isl_map_subtract.c

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/*
 * Copyright 2008-2009 Katholieke Universiteit Leuven
 *
 * 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
 */
 
#include <isl_map_private.h>
#include <isl_seq.h>
#include <isl/set.h>
#include <isl/map.h>
#include "isl_tab.h"
#include <isl_point_private.h>
#include <isl_vec_private.h>
 
#include <set_to_map.c>
#include <set_from_map.c>
 
/* Expand the constraint "c" into "v".  The initial "dim" dimensions
 * are the same, but "v" may have more divs than "c" and the divs of "c"
 * may appear in different positions in "v".
 * The number of divs in "c" is given by "n_div" and the mapping
 * of divs in "c" to divs in "v" is given by "div_map".
 *
 * Although it shouldn't happen in practice, it is theoretically
 * possible that two or more divs in "c" are mapped to the same div in "v".
 * These divs are then necessarily the same, so we simply add their
 * coefficients.
 */
static void expand_constraint(isl_vec *v, unsigned dim,
  isl_int *c, int *div_map, unsigned n_div)
{
  int i;
 
  isl_seq_cpy(v->el, c, 1 + dim);
  isl_seq_clr(v->el + 1 + dim, v->size - (1 + dim));
 
  for (i = 0; i < n_div; ++i) {
    int pos = 1 + dim + div_map[i];
    isl_int_add(v->el[pos], v->el[pos], c[1 + dim + i]);
  }
}
 
/* Add all constraints of bmap to tab.  The equalities of bmap
 * are added as a pair of inequalities.
 */
static isl_stat tab_add_constraints(struct isl_tab *tab,
  __isl_keep isl_basic_map *bmap, int *div_map)
{
  int i;
  unsigned dim;
  isl_size tab_total;
  isl_size bmap_n_div;
  isl_size bmap_total;
  isl_vec *v;
 
  if (!tab || !bmap)
    return isl_stat_error;
 
  tab_total = isl_basic_map_dim(tab->bmap, isl_dim_all);
  bmap_total = isl_basic_map_dim(bmap, isl_dim_all);
  bmap_n_div = isl_basic_map_dim(bmap, isl_dim_div);
  dim = bmap_total - bmap_n_div;
  if (tab_total < 0 || bmap_total < 0 || bmap_n_div < 0)
    return isl_stat_error;
 
  if (isl_tab_extend_cons(tab, 2 * bmap->n_eq + bmap->n_ineq) < 0)
    return isl_stat_error;
 
  v = isl_vec_alloc(bmap->ctx, 1 + tab_total);
  if (!v)
    return isl_stat_error;
 
  for (i = 0; i < bmap->n_eq; ++i) {
    expand_constraint(v, dim, bmap->eq[i], div_map, bmap_n_div);
    if (isl_tab_add_ineq(tab, v->el) < 0)
      goto error;
    isl_seq_neg(bmap->eq[i], bmap->eq[i], 1 + bmap_total);
    expand_constraint(v, dim, bmap->eq[i], div_map, bmap_n_div);
    if (isl_tab_add_ineq(tab, v->el) < 0)
      goto error;
    isl_seq_neg(bmap->eq[i], bmap->eq[i], 1 + bmap_total);
    if (tab->empty)
      break;
  }
 
  for (i = 0; i < bmap->n_ineq; ++i) {
    expand_constraint(v, dim, bmap->ineq[i], div_map, bmap_n_div);
    if (isl_tab_add_ineq(tab, v->el) < 0)
      goto error;
    if (tab->empty)
      break;
  }
 
  isl_vec_free(v);
  return isl_stat_ok;
error:
  isl_vec_free(v);
  return isl_stat_error;
}
 
/* Add a specific constraint of bmap (or its opposite) to tab.
 * The position of the constraint is specified by "c", where
 * the equalities of bmap are counted twice, once for the inequality
 * that is equal to the equality, and once for its negation.
 *
 * Each of these constraints has been added to "tab" before by
 * tab_add_constraints (and later removed again), so there should
 * already be a row available for the constraint.
 */
static isl_stat tab_add_constraint(struct isl_tab *tab,
  __isl_keep isl_basic_map *bmap, int *div_map, int c, int oppose)
{
  unsigned dim;
  isl_size tab_total;
  isl_size bmap_n_div;
  isl_size bmap_total;
  isl_vec *v;
  isl_stat r;
 
