int i;
 
    for (i = 0; i < 2; ++i) {
      if (!space->nested[i])
        continue;
      space->nested[i] =
        isl_space_reset_dim_id(space->nested[i],
              type, pos);
      if (!space->nested[i])
        goto error;
    }
  }
 
  isl_id_free(get_id(space, type, pos));
  return set_id(space, type, pos, NULL);
error:
  isl_space_free(space);
  return NULL;
}
 
isl_bool isl_space_has_dim_id(__isl_keep isl_space *space,
  enum isl_dim_type type, unsigned pos)
{
  if (!space)
    return isl_bool_error;
  return isl_bool_ok(get_id(space, type, pos) != NULL);
}
 
__isl_give isl_id *isl_space_get_dim_id(__isl_keep isl_space *space,
  enum isl_dim_type type, unsigned pos)
{
  if (!space)
    return NULL;
  if (!get_id(space, type, pos))
    isl_die(space->ctx, isl_error_invalid,
      "dim has no id", return NULL);
  return isl_id_copy(get_id(space, type, pos));
}
 
__isl_give isl_space *isl_space_set_tuple_name(__isl_take isl_space *space,
  enum isl_dim_type type, const char *s)
{
  isl_id *id;
 
  if (!space)
    return NULL;
 
  if (!s)
    return isl_space_reset_tuple_id(space, type);
 
  if (!name_ok(space->ctx, s))
    goto error;
 
  id = isl_id_alloc(space->ctx, s, NULL);
  return isl_space_set_tuple_id(space, type, id);
error:
  isl_space_free(space);
  return NULL;
}
 
/* Does the tuple have a name?
 */
isl_bool isl_space_has_tuple_name(__isl_keep isl_space *space,
  enum isl_dim_type type)
{
  isl_id *id;
 
  if (!space_can_have_id(space, type))
    return isl_bool_error;
  id = space->tuple_id[type - isl_dim_in];
  return isl_bool_ok(id && id->name);
}
 
__isl_keep const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
   enum isl_dim_type type)
{
  isl_id *id;
  if (!space)
    return NULL;
  if (type != isl_dim_in && type != isl_dim_out)
    return NULL;
  id = space->tuple_id[type - isl_dim_in];
  return id ? id->name : NULL;
}
 
__isl_give isl_space *isl_space_set_dim_name(__isl_take isl_space *space,
         enum isl_dim_type type, unsigned pos,
         const char *s)
{
  isl_id *id;
 
  if (!space)
    return NULL;
  if (!s)
    return isl_space_reset_dim_id(space, type, pos);
  if (!name_ok(space->ctx, s))
    goto error;
  id = isl_id_alloc(space->ctx, s, NULL);
  return isl_space_set_dim_id(space, type, pos, id);
error:
  isl_space_free(space);
  return NULL;
}
 
/* Does the given dimension have a name?
 */
isl_bool isl_space_has_dim_name(__isl_keep isl_space *space,
  enum isl_dim_type type, unsigned pos)
{
  isl_id *id;
 
  if (!space)
    return isl_bool_error;
  id = get_id(space, type, pos);
  return isl_bool_ok(id && id->name);
}
 
__isl_keep const char *isl_space_get_dim_name(__isl_keep isl_space *space,
         enum isl_dim_type type, unsigned pos)
{
  isl_id *id = get_id(space, type, pos);
  return id ? id->name : NULL;
}
 
int isl_space_find_dim_by_id(__isl_keep isl_space *space,
  enum isl_dim_type type, __isl_keep isl_id *id)
{
  int i;
  int offset;
  isl_size n;
 
  n = isl_space_dim(space, type);
  if (n < 0 || !id)
    return -1;
 
  offset = isl_space_offset(space, type);
  for (i = 0; i < n && offset + i < space->n_id; ++i)
    if (space->ids[offset + i] == id)
      return i;
 
  return -1;
}
 
int isl_space_find_dim_by_name(__isl_keep isl_space *space,
  enum isl_dim_type type, const char *name)
{
  int i;
  int offset;
  isl_size n;
 
  n = isl_space_dim(space, type);
  if (n < 0 || !name)
    return -1;
 
  offset = isl_space_offset(space, type);
  for (i = 0; i < n && offset + i < space->n_id; ++i) {
    isl_id *id = get_id(space, type, i);
    if (id && id->name && !strcmp(id->name, name))
      return i;
  }
 
  return -1;
}
 
/* Reset the user pointer on all identifiers of parameters and tuples
 * of "space".
 */
__isl_give isl_space *isl_space_reset_user(__isl_take isl_space *space)
{
  int i;
  isl_ctx *ctx;
  isl_id *id;
  const char *name;
 
  if (!space)
    return NULL;
 
  ctx = isl_space_get_ctx(space);
 
  for (i = 0; i < space->nparam && i < space->n_id; ++i) {
    if (!isl_id_get_user(space->ids[i]))
      continue;
    space = isl_space_cow(space);
    if (!space)
      return NULL;
    name = isl_id_get_name(space->ids[i]);
    id = isl_id_alloc(ctx, name, NULL);
    isl_id_free(space->ids[i]);
    space->ids[i] = id;
    if (!id)
      return isl_space_free(space);
  }
 
  for (i = 0; i < 2; ++i) {
    if (!space->tuple_id[i])
      continue;
    if (!isl_id_get_user(space->tuple_id[i]))
      continue;
    space = isl_space_cow(space);
    if (!space)
      return NULL;
    name = isl_id_get_name(space->tuple_id[i]);
    id = isl_id_alloc(ctx, name, NULL);
    isl_id_free(space->tuple_id[i]);
    space->tuple_id[i] = id;
    if (!id)
      return isl_space_free(space);
  }
 
  for (i = 0; i < 2; ++i) {
    isl_space *nested;
 
    if (!space->nested[i])
      continue;
    nested = isl_space_take_nested(space, i);
    nested = isl_space_reset_user(nested);
    space = isl_space_restore_nested(space, i, nested);
    if (!space)
      return NULL;
  }
 
  return space;
}
 
static __isl_keep isl_id *tuple_id(__isl_keep isl_space *space,
  enum isl_dim_type type)
{
  if (!space)
    return NULL;
  if (type == isl_dim_in)
    return space->tuple_id[0];
  if (type == isl_dim_out)
    return space->tuple_id[1];
  return NULL;
}
 
static __isl_keep isl_space *nested(__isl_keep isl_space *space,
  enum isl_dim_type type)
{
  if (!space)
    return NULL;
  if (type == isl_dim_in)
    return space->nested[0];
  if (type == isl_dim_out)
    return space->nested[1];
  return NULL;
}
 
/* Are the two spaces the same, apart from positions and names of parameters?
 */
isl_bool isl_space_has_equal_tuples(__isl_keep isl_space *space1,
  __isl_keep isl_space *space2)
{
  if (!space1 || !space2)
    return isl_bool_error;
  if (space1 == space2)
    return isl_bool_true;
  return isl_space_tuple_is_equal(space1, isl_dim_in,
          space2, isl_dim_in) &&
         isl_space_tuple_is_equal(space1, isl_dim_out,
          space2, isl_dim_out);
}
 
/* Check that a match involving "space" was successful.
 * That is, check that "match" is equal to isl_bool_true.
 */
static isl_stat check_match(__isl_keep isl_space *space, isl_bool match)
{
  if (match < 0)
    return isl_stat_error;
  if (!match)
    isl_die(isl_space_get_ctx(space), isl_error_invalid,
      "incompatible spaces", return isl_stat_error);
 
  return isl_stat_ok;
}
 
/* Check that the two spaces are the same,
 * apart from positions and names of parameters.
 */
isl_stat isl_space_check_equal_tuples(__isl_keep isl_space *space1,
  __isl_keep isl_space *space2)
{
  isl_bool is_equal;
 
  is_equal = isl_space_has_equal_tuples(space1, space2);
  return check_match(space1, is_equal);
}
 
/* Check if the tuple of type "type1" of "space1" is the same as
 * the tuple of type "type2" of "space2".
 *
 * That is, check if the tuples have the same identifier, the same dimension
 * and the same internal structure.
 * The identifiers of the dimensions inside the tuples do not affect the result.
 *
 * Note that this function only checks the tuples themselves.
 * If nested tuples are involved, then we need to be careful not
 * to have result affected by possibly differing parameters
 * in those nested tuples.
 */
isl_bool isl_space_tuple_is_equal(__isl_keep isl_space *space1,
  enum isl_dim_type type1, __isl_keep isl_space *space2,
  enum isl_dim_type type2)
{
  isl_id *id1, *id2;
  isl_space *nested1, *nested2;
 
  if (!space1 || !space2)
    return isl_bool_error;
 
  if (space1 == space2 && type1 == type2)
    return isl_bool_true;
 
  if (n(space1, type1) != n(space2, type2))
    return isl_bool_false;
  id1 = tuple_id(space1, type1);
  id2 = tuple_id(space2, type2);
  if (!id1 ^ !id2)
    return isl_bool_false;
  if (id1 && id1 != id2)
    return isl_bool_false;
  nested1 = nested(space1, type1);
  nested2 = nested(space2, type2);
  if (!nested1 ^ !nested2)
    return isl_bool_false;
  if (nested1 && !isl_space_has_equal_tuples(nested1, nested2))
    return isl_bool_false;
  return isl_bool_true;
}
 
/* Is the tuple "inner" within the wrapped relation inside tuple "outer"
 * of "space1" equal to tuple "type2" of "space2"?
 */
isl_bool isl_space_wrapped_tuple_is_equal(__isl_keep isl_space *space1,
  enum isl_dim_type outer, enum isl_dim_type inner,
  __isl_keep isl_space *space2, enum isl_dim_type type2)
{
  int pos;
  isl_space *nested;
 
  if (!space1)
    return isl_bool_error;
  if (outer != isl_dim_in && outer != isl_dim_out)
    isl_die(isl_space_get_ctx(space1), isl_error_invalid,
      "only input, output and set tuples "
      "can have nested relations", return isl_bool_error);
  pos = outer - isl_dim_in;
  nested = isl_space_peek_nested(space1, pos);
  return isl_space_tuple_is_equal(nested, inner, space2, type2);
}
 
