AUTHORS: change Uday's name to Uday Bondhugula

[isl.git] / isl_local_space.c

/*
 * Copyright 2011      INRIA Saclay
 * Copyright 2012-2014 Ecole Normale Superieure
 *
 * Use of this software is governed by the MIT license
 *
 * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
 * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
 * 91893 Orsay, France
 * and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
 */

#include <isl_ctx_private.h>
#include <isl/id.h>
#include <isl_map_private.h>
#include <isl_local_space_private.h>
#include <isl_space_private.h>
#include <isl_mat_private.h>
#include <isl_aff_private.h>
#include <isl_vec_private.h>
#include <isl_point_private.h>
#include <isl_seq.h>
#include <isl_local.h>

isl_ctx *isl_local_space_get_ctx(__isl_keep isl_local_space *ls)
{
        return ls ? ls->dim->ctx : NULL;
}

/* Return a hash value that digests "ls".
 */
uint32_t isl_local_space_get_hash(__isl_keep isl_local_space *ls)
{
        uint32_t hash, space_hash, div_hash;

        if (!ls)
                return 0;

        hash = isl_hash_init();
        space_hash = isl_space_get_hash(ls->dim);
        isl_hash_hash(hash, space_hash);
        div_hash = isl_mat_get_hash(ls->div);
        isl_hash_hash(hash, div_hash);

        return hash;
}

__isl_give isl_local_space *isl_local_space_alloc_div(__isl_take isl_space *dim,
        __isl_take isl_mat *div)
{
        isl_ctx *ctx;
        isl_local_space *ls = NULL;

        if (!dim || !div)
                goto error;

        ctx = isl_space_get_ctx(dim);
        ls = isl_calloc_type(ctx, struct isl_local_space);
        if (!ls)
                goto error;

        ls->ref = 1;
        ls->dim = dim;
        ls->div = div;

        return ls;
error:
        isl_mat_free(div);
        isl_space_free(dim);
        isl_local_space_free(ls);
        return NULL;
}

__isl_give isl_local_space *isl_local_space_alloc(__isl_take isl_space *dim,
        unsigned n_div)
{
        isl_ctx *ctx;
        isl_mat *div;
        unsigned total;

        if (!dim)
                return NULL;

        total = isl_space_dim(dim, isl_dim_all);

        ctx = isl_space_get_ctx(dim);
        div = isl_mat_alloc(ctx, n_div, 1 + 1 + total + n_div);
        return isl_local_space_alloc_div(dim, div);
}

__isl_give isl_local_space *isl_local_space_from_space(__isl_take isl_space *dim)
{
        return isl_local_space_alloc(dim, 0);
}

__isl_give isl_local_space *isl_local_space_copy(__isl_keep isl_local_space *ls)
{
        if (!ls)
                return NULL;

        ls->ref++;
        return ls;
}

__isl_give isl_local_space *isl_local_space_dup(__isl_keep isl_local_space *ls)
{
        if (!ls)
                return NULL;

        return isl_local_space_alloc_div(isl_space_copy(ls->dim),
                                         isl_mat_copy(ls->div));

}

__isl_give isl_local_space *isl_local_space_cow(__isl_take isl_local_space *ls)
{
        if (!ls)
                return NULL;

        if (ls->ref == 1)
                return ls;
        ls->ref--;
        return isl_local_space_dup(ls);
}

__isl_null isl_local_space *isl_local_space_free(
        __isl_take isl_local_space *ls)
{
        if (!ls)
                return NULL;

        if (--ls->ref > 0)
                return NULL;

        isl_space_free(ls->dim);
        isl_mat_free(ls->div);

        free(ls);

        return NULL;
}

/* Is the local space that of a parameter domain?
 */
isl_bool isl_local_space_is_params(__isl_keep isl_local_space *ls)
{
        if (!ls)
                return isl_bool_error;
        return isl_space_is_params(ls->dim);
}

/* Is the local space that of a set?
 */
isl_bool isl_local_space_is_set(__isl_keep isl_local_space *ls)
{
        return ls ? isl_space_is_set(ls->dim) : isl_bool_error;
}

/* Do "ls1" and "ls2" have the same space?
 */
isl_bool isl_local_space_has_equal_space(__isl_keep isl_local_space *ls1,
        __isl_keep isl_local_space *ls2)
{
        if (!ls1 || !ls2)
                return isl_bool_error;

        return isl_space_is_equal(ls1->dim, ls2->dim);
}

/* Is the space of "ls" equal to "space"?
 */
isl_bool isl_local_space_has_space(__isl_keep isl_local_space *ls,
        __isl_keep isl_space *space)
{
        return isl_space_is_equal(isl_local_space_peek_space(ls), space);
}

/* Check that the space of "ls" is equal to "space".
 */
static isl_stat isl_local_space_check_has_space(__isl_keep isl_local_space *ls,
        __isl_keep isl_space *space)
{
        isl_bool ok;

        ok = isl_local_space_has_space(ls, space);
        if (ok < 0)
                return isl_stat_error;
        if (!ok)
                isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
                        "spaces don't match", return isl_stat_error);
        return isl_stat_ok;
}

/* Return true if the two local spaces are identical, with identical
 * expressions for the integer divisions.
 */
isl_bool isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
        __isl_keep isl_local_space *ls2)
{
        isl_bool equal;

        equal = isl_local_space_has_equal_space(ls1, ls2);
        if (equal < 0 || !equal)
                return equal;

        if (!isl_local_space_divs_known(ls1))
                return isl_bool_false;
        if (!isl_local_space_divs_known(ls2))
                return isl_bool_false;

        return isl_mat_is_equal(ls1->div, ls2->div);
}

/* Compare two isl_local_spaces.
 *
 * Return -1 if "ls1" is "smaller" than "ls2", 1 if "ls1" is "greater"
 * than "ls2" and 0 if they are equal.
 */
int isl_local_space_cmp(__isl_keep isl_local_space *ls1,
        __isl_keep isl_local_space *ls2)
{
        int cmp;

        if (ls1 == ls2)
                return 0;
        if (!ls1)
                return -1;
        if (!ls2)
                return 1;

