isl_tab: add isl_basic_set field for optionally keeping track of inequalities

[isl.git] / isl_coalesce.c

#include "isl_map_private.h"
#include "isl_tab.h"

#define STATUS_ERROR            -1
#define STATUS_REDUNDANT         1
#define STATUS_VALID             2
#define STATUS_SEPARATE          3
#define STATUS_CUT               4
#define STATUS_ADJ_EQ            5
#define STATUS_ADJ_INEQ          6

static int status_in(isl_int *ineq, struct isl_tab *tab)
{
        enum isl_ineq_type type = isl_tab_ineq_type(tab, ineq);
        switch (type) {
        case isl_ineq_error:            return STATUS_ERROR;
        case isl_ineq_redundant:        return STATUS_VALID;
        case isl_ineq_separate:         return STATUS_SEPARATE;
        case isl_ineq_cut:              return STATUS_CUT;
        case isl_ineq_adj_eq:           return STATUS_ADJ_EQ;
        case isl_ineq_adj_ineq:         return STATUS_ADJ_INEQ;
        }
}

/* Compute the position of the equalities of basic map "i"
 * with respect to basic map "j".
 * The resulting array has twice as many entries as the number
 * of equalities corresponding to the two inequalties to which
 * each equality corresponds.
 */
static int *eq_status_in(struct isl_map *map, int i, int j,
        struct isl_tab **tabs)
{
        int k, l;
        int *eq = isl_calloc_array(map->ctx, int, 2 * map->p[i]->n_eq);
        unsigned dim;

        dim = isl_basic_map_total_dim(map->p[i]);
        for (k = 0; k < map->p[i]->n_eq; ++k) {
                for (l = 0; l < 2; ++l) {
                        isl_seq_neg(map->p[i]->eq[k], map->p[i]->eq[k], 1+dim);
                        eq[2 * k + l] = status_in(map->p[i]->eq[k], tabs[j]);
                        if (eq[2 * k + l] == STATUS_ERROR)
                                goto error;
                }
                if (eq[2 * k] == STATUS_SEPARATE ||
                    eq[2 * k + 1] == STATUS_SEPARATE)
                        break;
        }

        return eq;
error:
        free(eq);
        return NULL;
}

/* Compute the position of the inequalities of basic map "i"
 * with respect to basic map "j".
 */
static int *ineq_status_in(struct isl_map *map, int i, int j,
        struct isl_tab **tabs)
{
        int k;
        unsigned n_eq = map->p[i]->n_eq;
        int *ineq = isl_calloc_array(map->ctx, int, map->p[i]->n_ineq);

        for (k = 0; k < map->p[i]->n_ineq; ++k) {
                if (isl_tab_is_redundant(tabs[i], n_eq + k)) {
                        ineq[k] = STATUS_REDUNDANT;
                        continue;
                }
                ineq[k] = status_in(map->p[i]->ineq[k], tabs[j]);
                if (ineq[k] == STATUS_ERROR)
                        goto error;
                if (ineq[k] == STATUS_SEPARATE)
                        break;
        }

        return ineq;
error:
        free(ineq);
        return NULL;
}

static int any(int *con, unsigned len, int status)
{
        int i;

        for (i = 0; i < len ; ++i)
                if (con[i] == status)
                        return 1;
        return 0;
}

static int count(int *con, unsigned len, int status)
{
        int i;
        int c = 0;

        for (i = 0; i < len ; ++i)
                if (con[i] == status)
                        c++;
        return c;
}

static int all(int *con, unsigned len, int status)
{
        int i;

        for (i = 0; i < len ; ++i) {
                if (con[i] == STATUS_REDUNDANT)
                        continue;
                if (con[i] != status)
                        return 0;
        }
        return 1;
}

static void drop(struct isl_map *map, int i, struct isl_tab **tabs)
{
        isl_basic_map_free(map->p[i]);
        isl_tab_free(tabs[i]);

        if (i != map->n - 1) {
                map->p[i] = map->p[map->n - 1];
                tabs[i] = tabs[map->n - 1];
        }
        tabs[map->n - 1] = NULL;
        map->n--;
}