/* Check that the tuple "inner" within the wrapped relation inside tuple "outer"
 * of "space1" is equal to tuple "type2" of "space2".
 */
isl_stat isl_space_check_wrapped_tuple_is_equal(__isl_keep isl_space *space1,
  enum isl_dim_type outer, enum isl_dim_type inner,
  __isl_keep isl_space *space2, enum isl_dim_type type2)
{
  isl_bool is_equal;
 
  is_equal = isl_space_wrapped_tuple_is_equal(space1, outer, inner,
              space2, type2);
  return check_match(space1, is_equal);
}
 
static isl_bool match(__isl_keep isl_space *space1, enum isl_dim_type type1,
  __isl_keep isl_space *space2, enum isl_dim_type type2)
{
  int i;
  isl_bool equal;
 
  if (!space1 || !space2)
    return isl_bool_error;
 
  if (space1 == space2 && type1 == type2)
    return isl_bool_true;
 
  equal = isl_space_tuple_is_equal(space1, type1, space2, type2);
  if (equal < 0 || !equal)
    return equal;
 
  if (!space1->ids && !space2->ids)
    return isl_bool_true;
 
  for (i = 0; i < n(space1, type1); ++i) {
    if (get_id(space1, type1, i) != get_id(space2, type2, i))
      return isl_bool_false;
  }
  return isl_bool_true;
}
 
/* Do "space1" and "space2" have the same parameters?
 */
isl_bool isl_space_has_equal_params(__isl_keep isl_space *space1,
  __isl_keep isl_space *space2)
{
  return match(space1, isl_dim_param, space2, isl_dim_param);
}
 
/* Do "space1" and "space2" have the same identifiers for all
 * the tuple variables?
 */
isl_bool isl_space_has_equal_ids(__isl_keep isl_space *space1,
  __isl_keep isl_space *space2)
{
  isl_bool equal;
 
  equal = match(space1, isl_dim_in, space2, isl_dim_in);
  if (equal < 0 || !equal)
    return equal;
  return match(space1, isl_dim_out, space2, isl_dim_out);
}
 
isl_bool isl_space_match(__isl_keep isl_space *space1, enum isl_dim_type type1,
  __isl_keep isl_space *space2, enum isl_dim_type type2)
{
  return match(space1, type1, space2, type2);
}
 
static void get_ids(__isl_keep isl_space *space, enum isl_dim_type type,
  unsigned first, unsigned n, __isl_keep isl_id **ids)
{
  int i;
 
  for (i = 0; i < n ; ++i)
    ids[i] = get_id(space, type, first + i);
}
 
static __isl_give isl_space *space_extend(__isl_take isl_space *space,
      unsigned nparam, unsigned n_in, unsigned n_out)
{
  isl_id **ids = NULL;
 
  if (!space)
    return NULL;
  if (space->nparam == nparam &&
      space->n_in == n_in && space->n_out == n_out)
    return space;
 
  isl_assert(space->ctx, space->nparam <= nparam, goto error);
  isl_assert(space->ctx, space->n_in <= n_in, goto error);
  isl_assert(space->ctx, space->n_out <= n_out, goto error);
 
  space = isl_space_cow(space);
  if (!space)
    goto error;
 
  if (space->ids) {
    unsigned n;
    n = nparam + n_in + n_out;
    if (n < nparam || n < n_in || n < n_out)
      isl_die(isl_space_get_ctx(space), isl_error_invalid,
        "overflow in total number of dimensions",
        goto error);
    ids = isl_calloc_array(space->ctx, isl_id *, n);
    if (!ids)
      goto error;
    get_ids(space, isl_dim_param, 0, space->nparam, ids);
    get_ids(space, isl_dim_in, 0, space->n_in, ids + nparam);
    get_ids(space, isl_dim_out, 0, space->n_out,
      ids + nparam + n_in);
    free(space->ids);
    space->ids = ids;
    space->n_id = nparam + n_in + n_out;
  }
  space->nparam = nparam;
  space->n_in = n_in;
  space->n_out = n_out;
 
  return space;
error:
  free(ids);
  isl_space_free(space);
  return NULL;
}
 
__isl_give isl_space *isl_space_extend(__isl_take isl_space *space,
  unsigned nparam, unsigned n_in, unsigned n_out)
{
  return space_extend(space, nparam, n_in, n_out);
}
 
__isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
  enum isl_dim_type type, unsigned n)
{
  space = isl_space_reset(space, type);
  if (!space)
    return NULL;
  switch (type) {
  case isl_dim_param:
    space = space_extend(space,
        space->nparam + n, space->n_in, space->n_out);
    if (space && space->nested[0] &&
        !(space->nested[0] = isl_space_add_dims(space->nested[0],
                isl_dim_param, n)))
      goto error;
    if (space && space->nested[1] &&
        !(space->nested[1] = isl_space_add_dims(space->nested[1],
                isl_dim_param, n)))
      goto error;
    return space;
  case isl_dim_in:
    return space_extend(space,
        space->nparam, space->n_in + n, space->n_out);
  case isl_dim_out:
    return space_extend(space,
        space->nparam, space->n_in, space->n_out + n);
  default:
    isl_die(space->ctx, isl_error_invalid,
      "cannot add dimensions of specified type", goto error);
  }
error:
  isl_space_free(space);
  return NULL;
}
 
/* Add a parameter with identifier "id" to "space", provided
 * it does not already appear in "space".
 */
__isl_give isl_space *isl_space_add_param_id(__isl_take isl_space *space,
  __isl_take isl_id *id)
{
  isl_size pos;
 
  if (!space || !id)
    goto error;
 
  if (isl_space_find_dim_by_id(space, isl_dim_param, id) >= 0) {
    isl_id_free(id);
    return space;
  }
 
  pos = isl_space_dim(space, isl_dim_param);
  if (pos < 0)
    goto error;
  space = isl_space_add_dims(space, isl_dim_param, 1);
  space = isl_space_set_dim_id(space, isl_dim_param, pos, id);
 
  return space;
error:
  isl_space_free(space);
  isl_id_free(id);
  return NULL;
}
 
static int valid_dim_type(enum isl_dim_type type)
{
  switch (type) {
  case isl_dim_param:
  case isl_dim_in:
  case isl_dim_out:
    return 1;
  default:
    return 0;
  }
}
 
#undef TYPE
#define TYPE  isl_space
#include "check_type_range_templ.c"
 
/* Insert "n" dimensions of type "type" at position "pos".
 * If we are inserting parameters, then they are also inserted in
 * any nested spaces.
 */
__isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
  enum isl_dim_type type, unsigned pos, unsigned n)
{
  isl_ctx *ctx;
  isl_id **ids = NULL;
 
  if (!space)
    return NULL;
  if (n == 0)
    return isl_space_reset(space, type);
 
  ctx = isl_space_get_ctx(space);
  if (!valid_dim_type(type))
    isl_die(ctx, isl_error_invalid,
      "cannot insert dimensions of specified type",
      goto error);
 
  if (isl_space_check_range(space, type, pos, 0) < 0)
    return isl_space_free(space);
 
  space = isl_space_cow(space);
  if (!space)
    return NULL;
 
  if (space->ids) {
    enum isl_dim_type t, o = isl_dim_param;
    int off;
    int s[3];
    ids = isl_calloc_array(ctx, isl_id *,
           space->nparam + space->n_in + space->n_out + n);
    if (!ids)
      goto error;
    off = 0;
    s[isl_dim_param - o] = space->nparam;
    s[isl_dim_in - o] = space->n_in;
    s[isl_dim_out - o] = space->n_out;
    for (t = isl_dim_param; t <= isl_dim_out; ++t) {
      if (t != type) {
        get_ids(space, t, 0, s[t - o], ids + off);
        off += s[t - o];
      } else {
        get_ids(space, t, 0, pos, ids + off);
        off += pos + n;
        get_ids(space, t, pos, s[t - o] - pos,
          ids + off);
        off += s[t - o] - pos;
      }
    }
    free(space->ids);
    space->ids = ids;
    space->n_id = space->nparam + space->n_in + space->n_out + n;
  }
  switch (type) {
  case isl_dim_param: space->nparam += n; break;
  case isl_dim_in:  space->n_in += n; break;
  case isl_dim_out: space->n_out += n; break;
  default:    ;
  }
  space = isl_space_reset(space, type);
 
  if (type == isl_dim_param) {
    if (space && space->nested[0] &&
        !(space->nested[0] = isl_space_insert_dims(space->nested[0],
                isl_dim_param, pos, n)))
      goto error;
    if (space && space->nested[1] &&
        !(space->nested[1] = isl_space_insert_dims(space->nested[1],
                isl_dim_param, pos, n)))
      goto error;
  }
 
  return space;
error:
  isl_space_free(space);
  return NULL;
}
 
__isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
  enum isl_dim_type dst_type, unsigned dst_pos,
  enum isl_dim_type src_type, unsigned src_pos, unsigned n)
{
  int i;
 
  space = isl_space_reset(space, src_type);
  space = isl_space_reset(space, dst_type);
  if (!space)
    return NULL;
  if (n == 0)
    return space;
 
  if (isl_space_check_range(space, src_type, src_pos, n) < 0)
    return isl_space_free(space);
 
  if (dst_type == src_type && dst_pos == src_pos)
    return space;
 
  isl_assert(space->ctx, dst_type != src_type, goto error);
 
  space = isl_space_cow(space);
  if (!space)
    return NULL;
 