  if (!tab || !bmap)
    return isl_stat_error;
 
  tab_total = isl_basic_map_dim(tab->bmap, isl_dim_all);
  bmap_total = isl_basic_map_dim(bmap, isl_dim_all);
  bmap_n_div = isl_basic_map_dim(bmap, isl_dim_div);
  dim = bmap_total - bmap_n_div;
  if (tab_total < 0 || bmap_total < 0 || bmap_n_div < 0)
    return isl_stat_error;
 
  v = isl_vec_alloc(bmap->ctx, 1 + tab_total);
  if (!v)
    return isl_stat_error;
 
  if (c < 2 * bmap->n_eq) {
    if ((c % 2) != oppose)
      isl_seq_neg(bmap->eq[c/2], bmap->eq[c/2],
          1 + bmap_total);
    if (oppose)
      isl_int_sub_ui(bmap->eq[c/2][0], bmap->eq[c/2][0], 1);
    expand_constraint(v, dim, bmap->eq[c/2], div_map, bmap_n_div);
    r = isl_tab_add_ineq(tab, v->el);
    if (oppose)
      isl_int_add_ui(bmap->eq[c/2][0], bmap->eq[c/2][0], 1);
    if ((c % 2) != oppose)
      isl_seq_neg(bmap->eq[c/2], bmap->eq[c/2],
          1 + bmap_total);
  } else {
    c -= 2 * bmap->n_eq;
    if (oppose) {
      isl_seq_neg(bmap->ineq[c], bmap->ineq[c],
          1 + bmap_total);
      isl_int_sub_ui(bmap->ineq[c][0], bmap->ineq[c][0], 1);
    }
    expand_constraint(v, dim, bmap->ineq[c], div_map, bmap_n_div);
    r = isl_tab_add_ineq(tab, v->el);
    if (oppose) {
      isl_int_add_ui(bmap->ineq[c][0], bmap->ineq[c][0], 1);
      isl_seq_neg(bmap->ineq[c], bmap->ineq[c],
          1 + bmap_total);
    }
  }
 
  isl_vec_free(v);
  return r;
}
 
static isl_stat tab_add_divs(struct isl_tab *tab,
  __isl_keep isl_basic_map *bmap, int **div_map)
{
  int i, j;
  struct isl_vec *vec;
  isl_size total;
  unsigned dim;
 
  if (!bmap)
    return isl_stat_error;
  if (!bmap->n_div)
    return isl_stat_ok;
 
  if (!*div_map)
    *div_map = isl_alloc_array(bmap->ctx, int, bmap->n_div);
  if (!*div_map)
    return isl_stat_error;
 
  total = isl_basic_map_dim(tab->bmap, isl_dim_all);
  if (total < 0)
    return isl_stat_error;
  dim = total - tab->bmap->n_div;
  vec = isl_vec_alloc(bmap->ctx, 2 + total + bmap->n_div);
  if (!vec)
    return isl_stat_error;
 
  for (i = 0; i < bmap->n_div; ++i) {
    isl_seq_cpy(vec->el, bmap->div[i], 2 + dim);
    isl_seq_clr(vec->el + 2 + dim, tab->bmap->n_div);
    for (j = 0; j < i; ++j)
      isl_int_add(vec->el[2 + dim + (*div_map)[j]],
            vec->el[2 + dim + (*div_map)[j]],
          bmap->div[i][2 + dim + j]);
    for (j = 0; j < tab->bmap->n_div; ++j)
      if (isl_seq_eq(tab->bmap->div[j],
          vec->el, 2 + dim + tab->bmap->n_div))
        break;
    (*div_map)[i] = j;
    if (j == tab->bmap->n_div) {
      vec->size = 2 + dim + tab->bmap->n_div;
      if (isl_tab_add_div(tab, vec) < 0)
        goto error;
    }
  }
 
  isl_vec_free(vec);
 
  return isl_stat_ok;
error:
  isl_vec_free(vec);
 
  return isl_stat_error;
}
 
/* Freeze all constraints of tableau tab.
 */
static int tab_freeze_constraints(struct isl_tab *tab)
{
  int i;
 
  for (i = 0; i < tab->n_con; ++i)
    if (isl_tab_freeze_constraint(tab, i) < 0)
      return -1;
 
