isl_map_coalesce: avoid ignoring constraints redundant wrt implicit equalities

[isl.git] / isl_fold.c

/*
 * Copyright 2010      INRIA Saclay
 *
 * 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 
 */

#include <isl_map_private.h>
#include <isl_union_map_private.h>
#include <isl_polynomial_private.h>
#include <isl_point_private.h>
#include <isl_space_private.h>
#include <isl_lp_private.h>
#include <isl_seq.h>
#include <isl_mat_private.h>
#include <isl_val_private.h>
#include <isl_vec_private.h>
#include <isl_config.h>

#undef EL_BASE
#define EL_BASE pw_qpolynomial_fold

#include <isl_list_templ.c>

enum isl_fold isl_fold_type_negate(enum isl_fold type)
{
        switch (type) {
        case isl_fold_error:
                return isl_fold_error;
        case isl_fold_min:
                return isl_fold_max;
        case isl_fold_max:
                return isl_fold_min;
        case isl_fold_list:
                return isl_fold_list;
        }

        isl_die(NULL, isl_error_internal, "unhandled isl_fold type", abort());
}

/* Construct a new reduction with the given type, domain space and
 * list of polynomials.
 */
static __isl_give isl_qpolynomial_fold *qpolynomial_fold_alloc(
        enum isl_fold type, __isl_take isl_space *space,
        __isl_take isl_qpolynomial_list *list)
{
        isl_ctx *ctx;
        isl_qpolynomial_fold *fold;

        if (type < 0 || !space || !list)
                goto error;

        ctx = isl_space_get_ctx(space);
        fold = isl_calloc_type(ctx, struct isl_qpolynomial_fold);
        if (!fold)
                goto error;

        fold->ref = 1;
        fold->type = type;
        fold->dim = space;
        fold->list = list;

        return fold;
error:
        isl_space_free(space);
        isl_qpolynomial_list_free(list);
        return NULL;
}

isl_ctx *isl_qpolynomial_fold_get_ctx(__isl_keep isl_qpolynomial_fold *fold)
{
        return fold ? fold->dim->ctx : NULL;
}

/* Return the domain space of "fold".
 */
static __isl_keep isl_space *isl_qpolynomial_fold_peek_domain_space(
        __isl_keep isl_qpolynomial_fold *fold)
{
        return fold ? fold->dim : NULL;
}

__isl_give isl_space *isl_qpolynomial_fold_get_domain_space(
        __isl_keep isl_qpolynomial_fold *fold)
{
        return isl_space_copy(isl_qpolynomial_fold_peek_domain_space(fold));
}

/* Return the space of the domain of "fold".
 * This may be either a copy or the space itself
 * if there is only one reference to "fold".
 * This allows the space to be modified inplace
 * if both the expression and its space have only a single reference.
 * The caller is not allowed to modify "fold" between this call and
 * a subsequent call to isl_qpolynomial_fold_restore_domain_space.
 * The only exception is that isl_qpolynomial_fold_free can be called instead.
 */
static __isl_give isl_space *isl_qpolynomial_fold_take_domain_space(
        __isl_keep isl_qpolynomial_fold *fold)
{
        isl_space *space;

        if (!fold)
                return NULL;
        if (fold->ref != 1)
                return isl_qpolynomial_fold_get_domain_space(fold);
        space = fold->dim;
        fold->dim = NULL;
        return space;
}

/* Set the space of the domain of "fold" to "space",
 * where the space of "fold" may be missing
 * due to a preceding call to isl_qpolynomial_fold_take_domain_space.
 * However, in this case, "fold" only has a single reference and
 * then the call to isl_qpolynomial_fold_cow has no effect.
 */
static
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_restore_domain_space(
        __isl_keep isl_qpolynomial_fold *fold, __isl_take isl_space *space)
{
        if (!fold || !space)
                goto error;

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

        fold = isl_qpolynomial_fold_cow(fold);
        if (!fold)
                goto error;
        isl_space_free(fold->dim);
        fold->dim = space;

        return fold;
error:
        isl_qpolynomial_fold_free(fold);
        isl_space_free(space);
        return NULL;
}

__isl_give isl_space *isl_qpolynomial_fold_get_space(
        __isl_keep isl_qpolynomial_fold *fold)
{
        isl_space *space;
        if (!fold)
                return NULL;
        space = isl_space_copy(fold->dim);
        space = isl_space_from_domain(space);
        space = isl_space_add_dims(space, isl_dim_out, 1);
        return space;
}

/* Return the list of polynomials in the reduction "fold".
 */
__isl_keep isl_qpolynomial_list *isl_qpolynomial_fold_peek_list(
        __isl_keep isl_qpolynomial_fold *fold)
{
        return fold ? fold->list : NULL;
}

/* Return a copy of the list of polynomials in the reduction "fold".
 */
static __isl_give isl_qpolynomial_list *isl_qpolynomial_fold_get_list(
        __isl_keep isl_qpolynomial_fold *fold)
{
        return isl_qpolynomial_list_copy(isl_qpolynomial_fold_peek_list(fold));
}

/* Return the list of polynomials of "fold".
 * This may be either a copy or the list itself
 * if there is only one reference to "fold".
 * This allows the list to be modified inplace
 * if both the expression and its list have only a single reference.
 * The caller is not allowed to modify "fold" between this call and
 * a subsequent call to isl_qpolynomial_fold_restore_list.
 * The only exception is that isl_qpolynomial_fold_free can be called instead.
 */
static __isl_give isl_qpolynomial_list *isl_qpolynomial_fold_take_list(
        __isl_keep isl_qpolynomial_fold *fold)
{
        isl_qpolynomial_list *list;

        if (!fold)
                return NULL;
        if (fold->ref != 1)
                return isl_qpolynomial_fold_get_list(fold);
        list = fold->list;
        fold->list = NULL;
        return list;
}

/* Set the space of the list of polynomials of "fold" to "space",
 * where the list of polynomials of "fold" may be missing
 * due to a preceding call to isl_qpolynomial_fold_take_list.
 * However, in this case, "fold" only has a single reference and
 * then the call to isl_qpolynomial_fold_cow has no effect.
 */
static __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_restore_list(
        __isl_keep isl_qpolynomial_fold *fold,
        __isl_take isl_qpolynomial_list *list)
{
        if (!fold || !list)
                goto error;

        if (fold->list == list) {
                isl_qpolynomial_list_free(list);
                return fold;
        }

        fold = isl_qpolynomial_fold_cow(fold);
        if (!fold)
                goto error;
        isl_qpolynomial_list_free(fold->list);
        fold->list = list;

        return fold;
error:
        isl_qpolynomial_fold_free(fold);
        isl_qpolynomial_list_free(list);
        return NULL;
}

/* isl_qpolynomial_list_map callback that calls
 * isl_qpolynomial_reset_domain_space on "qp".
 */
static __isl_give isl_qpolynomial *reset_domain_space(
        __isl_take isl_qpolynomial *qp, void *user)
{
        isl_space *space = user;

        return isl_qpolynomial_reset_domain_space(qp, isl_space_copy(space));
}

/* Replace the domain space of "fold" by "space".
 *
 * Replace the domain space itself and that of all polynomials
 * in the list.
 */
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_reset_domain_space(
        __isl_take isl_qpolynomial_fold *fold, __isl_take isl_space *space)
{
        isl_qpolynomial_list *list;

        list = isl_qpolynomial_fold_take_list(fold);
        list = isl_qpolynomial_list_map(list, &reset_domain_space, space);
        fold = isl_qpolynomial_fold_restore_list(fold, list);

        isl_space_free(isl_qpolynomial_fold_take_domain_space(fold));
        fold = isl_qpolynomial_fold_restore_domain_space(fold, space);

        return fold;
}

/* Reset the space of "fold".  This function is called from isl_pw_templ.c
 * and doesn't know if the space of an element object is represented
 * directly or through its domain.  It therefore passes along both.
 */
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_reset_space_and_domain(
        __isl_take isl_qpolynomial_fold *fold, __isl_take isl_space *space,
        __isl_take isl_space *domain)
{
        isl_space_free(space);
        return isl_qpolynomial_fold_reset_domain_space(fold, domain);
}

/* Internal data structure for isl_qpolynomial_fold_*_dims
 * representing their arguments.
 */
struct isl_fold_dims_data {
        enum isl_dim_type type;
        unsigned first;
        unsigned n;
};

/* isl_qpolynomial_list_every callback that checks whether "qp"
 * does not involve any dimensions in the given range.
 */
static isl_bool not_involved(__isl_keep isl_qpolynomial *qp, void *user)
{
        struct isl_fold_dims_data *data = user;
        isl_bool involves;

        involves = isl_qpolynomial_involves_dims(qp, data->type,
                                                        data->first, data->n);
        return isl_bool_not(involves);
}

