fix typos in user manual

[isl.git] / isl_union_templ.c

/*
 * Copyright 2010      INRIA Saclay
 * Copyright 2013      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
 */

__isl_give UNION *FN(UNION,cow)(__isl_take UNION *u);

isl_ctx *FN(UNION,get_ctx)(__isl_keep UNION *u)
{
        return u ? u->space->ctx : NULL;
}

__isl_give isl_space *FN(UNION,get_space)(__isl_keep UNION *u)
{
        if (!u)
                return NULL;
        return isl_space_copy(u->space);
}

/* Return the number of parameters of "u", where "type"
 * is required to be set to isl_dim_param.
 */
unsigned FN(UNION,dim)(__isl_keep UNION *u, enum isl_dim_type type)
{
        if (!u)
                return 0;

        if (type != isl_dim_param)
                isl_die(FN(UNION,get_ctx)(u), isl_error_invalid,
                        "can only reference parameters", return 0);

        return isl_space_dim(u->space, type);
}

/* Return the position of the parameter with the given name
 * in "u".
 * Return -1 if no such dimension can be found.
 */
int FN(UNION,find_dim_by_name)(__isl_keep UNION *u, enum isl_dim_type type,
        const char *name)
{
        if (!u)
                return -1;
        return isl_space_find_dim_by_name(u->space, type, name);
}

#ifdef HAS_TYPE
static __isl_give UNION *FN(UNION,alloc)(__isl_take isl_space *dim,
        enum isl_fold type, int size)
#else
static __isl_give UNION *FN(UNION,alloc)(__isl_take isl_space *dim, int size)
#endif
{
        UNION *u;

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

        u = isl_calloc_type(dim->ctx, UNION);
        if (!u)
                goto error;

        u->ref = 1;
#ifdef HAS_TYPE
        u->type = type;
#endif
        u->space = dim;
        if (isl_hash_table_init(dim->ctx, &u->table, size) < 0)
                return FN(UNION,free)(u);

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

#ifdef HAS_TYPE
__isl_give UNION *FN(UNION,ZERO)(__isl_take isl_space *dim, enum isl_fold type)
{
        return FN(UNION,alloc)(dim, type, 16);
}
#else
__isl_give UNION *FN(UNION,ZERO)(__isl_take isl_space *dim)
{
        return FN(UNION,alloc)(dim, 16);
}
#endif

__isl_give UNION *FN(UNION,copy)(__isl_keep UNION *u)
{
        if (!u)
                return NULL;

        u->ref++;
        return u;
}

/* Extract the element of "u" living in "space" (ignoring parameters).
 *
 * Return the ZERO element if "u" does not contain any element
 * living in "space".
 */
__isl_give PART *FN(FN(UNION,extract),PARTS)(__isl_keep UNION *u,
        __isl_take isl_space *space)
{
        struct isl_hash_table_entry *entry;
        isl_bool equal_params;

        if (!u || !space)
                goto error;
        equal_params = isl_space_has_equal_params(u->space, space);
        if (equal_params < 0)
                goto error;
        if (!equal_params) {
                space = isl_space_drop_dims(space, isl_dim_param,
                                        0, isl_space_dim(space, isl_dim_param));
                space = isl_space_align_params(space,
                                        FN(UNION,get_space)(u));
                if (!space)
                        goto error;
        }

        entry = FN(UNION,find_part_entry)(u, space, 0);
        if (!entry)
                goto error;
        if (entry == isl_hash_table_entry_none)
#ifdef HAS_TYPE
                return FN(PART,ZERO)(space, u->type);
#else
                return FN(PART,ZERO)(space);
#endif
        isl_space_free(space);
        return FN(PART,copy)(entry->data);
error:
        isl_space_free(space);
        return NULL;
}

/* Add "part" to "u".
 * If "disjoint" is set, then "u" is not allowed to already have
 * a part that is defined over a domain that overlaps with the domain
 * of "part".
 * Otherwise, compute the union sum of "part" and the part in "u"
 * defined on the same space.
 */
static __isl_give UNION *FN(UNION,add_part_generic)(__isl_take UNION *u,
        __isl_take PART *part, int disjoint)
{
        int empty;
        struct isl_hash_table_entry *entry;

        if (!part)
                goto error;

        empty = FN(PART,IS_ZERO)(part);
        if (empty < 0)
                goto error;
        if (empty) {
                FN(PART,free)(part);
                return u;
        }

