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/*
 * Copyright 2008-2009 Katholieke Universiteit Leuven
 * Copyright 2010      INRIA Saclay
 *
 * Use of this software is governed by the GNU LGPLv2.1 license
 *
 * Written by Sven Verdoolaege, K.U.Leuven, Departement
 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
 * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
 * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France 
 */

#include <stdlib.h>
#include <isl_space_private.h>
#include <isl_id_private.h>
#include <isl_reordering.h>

isl_ctx *isl_space_get_ctx(__isl_keep isl_space *dim)
{
        return dim ? dim->ctx : NULL;
}

__isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
                        unsigned nparam, unsigned n_in, unsigned n_out)
{
        isl_space *dim;

        dim = isl_alloc_type(ctx, struct isl_space);
        if (!dim)
                return NULL;

        dim->ctx = ctx;
        isl_ctx_ref(ctx);
        dim->ref = 1;
        dim->nparam = nparam;
        dim->n_in = n_in;
        dim->n_out = n_out;

        dim->tuple_id[0] = NULL;
        dim->tuple_id[1] = NULL;

        dim->nested[0] = NULL;
        dim->nested[1] = NULL;

        dim->n_id = 0;
        dim->ids = NULL;

        return dim;
}

/* Mark the space as being that of a set, by setting the domain tuple
 * to isl_id_none.
 */
static __isl_give isl_space *mark_as_set(__isl_take isl_space *space)
{
        space = isl_space_cow(space);
        if (!space)
                return NULL;
        space = isl_space_set_tuple_id(space, isl_dim_in, &isl_id_none);
        return space;
}

/* Is the space that of a set?
 */
int isl_space_is_set(__isl_keep isl_space *space)
{
        if (!space)
                return -1;
        if (space->n_in != 0 || space->nested[0])
                return 0;
        if (space->tuple_id[0] != &isl_id_none)
                return 0;
        return 1;
}

__isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
                        unsigned nparam, unsigned dim)
{
        isl_space *space;
        space = isl_space_alloc(ctx, nparam, 0, dim);
        space = mark_as_set(space);
        return space;
}

/* Mark the space as being that of a parameter domain, by setting
 * both tuples to isl_id_none.
 */
static __isl_give isl_space *mark_as_params(isl_space *space)
{
        if (!space)
                return NULL;
        space = isl_space_set_tuple_id(space, isl_dim_in, &isl_id_none);
        space = isl_space_set_tuple_id(space, isl_dim_out, &isl_id_none);
        return space;
}

/* Is the space that of a parameter domain?
 */
int isl_space_is_params(__isl_keep isl_space *space)
{
        if (!space)
                return -1;
        if (space->n_in != 0 || space->nested[0] ||
            space->n_out != 0 || space->nested[1])
                return 0;
        if (space->tuple_id[0] != &isl_id_none)
                return 0;
        if (space->tuple_id[1] != &isl_id_none)
                return 0;
        return 1;
}

/* Create a space for a parameter domain.
 */
__isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx, unsigned nparam)
{
        isl_space *space;
        space = isl_space_alloc(ctx, nparam, 0, 0);
        space = mark_as_params(space);
        return space;
}

static unsigned global_pos(__isl_keep isl_space *dim,
                                 enum isl_dim_type type, unsigned pos)
{
        struct isl_ctx *ctx = dim->ctx;

        switch (type) {
        case isl_dim_param:
                isl_assert(ctx, pos < dim->nparam,
                            return isl_space_dim(dim, isl_dim_all));
                return pos;
        case isl_dim_in:
                isl_assert(ctx, pos < dim->n_in,
                            return isl_space_dim(dim, isl_dim_all));
                return pos + dim->nparam;
        case isl_dim_out:
                isl_assert(ctx, pos < dim->n_out,
                            return isl_space_dim(dim, isl_dim_all));
                return pos + dim->nparam + dim->n_in;
        default:
                isl_assert(ctx, 0, return isl_space_dim(dim, isl_dim_all));
        }
        return isl_space_dim(dim, isl_dim_all);
}

/* Extend length of ids array to the total number of dimensions.
 */
static __isl_give isl_space *extend_ids(__isl_take isl_space *dim)
{
        isl_id **ids;
        int i;

        if (isl_space_dim(dim, isl_dim_all) <= dim->n_id)
                return dim;

        if (!dim->ids) {
                dim->ids = isl_calloc_array(dim->ctx,
                                isl_id *, isl_space_dim(dim, isl_dim_all));
                if (!dim->ids)
                        goto error;
        } else {
                ids = isl_realloc_array(dim->ctx, dim->ids,
                                isl_id *, isl_space_dim(dim, isl_dim_all));
                if (!ids)
                        goto error;
                dim->ids = ids;
                for (i = dim->n_id; i < isl_space_dim(dim, isl_dim_all); ++i)
                        dim->ids[i] = NULL;
        }

        dim->n_id = isl_space_dim(dim, isl_dim_all);

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

static __isl_give isl_space *set_id(__isl_take isl_space *dim,
        enum isl_dim_type type, unsigned pos, __isl_take isl_id *id)
{
        dim = isl_space_cow(dim);

        if (!dim)
                goto error;

        pos = global_pos(dim, type, pos);
        if (pos == isl_space_dim(dim, isl_dim_all))
                goto error;

        if (pos >= dim->n_id) {
                if (!id)
                        return dim;
                dim = extend_ids(dim);
                if (!dim)
                        goto error;
        }

        dim->ids[pos] = id;

        return dim;
error:
        isl_id_free(id);
        isl_space_free(dim);
        return NULL;
}

static __isl_keep isl_id *get_id(__isl_keep isl_space *dim,
                                 enum isl_dim_type type, unsigned pos)
{
        if (!dim)
                return NULL;

        pos = global_pos(dim, type, pos);
        if (pos == isl_space_dim(dim, isl_dim_all))
                return NULL;
        if (pos >= dim->n_id)
                return NULL;
        return dim->ids[pos];
}

static unsigned offset(__isl_keep isl_space *dim, enum isl_dim_type type)
{
        switch (type) {
        case isl_dim_param:     return 0;
        case isl_dim_in:        return dim->nparam;
        case isl_dim_out:       return dim->nparam + dim->n_in;
        default:                return 0;
        }
}

static unsigned n(__isl_keep isl_space *dim, enum isl_dim_type type)
{
        switch (type) {
        case isl_dim_param:     return dim->nparam;
        case isl_dim_in:        return dim->n_in;
        case isl_dim_out:       return dim->n_out;
        case isl_dim_all:       return dim->nparam + dim->n_in + dim->n_out;
        default:                return 0;
        }
}

unsigned isl_space_dim(__isl_keep isl_space *dim, enum isl_dim_type type)
{
        if (!dim)
                return 0;
        return n(dim, type);
}

unsigned isl_space_offset(__isl_keep isl_space *dim, enum isl_dim_type type)
{
        if (!dim)
                return 0;
        return offset(dim, type);
}

static __isl_give isl_space *copy_ids(__isl_take isl_space *dst,
        enum isl_dim_type dst_type, unsigned offset, __isl_keep isl_space *src,
        enum isl_dim_type src_type)
{
        int i;
        isl_id *id;

        if (!dst)
                return NULL;

        for (i = 0; i < n(src, src_type); ++i) {
                id = get_id(src, src_type, i);
                if (!id)
                        continue;
                dst = set_id(dst, dst_type, offset + i, isl_id_copy(id));
                if (!dst)
                        return NULL;
        }
        return dst;
}