/* Replace the pair of basic maps i and j but the basic map bounded
 * by the valid constraints in both basic maps.
 */
static int fuse(struct isl_map *map, int i, int j, struct isl_tab **tabs,
        int *ineq_i, int *ineq_j)
{
        int k, l;
        struct isl_basic_map *fused = NULL;
        struct isl_tab *fused_tab = NULL;
        unsigned total = isl_basic_map_total_dim(map->p[i]);

        fused = isl_basic_map_alloc_dim(isl_dim_copy(map->p[i]->dim),
                        map->p[i]->n_div,
                        map->p[i]->n_eq + map->p[j]->n_eq,
                        map->p[i]->n_ineq + map->p[j]->n_ineq);
        if (!fused)
                goto error;

        for (k = 0; k < map->p[i]->n_eq; ++k) {
                int l = isl_basic_map_alloc_equality(fused);
                isl_seq_cpy(fused->eq[l], map->p[i]->eq[k], 1 + total);
        }

        for (k = 0; k < map->p[j]->n_eq; ++k) {
                int l = isl_basic_map_alloc_equality(fused);
                isl_seq_cpy(fused->eq[l], map->p[j]->eq[k], 1 + total);
        }

        for (k = 0; k < map->p[i]->n_ineq; ++k) {
                if (ineq_i[k] != STATUS_VALID)
                        continue;
                l = isl_basic_map_alloc_inequality(fused);
                isl_seq_cpy(fused->ineq[l], map->p[i]->ineq[k], 1 + total);
        }

        for (k = 0; k < map->p[j]->n_ineq; ++k) {
                if (ineq_j[k] != STATUS_VALID)
                        continue;
                l = isl_basic_map_alloc_inequality(fused);
                isl_seq_cpy(fused->ineq[l], map->p[j]->ineq[k], 1 + total);
        }

        for (k = 0; k < map->p[i]->n_div; ++k) {
                int l = isl_basic_map_alloc_div(fused);
                isl_seq_cpy(fused->div[l], map->p[i]->div[k], 1 + 1 + total);
        }

        fused = isl_basic_map_gauss(fused, NULL);
        ISL_F_SET(fused, ISL_BASIC_MAP_FINAL);
        if (ISL_F_ISSET(map->p[i], ISL_BASIC_MAP_RATIONAL) &&
            ISL_F_ISSET(map->p[j], ISL_BASIC_MAP_RATIONAL))
                ISL_F_SET(fused, ISL_BASIC_MAP_RATIONAL);

        fused_tab = isl_tab_from_basic_map(fused);
        fused_tab = isl_tab_detect_redundant(fused_tab);
        if (!fused_tab)
                goto error;

        isl_basic_map_free(map->p[i]);
        map->p[i] = fused;
        isl_tab_free(tabs[i]);
        tabs[i] = fused_tab;
        drop(map, j, tabs);

        return 1;
error:
        isl_basic_map_free(fused);
        return -1;
}

/* Given a pair of basic maps i and j such that all constraints are either
 * "valid" or "cut", check if the facets corresponding to the "cut"
 * constraints of i lie entirely within basic map j.
 * If so, replace the pair by the basic map consisting of the valid
 * constraints in both basic maps.
 *
 * To see that we are not introducing any extra points, call the
 * two basic maps A and B and the resulting map U and let x
 * be an element of U \setminus ( A \cup B ).
 * Then there is a pair of cut constraints c_1 and c_2 in A and B such that x
 * violates them.  Let X be the intersection of U with the opposites
 * of these constraints.  Then x \in X.
 * The facet corresponding to c_1 contains the corresponding facet of A.
 * This facet is entirely contained in B, so c_2 is valid on the facet.
 * However, since it is also (part of) a facet of X, -c_2 is also valid
 * on the facet.  This means c_2 is saturated on the facet, so c_1 and
 * c_2 must be opposites of each other, but then x could not violate
 * both of them.
 */
static int check_facets(struct isl_map *map, int i, int j,
        struct isl_tab **tabs, int *ineq_i, int *ineq_j)
{
        int k, l;
        struct isl_tab_undo *snap;
        unsigned n_eq = map->p[i]->n_eq;