        u = FN(UNION,align_params)(u, FN(PART,get_space)(part));
        part = FN(PART,align_params)(part, FN(UNION,get_space)(u));

        u = FN(UNION,cow)(u);

        if (!u)
                goto error;

        if (FN(UNION,check_disjoint_domain_other)(u, part) < 0)
                goto error;
        entry = FN(UNION,find_part_entry)(u, part->dim, 1);
        if (!entry)
                goto error;

        if (!entry->data)
                entry->data = part;
        else {
                if (disjoint &&
                    FN(UNION,check_disjoint_domain)(entry->data, part) < 0)
                        goto error;
                entry->data = FN(PART,union_add_)(entry->data,
                                                FN(PART,copy)(part));
                if (!entry->data)
                        goto error;
                empty = FN(PART,IS_ZERO)(part);
                if (empty < 0)
                        goto error;
                if (empty)
                        u = FN(UNION,remove_part_entry)(u, entry);
                FN(PART,free)(part);
        }

        return u;
error:
        FN(PART,free)(part);
        FN(UNION,free)(u);
        return NULL;
}

/* Add "part" to "u", where "u" is assumed not to already have
 * a part that is defined on the same space as "part".
 */
__isl_give UNION *FN(FN(UNION,add),PARTS)(__isl_take UNION *u,
        __isl_take PART *part)
{
        return FN(UNION,add_part_generic)(u, part, 1);
}

#ifdef HAS_TYPE
/* Allocate a UNION with the same type and the same size as "u" and
 * with space "space".
 */
static __isl_give UNION *FN(UNION,alloc_same_size_on_space)(__isl_keep UNION *u,
        __isl_take isl_space *space)
{
        if (!u)
                goto error;
        return FN(UNION,alloc)(space, u->type, u->table.n);
error:
        isl_space_free(space);
        return NULL;
}
#else
/* Allocate a UNION with the same size as "u" and with space "space".
 */
static __isl_give UNION *FN(UNION,alloc_same_size_on_space)(__isl_keep UNION *u,
        __isl_take isl_space *space)
{
        if (!u)
                goto error;
        return FN(UNION,alloc)(space, u->table.n);
error:
        isl_space_free(space);
        return NULL;
}
#endif

/* Allocate a UNION with the same space, the same type (if any) and
 * the same size as "u".
 */
static __isl_give UNION *FN(UNION,alloc_same_size)(__isl_keep UNION *u)
{
        return FN(UNION,alloc_same_size_on_space)(u, FN(UNION,get_space)(u));
}

/* Internal data structure for isl_union_*_transform_space.
 * "fn' is applied to each entry in the input.
 * "res" collects the results.
 */
S(UNION,transform_data)
{
        __isl_give PART *(*fn)(__isl_take PART *part, void *user);
        void *user;

        UNION *res;
};

/* Apply data->fn to "part" and add the result to data->res.
 */
static isl_stat FN(UNION,transform_entry)(__isl_take PART *part, void *user)
{
        S(UNION,transform_data) *data = (S(UNION,transform_data) *)user;

        part = data->fn(part, data->user);
        data->res = FN(FN(UNION,add),PARTS)(data->res, part);
        if (!data->res)
                return isl_stat_error;

        return isl_stat_ok;
}

/* Return a UNION living in "space" that is obtained by applying "fn"
 * to each of the entries in "u".
 */
static __isl_give UNION *FN(UNION,transform_space)(__isl_take UNION *u,
        isl_space *space,
        __isl_give PART *(*fn)(__isl_take PART *part, void *user), void *user)
{
        S(UNION,transform_data) data = { fn, user };

        data.res = FN(UNION,alloc_same_size_on_space)(u, space);
        if (FN(FN(UNION,foreach),PARTS)(u,
                                        &FN(UNION,transform_entry), &data) < 0)
                data.res = FN(UNION,free)(data.res);
        FN(UNION,free)(u);
        return data.res;
}

/* Return a UNION that lives in the same space as "u" and that is obtained
 * by applying "fn" to each of the entries in "u".
 */
static __isl_give UNION *FN(UNION,transform)(__isl_take UNION *u,
        __isl_give PART *(*fn)(__isl_take PART *part, void *user), void *user)
{
        return FN(UNION,transform_space)(u, FN(UNION,get_space)(u), fn, user);
}

/* Apply data->fn to *part and store the result back into *part.
 */
static isl_stat FN(UNION,transform_inplace_entry)(void **part, void *user)
{
        S(UNION,transform_data) *data = (S(UNION,transform_data) *) user;