__isl_take isl_space *isl_space_dup(__isl_keep isl_space *dim)
{
        isl_space *dup;
        if (!dim)
                return NULL;
        dup = isl_space_alloc(dim->ctx, dim->nparam, dim->n_in, dim->n_out);
        if (dim->tuple_id[0] &&
            !(dup->tuple_id[0] = isl_id_copy(dim->tuple_id[0])))
                goto error;
        if (dim->tuple_id[1] &&
            !(dup->tuple_id[1] = isl_id_copy(dim->tuple_id[1])))
                goto error;
        if (dim->nested[0] && !(dup->nested[0] = isl_space_copy(dim->nested[0])))
                goto error;
        if (dim->nested[1] && !(dup->nested[1] = isl_space_copy(dim->nested[1])))
                goto error;
        if (!dim->ids)
                return dup;
        dup = copy_ids(dup, isl_dim_param, 0, dim, isl_dim_param);
        dup = copy_ids(dup, isl_dim_in, 0, dim, isl_dim_in);
        dup = copy_ids(dup, isl_dim_out, 0, dim, isl_dim_out);
        return dup;
error:
        isl_space_free(dup);
        return NULL;
}

__isl_give isl_space *isl_space_cow(__isl_take isl_space *dim)
{
        if (!dim)
                return NULL;

        if (dim->ref == 1)
                return dim;
        dim->ref--;
        return isl_space_dup(dim);
}

__isl_give isl_space *isl_space_copy(__isl_keep isl_space *dim)
{
        if (!dim)
                return NULL;

        dim->ref++;
        return dim;
}

void isl_space_free(__isl_take isl_space *dim)
{
        int i;

        if (!dim)
                return;

        if (--dim->ref > 0)
                return;

        isl_id_free(dim->tuple_id[0]);
        isl_id_free(dim->tuple_id[1]);

        isl_space_free(dim->nested[0]);
        isl_space_free(dim->nested[1]);

        for (i = 0; i < dim->n_id; ++i)
                isl_id_free(dim->ids[i]);
        free(dim->ids);
        isl_ctx_deref(dim->ctx);
        
        free(dim);
}

/* Check if "s" is a valid dimension or tuple name.
 * We currently only forbid names that look like a number.
 *
 * s is assumed to be non-NULL.
 */
static int name_ok(isl_ctx *ctx, const char *s)
{
        char *p;
        long dummy;

        dummy = strtol(s, &p, 0);
        if (p != s)
                isl_die(ctx, isl_error_invalid, "name looks like a number",
                        return 0);

        return 1;
}

/* Is it possible for the given dimension type to have a tuple id?
 */
static int space_can_have_id(__isl_keep isl_space *space,
        enum isl_dim_type type)
{
        if (!space)
                return 0;
        if (isl_space_is_params(space))
                isl_die(space->ctx, isl_error_invalid,
                        "parameter spaces don't have tuple ids", return 0);
        if (isl_space_is_set(space) && type != isl_dim_set)
                isl_die(space->ctx, isl_error_invalid,
                        "set spaces can only have a set id", return 0);
        if (type != isl_dim_in && type != isl_dim_out)
                isl_die(space->ctx, isl_error_invalid,
                        "only input, output and set tuples can have ids",
                        return 0);

        return 1;
}

/* Does the tuple have an id?
 */
int isl_space_has_tuple_id(__isl_keep isl_space *dim, enum isl_dim_type type)
{
        if (!space_can_have_id(dim, type))
                return -1;
        return dim->tuple_id[type - isl_dim_in] != NULL;
}

__isl_give isl_id *isl_space_get_tuple_id(__isl_keep isl_space *dim,
        enum isl_dim_type type)
{
        int has_id;

        if (!dim)
                return NULL;
        has_id = isl_space_has_tuple_id(dim, type);
        if (has_id < 0)
                return NULL;
        if (!has_id)
                isl_die(dim->ctx, isl_error_invalid,
                        "tuple has no id", return NULL);
        return isl_id_copy(dim->tuple_id[type - isl_dim_in]);
}

__isl_give isl_space *isl_space_set_tuple_id(__isl_take isl_space *dim,
        enum isl_dim_type type, __isl_take isl_id *id)
{
        dim = isl_space_cow(dim);
        if (!dim || !id)
                goto error;
        if (type != isl_dim_in && type != isl_dim_out)
                isl_die(dim->ctx, isl_error_invalid,
                        "only input, output and set tuples can have names",
                        goto error);

        isl_id_free(dim->tuple_id[type - isl_dim_in]);
        dim->tuple_id[type - isl_dim_in] = id;

        return dim;
error:
        isl_id_free(id);
        isl_space_free(dim);
        return NULL;
}

__isl_give isl_space *isl_space_reset_tuple_id(__isl_take isl_space *dim,
        enum isl_dim_type type)
{
        dim = isl_space_cow(dim);
        if (!dim)
                return NULL;
        if (type != isl_dim_in && type != isl_dim_out)
                isl_die(dim->ctx, isl_error_invalid,
                        "only input, output and set tuples can have names",
                        goto error);

        isl_id_free(dim->tuple_id[type - isl_dim_in]);
        dim->tuple_id[type - isl_dim_in] = NULL;

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

/* Set the id of the given dimension of "space" to "id".
 * If the dimension already has an id, then it is replaced.
 * If the dimension is a parameter, then we need to change it
 * in the nested spaces (if any) as well.
 */
__isl_give isl_space *isl_space_set_dim_id(__isl_take isl_space *space,
        enum isl_dim_type type, unsigned pos, __isl_take isl_id *id)
{
        space = isl_space_cow(space);
        if (!space || !id)
                goto error;

        if (type == isl_dim_param) {
                int i;

                for (i = 0; i < 2; ++i) {
                        if (!space->nested[i])
                                continue;
                        space->nested[i] =
                                isl_space_set_dim_id(space->nested[i],
                                                type, pos, isl_id_copy(id));
                        if (!space->nested[i])
                                goto error;
                }
        }

        isl_id_free(get_id(space, type, pos));
        return set_id(space, type, pos, id);
error:
        isl_id_free(id);
        isl_space_free(space);
        return NULL;
}