        snap = isl_tab_snap(tabs[i]);

        for (k = 0; k < map->p[i]->n_ineq; ++k) {
                if (ineq_i[k] != STATUS_CUT)
                        continue;
                tabs[i] = isl_tab_select_facet(tabs[i], n_eq + k);
                for (l = 0; l < map->p[j]->n_ineq; ++l) {
                        int stat;
                        if (ineq_j[l] != STATUS_CUT)
                                continue;
                        stat = status_in(map->p[j]->ineq[l], tabs[i]);
                        if (stat != STATUS_VALID)
                                break;
                }
                isl_tab_rollback(tabs[i], snap);
                if (l < map->p[j]->n_ineq)
                        break;
        }

        if (k < map->p[i]->n_ineq)
                /* BAD CUT PAIR */
                return 0;
        return fuse(map, i, j, tabs, ineq_i, ineq_j);
}

/* Both basic maps have at least one inequality with and adjacent
 * (but opposite) inequality in the other basic map.
 * Check that there are no cut constraints and that there is only
 * a single pair of adjacent inequalities.
 * If so, we can replace the pair by a single basic map described
 * by all but the pair of adjacent inequalities.
 * Any additional points introduced lie strictly between the two
 * adjacent hyperplanes and can therefore be integral.
 *
 *        ____                    _____
 *       /    ||\                /     \
 *      /     || \              /       \
 *      \     ||  \     =>      \        \
 *       \    ||  /              \       /
 *        \___||_/                \_____/
 *
 * The test for a single pair of adjancent inequalities is important
 * for avoiding the combination of two basic maps like the following
 *
 *       /|
 *      / |
 *     /__|
 *         _____
 *         |   |
 *         |   |
 *         |___|
 */
static int check_adj_ineq(struct isl_map *map, int i, int j,
        struct isl_tab **tabs, int *ineq_i, int *ineq_j)
{
        int changed = 0;

        if (any(ineq_i, map->p[i]->n_ineq, STATUS_CUT) ||
            any(ineq_j, map->p[j]->n_ineq, STATUS_CUT))
                /* ADJ INEQ CUT */
                ;
        else if (count(ineq_i, map->p[i]->n_ineq, STATUS_ADJ_INEQ) == 1 &&
                 count(ineq_j, map->p[j]->n_ineq, STATUS_ADJ_INEQ) == 1)
                changed = fuse(map, i, j, tabs, ineq_i, ineq_j);
        /* else ADJ INEQ TOO MANY */

        return changed;
}

/* Check if basic map "i" contains the basic map represented
 * by the tableau "tab".
 */
static int contains(struct isl_map *map, int i, int *ineq_i,
        struct isl_tab *tab)
{
        int k, l;
        unsigned dim;

        dim = isl_basic_map_total_dim(map->p[i]);
        for (k = 0; k < map->p[i]->n_eq; ++k) {
                for (l = 0; l < 2; ++l) {
                        int stat;
                        isl_seq_neg(map->p[i]->eq[k], map->p[i]->eq[k], 1+dim);
                        stat = status_in(map->p[i]->eq[k], tab);
                        if (stat != STATUS_VALID)
                                return 0;
                }
        }

        for (k = 0; k < map->p[i]->n_ineq; ++k) {
                int stat;
                if (ineq_i[k] == STATUS_REDUNDANT)
                        continue;
                stat = status_in(map->p[i]->ineq[k], tab);
                if (stat != STATUS_VALID)
                        return 0;
        }
        return 1;
}

