isl_basic_map_gist: replace by new version based on tableaus

[isl.git] / isl_map_simplify.c

#include "isl_equalities.h"
#include "isl_map.h"
#include "isl_map_private.h"
#include "isl_tab.h"

static void swap_equality(struct isl_basic_map *bmap, int a, int b)
{
        isl_int *t = bmap->eq[a];
        bmap->eq[a] = bmap->eq[b];
        bmap->eq[b] = t;
}

static void swap_inequality(struct isl_basic_map *bmap, int a, int b)
{
        if (a != b) {
                isl_int *t = bmap->ineq[a];
                bmap->ineq[a] = bmap->ineq[b];
                bmap->ineq[b] = t;
        }
}

static void set_swap_inequality(struct isl_basic_set *bset, int a, int b)
{
        swap_inequality((struct isl_basic_map *)bset, a, b);
}

static void constraint_drop_vars(isl_int *c, unsigned n, unsigned rem)
{
        isl_seq_cpy(c, c + n, rem);
        isl_seq_clr(c + rem, n);
}

/* Drop n dimensions starting at first.
 *
 * In principle, this frees up some extra variables as the number
 * of columns remains constant, but we would have to extend
 * the div array too as the number of rows in this array is assumed
 * to be equal to extra.
 */
struct isl_basic_set *isl_basic_set_drop_dims(
                struct isl_basic_set *bset, unsigned first, unsigned n)
{
        int i;

        if (!bset)
                goto error;

        isl_assert(bset->ctx, first + n <= bset->dim->n_out, goto error);

        if (n == 0)
                return bset;

        bset = isl_basic_set_cow(bset);
        if (!bset)
                return NULL;

        for (i = 0; i < bset->n_eq; ++i)
                constraint_drop_vars(bset->eq[i]+1+bset->dim->nparam+first, n,
                                     (bset->dim->n_out-first-n)+bset->extra);

        for (i = 0; i < bset->n_ineq; ++i)
                constraint_drop_vars(bset->ineq[i]+1+bset->dim->nparam+first, n,
                                     (bset->dim->n_out-first-n)+bset->extra);

        for (i = 0; i < bset->n_div; ++i)
                constraint_drop_vars(bset->div[i]+1+1+bset->dim->nparam+first, n,
                                     (bset->dim->n_out-first-n)+bset->extra);

        bset->dim = isl_dim_drop_outputs(bset->dim, first, n);
        if (!bset->dim)
                goto error;

        ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
        bset = isl_basic_set_simplify(bset);
        return isl_basic_set_finalize(bset);
error:
        isl_basic_set_free(bset);
        return NULL;
}

struct isl_set *isl_set_drop_dims(
                struct isl_set *set, unsigned first, unsigned n)
{
        int i;

        if (!set)
                goto error;

        isl_assert(set->ctx, first + n <= set->dim->n_out, goto error);

        if (n == 0)
                return set;
        set = isl_set_cow(set);
        if (!set)
                goto error;
        set->dim = isl_dim_drop_outputs(set->dim, first, n);
        if (!set->dim)
                goto error;

        for (i = 0; i < set->n; ++i) {
                set->p[i] = isl_basic_set_drop_dims(set->p[i], first, n);
                if (!set->p[i])
                        goto error;
        }

        ISL_F_CLR(set, ISL_SET_NORMALIZED);
        return set;
error:
        isl_set_free(set);
        return NULL;
}

/* Drop n input dimensions starting at first.
 *
 * In principle, this frees up some extra variables as the number
 * of columns remains constant, but we would have to extend
 * the div array too as the number of rows in this array is assumed
 * to be equal to extra.
 */
struct isl_basic_map *isl_basic_map_drop(struct isl_basic_map *bmap,
        enum isl_dim_type type, unsigned first, unsigned n)
{
        int i;
        unsigned dim;
        unsigned offset;
        unsigned left;

        if (!bmap)
                goto error;

        dim = isl_basic_map_dim(bmap, type);
        isl_assert(bmap->ctx, first + n <= dim, goto error);

        if (n == 0)
                return bmap;

        bmap = isl_basic_map_cow(bmap);
        if (!bmap)
                return NULL;

        offset = isl_basic_map_offset(bmap, type) + first;
        left = isl_basic_map_total_dim(bmap) - (offset - 1) - n;
        for (i = 0; i < bmap->n_eq; ++i)
                constraint_drop_vars(bmap->eq[i]+offset, n, left);

        for (i = 0; i < bmap->n_ineq; ++i)
                constraint_drop_vars(bmap->ineq[i]+offset, n, left);

        for (i = 0; i < bmap->n_div; ++i)
                constraint_drop_vars(bmap->div[i]+1+offset, n, left);

        bmap->dim = isl_dim_drop(bmap->dim, type, first, n);
        if (!bmap->dim)
                goto error;

        ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
        bmap = isl_basic_map_simplify(bmap);
        return isl_basic_map_finalize(bmap);
error:
        isl_basic_map_free(bmap);
        return NULL;
}

struct isl_basic_map *isl_basic_map_drop_inputs(
                struct isl_basic_map *bmap, unsigned first, unsigned n)
{
        return isl_basic_map_drop(bmap, isl_dim_in, first, n);
}

struct isl_map *isl_map_drop(struct isl_map *map,
        enum isl_dim_type type, unsigned first, unsigned n)
{
        int i;

        if (!map)
                goto error;

        isl_assert(map->ctx, first + n <= isl_map_dim(map, type), goto error);

        if (n == 0)
                return map;
        map = isl_map_cow(map);
        if (!map)
                goto error;
        map->dim = isl_dim_drop(map->dim, type, first, n);
        if (!map->dim)
                goto error;

        for (i = 0; i < map->n; ++i) {
                map->p[i] = isl_basic_map_drop(map->p[i], type, first, n);
                if (!map->p[i])
                        goto error;
        }
        ISL_F_CLR(map, ISL_MAP_NORMALIZED);

        return map;
error:
        isl_map_free(map);
        return NULL;
}

struct isl_map *isl_map_drop_inputs(
                struct isl_map *map, unsigned first, unsigned n)
{
        return isl_map_drop(map, isl_dim_in, first, n);
}