  if (space->ids) {
    isl_id **ids;
    enum isl_dim_type t, o = isl_dim_param;
    int off;
    int s[3];
    ids = isl_calloc_array(space->ctx, isl_id *,
         space->nparam + space->n_in + space->n_out);
    if (!ids)
      goto error;
    off = 0;
    s[isl_dim_param - o] = space->nparam;
    s[isl_dim_in - o] = space->n_in;
    s[isl_dim_out - o] = space->n_out;
    for (t = isl_dim_param; t <= isl_dim_out; ++t) {
      if (t == dst_type) {
        get_ids(space, t, 0, dst_pos, ids + off);
        off += dst_pos;
        get_ids(space, src_type, src_pos, n, ids + off);
        off += n;
        get_ids(space, t, dst_pos, s[t - o] - dst_pos,
            ids + off);
        off += s[t - o] - dst_pos;
      } else if (t == src_type) {
        get_ids(space, t, 0, src_pos, ids + off);
        off += src_pos;
        get_ids(space, t, src_pos + n,
              s[t - o] - src_pos - n, ids + off);
        off += s[t - o] - src_pos - n;
      } else {
        get_ids(space, t, 0, s[t - o], ids + off);
        off += s[t - o];
      }
    }
    free(space->ids);
    space->ids = ids;
    space->n_id = space->nparam + space->n_in + space->n_out;
  }
 
  switch (dst_type) {
  case isl_dim_param: space->nparam += n; break;
  case isl_dim_in:  space->n_in += n; break;
  case isl_dim_out: space->n_out += n; break;
  default:    ;
  }
 
  switch (src_type) {
  case isl_dim_param: space->nparam -= n; break;
  case isl_dim_in:  space->n_in -= n; break;
  case isl_dim_out: space->n_out -= n; break;
  default:    ;
  }
 
  if (dst_type != isl_dim_param && src_type != isl_dim_param)
    return space;
 
  for (i = 0; i < 2; ++i) {
    isl_space *nested;
 
    if (!space->nested[i])
      continue;
    nested = isl_space_take_nested(space, i);
    nested = isl_space_replace_params(nested, space);
    space = isl_space_restore_nested(space, i, nested);
    if (!space)
      return NULL;
  }
 
  return space;
error:
  isl_space_free(space);
  return NULL;
}
 
/* Check that "space1" and "space2" have the same parameters,
 * reporting an error if they do not.
 */
isl_stat isl_space_check_equal_params(__isl_keep isl_space *space1,
  __isl_keep isl_space *space2)
{
  isl_bool equal;
 
  equal = isl_space_has_equal_params(space1, space2);
  if (equal < 0)
    return isl_stat_error;
  if (!equal)
    isl_die(isl_space_get_ctx(space1), isl_error_invalid,
      "parameters need to match", return isl_stat_error);
  return isl_stat_ok;
}
 
__isl_give isl_space *isl_space_join(__isl_take isl_space *left,
  __isl_take isl_space *right)
{
  isl_space *space;
 
  if (isl_space_check_equal_params(left, right) < 0)
    goto error;
 
  isl_assert(left->ctx,
    isl_space_tuple_is_equal(left, isl_dim_out, right, isl_dim_in),
    goto error);
 
  space = isl_space_alloc(left->ctx,
        left->nparam, left->n_in, right->n_out);
  if (!space)
    goto error;
 
  space = copy_ids(space, isl_dim_param, 0, left, isl_dim_param);
  space = copy_ids(space, isl_dim_in, 0, left, isl_dim_in);
  space = copy_ids(space, isl_dim_out, 0, right, isl_dim_out);
 
  if (space && left->tuple_id[0] &&
      !(space->tuple_id[0] = isl_id_copy(left->tuple_id[0])))
    goto error;
  if (space && right->tuple_id[1] &&
      !(space->tuple_id[1] = isl_id_copy(right->tuple_id[1])))
    goto error;
  if (space && left->nested[0] &&
      !(space->nested[0] = isl_space_copy(left->nested[0])))
    goto error;
  if (space && right->nested[1] &&
      !(space->nested[1] = isl_space_copy(right->nested[1])))
    goto error;
 
  isl_space_free(left);
  isl_space_free(right);
 
  return space;
error:
  isl_space_free(left);
  isl_space_free(right);
  return NULL;
}
 
/* Given two map spaces { A -> C } and { B -> D }, construct the space
 * { [A -> B] -> [C -> D] }.
 * Given two set spaces { A } and { B }, construct the space { [A -> B] }.
 */
__isl_give isl_space *isl_space_product(__isl_take isl_space *left,
  __isl_take isl_space *right)
{
  isl_space *dom1, *dom2, *nest1, *nest2;
  int is_set;
 
  if (!left || !right)
    goto error;
 
  is_set = isl_space_is_set(left);
  if (is_set != isl_space_is_set(right))
    isl_die(isl_space_get_ctx(left), isl_error_invalid,
      "expecting either two set spaces or two map spaces",
      goto error);
  if (is_set)
    return isl_space_range_product(left, right);
 
  if (isl_space_check_equal_params(left, right) < 0)
    goto error;
 
  dom1 = isl_space_domain(isl_space_copy(left));
  dom2 = isl_space_domain(isl_space_copy(right));
  nest1 = isl_space_wrap(isl_space_join(isl_space_reverse(dom1), dom2));
 
  dom1 = isl_space_range(left);
  dom2 = isl_space_range(right);
  nest2 = isl_space_wrap(isl_space_join(isl_space_reverse(dom1), dom2));
 
  return isl_space_join(isl_space_reverse(nest1), nest2);
error:
  isl_space_free(left);
  isl_space_free(right);
  return NULL;
}
 
/* Given two spaces { A -> C } and { B -> C }, construct the space
 * { [A -> B] -> C }
 */
__isl_give isl_space *isl_space_domain_product(__isl_take isl_space *left,
  __isl_take isl_space *right)
{
  isl_space *ran, *dom1, *dom2, *nest;
 
  if (isl_space_check_equal_params(left, right) < 0)
    goto error;
 
  if (!isl_space_tuple_is_equal(left, isl_dim_out, right, isl_dim_out))
    isl_die(left->ctx, isl_error_invalid,
      "ranges need to match", goto error);
 
  ran = isl_space_range(isl_space_copy(left));
 
  dom1 = isl_space_domain(left);
  dom2 = isl_space_domain(right);
  nest = isl_space_wrap(isl_space_join(isl_space_reverse(dom1), dom2));
 
  return isl_space_join(isl_space_reverse(nest), ran);
error:
  isl_space_free(left);
  isl_space_free(right);
  return NULL;
}
 
__isl_give isl_space *isl_space_range_product(__isl_take isl_space *left,
  __isl_take isl_space *right)
{
  isl_space *dom, *ran1, *ran2, *nest;
 
  if (isl_space_check_equal_params(left, right) < 0)
    goto error;
 
  if (!isl_space_tuple_is_equal(left, isl_dim_in, right, isl_dim_in))
    isl_die(left->ctx, isl_error_invalid,
      "domains need to match", goto error);
 
  dom = isl_space_domain(isl_space_copy(left));
 
  ran1 = isl_space_range(left);
  ran2 = isl_space_range(right);
  nest = isl_space_wrap(isl_space_join(isl_space_reverse(ran1), ran2));
 
  return isl_space_join(isl_space_reverse(dom), nest);
error:
  isl_space_free(left);
  isl_space_free(right);
  return NULL;
}
 
/* Given a space of the form [A -> B] -> C, return the space A -> C.
 */
__isl_give isl_space *isl_space_domain_factor_domain(
  __isl_take isl_space *space)
{
  isl_space *nested;
  isl_space *domain;
 
  if (isl_space_check_domain_is_wrapping(space) < 0)
    return isl_space_free(space);
 
  nested = space->nested[0];
  domain = isl_space_copy(space);
  domain = isl_space_drop_dims(domain, isl_dim_in,
          nested->n_in, nested->n_out);
  if (!domain)
    return isl_space_free(space);
  if (nested->tuple_id[0]) {
    domain->tuple_id[0] = isl_id_copy(nested->tuple_id[0]);
    if (!domain->tuple_id[0])
      goto error;
  }
  if (nested->nested[0]) {
    domain->nested[0] = isl_space_copy(nested->nested[0]);
    if (!domain->nested[0])
      goto error;
  }
 
  isl_space_free(space);
  return domain;
error:
  isl_space_free(space);
  isl_space_free(domain);
  return NULL;
}
 
/* Given a space of the form [A -> B] -> C, return the space B -> C.
 */
__isl_give isl_space *isl_space_domain_factor_range(
  __isl_take isl_space *space)
{
  isl_space *nested;
  isl_space *range;
 
  if (isl_space_check_domain_is_wrapping(space) < 0)
    return isl_space_free(space);
 
  nested = space->nested[0];
  range = isl_space_copy(space);
  range = isl_space_drop_dims(range, isl_dim_in, 0, nested->n_in);
  if (!range)
    return isl_space_free(space);
  if (nested->tuple_id[1]) {
    range->tuple_id[0] = isl_id_copy(nested->tuple_id[1]);
    if (!range->tuple_id[0])
      goto error;
  }
  if (nested->nested[1]) {
    range->nested[0] = isl_space_copy(nested->nested[1]);
    if (!range->nested[0])
      goto error;
  }
 
  isl_space_free(space);
  return range;
error:
  isl_space_free(space);
  isl_space_free(range);
  return NULL;
}
 
/* Internal function that selects the domain of the map that is
 * embedded in either a set space or the range of a map space.
 * In particular, given a space of the form [A -> B], return the space A.
 * Given a space of the form A -> [B -> C], return the space A -> B.
 */
static __isl_give isl_space *range_factor_domain(__isl_take isl_space *space)
{
  isl_space *nested;
  isl_space *domain;
 
  if (!space)
    return NULL;
 
  nested = space->nested[1];
  domain = isl_space_copy(space);
  domain = isl_space_drop_dims(domain, isl_dim_out,
          nested->n_in, nested->n_out);
  if (!domain)
    return isl_space_free(space);
  if (nested->tuple_id[0]) {
    domain->tuple_id[1] = isl_id_copy(nested->tuple_id[0]);
    if (!domain->tuple_id[1])
      goto error;
  }
  if (nested->nested[0]) {
    domain->nested[1] = isl_space_copy(nested->nested[0]);
    if (!domain->nested[1])
      goto error;
  }
 
  isl_space_free(space);
  return domain;
error:
  isl_space_free(space);
  isl_space_free(domain);
  return NULL;
}
 