        cmp = isl_space_cmp(ls1->dim, ls2->dim);
        if (cmp != 0)
                return cmp;

        return isl_local_cmp(ls1->div, ls2->div);
}

int isl_local_space_dim(__isl_keep isl_local_space *ls,
        enum isl_dim_type type)
{
        if (!ls)
                return 0;
        if (type == isl_dim_div)
                return ls->div->n_row;
        if (type == isl_dim_all)
                return isl_space_dim(ls->dim, isl_dim_all) + ls->div->n_row;
        return isl_space_dim(ls->dim, type);
}

unsigned isl_local_space_offset(__isl_keep isl_local_space *ls,
        enum isl_dim_type type)
{
        isl_space *dim;

        if (!ls)
                return 0;

        dim = ls->dim;
        switch (type) {
        case isl_dim_cst:       return 0;
        case isl_dim_param:     return 1;
        case isl_dim_in:        return 1 + dim->nparam;
        case isl_dim_out:       return 1 + dim->nparam + dim->n_in;
        case isl_dim_div:       return 1 + dim->nparam + dim->n_in + dim->n_out;
        default:                return 0;
        }
}

/* Return the position of the dimension of the given type and name
 * in "ls".
 * Return -1 if no such dimension can be found.
 */
int isl_local_space_find_dim_by_name(__isl_keep isl_local_space *ls,
        enum isl_dim_type type, const char *name)
{
        if (!ls)
                return -1;
        if (type == isl_dim_div)
                return -1;
        return isl_space_find_dim_by_name(ls->dim, type, name);
}

/* Does the given dimension have a name?
 */
isl_bool isl_local_space_has_dim_name(__isl_keep isl_local_space *ls,
        enum isl_dim_type type, unsigned pos)
{
        return ls ? isl_space_has_dim_name(ls->dim, type, pos) : isl_bool_error;
}

const char *isl_local_space_get_dim_name(__isl_keep isl_local_space *ls,
        enum isl_dim_type type, unsigned pos)
{
        return ls ? isl_space_get_dim_name(ls->dim, type, pos) : NULL;
}

isl_bool isl_local_space_has_dim_id(__isl_keep isl_local_space *ls,
        enum isl_dim_type type, unsigned pos)
{
        return ls ? isl_space_has_dim_id(ls->dim, type, pos) : isl_bool_error;
}

__isl_give isl_id *isl_local_space_get_dim_id(__isl_keep isl_local_space *ls,
        enum isl_dim_type type, unsigned pos)
{
        return ls ? isl_space_get_dim_id(ls->dim, type, pos) : NULL;
}

/* Return the argument of the integer division at position "pos" in "ls".
 * All local variables in "ls" are known to have a (complete) explicit
 * representation.
 */
static __isl_give isl_aff *extract_div(__isl_keep isl_local_space *ls, int pos)
{
        isl_aff *aff;

        aff = isl_aff_alloc(isl_local_space_copy(ls));
        if (!aff)
                return NULL;
        isl_seq_cpy(aff->v->el, ls->div->row[pos], aff->v->size);
        return aff;
}

/* Return the argument of the integer division at position "pos" in "ls".
 * The integer division at that position is known to have a complete
 * explicit representation, but some of the others do not.
 * Remove them first because the domain of an isl_aff
 * is not allowed to have unknown local variables.
 */
static __isl_give isl_aff *drop_unknown_divs_and_extract_div(
        __isl_keep isl_local_space *ls, int pos)
{
        int i, n;
        isl_bool unknown;
        isl_aff *aff;

        ls = isl_local_space_copy(ls);
        n = isl_local_space_dim(ls, isl_dim_div);
        for (i = n - 1; i >= 0; --i) {
                unknown = isl_local_space_div_is_marked_unknown(ls, i);
                if (unknown < 0)
                        ls = isl_local_space_free(ls);
                else if (!unknown)
                        continue;
                ls = isl_local_space_drop_dims(ls, isl_dim_div, i, 1);
                if (pos > i)
                        --pos;
        }
        aff = extract_div(ls, pos);
        isl_local_space_free(ls);
        return aff;
}

/* Return the argument of the integer division at position "pos" in "ls".
 * The integer division is assumed to have a complete explicit
 * representation.  If some of the other integer divisions
 * do not have an explicit representation, then they need
 * to be removed first because the domain of an isl_aff
 * is not allowed to have unknown local variables.
 */
__isl_give isl_aff *isl_local_space_get_div(__isl_keep isl_local_space *ls,
        int pos)
{
        isl_bool known;

        if (!ls)
                return NULL;

        if (pos < 0 || pos >= ls->div->n_row)
                isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
                        "index out of bounds", return NULL);

        known = isl_local_space_div_is_known(ls, pos);
        if (known < 0)
                return NULL;
        if (!known)
                isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
                        "expression of div unknown", return NULL);
        if (!isl_local_space_is_set(ls))
                isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
                        "cannot represent divs of map spaces", return NULL);

        known = isl_local_space_divs_known(ls);
        if (known < 0)
                return NULL;
        if (known)
                return extract_div(ls, pos);
        else
                return drop_unknown_divs_and_extract_div(ls, pos);
}

/* Return the space of "ls".
 */
__isl_keep isl_space *isl_local_space_peek_space(__isl_keep isl_local_space *ls)
{
        if (!ls)
                return NULL;

        return ls->dim;
}

__isl_give isl_space *isl_local_space_get_space(__isl_keep isl_local_space *ls)
{
        return isl_space_copy(isl_local_space_peek_space(ls));
}

/* Return the space of "ls".
 * This may be either a copy or the space itself
 * if there is only one reference to "ls".
 * This allows the space to be modified inplace
 * if both the local space and its space have only a single reference.
 * The caller is not allowed to modify "ls" between this call and
 * a subsequent call to isl_local_space_restore_space.
 * The only exception is that isl_local_space_free can be called instead.
 */
__isl_give isl_space *isl_local_space_take_space(__isl_keep isl_local_space *ls)
{
        isl_space *space;

        if (!ls)
                return NULL;
        if (ls->ref != 1)
                return isl_local_space_get_space(ls);
        space = ls->dim;
        ls->dim = NULL;
        return space;
}