/* At least one of the basic maps has an equality that is adjacent
 * to inequality.  Make sure that only one of the basic maps has
 * such an equality and that the other basic map has exactly one
 * inequality adjacent to an equality.
 * We call the basic map that has the inequality "i" and the basic
 * map that has the equality "j".
 * If "i" has any "cut" inequality, then relaxing the inequality
 * by one would not result in a basic map that contains the other
 * basic map.
 * Otherwise, we relax the constraint, compute the corresponding
 * facet and check whether it is included in the other basic map.
 * If so, we know that relaxing the constraint extend the basic
 * map with exactly the other basic map (we already know that this
 * other basic map is included in the extension, because there
 * were no "cut" inequalities in "i") and we can replace the
 * two basic maps by thie extension.
 *        ____                    _____
 *       /    ||                 /     |
 *      /     ||                /      |
 *      \     ||        =>      \      |
 *       \    ||                 \     |
 *        \___||                  \____|
 */
static int check_adj_eq(struct isl_map *map, int i, int j,
        struct isl_tab **tabs, int *eq_i, int *ineq_i, int *eq_j, int *ineq_j)
{
        int changed = 0;
        int super;
        int k;
        struct isl_tab_undo *snap, *snap2;
        unsigned n_eq = map->p[i]->n_eq;

        if (any(eq_i, 2 * map->p[i]->n_eq, STATUS_ADJ_INEQ) &&
            any(eq_j, 2 * map->p[j]->n_eq, STATUS_ADJ_INEQ))
                /* ADJ EQ TOO MANY */
                return 0;

        if (any(eq_i, 2 * map->p[i]->n_eq, STATUS_ADJ_INEQ))
                return check_adj_eq(map, j, i, tabs,
                                        eq_j, ineq_j, eq_i, ineq_i);

        /* j has an equality adjacent to an inequality in i */

        if (any(ineq_i, map->p[i]->n_ineq, STATUS_CUT))
                /* ADJ EQ CUT */
                return 0;
        if (count(eq_j, 2 * map->p[j]->n_eq, STATUS_ADJ_INEQ) != 1 ||
            count(ineq_i, map->p[i]->n_ineq, STATUS_ADJ_EQ) != 1 ||
            any(ineq_j, map->p[j]->n_ineq, STATUS_ADJ_EQ) ||
            any(ineq_i, map->p[i]->n_ineq, STATUS_ADJ_INEQ) ||
            any(ineq_j, map->p[j]->n_ineq, STATUS_ADJ_INEQ))
                /* ADJ EQ TOO MANY */
                return 0;

        for (k = 0; k < map->p[i]->n_ineq ; ++k)
                if (ineq_i[k] == STATUS_ADJ_EQ)
                        break;

        snap = isl_tab_snap(tabs[i]);
        tabs[i] = isl_tab_relax(tabs[i], n_eq + k);
        snap2 = isl_tab_snap(tabs[i]);
        tabs[i] = isl_tab_select_facet(tabs[i], n_eq + k);
        super = contains(map, j, ineq_j, tabs[i]);
        if (super) {
                isl_tab_rollback(tabs[i], snap2);
                map->p[i] = isl_basic_map_cow(map->p[i]);
                if (!map->p[i])
                        return -1;
                isl_int_add_ui(map->p[i]->ineq[k][0], map->p[i]->ineq[k][0], 1);
                ISL_F_SET(map->p[i], ISL_BASIC_MAP_FINAL);
                drop(map, j, tabs);
                changed = 1;
        } else
                isl_tab_rollback(tabs[i], snap);