/* Given a space of the form A -> [B -> C], return the space A -> B.
 */
__isl_give isl_space *isl_space_range_factor_domain(
  __isl_take isl_space *space)
{
  if (isl_space_check_range_is_wrapping(space) < 0)
    return isl_space_free(space);
 
  return range_factor_domain(space);
}
 
/* Given a space of the form [A -> B], return the space A.
 */
static __isl_give isl_space *set_factor_domain(__isl_take isl_space *space)
{
  if (!space)
    return NULL;
  if (!isl_space_is_wrapping(space))
    isl_die(isl_space_get_ctx(space), isl_error_invalid,
      "not a product", return isl_space_free(space));
 
  return range_factor_domain(space);
}
 
/* Given a space of the form [A -> B] -> [C -> D], return the space A -> C.
 * Given a space of the form [A -> B], return the space A.
 */
__isl_give isl_space *isl_space_factor_domain(__isl_take isl_space *space)
{
  if (!space)
    return NULL;
  if (isl_space_is_set(space))
    return set_factor_domain(space);
  space = isl_space_domain_factor_domain(space);
  space = isl_space_range_factor_domain(space);
  return space;
}
 
/* Internal function that selects the range of the map that is
 * embedded in either a set space or the range of a map space.
 * In particular, given a space of the form [A -> B], return the space B.
 * Given a space of the form A -> [B -> C], return the space A -> C.
 */
static __isl_give isl_space *range_factor_range(__isl_take isl_space *space)
{
  isl_space *nested;
  isl_space *range;
 
  if (!space)
    return NULL;
 
  nested = space->nested[1];
  range = isl_space_copy(space);
  range = isl_space_drop_dims(range, isl_dim_out, 0, nested->n_in);
  if (!range)
    return isl_space_free(space);
  if (nested->tuple_id[1]) {
    range->tuple_id[1] = isl_id_copy(nested->tuple_id[1]);
    if (!range->tuple_id[1])
      goto error;
  }
  if (nested->nested[1]) {
    range->nested[1] = isl_space_copy(nested->nested[1]);
    if (!range->nested[1])
      goto error;
  }
 
  isl_space_free(space);
  return range;
error:
  isl_space_free(space);
  isl_space_free(range);
  return NULL;
}
 
/* Given a space of the form A -> [B -> C], return the space A -> C.
 */
__isl_give isl_space *isl_space_range_factor_range(
  __isl_take isl_space *space)
{
  if (isl_space_check_range_is_wrapping(space) < 0)
    return isl_space_free(space);
 
  return range_factor_range(space);
}
 
/* Given a space of the form [A -> B], return the space B.
 */
static __isl_give isl_space *set_factor_range(__isl_take isl_space *space)
{
  if (!space)
    return NULL;
  if (!isl_space_is_wrapping(space))
    isl_die(isl_space_get_ctx(space), isl_error_invalid,
      "not a product", return isl_space_free(space));
 
  return range_factor_range(space);
}
 
/* Given a space of the form [A -> B] -> [C -> D], return the space B -> D.
 * Given a space of the form [A -> B], return the space B.
 */
__isl_give isl_space *isl_space_factor_range(__isl_take isl_space *space)
{
  if (!space)
    return NULL;
  if (isl_space_is_set(space))
    return set_factor_range(space);
  space = isl_space_domain_factor_range(space);
  space = isl_space_range_factor_range(space);
  return space;
}
 
/* Given a space of the form [A -> B] -> C, return the space A.
 */
__isl_give isl_space *isl_space_domain_wrapped_domain(
  __isl_take isl_space *space)
{
  return isl_space_factor_domain(isl_space_domain(space));
}
 
/* Given a space of the form [A -> B] -> C, return the space B.
 */
__isl_give isl_space *isl_space_domain_wrapped_range(
  __isl_take isl_space *space)
{
  return isl_space_factor_range(isl_space_domain(space));
}
 
/* Given a space of the form A -> [B -> C], return the space B.
 */
__isl_give isl_space *isl_space_range_wrapped_domain(
  __isl_take isl_space *space)
{
  return isl_space_factor_domain(isl_space_range(space));
}
 
/* Given a space of the form A -> [B -> C], return the space C.
 */
__isl_give isl_space *isl_space_range_wrapped_range(
  __isl_take isl_space *space)
{
  return isl_space_factor_range(isl_space_range(space));
}
 
__isl_give isl_space *isl_space_map_from_set(__isl_take isl_space *space)
{
  isl_ctx *ctx;
  isl_id **ids = NULL;
  int n_id;
 
  if (!space)
    return NULL;
  ctx = isl_space_get_ctx(space);
  if (!isl_space_is_set(space))
    isl_die(ctx, isl_error_invalid, "not a set space", goto error);
  space = isl_space_cow(space);
  if (!space)
    return NULL;
  n_id = space->nparam + space->n_out + space->n_out;
  if (n_id > 0 && space->ids) {
    ids = isl_calloc_array(space->ctx, isl_id *, n_id);
    if (!ids)
      goto error;
    get_ids(space, isl_dim_param, 0, space->nparam, ids);
    get_ids(space, isl_dim_out, 0, space->n_out,
      ids + space->nparam);
  }
  space->n_in = space->n_out;
  if (ids) {
    free(space->ids);
    space->ids = ids;
    space->n_id = n_id;
    space = copy_ids(space, isl_dim_out, 0, space, isl_dim_in);
  }
  isl_id_free(space->tuple_id[0]);
  space->tuple_id[0] = isl_id_copy(space->tuple_id[1]);
  isl_space_free(space->nested[0]);
  space->nested[0] = isl_space_copy(space->nested[1]);
  return space;
error:
  isl_space_free(space);
  return NULL;
}
 
__isl_give isl_space *isl_space_map_from_domain_and_range(
  __isl_take isl_space *domain, __isl_take isl_space *range)
{
  if (!domain || !range)
    goto error;
  if (!isl_space_is_set(domain))
    isl_die(isl_space_get_ctx(domain), isl_error_invalid,
      "domain is not a set space", goto error);
  if (!isl_space_is_set(range))
    isl_die(isl_space_get_ctx(range), isl_error_invalid,
      "range is not a set space", goto error);
  return isl_space_join(isl_space_reverse(domain), range);
error:
  isl_space_free(domain);
  isl_space_free(range);
  return NULL;
}
 
static __isl_give isl_space *set_ids(__isl_take isl_space *space,
  enum isl_dim_type type,
  unsigned first, unsigned n, __isl_take isl_id **ids)
{
  int i;
 
  for (i = 0; i < n ; ++i)
    space = set_id(space, type, first + i, ids[i]);
 
  return space;
}
 
__isl_give isl_space *isl_space_reverse(__isl_take isl_space *space)
{
  unsigned t;
  isl_bool equal;
  isl_space *nested;
  isl_id **ids = NULL;
  isl_id *id;
 
  equal = match(space, isl_dim_in, space, isl_dim_out);
  if (equal < 0)
    return isl_space_free(space);
  if (equal)
    return space;
 
  space = isl_space_cow(space);
  if (!space)
    return NULL;
 
  id = space->tuple_id[0];
  space->tuple_id[0] = space->tuple_id[1];
  space->tuple_id[1] = id;
 
  nested = space->nested[0];
  space->nested[0] = space->nested[1];
  space->nested[1] = nested;
 
  if (space->ids) {
    int n_id = space->n_in + space->n_out;
    ids = isl_alloc_array(space->ctx, isl_id *, n_id);
    if (n_id && !ids)
      goto error;
    get_ids(space, isl_dim_in, 0, space->n_in, ids);
    get_ids(space, isl_dim_out, 0, space->n_out, ids + space->n_in);
  }
 
  t = space->n_in;
  space->n_in = space->n_out;
  space->n_out = t;
 
  if (space->ids) {
    space = set_ids(space, isl_dim_out, 0, space->n_out, ids);
    space = set_ids(space, isl_dim_in, 0, space->n_in,
        ids + space->n_out);
    free(ids);
  }
 
  return space;
error:
  free(ids);
  isl_space_free(space);
  return NULL;
}
 
/* Given a space A -> (B -> C), return the corresponding space
 * A -> (C -> B).
 *
 * If the range tuple is named, then the name is only preserved
 * if B and C are equal tuples, in which case the output
 * of this function is identical to the input.
 */
__isl_give isl_space *isl_space_range_reverse(__isl_take isl_space *space)
{
  isl_space *nested;
  isl_bool equal;
 
  if (isl_space_check_range_is_wrapping(space) < 0)
    return isl_space_free(space);
 
  nested = isl_space_peek_nested(space, 1);
  equal = isl_space_tuple_is_equal(nested, isl_dim_in,
          nested, isl_dim_out);
  if (equal < 0)
    return isl_space_free(space);
 
  nested = isl_space_take_nested(space, 1);
  nested = isl_space_reverse(nested);
  space = isl_space_restore_nested(space, 1, nested);
  if (!equal)
    space = isl_space_reset_tuple_id(space, isl_dim_out);
 
  return space;
}
 
__isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
  enum isl_dim_type type, unsigned first, unsigned num)
{
  int i;
 
  if (!space)
    return NULL;
 
  if (num == 0)
    return isl_space_reset(space, type);
 
  if (!valid_dim_type(type))
    isl_die(space->ctx, isl_error_invalid,
      "cannot drop dimensions of specified type", goto error);
 
  if (isl_space_check_range(space, type, first, num) < 0)
    return isl_space_free(space);
  space = isl_space_cow(space);
  if (!space)
    goto error;
  if (space->ids) {
    space = extend_ids(space);
    if (!space)
      goto error;
    for (i = 0; i < num; ++i)
      isl_id_free(get_id(space, type, first + i));
    for (i = first+num; i < n(space, type); ++i)
      set_id(space, type, i - num, get_id(space, type, i));
    switch (type) {
    case isl_dim_param:
      get_ids(space, isl_dim_in, 0, space->n_in,
        space->ids + offset(space, isl_dim_in) - num);
    case isl_dim_in:
      get_ids(space, isl_dim_out, 0, space->n_out,
        space->ids + offset(space, isl_dim_out) - num);
    default:
      ;
    }
    space->n_id -= num;
  }
  switch (type) {
  case isl_dim_param: space->nparam -= num; break;
  case isl_dim_in:  space->n_in -= num; break;
  case isl_dim_out: space->n_out -= num; break;
  default:    ;
  }
  space = isl_space_reset(space, type);
  if (type == isl_dim_param) {
    if (space && space->nested[0] &&
        !(space->nested[0] = isl_space_drop_dims(space->nested[0],
                isl_dim_param, first, num)))
      goto error;
    if (space && space->nested[1] &&
        !(space->nested[1] = isl_space_drop_dims(space->nested[1],
                isl_dim_param, first, num)))
      goto error;
  }
  return space;
error:
  isl_space_free(space);
  return NULL;
}
 