/* Reset the id of the given dimension of "space".
 * If the dimension already has an id, then it is removed.
 * If the dimension is a parameter, then we need to reset it
 * in the nested spaces (if any) as well.
 */
__isl_give isl_space *isl_space_reset_dim_id(__isl_take isl_space *space,
        enum isl_dim_type type, unsigned pos)
{
        space = isl_space_cow(space);
        if (!space)
                goto error;

        if (type == isl_dim_param) {
                int i;

                for (i = 0; i < 2; ++i) {
                        if (!space->nested[i])
                                continue;
                        space->nested[i] =
                                isl_space_reset_dim_id(space->nested[i],
                                                        type, pos);
                        if (!space->nested[i])
                                goto error;
                }
        }

        isl_id_free(get_id(space, type, pos));
        return set_id(space, type, pos, NULL);
error:
        isl_space_free(space);
        return NULL;
}

int isl_space_has_dim_id(__isl_keep isl_space *dim,
        enum isl_dim_type type, unsigned pos)
{
        if (!dim)
                return -1;
        return get_id(dim, type, pos) != NULL;
}

__isl_give isl_id *isl_space_get_dim_id(__isl_keep isl_space *dim,
        enum isl_dim_type type, unsigned pos)
{
        if (!dim)
                return NULL;
        if (!get_id(dim, type, pos))
                isl_die(dim->ctx, isl_error_invalid,
                        "dim has no id", return NULL);
        return isl_id_copy(get_id(dim, type, pos));
}

__isl_give isl_space *isl_space_set_tuple_name(__isl_take isl_space *dim,
        enum isl_dim_type type, const char *s)
{
        isl_id *id;

        if (!dim)
                return NULL;

        if (!s)
                return isl_space_reset_tuple_id(dim, type);

        if (!name_ok(dim->ctx, s))
                goto error;

        id = isl_id_alloc(dim->ctx, s, NULL);
        return isl_space_set_tuple_id(dim, type, id);
error:
        isl_space_free(dim);
        return NULL;
}

/* Does the tuple have a name?
 */
int isl_space_has_tuple_name(__isl_keep isl_space *space,
        enum isl_dim_type type)
{
        isl_id *id;

        if (!space_can_have_id(space, type))
                return -1;
        id = space->tuple_id[type - isl_dim_in];
        return id && id->name;
}

const char *isl_space_get_tuple_name(__isl_keep isl_space *dim,
         enum isl_dim_type type)
{
        isl_id *id;
        if (!dim)
                return NULL;
        if (type != isl_dim_in && type != isl_dim_out)
                return NULL;
        id = dim->tuple_id[type - isl_dim_in];
        return id ? id->name : NULL;
}

__isl_give isl_space *isl_space_set_dim_name(__isl_take isl_space *dim,
                                 enum isl_dim_type type, unsigned pos,
                                 const char *s)
{
        isl_id *id;

        if (!dim)
                return NULL;
        if (!s)
                return isl_space_reset_dim_id(dim, type, pos);
        if (!name_ok(dim->ctx, s))
                goto error;
        id = isl_id_alloc(dim->ctx, s, NULL);
        return isl_space_set_dim_id(dim, type, pos, id);
error:
        isl_space_free(dim);
        return NULL;
}

/* Does the given dimension have a name?
 */
int isl_space_has_dim_name(__isl_keep isl_space *space,
        enum isl_dim_type type, unsigned pos)
{
        isl_id *id;

        if (!space)
                return -1;
        id = get_id(space, type, pos);
        return id && id->name;
}

__isl_keep const char *isl_space_get_dim_name(__isl_keep isl_space *dim,
                                 enum isl_dim_type type, unsigned pos)
{
        isl_id *id = get_id(dim, type, pos);
        return id ? id->name : NULL;
}

int isl_space_find_dim_by_id(__isl_keep isl_space *dim, enum isl_dim_type type,
        __isl_keep isl_id *id)
{
        int i;
        int offset;
        int n;

        if (!dim || !id)
                return -1;

        offset = isl_space_offset(dim, type);
        n = isl_space_dim(dim, type);
        for (i = 0; i < n && offset + i < dim->n_id; ++i)
                if (dim->ids[offset + i] == id)
                        return i;

        return -1;
}

int isl_space_find_dim_by_name(__isl_keep isl_space *space,
        enum isl_dim_type type, const char *name)
{
        int i;
        int offset;
        int n;

        if (!space || !name)
                return -1;

        offset = isl_space_offset(space, type);
        n = isl_space_dim(space, type);
        for (i = 0; i < n && offset + i < space->n_id; ++i)
                if (space->ids[offset + i]->name &&
                    !strcmp(space->ids[offset + i]->name, name))
                        return i;

        return -1;
}

static __isl_keep isl_id *tuple_id(__isl_keep isl_space *dim,
        enum isl_dim_type type)
{
        if (!dim)
                return NULL;
        if (type == isl_dim_in)
                return dim->tuple_id[0];
        if (type == isl_dim_out)
                return dim->tuple_id[1];
        return NULL;
}

static __isl_keep isl_space *nested(__isl_keep isl_space *dim,
        enum isl_dim_type type)
{
        if (!dim)
                return NULL;
        if (type == isl_dim_in)
                return dim->nested[0];
        if (type == isl_dim_out)
                return dim->nested[1];
        return NULL;
}

int isl_space_tuple_match(__isl_keep isl_space *dim1, enum isl_dim_type dim1_type,
                        __isl_keep isl_space *dim2, enum isl_dim_type dim2_type)
{
        isl_id *id1, *id2;
        isl_space *nested1, *nested2;

        if (!dim1 || !dim2)
                return -1;

        if (dim1 == dim2 && dim1_type == dim2_type)
                return 1;

        if (n(dim1, dim1_type) != n(dim2, dim2_type))
                return 0;
        id1 = tuple_id(dim1, dim1_type);
        id2 = tuple_id(dim2, dim2_type);
        if (!id1 ^ !id2)
                return 0;
        if (id1 && id1 != id2)
                return 0;
        nested1 = nested(dim1, dim1_type);
        nested2 = nested(dim2, dim2_type);
        if (!nested1 ^ !nested2)
                return 0;
        if (nested1 && !isl_space_is_equal(nested1, nested2))
                return 0;
        return 1;
}

static int match(__isl_keep isl_space *dim1, enum isl_dim_type dim1_type,
        __isl_keep isl_space *dim2, enum isl_dim_type dim2_type)
{
        int i;

        if (dim1 == dim2 && dim1_type == dim2_type)
                return 1;

        if (!isl_space_tuple_match(dim1, dim1_type, dim2, dim2_type))
                return 0;

        if (!dim1->ids && !dim2->ids)
                return 1;

        for (i = 0; i < n(dim1, dim1_type); ++i) {
                if (get_id(dim1, dim1_type, i) != get_id(dim2, dim2_type, i))
                        return 0;
        }
        return 1;
}

int isl_space_match(__isl_keep isl_space *dim1, enum isl_dim_type dim1_type,
        __isl_keep isl_space *dim2, enum isl_dim_type dim2_type)
{
        if (!dim1 || !dim2)
                return -1;

        return match(dim1, dim1_type, dim2, dim2_type);
}

static void get_ids(__isl_keep isl_space *dim, enum isl_dim_type type,
        unsigned first, unsigned n, __isl_keep isl_id **ids)
{
        int i;

        for (i = 0; i < n ; ++i)
                ids[i] = get_id(dim, type, first + i);
}