/* Set the space of "ls" to "space", where the space of "ls" may be missing
 * due to a preceding call to isl_local_space_take_space.
 * However, in this case, "ls" only has a single reference and
 * then the call to isl_local_space_cow has no effect.
 */
__isl_give isl_local_space *isl_local_space_restore_space(
        __isl_take isl_local_space *ls, __isl_take isl_space *space)
{
        if (!ls || !space)
                goto error;

        if (ls->dim == space) {
                isl_space_free(space);
                return ls;
        }

        ls = isl_local_space_cow(ls);
        if (!ls)
                goto error;
        isl_space_free(ls->dim);
        ls->dim = space;

        return ls;
error:
        isl_local_space_free(ls);
        isl_space_free(space);
        return NULL;
}

/* Return the local variables of "ls".
 */
__isl_keep isl_local *isl_local_space_peek_local(__isl_keep isl_local_space *ls)
{
        return ls ? ls->div : NULL;
}

/* Replace the identifier of the tuple of type "type" by "id".
 */
__isl_give isl_local_space *isl_local_space_set_tuple_id(
        __isl_take isl_local_space *ls,
        enum isl_dim_type type, __isl_take isl_id *id)
{
        ls = isl_local_space_cow(ls);
        if (!ls)
                goto error;
        ls->dim = isl_space_set_tuple_id(ls->dim, type, id);
        if (!ls->dim)
                return isl_local_space_free(ls);
        return ls;
error:
        isl_id_free(id);
        return NULL;
}

__isl_give isl_local_space *isl_local_space_set_dim_name(
        __isl_take isl_local_space *ls,
        enum isl_dim_type type, unsigned pos, const char *s)
{
        ls = isl_local_space_cow(ls);
        if (!ls)
                return NULL;
        ls->dim = isl_space_set_dim_name(ls->dim, type, pos, s);
        if (!ls->dim)
                return isl_local_space_free(ls);

        return ls;
}

__isl_give isl_local_space *isl_local_space_set_dim_id(
        __isl_take isl_local_space *ls,
        enum isl_dim_type type, unsigned pos, __isl_take isl_id *id)
{
        ls = isl_local_space_cow(ls);
        if (!ls)
                goto error;
        ls->dim = isl_space_set_dim_id(ls->dim, type, pos, id);
        if (!ls->dim)
                return isl_local_space_free(ls);

        return ls;
error:
        isl_id_free(id);
        return NULL;
}

/* Construct a zero-dimensional local space with the given parameter domain.
 */
__isl_give isl_local_space *isl_local_space_set_from_params(
        __isl_take isl_local_space *ls)
{
        isl_space *space;

        space = isl_local_space_take_space(ls);
        space = isl_space_set_from_params(space);
        ls = isl_local_space_restore_space(ls, space);

        return ls;
}

__isl_give isl_local_space *isl_local_space_reset_space(
        __isl_take isl_local_space *ls, __isl_take isl_space *dim)
{
        ls = isl_local_space_cow(ls);
        if (!ls || !dim)
                goto error;

        isl_space_free(ls->dim);
        ls->dim = dim;

        return ls;
error:
        isl_local_space_free(ls);
        isl_space_free(dim);
        return NULL;
}

/* Reorder the columns of the given div definitions according to the
 * given reordering.
 * The order of the divs themselves is assumed not to change.
 */
static __isl_give isl_mat *reorder_divs(__isl_take isl_mat *div,
        __isl_take isl_reordering *r)
{
        int i, j;
        isl_mat *mat;
        int extra;

        if (!div || !r)
                goto error;

        extra = isl_space_dim(r->dim, isl_dim_all) + div->n_row - r->len;
        mat = isl_mat_alloc(div->ctx, div->n_row, div->n_col + extra);
        if (!mat)
                goto error;

        for (i = 0; i < div->n_row; ++i) {
                isl_seq_cpy(mat->row[i], div->row[i], 2);
                isl_seq_clr(mat->row[i] + 2, mat->n_col - 2);
                for (j = 0; j < r->len; ++j)
                        isl_int_set(mat->row[i][2 + r->pos[j]],
                                    div->row[i][2 + j]);
        }

        isl_reordering_free(r);
        isl_mat_free(div);
        return mat;
error:
        isl_reordering_free(r);
        isl_mat_free(div);
        return NULL;
}

/* Reorder the dimensions of "ls" according to the given reordering.
 * The reordering r is assumed to have been extended with the local
 * variables, leaving them in the same order.
 */
__isl_give isl_local_space *isl_local_space_realign(
        __isl_take isl_local_space *ls, __isl_take isl_reordering *r)
{
        ls = isl_local_space_cow(ls);
        if (!ls || !r)
                goto error;

        ls->div = reorder_divs(ls->div, isl_reordering_copy(r));
        if (!ls->div)
                goto error;

        ls = isl_local_space_reset_space(ls, isl_space_copy(r->dim));

        isl_reordering_free(r);
        return ls;
error:
        isl_local_space_free(ls);
        isl_reordering_free(r);
        return NULL;
}

__isl_give isl_local_space *isl_local_space_add_div(
        __isl_take isl_local_space *ls, __isl_take isl_vec *div)
{
        ls = isl_local_space_cow(ls);
        if (!ls || !div)
                goto error;

        if (ls->div->n_col != div->size)
                isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
                        "incompatible dimensions", goto error);

        ls->div = isl_mat_add_zero_cols(ls->div, 1);
        ls->div = isl_mat_add_rows(ls->div, 1);
        if (!ls->div)
                goto error;

        isl_seq_cpy(ls->div->row[ls->div->n_row - 1], div->el, div->size);
        isl_int_set_si(ls->div->row[ls->div->n_row - 1][div->size], 0);

        isl_vec_free(div);
        return ls;
error:
        isl_local_space_free(ls);
        isl_vec_free(div);
        return NULL;
}