  return 0;
}
 
/* Check for redundant constraints starting at offset.
 * Put the indices of the non-redundant constraints in index
 * and return the number of non-redundant constraints.
 */
static int n_non_redundant(isl_ctx *ctx, struct isl_tab *tab,
  int offset, int **index)
{
  int i, n;
  int n_test = tab->n_con - offset;
 
  if (isl_tab_detect_redundant(tab) < 0)
    return -1;
 
  if (n_test == 0)
    return 0;
  if (!*index)
    *index = isl_alloc_array(ctx, int, n_test);
  if (!*index)
    return -1;
 
  for (n = 0, i = 0; i < n_test; ++i) {
    int r;
    r = isl_tab_is_redundant(tab, offset + i);
    if (r < 0)
      return -1;
    if (r)
      continue;
    (*index)[n++] = i;
  }
 
  return n;
}
 
/* basic_map_collect_diff calls add on each of the pieces of
 * the set difference between bmap and map until the add method
 * return a negative value.
 */
struct isl_diff_collector {
  isl_stat (*add)(struct isl_diff_collector *dc,
        __isl_take isl_basic_map *bmap);
};
 
/* Compute the set difference between bmap and map and call
 * dc->add on each of the piece until this function returns
 * a negative value.
 * Return 0 on success and -1 on error.  dc->add returning
 * a negative value is treated as an error, but the calling
 * function can interpret the results based on the state of dc.
 *
 * Assumes that map has known divs.
 *
 * The difference is computed by a backtracking algorithm.
 * Each level corresponds to a basic map in "map".
 * When a node in entered for the first time, we check
 * if the corresonding basic map intersects the current piece
 * of "bmap".  If not, we move to the next level.
 * Otherwise, we split the current piece into as many
 * pieces as there are non-redundant constraints of the current
 * basic map in the intersection.  Each of these pieces is
 * handled by a child of the current node.
 * In particular, if there are n non-redundant constraints,
 * then for each 0 <= i < n, a piece is cut off by adding
 * constraints 0 <= j < i and adding the opposite of constraint i.
 * If there are no non-redundant constraints, meaning that the current
 * piece is a subset of the current basic map, then we simply backtrack.
 *
 * In the leaves, we check if the remaining piece has any integer points
 * and if so, pass it along to dc->add.  As a special case, if nothing
 * has been removed when we end up in a leaf, we simply pass along
 * the original basic map.
 */
static isl_stat basic_map_collect_diff(__isl_take isl_basic_map *bmap,
  __isl_take isl_map *map, struct isl_diff_collector *dc)
{
  int i;
  int modified;
  int level;
  int init;
  isl_bool empty;
  isl_ctx *ctx;
  struct isl_tab *tab = NULL;
  struct isl_tab_undo **snap = NULL;
  int *k = NULL;
  int *n = NULL;
  int **index = NULL;
  int **div_map = NULL;
 
  empty = isl_basic_map_is_empty(bmap);
  if (empty) {
    isl_basic_map_free(bmap);
    isl_map_free(map);
    return empty < 0 ? isl_stat_error : isl_stat_ok;
  }
 
  bmap = isl_basic_map_cow(bmap);
  map = isl_map_cow(map);
 
  if (!bmap || !map)
    goto error;
 
  ctx = map->ctx;
  snap = isl_alloc_array(map->ctx, struct isl_tab_undo *, map->n);
  k = isl_alloc_array(map->ctx, int, map->n);
  n = isl_alloc_array(map->ctx, int, map->n);
  index = isl_calloc_array(map->ctx, int *, map->n);
  div_map = isl_calloc_array(map->ctx, int *, map->n);
  if (!snap || !k || !n || !index || !div_map)
    goto error;
 
  bmap = isl_basic_map_order_divs(bmap);
  map = isl_map_order_divs(map);
 
  tab = isl_tab_from_basic_map(bmap, 1);
  if (!tab)
    goto error;
 
  modified = 0;
  level = 0;
  init = 1;
 