__isl_give isl_space *isl_space_extend(__isl_take isl_space *dim,
                        unsigned nparam, unsigned n_in, unsigned n_out)
{
        isl_id **ids = NULL;

        if (!dim)
                return NULL;
        if (dim->nparam == nparam && dim->n_in == n_in && dim->n_out == n_out)
                return dim;

        isl_assert(dim->ctx, dim->nparam <= nparam, goto error);
        isl_assert(dim->ctx, dim->n_in <= n_in, goto error);
        isl_assert(dim->ctx, dim->n_out <= n_out, goto error);

        dim = isl_space_cow(dim);

        if (dim->ids) {
                ids = isl_calloc_array(dim->ctx, isl_id *,
                                         nparam + n_in + n_out);
                if (!ids)
                        goto error;
                get_ids(dim, isl_dim_param, 0, dim->nparam, ids);
                get_ids(dim, isl_dim_in, 0, dim->n_in, ids + nparam);
                get_ids(dim, isl_dim_out, 0, dim->n_out, ids + nparam + n_in);
                free(dim->ids);
                dim->ids = ids;
                dim->n_id = nparam + n_in + n_out;
        }
        dim->nparam = nparam;
        dim->n_in = n_in;
        dim->n_out = n_out;

        return dim;
error:
        free(ids);
        isl_space_free(dim);
        return NULL;
}

__isl_give isl_space *isl_space_add_dims(__isl_take isl_space *dim,
        enum isl_dim_type type, unsigned n)
{
        if (!dim)
                return NULL;
        dim = isl_space_reset(dim, type);
        switch (type) {
        case isl_dim_param:
                dim = isl_space_extend(dim,
                                        dim->nparam + n, dim->n_in, dim->n_out);
                if (dim && dim->nested[0] &&
                    !(dim->nested[0] = isl_space_add_dims(dim->nested[0],
                                                    isl_dim_param, n)))
                        goto error;
                if (dim && dim->nested[1] &&
                    !(dim->nested[1] = isl_space_add_dims(dim->nested[1],
                                                    isl_dim_param, n)))
                        goto error;
                return dim;
        case isl_dim_in:
                return isl_space_extend(dim,
                                        dim->nparam, dim->n_in + n, dim->n_out);
        case isl_dim_out:
                return isl_space_extend(dim,
                                        dim->nparam, dim->n_in, dim->n_out + n);
        default:
                isl_die(dim->ctx, isl_error_invalid,
                        "cannot add dimensions of specified type", goto error);
        }
error:
        isl_space_free(dim);
        return NULL;
}

static int valid_dim_type(enum isl_dim_type type)
{
        switch (type) {
        case isl_dim_param:
        case isl_dim_in:
        case isl_dim_out:
                return 1;
        default:
                return 0;
        }
}

/* Insert "n" dimensions of type "type" at position "pos".
 * If we are inserting parameters, then they are also inserted in
 * any nested spaces.
 */
__isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *dim,
        enum isl_dim_type type, unsigned pos, unsigned n)
{
        isl_id **ids = NULL;

        if (!dim)
                return NULL;
        if (n == 0)
                return isl_space_reset(dim, type);

        if (!valid_dim_type(type))
                isl_die(dim->ctx, isl_error_invalid,
                        "cannot insert dimensions of specified type",
                        goto error);

        isl_assert(dim->ctx, pos <= isl_space_dim(dim, type), goto error);

        dim = isl_space_cow(dim);
        if (!dim)
                return NULL;

        if (dim->ids) {
                enum isl_dim_type t, o = isl_dim_param;
                int off;
                int s[3];
                ids = isl_calloc_array(dim->ctx, isl_id *,
                                     dim->nparam + dim->n_in + dim->n_out + n);
                if (!ids)
                        goto error;
                off = 0;
                s[isl_dim_param - o] = dim->nparam;
                s[isl_dim_in - o] = dim->n_in;
                s[isl_dim_out - o] = dim->n_out;
                for (t = isl_dim_param; t <= isl_dim_out; ++t) {
                        if (t != type) {
                                get_ids(dim, t, 0, s[t - o], ids + off);
                                off += s[t - o];
                        } else {
                                get_ids(dim, t, 0, pos, ids + off);
                                off += pos + n;
                                get_ids(dim, t, pos, s[t - o] - pos, ids + off);
                                off += s[t - o] - pos;
                        }
                }
                free(dim->ids);
                dim->ids = ids;
                dim->n_id = dim->nparam + dim->n_in + dim->n_out + n;
        }
        switch (type) {
        case isl_dim_param:     dim->nparam += n; break;
        case isl_dim_in:        dim->n_in += n; break;
        case isl_dim_out:       dim->n_out += n; break;
        default:                ;
        }
        dim = isl_space_reset(dim, type);

        if (type == isl_dim_param) {
                if (dim && dim->nested[0] &&
                    !(dim->nested[0] = isl_space_insert_dims(dim->nested[0],
                                                    isl_dim_param, pos, n)))
                        goto error;
                if (dim && dim->nested[1] &&
                    !(dim->nested[1] = isl_space_insert_dims(dim->nested[1],
                                                    isl_dim_param, pos, n)))
                        goto error;
        }

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

__isl_give isl_space *isl_space_move_dims(__isl_take isl_space *dim,
        enum isl_dim_type dst_type, unsigned dst_pos,
        enum isl_dim_type src_type, unsigned src_pos, unsigned n)
{
        int i;

        if (!dim)
                return NULL;
        if (n == 0)
                return dim;

        isl_assert(dim->ctx, src_pos + n <= isl_space_dim(dim, src_type),
                goto error);

        if (dst_type == src_type && dst_pos == src_pos)
                return dim;

        isl_assert(dim->ctx, dst_type != src_type, goto error);

        dim = isl_space_reset(dim, src_type);
        dim = isl_space_reset(dim, dst_type);

        dim = isl_space_cow(dim);
        if (!dim)
                return NULL;

        if (dim->ids) {
                isl_id **ids;
                enum isl_dim_type t, o = isl_dim_param;
                int off;
                int s[3];
                ids = isl_calloc_array(dim->ctx, isl_id *,
                                         dim->nparam + dim->n_in + dim->n_out);
                if (!ids)
                        goto error;
                off = 0;
                s[isl_dim_param - o] = dim->nparam;
                s[isl_dim_in - o] = dim->n_in;
                s[isl_dim_out - o] = dim->n_out;
                for (t = isl_dim_param; t <= isl_dim_out; ++t) {
                        if (t == dst_type) {
                                get_ids(dim, t, 0, dst_pos, ids + off);
                                off += dst_pos;
                                get_ids(dim, src_type, src_pos, n, ids + off);
                                off += n;
                                get_ids(dim, t, dst_pos, s[t - o] - dst_pos,
                                                ids + off);
                                off += s[t - o] - dst_pos;
                        } else if (t == src_type) {
                                get_ids(dim, t, 0, src_pos, ids + off);
                                off += src_pos;
                                get_ids(dim, t, src_pos + n,
                                            s[t - o] - src_pos - n, ids + off);
                                off += s[t - o] - src_pos - n;
                        } else {
                                get_ids(dim, t, 0, s[t - o], ids + off);
                                off += s[t - o];
                        }
                }
                free(dim->ids);
                dim->ids = ids;
                dim->n_id = dim->nparam + dim->n_in + dim->n_out;
        }