/*
 * We don't cow, as the div is assumed to be redundant.
 */
static struct isl_basic_map *isl_basic_map_drop_div(
                struct isl_basic_map *bmap, unsigned div)
{
        int i;
        unsigned pos;

        if (!bmap)
                goto error;

        pos = 1 + isl_dim_total(bmap->dim) + div;

        isl_assert(bmap->ctx, div < bmap->n_div, goto error);

        for (i = 0; i < bmap->n_eq; ++i)
                constraint_drop_vars(bmap->eq[i]+pos, 1, bmap->extra-div-1);

        for (i = 0; i < bmap->n_ineq; ++i) {
                if (!isl_int_is_zero(bmap->ineq[i][pos])) {
                        isl_basic_map_drop_inequality(bmap, i);
                        --i;
                        continue;
                }
                constraint_drop_vars(bmap->ineq[i]+pos, 1, bmap->extra-div-1);
        }

        for (i = 0; i < bmap->n_div; ++i)
                constraint_drop_vars(bmap->div[i]+1+pos, 1, bmap->extra-div-1);

        if (div != bmap->n_div - 1) {
                int j;
                isl_int *t = bmap->div[div];

                for (j = div; j < bmap->n_div - 1; ++j)
                        bmap->div[j] = bmap->div[j+1];

                bmap->div[bmap->n_div - 1] = t;
        }
        ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
        isl_basic_map_free_div(bmap, 1);

        return bmap;
error:
        isl_basic_map_free(bmap);
        return NULL;
}

struct isl_basic_map *isl_basic_map_normalize_constraints(
        struct isl_basic_map *bmap)
{
        int i;
        isl_int gcd;
        unsigned total = isl_basic_map_total_dim(bmap);

        isl_int_init(gcd);
        for (i = bmap->n_eq - 1; i >= 0; --i) {
                isl_seq_gcd(bmap->eq[i]+1, total, &gcd);
                if (isl_int_is_zero(gcd)) {
                        if (!isl_int_is_zero(bmap->eq[i][0])) {
                                bmap = isl_basic_map_set_to_empty(bmap);
                                break;
                        }
                        isl_basic_map_drop_equality(bmap, i);
                        continue;
                }
                if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
                        isl_int_gcd(gcd, gcd, bmap->eq[i][0]);
                if (isl_int_is_one(gcd))
                        continue;
                if (!isl_int_is_divisible_by(bmap->eq[i][0], gcd)) {
                        bmap = isl_basic_map_set_to_empty(bmap);
                        break;
                }
                isl_seq_scale_down(bmap->eq[i], bmap->eq[i], gcd, 1+total);
        }

        for (i = bmap->n_ineq - 1; i >= 0; --i) {
                isl_seq_gcd(bmap->ineq[i]+1, total, &gcd);
                if (isl_int_is_zero(gcd)) {
                        if (isl_int_is_neg(bmap->ineq[i][0])) {
                                bmap = isl_basic_map_set_to_empty(bmap);
                                break;
                        }
                        isl_basic_map_drop_inequality(bmap, i);
                        continue;
                }
                if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
                        isl_int_gcd(gcd, gcd, bmap->ineq[i][0]);
                if (isl_int_is_one(gcd))
                        continue;
                isl_int_fdiv_q(bmap->ineq[i][0], bmap->ineq[i][0], gcd);
                isl_seq_scale_down(bmap->ineq[i]+1, bmap->ineq[i]+1, gcd, total);
        }
        isl_int_clear(gcd);

        return bmap;
}

struct isl_basic_set *isl_basic_set_normalize_constraints(
        struct isl_basic_set *bset)
{
        (struct isl_basic_set *)isl_basic_map_normalize_constraints(
                (struct isl_basic_map *)bset);
}

static void eliminate_div(struct isl_basic_map *bmap, isl_int *eq, unsigned div)
{
        int i;
        unsigned pos = 1 + isl_dim_total(bmap->dim) + div;
        unsigned len;
        len = 1 + isl_basic_map_total_dim(bmap);

        for (i = 0; i < bmap->n_eq; ++i)
                if (bmap->eq[i] != eq)
                        isl_seq_elim(bmap->eq[i], eq, pos, len, NULL);

        for (i = 0; i < bmap->n_ineq; ++i)
                isl_seq_elim(bmap->ineq[i], eq, pos, len, NULL);

        /* We need to be careful about circular definitions,
         * so for now we just remove the definitions of other divs that
         * depend on this div and (possibly) recompute them later.
         */
        for (i = 0; i < bmap->n_div; ++i)
                if (!isl_int_is_zero(bmap->div[i][0]) &&
                    !isl_int_is_zero(bmap->div[i][1 + pos]))
                        isl_seq_clr(bmap->div[i], 1 + len);

        isl_basic_map_drop_div(bmap, div);
}

/* Elimininate divs based on equalities
 */
static struct isl_basic_map *eliminate_divs_eq(
                struct isl_basic_map *bmap, int *progress)
{
        int d;
        int i;
        int modified = 0;
        unsigned off;

        if (!bmap)
                return NULL;

        off = 1 + isl_dim_total(bmap->dim);

        for (d = bmap->n_div - 1; d >= 0 ; --d) {
                for (i = 0; i < bmap->n_eq; ++i) {
                        if (!isl_int_is_one(bmap->eq[i][off + d]) &&
                            !isl_int_is_negone(bmap->eq[i][off + d]))
                                continue;
                        modified = 1;
                        *progress = 1;
                        eliminate_div(bmap, bmap->eq[i], d);
                        isl_basic_map_drop_equality(bmap, i);
                        break;
                }
        }
        if (modified)
                return eliminate_divs_eq(bmap, progress);
        return bmap;
}

/* Elimininate divs based on inequalities
 */
static struct isl_basic_map *eliminate_divs_ineq(
                struct isl_basic_map *bmap, int *progress)
{
        int d;
        int i;
        unsigned off;
        struct isl_ctx *ctx;

        if (!bmap)
                return NULL;

        ctx = bmap->ctx;
        off = 1 + isl_dim_total(bmap->dim);

        for (d = bmap->n_div - 1; d >= 0 ; --d) {
                for (i = 0; i < bmap->n_eq; ++i)
                        if (!isl_int_is_zero(bmap->eq[i][off + d]))
                                break;
                if (i < bmap->n_eq)
                        continue;
                for (i = 0; i < bmap->n_ineq; ++i)
                        if (isl_int_abs_gt(bmap->ineq[i][off + d], ctx->one))
                                break;
                if (i < bmap->n_ineq)
                        continue;
                *progress = 1;
                bmap = isl_basic_map_eliminate_vars(bmap, (off-1)+d, 1);
                if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
                        break;
                bmap = isl_basic_map_drop_div(bmap, d);
                if (!bmap)
                        break;
        }
        return bmap;
}

static void eliminate_var_using_equality(struct isl_basic_map *bmap,
        unsigned pos, isl_int *eq, int *progress)
{
        unsigned total;
        int k;
        int contains_divs;