  while (level >= 0) {
    if (level >= map->n) {
      int empty;
      struct isl_basic_map *bm;
      if (!modified) {
        if (dc->add(dc, isl_basic_map_copy(bmap)) < 0)
          goto error;
        break;
      }
      bm = isl_basic_map_copy(tab->bmap);
      bm = isl_basic_map_cow(bm);
      bm = isl_basic_map_update_from_tab(bm, tab);
      bm = isl_basic_map_simplify(bm);
      bm = isl_basic_map_finalize(bm);
      empty = isl_basic_map_is_empty(bm);
      if (empty)
        isl_basic_map_free(bm);
      else if (dc->add(dc, bm) < 0)
        goto error;
      if (empty < 0)
        goto error;
      level--;
      init = 0;
      continue;
    }
    if (init) {
      int offset;
      struct isl_tab_undo *snap2;
      snap2 = isl_tab_snap(tab);
      if (tab_add_divs(tab, map->p[level],
           &div_map[level]) < 0)
        goto error;
      offset = tab->n_con;
      snap[level] = isl_tab_snap(tab);
      if (tab_freeze_constraints(tab) < 0)
        goto error;
      if (tab_add_constraints(tab, map->p[level],
            div_map[level]) < 0)
        goto error;
      k[level] = 0;
      n[level] = 0;
      if (tab->empty) {
        if (isl_tab_rollback(tab, snap2) < 0)
          goto error;
        level++;
        continue;
      }
      modified = 1;
      n[level] = n_non_redundant(ctx, tab, offset,
                &index[level]);
      if (n[level] < 0)
        goto error;
      if (n[level] == 0) {
        level--;
        init = 0;
        continue;
      }
      if (isl_tab_rollback(tab, snap[level]) < 0)
        goto error;
      if (tab_add_constraint(tab, map->p[level],
          div_map[level], index[level][0], 1) < 0)
        goto error;
      level++;
      continue;
    } else {
      if (k[level] + 1 >= n[level]) {
        level--;
        continue;
      }
      if (isl_tab_rollback(tab, snap[level]) < 0)
        goto error;
      if (tab_add_constraint(tab, map->p[level],
            div_map[level],
            index[level][k[level]], 0) < 0)
        goto error;
      snap[level] = isl_tab_snap(tab);
      k[level]++;
      if (tab_add_constraint(tab, map->p[level],
            div_map[level],
            index[level][k[level]], 1) < 0)
        goto error;
      level++;
      init = 1;
      continue;
    }
  }
 
  isl_tab_free(tab);
  free(snap);
  free(n);
  free(k);
  for (i = 0; index && i < map->n; ++i)
    free(index[i]);
  free(index);
  for (i = 0; div_map && i < map->n; ++i)
    free(div_map[i]);
  free(div_map);
 
  isl_basic_map_free(bmap);
  isl_map_free(map);
 
  return isl_stat_ok;
error:
  isl_tab_free(tab);
  free(snap);
  free(n);
  free(k);
  for (i = 0; index && i < map->n; ++i)
    free(index[i]);
  free(index);
  for (i = 0; div_map && i < map->n; ++i)
    free(div_map[i]);
  free(div_map);
  isl_basic_map_free(bmap);
  isl_map_free(map);
  return isl_stat_error;
}
 
/* A diff collector that actually collects all parts of the
 * set difference in the field diff.
 */
struct isl_subtract_diff_collector {
  struct isl_diff_collector dc;
  struct isl_map *diff;
};
 
/* isl_subtract_diff_collector callback.
 */
static isl_stat basic_map_subtract_add(struct isl_diff_collector *dc,
          __isl_take isl_basic_map *bmap)
{
  struct isl_subtract_diff_collector *sdc;
  sdc = (struct isl_subtract_diff_collector *)dc;
 
  sdc->diff = isl_map_union_disjoint(sdc->diff,
      isl_map_from_basic_map(bmap));
 
  return sdc->diff ? isl_stat_ok : isl_stat_error;
}
 
/* Return the set difference between bmap and map.
 */
static __isl_give isl_map *basic_map_subtract(__isl_take isl_basic_map *bmap,
  __isl_take isl_map *map)
{
  struct isl_subtract_diff_collector sdc;
  sdc.dc.add = &basic_map_subtract_add;
  sdc.diff = isl_map_empty(isl_basic_map_get_space(bmap));
  if (basic_map_collect_diff(bmap, map, &sdc.dc) < 0) {
    isl_map_free(sdc.diff);
    sdc.diff = NULL;
  }
  return sdc.diff;
}
 
/* Return an empty map living in the same space as "map1" and "map2".
 */
static __isl_give isl_map *replace_pair_by_empty( __isl_take isl_map *map1,
  __isl_take isl_map *map2)
{
  isl_space *space;
 
  space = isl_map_get_space(map1);
  isl_map_free(map1);
  isl_map_free(map2);
  return isl_map_empty(space);
}
 