__isl_give isl_local_space *isl_local_space_replace_divs(
        __isl_take isl_local_space *ls, __isl_take isl_mat *div)
{
        ls = isl_local_space_cow(ls);

        if (!ls || !div)
                goto error;

        isl_mat_free(ls->div);
        ls->div = div;
        return ls;
error:
        isl_mat_free(div);
        isl_local_space_free(ls);
        return NULL;
}

/* Copy row "s" of "src" to row "d" of "dst", applying the expansion
 * defined by "exp".
 */
static void expand_row(__isl_keep isl_mat *dst, int d,
        __isl_keep isl_mat *src, int s, int *exp)
{
        int i;
        unsigned c = src->n_col - src->n_row;

        isl_seq_cpy(dst->row[d], src->row[s], c);
        isl_seq_clr(dst->row[d] + c, dst->n_col - c);

        for (i = 0; i < s; ++i)
                isl_int_set(dst->row[d][c + exp[i]], src->row[s][c + i]);
}

/* Compare (known) divs.
 * Return non-zero if at least one of the two divs is unknown.
 * In particular, if both divs are unknown, we respect their
 * current order.  Otherwise, we sort the known div after the unknown
 * div only if the known div depends on the unknown div.
 */
static int cmp_row(isl_int *row_i, isl_int *row_j, int i, int j,
        unsigned n_row, unsigned n_col)
{
        int li, lj;
        int unknown_i, unknown_j;

        unknown_i = isl_int_is_zero(row_i[0]);
        unknown_j = isl_int_is_zero(row_j[0]);

        if (unknown_i && unknown_j)
                return i - j;

        if (unknown_i)
                li = n_col - n_row + i;
        else
                li = isl_seq_last_non_zero(row_i, n_col);
        if (unknown_j)
                lj = n_col - n_row + j;
        else
                lj = isl_seq_last_non_zero(row_j, n_col);

        if (li != lj)
                return li - lj;

        return isl_seq_cmp(row_i, row_j, n_col);
}

/* Call cmp_row for divs in a matrix.
 */
int isl_mat_cmp_div(__isl_keep isl_mat *div, int i, int j)
{
        return cmp_row(div->row[i], div->row[j], i, j, div->n_row, div->n_col);
}

/* Call cmp_row for divs in a basic map.
 */
static int bmap_cmp_row(__isl_keep isl_basic_map *bmap, int i, int j,
        unsigned total)
{
        return cmp_row(bmap->div[i], bmap->div[j], i, j, bmap->n_div, total);
}

/* Sort the divs in "bmap".
 *
 * We first make sure divs are placed after divs on which they depend.
 * Then we perform a simple insertion sort based on the same ordering
 * that is used in isl_merge_divs.
 */
__isl_give isl_basic_map *isl_basic_map_sort_divs(
        __isl_take isl_basic_map *bmap)
{
        int i, j;
        unsigned total;

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

        total = 2 + isl_basic_map_total_dim(bmap);
        for (i = 1; i < bmap->n_div; ++i) {
                for (j = i - 1; j >= 0; --j) {
                        if (bmap_cmp_row(bmap, j, j + 1, total) <= 0)
                                break;
                        isl_basic_map_swap_div(bmap, j, j + 1);
                }
        }

        return bmap;
}

/* Sort the divs in the basic maps of "map".
 */
__isl_give isl_map *isl_map_sort_divs(__isl_take isl_map *map)
{
        return isl_map_inline_foreach_basic_map(map, &isl_basic_map_sort_divs);
}

/* Combine the two lists of divs into a single list.
 * For each row i in div1, exp1[i] is set to the position of the corresponding
 * row in the result.  Similarly for div2 and exp2.
 * This function guarantees
 *      exp1[i] >= i
 *      exp1[i+1] > exp1[i]
 * For optimal merging, the two input list should have been sorted.
 */
__isl_give isl_mat *isl_merge_divs(__isl_keep isl_mat *div1,
        __isl_keep isl_mat *div2, int *exp1, int *exp2)
{
        int i, j, k;
        isl_mat *div = NULL;
        unsigned d;

        if (!div1 || !div2)
                return NULL;

        d = div1->n_col - div1->n_row;
        div = isl_mat_alloc(div1->ctx, 1 + div1->n_row + div2->n_row,
                                d + div1->n_row + div2->n_row);
        if (!div)
                return NULL;

        for (i = 0, j = 0, k = 0; i < div1->n_row && j < div2->n_row; ++k) {
                int cmp;

                expand_row(div, k, div1, i, exp1);
                expand_row(div, k + 1, div2, j, exp2);

                cmp = isl_mat_cmp_div(div, k, k + 1);
                if (cmp == 0) {
                        exp1[i++] = k;
                        exp2[j++] = k;
                } else if (cmp < 0) {
                        exp1[i++] = k;
                } else {
                        exp2[j++] = k;
                        isl_seq_cpy(div->row[k], div->row[k + 1], div->n_col);
                }
        }
        for (; i < div1->n_row; ++i, ++k) {
                expand_row(div, k, div1, i, exp1);
                exp1[i] = k;
        }
        for (; j < div2->n_row; ++j, ++k) {
                expand_row(div, k, div2, j, exp2);
                exp2[j] = k;
        }

        div->n_row = k;
        div->n_col = d + k;

        return div;
}

/* Swap divs "a" and "b" in "ls".
 */
__isl_give isl_local_space *isl_local_space_swap_div(
        __isl_take isl_local_space *ls, int a, int b)
{
        int offset;

        ls = isl_local_space_cow(ls);
        if (!ls)
                return NULL;
        if (a < 0 || a >= ls->div->n_row || b < 0 || b >= ls->div->n_row)
                isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
                        "index out of bounds", return isl_local_space_free(ls));
        offset = ls->div->n_col - ls->div->n_row;
        ls->div = isl_mat_swap_cols(ls->div, offset + a, offset + b);
        ls->div = isl_mat_swap_rows(ls->div, a, b);
        if (!ls->div)
                return isl_local_space_free(ls);
        return ls;
}