        *part = data->fn(*part, data->user);
        if (!*part)
                return isl_stat_error;
        return isl_stat_ok;
}

/* Update "u" by applying "fn" to each entry.
 * This operation is assumed not to change the number of entries nor
 * the spaces of the entries.
 *
 * If there is only one reference to "u", then change "u" inplace.
 * Otherwise, create a new UNION from "u" and discard the original.
 */
static __isl_give UNION *FN(UNION,transform_inplace)(__isl_take UNION *u,
        __isl_give PART *(*fn)(__isl_take PART *part, void *user), void *user)
{
        isl_bool single_ref;

        single_ref = FN(UNION,has_single_reference)(u);
        if (single_ref < 0)
                return FN(UNION,free)(u);
        if (single_ref) {
                S(UNION,transform_data) data = { fn, user };
                if (FN(UNION,foreach_inplace)(u,
                                &FN(UNION,transform_inplace_entry), &data) < 0)
                        return FN(UNION,free)(u);
                return u;
        }
        return FN(UNION,transform)(u, fn, user);
}

/* An isl_union_*_transform callback for use in isl_union_*_dup
 * that simply returns "part".
 */
static __isl_give PART *FN(UNION,copy_part)(__isl_take PART *part, void *user)
{
        return part;
}

__isl_give UNION *FN(UNION,dup)(__isl_keep UNION *u)
{
        u = FN(UNION,copy)(u);
        return FN(UNION,transform)(u, &FN(UNION,copy_part), NULL);
}

__isl_give UNION *FN(UNION,cow)(__isl_take UNION *u)
{
        if (!u)
                return NULL;

        if (u->ref == 1)
                return u;
        u->ref--;
        return FN(UNION,dup)(u);
}

__isl_null UNION *FN(UNION,free)(__isl_take UNION *u)
{
        if (!u)
                return NULL;

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

        isl_hash_table_foreach(u->space->ctx, &u->table,
                                &FN(UNION,free_u_entry), NULL);
        isl_hash_table_clear(&u->table);
        isl_space_free(u->space);
        free(u);
        return NULL;
}

static __isl_give PART *FN(UNION,align_entry)(__isl_take PART *part, void *user)
{
        isl_reordering *exp = user;

        exp = isl_reordering_extend_space(isl_reordering_copy(exp),
                                    FN(PART,get_domain_space)(part));
        return FN(PART,realign_domain)(part, exp);
}

/* Reorder the parameters of "u" according to the given reordering.
 */
static __isl_give UNION *FN(UNION,realign_domain)(__isl_take UNION *u,
        __isl_take isl_reordering *r)
{
        isl_space *space;

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

        space = isl_space_copy(r->dim);
        u = FN(UNION,transform_space)(u, space, &FN(UNION,align_entry), r);
        isl_reordering_free(r);
        return u;
error:
        FN(UNION,free)(u);
        isl_reordering_free(r);
        return NULL;
}

/* Align the parameters of "u" to those of "model".
 */
__isl_give UNION *FN(UNION,align_params)(__isl_take UNION *u,
        __isl_take isl_space *model)
{
        isl_bool equal_params;
        isl_reordering *r;

        if (!u || !model)
                goto error;

        equal_params = isl_space_has_equal_params(u->space, model);
        if (equal_params < 0)
                goto error;
        if (equal_params) {
                isl_space_free(model);
                return u;
        }

        model = isl_space_params(model);
        r = isl_parameter_alignment_reordering(u->space, model);
        isl_space_free(model);

        return FN(UNION,realign_domain)(u, r);
error:
        isl_space_free(model);
        FN(UNION,free)(u);
        return NULL;
}

/* Add "part" to *u, taking the union sum if "u" already has
 * a part defined on the same space as "part".
 */
static isl_stat FN(UNION,union_add_part)(__isl_take PART *part, void *user)
{
        UNION **u = (UNION **)user;

        *u = FN(UNION,add_part_generic)(*u, part, 0);

        return isl_stat_ok;
}

/* Compute the sum of "u1" and "u2" on the union of their domains,
 * with the actual sum on the shared domain and
 * the defined expression on the symmetric difference of the domains.
 *
 * This is an internal function that is exposed under different
 * names depending on whether the base expressions have a zero default
 * value.
 * If they do, then this function is called "add".
 * Otherwise, it is called "union_add".
 */
static __isl_give UNION *FN(UNION,union_add_)(__isl_take UNION *u1,
        __isl_take UNION *u2)
{
        u1 = FN(UNION,align_params)(u1, FN(UNION,get_space)(u2));
        u2 = FN(UNION,align_params)(u2, FN(UNION,get_space)(u1));

        u1 = FN(UNION,cow)(u1);

        if (!u1 || !u2)
                goto error;

        if (FN(FN(UNION,foreach),PARTS)(u2, &FN(UNION,union_add_part), &u1) < 0)
                goto error;