/* Return the set difference between map1 and map2.
 * (U_i A_i) \ (U_j B_j) is computed as U_i (A_i \ (U_j B_j))
 *
 * If "map1" and "map2" are obviously equal to each other,
 * then return an empty map in the same space.
 *
 * If "map1" and "map2" are disjoint, then simply return "map1".
 */
__isl_give isl_map *isl_map_subtract( __isl_take isl_map *map1,
  __isl_take isl_map *map2)
{
  int i;
  int equal, disjoint;
  struct isl_map *diff;
 
  if (isl_map_align_params_bin(&map1, &map2) < 0)
    goto error;
  if (isl_map_check_equal_space(map1, map2) < 0)
    goto error;
 
  equal = isl_map_plain_is_equal(map1, map2);
  if (equal < 0)
    goto error;
  if (equal)
    return replace_pair_by_empty(map1, map2);
 
  disjoint = isl_map_is_disjoint(map1, map2);
  if (disjoint < 0)
    goto error;
  if (disjoint) {
    isl_map_free(map2);
    return map1;
  }
 
  map1 = isl_map_compute_divs(map1);
  map2 = isl_map_compute_divs(map2);
  if (!map1 || !map2)
    goto error;
 
  map1 = isl_map_remove_empty_parts(map1);
  map2 = isl_map_remove_empty_parts(map2);
 
  diff = isl_map_empty(isl_map_get_space(map1));
  for (i = 0; i < map1->n; ++i) {
    struct isl_map *d;
    d = basic_map_subtract(isl_basic_map_copy(map1->p[i]),
               isl_map_copy(map2));
    if (ISL_F_ISSET(map1, ISL_MAP_DISJOINT))
      diff = isl_map_union_disjoint(diff, d);
    else
      diff = isl_map_union(diff, d);
  }
 
  isl_map_free(map1);
  isl_map_free(map2);
 
  return diff;
error:
  isl_map_free(map1);
  isl_map_free(map2);
  return NULL;
}
 
__isl_give isl_set *isl_set_subtract(__isl_take isl_set *set1,
  __isl_take isl_set *set2)
{
  return set_from_map(isl_map_subtract(set_to_map(set1),
              set_to_map(set2)));
}
 
/* Remove the elements of "dom" from the domain of "map".
 */
__isl_give isl_map *isl_map_subtract_domain(__isl_take isl_map *map,
  __isl_take isl_set *dom)
{
  isl_bool ok;
  isl_map *ext_dom;
 
  isl_map_align_params_set(&map, &dom);
  ok = isl_map_compatible_domain(map, dom);
  if (ok < 0)
    goto error;
  if (!ok)
    isl_die(isl_set_get_ctx(dom), isl_error_invalid,
      "incompatible spaces", goto error);
  
  ext_dom = isl_map_universe(isl_map_get_space(map));
  ext_dom = isl_map_intersect_domain(ext_dom, dom);
  return isl_map_subtract(map, ext_dom);
error:
  isl_map_free(map);
  isl_set_free(dom);
  return NULL;
}
 
/* Remove the elements of "dom" from the range of "map".
 */
__isl_give isl_map *isl_map_subtract_range(__isl_take isl_map *map,
  __isl_take isl_set *dom)
{
  isl_bool ok;
  isl_map *ext_dom;
 
  isl_map_align_params_set(&map, &dom);
  ok = isl_map_compatible_range(map, dom);
  if (ok < 0)
    goto error;
  if (!ok)
    isl_die(isl_set_get_ctx(dom), isl_error_invalid,
      "incompatible spaces", goto error);
  
  ext_dom = isl_map_universe(isl_map_get_space(map));
  ext_dom = isl_map_intersect_range(ext_dom, dom);
  return isl_map_subtract(map, ext_dom);
error:
  isl_map_free(map);
  isl_set_free(dom);
  return NULL;
}
 
/* A diff collector that aborts as soon as its add function is called,
 * setting empty to isl_false.
 */
struct isl_is_empty_diff_collector {
  struct isl_diff_collector dc;
  isl_bool empty;
};
 