/* Construct a local space that contains all the divs in either
 * "ls1" or "ls2".
 */
__isl_give isl_local_space *isl_local_space_intersect(
        __isl_take isl_local_space *ls1, __isl_take isl_local_space *ls2)
{
        isl_ctx *ctx;
        int *exp1 = NULL;
        int *exp2 = NULL;
        isl_mat *div = NULL;
        isl_bool equal;

        if (!ls1 || !ls2)
                goto error;

        ctx = isl_local_space_get_ctx(ls1);
        if (!isl_space_is_equal(ls1->dim, ls2->dim))
                isl_die(ctx, isl_error_invalid,
                        "spaces should be identical", goto error);

        if (ls2->div->n_row == 0) {
                isl_local_space_free(ls2);
                return ls1;
        }

        if (ls1->div->n_row == 0) {
                isl_local_space_free(ls1);
                return ls2;
        }

        exp1 = isl_alloc_array(ctx, int, ls1->div->n_row);
        exp2 = isl_alloc_array(ctx, int, ls2->div->n_row);
        if (!exp1 || !exp2)
                goto error;

        div = isl_merge_divs(ls1->div, ls2->div, exp1, exp2);
        if (!div)
                goto error;

        equal = isl_mat_is_equal(ls1->div, div);
        if (equal < 0)
                goto error;
        if (!equal)
                ls1 = isl_local_space_cow(ls1);
        if (!ls1)
                goto error;

        free(exp1);
        free(exp2);
        isl_local_space_free(ls2);
        isl_mat_free(ls1->div);
        ls1->div = div;

        return ls1;
error:
        free(exp1);
        free(exp2);
        isl_mat_free(div);
        isl_local_space_free(ls1);
        isl_local_space_free(ls2);
        return NULL;
}

/* Is the local variable "div" of "ls" marked as not having
 * an explicit representation?
 * Note that even if this variable is not marked in this way and therefore
 * does have an explicit representation, this representation may still
 * depend (indirectly) on other local variables that do not
 * have an explicit representation.
 */
isl_bool isl_local_space_div_is_marked_unknown(__isl_keep isl_local_space *ls,
        int div)
{
        if (!ls)
                return isl_bool_error;
        return isl_local_div_is_marked_unknown(ls->div, div);
}

/* Does "ls" have a complete explicit representation for div "div"?
 */
isl_bool isl_local_space_div_is_known(__isl_keep isl_local_space *ls, int div)
{
        if (!ls)
                return isl_bool_error;
        return isl_local_div_is_known(ls->div, div);
}

/* Does "ls" have an explicit representation for all local variables?
 */
isl_bool isl_local_space_divs_known(__isl_keep isl_local_space *ls)
{
        if (!ls)
                return isl_bool_error;
        return isl_local_divs_known(ls->div);
}

__isl_give isl_local_space *isl_local_space_domain(
        __isl_take isl_local_space *ls)
{
        ls = isl_local_space_drop_dims(ls, isl_dim_out,
                                        0, isl_local_space_dim(ls, isl_dim_out));
        ls = isl_local_space_cow(ls);
        if (!ls)
                return NULL;
        ls->dim = isl_space_domain(ls->dim);
        if (!ls->dim)
                return isl_local_space_free(ls);
        return ls;
}

__isl_give isl_local_space *isl_local_space_range(
        __isl_take isl_local_space *ls)
{
        ls = isl_local_space_drop_dims(ls, isl_dim_in,
                                        0, isl_local_space_dim(ls, isl_dim_in));
        ls = isl_local_space_cow(ls);
        if (!ls)
                return NULL;

        ls->dim = isl_space_range(ls->dim);
        if (!ls->dim)
                return isl_local_space_free(ls);
        return ls;
}

/* Construct a local space for a map that has the given local
 * space as domain and that has a zero-dimensional range.
 */
__isl_give isl_local_space *isl_local_space_from_domain(
        __isl_take isl_local_space *ls)
{
        ls = isl_local_space_cow(ls);
        if (!ls)
                return NULL;
        ls->dim = isl_space_from_domain(ls->dim);
        if (!ls->dim)
                return isl_local_space_free(ls);
        return ls;
}

__isl_give isl_local_space *isl_local_space_add_dims(
        __isl_take isl_local_space *ls, enum isl_dim_type type, unsigned n)
{
        int pos;

        if (!ls)
                return NULL;
        pos = isl_local_space_dim(ls, type);
        return isl_local_space_insert_dims(ls, type, pos, n);
}

/* Remove common factor of non-constant terms and denominator.
 */
static void normalize_div(__isl_keep isl_local_space *ls, int div)
{
        isl_ctx *ctx = ls->div->ctx;
        unsigned total = ls->div->n_col - 2;

        isl_seq_gcd(ls->div->row[div] + 2, total, &ctx->normalize_gcd);
        isl_int_gcd(ctx->normalize_gcd,
                    ctx->normalize_gcd, ls->div->row[div][0]);
        if (isl_int_is_one(ctx->normalize_gcd))
                return;

        isl_seq_scale_down(ls->div->row[div] + 2, ls->div->row[div] + 2,
                            ctx->normalize_gcd, total);
        isl_int_divexact(ls->div->row[div][0], ls->div->row[div][0],
                            ctx->normalize_gcd);
        isl_int_fdiv_q(ls->div->row[div][1], ls->div->row[div][1],
                            ctx->normalize_gcd);
}