        return changed;
}

/* Check if the union of the given pair of basic maps
 * can be represented by a single basic map.
 * If so, replace the pair by the single basic map and return 1.
 * Otherwise, return 0;
 *
 * We first check the effect of each constraint of one basic map
 * on the other basic map.
 * The constraint may be
 *      redundant       the constraint is redundant in its own
 *                      basic map and should be ignore and removed
 *                      in the end
 *      valid           all (integer) points of the other basic map
 *                      satisfy the constraint
 *      separate        no (integer) point of the other basic map
 *                      satisfies the constraint
 *      cut             some but not all points of the other basic map
 *                      satisfy the constraint
 *      adj_eq          the given constraint is adjacent (on the outside)
 *                      to an equality of the other basic map
 *      adj_ineq        the given constraint is adjacent (on the outside)
 *                      to an inequality of the other basic map
 *
 * We consider four cases in which we can replace the pair by a single
 * basic map.  We ignore all "redundant" constraints.
 *
 *      1. all constraints of one basic map are valid
 *              => the other basic map is a subset and can be removed
 *
 *      2. all constraints of both basic maps are either "valid" or "cut"
 *         and the facets corresponding to the "cut" constraints
 *         of one of the basic maps lies entirely inside the other basic map
 *              => the pair can be replaced by a basic map consisting
 *                 of the valid constraints in both basic maps
 *
 *      3. there is a single pair of adjacent inequalities
 *         (all other constraints are "valid")
 *              => the pair can be replaced by a basic map consisting
 *                 of the valid constraints in both basic maps
 *
 *      4. there is a single adjacent pair of an inequality and an equality,
 *         the other constraints of the basic map containing the inequality are
 *         "valid".  Moreover, if the inequality the basic map is relaxed
 *         and then turned into an equality, then resulting facet lies
 *         entirely inside the other basic map
 *              => the pair can be replaced by the basic map containing
 *                 the inequality, with the inequality relaxed.
 *
 * Throughout the computation, we maintain a collection of tableaus
 * corresponding to the basic maps.  When the basic maps are dropped
 * or combined, the tableaus are modified accordingly.
 */
static int coalesce_pair(struct isl_map *map, int i, int j,
        struct isl_tab **tabs)
{
        int changed = 0;
        int *eq_i = NULL;
        int *eq_j = NULL;
        int *ineq_i = NULL;
        int *ineq_j = NULL;

        eq_i = eq_status_in(map, i, j, tabs);
        if (any(eq_i, 2 * map->p[i]->n_eq, STATUS_ERROR))
                goto error;
        if (any(eq_i, 2 * map->p[i]->n_eq, STATUS_SEPARATE))
                goto done;

        eq_j = eq_status_in(map, j, i, tabs);
        if (any(eq_j, 2 * map->p[j]->n_eq, STATUS_ERROR))
                goto error;
        if (any(eq_j, 2 * map->p[j]->n_eq, STATUS_SEPARATE))
                goto done;

        ineq_i = ineq_status_in(map, i, j, tabs);
        if (any(ineq_i, map->p[i]->n_ineq, STATUS_ERROR))
                goto error;
        if (any(ineq_i, map->p[i]->n_ineq, STATUS_SEPARATE))
                goto done;

        ineq_j = ineq_status_in(map, j, i, tabs);
        if (any(ineq_j, map->p[j]->n_ineq, STATUS_ERROR))
                goto error;
        if (any(ineq_j, map->p[j]->n_ineq, STATUS_SEPARATE))
                goto done;

        if (all(eq_i, 2 * map->p[i]->n_eq, STATUS_VALID) &&
            all(ineq_i, map->p[i]->n_ineq, STATUS_VALID)) {
                drop(map, j, tabs);
                changed = 1;
        } else if (all(eq_j, 2 * map->p[j]->n_eq, STATUS_VALID) &&
                   all(ineq_j, map->p[j]->n_ineq, STATUS_VALID)) {
                drop(map, i, tabs);
                changed = 1;
        } else if (any(eq_i, 2 * map->p[i]->n_eq, STATUS_CUT) ||
                   any(eq_j, 2 * map->p[j]->n_eq, STATUS_CUT)) {
                /* BAD CUT */
        } else if (any(eq_i, 2 * map->p[i]->n_eq, STATUS_ADJ_EQ) ||
                   any(eq_j, 2 * map->p[j]->n_eq, STATUS_ADJ_EQ)) {
                /* ADJ EQ PAIR */
        } else if (any(eq_i, 2 * map->p[i]->n_eq, STATUS_ADJ_INEQ) ||
                   any(eq_j, 2 * map->p[j]->n_eq, STATUS_ADJ_INEQ)) {
                changed = check_adj_eq(map, i, j, tabs,
                                        eq_i, ineq_i, eq_j, ineq_j);
        } else if (any(ineq_i, map->p[i]->n_ineq, STATUS_ADJ_EQ) ||
                   any(ineq_j, map->p[j]->n_ineq, STATUS_ADJ_EQ)) {
                /* Can't happen */
                /* BAD ADJ INEQ */
        } else if (any(ineq_i, map->p[i]->n_ineq, STATUS_ADJ_INEQ) ||
                   any(ineq_j, map->p[j]->n_ineq, STATUS_ADJ_INEQ)) {
                changed = check_adj_ineq(map, i, j, tabs, ineq_i, ineq_j);
        } else
                changed = check_facets(map, i, j, tabs, ineq_i, ineq_j);