        FN(UNION,free)(u2);

        return u1;
error:
        FN(UNION,free)(u1);
        FN(UNION,free)(u2);
        return NULL;
}

__isl_give UNION *FN(FN(UNION,from),PARTS)(__isl_take PART *part)
{
        isl_space *dim;
        UNION *u;

        if (!part)
                return NULL;

        dim = FN(PART,get_space)(part);
        dim = isl_space_drop_dims(dim, isl_dim_in, 0, isl_space_dim(dim, isl_dim_in));
        dim = isl_space_drop_dims(dim, isl_dim_out, 0, isl_space_dim(dim, isl_dim_out));
#ifdef HAS_TYPE
        u = FN(UNION,ZERO)(dim, part->type);
#else
        u = FN(UNION,ZERO)(dim);
#endif
        u = FN(FN(UNION,add),PARTS)(u, part);

        return u;
}

S(UNION,match_bin_data) {
        UNION *u2;
        UNION *res;
        __isl_give PART *(*fn)(__isl_take PART *, __isl_take PART *);
};

/* Check if data->u2 has an element living in the same space as "part".
 * If so, call data->fn on the two elements and add the result to
 * data->res.
 */
static isl_stat FN(UNION,match_bin_entry)(__isl_take PART *part, void *user)
{
        S(UNION,match_bin_data) *data = user;
        struct isl_hash_table_entry *entry2;
        isl_space *space;
        PART *part2;

        space = FN(PART,get_space)(part);
        entry2 = FN(UNION,find_part_entry)(data->u2, space, 0);
        isl_space_free(space);
        if (!entry2)
                goto error;
        if (entry2 == isl_hash_table_entry_none) {
                FN(PART,free)(part);
                return isl_stat_ok;
        }

        part2 = entry2->data;
        if (!isl_space_tuple_is_equal(part->dim, isl_dim_out,
                                        part2->dim, isl_dim_out))
                isl_die(FN(UNION,get_ctx)(data->u2), isl_error_invalid,
                        "entries should have the same range space",
                        goto error);

        part = data->fn(part, FN(PART, copy)(entry2->data));

        data->res = FN(FN(UNION,add),PARTS)(data->res, part);
        if (!data->res)
                return isl_stat_error;

        return isl_stat_ok;
error:
        FN(PART,free)(part);
        return isl_stat_error;
}

/* This function is currently only used from isl_polynomial.c
 * and not from isl_fold.c.
 */
static __isl_give UNION *FN(UNION,match_bin_op)(__isl_take UNION *u1,
        __isl_take UNION *u2,
        __isl_give PART *(*fn)(__isl_take PART *, __isl_take PART *))
        __attribute__ ((unused));
/* For each pair of elements in "u1" and "u2" living in the same space,
 * call "fn" and collect the results.
 */
static __isl_give UNION *FN(UNION,match_bin_op)(__isl_take UNION *u1,
        __isl_take UNION *u2,
        __isl_give PART *(*fn)(__isl_take PART *, __isl_take PART *))
{
        S(UNION,match_bin_data) data = { NULL, NULL, fn };

        u1 = FN(UNION,align_params)(u1, FN(UNION,get_space)(u2));
        u2 = FN(UNION,align_params)(u2, FN(UNION,get_space)(u1));

        if (!u1 || !u2)
                goto error;

        data.u2 = u2;
        data.res = FN(UNION,alloc_same_size)(u1);
        if (FN(FN(UNION,foreach),PARTS)(u1,
                                    &FN(UNION,match_bin_entry), &data) < 0)
                goto error;

        FN(UNION,free)(u1);
        FN(UNION,free)(u2);
        return data.res;
error:
        FN(UNION,free)(u1);
        FN(UNION,free)(u2);
        FN(UNION,free)(data.res);
        return NULL;
}

/* Compute the sum of "u1" and "u2".
 *
 * If the base expressions have a default zero value, then the sum
 * is computed on the union of the domains of "u1" and "u2".
 * Otherwise, it is computed on their shared domains.
 */
__isl_give UNION *FN(UNION,add)(__isl_take UNION *u1, __isl_take UNION *u2)
{
#if DEFAULT_IS_ZERO
        return FN(UNION,union_add_)(u1, u2);
#else
        return FN(UNION,match_bin_op)(u1, u2, &FN(PART,add));
#endif
}