/* isl_is_empty_diff_collector callback.
 */
static isl_stat basic_map_is_empty_add(struct isl_diff_collector *dc,
          __isl_take isl_basic_map *bmap)
{
  struct isl_is_empty_diff_collector *edc;
  edc = (struct isl_is_empty_diff_collector *)dc;
 
  edc->empty = isl_bool_false;
 
  isl_basic_map_free(bmap);
  return isl_stat_error;
}
 
/* Check if bmap \ map is empty by computing this set difference
 * and breaking off as soon as the difference is known to be non-empty.
 */
static isl_bool basic_map_diff_is_empty(__isl_keep isl_basic_map *bmap,
  __isl_keep isl_map *map)
{
  isl_bool empty;
  isl_stat r;
  struct isl_is_empty_diff_collector edc;
 
  empty = isl_basic_map_plain_is_empty(bmap);
  if (empty)
    return empty;
 
  edc.dc.add = &basic_map_is_empty_add;
  edc.empty = isl_bool_true;
  r = basic_map_collect_diff(isl_basic_map_copy(bmap),
           isl_map_copy(map), &edc.dc);
  if (!edc.empty)
    return isl_bool_false;
 
  return r < 0 ? isl_bool_error : isl_bool_true;
}
 
/* Check if map1 \ map2 is empty by checking if the set difference is empty
 * for each of the basic maps in map1.
 */
static isl_bool map_diff_is_empty(__isl_keep isl_map *map1,
  __isl_keep isl_map *map2)
{
  int i;
  isl_bool is_empty = isl_bool_true;
 
  if (!map1 || !map2)
    return isl_bool_error;
  
  for (i = 0; i < map1->n; ++i) {
    is_empty = basic_map_diff_is_empty(map1->p[i], map2);
    if (is_empty < 0 || !is_empty)
       break;
  }
 
  return is_empty;
}
 
/* Return true if "bmap" contains a single element.
 */
isl_bool isl_basic_map_plain_is_singleton(__isl_keep isl_basic_map *bmap)
{
  isl_size total;
 
  if (!bmap)
    return isl_bool_error;
  if (bmap->n_div)
    return isl_bool_false;
  if (bmap->n_ineq)
    return isl_bool_false;
  total = isl_basic_map_dim(bmap, isl_dim_all);
  if (total < 0)
    return isl_bool_error;
  return bmap->n_eq == total;
}
 
/* Return true if "map" contains a single element.
 */
isl_bool isl_map_plain_is_singleton(__isl_keep isl_map *map)
{
  if (!map)
    return isl_bool_error;
  if (map->n != 1)
    return isl_bool_false;
 
  return isl_basic_map_plain_is_singleton(map->p[0]);
}
 
/* Given a singleton basic map, extract the single element
 * as an isl_point.
 */
static __isl_give isl_point *singleton_extract_point(
  __isl_keep isl_basic_map *bmap)
{
  int j;
  isl_size dim;
  struct isl_vec *point;
  isl_int m;
 
  dim = isl_basic_map_dim(bmap, isl_dim_all);
  if (dim < 0)
    return NULL;
 
  isl_assert(bmap->ctx, bmap->n_eq == dim, return NULL);
  point = isl_vec_alloc(bmap->ctx, 1 + dim);
  if (!point)
    return NULL;
 
  isl_int_init(m);
 
  isl_int_set_si(point->el[0], 1);
  for (j = 0; j < bmap->n_eq; ++j) {
    int i = dim - 1 - j;
    isl_assert(bmap->ctx,
        isl_seq_first_non_zero(bmap->eq[j] + 1, i) == -1,
        goto error);
    isl_assert(bmap->ctx,
        isl_int_is_one(bmap->eq[j][1 + i]) ||
        isl_int_is_negone(bmap->eq[j][1 + i]),
        goto error);
    isl_assert(bmap->ctx,
        isl_seq_first_non_zero(bmap->eq[j]+1+i+1, dim-i-1) == -1,
        goto error);
 
    isl_int_gcd(m, point->el[0], bmap->eq[j][1 + i]);
    isl_int_divexact(m, bmap->eq[j][1 + i], m);
    isl_int_abs(m, m);
    isl_seq_scale(point->el, point->el, m, 1 + i);
    isl_int_divexact(m, point->el[0], bmap->eq[j][1 + i]);
    isl_int_neg(m, m);
    isl_int_mul(point->el[1 + i], m, bmap->eq[j][0]);
  }
 
  isl_int_clear(m);
  return isl_point_alloc(isl_basic_map_get_space(bmap), point);
error:
  isl_int_clear(m);
  isl_vec_free(point);
  return NULL;
}
 
