/*

 * 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; 
++i54.1k
) {

    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;

  unsigned tab_total;

  unsigned bmap_total;

  isl_vec *v;

  if (!tab || !bmap)

    return isl_stat_error;

  tab_total = isl_basic_map_total_dim(tab->bmap);

  bmap_total = isl_basic_map_total_dim(bmap);

  dim = isl_space_dim(tab->bmap->dim, isl_dim_all);

  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; 76.6k
i < bmap->n_eq; 
++i34.8k
) {

    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; 76.6k
i < bmap->n_ineq; 
++i181k
) {

    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;

  unsigned tab_total;

  unsigned bmap_total;

  isl_vec *v;

  isl_stat r;

  if (!tab || !bmap)

    return isl_stat_error;

  tab_total = isl_basic_map_total_dim(tab->bmap);

  bmap_total = isl_basic_map_total_dim(bmap);

  dim = isl_space_dim(tab->bmap->dim, isl_dim_all);

  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_ui15.9k
(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_ui15.9k
(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;

  unsigned 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_total_dim(tab->bmap);

  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; 5.86k
i < bmap->n_div; 
++i9.10k
) {

    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; 
++j3.89k
)

      
isl_int_add3.89k
(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; 
++j7.71k
)

      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; 
++i424k
)

    if (isl_tab_freeze_constraint(tab, i) < 0)

      return -1;

  return 0;

}

/* Check for redundant constraints starting at offset.

 * Put the indices of the redundant constraints in index

 * and return the number of 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; 47.2k
i < n_test; 
++i214k
) {

    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_error0
 : 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; 
++i56.8k
)

    free(index[i]);

  free(index);

  for (i = 0; div_map && i < map->n; 
++i56.8k
)

    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; 
++i16.9k
)

    free(index[i]);

  free(index);

  for (i = 0; div_map && i < map->n; 
++i16.9k
)

    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_error0
;

}

/* 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".

 */

static __isl_give isl_map *map_subtract( __isl_take isl_map *map1,

  __isl_take isl_map *map2)

{

  int i;

  int equal, disjoint;

  struct isl_map *diff;

  if (!map1 || !map2)

    goto error;

  isl_assert(map1->ctx, isl_space_is_equal(map1->dim, map2->dim), 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; 
++i26.0k
) {

    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)9.81k
;

    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_map *isl_map_subtract( __isl_take isl_map *map1,

  __isl_take isl_map *map2)

{

  return isl_map_align_params_map_map_and(map1, map2, &map_subtract);

}

struct isl_set *isl_set_subtract(struct isl_set *set1, struct 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".

 */

static __isl_give isl_map *map_subtract_domain(__isl_take isl_map *map,

  __isl_take isl_set *dom)

{

  isl_bool ok;

  isl_map *ext_dom;

  ok = isl_map_compatible_domain(map, dom);

  if (ok < 0)

    goto error;

  if (!ok)

    
isl_die0
(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;

}

__isl_give isl_map *isl_map_subtract_domain(__isl_take isl_map *map,

  __isl_take isl_set *dom)

{

  return isl_map_align_params_map_map_and(map, dom, &map_subtract_domain);

}

/* Remove the elements of "dom" from the range of "map".

 */

static __isl_give isl_map *map_subtract_range(__isl_take isl_map *map,

  __isl_take isl_set *dom)

{

  isl_bool ok;

  isl_map *ext_dom;

  ok = isl_map_compatible_range(map, dom);

  if (ok < 0)

    goto error;

  if (!ok)

    
isl_die0
(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;

}

__isl_give isl_map *isl_map_subtract_range(__isl_take isl_map *map,

  __isl_take isl_set *dom)

{

  return isl_map_align_params_map_map_and(map, dom, &map_subtract_range);

}

/* A diff collector that aborts as soon as its add function is called,

 * setting empty to 0.

 */

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 = 0;

  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_error0
 : 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; 19.7k
i < map1->n; 
++i11.4k
) {

    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)

{

  if (!bmap)

    return isl_bool_error;

  if (bmap->n_div)

    return isl_bool_false;

  if (bmap->n_ineq)

    return isl_bool_false;

  return bmap->n_eq == isl_basic_map_total_dim(bmap);

}

/* 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;

  unsigned dim;

  struct isl_vec *point;

  isl_int m;

  if (!bmap)

    return NULL;

  dim = isl_basic_map_total_dim(bmap);

  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; 
++j488
) {

    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_die0
(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; 404
i < map2->n; 
++i66
) {

    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 && 
!rat214
)

    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 map3.57k
;

  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; 
++i430
) {

    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);

}