#ifndef NO_SUB
/* Subtract "u2" from "u1" and return the result.
 */
__isl_give UNION *FN(UNION,sub)(__isl_take UNION *u1, __isl_take UNION *u2)
{
        return FN(UNION,match_bin_op)(u1, u2, &FN(PART,sub));
}
#endif

S(UNION,any_set_data) {
        isl_set *set;
        __isl_give PW *(*fn)(__isl_take PW*, __isl_take isl_set*);
};

static __isl_give PART *FN(UNION,any_set_entry)(__isl_take PART *part,
        void *user)
{
        S(UNION,any_set_data) *data = user;

        return data->fn(part, isl_set_copy(data->set));
}

/* Update each element of "u" by calling "fn" on the element and "set".
 */
static __isl_give UNION *FN(UNION,any_set_op)(__isl_take UNION *u,
        __isl_take isl_set *set,
        __isl_give PW *(*fn)(__isl_take PW*, __isl_take isl_set*))
{
        S(UNION,any_set_data) data = { NULL, fn };

        u = FN(UNION,align_params)(u, isl_set_get_space(set));
        set = isl_set_align_params(set, FN(UNION,get_space)(u));

        if (!u || !set)
                goto error;

        data.set = set;
        u = FN(UNION,transform)(u, &FN(UNION,any_set_entry), &data);
        isl_set_free(set);
        return u;
error:
        FN(UNION,free)(u);
        isl_set_free(set);
        return NULL;
}

/* Intersect the domain of "u" with the parameter domain "context".
 */
__isl_give UNION *FN(UNION,intersect_params)(__isl_take UNION *u,
        __isl_take isl_set *set)
{
        return FN(UNION,any_set_op)(u, set, &FN(PW,intersect_params));
}

/* Compute the gist of the domain of "u" with respect to
 * the parameter domain "context".
 */
__isl_give UNION *FN(UNION,gist_params)(__isl_take UNION *u,
        __isl_take isl_set *set)
{
        return FN(UNION,any_set_op)(u, set, &FN(PW,gist_params));
}

S(UNION,match_domain_data) {
        isl_union_set *uset;
        UNION *res;
        __isl_give PW *(*fn)(__isl_take PW*, __isl_take isl_set*);
};

static int FN(UNION,set_has_dim)(const void *entry, const void *val)
{
        isl_set *set = (isl_set *)entry;
        isl_space *dim = (isl_space *)val;

        return isl_space_is_equal(set->dim, dim);
}

/* Find the set in data->uset that lives in the same space as the domain
 * of "part", apply data->fn to *entry and this set (if any), and add
 * the result to data->res.
 */
static isl_stat FN(UNION,match_domain_entry)(__isl_take PART *part, void *user)
{
        S(UNION,match_domain_data) *data = user;
        uint32_t hash;
        struct isl_hash_table_entry *entry2;
        isl_space *space;

        space = FN(PART,get_domain_space)(part);
        hash = isl_space_get_hash(space);
        entry2 = isl_hash_table_find(data->uset->dim->ctx, &data->uset->table,
                                     hash, &FN(UNION,set_has_dim), space, 0);
        isl_space_free(space);
        if (!entry2) {
                FN(PART,free)(part);
                return isl_stat_ok;
        }

        part = data->fn(part, isl_set_copy(entry2->data));

        data->res = FN(FN(UNION,add),PARTS)(data->res, part);
        if (!data->res)
                return isl_stat_error;

        return isl_stat_ok;
}

/* Apply fn to each pair of PW in u and set in uset such that
 * the set lives in the same space as the domain of PW
 * and collect the results.
 */
static __isl_give UNION *FN(UNION,match_domain_op)(__isl_take UNION *u,
        __isl_take isl_union_set *uset,
        __isl_give PW *(*fn)(__isl_take PW*, __isl_take isl_set*))
{
        S(UNION,match_domain_data) data = { NULL, NULL, fn };

        u = FN(UNION,align_params)(u, isl_union_set_get_space(uset));
        uset = isl_union_set_align_params(uset, FN(UNION,get_space)(u));

        if (!u || !uset)
                goto error;

        data.uset = uset;
        data.res = FN(UNION,alloc_same_size)(u);
        if (FN(FN(UNION,foreach),PARTS)(u,
                                   &FN(UNION,match_domain_entry), &data) < 0)
                goto error;