/* Exploit the equalities in "eq" to simplify the expressions of
 * the integer divisions in "ls".
 * The integer divisions in "ls" are assumed to appear as regular
 * dimensions in "eq".
 */
__isl_give isl_local_space *isl_local_space_substitute_equalities(
        __isl_take isl_local_space *ls, __isl_take isl_basic_set *eq)
{
        int i, j, k;
        unsigned total;
        unsigned n_div;

        if (!ls || !eq)
                goto error;

        total = isl_space_dim(eq->dim, isl_dim_all);
        if (isl_local_space_dim(ls, isl_dim_all) != total)
                isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
                        "spaces don't match", goto error);
        total++;
        n_div = eq->n_div;
        for (i = 0; i < eq->n_eq; ++i) {
                j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
                if (j < 0 || j == 0 || j >= total)
                        continue;

                for (k = 0; k < ls->div->n_row; ++k) {
                        if (isl_int_is_zero(ls->div->row[k][1 + j]))
                                continue;
                        ls = isl_local_space_cow(ls);
                        if (!ls)
                                goto error;
                        ls->div = isl_mat_cow(ls->div);
                        if (!ls->div)
                                goto error;
                        isl_seq_elim(ls->div->row[k] + 1, eq->eq[i], j, total,
                                        &ls->div->row[k][0]);
                        normalize_div(ls, k);
                }
        }

        isl_basic_set_free(eq);
        return ls;
error:
        isl_basic_set_free(eq);
        isl_local_space_free(ls);
        return NULL;
}

/* Plug in the affine expressions "subs" of length "subs_len" (including
 * the denominator and the constant term) into the variable at position "pos"
 * of the "n" div expressions starting at "first".
 *
 * Let i be the dimension to replace and let "subs" be of the form
 *
 *      f/d
 *
 * Any integer division starting at "first" with a non-zero coefficient for i,
 *
 *      floor((a i + g)/m)
 *
 * is replaced by
 *
 *      floor((a f + d g)/(m d))
 */
__isl_give isl_local_space *isl_local_space_substitute_seq(
        __isl_take isl_local_space *ls,
        enum isl_dim_type type, unsigned pos, isl_int *subs, int subs_len,
        int first, int n)
{
        int i;
        isl_int v;

        if (n == 0)
                return ls;
        ls = isl_local_space_cow(ls);
        if (!ls)
                return NULL;
        ls->div = isl_mat_cow(ls->div);
        if (!ls->div)
                return isl_local_space_free(ls);

        if (first + n > ls->div->n_row)
                isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
                        "index out of bounds", return isl_local_space_free(ls));

        pos += isl_local_space_offset(ls, type);

        isl_int_init(v);
        for (i = first; i < first + n; ++i) {
                if (isl_int_is_zero(ls->div->row[i][1 + pos]))
                        continue;
                isl_seq_substitute(ls->div->row[i], pos, subs,
                        ls->div->n_col, subs_len, v);
                normalize_div(ls, i);
        }
        isl_int_clear(v);

        return ls;
}

/* Plug in "subs" for dimension "type", "pos" in the integer divisions
 * of "ls".
 *
 * Let i be the dimension to replace and let "subs" be of the form
 *
 *      f/d
 *
 * Any integer division with a non-zero coefficient for i,
 *
 *      floor((a i + g)/m)
 *
 * is replaced by
 *
 *      floor((a f + d g)/(m d))
 */
__isl_give isl_local_space *isl_local_space_substitute(
        __isl_take isl_local_space *ls,
        enum isl_dim_type type, unsigned pos, __isl_keep isl_aff *subs)
{
        ls = isl_local_space_cow(ls);
        if (!ls || !subs)
                return isl_local_space_free(ls);

        if (!isl_space_is_equal(ls->dim, subs->ls->dim))
                isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
                        "spaces don't match", return isl_local_space_free(ls));
        if (isl_local_space_dim(subs->ls, isl_dim_div) != 0)
                isl_die(isl_local_space_get_ctx(ls), isl_error_unsupported,
                        "cannot handle divs yet",
                        return isl_local_space_free(ls));

        return isl_local_space_substitute_seq(ls, type, pos, subs->v->el,
                                            subs->v->size, 0, ls->div->n_row);
}

isl_bool isl_local_space_is_named_or_nested(__isl_keep isl_local_space *ls,
        enum isl_dim_type type)
{
        if (!ls)
                return isl_bool_error;
        return isl_space_is_named_or_nested(ls->dim, type);
}

__isl_give isl_local_space *isl_local_space_drop_dims(
        __isl_take isl_local_space *ls,
        enum isl_dim_type type, unsigned first, unsigned n)
{
        isl_ctx *ctx;

        if (!ls)
                return NULL;
        if (n == 0 && !isl_local_space_is_named_or_nested(ls, type))
                return ls;

        ctx = isl_local_space_get_ctx(ls);
        if (first + n > isl_local_space_dim(ls, type))
                isl_die(ctx, isl_error_invalid, "range out of bounds",
                        return isl_local_space_free(ls));

        ls = isl_local_space_cow(ls);
        if (!ls)
                return NULL;

        if (type == isl_dim_div) {
                ls->div = isl_mat_drop_rows(ls->div, first, n);
        } else {
                ls->dim = isl_space_drop_dims(ls->dim, type, first, n);
                if (!ls->dim)
                        return isl_local_space_free(ls);
        }

        first += 1 + isl_local_space_offset(ls, type);
        ls->div = isl_mat_drop_cols(ls->div, first, n);
        if (!ls->div)
                return isl_local_space_free(ls);

        return ls;
}

__isl_give isl_local_space *isl_local_space_insert_dims(
        __isl_take isl_local_space *ls,
        enum isl_dim_type type, unsigned first, unsigned n)
{
        isl_ctx *ctx;

        if (!ls)
                return NULL;
        if (n == 0 && !isl_local_space_is_named_or_nested(ls, type))
                return ls;

        ctx = isl_local_space_get_ctx(ls);
        if (first > isl_local_space_dim(ls, type))
                isl_die(ctx, isl_error_invalid, "position out of bounds",
                        return isl_local_space_free(ls));

        ls = isl_local_space_cow(ls);
        if (!ls)
                return NULL;

        if (type == isl_dim_div) {
                ls->div = isl_mat_insert_zero_rows(ls->div, first, n);
        } else {
                ls->dim = isl_space_insert_dims(ls->dim, type, first, n);
                if (!ls->dim)
                        return isl_local_space_free(ls);
        }

        first += 1 + isl_local_space_offset(ls, type);
        ls->div = isl_mat_insert_zero_cols(ls->div, first, n);
        if (!ls->div)
                return isl_local_space_free(ls);