/* Return isl_bool_true if the singleton map "map1" is a subset of "map2",
 * i.e., if the single element of "map1" is also an element of "map2".
 * Assumes "map2" has known divs.
 */
static isl_bool map_is_singleton_subset(__isl_keep isl_map *map1,
  __isl_keep isl_map *map2)
{
  int i;
  isl_bool is_subset = isl_bool_false;
  struct isl_point *point;
 
  if (!map1 || !map2)
    return isl_bool_error;
  if (map1->n != 1)
    isl_die(isl_map_get_ctx(map1), isl_error_invalid,
      "expecting single-disjunct input",
      return isl_bool_error);
 
  point = singleton_extract_point(map1->p[0]);
  if (!point)
    return isl_bool_error;
 
  for (i = 0; i < map2->n; ++i) {
    is_subset = isl_basic_map_contains_point(map2->p[i], point);
    if (is_subset)
      break;
  }
 
  isl_point_free(point);
  return is_subset;
}
 
static isl_bool map_is_subset(__isl_keep isl_map *map1,
  __isl_keep isl_map *map2)
{
  isl_bool is_subset = isl_bool_false;
  isl_bool empty, single;
  isl_bool rat1, rat2;
 
  if (!map1 || !map2)
    return isl_bool_error;
 
  if (!isl_map_has_equal_space(map1, map2))
    return isl_bool_false;
 
  empty = isl_map_is_empty(map1);
  if (empty < 0)
    return isl_bool_error;
  if (empty)
    return isl_bool_true;
 
  empty = isl_map_is_empty(map2);
  if (empty < 0)
    return isl_bool_error;
  if (empty)
    return isl_bool_false;
 
  rat1 = isl_map_has_rational(map1);
  rat2 = isl_map_has_rational(map2);
  if (rat1 < 0 || rat2 < 0)
    return isl_bool_error;
  if (rat1 && !rat2)
    return isl_bool_false;
 
  if (isl_map_plain_is_universe(map2))
    return isl_bool_true;
 
  single = isl_map_plain_is_singleton(map1);
  if (single < 0)
    return isl_bool_error;
  map2 = isl_map_compute_divs(isl_map_copy(map2));
  if (single) {
    is_subset = map_is_singleton_subset(map1, map2);
    isl_map_free(map2);
    return is_subset;
  }
  is_subset = map_diff_is_empty(map1, map2);
  isl_map_free(map2);
 
  return is_subset;
}
 
isl_bool isl_map_is_subset(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
{
  return isl_map_align_params_map_map_and_test(map1, map2,
              &map_is_subset);
}
 
isl_bool isl_set_is_subset(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
{
  return isl_map_is_subset(set_to_map(set1), set_to_map(set2));
}
 
__isl_give isl_map *isl_map_make_disjoint(__isl_take isl_map *map)
{
  int i;
  struct isl_subtract_diff_collector sdc;
  sdc.dc.add = &basic_map_subtract_add;
 
  if (!map)
    return NULL;
  if (ISL_F_ISSET(map, ISL_MAP_DISJOINT))
    return map;
  if (map->n <= 1)
    return map;
 
  map = isl_map_compute_divs(map);
  map = isl_map_remove_empty_parts(map);
 
  if (!map || map->n <= 1)
    return map;
 
  sdc.diff = isl_map_from_basic_map(isl_basic_map_copy(map->p[0]));
 
  for (i = 1; i < map->n; ++i) {
    struct isl_basic_map *bmap = isl_basic_map_copy(map->p[i]);
    struct isl_map *copy = isl_map_copy(sdc.diff);
    if (basic_map_collect_diff(bmap, copy, &sdc.dc) < 0) {
      isl_map_free(sdc.diff);
      sdc.diff = NULL;
      break;
    }
  }
 
  isl_map_free(map);
 
  return sdc.diff;
}
 
__isl_give isl_set *isl_set_make_disjoint(__isl_take isl_set *set)
{
  return set_from_map(isl_map_make_disjoint(set_to_map(set)));
}
 
__isl_give isl_map *isl_map_complement(__isl_take isl_map *map)
{
  isl_map *universe;
 
  if (!map)
    return NULL;
 
  universe = isl_map_universe(isl_map_get_space(map));
 
  return isl_map_subtract(universe, map);
}
 
__isl_give isl_set *isl_set_complement(__isl_take isl_set *set)
{
  return isl_map_complement(set);
}