/* Does "fold" involve any dimensions in the given range.
 *
 * It involves any of those dimensions if it is not the case
 * that every polynomial in the reduction does not involve
 * any of the dimensions.
 */
static isl_bool isl_qpolynomial_fold_involves_dims(
        __isl_keep isl_qpolynomial_fold *fold,
        enum isl_dim_type type, unsigned first, unsigned n)
{
        struct isl_fold_dims_data data = { type, first, n };
        isl_qpolynomial_list *list;
        isl_bool not;

        if (!fold)
                return isl_bool_error;
        if (n == 0)
                return isl_bool_false;

        list = isl_qpolynomial_fold_peek_list(fold);
        not = isl_qpolynomial_list_every(list, &not_involved, &data);
        return isl_bool_not(not);
}

/* Internal data structure for isl_qpolynomial_fold_set_dim_name
 * representing its arguments.
 */
struct isl_fold_set_dim_name_data {
        enum isl_dim_type type;
        unsigned pos;
        const char *s;
};

/* isl_qpolynomial_list_map callback for calling
 * isl_qpolynomial_set_dim_name on "qp".
 */
static __isl_give isl_qpolynomial *set_dim_name(__isl_take isl_qpolynomial *qp,
        void *user)
{
        struct isl_fold_set_dim_name_data *data = user;

        qp = isl_qpolynomial_set_dim_name(qp, data->type, data->pos, data->s);
        return qp;
}

/* Given a dimension type for an isl_qpolynomial_fold,
 * return the corresponding type for the domain.
 */
static enum isl_dim_type domain_type(enum isl_dim_type type)
{
        if (type == isl_dim_in)
                return isl_dim_set;
        return type;
}

__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_set_dim_name(
        __isl_take isl_qpolynomial_fold *fold,
        enum isl_dim_type type, unsigned pos, const char *s)
{
        struct isl_fold_set_dim_name_data data = { type, pos, s };
        enum isl_dim_type set_type;
        isl_space *space;
        isl_qpolynomial_list *list;

        list = isl_qpolynomial_fold_take_list(fold);
        list = isl_qpolynomial_list_map(list, &set_dim_name, &data);
        fold = isl_qpolynomial_fold_restore_list(fold, list);

        set_type = domain_type(type);
        space = isl_qpolynomial_fold_take_domain_space(fold);
        space = isl_space_set_dim_name(space, set_type, pos, s);
        fold = isl_qpolynomial_fold_restore_domain_space(fold, space);

        return fold;
}

/* isl_qpolynomial_list_map callback for calling
 * isl_qpolynomial_drop_dims on "qp".
 */
static __isl_give isl_qpolynomial *drop_dims(__isl_take isl_qpolynomial *qp,
        void *user)
{
        struct isl_fold_dims_data *data = user;

        qp = isl_qpolynomial_drop_dims(qp, data->type, data->first, data->n);
        return qp;
}

__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_drop_dims(
        __isl_take isl_qpolynomial_fold *fold,
        enum isl_dim_type type, unsigned first, unsigned n)
{
        struct isl_fold_dims_data data = { type, first, n };
        enum isl_dim_type set_type;
        isl_space *space;
        isl_qpolynomial_list *list;

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

        set_type = domain_type(type);

        list = isl_qpolynomial_fold_take_list(fold);
        list = isl_qpolynomial_list_map(list, &drop_dims, &data);
        fold = isl_qpolynomial_fold_restore_list(fold, list);

        space = isl_qpolynomial_fold_take_domain_space(fold);
        space = isl_space_drop_dims(space, set_type, first, n);
        fold = isl_qpolynomial_fold_restore_domain_space(fold, space);

        return fold;
}

/* isl_qpolynomial_list_map callback for calling
 * isl_qpolynomial_insert_dims on "qp".
 */
static __isl_give isl_qpolynomial *insert_dims(__isl_take isl_qpolynomial *qp,
        void *user)
{
        struct isl_fold_dims_data *data = user;

        qp = isl_qpolynomial_insert_dims(qp, data->type, data->first, data->n);
        return qp;
}

__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_insert_dims(
        __isl_take isl_qpolynomial_fold *fold,
        enum isl_dim_type type, unsigned first, unsigned n)
{
        struct isl_fold_dims_data data = { type, first, n };
        enum isl_dim_type set_type;
        isl_space *space;
        isl_qpolynomial_list *list;

        if (!fold)
                return NULL;
        if (n == 0 && !isl_space_is_named_or_nested(fold->dim, type))
                return fold;

        list = isl_qpolynomial_fold_take_list(fold);
        list = isl_qpolynomial_list_map(list, &insert_dims, &data);
        fold = isl_qpolynomial_fold_restore_list(fold, list);

        set_type = domain_type(type);
        space = isl_qpolynomial_fold_take_domain_space(fold);
        space = isl_space_insert_dims(space, set_type, first, n);
        fold = isl_qpolynomial_fold_restore_domain_space(fold, space);

        return fold;
}

/* Determine the sign of the constant quasipolynomial "qp".
 *
 * Return
 *      -1 if qp <= 0
 *       1 if qp >= 0
 *       0 if unknown
 *
 * For qp == 0, we can return either -1 or 1.  In practice, we return 1.
 * For qp == NaN, the sign is undefined, so we return 0.
 */
static int isl_qpolynomial_cst_sign(__isl_keep isl_qpolynomial *qp)
{
        isl_poly_cst *cst;

        if (isl_qpolynomial_is_nan(qp))
                return 0;

        cst = isl_poly_as_cst(qp->poly);
        if (!cst)
                return 0;

        return isl_int_sgn(cst->n) < 0 ? -1 : 1;
}

static int isl_qpolynomial_aff_sign(__isl_keep isl_set *set,
        __isl_keep isl_qpolynomial *qp)
{
        enum isl_lp_result res;
        isl_vec *aff;
        isl_int opt;
        int sgn = 0;

        aff = isl_qpolynomial_extract_affine(qp);
        if (!aff)
                return 0;

        isl_int_init(opt);

        res = isl_set_solve_lp(set, 0, aff->el + 1, aff->el[0],
                                &opt, NULL, NULL);
        if (res == isl_lp_error)
                goto done;
        if (res == isl_lp_empty ||
            (res == isl_lp_ok && !isl_int_is_neg(opt))) {
                sgn = 1;
                goto done;
        }

        res = isl_set_solve_lp(set, 1, aff->el + 1, aff->el[0],
                                &opt, NULL, NULL);
        if (res == isl_lp_ok && !isl_int_is_pos(opt))
                sgn = -1;

done:
        isl_int_clear(opt);
        isl_vec_free(aff);
        return sgn;
}

/* Determine, if possible, the sign of the quasipolynomial "qp" on
 * the domain "set".
 *
 * If qp is a constant, then the problem is trivial.
 * If qp is linear, then we check if the minimum of the corresponding
 * affine constraint is non-negative or if the maximum is non-positive.
 *
 * Otherwise, we check if the outermost variable "v" has a lower bound "l"
 * in "set".  If so, we write qp(v,v') as
 *
 *      q(v,v') * (v - l) + r(v')
 *
 * if q(v,v') and r(v') have the same known sign, then the original
 * quasipolynomial has the same sign as well.
 *
 * Return
 *      -1 if qp <= 0
 *       1 if qp >= 0
 *       0 if unknown
 */
static int isl_qpolynomial_sign(__isl_keep isl_set *set,
        __isl_keep isl_qpolynomial *qp)
{
        isl_size d;
        int i;
        isl_bool is;
        isl_poly_rec *rec;
        isl_vec *v;
        isl_int l;
        enum isl_lp_result res;
        int sgn = 0;

        is = isl_qpolynomial_is_cst(qp, NULL, NULL);
        if (is < 0)
                return 0;
        if (is)
                return isl_qpolynomial_cst_sign(qp);

        is = isl_qpolynomial_is_affine(qp);
        if (is < 0)
                return 0;
        if (is)
                return isl_qpolynomial_aff_sign(set, qp);

        if (qp->div->n_row > 0)
                return 0;

        rec = isl_poly_as_rec(qp->poly);
        if (!rec)
                return 0;

        d = isl_space_dim(qp->dim, isl_dim_all);
        if (d < 0)
                return 0;
        v = isl_vec_alloc(set->ctx, 2 + d);
        if (!v)
                return 0;

        isl_seq_clr(v->el + 1, 1 + d);
        isl_int_set_si(v->el[0], 1);
        isl_int_set_si(v->el[2 + qp->poly->var], 1);

        isl_int_init(l);

        res = isl_set_solve_lp(set, 0, v->el + 1, v->el[0], &l, NULL, NULL);
        if (res == isl_lp_ok) {
                isl_qpolynomial *min;
                isl_qpolynomial *base;
                isl_qpolynomial *r, *q;
                isl_qpolynomial *t;

                min = isl_qpolynomial_cst_on_domain(isl_space_copy(qp->dim), l);
                base = isl_qpolynomial_var_pow_on_domain(isl_space_copy(qp->dim),
                                                qp->poly->var, 1);