        FN(UNION,free)(u);
        isl_union_set_free(uset);
        return data.res;
error:
        FN(UNION,free)(u);
        isl_union_set_free(uset);
        FN(UNION,free)(data.res);
        return NULL;
}

/* Intersect the domain of "u" with "uset".
 * If "uset" is a parameters domain, then intersect the parameter
 * domain of "u" with this set.
 */
__isl_give UNION *FN(UNION,intersect_domain)(__isl_take UNION *u,
        __isl_take isl_union_set *uset)
{
        if (isl_union_set_is_params(uset))
                return FN(UNION,intersect_params)(u,
                                                isl_set_from_union_set(uset));
        return FN(UNION,match_domain_op)(u, uset, &FN(PW,intersect_domain));
}

/* Take the set (which may be empty) in data->uset that lives
 * in the same space as the domain of "pw", subtract it from the domain
 * of "part" and return the result.
 */
static __isl_give PART *FN(UNION,subtract_domain_entry)(__isl_take PART *part,
        void *user)
{
        isl_union_set *uset = user;
        isl_space *space;
        isl_set *set;

        space = FN(PART,get_domain_space)(part);
        set = isl_union_set_extract_set(uset, space);
        return FN(PART,subtract_domain)(part, set);
}

/* Subtract "uset' from the domain of "u".
 */
__isl_give UNION *FN(UNION,subtract_domain)(__isl_take UNION *u,
        __isl_take isl_union_set *uset)
{
        u = FN(UNION,transform)(u, &FN(UNION,subtract_domain_entry), uset);
        isl_union_set_free(uset);
        return u;
}

__isl_give UNION *FN(UNION,gist)(__isl_take UNION *u,
        __isl_take isl_union_set *uset)
{
        if (isl_union_set_is_params(uset))
                return FN(UNION,gist_params)(u, isl_set_from_union_set(uset));
        return FN(UNION,match_domain_op)(u, uset, &FN(PW,gist));
}

/* Coalesce an entry in a UNION.  Coalescing is performed in-place.
 * Since the UNION may have several references, the entry is only
 * replaced if the coalescing is successful.
 */
static isl_stat FN(UNION,coalesce_entry)(void **entry, void *user)
{
        PART **part_p = (PART **) entry;
        PART *part;

        part = FN(PART,copy)(*part_p);
        part = FN(PW,coalesce)(part);
        if (!part)
                return isl_stat_error;
        FN(PART,free)(*part_p);
        *part_p = part;

        return isl_stat_ok;
}

__isl_give UNION *FN(UNION,coalesce)(__isl_take UNION *u)
{
        if (FN(UNION,foreach_inplace)(u, &FN(UNION,coalesce_entry), NULL) < 0)
                goto error;

        return u;
error:
        FN(UNION,free)(u);
        return NULL;
}

static isl_stat FN(UNION,domain_entry)(__isl_take PART *part, void *user)
{
        isl_union_set **uset = (isl_union_set **)user;

        *uset = isl_union_set_add_set(*uset, FN(PART,domain)(part));

        return isl_stat_ok;
}

__isl_give isl_union_set *FN(UNION,domain)(__isl_take UNION *u)
{
        isl_union_set *uset;

        uset = isl_union_set_empty(FN(UNION,get_space)(u));
        if (FN(FN(UNION,foreach),PARTS)(u, &FN(UNION,domain_entry), &uset) < 0)
                goto error;

        FN(UNION,free)(u);
        
        return uset;
error:
        isl_union_set_free(uset);
        FN(UNION,free)(u);
        return NULL;
}

#ifdef HAS_TYPE
/* Negate the type of "u".
 */
static __isl_give UNION *FN(UNION,negate_type)(__isl_take UNION *u)
{
        u = FN(UNION,cow)(u);
        if (!u)
                return NULL;
        u->type = isl_fold_type_negate(u->type);
        return u;
}
#else
/* Negate the type of "u".
 * Since "u" does not have a type, do nothing.
 */
static __isl_give UNION *FN(UNION,negate_type)(__isl_take UNION *u)
{
        return u;
}
#endif

