isl_scheduler.c: non_neg_lexmin: improve documentation

[isl.git] / isl_map_subtract.c

/*
 * 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;
        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; 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;
        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_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;
        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; 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_set(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 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; 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".
 */
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; ++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_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_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;
}

__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_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;
}

__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_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)
{
        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; ++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);
}