__isl_give isl_space *isl_space_drop_inputs(__isl_take isl_space *space,
    unsigned first, unsigned n)
{
  if (!space)
    return NULL;
  return isl_space_drop_dims(space, isl_dim_in, first, n);
}
 
__isl_give isl_space *isl_space_drop_outputs(__isl_take isl_space *space,
    unsigned first, unsigned n)
{
  if (!space)
    return NULL;
  return isl_space_drop_dims(space, isl_dim_out, first, n);
}
 
/* Remove all parameters from "space".
 */
__isl_give isl_space *isl_space_drop_all_params(__isl_take isl_space *space)
{
  isl_size nparam;
 
  nparam = isl_space_dim(space, isl_dim_param);
  if (nparam < 0)
    return isl_space_free(space);
  return isl_space_drop_dims(space, isl_dim_param, 0, nparam);
}
 
__isl_give isl_space *isl_space_domain(__isl_take isl_space *space)
{
  if (!space)
    return NULL;
  space = isl_space_drop_dims(space, isl_dim_out, 0, space->n_out);
  space = isl_space_reverse(space);
  space = mark_as_set(space);
  return space;
}
 
__isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space)
{
  if (!space)
    return NULL;
  if (!isl_space_is_set(space))
    isl_die(isl_space_get_ctx(space), isl_error_invalid,
      "not a set space", goto error);
  space = isl_space_reverse(space);
  space = isl_space_reset(space, isl_dim_out);
  return space;
error:
  isl_space_free(space);
  return NULL;
}
 
__isl_give isl_space *isl_space_range(__isl_take isl_space *space)
{
  if (!space)
    return NULL;
  space = isl_space_drop_dims(space, isl_dim_in, 0, space->n_in);
  space = mark_as_set(space);
  return space;
}
 
__isl_give isl_space *isl_space_from_range(__isl_take isl_space *space)
{
  if (!space)
    return NULL;
  if (!isl_space_is_set(space))
    isl_die(isl_space_get_ctx(space), isl_error_invalid,
      "not a set space", goto error);
  return isl_space_reset(space, isl_dim_in);
error:
  isl_space_free(space);
  return NULL;
}
 
/* Given a map space A -> B, return the map space [A -> B] -> A.
 */
__isl_give isl_space *isl_space_domain_map(__isl_take isl_space *space)
{
  isl_space *domain;
 
  domain = isl_space_from_range(isl_space_domain(isl_space_copy(space)));
  space = isl_space_from_domain(isl_space_wrap(space));
  space = isl_space_join(space, domain);
 
  return space;
}
 
/* Given a map space A -> B, return the map space [A -> B] -> B.
 */
__isl_give isl_space *isl_space_range_map(__isl_take isl_space *space)
{
  isl_space *range;
 
  range = isl_space_from_range(isl_space_range(isl_space_copy(space)));
  space = isl_space_from_domain(isl_space_wrap(space));
  space = isl_space_join(space, range);
 
  return space;
}
 
__isl_give isl_space *isl_space_params(__isl_take isl_space *space)
{
  isl_size n_in, n_out;
 
  if (isl_space_is_params(space))
    return space;
  n_in = isl_space_dim(space, isl_dim_in);
  n_out = isl_space_dim(space, isl_dim_out);
  if (n_in < 0 || n_out < 0)
    return isl_space_free(space);
  space = isl_space_drop_dims(space, isl_dim_in, 0, n_in);
  space = isl_space_drop_dims(space, isl_dim_out, 0, n_out);
  space = mark_as_params(space);
  return space;
}
 
__isl_give isl_space *isl_space_set_from_params(__isl_take isl_space *space)
{
  if (!space)
    return NULL;
  if (!isl_space_is_params(space))
    isl_die(isl_space_get_ctx(space), isl_error_invalid,
      "not a parameter space", goto error);
  return isl_space_reset(space, isl_dim_set);
error:
  isl_space_free(space);
  return NULL;
}
 
/* Add an unnamed tuple of dimension "dim" to "space".
 * This requires "space" to be a parameter or set space.
 *
 * In particular, if "space" is a parameter space, then return
 * a set space with the given dimension.
 * If "space" is a set space, then return a map space
 * with "space" as domain and a range of the given dimension.
 */
__isl_give isl_space *isl_space_add_unnamed_tuple_ui(
  __isl_take isl_space *space, unsigned dim)
{
  isl_bool is_params, is_set;
 
  is_params = isl_space_is_params(space);
  is_set = isl_space_is_set(space);
  if (is_params < 0 || is_set < 0)
    return isl_space_free(space);
  if (!is_params && !is_set)
    isl_die(isl_space_get_ctx(space), isl_error_invalid,
      "cannot add tuple to map space",
      return isl_space_free(space));
  if (is_params)
    space = isl_space_set_from_params(space);
  else
    space = isl_space_from_domain(space);
  space = isl_space_add_dims(space, isl_dim_out, dim);
  return space;
}
 
/* Add a tuple of dimension "dim" and with tuple identifier "tuple_id"
 * to "space".
 * This requires "space" to be a parameter or set space.
 */
__isl_give isl_space *isl_space_add_named_tuple_id_ui(
  __isl_take isl_space *space, __isl_take isl_id *tuple_id, unsigned dim)
{
  space = isl_space_add_unnamed_tuple_ui(space, dim);
  space = isl_space_set_tuple_id(space, isl_dim_out, tuple_id);
  return space;
}
 
/* Check that the identifiers in "tuple" do not appear as parameters
 * in "space".
 */
static isl_stat check_fresh_params(__isl_keep isl_space *space,
  __isl_keep isl_multi_id *tuple)
{
  int i;
  isl_size n;
 
  n = isl_multi_id_size(tuple);
  if (n < 0)
    return isl_stat_error;
  for (i = 0; i < n; ++i) {
    isl_id *id;
    int pos;
 
    id = isl_multi_id_get_at(tuple, i);
    if (!id)
      return isl_stat_error;
    pos = isl_space_find_dim_by_id(space, isl_dim_param, id);
    isl_id_free(id);
    if (pos >= 0)
      isl_die(isl_space_get_ctx(space), isl_error_invalid,
        "parameters not unique", return isl_stat_error);
  }
 
  return isl_stat_ok;
}
 
/* Add the identifiers in "tuple" as parameters of "space"
 * that are known to be fresh.
 */
static __isl_give isl_space *add_bind_params(__isl_take isl_space *space,
  __isl_keep isl_multi_id *tuple)
{
  int i;
  isl_size first, n;
 
  first = isl_space_dim(space, isl_dim_param);
  n = isl_multi_id_size(tuple);
  if (first < 0 || n < 0)
    return isl_space_free(space);
  space = isl_space_add_dims(space, isl_dim_param, n);
  for (i = 0; i < n; ++i) {
    isl_id *id;
 
    id = isl_multi_id_get_at(tuple, i);
    space = isl_space_set_dim_id(space,
            isl_dim_param, first + i, id);
  }
 
  return space;
}
 
/* Internal function that removes the set tuple of "space",
 * which is assumed to correspond to the range space of "tuple", and
 * adds the identifiers in "tuple" as fresh parameters.
 * In other words, the set dimensions of "space" are reinterpreted
 * as parameters, but stay in the same global positions.
 */
__isl_give isl_space *isl_space_bind_set(__isl_take isl_space *space,
  __isl_keep isl_multi_id *tuple)
{
  isl_space *tuple_space;
 
  if (isl_space_check_is_set(space) < 0)
    return isl_space_free(space);
  tuple_space = isl_multi_id_peek_space(tuple);
  if (isl_space_check_equal_tuples(tuple_space, space) < 0)
    return isl_space_free(space);
  if (check_fresh_params(space, tuple) < 0)
    return isl_space_free(space);
  space = isl_space_params(space);
  space = add_bind_params(space, tuple);
  return space;
}
 
/* Internal function that removes the domain tuple of the map space "space",
 * which is assumed to correspond to the range space of "tuple", and
 * adds the identifiers in "tuple" as fresh parameters.
 * In other words, the domain dimensions of "space" are reinterpreted
 * as parameters, but stay in the same global positions.
 */
__isl_give isl_space *isl_space_bind_map_domain(__isl_take isl_space *space,
  __isl_keep isl_multi_id *tuple)
{
  isl_space *tuple_space;
 
  if (isl_space_check_is_map(space) < 0)
    return isl_space_free(space);
  tuple_space = isl_multi_id_peek_space(tuple);
  if (isl_space_check_domain_tuples(tuple_space, space) < 0)
    return isl_space_free(space);
  if (check_fresh_params(space, tuple) < 0)
    return isl_space_free(space);
  space = isl_space_range(space);
  space = add_bind_params(space, tuple);
  return space;
}
 
/* Internal function that, given a space of the form [A -> B] -> C and
 * a tuple of identifiers in A, returns a space B -> C with
 * the identifiers in "tuple" added as fresh parameters.
 * In other words, the domain dimensions of the wrapped relation
 * in the domain of "space" are reinterpreted
 * as parameters, but stay in the same global positions.
 */
__isl_give isl_space *isl_space_bind_domain_wrapped_domain(
  __isl_take isl_space *space, __isl_keep isl_multi_id *tuple)
{
  isl_space *tuple_space;
 
  if (isl_space_check_is_map(space) < 0)
    return isl_space_free(space);
  tuple_space = isl_multi_id_peek_space(tuple);
  if (isl_space_check_domain_wrapped_domain_tuples(tuple_space,
              space) < 0)
      return isl_space_free(space);
  if (check_fresh_params(space, tuple) < 0)
    return isl_space_free(space);
  space = isl_space_domain_factor_range(space);
  space = add_bind_params(space, tuple);
  return space;
}
 