        switch (dst_type) {
        case isl_dim_param:     dim->nparam += n; break;
        case isl_dim_in:        dim->n_in += n; break;
        case isl_dim_out:       dim->n_out += n; break;
        default:                ;
        }

        switch (src_type) {
        case isl_dim_param:     dim->nparam -= n; break;
        case isl_dim_in:        dim->n_in -= n; break;
        case isl_dim_out:       dim->n_out -= n; break;
        default:                ;
        }

        if (dst_type != isl_dim_param && src_type != isl_dim_param)
                return dim;

        for (i = 0; i < 2; ++i) {
                if (!dim->nested[i])
                        continue;
                dim->nested[i] = isl_space_replace(dim->nested[i],
                                                 isl_dim_param, dim);
                if (!dim->nested[i])
                        goto error;
        }

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

__isl_give isl_space *isl_space_join(__isl_take isl_space *left,
        __isl_take isl_space *right)
{
        isl_space *dim;

        if (!left || !right)
                goto error;

        isl_assert(left->ctx, match(left, isl_dim_param, right, isl_dim_param),
                        goto error);
        isl_assert(left->ctx,
                isl_space_tuple_match(left, isl_dim_out, right, isl_dim_in),
                goto error);

        dim = isl_space_alloc(left->ctx, left->nparam, left->n_in, right->n_out);
        if (!dim)
                goto error;

        dim = copy_ids(dim, isl_dim_param, 0, left, isl_dim_param);
        dim = copy_ids(dim, isl_dim_in, 0, left, isl_dim_in);
        dim = copy_ids(dim, isl_dim_out, 0, right, isl_dim_out);

        if (dim && left->tuple_id[0] &&
            !(dim->tuple_id[0] = isl_id_copy(left->tuple_id[0])))
                goto error;
        if (dim && right->tuple_id[1] &&
            !(dim->tuple_id[1] = isl_id_copy(right->tuple_id[1])))
                goto error;
        if (dim && left->nested[0] &&
            !(dim->nested[0] = isl_space_copy(left->nested[0])))
                goto error;
        if (dim && right->nested[1] &&
            !(dim->nested[1] = isl_space_copy(right->nested[1])))
                goto error;

        isl_space_free(left);
        isl_space_free(right);

        return dim;
error:
        isl_space_free(left);
        isl_space_free(right);
        return NULL;
}

__isl_give isl_space *isl_space_product(__isl_take isl_space *left,
        __isl_take isl_space *right)
{
        isl_space *dom1, *dom2, *nest1, *nest2;

        if (!left || !right)
                goto error;

        isl_assert(left->ctx, match(left, isl_dim_param, right, isl_dim_param),
                        goto error);

        dom1 = isl_space_domain(isl_space_copy(left));
        dom2 = isl_space_domain(isl_space_copy(right));
        nest1 = isl_space_wrap(isl_space_join(isl_space_reverse(dom1), dom2));

        dom1 = isl_space_range(left);
        dom2 = isl_space_range(right);
        nest2 = isl_space_wrap(isl_space_join(isl_space_reverse(dom1), dom2));

        return isl_space_join(isl_space_reverse(nest1), nest2);
error:
        isl_space_free(left);
        isl_space_free(right);
        return NULL;
}

/* Given two spaces { A -> C } and { B -> C }, construct the space
 * { [A -> B] -> C }
 */
__isl_give isl_space *isl_space_domain_product(__isl_take isl_space *left,
        __isl_take isl_space *right)
{
        isl_space *ran, *dom1, *dom2, *nest;

        if (!left || !right)
                goto error;

        if (!match(left, isl_dim_param, right, isl_dim_param))
                isl_die(left->ctx, isl_error_invalid,
                        "parameters need to match", goto error);
        if (!isl_space_tuple_match(left, isl_dim_out, right, isl_dim_out))
                isl_die(left->ctx, isl_error_invalid,
                        "ranges need to match", goto error);

        ran = isl_space_range(isl_space_copy(left));

        dom1 = isl_space_domain(left);
        dom2 = isl_space_domain(right);
        nest = isl_space_wrap(isl_space_join(isl_space_reverse(dom1), dom2));

        return isl_space_join(isl_space_reverse(nest), ran);
error:
        isl_space_free(left);
        isl_space_free(right);
        return NULL;
}

__isl_give isl_space *isl_space_range_product(__isl_take isl_space *left,
        __isl_take isl_space *right)
{
        isl_space *dom, *ran1, *ran2, *nest;

        if (!left || !right)
                goto error;

        isl_assert(left->ctx, match(left, isl_dim_param, right, isl_dim_param),
                        goto error);
        if (!isl_space_tuple_match(left, isl_dim_in, right, isl_dim_in))
                isl_die(left->ctx, isl_error_invalid,
                        "domains need to match", goto error);

        dom = isl_space_domain(isl_space_copy(left));

        ran1 = isl_space_range(left);
        ran2 = isl_space_range(right);
        nest = isl_space_wrap(isl_space_join(isl_space_reverse(ran1), ran2));

        return isl_space_join(isl_space_reverse(dom), nest);
error:
        isl_space_free(left);
        isl_space_free(right);
        return NULL;
}

__isl_give isl_space *isl_space_map_from_set(__isl_take isl_space *dim)
{
        isl_ctx *ctx;
        isl_id **ids = NULL;

        if (!dim)
                return NULL;
        ctx = isl_space_get_ctx(dim);
        if (!isl_space_is_set(dim))
                isl_die(ctx, isl_error_invalid, "not a set space", goto error);
        dim = isl_space_cow(dim);
        if (!dim)
                return NULL;
        if (dim->ids) {
                ids = isl_calloc_array(dim->ctx, isl_id *,
                                        dim->nparam + dim->n_out + dim->n_out);
                if (!ids)
                        goto error;
                get_ids(dim, isl_dim_param, 0, dim->nparam, ids);
                get_ids(dim, isl_dim_out, 0, dim->n_out, ids + dim->nparam);
        }
        dim->n_in = dim->n_out;
        if (ids) {
                free(dim->ids);
                dim->ids = ids;
                dim->n_id = dim->nparam + dim->n_out + dim->n_out;
                dim = copy_ids(dim, isl_dim_out, 0, dim, isl_dim_in);
        }
        isl_id_free(dim->tuple_id[0]);
        dim->tuple_id[0] = isl_id_copy(dim->tuple_id[1]);
        isl_space_free(dim->nested[0]);
        dim->nested[0] = isl_space_copy(dim->nested[1]);
        return dim;
error:
        isl_space_free(dim);
        return NULL;
}