        total = isl_basic_map_total_dim(bmap);
        contains_divs =
                isl_seq_first_non_zero(eq + 1 + isl_dim_total(bmap->dim),
                                                bmap->n_div) != -1;
        for (k = 0; k < bmap->n_eq; ++k) {
                if (bmap->eq[k] == eq)
                        continue;
                if (isl_int_is_zero(bmap->eq[k][1+pos]))
                        continue;
                if (progress)
                        *progress = 1;
                isl_seq_elim(bmap->eq[k], eq, 1+pos, 1+total, NULL);
        }

        for (k = 0; k < bmap->n_ineq; ++k) {
                if (isl_int_is_zero(bmap->ineq[k][1+pos]))
                        continue;
                if (progress)
                        *progress = 1;
                isl_seq_elim(bmap->ineq[k], eq, 1+pos, 1+total, NULL);
                ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
        }

        for (k = 0; k < bmap->n_div; ++k) {
                if (isl_int_is_zero(bmap->div[k][0]))
                        continue;
                if (isl_int_is_zero(bmap->div[k][1+1+pos]))
                        continue;
                if (progress)
                        *progress = 1;
                /* We need to be careful about circular definitions,
                 * so for now we just remove the definition of div k
                 * if the equality contains any divs.
                 */
                if (contains_divs)
                        isl_seq_clr(bmap->div[k], 1 + total);
                else
                        isl_seq_elim(bmap->div[k]+1, eq,
                                        1+pos, 1+total, &bmap->div[k][0]);
                ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
        }
}

struct isl_basic_map *isl_basic_map_gauss(
        struct isl_basic_map *bmap, int *progress)
{
        int k;
        int done;
        int last_var;
        unsigned total_var;
        unsigned total;

        if (!bmap)
                return NULL;

        total = isl_basic_map_total_dim(bmap);
        total_var = total - bmap->n_div;

        last_var = total - 1;
        for (done = 0; done < bmap->n_eq; ++done) {
                for (; last_var >= 0; --last_var) {
                        for (k = done; k < bmap->n_eq; ++k)
                                if (!isl_int_is_zero(bmap->eq[k][1+last_var]))
                                        break;
                        if (k < bmap->n_eq)
                                break;
                }
                if (last_var < 0)
                        break;
                if (k != done)
                        swap_equality(bmap, k, done);
                if (isl_int_is_neg(bmap->eq[done][1+last_var]))
                        isl_seq_neg(bmap->eq[done], bmap->eq[done], 1+total);

                eliminate_var_using_equality(bmap, last_var, bmap->eq[done],
                                                progress);

                if (last_var >= total_var &&
                    isl_int_is_zero(bmap->div[last_var - total_var][0])) {
                        unsigned div = last_var - total_var;
                        isl_seq_neg(bmap->div[div]+1, bmap->eq[done], 1+total);
                        isl_int_set_si(bmap->div[div][1+1+last_var], 0);
                        isl_int_set(bmap->div[div][0],
                                    bmap->eq[done][1+last_var]);
                        ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
                }
        }
        if (done == bmap->n_eq)
                return bmap;
        for (k = done; k < bmap->n_eq; ++k) {
                if (isl_int_is_zero(bmap->eq[k][0]))
                        continue;
                return isl_basic_map_set_to_empty(bmap);
        }
        isl_basic_map_free_equality(bmap, bmap->n_eq-done);
        return bmap;
}

struct isl_basic_set *isl_basic_set_gauss(
        struct isl_basic_set *bset, int *progress)
{
        return (struct isl_basic_set*)isl_basic_map_gauss(
                        (struct isl_basic_map *)bset, progress);
}


static unsigned int round_up(unsigned int v)
{
        int old_v = v;

        while (v) {
                old_v = v;
                v ^= v & -v;
        }
        return old_v << 1;
}

static int hash_index(isl_int ***index, unsigned int size, int bits,
                        struct isl_basic_map *bmap, int k)
{
        int h;
        unsigned total = isl_basic_map_total_dim(bmap);
        uint32_t hash = isl_seq_get_hash_bits(bmap->ineq[k]+1, total, bits);
        for (h = hash; index[h]; h = (h+1) % size)
                if (&bmap->ineq[k] != index[h] &&
                    isl_seq_eq(bmap->ineq[k]+1, index[h][0]+1, total))
                        break;
        return h;
}

static int set_hash_index(isl_int ***index, unsigned int size, int bits,
                          struct isl_basic_set *bset, int k)
{
        return hash_index(index, size, bits, (struct isl_basic_map *)bset, k);
}

/* If we can eliminate more than one div, then we need to make
 * sure we do it from last div to first div, in order not to
 * change the position of the other divs that still need to
 * be removed.
 */
static struct isl_basic_map *remove_duplicate_divs(
        struct isl_basic_map *bmap, int *progress)
{
        unsigned int size;
        int *index;
        int *elim_for;
        int k, l, h;
        int bits;
        struct isl_blk eq;
        unsigned total_var = isl_dim_total(bmap->dim);
        unsigned total = total_var + bmap->n_div;
        struct isl_ctx *ctx;

        if (bmap->n_div <= 1)
                return bmap;

        ctx = bmap->ctx;
        for (k = bmap->n_div - 1; k >= 0; --k)
                if (!isl_int_is_zero(bmap->div[k][0]))
                        break;
        if (k <= 0)
                return bmap;

        elim_for = isl_calloc_array(ctx, int, bmap->n_div);
        size = round_up(4 * bmap->n_div / 3 - 1);
        bits = ffs(size) - 1;
        index = isl_calloc_array(ctx, int, size);
        if (!index)
                return bmap;
        eq = isl_blk_alloc(ctx, 1+total);
        if (isl_blk_is_error(eq))
                goto out;

        isl_seq_clr(eq.data, 1+total);
        index[isl_seq_get_hash_bits(bmap->div[k], 2+total, bits)] = k + 1;
        for (--k; k >= 0; --k) {
                uint32_t hash;

                if (isl_int_is_zero(bmap->div[k][0]))
                        continue;

                hash = isl_seq_get_hash_bits(bmap->div[k], 2+total, bits);
                for (h = hash; index[h]; h = (h+1) % size)
                        if (isl_seq_eq(bmap->div[k],
                                       bmap->div[index[h]-1], 2+total))
                                break;
                if (index[h]) {
                        *progress = 1;
                        l = index[h] - 1;
                        elim_for[l] = k + 1;
                }
                index[h] = k+1;
        }
        for (l = bmap->n_div - 1; l >= 0; --l) {
                if (!elim_for[l])
                        continue;
                k = elim_for[l] - 1;
                isl_int_set_si(eq.data[1+total_var+k], -1);
                isl_int_set_si(eq.data[1+total_var+l], 1);
                eliminate_div(bmap, eq.data, l);
                isl_int_set_si(eq.data[1+total_var+k], 0);
                isl_int_set_si(eq.data[1+total_var+l], 0);
        }

        isl_blk_free(ctx, eq);
out:
        free(index);
        free(elim_for);
        return bmap;
}