                r = isl_qpolynomial_alloc(isl_space_copy(qp->dim), 0,
                                          isl_poly_copy(rec->p[rec->n - 1]));
                q = isl_qpolynomial_copy(r);

                for (i = rec->n - 2; i >= 0; --i) {
                        r = isl_qpolynomial_mul(r, isl_qpolynomial_copy(min));
                        t = isl_qpolynomial_alloc(isl_space_copy(qp->dim), 0,
                                                  isl_poly_copy(rec->p[i]));
                        r = isl_qpolynomial_add(r, t);
                        if (i == 0)
                                break;
                        q = isl_qpolynomial_mul(q, isl_qpolynomial_copy(base));
                        q = isl_qpolynomial_add(q, isl_qpolynomial_copy(r));
                }

                if (isl_qpolynomial_is_zero(q))
                        sgn = isl_qpolynomial_sign(set, r);
                else if (isl_qpolynomial_is_zero(r))
                        sgn = isl_qpolynomial_sign(set, q);
                else {
                        int sgn_q, sgn_r;
                        sgn_r = isl_qpolynomial_sign(set, r);
                        sgn_q = isl_qpolynomial_sign(set, q);
                        if (sgn_r == sgn_q)
                                sgn = sgn_r;
                }

                isl_qpolynomial_free(min);
                isl_qpolynomial_free(base);
                isl_qpolynomial_free(q);
                isl_qpolynomial_free(r);
        }

        isl_int_clear(l);

        isl_vec_free(v);

        return sgn;
}

/* Check that "fold1" and "fold2" have the same type.
 */
static isl_stat isl_qpolynomial_fold_check_equal_type(
        __isl_keep isl_qpolynomial_fold *fold1,
        __isl_keep isl_qpolynomial_fold *fold2)
{
        enum isl_fold type1, type2;

        type1 = isl_qpolynomial_fold_get_type(fold1);
        type2 = isl_qpolynomial_fold_get_type(fold2);
        if (type1 < 0 || type2 < 0)
                return isl_stat_error;
        if (type1 != type2)
                isl_die(isl_qpolynomial_fold_get_ctx(fold1), isl_error_invalid,
                        "fold types don't match", return isl_stat_error);
        return isl_stat_ok;
}

/* Check that "fold1" and "fold2" have the same (domain) space.
 */
static isl_stat isl_qpolynomial_fold_check_equal_space(
        __isl_keep isl_qpolynomial_fold *fold1,
        __isl_keep isl_qpolynomial_fold *fold2)
{
        isl_bool equal;
        isl_space *space1, *space2;

        space1 = isl_qpolynomial_fold_peek_domain_space(fold1);
        space2 = isl_qpolynomial_fold_peek_domain_space(fold2);
        equal = isl_space_is_equal(space1, space2);
        if (equal < 0)
                return isl_stat_error;
        if (!equal)
                isl_die(isl_qpolynomial_fold_get_ctx(fold1), isl_error_invalid,
                        "spaces don't match", return isl_stat_error);
        return isl_stat_ok;
}

/* Combine "list1" and "list2" into a single list, eliminating
 * those elements of one list that are already covered by the other
 * list on "set".
 *
 * "better" is the sign that the difference qp1 - qp2 needs to have for qp1
 * to be covered by qp2.
 */
static __isl_give isl_qpolynomial_list *merge_lists(__isl_keep isl_set *set,
        __isl_take isl_qpolynomial_list *list1,
        __isl_take isl_qpolynomial_list *list2, int better)
{
        int i, j;
        isl_size n1, n2;

        n1 = isl_qpolynomial_list_size(list1);
        n2 = isl_qpolynomial_list_size(list2);
        if (n1 < 0 || n2 < 0)
                goto error;

        for (i = n2 - 1; i >= 0; --i) {
                for (j = n1 - 1; j >= 0; --j) {
                        isl_qpolynomial *qp1, *qp2, *d;
                        int sgn;
                        isl_bool equal;

                        qp1 = isl_qpolynomial_list_peek(list1, j);
                        qp2 = isl_qpolynomial_list_peek(list2, i);
                        equal = isl_qpolynomial_plain_is_equal(qp1, qp2);
                        if (equal < 0)
                                goto error;
                        if (equal)
                                break;
                        d = isl_qpolynomial_sub(
                                isl_qpolynomial_copy(qp1),
                                isl_qpolynomial_copy(qp2));
                        sgn = isl_qpolynomial_sign(set, d);
                        isl_qpolynomial_free(d);
                        if (sgn == 0)
                                continue;
                        if (sgn != better)
                                break;
                        list1 = isl_qpolynomial_list_drop(list1, j, 1);
                        n1--;
                }
                if (j < 0)
                        continue;
                list2 = isl_qpolynomial_list_drop(list2, i, 1);
                n2--;
        }

        return isl_qpolynomial_list_concat(list1, list2);
error:
        isl_qpolynomial_list_free(list1);
        isl_qpolynomial_list_free(list2);
        return NULL;
}

/* Combine "fold1" and "fold2" into a single reduction, eliminating
 * those elements of one reduction that are already covered by the other
 * reduction on "set".
 *
 * If "fold1" or "fold2" is an empty reduction, then return
 * the other reduction.
 * If "fold1" or "fold2" is a NaN, then return this NaN.
 */
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_fold_on_domain(
        __isl_keep isl_set *set,
        __isl_take isl_qpolynomial_fold *fold1,
        __isl_take isl_qpolynomial_fold *fold2)
{
        isl_qpolynomial_list *list1;
        isl_qpolynomial_list *list2;
        int better;

        if (isl_qpolynomial_fold_check_equal_type(fold1, fold2) < 0)
                goto error;
        if (isl_qpolynomial_fold_check_equal_space(fold1, fold2) < 0)
                goto error;

        better = fold1->type == isl_fold_max ? -1 : 1;

        if (isl_qpolynomial_fold_is_empty(fold1) ||
            isl_qpolynomial_fold_is_nan(fold2)) {
                isl_qpolynomial_fold_free(fold1);
                return fold2;
        }

        if (isl_qpolynomial_fold_is_empty(fold2) ||
            isl_qpolynomial_fold_is_nan(fold1)) {
                isl_qpolynomial_fold_free(fold2);
                return fold1;
        }

        list1 = isl_qpolynomial_fold_take_list(fold1);
        list2 = isl_qpolynomial_fold_take_list(fold2);

        list1 = merge_lists(set, list1, list2, better);

        fold1 = isl_qpolynomial_fold_restore_list(fold1, list1);
        isl_qpolynomial_fold_free(fold2);

        return fold1;
error:
        isl_qpolynomial_fold_free(fold1);
        isl_qpolynomial_fold_free(fold2);
        return NULL;
}

/* isl_qpolynomial_list_map callback for adding "qp2" to "qp".
 */
static __isl_give isl_qpolynomial *add_qpolynomial(
        __isl_take isl_qpolynomial *qp, void *user)
{
        isl_qpolynomial *qp2 = user;

        return isl_qpolynomial_add(qp, isl_qpolynomial_copy(qp2));
}

__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_add_qpolynomial(
        __isl_take isl_qpolynomial_fold *fold, __isl_take isl_qpolynomial *qp)
{
        isl_qpolynomial_list *list;

        if (!fold || !qp)
                goto error;

        if (isl_qpolynomial_is_zero(qp)) {
                isl_qpolynomial_free(qp);
                return fold;
        }

        list = isl_qpolynomial_fold_take_list(fold);
        list = isl_qpolynomial_list_map(list, &add_qpolynomial, qp);
        fold = isl_qpolynomial_fold_restore_list(fold, list);

        isl_qpolynomial_free(qp);
        return fold;
error:
        isl_qpolynomial_fold_free(fold);
        isl_qpolynomial_free(qp);
        return NULL;
}