__isl_give isl_space *isl_space_map_from_domain_and_range(
        __isl_take isl_space *domain, __isl_take isl_space *range)
{
        if (!domain || !range)
                goto error;
        if (!isl_space_is_set(domain))
                isl_die(isl_space_get_ctx(domain), isl_error_invalid,
                        "domain is not a set space", goto error);
        if (!isl_space_is_set(range))
                isl_die(isl_space_get_ctx(range), isl_error_invalid,
                        "range is not a set space", goto error);
        return isl_space_join(isl_space_reverse(domain), range);
error:
        isl_space_free(domain);
        isl_space_free(range);
        return NULL;
}

static __isl_give isl_space *set_ids(__isl_take isl_space *dim,
        enum isl_dim_type type,
        unsigned first, unsigned n, __isl_take isl_id **ids)
{
        int i;

        for (i = 0; i < n ; ++i)
                dim = set_id(dim, type, first + i, ids[i]);

        return dim;
}

__isl_give isl_space *isl_space_reverse(__isl_take isl_space *dim)
{
        unsigned t;
        isl_space *nested;
        isl_id **ids = NULL;
        isl_id *id;

        if (!dim)
                return NULL;
        if (match(dim, isl_dim_in, dim, isl_dim_out))
                return dim;

        dim = isl_space_cow(dim);
        if (!dim)
                return NULL;

        id = dim->tuple_id[0];
        dim->tuple_id[0] = dim->tuple_id[1];
        dim->tuple_id[1] = id;

        nested = dim->nested[0];
        dim->nested[0] = dim->nested[1];
        dim->nested[1] = nested;

        if (dim->ids) {
                ids = isl_alloc_array(dim->ctx, isl_id *,
                                        dim->n_in + dim->n_out);
                if (!ids)
                        goto error;
                get_ids(dim, isl_dim_in, 0, dim->n_in, ids);
                get_ids(dim, isl_dim_out, 0, dim->n_out, ids + dim->n_in);
        }

        t = dim->n_in;
        dim->n_in = dim->n_out;
        dim->n_out = t;

        if (dim->ids) {
                dim = set_ids(dim, isl_dim_out, 0, dim->n_out, ids);
                dim = set_ids(dim, isl_dim_in, 0, dim->n_in, ids + dim->n_out);
                free(ids);
        }

        return dim;
error:
        free(ids);
        isl_space_free(dim);
        return NULL;
}

__isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *dim,
        enum isl_dim_type type, unsigned first, unsigned num)
{
        int i;

        if (!dim)
                return NULL;

        if (num == 0)
                return isl_space_reset(dim, type);

        if (!valid_dim_type(type))
                isl_die(dim->ctx, isl_error_invalid,
                        "cannot drop dimensions of specified type", goto error);

        isl_assert(dim->ctx, first + num <= n(dim, type), goto error);
        dim = isl_space_cow(dim);
        if (!dim)
                goto error;
        if (dim->ids) {
                dim = extend_ids(dim);
                if (!dim)
                        goto error;
                for (i = 0; i < num; ++i)
                        isl_id_free(get_id(dim, type, first + i));
                for (i = first+num; i < n(dim, type); ++i)
                        set_id(dim, type, i - num, get_id(dim, type, i));
                switch (type) {
                case isl_dim_param:
                        get_ids(dim, isl_dim_in, 0, dim->n_in,
                                dim->ids + offset(dim, isl_dim_in) - num);
                case isl_dim_in:
                        get_ids(dim, isl_dim_out, 0, dim->n_out,
                                dim->ids + offset(dim, isl_dim_out) - num);
                default:
                        ;
                }
                dim->n_id -= num;
        }
        switch (type) {
        case isl_dim_param:     dim->nparam -= num; break;
        case isl_dim_in:        dim->n_in -= num; break;
        case isl_dim_out:       dim->n_out -= num; break;
        default:                ;
        }
        dim = isl_space_reset(dim, type);
        if (type == isl_dim_param) {
                if (dim && dim->nested[0] &&
                    !(dim->nested[0] = isl_space_drop_dims(dim->nested[0],
                                                    isl_dim_param, first, num)))
                        goto error;
                if (dim && dim->nested[1] &&
                    !(dim->nested[1] = isl_space_drop_dims(dim->nested[1],
                                                    isl_dim_param, first, num)))
                        goto error;
        }
        return dim;
error:
        isl_space_free(dim);
        return NULL;
}

__isl_give isl_space *isl_space_drop_inputs(__isl_take isl_space *dim,
                unsigned first, unsigned n)
{
        if (!dim)
                return NULL;
        return isl_space_drop_dims(dim, isl_dim_in, first, n);
}

__isl_give isl_space *isl_space_drop_outputs(__isl_take isl_space *dim,
                unsigned first, unsigned n)
{
        if (!dim)
                return NULL;
        return isl_space_drop_dims(dim, isl_dim_out, first, n);
}

__isl_give isl_space *isl_space_domain(__isl_take isl_space *dim)
{
        if (!dim)
                return NULL;
        dim = isl_space_drop_outputs(dim, 0, dim->n_out);
        dim = isl_space_reverse(dim);
        dim = mark_as_set(dim);
        return dim;
}

__isl_give isl_space *isl_space_from_domain(__isl_take isl_space *dim)
{
        if (!dim)
                return NULL;
        if (!isl_space_is_set(dim))
                isl_die(isl_space_get_ctx(dim), isl_error_invalid,
                        "not a set space", goto error);
        dim = isl_space_reverse(dim);
        dim = isl_space_reset(dim, isl_dim_out);
        return dim;
error:
        isl_space_free(dim);
        return NULL;
}

__isl_give isl_space *isl_space_range(__isl_take isl_space *dim)
{
        if (!dim)
                return NULL;
        dim = isl_space_drop_inputs(dim, 0, dim->n_in);
        dim = mark_as_set(dim);
        return dim;
}

__isl_give isl_space *isl_space_from_range(__isl_take isl_space *dim)
{
        if (!dim)
                return NULL;
        if (!isl_space_is_set(dim))
                isl_die(isl_space_get_ctx(dim), isl_error_invalid,
                        "not a set space", goto error);
        return isl_space_reset(dim, isl_dim_in);
error:
        isl_space_free(dim);
        return NULL;
}

__isl_give isl_space *isl_space_params(__isl_take isl_space *space)
{
        if (isl_space_is_params(space))
                return space;
        space = isl_space_drop_dims(space,
                            isl_dim_in, 0, isl_space_dim(space, isl_dim_in));
        space = isl_space_drop_dims(space,
                            isl_dim_out, 0, isl_space_dim(space, isl_dim_out));
        space = mark_as_params(space);
        return space;
}