/* Normalize divs that appear in equalities.
 *
 * In particular, we assume that bmap contains some equalities
 * of the form
 *
 *      a x = m * e_i
 *
 * and we want to replace the set of e_i by a minimal set and
 * such that the new e_i have a canonical representation in terms
 * of the vector x.
 * If any of the equalities involves more than one divs, then
 * we currently simply bail out.
 *
 * Let us first additionally assume that all equalities involve
 * a div.  The equalities then express modulo constraints on the
 * remaining variables and we can use "parameter compression"
 * to find a minimal set of constraints.  The result is a transformation
 *
 *      x = T(x') = x_0 + G x'
 *
 * with G a lower-triangular matrix with all elements below the diagonal
 * non-negative and smaller than the diagonal element on the same row.
 * We first normalize x_0 by making the same property hold in the affine
 * T matrix.
 * The rows i of G with a 1 on the diagonal do not impose any modulo
 * constraint and simply express x_i = x'_i.
 * For each of the remaining rows i, we introduce a div and a corresponding
 * equality.  In particular
 *
 *      g_ii e_j = x_i - g_i(x')
 *
 * where each x'_k is replaced either by x_k (if g_kk = 1) or the
 * corresponding div (if g_kk != 1).
 *
 * If there are any equalities not involving any div, then we
 * first apply a variable compression on the variables x:
 *
 *      x = C x''       x'' = C_2 x
 *
 * and perform the above parameter compression on A C instead of on A.
 * The resulting compression is then of the form
 *
 *      x'' = T(x') = x_0 + G x'
 *
 * and in constructing the new divs and the corresponding equalities,
 * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
 * by the corresponding row from C_2.
 */
static struct isl_basic_map *normalize_divs(
        struct isl_basic_map *bmap, int *progress)
{
        int i, j, k;
        int total;
        int div_eq;
        struct isl_mat *B;
        struct isl_vec *d;
        struct isl_mat *T = NULL;
        struct isl_mat *C = NULL;
        struct isl_mat *C2 = NULL;
        isl_int v;
        int *pos;
        int dropped, needed;

        if (!bmap)
                return NULL;

        if (bmap->n_div == 0)
                return bmap;

        if (bmap->n_eq == 0)
                return bmap;

        if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS))
                return bmap;

        total = isl_dim_total(bmap->dim);
        for (i = 0, j = bmap->n_div-1; i < bmap->n_eq; ++i) {
                while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
                        --j;
                if (j < 0)
                        break;
                if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total, j) != -1)
                        goto done;
        }
        div_eq = i;
        if (div_eq == 0)
                return bmap;

        if (div_eq < bmap->n_eq) {
                B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, div_eq,
                                        bmap->n_eq - div_eq, 0, 1 + total);
                C = isl_mat_variable_compression(bmap->ctx, B, &C2);
                if (!C || !C2)
                        goto error;
                if (C->n_col == 0) {
                        bmap = isl_basic_map_set_to_empty(bmap);
                        isl_mat_free(bmap->ctx, C);
                        isl_mat_free(bmap->ctx, C2);
                        goto done;
                }
        }

        d = isl_vec_alloc(bmap->ctx, div_eq);
        if (!d)
                goto error;
        for (i = 0, j = bmap->n_div-1; i < div_eq; ++i) {
                while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
                        --j;
                isl_int_set(d->block.data[i], bmap->eq[i][1 + total + j]);
        }
        B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, 0, div_eq, 0, 1 + total);

        if (C) {
                B = isl_mat_product(bmap->ctx, B, C);
                C = NULL;
        }

        T = isl_mat_parameter_compression(bmap->ctx, B, d);
        if (!T)
                goto error;
        if (T->n_col == 0) {
                bmap = isl_basic_map_set_to_empty(bmap);
                isl_mat_free(bmap->ctx, C2);
                isl_mat_free(bmap->ctx, T);
                goto done;
        }
        isl_int_init(v);
        for (i = 0; i < T->n_row - 1; ++i) {
                isl_int_fdiv_q(v, T->row[1 + i][0], T->row[1 + i][1 + i]);
                if (isl_int_is_zero(v))
                        continue;
                isl_mat_col_submul(T, 0, v, 1 + i);
        }
        isl_int_clear(v);
        pos = isl_alloc_array(bmap->ctx, int, T->n_row);
        /* We have to be careful because dropping equalities may reorder them */
        dropped = 0;
        for (j = bmap->n_div - 1; j >= 0; --j) {
                for (i = 0; i < bmap->n_eq; ++i)
                        if (!isl_int_is_zero(bmap->eq[i][1 + total + j]))
                                break;
                if (i < bmap->n_eq) {
                        bmap = isl_basic_map_drop_div(bmap, j);
                        isl_basic_map_drop_equality(bmap, i);
                        ++dropped;
                }
        }
        pos[0] = 0;
        needed = 0;
        for (i = 1; i < T->n_row; ++i) {
                if (isl_int_is_one(T->row[i][i]))
                        pos[i] = i;
                else
                        needed++;
        }
        if (needed > dropped) {
                bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim),
                                needed, needed, 0);
                if (!bmap)
                        goto error;
        }
        for (i = 1; i < T->n_row; ++i) {
                if (isl_int_is_one(T->row[i][i]))
                        continue;
                k = isl_basic_map_alloc_div(bmap);
                pos[i] = 1 + total + k;
                isl_seq_clr(bmap->div[k] + 1, 1 + total + bmap->n_div);
                isl_int_set(bmap->div[k][0], T->row[i][i]);
                if (C2)
                        isl_seq_cpy(bmap->div[k] + 1, C2->row[i], 1 + total);
                else
                        isl_int_set_si(bmap->div[k][1 + i], 1);
                for (j = 0; j < i; ++j) {
                        if (isl_int_is_zero(T->row[i][j]))
                                continue;
                        if (pos[j] < T->n_row && C2)
                                isl_seq_submul(bmap->div[k] + 1, T->row[i][j],
                                                C2->row[pos[j]], 1 + total);
                        else
                                isl_int_neg(bmap->div[k][1 + pos[j]],
                                                                T->row[i][j]);
                }
                j = isl_basic_map_alloc_equality(bmap);
                isl_seq_neg(bmap->eq[j], bmap->div[k]+1, 1+total+bmap->n_div);
                isl_int_set(bmap->eq[j][pos[i]], bmap->div[k][0]);
        }
        free(pos);
        isl_mat_free(bmap->ctx, C2);
        isl_mat_free(bmap->ctx, T);