        return ls;
}

/* Check if the constraints pointed to by "constraint" is a div
 * constraint corresponding to div "div" in "ls".
 *
 * That is, if div = floor(f/m), then check if the constraint is
 *
 *              f - m d >= 0
 * or
 *              -(f-(m-1)) + m d >= 0
 */
isl_bool isl_local_space_is_div_constraint(__isl_keep isl_local_space *ls,
        isl_int *constraint, unsigned div)
{
        unsigned pos;

        if (!ls)
                return isl_bool_error;

        if (isl_int_is_zero(ls->div->row[div][0]))
                return isl_bool_false;

        pos = isl_local_space_offset(ls, isl_dim_div) + div;

        if (isl_int_eq(constraint[pos], ls->div->row[div][0])) {
                int neg;
                isl_int_sub(ls->div->row[div][1],
                                ls->div->row[div][1], ls->div->row[div][0]);
                isl_int_add_ui(ls->div->row[div][1], ls->div->row[div][1], 1);
                neg = isl_seq_is_neg(constraint, ls->div->row[div]+1, pos);
                isl_int_sub_ui(ls->div->row[div][1], ls->div->row[div][1], 1);
                isl_int_add(ls->div->row[div][1],
                                ls->div->row[div][1], ls->div->row[div][0]);
                if (!neg)
                        return isl_bool_false;
                if (isl_seq_first_non_zero(constraint+pos+1,
                                            ls->div->n_row-div-1) != -1)
                        return isl_bool_false;
        } else if (isl_int_abs_eq(constraint[pos], ls->div->row[div][0])) {
                if (!isl_seq_eq(constraint, ls->div->row[div]+1, pos))
                        return isl_bool_false;
                if (isl_seq_first_non_zero(constraint+pos+1,
                                            ls->div->n_row-div-1) != -1)
                        return isl_bool_false;
        } else
                return isl_bool_false;

        return isl_bool_true;
}

/*
 * Set active[i] to 1 if the dimension at position i is involved
 * in the linear expression l.
 */
int *isl_local_space_get_active(__isl_keep isl_local_space *ls, isl_int *l)
{
        int i, j;
        isl_ctx *ctx;
        int *active = NULL;
        unsigned total;
        unsigned offset;

        ctx = isl_local_space_get_ctx(ls);
        total = isl_local_space_dim(ls, isl_dim_all);
        active = isl_calloc_array(ctx, int, total);
        if (total && !active)
                return NULL;

        for (i = 0; i < total; ++i)
                active[i] = !isl_int_is_zero(l[i]);

        offset = isl_local_space_offset(ls, isl_dim_div) - 1;
        for (i = ls->div->n_row - 1; i >= 0; --i) {
                if (!active[offset + i])
                        continue;
                for (j = 0; j < total; ++j)
                        active[j] |= !isl_int_is_zero(ls->div->row[i][2 + j]);
        }

        return active;
}

/* Given a local space "ls" of a set, create a local space
 * for the lift of the set.  In particular, the result
 * is of the form [dim -> local[..]], with ls->div->n_row variables in the
 * range of the wrapped map.
 */
__isl_give isl_local_space *isl_local_space_lift(
        __isl_take isl_local_space *ls)
{
        ls = isl_local_space_cow(ls);
        if (!ls)
                return NULL;

        ls->dim = isl_space_lift(ls->dim, ls->div->n_row);
        ls->div = isl_mat_drop_rows(ls->div, 0, ls->div->n_row);
        if (!ls->dim || !ls->div)
                return isl_local_space_free(ls);

        return ls;
}

/* Construct a basic map that maps a set living in local space "ls"
 * to the corresponding lifted local space.
 */
__isl_give isl_basic_map *isl_local_space_lifting(
        __isl_take isl_local_space *ls)
{
        isl_basic_map *lifting;
        isl_basic_set *bset;

        if (!ls)
                return NULL;
        if (!isl_local_space_is_set(ls))
                isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
                        "lifting only defined on set spaces", goto error);

        bset = isl_basic_set_from_local_space(ls);
        lifting = isl_basic_set_unwrap(isl_basic_set_lift(bset));
        lifting = isl_basic_map_domain_map(lifting);
        lifting = isl_basic_map_reverse(lifting);

        return lifting;
error:
        isl_local_space_free(ls);
        return NULL;
}

/* Compute the preimage of "ls" under the function represented by "ma".
 * In other words, plug in "ma" in "ls".  The result is a local space
 * that is part of the domain space of "ma".
 *
 * If the divs in "ls" are represented as
 *
 *      floor((a_i(p) + b_i x + c_i(divs))/n_i)
 *
 * and ma is represented by
 *
 *      x = D(p) + F(y) + G(divs')
 *
 * then the resulting divs are
 *
 *      floor((a_i(p) + b_i D(p) + b_i F(y) + B_i G(divs') + c_i(divs))/n_i)
 *
 * We first copy over the divs from "ma" and then
 * we add the modified divs from "ls".
 */
__isl_give isl_local_space *isl_local_space_preimage_multi_aff(
        __isl_take isl_local_space *ls, __isl_take isl_multi_aff *ma)
{
        int i;
        isl_space *space;
        isl_local_space *res = NULL;
        int n_div_ls, n_div_ma;
        isl_int f, c1, c2, g;

        ma = isl_multi_aff_align_divs(ma);
        if (!ls || !ma)
                goto error;
        if (!isl_space_is_range_internal(ls->dim, ma->space))
                isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
                        "spaces don't match", goto error);

        n_div_ls = isl_local_space_dim(ls, isl_dim_div);
        n_div_ma = ma->n ? isl_aff_dim(ma->u.p[0], isl_dim_div) : 0;

        space = isl_space_domain(isl_multi_aff_get_space(ma));
        res = isl_local_space_alloc(space, n_div_ma + n_div_ls);
        if (!res)
                goto error;

        if (n_div_ma) {
                isl_mat_free(res->div);
                res->div = isl_mat_copy(ma->u.p[0]->ls->div);
                res->div = isl_mat_add_zero_cols(res->div, n_div_ls);
                res->div = isl_mat_add_rows(res->div, n_div_ls);
                if (!res->div)
                        goto error;
        }