__isl_give isl_space *isl_space_set_from_params(__isl_take isl_space *space)
{
        if (!space)
                return NULL;
        if (!isl_space_is_params(space))
                isl_die(isl_space_get_ctx(space), isl_error_invalid,
                        "not a parameter space", goto error);
        return isl_space_reset(space, isl_dim_set);
error:
        isl_space_free(space);
        return NULL;
}

__isl_give isl_space *isl_space_as_set_space(__isl_take isl_space *dim)
{
        dim = isl_space_cow(dim);
        if (!dim)
                return NULL;

        dim->n_out += dim->n_in;
        dim->n_in = 0;
        dim = isl_space_reset(dim, isl_dim_in);
        dim = isl_space_reset(dim, isl_dim_out);

        return dim;
}

__isl_give isl_space *isl_space_underlying(__isl_take isl_space *dim,
        unsigned n_div)
{
        int i;

        if (!dim)
                return NULL;
        if (n_div == 0 &&
            dim->nparam == 0 && dim->n_in == 0 && dim->n_id == 0)
                return isl_space_reset(isl_space_reset(dim, isl_dim_in), isl_dim_out);
        dim = isl_space_cow(dim);
        if (!dim)
                return NULL;
        dim->n_out += dim->nparam + dim->n_in + n_div;
        dim->nparam = 0;
        dim->n_in = 0;

        for (i = 0; i < dim->n_id; ++i)
                isl_id_free(get_id(dim, isl_dim_out, i));
        dim->n_id = 0;
        dim = isl_space_reset(dim, isl_dim_in);
        dim = isl_space_reset(dim, isl_dim_out);

        return dim;
}

int isl_space_is_equal(__isl_keep isl_space *dim1, __isl_keep isl_space *dim2)
{
        if (!dim1 || !dim2)
                return -1;
        if (dim1 == dim2)
                return 1;
        return match(dim1, isl_dim_param, dim2, isl_dim_param) &&
               isl_space_tuple_match(dim1, isl_dim_in, dim2, isl_dim_in) &&
               isl_space_tuple_match(dim1, isl_dim_out, dim2, isl_dim_out);
}

/* Is space1 equal to the domain of space2?
 */
int isl_space_is_domain(__isl_keep isl_space *space1,
        __isl_keep isl_space *space2)
{
        if (!space1 || !space2)
                return -1;
        if (!isl_space_is_set(space1))
                return 0;
        return match(space1, isl_dim_param, space2, isl_dim_param) &&
               isl_space_tuple_match(space1, isl_dim_set, space2, isl_dim_in);
}

int isl_space_compatible(__isl_keep isl_space *dim1,
        __isl_keep isl_space *dim2)
{
        return dim1->nparam == dim2->nparam &&
               dim1->n_in + dim1->n_out == dim2->n_in + dim2->n_out;
}

static uint32_t isl_hash_dim(uint32_t hash, __isl_keep isl_space *dim)
{
        int i;
        isl_id *id;

        if (!dim)
                return hash;

        hash = isl_hash_builtin(hash, dim->nparam);
        hash = isl_hash_builtin(hash, dim->n_in);
        hash = isl_hash_builtin(hash, dim->n_out);

        for (i = 0; i < dim->nparam; ++i) {
                id = get_id(dim, isl_dim_param, i);
                hash = isl_hash_id(hash, id);
        }

        id = tuple_id(dim, isl_dim_in);
        hash = isl_hash_id(hash, id);
        id = tuple_id(dim, isl_dim_out);
        hash = isl_hash_id(hash, id);

        hash = isl_hash_dim(hash, dim->nested[0]);
        hash = isl_hash_dim(hash, dim->nested[1]);

        return hash;
}

uint32_t isl_space_get_hash(__isl_keep isl_space *dim)
{
        uint32_t hash;

        if (!dim)
                return 0;

        hash = isl_hash_init();
        hash = isl_hash_dim(hash, dim);

        return hash;
}

int isl_space_is_wrapping(__isl_keep isl_space *dim)
{
        if (!dim)
                return -1;

        if (!isl_space_is_set(dim))
                return 0;

        return dim->nested[1] != NULL;
}

__isl_give isl_space *isl_space_wrap(__isl_take isl_space *dim)
{
        isl_space *wrap;

        if (!dim)
                return NULL;

        wrap = isl_space_set_alloc(dim->ctx,
                                    dim->nparam, dim->n_in + dim->n_out);

        wrap = copy_ids(wrap, isl_dim_param, 0, dim, isl_dim_param);
        wrap = copy_ids(wrap, isl_dim_set, 0, dim, isl_dim_in);
        wrap = copy_ids(wrap, isl_dim_set, dim->n_in, dim, isl_dim_out);

        if (!wrap)
                goto error;

        wrap->nested[1] = dim;

        return wrap;
error:
        isl_space_free(dim);
        return NULL;
}

__isl_give isl_space *isl_space_unwrap(__isl_take isl_space *dim)
{
        isl_space *unwrap;

        if (!dim)
                return NULL;

        if (!isl_space_is_wrapping(dim))
                isl_die(dim->ctx, isl_error_invalid, "not a wrapping space",
                        goto error);

        unwrap = isl_space_copy(dim->nested[1]);
        isl_space_free(dim);

        return unwrap;
error:
        isl_space_free(dim);
        return NULL;
}

int isl_space_is_named_or_nested(__isl_keep isl_space *dim, enum isl_dim_type type)
{
        if (type != isl_dim_in && type != isl_dim_out)
                return 0;
        if (!dim)
                return -1;
        if (dim->tuple_id[type - isl_dim_in])
                return 1;
        if (dim->nested[type - isl_dim_in])
                return 1;
        return 0;
}

int isl_space_may_be_set(__isl_keep isl_space *dim)
{
        if (!dim)
                return -1;
        if (isl_space_is_set(dim))
                return 1;
        if (isl_space_dim(dim, isl_dim_in) != 0)
                return 0;
        if (isl_space_is_named_or_nested(dim, isl_dim_in))
                return 0;
        return 1;
}