__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_add_on_domain(
        __isl_keep isl_set *dom,
        __isl_take isl_qpolynomial_fold *fold1,
        __isl_take isl_qpolynomial_fold *fold2)
{
        int i;
        isl_size n1, n2;
        isl_qpolynomial_fold *res = NULL;
        isl_qpolynomial *qp;
        isl_qpolynomial_list *list1, *list2;

        if (!fold1 || !fold2)
                goto error;

        if (isl_qpolynomial_fold_is_empty(fold1)) {
                isl_qpolynomial_fold_free(fold1);
                return fold2;
        }

        if (isl_qpolynomial_fold_is_empty(fold2)) {
                isl_qpolynomial_fold_free(fold2);
                return fold1;
        }

        list1 = isl_qpolynomial_fold_peek_list(fold1);
        list2 = isl_qpolynomial_fold_peek_list(fold2);
        n1 = isl_qpolynomial_list_size(list1);
        n2 = isl_qpolynomial_list_size(list2);
        if (n1 < 0 || n2 < 0)
                goto error;

        if (n1 == 1 && n2 != 1)
                return isl_qpolynomial_fold_add_on_domain(dom, fold2, fold1);

        qp = isl_qpolynomial_list_get_at(list2, 0);
        if (n2 == 1) {
                res = isl_qpolynomial_fold_add_qpolynomial(fold1, qp);
                isl_qpolynomial_fold_free(fold2);
                return res;
        }

        res = isl_qpolynomial_fold_add_qpolynomial(
                                isl_qpolynomial_fold_copy(fold1), qp);

        for (i = 1; i < n2; ++i) {
                isl_qpolynomial_fold *res_i;

                qp = isl_qpolynomial_list_get_at(list2, i);
                res_i = isl_qpolynomial_fold_add_qpolynomial(
                                        isl_qpolynomial_fold_copy(fold1), qp);
                res = isl_qpolynomial_fold_fold_on_domain(dom, res, res_i);
        }

        isl_qpolynomial_fold_free(fold1);
        isl_qpolynomial_fold_free(fold2);
        return res;
error:
        isl_qpolynomial_fold_free(res);
        isl_qpolynomial_fold_free(fold1);
        isl_qpolynomial_fold_free(fold2);
        return NULL;
}

/* isl_qpolynomial_list_map callback for calling
 * isl_qpolynomial_substitute_equalities on "qp" and "eq".
 */
static __isl_give isl_qpolynomial *substitute_equalities(
        __isl_take isl_qpolynomial *qp, void *user)
{
        isl_basic_set *eq = user;

        eq = isl_basic_set_copy(eq);
        return isl_qpolynomial_substitute_equalities(qp, eq);
}

__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_substitute_equalities(
        __isl_take isl_qpolynomial_fold *fold, __isl_take isl_basic_set *eq)
{
        isl_qpolynomial_list *list;

        list = isl_qpolynomial_fold_take_list(fold);
        list = isl_qpolynomial_list_map(list, &substitute_equalities, eq);
        fold = isl_qpolynomial_fold_restore_list(fold, list);

        isl_basic_set_free(eq);
        return fold;
}

/* isl_qpolynomial_list_map callback for calling
 * isl_qpolynomial_substitute_equalities on "qp" and "context".
 */
static __isl_give isl_qpolynomial *gist(__isl_take isl_qpolynomial *qp,
        void *user)
{
        isl_set *context = user;

        return isl_qpolynomial_gist(qp, isl_set_copy(context));
}

__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
        __isl_take isl_qpolynomial_fold *fold, __isl_take isl_set *context)
{
        isl_qpolynomial_list *list;

        list = isl_qpolynomial_fold_take_list(fold);
        list = isl_qpolynomial_list_map(list, &gist, context);
        fold = isl_qpolynomial_fold_restore_list(fold, list);

        isl_set_free(context);
        return fold;
}

__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
        __isl_take isl_qpolynomial_fold *fold, __isl_take isl_set *context)
{
        isl_space *space = isl_qpolynomial_fold_get_domain_space(fold);
        isl_set *dom_context = isl_set_universe(space);
        dom_context = isl_set_intersect_params(dom_context, context);
        return isl_qpolynomial_fold_gist(fold, dom_context);
}

/* Return a zero (i.e., empty) isl_qpolynomial_fold in the given space.
 *
 * This is a helper function for isl_pw_*_as_* that ensures a uniform
 * interface over all piecewise types.
 */
static __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_zero_in_space(
        __isl_take isl_space *space, enum isl_fold type)
{
        return isl_qpolynomial_fold_empty(type, isl_space_domain(space));
}

#define isl_qpolynomial_fold_involves_nan isl_qpolynomial_fold_is_nan

#define HAS_TYPE

#undef PW
#define PW isl_pw_qpolynomial_fold
#undef BASE
#define BASE qpolynomial_fold
#undef EL_IS_ZERO
#define EL_IS_ZERO is_empty
#undef ZERO
#define ZERO zero
#undef IS_ZERO
#define IS_ZERO is_zero
#undef FIELD
#define FIELD fold
#undef DEFAULT_IS_ZERO
#define DEFAULT_IS_ZERO 1

#include <isl_pw_templ.c>
#include <isl_pw_add_disjoint_templ.c>
#include <isl_pw_eval.c>
#include <isl_pw_fix_templ.c>
#include <isl_pw_from_range_templ.c>
#include <isl_pw_insert_dims_templ.c>
#include <isl_pw_lift_templ.c>
#include <isl_pw_morph_templ.c>
#include <isl_pw_move_dims_templ.c>
#include <isl_pw_opt_templ.c>

#undef BASE
#define BASE pw_qpolynomial_fold

#include <isl_union_single.c>
#include <isl_union_eval.c>

/* Construct a new reduction of the given type and space
 * with an empty list of polynomials.
 */
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_empty(enum isl_fold type,
        __isl_take isl_space *space)
{
        isl_ctx *ctx;
        isl_qpolynomial_list *list;

        if (!space)
                return NULL;
        ctx = isl_space_get_ctx(space);
        list = isl_qpolynomial_list_alloc(ctx, 0);
        return qpolynomial_fold_alloc(type, space, list);
}

/* Construct a new reduction of the given type and
 * a single given polynomial.
 */
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_alloc(
        enum isl_fold type, __isl_take isl_qpolynomial *qp)
{
        isl_space *space;
        isl_qpolynomial_list *list;

        space = isl_qpolynomial_get_domain_space(qp);
        list = isl_qpolynomial_list_from_qpolynomial(qp);
        return qpolynomial_fold_alloc(type, space, list);
}

__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
        __isl_keep isl_qpolynomial_fold *fold)
{
        if (!fold)
                return NULL;

        fold->ref++;
        return fold;
}

__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_dup(
        __isl_keep isl_qpolynomial_fold *fold)
{
        enum isl_fold type;
        isl_space *space;
        isl_qpolynomial_list *list;

        type = isl_qpolynomial_fold_get_type(fold);
        space = isl_qpolynomial_fold_get_domain_space(fold);
        list = isl_qpolynomial_fold_get_list(fold);
        return qpolynomial_fold_alloc(type, space, list);
}

__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_cow(
        __isl_take isl_qpolynomial_fold *fold)
{
        if (!fold)
                return NULL;

        if (fold->ref == 1)
                return fold;
        fold->ref--;
        return isl_qpolynomial_fold_dup(fold);
}

__isl_null isl_qpolynomial_fold *isl_qpolynomial_fold_free(
        __isl_take isl_qpolynomial_fold *fold)
{
        if (!fold)
                return NULL;
        if (--fold->ref > 0)
                return NULL;

        isl_qpolynomial_list_free(fold->list);
        isl_space_free(fold->dim);
        free(fold);

        return NULL;
}

isl_bool isl_qpolynomial_fold_is_empty(__isl_keep isl_qpolynomial_fold *fold)
{
        isl_size n;
        isl_qpolynomial_list *list;

        list = isl_qpolynomial_fold_peek_list(fold);
        n = isl_qpolynomial_list_size(list);
        if (n < 0)
                return isl_bool_error;

        return isl_bool_ok(n == 0);
}

/* Does "fold" represent max(NaN) or min(NaN)?
 */
isl_bool isl_qpolynomial_fold_is_nan(__isl_keep isl_qpolynomial_fold *fold)
{
        isl_size n;
        isl_qpolynomial *qp;
        isl_qpolynomial_list *list;

        list = isl_qpolynomial_fold_peek_list(fold);
        n = isl_qpolynomial_list_size(list);
        if (n < 0)
                return isl_bool_error;
        if (n != 1)
                return isl_bool_false;
        qp = isl_qpolynomial_list_peek(list, 0);
        return isl_qpolynomial_is_nan(qp);
}

__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_fold(
        __isl_take isl_qpolynomial_fold *fold1,
        __isl_take isl_qpolynomial_fold *fold2)
{
        isl_qpolynomial_list *list1, *list2;

        if (isl_qpolynomial_fold_check_equal_type(fold1, fold2) < 0)
                goto error;
        if (isl_qpolynomial_fold_check_equal_space(fold1, fold2) < 0)
                goto error;

        if (isl_qpolynomial_fold_is_empty(fold1)) {
                isl_qpolynomial_fold_free(fold1);
                return fold2;
        }

        if (isl_qpolynomial_fold_is_empty(fold2)) {
                isl_qpolynomial_fold_free(fold2);
                return fold1;
        }

        list1 = isl_qpolynomial_fold_take_list(fold1);
        list2 = isl_qpolynomial_fold_take_list(fold2);
        list1 = isl_qpolynomial_list_concat(list1, list2);
        fold1 = isl_qpolynomial_fold_restore_list(fold1, list1);
        isl_qpolynomial_fold_free(fold2);

        return fold1;
error:
        isl_qpolynomial_fold_free(fold1);
        isl_qpolynomial_fold_free(fold2);
        return NULL;
}

__isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
        __isl_take isl_pw_qpolynomial_fold *pw1,
        __isl_take isl_pw_qpolynomial_fold *pw2)
{
        int i, j, n;
        struct isl_pw_qpolynomial_fold *res;
        isl_set *set;

        if (!pw1 || !pw2)
                goto error;

        isl_assert(pw1->dim->ctx, isl_space_is_equal(pw1->dim, pw2->dim), goto error);

        if (isl_pw_qpolynomial_fold_is_zero(pw1)) {
                isl_pw_qpolynomial_fold_free(pw1);
                return pw2;
        }

        if (isl_pw_qpolynomial_fold_is_zero(pw2)) {
                isl_pw_qpolynomial_fold_free(pw2);
                return pw1;
        }

        if (pw1->type != pw2->type)
                isl_die(pw1->dim->ctx, isl_error_invalid,
                        "fold types don't match", goto error);

        n = (pw1->n + 1) * (pw2->n + 1);
        res = isl_pw_qpolynomial_fold_alloc_size(isl_space_copy(pw1->dim),
                                                pw1->type, n);

        for (i = 0; i < pw1->n; ++i) {
                set = isl_set_copy(pw1->p[i].set);
                for (j = 0; j < pw2->n; ++j) {
                        struct isl_set *common;
                        isl_qpolynomial_fold *sum;
                        set = isl_set_subtract(set,
                                        isl_set_copy(pw2->p[j].set));
                        common = isl_set_intersect(isl_set_copy(pw1->p[i].set),
                                                isl_set_copy(pw2->p[j].set));
                        if (isl_set_plain_is_empty(common)) {
                                isl_set_free(common);
                                continue;
                        }

                        sum = isl_qpolynomial_fold_fold_on_domain(common,
                               isl_qpolynomial_fold_copy(pw1->p[i].fold),
                               isl_qpolynomial_fold_copy(pw2->p[j].fold));

                        res = isl_pw_qpolynomial_fold_add_piece(res, common, sum);
                }
                res = isl_pw_qpolynomial_fold_add_piece(res, set,
                        isl_qpolynomial_fold_copy(pw1->p[i].fold));
        }

        for (j = 0; j < pw2->n; ++j) {
                set = isl_set_copy(pw2->p[j].set);
                for (i = 0; i < pw1->n; ++i)
                        set = isl_set_subtract(set, isl_set_copy(pw1->p[i].set));
                res = isl_pw_qpolynomial_fold_add_piece(res, set,
                                    isl_qpolynomial_fold_copy(pw2->p[j].fold));
        }

        isl_pw_qpolynomial_fold_free(pw1);
        isl_pw_qpolynomial_fold_free(pw2);

        return res;
error:
        isl_pw_qpolynomial_fold_free(pw1);
        isl_pw_qpolynomial_fold_free(pw2);
        return NULL;
}

__isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold_pw_qpolynomial_fold(
        __isl_take isl_union_pw_qpolynomial_fold *u,
        __isl_take isl_pw_qpolynomial_fold *part)
{
        struct isl_hash_table_entry *entry;

        u = isl_union_pw_qpolynomial_fold_cow(u);

        if (!part || !u)
                goto error;
        if (isl_space_check_equal_params(part->dim, u->space) < 0)
                goto error;

        entry = isl_union_pw_qpolynomial_fold_find_part_entry(u, part->dim, 1);
        if (!entry)
                goto error;

        if (!entry->data)
                entry->data = part;
        else {
                entry->data = isl_pw_qpolynomial_fold_fold(entry->data,
                                            isl_pw_qpolynomial_fold_copy(part));
                if (!entry->data)
                        goto error;
                isl_pw_qpolynomial_fold_free(part);
        }

        return u;
error:
        isl_pw_qpolynomial_fold_free(part);
        isl_union_pw_qpolynomial_fold_free(u);
        return NULL;
}

static isl_stat fold_part(__isl_take isl_pw_qpolynomial_fold *part, void *user)
{
        isl_union_pw_qpolynomial_fold **u;
        u = (isl_union_pw_qpolynomial_fold **)user;

        *u = isl_union_pw_qpolynomial_fold_fold_pw_qpolynomial_fold(*u, part);

        return isl_stat_ok;
}

__isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
        __isl_take isl_union_pw_qpolynomial_fold *u1,
        __isl_take isl_union_pw_qpolynomial_fold *u2)
{
        u1 = isl_union_pw_qpolynomial_fold_cow(u1);

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

        if (isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(u2,
                                                        &fold_part, &u1) < 0)
                goto error;

        isl_union_pw_qpolynomial_fold_free(u2);

        return u1;
error:
        isl_union_pw_qpolynomial_fold_free(u1);
        isl_union_pw_qpolynomial_fold_free(u2);
        return NULL;
}

__isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_from_pw_qpolynomial(
        enum isl_fold type, __isl_take isl_pw_qpolynomial *pwqp)
{
        int i;
        isl_pw_qpolynomial_fold *pwf;

        if (!pwqp)
                return NULL;
        
        pwf = isl_pw_qpolynomial_fold_alloc_size(isl_space_copy(pwqp->dim),
                                                type, pwqp->n);

        for (i = 0; i < pwqp->n; ++i)
                pwf = isl_pw_qpolynomial_fold_add_piece(pwf,
                        isl_set_copy(pwqp->p[i].set),
                        isl_qpolynomial_fold_alloc(type,
                                isl_qpolynomial_copy(pwqp->p[i].qp)));

        isl_pw_qpolynomial_free(pwqp);

        return pwf;
}

__isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
        __isl_take isl_pw_qpolynomial_fold *pwf1,
        __isl_take isl_pw_qpolynomial_fold *pwf2)
{
        return isl_pw_qpolynomial_fold_union_add_(pwf1, pwf2);
}

/* Compare two quasi-polynomial reductions.
 *
 * Return -1 if "fold1" is "smaller" than "fold2", 1 if "fold1" is "greater"
 * than "fold2" and 0 if they are equal.
 */
int isl_qpolynomial_fold_plain_cmp(__isl_keep isl_qpolynomial_fold *fold1,
        __isl_keep isl_qpolynomial_fold *fold2)
{
        int i;
        isl_size n1, n2;
        isl_qpolynomial_list *list1, *list2;

        if (fold1 == fold2)
                return 0;
        list1 = isl_qpolynomial_fold_peek_list(fold1);
        list2 = isl_qpolynomial_fold_peek_list(fold2);
        n1 = isl_qpolynomial_list_size(list1);
        n2 = isl_qpolynomial_list_size(list2);
        if (n1 < 0)
                return -1;
        if (n2 < 0)
                return 1;

        if (n1 != n2)
                return n1 - n2;

        for (i = 0; i < n1; ++i) {
                int cmp;
                isl_qpolynomial *qp1, *qp2;

                qp1 = isl_qpolynomial_list_peek(list1, i);
                qp2 = isl_qpolynomial_list_peek(list2, i);
                cmp = isl_qpolynomial_plain_cmp(qp1, qp2);
                if (cmp != 0)
                        return cmp;
        }

        return 0;
}

/* Are the lists "list1" and "list2", both consisting of "n" elements
 * obviously equal to each other?
 */
static isl_bool isl_qpolynomial_list_plain_is_equal(unsigned n,
        isl_qpolynomial_list *list1, isl_qpolynomial_list *list2)
{
        int i;

        for (i = 0; i < n; ++i) {
                isl_bool eq;
                isl_qpolynomial *qp1, *qp2;

                qp1 = isl_qpolynomial_list_peek(list1, i);
                qp2 = isl_qpolynomial_list_peek(list2, i);
                eq = isl_qpolynomial_plain_is_equal(qp1, qp2);
                if (eq < 0 || !eq)
                        return eq;
        }

        return isl_bool_true;
}

/* Wrapper around isl_qpolynomial_plain_cmp for use
 * as a isl_qpolynomial_list_sort callback.
 */
static int qpolynomial_cmp(__isl_keep isl_qpolynomial *a,
        __isl_keep isl_qpolynomial *b, void *user)
{
        return isl_qpolynomial_plain_cmp(a, b);
}

isl_bool isl_qpolynomial_fold_plain_is_equal(
        __isl_keep isl_qpolynomial_fold *fold1,
        __isl_keep isl_qpolynomial_fold *fold2)
{
        isl_bool equal;
        isl_size n1, n2;
        isl_qpolynomial_list *list1, *list2;

        list1 = isl_qpolynomial_fold_peek_list(fold1);
        list2 = isl_qpolynomial_fold_peek_list(fold2);
        n1 = isl_qpolynomial_list_size(list1);
        n2 = isl_qpolynomial_list_size(list2);
        if (n1 < 0 || n2 < 0)
                return isl_bool_error;

        if (n1 != n2)
                return isl_bool_false;

        list1 = isl_qpolynomial_list_copy(list1);
        list1 = isl_qpolynomial_list_sort(list1, &qpolynomial_cmp, NULL);
        list2 = isl_qpolynomial_list_copy(list2);
        list2 = isl_qpolynomial_list_sort(list2, &qpolynomial_cmp, NULL);
        equal = isl_qpolynomial_list_plain_is_equal(n1, list1, list2);
        isl_qpolynomial_list_free(list1);
        isl_qpolynomial_list_free(list2);
        return equal;
}