        *progress = 1;
done:
        ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);

        return bmap;
error:
        isl_mat_free(bmap->ctx, C);
        isl_mat_free(bmap->ctx, C2);
        isl_mat_free(bmap->ctx, T);
        return bmap;
}

static struct isl_basic_map *remove_duplicate_constraints(
        struct isl_basic_map *bmap, int *progress)
{
        unsigned int size;
        isl_int ***index;
        int k, l, h;
        int bits;
        unsigned total = isl_basic_map_total_dim(bmap);
        isl_int sum;

        if (bmap->n_ineq <= 1)
                return bmap;

        size = round_up(4 * (bmap->n_ineq+1) / 3 - 1);
        bits = ffs(size) - 1;
        index = isl_calloc_array(ctx, isl_int **, size);
        if (!index)
                return bmap;

        index[isl_seq_get_hash_bits(bmap->ineq[0]+1, total, bits)] = &bmap->ineq[0];
        for (k = 1; k < bmap->n_ineq; ++k) {
                h = hash_index(index, size, bits, bmap, k);
                if (!index[h]) {
                        index[h] = &bmap->ineq[k];
                        continue;
                }
                if (progress)
                        *progress = 1;
                l = index[h] - &bmap->ineq[0];
                if (isl_int_lt(bmap->ineq[k][0], bmap->ineq[l][0]))
                        swap_inequality(bmap, k, l);
                isl_basic_map_drop_inequality(bmap, k);
                --k;
        }
        isl_int_init(sum);
        for (k = 0; k < bmap->n_ineq-1; ++k) {
                isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
                h = hash_index(index, size, bits, bmap, k);
                isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
                if (!index[h])
                        continue;
                l = index[h] - &bmap->ineq[0];
                isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0]);
                if (isl_int_is_pos(sum))
                        continue;
                if (isl_int_is_zero(sum)) {
                        /* We need to break out of the loop after these
                         * changes since the contents of the hash
                         * will no longer be valid.
                         * Plus, we probably we want to regauss first.
                         */
                        isl_basic_map_drop_inequality(bmap, l);
                        isl_basic_map_inequality_to_equality(bmap, k);
                } else
                        bmap = isl_basic_map_set_to_empty(bmap);
                break;
        }
        isl_int_clear(sum);

        free(index);
        return bmap;
}


struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
{
        int progress = 1;
        if (!bmap)
                return NULL;
        while (progress) {
                progress = 0;
                bmap = isl_basic_map_normalize_constraints(bmap);
                bmap = eliminate_divs_eq(bmap, &progress);
                bmap = eliminate_divs_ineq(bmap, &progress);
                bmap = isl_basic_map_gauss(bmap, &progress);
                /* requires equalities in normal form */
                bmap = normalize_divs(bmap, &progress);
                bmap = remove_duplicate_divs(bmap, &progress);
                bmap = remove_duplicate_constraints(bmap, &progress);
        }
        return bmap;
}

struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset)
{
        return (struct isl_basic_set *)
                isl_basic_map_simplify((struct isl_basic_map *)bset);
}


/* If the only constraints a div d=floor(f/m)
 * appears in are its two defining constraints
 *
 *      f - m d >=0
 *      -(f - (m - 1)) + m d >= 0
 *
 * then it can safely be removed.
 */
static int div_is_redundant(struct isl_basic_map *bmap, int div)
{
        int i;
        unsigned pos = 1 + isl_dim_total(bmap->dim) + div;

        for (i = 0; i < bmap->n_eq; ++i)
                if (!isl_int_is_zero(bmap->eq[i][pos]))
                        return 0;

        for (i = 0; i < bmap->n_ineq; ++i) {
                if (isl_int_is_zero(bmap->ineq[i][pos]))
                        continue;
                if (isl_int_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
                        int neg;
                        isl_int_sub(bmap->div[div][1],
                                        bmap->div[div][1], bmap->div[div][0]);
                        isl_int_add_ui(bmap->div[div][1], bmap->div[div][1], 1);
                        neg = isl_seq_is_neg(bmap->ineq[i], bmap->div[div]+1, pos);
                        isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
                        isl_int_add(bmap->div[div][1],
                                        bmap->div[div][1], bmap->div[div][0]);
                        if (!neg)
                                return 0;
                        if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
                                                    bmap->n_div-div-1) != -1)
                                return 0;
                } else if (isl_int_abs_eq(bmap->ineq[i][pos], bmap->div[div][0])) {
                        if (!isl_seq_eq(bmap->ineq[i], bmap->div[div]+1, pos))
                                return 0;
                        if (isl_seq_first_non_zero(bmap->ineq[i]+pos+1,
                                                    bmap->n_div-div-1) != -1)
                                return 0;
                } else
                        return 0;
        }

        for (i = 0; i < bmap->n_div; ++i)
                if (!isl_int_is_zero(bmap->div[i][1+pos]))
                        return 0;

        return 1;
}

/*
 * Remove divs that don't occur in any of the constraints or other divs.
 * These can arise when dropping some of the variables in a quast
 * returned by piplib.
 */
static struct isl_basic_map *remove_redundant_divs(struct isl_basic_map *bmap)
{
        int i;

        if (!bmap)
                return NULL;

        for (i = bmap->n_div-1; i >= 0; --i) {
                if (!div_is_redundant(bmap, i))
                        continue;
                bmap = isl_basic_map_drop_div(bmap, i);
        }
        return bmap;
}

struct isl_basic_map *isl_basic_map_finalize(struct isl_basic_map *bmap)
{
        bmap = remove_redundant_divs(bmap);
        if (!bmap)
                return NULL;
        ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
        return bmap;
}

struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset)
{
        return (struct isl_basic_set *)
                isl_basic_map_finalize((struct isl_basic_map *)bset);
}

struct isl_set *isl_set_finalize(struct isl_set *set)
{
        int i;

        if (!set)
                return NULL;
        for (i = 0; i < set->n; ++i) {
                set->p[i] = isl_basic_set_finalize(set->p[i]);
                if (!set->p[i])
                        goto error;
        }
        return set;
error:
        isl_set_free(set);
        return NULL;
}

struct isl_map *isl_map_finalize(struct isl_map *map)
{
        int i;

        if (!map)
                return NULL;
        for (i = 0; i < map->n; ++i) {
                map->p[i] = isl_basic_map_finalize(map->p[i]);
                if (!map->p[i])
                        goto error;
        }
        ISL_F_CLR(map, ISL_MAP_NORMALIZED);
        return map;
error:
        isl_map_free(map);
        return NULL;
}