done:
        free(eq_i);
        free(eq_j);
        free(ineq_i);
        free(ineq_j);
        return changed;
error:
        free(eq_i);
        free(eq_j);
        free(ineq_i);
        free(ineq_j);
        return -1;
}

static struct isl_map *coalesce(struct isl_map *map, struct isl_tab **tabs)
{
        int i, j;

        for (i = 0; i < map->n - 1; ++i)
                for (j = i + 1; j < map->n; ++j) {
                        int changed;
                        changed = coalesce_pair(map, i, j, tabs);
                        if (changed < 0)
                                goto error;
                        if (changed)
                                return coalesce(map, tabs);
                }
        return map;
error:
        isl_map_free(map);
        return NULL;
}

/* For each pair of basic maps in the map, check if the union of the two
 * can be represented by a single basic map.
 * If so, replace the pair by the single basic map and start over.
 */
struct isl_map *isl_map_coalesce(struct isl_map *map)
{
        int i;
        unsigned n;
        struct isl_tab **tabs = NULL;

        if (!map)
                return NULL;

        if (map->n <= 1)
                return map;

        map = isl_map_align_divs(map);

        tabs = isl_calloc_array(map->ctx, struct isl_tab *, map->n);
        if (!tabs)
                goto error;

        n = map->n;
        for (i = 0; i < map->n; ++i) {
                tabs[i] = isl_tab_from_basic_map(map->p[i]);
                if (!tabs[i])
                        goto error;
                if (!ISL_F_ISSET(map->p[i], ISL_BASIC_MAP_NO_IMPLICIT))
                        tabs[i] = isl_tab_detect_equalities(tabs[i]);
                if (!ISL_F_ISSET(map->p[i], ISL_BASIC_MAP_NO_REDUNDANT))
                        tabs[i] = isl_tab_detect_redundant(tabs[i]);
        }
        for (i = map->n - 1; i >= 0; --i)
                if (tabs[i]->empty)
                        drop(map, i, tabs);

        map = coalesce(map, tabs);

        if (map)
                for (i = 0; i < map->n; ++i) {
                        map->p[i] = isl_basic_map_update_from_tab(map->p[i],
                                                                    tabs[i]);
                        map->p[i] = isl_basic_map_finalize(map->p[i]);
                        if (!map->p[i])
                                goto error;
                        ISL_F_SET(map->p[i], ISL_BASIC_MAP_NO_IMPLICIT);
                        ISL_F_SET(map->p[i], ISL_BASIC_MAP_NO_REDUNDANT);
                }

        for (i = 0; i < n; ++i)
                isl_tab_free(tabs[i]);

        free(tabs);

        return map;
error:
        if (tabs)
                for (i = 0; i < n; ++i)
                        isl_tab_free(tabs[i]);
        free(tabs);
        return NULL;
}

/* For each pair of basic sets in the set, check if the union of the two
 * can be represented by a single basic set.
 * If so, replace the pair by the single basic set and start over.
 */
struct isl_set *isl_set_coalesce(struct isl_set *set)
{
        (struct isl_set *)isl_map_coalesce((struct isl_map *)set);
}