/* Multiply "part" by the isl_val "user" and return the result.
 */
static __isl_give PART *FN(UNION,scale_val_entry)(__isl_take PART *part,
        void *user)
{
        isl_val *v = user;

        return FN(PART,scale_val)(part, isl_val_copy(v));
}

/* Multiply "u" by "v" and return the result.
 */
__isl_give UNION *FN(UNION,scale_val)(__isl_take UNION *u,
        __isl_take isl_val *v)
{
        if (!u || !v)
                goto error;
        if (isl_val_is_one(v)) {
                isl_val_free(v);
                return u;
        }

        if (DEFAULT_IS_ZERO && u && isl_val_is_zero(v)) {
                UNION *zero;
                isl_space *space = FN(UNION,get_space)(u);
#ifdef HAS_TYPE
                zero = FN(UNION,ZERO)(space, u->type);
#else
                zero = FN(UNION,ZERO)(space);
#endif
                FN(UNION,free)(u);
                isl_val_free(v);
                return zero;
        }

        if (!isl_val_is_rat(v))
                isl_die(isl_val_get_ctx(v), isl_error_invalid,
                        "expecting rational factor", goto error);

        u = FN(UNION,transform_inplace)(u, &FN(UNION,scale_val_entry), v);
        if (isl_val_is_neg(v))
                u = FN(UNION,negate_type)(u);

        isl_val_free(v);
        return u;
error:
        isl_val_free(v);
        FN(UNION,free)(u);
        return NULL;
}

/* Divide "part" by the isl_val "user" and return the result.
 */
static __isl_give PART *FN(UNION,scale_down_val_entry)(__isl_take PART *part,
        void *user)
{
        isl_val *v = user;

        return FN(PART,scale_down_val)(part, isl_val_copy(v));
}

/* Divide "u" by "v" and return the result.
 */
__isl_give UNION *FN(UNION,scale_down_val)(__isl_take UNION *u,
        __isl_take isl_val *v)
{
        if (!u || !v)
                goto error;
        if (isl_val_is_one(v)) {
                isl_val_free(v);
                return u;
        }

        if (!isl_val_is_rat(v))
                isl_die(isl_val_get_ctx(v), isl_error_invalid,
                        "expecting rational factor", goto error);
        if (isl_val_is_zero(v))
                isl_die(isl_val_get_ctx(v), isl_error_invalid,
                        "cannot scale down by zero", goto error);

        u = FN(UNION,transform_inplace)(u, &FN(UNION,scale_down_val_entry), v);
        if (isl_val_is_neg(v))
                u = FN(UNION,negate_type)(u);

        isl_val_free(v);
        return u;
error:
        isl_val_free(v);
        FN(UNION,free)(u);
        return NULL;
}

S(UNION,plain_is_equal_data)
{
        UNION *u2;
        isl_bool is_equal;
};

static isl_stat FN(UNION,plain_is_equal_entry)(void **entry, void *user)
{
        S(UNION,plain_is_equal_data) *data = user;
        struct isl_hash_table_entry *entry2;
        PW *pw = *entry;

        entry2 = FN(UNION,find_part_entry)(data->u2, pw->dim, 0);
        if (!entry2 || entry2 == isl_hash_table_entry_none) {
                if (!entry2)
                        data->is_equal = isl_bool_error;
                else
                        data->is_equal = isl_bool_false;
                return isl_stat_error;
        }

        data->is_equal = FN(PW,plain_is_equal)(pw, entry2->data);
        if (data->is_equal < 0 || !data->is_equal)
                return isl_stat_error;

        return isl_stat_ok;
}

isl_bool FN(UNION,plain_is_equal)(__isl_keep UNION *u1, __isl_keep UNION *u2)
{
        S(UNION,plain_is_equal_data) data = { NULL, isl_bool_true };
        int n1, n2;

        if (!u1 || !u2)
                return isl_bool_error;
        if (u1 == u2)
                return isl_bool_true;
        if (u1->table.n != u2->table.n)
                return isl_bool_false;
        n1 = FN(FN(UNION,n),PARTS)(u1);
        n2 = FN(FN(UNION,n),PARTS)(u2);
        if (n1 < 0 || n2 < 0)
                return isl_bool_error;
        if (n1 != n2)
                return isl_bool_false;

        u1 = FN(UNION,copy)(u1);
        u2 = FN(UNION,copy)(u2);
        u1 = FN(UNION,align_params)(u1, FN(UNION,get_space)(u2));
        u2 = FN(UNION,align_params)(u2, FN(UNION,get_space)(u1));
        if (!u1 || !u2)
                goto error;

        data.u2 = u2;
        if (FN(UNION,foreach_inplace)(u1,
                               &FN(UNION,plain_is_equal_entry), &data) < 0 &&
            data.is_equal)
                goto error;