/* Remove any div that is defined in terms of the given variable.
 */
static struct isl_basic_map *remove_dependent_vars(struct isl_basic_map *bmap,
                                                                        int pos)
{
        int i;
        unsigned dim = isl_dim_total(bmap->dim);

        for (i = 0; i < bmap->n_div; ++i) {
                if (isl_int_is_zero(bmap->div[i][0]))
                        continue;
                if (isl_int_is_zero(bmap->div[i][1+1+pos]))
                        continue;
                bmap = isl_basic_map_eliminate_vars(bmap, dim + i, 1);
                if (!bmap)
                        return NULL;
        }
        return bmap;
}

/* Eliminate the specified variables from the constraints using
 * Fourier-Motzkin.  The variables themselves are not removed.
 */
struct isl_basic_map *isl_basic_map_eliminate_vars(
        struct isl_basic_map *bmap, unsigned pos, unsigned n)
{
        int d;
        int i, j, k;
        unsigned total;

        if (n == 0)
                return bmap;
        if (!bmap)
                return NULL;
        total = isl_basic_map_total_dim(bmap);

        bmap = isl_basic_map_cow(bmap);
        for (d = pos + n - 1; d >= 0 && d >= pos; --d)
                bmap = remove_dependent_vars(bmap, d);

        for (d = pos + n - 1;
             d >= 0 && d >= total - bmap->n_div && d >= pos; --d)
                isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total);
        for (d = pos + n - 1; d >= 0 && d >= pos; --d) {
                int n_lower, n_upper;
                if (!bmap)
                        return NULL;
                for (i = 0; i < bmap->n_eq; ++i) {
                        if (isl_int_is_zero(bmap->eq[i][1+d]))
                                continue;
                        eliminate_var_using_equality(bmap, d, bmap->eq[i], NULL);
                        isl_basic_map_drop_equality(bmap, i);
                        break;
                }
                if (i < bmap->n_eq)
                        continue;
                n_lower = 0;
                n_upper = 0;
                for (i = 0; i < bmap->n_ineq; ++i) {
                        if (isl_int_is_pos(bmap->ineq[i][1+d]))
                                n_lower++;
                        else if (isl_int_is_neg(bmap->ineq[i][1+d]))
                                n_upper++;
                }
                bmap = isl_basic_map_extend_constraints(bmap,
                                0, n_lower * n_upper);
                for (i = bmap->n_ineq - 1; i >= 0; --i) {
                        int last;
                        if (isl_int_is_zero(bmap->ineq[i][1+d]))
                                continue;
                        last = -1;
                        for (j = 0; j < i; ++j) {
                                if (isl_int_is_zero(bmap->ineq[j][1+d]))
                                        continue;
                                last = j;
                                if (isl_int_sgn(bmap->ineq[i][1+d]) ==
                                    isl_int_sgn(bmap->ineq[j][1+d]))
                                        continue;
                                k = isl_basic_map_alloc_inequality(bmap);
                                if (k < 0)
                                        goto error;
                                isl_seq_cpy(bmap->ineq[k], bmap->ineq[i],
                                                1+total);
                                isl_seq_elim(bmap->ineq[k], bmap->ineq[j],
                                                1+d, 1+total, NULL);
                        }
                        isl_basic_map_drop_inequality(bmap, i);
                        i = last + 1;
                }
                if (n_lower > 0 && n_upper > 0) {
                        bmap = isl_basic_map_normalize_constraints(bmap);
                        bmap = remove_duplicate_constraints(bmap, NULL);
                        bmap = isl_basic_map_gauss(bmap, NULL);
                        bmap = isl_basic_map_convex_hull(bmap);
                        if (!bmap)
                                goto error;
                        if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
                                break;
                }
        }
        ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
        return bmap;
error:
        isl_basic_map_free(bmap);
        return NULL;
}

struct isl_basic_set *isl_basic_set_eliminate_vars(
        struct isl_basic_set *bset, unsigned pos, unsigned n)
{
        return (struct isl_basic_set *)isl_basic_map_eliminate_vars(
                        (struct isl_basic_map *)bset, pos, n);
}

/* Don't assume equalities are in order, because align_divs
 * may have changed the order of the divs.
 */
static void compute_elimination_index(struct isl_basic_map *bmap, int *elim)
{
        int d, i;
        unsigned total;

        total = isl_dim_total(bmap->dim);
        for (d = 0; d < total; ++d)
                elim[d] = -1;
        for (i = 0; i < bmap->n_eq; ++i) {
                for (d = total - 1; d >= 0; --d) {
                        if (isl_int_is_zero(bmap->eq[i][1+d]))
                                continue;
                        elim[d] = i;
                        break;
                }
        }
}

static void set_compute_elimination_index(struct isl_basic_set *bset, int *elim)
{
        return compute_elimination_index((struct isl_basic_map *)bset, elim);
}

static int reduced_using_equalities(isl_int *dst, isl_int *src,
        struct isl_basic_map *bmap, int *elim)
{
        int d, i;
        int copied = 0;
        unsigned total;

        total = isl_dim_total(bmap->dim);
        for (d = total - 1; d >= 0; --d) {
                if (isl_int_is_zero(src[1+d]))
                        continue;
                if (elim[d] == -1)
                        continue;
                if (!copied) {
                        isl_seq_cpy(dst, src, 1 + total);
                        copied = 1;
                }
                isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL);
        }
        return copied;
}

static int set_reduced_using_equalities(isl_int *dst, isl_int *src,
        struct isl_basic_set *bset, int *elim)
{
        return reduced_using_equalities(dst, src,
                                        (struct isl_basic_map *)bset, elim);
}

static struct isl_basic_set *isl_basic_set_reduce_using_equalities(
        struct isl_basic_set *bset, struct isl_basic_set *context)
{
        int i;
        int *elim;

        if (!bset || !context)
                goto error;

        bset = isl_basic_set_cow(bset);
        if (!bset)
                goto error;

        elim = isl_alloc_array(ctx, int, isl_basic_set_n_dim(bset));
        if (!elim)
                goto error;
        set_compute_elimination_index(context, elim);
        for (i = 0; i < bset->n_eq; ++i)
                set_reduced_using_equalities(bset->eq[i], bset->eq[i],
                                                        context, elim);
        for (i = 0; i < bset->n_ineq; ++i)
                set_reduced_using_equalities(bset->ineq[i], bset->ineq[i],
                                                        context, elim);
        isl_basic_set_free(context);
        free(elim);
        bset = isl_basic_set_simplify(bset);
        bset = isl_basic_set_finalize(bset);
        return bset;
error:
        isl_basic_set_free(bset);
        isl_basic_set_free(context);
        return NULL;
}