        isl_int_init(f);
        isl_int_init(c1);
        isl_int_init(c2);
        isl_int_init(g);

        for (i = 0; i < ls->div->n_row; ++i) {
                if (isl_int_is_zero(ls->div->row[i][0])) {
                        isl_int_set_si(res->div->row[n_div_ma + i][0], 0);
                        continue;
                }
                isl_seq_preimage(res->div->row[n_div_ma + i], ls->div->row[i],
                                ma, 0, 0, n_div_ma, n_div_ls, f, c1, c2, g, 1);
                normalize_div(res, n_div_ma + i);
        }

        isl_int_clear(f);
        isl_int_clear(c1);
        isl_int_clear(c2);
        isl_int_clear(g);

        isl_local_space_free(ls);
        isl_multi_aff_free(ma);
        return res;
error:
        isl_local_space_free(ls);
        isl_multi_aff_free(ma);
        isl_local_space_free(res);
        return NULL;
}

/* Move the "n" dimensions of "src_type" starting at "src_pos" of "ls"
 * to dimensions of "dst_type" at "dst_pos".
 *
 * Moving to/from local dimensions is not allowed.
 * We currently assume that the dimension type changes.
 */
__isl_give isl_local_space *isl_local_space_move_dims(
        __isl_take isl_local_space *ls,
        enum isl_dim_type dst_type, unsigned dst_pos,
        enum isl_dim_type src_type, unsigned src_pos, unsigned n)
{
        unsigned g_dst_pos;
        unsigned g_src_pos;

        if (!ls)
                return NULL;
        if (n == 0 &&
            !isl_local_space_is_named_or_nested(ls, src_type) &&
            !isl_local_space_is_named_or_nested(ls, dst_type))
                return ls;

        if (src_pos + n > isl_local_space_dim(ls, src_type))
                isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
                        "range out of bounds", return isl_local_space_free(ls));
        if (dst_pos > isl_local_space_dim(ls, dst_type))
                isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
                        "position out of bounds",
                        return isl_local_space_free(ls));
        if (src_type == isl_dim_div)
                isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
                        "cannot move divs", return isl_local_space_free(ls));
        if (dst_type == isl_dim_div)
                isl_die(isl_local_space_get_ctx(ls), isl_error_invalid,
                        "cannot move to divs", return isl_local_space_free(ls));
        if (dst_type == src_type && dst_pos == src_pos)
                return ls;
        if (dst_type == src_type)
                isl_die(isl_local_space_get_ctx(ls), isl_error_unsupported,
                        "moving dims within the same type not supported",
                        return isl_local_space_free(ls));

        ls = isl_local_space_cow(ls);
        if (!ls)
                return NULL;

        g_src_pos = 1 + isl_local_space_offset(ls, src_type) + src_pos;
        g_dst_pos = 1 + isl_local_space_offset(ls, dst_type) + dst_pos;
        if (dst_type > src_type)
                g_dst_pos -= n;
        ls->div = isl_mat_move_cols(ls->div, g_dst_pos, g_src_pos, n);
        if (!ls->div)
                return isl_local_space_free(ls);
        ls->dim = isl_space_move_dims(ls->dim, dst_type, dst_pos,
                                        src_type, src_pos, n);
        if (!ls->dim)
                return isl_local_space_free(ls);

        return ls;
}

/* Remove any internal structure of the domain of "ls".
 * If there is any such internal structure in the input,
 * then the name of the corresponding space is also removed.
 */
__isl_give isl_local_space *isl_local_space_flatten_domain(
        __isl_take isl_local_space *ls)
{
        if (!ls)
                return NULL;

        if (!ls->dim->nested[0])
                return ls;

        ls = isl_local_space_cow(ls);
        if (!ls)
                return NULL;

        ls->dim = isl_space_flatten_domain(ls->dim);
        if (!ls->dim)
                return isl_local_space_free(ls);

        return ls;
}

/* Remove any internal structure of the range of "ls".
 * If there is any such internal structure in the input,
 * then the name of the corresponding space is also removed.
 */
__isl_give isl_local_space *isl_local_space_flatten_range(
        __isl_take isl_local_space *ls)
{
        if (!ls)
                return NULL;

        if (!ls->dim->nested[1])
                return ls;

        ls = isl_local_space_cow(ls);
        if (!ls)
                return NULL;

        ls->dim = isl_space_flatten_range(ls->dim);
        if (!ls->dim)
                return isl_local_space_free(ls);

        return ls;
}

/* Given the local space "ls" of a map, return the local space of a set
 * that lives in a space that wraps the space of "ls" and that has
 * the same divs.
 */
__isl_give isl_local_space *isl_local_space_wrap(__isl_take isl_local_space *ls)
{
        ls = isl_local_space_cow(ls);
        if (!ls)
                return NULL;

        ls->dim = isl_space_wrap(ls->dim);
        if (!ls->dim)
                return isl_local_space_free(ls);

        return ls;
}

/* Lift the point "pnt", living in the space of "ls"
 * to live in a space with extra coordinates corresponding
 * to the local variables of "ls".
 */
__isl_give isl_point *isl_local_space_lift_point(__isl_take isl_local_space *ls,
        __isl_take isl_point *pnt)
{
        unsigned n_local;
        isl_space *space;
        isl_local *local;
        isl_vec *vec;

        if (isl_local_space_check_has_space(ls, isl_point_peek_space(pnt)) < 0)
                goto error;

        local = isl_local_space_peek_local(ls);
        n_local = isl_local_space_dim(ls, isl_dim_div);

        space = isl_point_take_space(pnt);
        vec = isl_point_take_vec(pnt);

        space = isl_space_lift(space, n_local);
        vec = isl_local_extend_point_vec(local, vec);

        pnt = isl_point_restore_vec(pnt, vec);
        pnt = isl_point_restore_space(pnt, space);

        isl_local_space_free(ls);

        return pnt;
error:
        isl_local_space_free(ls);
        isl_point_free(pnt);
        return NULL;
}