/* Insert a domain tuple in "space" corresponding to the set space "domain".
 * In particular, if "space" is a parameter space, then the result
 * is the set space "domain" combined with the parameters of "space".
 * If "space" is a set space, then the result
 * is a map space with "domain" as domain and the original space as range.
 */
static __isl_give isl_space *isl_space_insert_domain(
  __isl_take isl_space *space, __isl_take isl_space *domain)
{
  isl_bool is_params;
 
  domain = isl_space_replace_params(domain, space);
 
  is_params = isl_space_is_params(space);
  if (is_params < 0) {
    isl_space_free(domain);
    space = isl_space_free(space);
  } else if (is_params) {
    isl_space_free(space);
    space = domain;
  } else {
    space = isl_space_map_from_domain_and_range(domain, space);
  }
  return space;
}
 
/* Internal function that introduces a domain in "space"
 * corresponding to the range space of "tuple".
 * In particular, if "space" is a parameter space, then the result
 * is a set space.  If "space" is a set space, then the result
 * is a map space with the original space as range.
 * Parameters that correspond to the identifiers in "tuple" are removed.
 *
 * The parameters are removed in reverse order (under the assumption
 * that they appear in the same order in "multi") because
 * it is slightly more efficient to remove parameters at the end.
 *
 * For pretty-printing purposes, the identifiers of the set dimensions
 * of the introduced domain are set to the identifiers in "tuple".
 */
__isl_give isl_space *isl_space_unbind_params_insert_domain(
  __isl_take isl_space *space, __isl_keep isl_multi_id *tuple)
{
  int i;
  isl_size n;
  isl_space *tuple_space;
 
  n = isl_multi_id_size(tuple);
  if (!space || n < 0)
    return isl_space_free(space);
  for (i = n - 1; i >= 0; --i) {
    isl_id *id;
    int pos;
 
    id = isl_multi_id_get_id(tuple, i);
    if (!id)
      return isl_space_free(space);
    pos = isl_space_find_dim_by_id(space, isl_dim_param, id);
    isl_id_free(id);
    if (pos < 0)
      continue;
    space = isl_space_drop_dims(space, isl_dim_param, pos, 1);
  }
  tuple_space = isl_multi_id_get_space(tuple);
  for (i = 0; i < n; ++i) {
    isl_id *id;
 
    id = isl_multi_id_get_id(tuple, i);
    tuple_space = isl_space_set_dim_id(tuple_space,
                isl_dim_set, i, id);
  }
  return isl_space_insert_domain(space, tuple_space);
}
 
__isl_give isl_space *isl_space_underlying(__isl_take isl_space *space,
  unsigned n_div)
{
  int i;
  isl_bool is_set;
 
  is_set = isl_space_is_set(space);
  if (is_set < 0)
    return isl_space_free(space);
  if (n_div == 0 && is_set &&
      space->nparam == 0 && space->n_in == 0 && space->n_id == 0)
    return isl_space_reset(space, isl_dim_out);
  space = isl_space_cow(space);
  if (!space)
    return NULL;
  space->n_out += space->nparam + space->n_in + n_div;
  space->nparam = 0;
  space->n_in = 0;
 
  for (i = 0; i < space->n_id; ++i)
    isl_id_free(get_id(space, isl_dim_out, i));
  space->n_id = 0;
  space = isl_space_reset(space, isl_dim_in);
  space = isl_space_reset(space, isl_dim_out);
  space = mark_as_set(space);
 
  return space;
}
 
/* Are the two spaces the same, including positions and names of parameters?
 */
isl_bool isl_space_is_equal(__isl_keep isl_space *space1,
  __isl_keep isl_space *space2)
{
  isl_bool equal;
 
  if (!space1 || !space2)
    return isl_bool_error;
  if (space1 == space2)
    return isl_bool_true;
  equal = isl_space_has_equal_params(space1, space2);
  if (equal < 0 || !equal)
    return equal;
  return isl_space_has_equal_tuples(space1, space2);
}
 
/* Do the tuples of "space1" correspond to those of the domain of "space2"?
 * That is, is "space1" equal to the domain of "space2", ignoring parameters.
 *
 * "space2" is allowed to be a set space, in which case "space1"
 * should be a parameter space.
 */
isl_bool isl_space_has_domain_tuples(__isl_keep isl_space *space1,
  __isl_keep isl_space *space2)
{
  isl_bool is_set;
 
  is_set = isl_space_is_set(space1);
  if (is_set < 0 || !is_set)
    return is_set;
  return isl_space_tuple_is_equal(space1, isl_dim_set,
          space2, isl_dim_in);
}
 
/* Do the tuples of "space1" correspond to those of the range of "space2"?
 * That is, is "space1" equal to the range of "space2", ignoring parameters.
 *
 * "space2" is allowed to be the space of a set,
 * in which case it should be equal to "space1", ignoring parameters.
 */
isl_bool isl_space_has_range_tuples(__isl_keep isl_space *space1,
  __isl_keep isl_space *space2)
{
  isl_bool is_set;
 
  is_set = isl_space_is_set(space1);
  if (is_set < 0 || !is_set)
    return is_set;
  return isl_space_tuple_is_equal(space1, isl_dim_set,
          space2, isl_dim_out);
}
 
/* Check that the tuples of "space1" correspond to those
 * of the domain of "space2".
 * That is, check that "space1" is equal to the domain of "space2",
 * ignoring parameters.
 */
isl_stat isl_space_check_domain_tuples(__isl_keep isl_space *space1,
  __isl_keep isl_space *space2)
{
  isl_bool is_equal;
 
  is_equal = isl_space_has_domain_tuples(space1, space2);
  return check_match(space1, is_equal);
}
 
/* Check that the tuples of "space1" correspond to those
 * of the domain of the wrapped relation in the domain of "space2".
 * That is, check that "space1" is equal to this domain,
 * ignoring parameters.
 */
isl_stat isl_space_check_domain_wrapped_domain_tuples(
  __isl_keep isl_space *space1, __isl_keep isl_space *space2)
{
  isl_space *domain;
  isl_stat r;
 
  domain = isl_space_unwrap(isl_space_domain(isl_space_copy(space2)));
  r = isl_space_check_domain_tuples(space1, domain);
  isl_space_free(domain);
 
  return r;
}
 
/* Is space1 equal to the domain of space2?
 *
 * In the internal version we also allow space2 to be the space of a set,
 * provided space1 is a parameter space.
 */
isl_bool isl_space_is_domain_internal(__isl_keep isl_space *space1,
  __isl_keep isl_space *space2)
{
  isl_bool equal_params;
 
  if (!space1 || !space2)
    return isl_bool_error;
  equal_params = isl_space_has_equal_params(space1, space2);
  if (equal_params < 0 || !equal_params)
    return equal_params;
  return isl_space_has_domain_tuples(space1, space2);
}
 
/* Is space1 equal to the domain of space2?
 */
isl_bool isl_space_is_domain(__isl_keep isl_space *space1,
  __isl_keep isl_space *space2)
{
  if (!space2)
    return isl_bool_error;
  if (!isl_space_is_map(space2))
    return isl_bool_false;
  return isl_space_is_domain_internal(space1, space2);
}
 
/* Is space1 equal to the range of space2?
 *
 * In the internal version, space2 is allowed to be the space of a set,
 * in which case it should be equal to space1.
 */
isl_bool isl_space_is_range_internal(__isl_keep isl_space *space1,
  __isl_keep isl_space *space2)
{
  isl_bool equal_params;
 
  if (!space1 || !space2)
    return isl_bool_error;
  equal_params = isl_space_has_equal_params(space1, space2);
  if (equal_params < 0 || !equal_params)
    return equal_params;
  return isl_space_has_range_tuples(space1, space2);
}
 
/* Is space1 equal to the range of space2?
 */
isl_bool isl_space_is_range(__isl_keep isl_space *space1,
  __isl_keep isl_space *space2)
{
  if (!space2)
    return isl_bool_error;
  if (!isl_space_is_map(space2))
    return isl_bool_false;
  return isl_space_is_range_internal(space1, space2);
}
 
/* Update "hash" by hashing in the parameters of "space".
 */
static uint32_t isl_hash_params(uint32_t hash, __isl_keep isl_space *space)
{
  int i;
  isl_id *id;
 
  if (!space)
    return hash;
 
  isl_hash_byte(hash, space->nparam % 256);
 
  for (i = 0; i < space->nparam; ++i) {
    id = get_id(space, isl_dim_param, i);
    hash = isl_hash_id(hash, id);
  }
 
  return hash;
}
 
/* Update "hash" by hashing in the tuples of "space".
 * Changes in this function should be reflected in isl_hash_tuples_domain.
 */
static uint32_t isl_hash_tuples(uint32_t hash, __isl_keep isl_space *space)
{
  isl_id *id;
 
  if (!space)
    return hash;
 
  isl_hash_byte(hash, space->n_in % 256);
  isl_hash_byte(hash, space->n_out % 256);
 
  id = tuple_id(space, isl_dim_in);
  hash = isl_hash_id(hash, id);
  id = tuple_id(space, isl_dim_out);
  hash = isl_hash_id(hash, id);
 
  hash = isl_hash_tuples(hash, space->nested[0]);
  hash = isl_hash_tuples(hash, space->nested[1]);
 
  return hash;
}
 
/* Update "hash" by hashing in the domain tuple of "space".
 * The result of this function is equal to the result of applying
 * isl_hash_tuples to the domain of "space".
 */
static uint32_t isl_hash_tuples_domain(uint32_t hash,
  __isl_keep isl_space *space)
{
  isl_id *id;
 
  if (!space)
    return hash;
 
  isl_hash_byte(hash, 0);
  isl_hash_byte(hash, space->n_in % 256);
 