static struct isl_basic_set *remove_shifted_constraints(
        struct isl_basic_set *bset, struct isl_basic_set *context)
{
        unsigned int size;
        isl_int ***index;
        int bits;
        int k, h, l;

        if (!bset)
                return NULL;

        size = round_up(4 * (context->n_ineq+1) / 3 - 1);
        bits = ffs(size) - 1;
        index = isl_calloc_array(ctx, isl_int **, size);
        if (!index)
                return bset;

        for (k = 0; k < context->n_ineq; ++k) {
                h = set_hash_index(index, size, bits, context, k);
                index[h] = &context->ineq[k];
        }
        for (k = 0; k < bset->n_ineq; ++k) {
                h = set_hash_index(index, size, bits, bset, k);
                if (!index[h])
                        continue;
                l = index[h] - &context->ineq[0];
                if (isl_int_lt(bset->ineq[k][0], context->ineq[l][0]))
                        continue;
                bset = isl_basic_set_cow(bset);
                if (!bset)
                        goto error;
                isl_basic_set_drop_inequality(bset, k);
                --k;
        }
        free(index);
        return bset;
error:
        free(index);
        return bset;
}

/* Tighten (decrease) the constant terms of the inequalities based
 * on the equalities, without removing any integer points.
 * For example, if there is an equality
 *
 *              i = 3 * j
 *
 * and an inequality
 *
 *              i >= 1
 *
 * then we want to replace the inequality by
 *
 *              i >= 3
 *
 * We do this by computing a variable compression and translating
 * the constraints to the compressed space.
 * If any constraint has coefficients (except the contant term)
 * with a common factor "f", then we can replace the constant term "c"
 * by
 *
 *              f * floor(c/f)
 *
 * That is, we add
 *
 *              f * floor(c/f) - c = -fract(c/f)
 *
 * and we can add the same value to the original constraint.
 *
 * In the example, the compressed space only contains "j",
 * and the inequality translates to
 *
 *              3 * j - 1 >= 0
 *
 * We add -fract(-1/3) = -2 to the original constraint to obtain
 *
 *              i - 3 >= 0
 */
static struct isl_basic_set *normalize_constraints_in_compressed_space(
        struct isl_basic_set *bset)
{
        int i;
        unsigned total;
        struct isl_mat *B, *C;
        isl_int gcd;

        if (!bset)
                return NULL;

        if (ISL_F_ISSET(bset, ISL_BASIC_SET_RATIONAL))
                return bset;

        bset = isl_basic_set_cow(bset);
        if (!bset)
                return NULL;

        total = isl_basic_set_total_dim(bset);
        B = isl_mat_sub_alloc(bset->ctx, bset->eq, 0, bset->n_eq, 0, 1 + total);
        C = isl_mat_variable_compression(bset->ctx, B, NULL);
        if (!C)
                return bset;
        if (C->n_col == 0) {
                isl_mat_free(bset->ctx, C);
                return isl_basic_set_set_to_empty(bset);
        }
        B = isl_mat_sub_alloc(bset->ctx, bset->ineq,
                                                0, bset->n_ineq, 0, 1 + total);
        C = isl_mat_product(bset->ctx, B, C);
        if (!C)
                return bset;

        isl_int_init(gcd);
        for (i = 0; i < bset->n_ineq; ++i) {
                isl_seq_gcd(C->row[i] + 1, C->n_col - 1, &gcd);
                if (isl_int_is_one(gcd))
                        continue;
                isl_int_fdiv_r(C->row[i][0], C->row[i][0], gcd);
                isl_int_sub(bset->ineq[i][0], bset->ineq[i][0], C->row[i][0]);
        }
        isl_int_clear(gcd);

        isl_mat_free(bset->ctx, C);

        return bset;
}

/* Remove all information from bset that is redundant in the context
 * of context.  In particular, equalities that are linear combinations
 * of those in context are removed.  Then the inequalities that are
 * redundant in the context of the equalities and inequalities of
 * context are removed.
 *
 * We first simplify the constraints of "bset" in the context of the
 * equalities of "context".
 * Then we simplify the inequalities of the context in the context
 * of the equalities of bset and remove the inequalities from "bset"
 * that are obviously redundant with respect to some inequality in "context".
 *
 * If there are any inequalities left, we construct a tableau for
 * the context and then add the inequalities of "bset".
 * Before adding these equalities, we freeze all constraints such that
 * they won't be considered redundant in terms of the constraints of "bset".
 * Then we detect all equalities and redundant constraints (among the
 * constraints that weren't frozen) and update bset according to the results.
 * We have to be careful here because we don't want any of the context
 * constraints to remain and because we haven't added the equalities of "bset"
 * to the tableau so we temporarily have to pretend that there were no
 * equalities.
 */
static struct isl_basic_set *uset_gist(struct isl_basic_set *bset,
        struct isl_basic_set *context)
{
        int i;
        struct isl_tab *tab;
        unsigned context_ineq, bset_eq;
        struct isl_basic_set *combined = NULL;

        if (!context || !bset)
                goto error;

        if (context->n_eq > 0)
                bset = isl_basic_set_reduce_using_equalities(bset,
                                        isl_basic_set_copy(context));
        if (!bset)
                goto error;

        if (bset->n_eq > 0) {
                struct isl_basic_set *affine_hull;
                affine_hull = isl_basic_set_copy(bset);
                affine_hull = isl_basic_set_cow(affine_hull);
                if (!affine_hull)
                        goto error;
                isl_basic_set_free_inequality(affine_hull, affine_hull->n_ineq);
                context = isl_basic_set_intersect(context, affine_hull);
                context = isl_basic_set_gauss(context, NULL);
                context = normalize_constraints_in_compressed_space(context);
        }
        if (!context)
                goto error;
        if (ISL_F_ISSET(context, ISL_BASIC_SET_EMPTY)) {
                isl_basic_set_free(bset);
                return context;
        }
        if (!context->n_ineq)
                goto done;
        bset = remove_shifted_constraints(bset, context);
        if (!bset->n_ineq)
                goto done;
        isl_basic_set_free_equality(context, context->n_eq);
        context_ineq = context->n_ineq;
        combined = isl_basic_set_cow(isl_basic_set_copy(context));
        combined = isl_basic_set_extend_constraints(combined,
                                                    bset->n_eq, bset->n_ineq);
        tab = isl_tab_from_basic_set(combined);
        if (!tab)
                goto error;
        for (i = 0; i < context_ineq; ++i)
                tab->con[i].frozen = 1;
        tab = isl_tab_extend(bset->ctx, tab, bset->n_ineq);
        if (!tab)
                goto error;
        for (i = 0; i < bset->n_ineq; ++i)
                tab = isl_tab_add_ineq(bset->ctx, tab, bset->ineq[i]);
        bset = isl_basic_set_add_constraints(combined, bset, 0);
        tab = isl_tab_detect_equalities(bset->ctx, tab);
        tab = isl_tab_detect_redundant(bset->ctx, tab);
        if (!tab)
                goto error2;
        for (i = 0; i < context_ineq; ++i) {
                tab->con[i].is_zero = 0;
                tab->con[i].is_redundant = 1;
        }
        bset_eq = bset->n_eq;
        bset->n_eq = 0;
        bset = isl_basic_set_update_from_tab(bset, tab);
        bset->n_eq = bset_eq;
        isl_tab_free(bset->ctx, tab);
        ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
        ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
done:
        bset = isl_basic_set_simplify(bset);
        bset = isl_basic_set_finalize(bset);
        isl_basic_set_free(context);
        return bset;
error:
        isl_basic_set_free(combined);
error2:
        isl_basic_set_free(bset);
        isl_basic_set_free(context);
        return NULL;
}

struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
        struct isl_basic_map *context)
{
        struct isl_basic_set *bset;

        if (!bmap || !context)
                goto error;

        bmap = isl_basic_map_convex_hull(bmap);
        context = isl_basic_map_convex_hull(context);

        context = isl_basic_map_align_divs(context, bmap);
        bmap = isl_basic_map_align_divs(bmap, context);

        bset = uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap)),
                         isl_basic_map_underlying_set(context));

        return isl_basic_map_overlying_set(bset, bmap);
error:
        isl_basic_map_free(bmap);
        isl_basic_map_free(context);
        return NULL;
}

/*
 * Assumes context has no implicit divs.
 */
struct isl_map *isl_map_gist(struct isl_map *map, struct isl_basic_map *context)
{
        int i;

        context = isl_basic_map_convex_hull(context);
        map = isl_map_cow(map);
        if (!map || !context)
                return NULL;
        isl_assert(map->ctx, isl_dim_equal(map->dim, context->dim), goto error);
        map = isl_map_compute_divs(map);
        for (i = 0; i < map->n; ++i)
                context = isl_basic_map_align_divs(context, map->p[i]);
        for (i = 0; i < map->n; ++i) {
                map->p[i] = isl_basic_map_gist(map->p[i],
                                                isl_basic_map_copy(context));
                if (!map->p[i])
                        goto error;
        }
        isl_basic_map_free(context);
        ISL_F_CLR(map, ISL_MAP_NORMALIZED);
        return map;
error:
        isl_map_free(map);
        isl_basic_map_free(context);
        return NULL;
}

struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
                                                struct isl_basic_set *context)
{
        return (struct isl_basic_set *)isl_basic_map_gist(
                (struct isl_basic_map *)bset, (struct isl_basic_map *)context);
}

struct isl_set *isl_set_gist(struct isl_set *set, struct isl_basic_set *context)
{
        return (struct isl_set *)isl_map_gist((struct isl_map *)set,
                                        (struct isl_basic_map *)context);
}

/* Quick check to see if two basic maps are disjoint.
 * In particular, we reduce the equalities and inequalities of
 * one basic map in the context of the equalities of the other
 * basic map and check if we get a contradiction.
 */
int isl_basic_map_fast_is_disjoint(struct isl_basic_map *bmap1,
        struct isl_basic_map *bmap2)
{
        struct isl_vec *v = NULL;
        int *elim = NULL;
        unsigned total;
        int d, i;

        if (!bmap1 || !bmap2)
                return -1;
        isl_assert(bmap1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim),
                        return -1);
        if (bmap1->n_div || bmap2->n_div)
                return 0;
        if (!bmap1->n_eq && !bmap2->n_eq)
                return 0;

        total = isl_dim_total(bmap1->dim);
        if (total == 0)
                return 0;
        v = isl_vec_alloc(bmap1->ctx, 1 + total);
        if (!v)
                goto error;
        elim = isl_alloc_array(bmap1->ctx, int, total);
        if (!elim)
                goto error;
        compute_elimination_index(bmap1, elim);
        for (i = 0; i < bmap2->n_eq; ++i) {
                int reduced;
                reduced = reduced_using_equalities(v->block.data, bmap2->eq[i],
                                                        bmap1, elim);
                if (reduced && !isl_int_is_zero(v->block.data[0]) &&
                    isl_seq_first_non_zero(v->block.data + 1, total) == -1)
                        goto disjoint;
        }
        for (i = 0; i < bmap2->n_ineq; ++i) {
                int reduced;
                reduced = reduced_using_equalities(v->block.data,
                                                bmap2->ineq[i], bmap1, elim);
                if (reduced && isl_int_is_neg(v->block.data[0]) &&
                    isl_seq_first_non_zero(v->block.data + 1, total) == -1)
                        goto disjoint;
        }
        compute_elimination_index(bmap2, elim);
        for (i = 0; i < bmap1->n_ineq; ++i) {
                int reduced;
                reduced = reduced_using_equalities(v->block.data,
                                                bmap1->ineq[i], bmap2, elim);
                if (reduced && isl_int_is_neg(v->block.data[0]) &&
                    isl_seq_first_non_zero(v->block.data + 1, total) == -1)
                        goto disjoint;
        }
        isl_vec_free(bmap1->ctx, v);
        free(elim);
        return 0;
disjoint:
        isl_vec_free(bmap1->ctx, v);
        free(elim);
        return 1;
error:
        isl_vec_free(bmap1->ctx, v);
        free(elim);
        return -1;
}

int isl_basic_set_fast_is_disjoint(struct isl_basic_set *bset1,
        struct isl_basic_set *bset2)
{
        return isl_basic_map_fast_is_disjoint((struct isl_basic_map *)bset1,
                                              (struct isl_basic_map *)bset2);
}

int isl_map_fast_is_disjoint(struct isl_map *map1, struct isl_map *map2)
{
        int i, j;

        if (!map1 || !map2)
                return -1;

        if (isl_map_fast_is_equal(map1, map2))
                return 0;

        for (i = 0; i < map1->n; ++i) {
                for (j = 0; j < map2->n; ++j) {
                        int d = isl_basic_map_fast_is_disjoint(map1->p[i],
                                                               map2->p[j]);
                        if (d != 1)
                                return d;
                }
        }
        return 1;
}

int isl_set_fast_is_disjoint(struct isl_set *set1, struct isl_set *set2)
{
        return isl_map_fast_is_disjoint((struct isl_map *)set1,
                                        (struct isl_map *)set2);
}