__isl_give isl_val *isl_qpolynomial_fold_eval(
        __isl_take isl_qpolynomial_fold *fold, __isl_take isl_point *pnt)
{
        isl_size n;
        isl_ctx *ctx;
        isl_val *v;
        isl_qpolynomial *qp;
        isl_qpolynomial_list *list;

        if (!fold || !pnt)
                goto error;
        ctx = isl_point_get_ctx(pnt);
        isl_assert(pnt->dim->ctx, isl_space_is_equal(pnt->dim, fold->dim), goto error);
        isl_assert(pnt->dim->ctx,
                fold->type == isl_fold_max || fold->type == isl_fold_min,
                goto error);

        list = isl_qpolynomial_fold_peek_list(fold);
        n = isl_qpolynomial_list_size(list);
        if (n < 0)
                goto error;

        if (n == 0)
                v = isl_val_zero(ctx);
        else {
                int i;

                qp = isl_qpolynomial_list_get_at(list, 0);
                v = isl_qpolynomial_eval(qp, isl_point_copy(pnt));
                for (i = 1; i < n; ++i) {
                        isl_val *v_i;

                        qp = isl_qpolynomial_list_get_at(list, i);
                        v_i = isl_qpolynomial_eval(qp, isl_point_copy(pnt));
                        if (fold->type == isl_fold_max)
                                v = isl_val_max(v, v_i);
                        else
                                v = isl_val_min(v, v_i);
                }
        }
        isl_qpolynomial_fold_free(fold);
        isl_point_free(pnt);

        return v;
error:
        isl_qpolynomial_fold_free(fold);
        isl_point_free(pnt);
        return NULL;
}

size_t isl_pw_qpolynomial_fold_size(__isl_keep isl_pw_qpolynomial_fold *pwf)
{
        int i;
        size_t n = 0;

        for (i = 0; i < pwf->n; ++i) {
                isl_size n_i;
                isl_qpolynomial_list *list;

                list = isl_qpolynomial_fold_peek_list(pwf->p[i].fold);
                n_i = isl_qpolynomial_list_size(list);
                if (n_i < 0)
                        return isl_size_error;

                n += n_i;
        }

        return n;
}

__isl_give isl_val *isl_qpolynomial_fold_opt_on_domain(
        __isl_take isl_qpolynomial_fold *fold, __isl_take isl_set *set, int max)
{
        int i;
        isl_size n;
        isl_val *opt;
        isl_qpolynomial *qp;
        isl_qpolynomial_list *list;

        list = isl_qpolynomial_fold_peek_list(fold);
        n = isl_qpolynomial_list_size(list);
        if (!set || n < 0)
                goto error;

        if (n == 0) {
                opt = isl_val_zero(isl_set_get_ctx(set));
                isl_set_free(set);
                isl_qpolynomial_fold_free(fold);
                return opt;
        }

        qp = isl_qpolynomial_list_get_at(list, 0);
        opt = isl_qpolynomial_opt_on_domain(qp, isl_set_copy(set), max);
        for (i = 1; i < n; ++i) {
                isl_val *opt_i;

                qp = isl_qpolynomial_list_get_at(list, i);
                opt_i = isl_qpolynomial_opt_on_domain(qp,
                                isl_set_copy(set), max);
                if (max)
                        opt = isl_val_max(opt, opt_i);
                else
                        opt = isl_val_min(opt, opt_i);
        }

        isl_set_free(set);
        isl_qpolynomial_fold_free(fold);

        return opt;
error:
        isl_set_free(set);
        isl_qpolynomial_fold_free(fold);
        return NULL;
}

/* Check whether for each quasi-polynomial in "fold2" there is
 * a quasi-polynomial in "fold1" that dominates it on "set".
 */
static isl_bool qpolynomial_fold_covers_on_domain(__isl_keep isl_set *set,
        __isl_keep isl_qpolynomial_fold *fold1,
        __isl_keep isl_qpolynomial_fold *fold2)
{
        int i, j;
        int covers;
        isl_size n1, n2;
        isl_qpolynomial_list *list1, *list2;

        list1 = isl_qpolynomial_fold_peek_list(fold1);
        list2 = isl_qpolynomial_fold_peek_list(fold2);
        n1 = isl_qpolynomial_list_size(list1);
        n2 = isl_qpolynomial_list_size(list2);
        if (!set || n1 < 0 || n2 < 0)
                return isl_bool_error;

        covers = fold1->type == isl_fold_max ? 1 : -1;

        for (i = 0; i < n2; ++i) {
                for (j = 0; j < n1; ++j) {
                        isl_qpolynomial *qp1, *qp2, *d;
                        int sgn;

                        qp1 = isl_qpolynomial_list_get_at(list1, j);
                        qp2 = isl_qpolynomial_list_get_at(list2, i);
                        d = isl_qpolynomial_sub(qp1, qp2);
                        sgn = isl_qpolynomial_sign(set, d);
                        isl_qpolynomial_free(d);
                        if (sgn == covers)
                                break;
                }
                if (j >= n1)
                        return isl_bool_false;
        }

        return isl_bool_true;
}

/* Check whether "pwf1" dominated "pwf2", i.e., the domain of "pwf1" contains
 * that of "pwf2" and on each cell, the corresponding fold from pwf1 dominates
 * that of pwf2.
 */
isl_bool isl_pw_qpolynomial_fold_covers(
        __isl_keep isl_pw_qpolynomial_fold *pwf1,
        __isl_keep isl_pw_qpolynomial_fold *pwf2)
{
        int i, j;
        isl_set *dom1, *dom2;
        isl_bool is_subset;

        if (!pwf1 || !pwf2)
                return isl_bool_error;

        if (pwf2->n == 0)
                return isl_bool_true;
        if (pwf1->n == 0)
                return isl_bool_false;

        dom1 = isl_pw_qpolynomial_fold_domain(isl_pw_qpolynomial_fold_copy(pwf1));
        dom2 = isl_pw_qpolynomial_fold_domain(isl_pw_qpolynomial_fold_copy(pwf2));
        is_subset = isl_set_is_subset(dom2, dom1);
        isl_set_free(dom1);
        isl_set_free(dom2);

        if (is_subset < 0 || !is_subset)
                return is_subset;

        for (i = 0; i < pwf2->n; ++i) {
                for (j = 0; j < pwf1->n; ++j) {
                        isl_bool is_empty;
                        isl_set *common;
                        isl_bool covers;

                        common = isl_set_intersect(isl_set_copy(pwf1->p[j].set),
                                                   isl_set_copy(pwf2->p[i].set));
                        is_empty = isl_set_is_empty(common);
                        if (is_empty < 0 || is_empty) {
                                isl_set_free(common);
                                if (is_empty < 0)
                                        return isl_bool_error;
                                continue;
                        }
                        covers = qpolynomial_fold_covers_on_domain(common,
                                        pwf1->p[j].fold, pwf2->p[i].fold);
                        isl_set_free(common);
                        if (covers < 0 || !covers)
                                return covers;
                }
        }

        return isl_bool_true;
}

/* isl_qpolynomial_list_map callback that calls
 * isl_qpolynomial_morph_domain on "qp".
 */
static __isl_give isl_qpolynomial *morph_domain(
        __isl_take isl_qpolynomial *qp, void *user)
{
        isl_morph *morph = user;

        return isl_qpolynomial_morph_domain(qp, isl_morph_copy(morph));
}

__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_morph_domain(
        __isl_take isl_qpolynomial_fold *fold, __isl_take isl_morph *morph)
{
        isl_space *space;
        isl_qpolynomial_list *list;

        space = isl_qpolynomial_fold_peek_domain_space(fold);
        if (isl_morph_check_applies(morph, space) < 0)
                goto error;

        list = isl_qpolynomial_fold_take_list(fold);
        list = isl_qpolynomial_list_map(list, &morph_domain, morph);
        fold = isl_qpolynomial_fold_restore_list(fold, list);

        space = isl_morph_get_ran_space(morph);
        isl_space_free(isl_qpolynomial_fold_take_domain_space(fold));
        fold = isl_qpolynomial_fold_restore_domain_space(fold, space);

        isl_morph_free(morph);

        return fold;
error:
        isl_qpolynomial_fold_free(fold);
        isl_morph_free(morph);
        return NULL;
}

enum isl_fold isl_qpolynomial_fold_get_type(__isl_keep isl_qpolynomial_fold *fold)
{
        if (!fold)
                return isl_fold_error;
        return fold->type;
}