  hash = isl_hash_id(hash, &isl_id_none);
  id = tuple_id(space, isl_dim_in);
  hash = isl_hash_id(hash, id);
 
  hash = isl_hash_tuples(hash, space->nested[0]);
 
  return hash;
}
 
/* Return a hash value that digests the tuples of "space",
 * i.e., that ignores the parameters.
 * Changes in this function should be reflected
 * in isl_space_get_tuple_domain_hash.
 */
uint32_t isl_space_get_tuple_hash(__isl_keep isl_space *space)
{
  uint32_t hash;
 
  if (!space)
    return 0;
 
  hash = isl_hash_init();
  hash = isl_hash_tuples(hash, space);
 
  return hash;
}
 
/* Return the hash value of "space".
 */
uint32_t isl_space_get_full_hash(__isl_keep isl_space *space)
{
  uint32_t hash;
 
  if (!space)
    return 0;
 
  hash = isl_hash_init();
  hash = isl_hash_params(hash, space);
  hash = isl_hash_tuples(hash, space);
 
  return hash;
}
 
/* Return the hash value of the domain tuple of "space".
 * That is, isl_space_get_tuple_domain_hash(space) is equal to
 * isl_space_get_tuple_hash(isl_space_domain(space)).
 */
uint32_t isl_space_get_tuple_domain_hash(__isl_keep isl_space *space)
{
  uint32_t hash;
 
  if (!space)
    return 0;
 
  hash = isl_hash_init();
  hash = isl_hash_tuples_domain(hash, space);
 
  return hash;
}
 
/* Is "space" the space of a set wrapping a map space?
 */
isl_bool isl_space_is_wrapping(__isl_keep isl_space *space)
{
  if (!space)
    return isl_bool_error;
 
  if (!isl_space_is_set(space))
    return isl_bool_false;
 
  return isl_bool_ok(space->nested[1] != NULL);
}
 
/* Is "space" the space of a map where the domain is a wrapped map space?
 */
isl_bool isl_space_domain_is_wrapping(__isl_keep isl_space *space)
{
  if (!space)
    return isl_bool_error;
 
  if (isl_space_is_set(space))
    return isl_bool_false;
 
  return isl_bool_ok(space->nested[0] != NULL);
}
 
/* Is "space" the space of a map where the range is a wrapped map space?
 */
isl_bool isl_space_range_is_wrapping(__isl_keep isl_space *space)
{
  if (!space)
    return isl_bool_error;
 
  if (isl_space_is_set(space))
    return isl_bool_false;
 
  return isl_bool_ok(space->nested[1] != NULL);
}
 
/* Is "space" a product of two spaces?
 * That is, is it a wrapping set space or a map space
 * with wrapping domain and range?
 */
isl_bool isl_space_is_product(__isl_keep isl_space *space)
{
  isl_bool is_set;
  isl_bool is_product;
 
  is_set = isl_space_is_set(space);
  if (is_set < 0)
    return isl_bool_error;
  if (is_set)
    return isl_space_is_wrapping(space);
  is_product = isl_space_domain_is_wrapping(space);
  if (is_product < 0 || !is_product)
    return is_product;
  return isl_space_range_is_wrapping(space);
}
 
__isl_give isl_space *isl_space_wrap(__isl_take isl_space *space)
{
  isl_space *wrap;
 
  if (!space)
    return NULL;
 
  wrap = isl_space_set_alloc(space->ctx,
            space->nparam, space->n_in + space->n_out);
 
  wrap = copy_ids(wrap, isl_dim_param, 0, space, isl_dim_param);
  wrap = copy_ids(wrap, isl_dim_set, 0, space, isl_dim_in);
  wrap = copy_ids(wrap, isl_dim_set, space->n_in, space, isl_dim_out);
 
  if (!wrap)
    goto error;
 
  wrap->nested[1] = space;
 
  return wrap;
error:
  isl_space_free(space);
  return NULL;
}
 
__isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space)
{
  isl_space *unwrap;
 
  if (!space)
    return NULL;
 
  if (!isl_space_is_wrapping(space))
    isl_die(space->ctx, isl_error_invalid, "not a wrapping space",
      goto error);
 
  unwrap = isl_space_copy(space->nested[1]);
  isl_space_free(space);
 
  return unwrap;
error:
  isl_space_free(space);
  return NULL;
}
 
isl_bool isl_space_is_named_or_nested(__isl_keep isl_space *space,
  enum isl_dim_type type)
{
  if (type != isl_dim_in && type != isl_dim_out)
    return isl_bool_false;
  if (!space)
    return isl_bool_error;
  if (space->tuple_id[type - isl_dim_in])
    return isl_bool_true;
  if (space->nested[type - isl_dim_in])
    return isl_bool_true;
  return isl_bool_false;
}
 
isl_bool isl_space_may_be_set(__isl_keep isl_space *space)
{
  isl_bool nested;
  isl_size n_in;
 
  if (!space)
    return isl_bool_error;
  if (isl_space_is_set(space))
    return isl_bool_true;
  n_in = isl_space_dim(space, isl_dim_in);
  if (n_in < 0)
    return isl_bool_error;
  if (n_in != 0)
    return isl_bool_false;
  nested = isl_space_is_named_or_nested(space, isl_dim_in);
  if (nested < 0 || nested)
    return isl_bool_not(nested);
  return isl_bool_true;
}
 
__isl_give isl_space *isl_space_reset(__isl_take isl_space *space,
  enum isl_dim_type type)
{
  if (!isl_space_is_named_or_nested(space, type))
    return space;
 
  space = isl_space_cow(space);
  if (!space)
    return NULL;
 
  isl_id_free(space->tuple_id[type - isl_dim_in]);
  space->tuple_id[type - isl_dim_in] = NULL;
  isl_space_free(space->nested[type - isl_dim_in]);
  space->nested[type - isl_dim_in] = NULL;
 
  return space;
}
 
__isl_give isl_space *isl_space_flatten(__isl_take isl_space *space)
{
  if (!space)
    return NULL;
  if (!space->nested[0] && !space->nested[1])
    return space;
 
  if (space->nested[0])
    space = isl_space_reset(space, isl_dim_in);
  if (space && space->nested[1])
    space = isl_space_reset(space, isl_dim_out);
 
  return space;
}
 
__isl_give isl_space *isl_space_flatten_domain(__isl_take isl_space *space)
{
  if (!space)
    return NULL;
  if (!space->nested[0])
    return space;
 
  return isl_space_reset(space, isl_dim_in);
}
 
__isl_give isl_space *isl_space_flatten_range(__isl_take isl_space *space)
{
  if (!space)
    return NULL;
  if (!space->nested[1])
    return space;
 
  return isl_space_reset(space, isl_dim_out);
}
 
/* Replace the parameters of dst by those of src.
 */
__isl_give isl_space *isl_space_replace_params(__isl_take isl_space *dst,
  __isl_keep isl_space *src)
{
  isl_size dst_dim, src_dim;
  isl_bool equal_params;
  enum isl_dim_type type = isl_dim_param;
 
  equal_params = isl_space_has_equal_params(dst, src);
  if (equal_params < 0)
    return isl_space_free(dst);
  if (equal_params)
    return dst;
 
  dst = isl_space_cow(dst);
 
  dst_dim = isl_space_dim(dst, type);
  src_dim = isl_space_dim(src, type);
  if (dst_dim < 0 || src_dim < 0)
    goto error;
 
  dst = isl_space_drop_dims(dst, type, 0, dst_dim);
  dst = isl_space_add_dims(dst, type, src_dim);
  dst = copy_ids(dst, type, 0, src, type);
 
  if (dst) {
    int i;
    for (i = 0; i <= 1; ++i) {
      isl_space *nested;
 
      if (!dst->nested[i])
        continue;
      nested = isl_space_take_nested(dst, i);
      nested = isl_space_replace_params(nested, src);
      dst = isl_space_restore_nested(dst, i, nested);
      if (!dst)
        return NULL;
    }
  }
 
  return dst;
error:
  isl_space_free(dst);
  return NULL;
}
 
/* Given two tuples ("dst_type" in "dst" and "src_type" in "src")
 * of the same size, check if any of the dimensions in the "dst" tuple
 * have no identifier, while the corresponding dimensions in "src"
 * does have an identifier,
 * If so, copy the identifier over to "dst".
 */
__isl_give isl_space *isl_space_copy_ids_if_unset(__isl_take isl_space *dst,
  enum isl_dim_type dst_type, __isl_keep isl_space *src,
  enum isl_dim_type src_type)
{
  int i;
  isl_size n;
 
  n = isl_space_dim(dst, dst_type);
  if (n < 0)
    return isl_space_free(dst);
  for (i = 0; i < n; ++i) {
    isl_bool set;
    isl_id *id;
 
    set = isl_space_has_dim_id(dst, dst_type, i);
    if (set < 0)
      return isl_space_free(dst);
    if (set)
      continue;
 
    set = isl_space_has_dim_id(src, src_type, i);
    if (set < 0)
      return isl_space_free(dst);
    if (!set)
      continue;
 
    id = isl_space_get_dim_id(src, src_type, i);
    dst = isl_space_set_dim_id(dst, dst_type, i, id);
  }
 
  return dst;
}
 
/* Given a space "space" of a set, create a space
 * for the lift of the set.  In particular, the result
 * is of the form lifted[space -> local[..]], with n_local variables in the
 * range of the wrapped map.
 */
__isl_give isl_space *isl_space_lift(__isl_take isl_space *space,
  unsigned n_local)
{
  isl_space *local_space;
 
  if (!space)
    return NULL;
 
  local_space = isl_space_dup(space);
  local_space = isl_space_drop_dims(local_space, isl_dim_set, 0,
          space->n_out);
  local_space = isl_space_add_dims(local_space, isl_dim_set, n_local);
  local_space = isl_space_set_tuple_name(local_space,
            isl_dim_set, "local");
  space = isl_space_join(isl_space_from_domain(space),
          isl_space_from_range(local_space));
  space = isl_space_wrap(space);
  space = isl_space_set_tuple_name(space, isl_dim_set, "lifted");
 
  return space;
}
 
isl_bool isl_space_can_zip(__isl_keep isl_space *space)
{
  isl_bool is_set;
 
  is_set = isl_space_is_set(space);
  if (is_set < 0)
    return isl_bool_error;
  if (is_set)
    return isl_bool_false;
  return isl_space_is_product(space);
}
 