__isl_give isl_space *isl_space_reset(__isl_take isl_space *dim,
        enum isl_dim_type type)
{
        if (!isl_space_is_named_or_nested(dim, type))
                return dim;

        dim = isl_space_cow(dim);
        if (!dim)
                return NULL;

        isl_id_free(dim->tuple_id[type - isl_dim_in]);
        dim->tuple_id[type - isl_dim_in] = NULL;
        isl_space_free(dim->nested[type - isl_dim_in]);
        dim->nested[type - isl_dim_in] = NULL;

        return dim;
}

__isl_give isl_space *isl_space_flatten(__isl_take isl_space *dim)
{
        if (!dim)
                return NULL;
        if (!dim->nested[0] && !dim->nested[1])
                return dim;

        if (dim->nested[0])
                dim = isl_space_reset(dim, isl_dim_in);
        if (dim && dim->nested[1])
                dim = isl_space_reset(dim, isl_dim_out);

        return dim;
}

__isl_give isl_space *isl_space_flatten_domain(__isl_take isl_space *dim)
{
        if (!dim)
                return NULL;
        if (!dim->nested[0])
                return dim;

        return isl_space_reset(dim, isl_dim_in);
}

__isl_give isl_space *isl_space_flatten_range(__isl_take isl_space *dim)
{
        if (!dim)
                return NULL;
        if (!dim->nested[1])
                return dim;

        return isl_space_reset(dim, isl_dim_out);
}

/* Replace the dimensions of the given type of dst by those of src.
 */
__isl_give isl_space *isl_space_replace(__isl_take isl_space *dst,
        enum isl_dim_type type, __isl_keep isl_space *src)
{
        dst = isl_space_cow(dst);

        if (!dst || !src)
                goto error;

        dst = isl_space_drop_dims(dst, type, 0, isl_space_dim(dst, type));
        dst = isl_space_add_dims(dst, type, isl_space_dim(src, type));
        dst = copy_ids(dst, type, 0, src, type);

        if (dst && type == isl_dim_param) {
                int i;
                for (i = 0; i <= 1; ++i) {
                        if (!dst->nested[i])
                                continue;
                        dst->nested[i] = isl_space_replace(dst->nested[i],
                                                         type, src);
                        if (!dst->nested[i])
                                goto error;
                }
        }

        return dst;
error:
        isl_space_free(dst);
        return NULL;
}

/* Given a dimension specification "dim" of a set, create a dimension
 * specification for the lift of the set.  In particular, the result
 * is of the form [dim -> local[..]], with n_local variables in the
 * range of the wrapped map.
 */
__isl_give isl_space *isl_space_lift(__isl_take isl_space *dim, unsigned n_local)
{
        isl_space *local_dim;

        if (!dim)
                return NULL;

        local_dim = isl_space_dup(dim);
        local_dim = isl_space_drop_dims(local_dim, isl_dim_set, 0, dim->n_out);
        local_dim = isl_space_add_dims(local_dim, isl_dim_set, n_local);
        local_dim = isl_space_set_tuple_name(local_dim, isl_dim_set, "local");
        dim = isl_space_join(isl_space_from_domain(dim),
                            isl_space_from_range(local_dim));
        dim = isl_space_wrap(dim);
        dim = isl_space_set_tuple_name(dim, isl_dim_set, "lifted");

        return dim;
}

int isl_space_can_zip(__isl_keep isl_space *dim)
{
        if (!dim)
                return -1;

        return dim->nested[0] && dim->nested[1];
}

__isl_give isl_space *isl_space_zip(__isl_take isl_space *dim)
{
        isl_space *dom, *ran;
        isl_space *dom_dom, *dom_ran, *ran_dom, *ran_ran;

        if (!isl_space_can_zip(dim))
                isl_die(dim->ctx, isl_error_invalid, "dim cannot be zipped",
                        goto error);

        if (!dim)
                return NULL;
        dom = isl_space_unwrap(isl_space_domain(isl_space_copy(dim)));
        ran = isl_space_unwrap(isl_space_range(dim));
        dom_dom = isl_space_domain(isl_space_copy(dom));
        dom_ran = isl_space_range(dom);
        ran_dom = isl_space_domain(isl_space_copy(ran));
        ran_ran = isl_space_range(ran);
        dom = isl_space_join(isl_space_from_domain(dom_dom),
                           isl_space_from_range(ran_dom));
        ran = isl_space_join(isl_space_from_domain(dom_ran),
                           isl_space_from_range(ran_ran));
        return isl_space_join(isl_space_from_domain(isl_space_wrap(dom)),
                            isl_space_from_range(isl_space_wrap(ran)));
error:
        isl_space_free(dim);
        return NULL;
}

/* Can we apply isl_space_curry to "space"?
 * That is, does it have a nested relation in its domain?
 */
int isl_space_can_curry(__isl_keep isl_space *space)
{
        if (!space)
                return -1;

        return !!space->nested[0];
}

/* Given a space (A -> B) -> C, return the corresponding space
 * A -> (B -> C).
 */
__isl_give isl_space *isl_space_curry(__isl_take isl_space *space)
{
        isl_space *dom, *ran;
        isl_space *dom_dom, *dom_ran;

        if (!space)
                return NULL;

        if (!isl_space_can_curry(space))
                isl_die(space->ctx, isl_error_invalid,
                        "space cannot be curried", goto error);

        dom = isl_space_unwrap(isl_space_domain(isl_space_copy(space)));
        ran = isl_space_range(space);
        dom_dom = isl_space_domain(isl_space_copy(dom));
        dom_ran = isl_space_range(dom);
        ran = isl_space_join(isl_space_from_domain(dom_ran),
                           isl_space_from_range(ran));
        return isl_space_join(isl_space_from_domain(dom_dom),
                            isl_space_from_range(isl_space_wrap(ran)));
error:
        isl_space_free(space);
        return NULL;
}

int isl_space_has_named_params(__isl_keep isl_space *dim)
{
        int i;
        unsigned off;

        if (!dim)
                return -1;
        if (dim->nparam == 0)
                return 1;
        off = isl_space_offset(dim, isl_dim_param);
        if (off + dim->nparam > dim->n_id)
                return 0;
        for (i = 0; i < dim->nparam; ++i)
                if (!dim->ids[off + i])
                        return 0;
        return 1;
}

/* Align the initial parameters of dim1 to match the order in dim2.
 */
__isl_give isl_space *isl_space_align_params(__isl_take isl_space *dim1,
        __isl_take isl_space *dim2)
{
        isl_reordering *exp;

        if (!isl_space_has_named_params(dim1) || !isl_space_has_named_params(dim2))
                isl_die(isl_space_get_ctx(dim1), isl_error_invalid,
                        "parameter alignment requires named parameters",
                        goto error);

        dim2 = isl_space_params(dim2);
        exp = isl_parameter_alignment_reordering(dim1, dim2);
        exp = isl_reordering_extend_space(exp, dim1);
        isl_space_free(dim2);
        if (!exp)
                return NULL;
        dim1 = isl_space_copy(exp->dim);
        isl_reordering_free(exp);
        return dim1;
error:
        isl_space_free(dim1);
        isl_space_free(dim2);
        return NULL;
}

/* Given the space of set (domain), construct a space for a map
 * with as domain the given space and as range the range of "model".
 */
__isl_give isl_space *isl_space_extend_domain_with_range(
        __isl_take isl_space *domain, __isl_take isl_space *model)
{
        isl_space *space;

        space = isl_space_from_domain(domain);
        space = isl_space_add_dims(space, isl_dim_out,
                                    isl_space_dim(model, isl_dim_out));
        if (isl_space_has_tuple_id(model, isl_dim_out))
                space = isl_space_set_tuple_id(space, isl_dim_out,
                                isl_space_get_tuple_id(model, isl_dim_out));
        isl_space_free(model);
        return space;
}