/* Return the type of this piecewise quasipolynomial reduction.
 */
enum isl_fold isl_pw_qpolynomial_fold_get_type(
        __isl_keep isl_pw_qpolynomial_fold *pwf)
{
        if (!pwf)
                return isl_fold_error;
        return pwf->type;
}

enum isl_fold isl_union_pw_qpolynomial_fold_get_type(
        __isl_keep isl_union_pw_qpolynomial_fold *upwf)
{
        if (!upwf)
                return isl_fold_error;
        return upwf->type;
}

/* isl_qpolynomial_list_map callback that calls
 * isl_qpolynomial_lift on "qp".
 */
static __isl_give isl_qpolynomial *lift(__isl_take isl_qpolynomial *qp,
        void *user)
{
        isl_space *space = user;

        return isl_qpolynomial_lift(qp, isl_space_copy(space));
}

__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_lift(
        __isl_take isl_qpolynomial_fold *fold, __isl_take isl_space *space)
{
        isl_qpolynomial_list *list;

        if (!fold || !space)
                goto error;

        if (isl_space_is_equal(fold->dim, space)) {
                isl_space_free(space);
                return fold;
        }

        list = isl_qpolynomial_fold_take_list(fold);
        list = isl_qpolynomial_list_map(list, &lift, space);
        fold = isl_qpolynomial_fold_restore_list(fold, list);

        isl_space_free(isl_qpolynomial_fold_take_domain_space(fold));
        fold = isl_qpolynomial_fold_restore_domain_space(fold, space);

        return fold;
error:
        isl_qpolynomial_fold_free(fold);
        isl_space_free(space);
        return NULL;
}

isl_stat isl_qpolynomial_fold_foreach_qpolynomial(
        __isl_keep isl_qpolynomial_fold *fold,
        isl_stat (*fn)(__isl_take isl_qpolynomial *qp, void *user), void *user)
{
        isl_qpolynomial_list *list;

        list = isl_qpolynomial_fold_peek_list(fold);
        return isl_qpolynomial_list_foreach(list, fn, user);
}

/* Internal data structure for isl_qpolynomial_fold_move_dims
 * representing its arguments.
 */
struct isl_fold_move_dims_data {
        enum isl_dim_type dst_type;
        unsigned dst_pos;
        enum isl_dim_type src_type;
        unsigned src_pos;
        unsigned n;
};

/* isl_qpolynomial_list_map callback for calling
 * isl_qpolynomial_move_dims on "qp".
 */
static __isl_give isl_qpolynomial *move_dims(__isl_take isl_qpolynomial *qp,
        void *user)
{
        struct isl_fold_move_dims_data *data = user;

        qp = isl_qpolynomial_move_dims(qp, data->dst_type, data->dst_pos,
                                        data->src_type, data->src_pos, data->n);
        return qp;
}

__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_move_dims(
        __isl_take isl_qpolynomial_fold *fold,
        enum isl_dim_type dst_type, unsigned dst_pos,
        enum isl_dim_type src_type, unsigned src_pos, unsigned n)
{
        struct isl_fold_move_dims_data data =
                { dst_type, dst_pos, src_type, src_pos, n };
        enum isl_dim_type set_src_type, set_dst_type;
        isl_space *space;
        isl_qpolynomial_list *list;

        if (n == 0)
                return fold;

        fold = isl_qpolynomial_fold_cow(fold);
        if (!fold)
                return NULL;

        set_src_type = domain_type(src_type);
        set_dst_type = domain_type(dst_type);

        list = isl_qpolynomial_fold_take_list(fold);
        list = isl_qpolynomial_list_map(list, &move_dims, &data);
        fold = isl_qpolynomial_fold_restore_list(fold, list);

        space = isl_qpolynomial_fold_take_domain_space(fold);
        space = isl_space_move_dims(space, set_dst_type, dst_pos,
                                                set_src_type, src_pos, n);
        fold = isl_qpolynomial_fold_restore_domain_space(fold, space);

        return fold;
}

/* Internal data structure for isl_qpolynomial_fold_substitute
 * representing its arguments.
 */
struct isl_fold_substitute {
        enum isl_dim_type type;
        unsigned first;
        unsigned n;
        isl_qpolynomial **subs;
};

/* isl_qpolynomial_list_map callback for calling
 * isl_qpolynomial_substitute on "qp".
 */
static __isl_give isl_qpolynomial *substitute(__isl_take isl_qpolynomial *qp,
        void *user)
{
        struct isl_fold_substitute *data = user;

        qp = isl_qpolynomial_substitute(qp,
                                data->type, data->first, data->n, data->subs);
        return qp;
}

/* For each 0 <= i < "n", replace variable "first" + i of type "type"
 * in fold->qp[k] by subs[i].
 */
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_substitute(
        __isl_take isl_qpolynomial_fold *fold,
        enum isl_dim_type type, unsigned first, unsigned n,
        __isl_keep isl_qpolynomial **subs)
{
        struct isl_fold_substitute data = { type, first, n, subs };
        isl_qpolynomial_list *list;

        if (n == 0)
                return fold;

        list = isl_qpolynomial_fold_take_list(fold);
        list = isl_qpolynomial_list_map(list, &substitute, &data);
        fold = isl_qpolynomial_fold_restore_list(fold, list);

        return fold;
}

static isl_stat add_pwqp(__isl_take isl_pw_qpolynomial *pwqp, void *user)
{
        isl_pw_qpolynomial_fold *pwf;
        isl_union_pw_qpolynomial_fold **upwf;
        struct isl_hash_table_entry *entry;

        upwf = (isl_union_pw_qpolynomial_fold **)user;

        entry = isl_union_pw_qpolynomial_fold_find_part_entry(*upwf,
                         pwqp->dim, 1);
        if (!entry)
                goto error;

        pwf = isl_pw_qpolynomial_fold_from_pw_qpolynomial((*upwf)->type, pwqp);
        if (!entry->data)
                entry->data = pwf;
        else {
                entry->data = isl_pw_qpolynomial_fold_add(entry->data, pwf);
                if (!entry->data)
                        return isl_stat_error;
                if (isl_pw_qpolynomial_fold_is_zero(entry->data))
                        *upwf = isl_union_pw_qpolynomial_fold_remove_part_entry(
                                                                *upwf, entry);
        }

        return isl_stat_ok;
error:
        isl_pw_qpolynomial_free(pwqp);
        return isl_stat_error;
}

__isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_add_union_pw_qpolynomial(
        __isl_take isl_union_pw_qpolynomial_fold *upwf,
        __isl_take isl_union_pw_qpolynomial *upwqp)
{
        upwf = isl_union_pw_qpolynomial_fold_align_params(upwf,
                                isl_union_pw_qpolynomial_get_space(upwqp));
        upwqp = isl_union_pw_qpolynomial_align_params(upwqp,
                                isl_union_pw_qpolynomial_fold_get_space(upwf));

        upwf = isl_union_pw_qpolynomial_fold_cow(upwf);
        if (!upwf || !upwqp)
                goto error;

        if (isl_union_pw_qpolynomial_foreach_pw_qpolynomial(upwqp, &add_pwqp,
                                                         &upwf) < 0)
                goto error;

        isl_union_pw_qpolynomial_free(upwqp);

        return upwf;
error:
        isl_union_pw_qpolynomial_fold_free(upwf);
        isl_union_pw_qpolynomial_free(upwqp);
        return NULL;
}

static isl_bool join_compatible(__isl_keep isl_space *space1,
        __isl_keep isl_space *space2)
{
        isl_bool m;
        m = isl_space_has_equal_params(space1, space2);
        if (m < 0 || !m)
                return m;
        return isl_space_tuple_is_equal(space1, isl_dim_out,
                                        space2, isl_dim_in);
}

/* Compute the intersection of the range of the map and the domain
 * of the piecewise quasipolynomial reduction and then compute a bound
 * on the associated quasipolynomial reduction over all elements
 * in this intersection.
 *
 * We first introduce some unconstrained dimensions in the
 * piecewise quasipolynomial, intersect the resulting domain
 * with the wrapped map and the compute the sum.
 */
__isl_give isl_pw_qpolynomial_fold *isl_map_apply_pw_qpolynomial_fold(
        __isl_take isl_map *map, __isl_take isl_pw_qpolynomial_fold *pwf,
        isl_bool *tight)
{
        isl_ctx *ctx;
        isl_set *dom;
        isl_space *map_space;
        isl_space *pwf_space;
        isl_size n_in;
        isl_bool ok;

        ctx = isl_map_get_ctx(map);
        if (!ctx)
                goto error;

        map_space = isl_map_get_space(map);
        pwf_space = isl_pw_qpolynomial_fold_get_space(pwf);
        ok = join_compatible(map_space, pwf_space);
        isl_space_free(map_space);
        isl_space_free(pwf_space);
        if (ok < 0)
                goto error;
        if (!ok)
                isl_die(ctx, isl_error_invalid, "incompatible dimensions",
                        goto error);

        n_in = isl_map_dim(map, isl_dim_in);
        if (n_in < 0)
                goto error;
        pwf = isl_pw_qpolynomial_fold_insert_dims(pwf, isl_dim_in, 0, n_in);

        dom = isl_map_wrap(map);
        pwf = isl_pw_qpolynomial_fold_reset_domain_space(pwf,
                                                isl_set_get_space(dom));

        pwf = isl_pw_qpolynomial_fold_intersect_domain(pwf, dom);
        pwf = isl_pw_qpolynomial_fold_bound(pwf, tight);
        
        return pwf;
error:
        isl_map_free(map);
        isl_pw_qpolynomial_fold_free(pwf);
        return NULL;
}