        FN(UNION,free)(u1);
        FN(UNION,free)(u2);

        return data.is_equal;
error:
        FN(UNION,free)(u1);
        FN(UNION,free)(u2);
        return isl_bool_error;
}

/* Check whether the element that "entry" points to involves any NaNs and
 * store the result in *nan.
 * Abort as soon as one such element has been found.
 */
static isl_stat FN(UNION,involves_nan_entry)(void **entry, void *user)
{
        isl_bool *nan = user;
        PW *pw = *entry;

        *nan = FN(PW,involves_nan)(pw);
        if (*nan < 0 || !nan)
                return isl_stat_error;

        return isl_stat_ok;
}

/* Does "u" involve any NaNs?
 */
isl_bool FN(UNION,involves_nan)(__isl_keep UNION *u)
{
        isl_bool nan = isl_bool_false;

        if (!u)
                return isl_bool_error;

        if (FN(UNION,foreach_inplace)(u,
                                    &FN(UNION,involves_nan_entry), &nan) < 0 &&
            !nan)
                return isl_bool_error;

        return nan;
}

/* Internal data structure for isl_union_*_drop_dims.
 * type, first and n are passed to isl_*_drop_dims.
 */
S(UNION,drop_dims_data) {
        enum isl_dim_type type;
        unsigned first;
        unsigned n;
};

/* Drop the parameters specified by "data" from "part" and return the result.
 */
static __isl_give PART *FN(UNION,drop_dims_entry)(__isl_take PART *part,
        void *user)
{
        S(UNION,drop_dims_data) *data = user;

        return FN(PART,drop_dims)(part, data->type, data->first, data->n);
}

/* Drop the specified parameters from "u".
 * That is, type is required to be isl_dim_param.
 */
__isl_give UNION *FN(UNION,drop_dims)( __isl_take UNION *u,
        enum isl_dim_type type, unsigned first, unsigned n)
{
        isl_space *space;
        S(UNION,drop_dims_data) data = { type, first, n };

        if (!u)
                return NULL;

        if (type != isl_dim_param)
                isl_die(FN(UNION,get_ctx)(u), isl_error_invalid,
                        "can only project out parameters",
                        return FN(UNION,free)(u));

        space = FN(UNION,get_space)(u);
        space = isl_space_drop_dims(space, type, first, n);
        return FN(UNION,transform_space)(u, space, &FN(UNION,drop_dims_entry),
                                        &data);
}

/* Internal data structure for isl_union_*_set_dim_name.
 * pos is the position of the parameter that needs to be renamed.
 * s is the new name.
 */
S(UNION,set_dim_name_data) {
        unsigned pos;
        const char *s;
};

/* Change the name of the parameter at position data->pos of "part" to data->s
 * and return the result.
 */
static __isl_give PART *FN(UNION,set_dim_name_entry)(__isl_take PART *part,
        void *user)
{
        S(UNION,set_dim_name_data) *data = user;

        return FN(PART,set_dim_name)(part, isl_dim_param, data->pos, data->s);
}

/* Change the name of the parameter at position "pos" to "s".
 * That is, type is required to be isl_dim_param.
 */
__isl_give UNION *FN(UNION,set_dim_name)(__isl_take UNION *u,
        enum isl_dim_type type, unsigned pos, const char *s)
{
        S(UNION,set_dim_name_data) data = { pos, s };
        isl_space *space;

        if (!u)
                return NULL;

        if (type != isl_dim_param)
                isl_die(FN(UNION,get_ctx)(u), isl_error_invalid,
                        "can only set parameter names",
                        return FN(UNION,free)(u));

        space = FN(UNION,get_space)(u);
        space = isl_space_set_dim_name(space, type, pos, s);
        return FN(UNION,transform_space)(u, space,
                                        &FN(UNION,set_dim_name_entry), &data);
}

/* Reset the user pointer on all identifiers of parameters and tuples
 * of the space of "part" and return the result.
 */
static __isl_give PART *FN(UNION,reset_user_entry)(__isl_take PART *part,
        void *user)
{
        return FN(PART,reset_user)(part);
}

/* Reset the user pointer on all identifiers of parameters and tuples
 * of the spaces of "u".
 */
__isl_give UNION *FN(UNION,reset_user)(__isl_take UNION *u)
{
        isl_space *space;

        space = FN(UNION,get_space)(u);
        space = isl_space_reset_user(space);
        return FN(UNION,transform_space)(u, space, &FN(UNION,reset_user_entry),
                                        NULL);
}