__isl_give isl_space *isl_space_zip(__isl_take isl_space *space)
{
  isl_space *dom, *ran;
  isl_space *dom_dom, *dom_ran, *ran_dom, *ran_ran;
 
  if (!isl_space_can_zip(space))
    isl_die(space->ctx, isl_error_invalid, "space cannot be zipped",
      goto error);
 
  if (!space)
    return NULL;
  dom = isl_space_unwrap(isl_space_domain(isl_space_copy(space)));
  ran = isl_space_unwrap(isl_space_range(space));
  dom_dom = isl_space_domain(isl_space_copy(dom));
  dom_ran = isl_space_range(dom);
  ran_dom = isl_space_domain(isl_space_copy(ran));
  ran_ran = isl_space_range(ran);
  dom = isl_space_join(isl_space_from_domain(dom_dom),
         isl_space_from_range(ran_dom));
  ran = isl_space_join(isl_space_from_domain(dom_ran),
         isl_space_from_range(ran_ran));
  return isl_space_join(isl_space_from_domain(isl_space_wrap(dom)),
          isl_space_from_range(isl_space_wrap(ran)));
error:
  isl_space_free(space);
  return NULL;
}
 
/* Can we apply isl_space_curry to "space"?
 * That is, does is it have a map space with a nested relation in its domain?
 */
isl_bool isl_space_can_curry(__isl_keep isl_space *space)
{
  return isl_space_domain_is_wrapping(space);
}
 
/* Given a space (A -> B) -> C, return the corresponding space
 * A -> (B -> C).
 */
__isl_give isl_space *isl_space_curry(__isl_take isl_space *space)
{
  isl_space *dom, *ran;
  isl_space *dom_dom, *dom_ran;
 
  if (!space)
    return NULL;
 
  if (!isl_space_can_curry(space))
    isl_die(space->ctx, isl_error_invalid,
      "space cannot be curried", goto error);
 
  dom = isl_space_unwrap(isl_space_domain(isl_space_copy(space)));
  ran = isl_space_range(space);
  dom_dom = isl_space_domain(isl_space_copy(dom));
  dom_ran = isl_space_range(dom);
  ran = isl_space_join(isl_space_from_domain(dom_ran),
         isl_space_from_range(ran));
  return isl_space_join(isl_space_from_domain(dom_dom),
          isl_space_from_range(isl_space_wrap(ran)));
error:
  isl_space_free(space);
  return NULL;
}
 
/* Can isl_space_range_curry be applied to "space"?
 * That is, does it have a nested relation in its range,
 * the domain of which is itself a nested relation?
 */
isl_bool isl_space_can_range_curry(__isl_keep isl_space *space)
{
  isl_bool can;
 
  if (!space)
    return isl_bool_error;
  can = isl_space_range_is_wrapping(space);
  if (can < 0 || !can)
    return can;
  return isl_space_can_curry(space->nested[1]);
}
 
/* Given a space A -> ((B -> C) -> D), return the corresponding space
 * A -> (B -> (C -> D)).
 */
__isl_give isl_space *isl_space_range_curry(__isl_take isl_space *space)
{
  isl_space *nested;
 
  if (!space)
    return NULL;
 
  if (!isl_space_can_range_curry(space))
    isl_die(isl_space_get_ctx(space), isl_error_invalid,
      "space range cannot be curried",
      return isl_space_free(space));
 
  nested = isl_space_take_nested(space, 1);
  nested = isl_space_curry(nested);
  space = isl_space_restore_nested(space, 1, nested);
 
  return space;
}
 
/* Can we apply isl_space_uncurry to "space"?
 * That is, does it have a map space with a nested relation in its range?
 */
isl_bool isl_space_can_uncurry(__isl_keep isl_space *space)
{
  return isl_space_range_is_wrapping(space);
}
 
/* Given a space A -> (B -> C), return the corresponding space
 * (A -> B) -> C.
 */
__isl_give isl_space *isl_space_uncurry(__isl_take isl_space *space)
{
  isl_space *dom, *ran;
  isl_space *ran_dom, *ran_ran;
 
  if (!space)
    return NULL;
 
  if (!isl_space_can_uncurry(space))
    isl_die(space->ctx, isl_error_invalid,
      "space cannot be uncurried",
      return isl_space_free(space));
 
  dom = isl_space_domain(isl_space_copy(space));
  ran = isl_space_unwrap(isl_space_range(space));
  ran_dom = isl_space_domain(isl_space_copy(ran));
  ran_ran = isl_space_range(ran);
  dom = isl_space_join(isl_space_from_domain(dom),
         isl_space_from_range(ran_dom));
  return isl_space_join(isl_space_from_domain(isl_space_wrap(dom)),
          isl_space_from_range(ran_ran));
}
 
isl_bool isl_space_has_named_params(__isl_keep isl_space *space)
{
  int i;
  unsigned off;
 
  if (!space)
    return isl_bool_error;
  if (space->nparam == 0)
    return isl_bool_true;
  off = isl_space_offset(space, isl_dim_param);
  if (off + space->nparam > space->n_id)
    return isl_bool_false;
  for (i = 0; i < space->nparam; ++i)
    if (!space->ids[off + i])
      return isl_bool_false;
  return isl_bool_true;
}
 
/* Check that "space" has only named parameters, reporting an error
 * if it does not.
 */
isl_stat isl_space_check_named_params(__isl_keep isl_space *space)
{
  isl_bool named;
 
  named = isl_space_has_named_params(space);
  if (named < 0)
    return isl_stat_error;
  if (!named)
    isl_die(isl_space_get_ctx(space), isl_error_invalid,
      "unexpected unnamed parameters", return isl_stat_error);
 
  return isl_stat_ok;
}
 
/* Align the initial parameters of space1 to match the order in space2.
 */
__isl_give isl_space *isl_space_align_params(__isl_take isl_space *space1,
  __isl_take isl_space *space2)
{
  isl_reordering *exp;
 
  if (isl_space_check_named_params(space1) < 0 ||
      isl_space_check_named_params(space2) < 0)
    goto error;
 
  exp = isl_parameter_alignment_reordering(space1, space2);
  isl_space_free(space1);
  isl_space_free(space2);
  space1 = isl_reordering_get_space(exp);
  isl_reordering_free(exp);
  return space1;
error:
  isl_space_free(space1);
  isl_space_free(space2);
  return NULL;
}
 
/* Given the space of set (domain), construct a space for a map
 * with as domain the given space and as range the range of "model".
 */
__isl_give isl_space *isl_space_extend_domain_with_range(
  __isl_take isl_space *space, __isl_take isl_space *model)
{
  isl_size n_out;
 
  if (!model)
    goto error;
 
  space = isl_space_from_domain(space);
  n_out = isl_space_dim(model, isl_dim_out);
  if (n_out < 0)
    goto error;
  space = isl_space_add_dims(space, isl_dim_out, n_out);
  if (isl_space_has_tuple_id(model, isl_dim_out))
    space = isl_space_set_tuple_id(space, isl_dim_out,
        isl_space_get_tuple_id(model, isl_dim_out));
  if (!space)
    goto error;
  if (model->nested[1]) {
    isl_space *nested = isl_space_copy(model->nested[1]);
    isl_size n_nested, n_space;
    nested = isl_space_align_params(nested, isl_space_copy(space));
    n_nested = isl_space_dim(nested, isl_dim_param);
    n_space = isl_space_dim(space, isl_dim_param);
    if (n_nested < 0 || n_space < 0)
      goto error;
    if (n_nested > n_space)
      nested = isl_space_drop_dims(nested, isl_dim_param,
            n_space, n_nested - n_space);
    if (!nested)
      goto error;
    space->nested[1] = nested;
  }
  isl_space_free(model);
  return space;
error:
  isl_space_free(model);
  isl_space_free(space);
  return NULL;
}
 
/* Compare the "type" dimensions of two isl_spaces.
 *
 * The order is fairly arbitrary.
 */
static int isl_space_cmp_type(__isl_keep isl_space *space1,
  __isl_keep isl_space *space2, enum isl_dim_type type)
{
  int cmp;
  isl_size dim1, dim2;
  isl_space *nested1, *nested2;
 
  dim1 = isl_space_dim(space1, type);
  dim2 = isl_space_dim(space2, type);
  if (dim1 < 0 || dim2 < 0)
    return 0;
  if (dim1 != dim2)
    return dim1 - dim2;
 
  cmp = isl_id_cmp(tuple_id(space1, type), tuple_id(space2, type));
  if (cmp != 0)
    return cmp;
 
  nested1 = nested(space1, type);
  nested2 = nested(space2, type);
  if (!nested1 != !nested2)
    return !nested1 - !nested2;
 
  if (nested1)
    return isl_space_cmp(nested1, nested2);
 
  return 0;
}
 
/* Compare two isl_spaces.
 *
 * The order is fairly arbitrary.
 */
int isl_space_cmp(__isl_keep isl_space *space1, __isl_keep isl_space *space2)
{
  int i;
  int cmp;
 
  if (space1 == space2)
    return 0;
  if (!space1)
    return -1;
  if (!space2)
    return 1;
 
  cmp = isl_space_cmp_type(space1, space2, isl_dim_param);
  if (cmp != 0)
    return cmp;
  cmp = isl_space_cmp_type(space1, space2, isl_dim_in);
  if (cmp != 0)
    return cmp;
  cmp = isl_space_cmp_type(space1, space2, isl_dim_out);
  if (cmp != 0)
    return cmp;
 
  if (!space1->ids && !space2->ids)
    return 0;
 
  for (i = 0; i < n(space1, isl_dim_param); ++i) {
    cmp = isl_id_cmp(get_id(space1, isl_dim_param, i),
         get_id(space2, isl_dim_param, i));
    if (cmp != 0)
      return cmp;
  }
 
  return 0;
}