__isl_give isl_pw_qpolynomial_fold *isl_set_apply_pw_qpolynomial_fold(
        __isl_take isl_set *set, __isl_take isl_pw_qpolynomial_fold *pwf,
        isl_bool *tight)
{
        return isl_map_apply_pw_qpolynomial_fold(set, pwf, tight);
}

struct isl_apply_fold_data {
        isl_union_pw_qpolynomial_fold *upwf;
        isl_union_pw_qpolynomial_fold *res;
        isl_map *map;
        isl_bool tight;
};

static isl_stat pw_qpolynomial_fold_apply(
        __isl_take isl_pw_qpolynomial_fold *pwf, void *user)
{
        isl_space *map_dim;
        isl_space *pwf_dim;
        struct isl_apply_fold_data *data = user;
        isl_bool ok;

        map_dim = isl_map_get_space(data->map);
        pwf_dim = isl_pw_qpolynomial_fold_get_space(pwf);
        ok = join_compatible(map_dim, pwf_dim);
        isl_space_free(map_dim);
        isl_space_free(pwf_dim);

        if (ok < 0)
                return isl_stat_error;
        if (ok) {
                pwf = isl_map_apply_pw_qpolynomial_fold(isl_map_copy(data->map),
                                    pwf, data->tight ? &data->tight : NULL);
                data->res = isl_union_pw_qpolynomial_fold_fold_pw_qpolynomial_fold(
                                                        data->res, pwf);
        } else
                isl_pw_qpolynomial_fold_free(pwf);

        return isl_stat_ok;
}

static isl_stat map_apply(__isl_take isl_map *map, void *user)
{
        struct isl_apply_fold_data *data = user;
        isl_stat r;

        data->map = map;
        r = isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
                                data->upwf, &pw_qpolynomial_fold_apply, data);

        isl_map_free(map);
        return r;
}

__isl_give isl_union_pw_qpolynomial_fold *isl_union_map_apply_union_pw_qpolynomial_fold(
        __isl_take isl_union_map *umap,
        __isl_take isl_union_pw_qpolynomial_fold *upwf, isl_bool *tight)
{
        isl_space *space;
        enum isl_fold type;
        struct isl_apply_fold_data data;

        upwf = isl_union_pw_qpolynomial_fold_align_params(upwf,
                                isl_union_map_get_space(umap));
        umap = isl_union_map_align_params(umap,
                                isl_union_pw_qpolynomial_fold_get_space(upwf));

        data.upwf = upwf;
        data.tight = tight ? isl_bool_true : isl_bool_false;
        space = isl_union_pw_qpolynomial_fold_get_space(upwf);
        type = isl_union_pw_qpolynomial_fold_get_type(upwf);
        data.res = isl_union_pw_qpolynomial_fold_zero(space, type);
        if (isl_union_map_foreach_map(umap, &map_apply, &data) < 0)
                goto error;

        isl_union_map_free(umap);
        isl_union_pw_qpolynomial_fold_free(upwf);

        if (tight)
                *tight = data.tight;

        return data.res;
error:
        isl_union_map_free(umap);
        isl_union_pw_qpolynomial_fold_free(upwf);
        isl_union_pw_qpolynomial_fold_free(data.res);
        return NULL;
}

__isl_give isl_union_pw_qpolynomial_fold *isl_union_set_apply_union_pw_qpolynomial_fold(
        __isl_take isl_union_set *uset,
        __isl_take isl_union_pw_qpolynomial_fold *upwf, isl_bool *tight)
{
        return isl_union_map_apply_union_pw_qpolynomial_fold(uset, upwf, tight);
}

/* isl_qpolynomial_list_map callback for calling
 * isl_qpolynomial_realign_domain on "qp".
 */
static __isl_give isl_qpolynomial *realign_domain(
        __isl_take isl_qpolynomial *qp, void *user)
{
        isl_reordering *r = user;

        qp = isl_qpolynomial_realign_domain(qp, isl_reordering_copy(r));
        return qp;
}

/* Reorder the dimension of "fold" according to the given reordering.
 */
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_realign_domain(
        __isl_take isl_qpolynomial_fold *fold, __isl_take isl_reordering *r)
{
        isl_space *space;
        isl_qpolynomial_list *list;

        list = isl_qpolynomial_fold_take_list(fold);
        list = isl_qpolynomial_list_map(list, &realign_domain, r);
        fold = isl_qpolynomial_fold_restore_list(fold, list);

        space = isl_reordering_get_space(r);
        fold = isl_qpolynomial_fold_reset_domain_space(fold, space);

        isl_reordering_free(r);

        return fold;
}

/* isl_qpolynomial_list_map callback for calling
 * isl_qpolynomial_mul_isl_int on "qp".
 */
static __isl_give isl_qpolynomial *mul_int(__isl_take isl_qpolynomial *qp,
        void *user)
{
        isl_int *v = user;

        qp = isl_qpolynomial_mul_isl_int(qp, *v);
        return qp;
}

__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_mul_isl_int(
        __isl_take isl_qpolynomial_fold *fold, isl_int v)
{
        isl_qpolynomial_list *list;

        if (isl_int_is_one(v))
                return fold;
        if (fold && isl_int_is_zero(v)) {
                isl_qpolynomial_fold *zero;
                isl_space *space = isl_space_copy(fold->dim);
                zero = isl_qpolynomial_fold_empty(fold->type, space);
                isl_qpolynomial_fold_free(fold);
                return zero;
        }

        fold = isl_qpolynomial_fold_cow(fold);
        if (!fold)
                return NULL;

        if (isl_int_is_neg(v))
                fold->type = isl_fold_type_negate(fold->type);

        list = isl_qpolynomial_fold_take_list(fold);
        list = isl_qpolynomial_list_map(list, &mul_int, &v);
        fold = isl_qpolynomial_fold_restore_list(fold, list);

        return fold;
}

__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
        __isl_take isl_qpolynomial_fold *fold, isl_int v)
{
        return isl_qpolynomial_fold_mul_isl_int(fold, v);
}

/* isl_qpolynomial_list_map callback for calling
 * isl_qpolynomial_scale_val on "qp".
 */
static __isl_give isl_qpolynomial *scale_val(__isl_take isl_qpolynomial *qp,
        void *user)
{
        isl_val *v = user;

        qp = isl_qpolynomial_scale_val(qp, isl_val_copy(v));
        return qp;
}

/* Multiply "fold" by "v".
 */
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale_val(
        __isl_take isl_qpolynomial_fold *fold, __isl_take isl_val *v)
{
        isl_qpolynomial_list *list;

        if (!fold || !v)
                goto error;

        if (isl_val_is_one(v)) {
                isl_val_free(v);
                return fold;
        }
        if (isl_val_is_zero(v)) {
                isl_qpolynomial_fold *zero;
                isl_space *space = isl_qpolynomial_fold_get_domain_space(fold);
                zero = isl_qpolynomial_fold_empty(fold->type, space);
                isl_qpolynomial_fold_free(fold);
                isl_val_free(v);
                return zero;
        }
        if (!isl_val_is_rat(v))
                isl_die(isl_qpolynomial_fold_get_ctx(fold), isl_error_invalid,
                        "expecting rational factor", goto error);

        fold = isl_qpolynomial_fold_cow(fold);
        if (!fold)
                goto error;

        if (isl_val_is_neg(v))
                fold->type = isl_fold_type_negate(fold->type);

        list = isl_qpolynomial_fold_take_list(fold);
        list = isl_qpolynomial_list_map(list, &scale_val, v);
        fold = isl_qpolynomial_fold_restore_list(fold, list);

        isl_val_free(v);
        return fold;
error:
        isl_val_free(v);
        isl_qpolynomial_fold_free(fold);
        return NULL;
}

/* Divide "fold" by "v".
 */
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale_down_val(
        __isl_take isl_qpolynomial_fold *fold, __isl_take isl_val *v)
{
        if (!fold || !v)
                goto error;

        if (isl_val_is_one(v)) {
                isl_val_free(v);
                return fold;
        }
        if (!isl_val_is_rat(v))
                isl_die(isl_qpolynomial_fold_get_ctx(fold), 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);

        return isl_qpolynomial_fold_scale_val(fold, isl_val_inv(v));
error:
        isl_val_free(v);
        isl_qpolynomial_fold_free(fold);
        return NULL;
}