isl_map_simplify.c: div_find_coalesce: return isl_size

[isl.git] / isl_pw_templ.c

/*
 * Copyright 2010-2011 INRIA Saclay
 * Copyright 2011      Sven Verdoolaege
 * Copyright 2012-2014 Ecole Normale Superieure
 *
 * Use of this software is governed by the MIT license
 *
 * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
 * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
 * 91893 Orsay, France
 * and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
 */

#include <isl/id.h>
#include <isl/aff.h>
#include <isl_sort.h>
#include <isl_val_private.h>

#include <isl_pw_macro.h>

#include "opt_type.h"

__isl_give PW *FN(PW,alloc_size)(__isl_take isl_space *space
        OPT_TYPE_PARAM, int n)
{
        isl_ctx *ctx;
        struct PW *pw;

        if (!space)
                return NULL;
        ctx = isl_space_get_ctx(space);
        isl_assert(ctx, n >= 0, goto error);
        pw = isl_alloc(ctx, struct PW,
                        sizeof(struct PW) + (n - 1) * sizeof(S(PW,piece)));
        if (!pw)
                goto error;

        pw->ref = 1;
        OPT_SET_TYPE(pw->, type);
        pw->size = n;
        pw->n = 0;
        pw->dim = space;
        return pw;
error:
        isl_space_free(space);
        return NULL;
}

__isl_give PW *FN(PW,ZERO)(__isl_take isl_space *space OPT_TYPE_PARAM)
{
        return FN(PW,alloc_size)(space OPT_TYPE_ARG(NO_LOC), 0);
}

/* Add a piece with domain "set" and base expression "el"
 * to the piecewise expression "pw".
 *
 * Do this independently of the values of "set" and "el",
 * such that this function can be used by isl_pw_*_dup.
 */
static __isl_give PW *FN(PW,add_dup_piece)(__isl_take PW *pw,
        __isl_take isl_set *set, __isl_take EL *el)
{
        isl_ctx *ctx;
        isl_space *el_dim = NULL;

        if (!pw || !set || !el)
                goto error;

        ctx = isl_set_get_ctx(set);
        if (!OPT_EQUAL_TYPES(pw->, el->))
                isl_die(ctx, isl_error_invalid, "fold types don't match",
                        goto error);
        el_dim = FN(EL,get_space(el));
        isl_assert(ctx, isl_space_is_equal(pw->dim, el_dim), goto error);
        isl_assert(ctx, pw->n < pw->size, goto error);

        pw->p[pw->n].set = set;
        pw->p[pw->n].FIELD = el;
        pw->n++;
        
        isl_space_free(el_dim);
        return pw;
error:
        isl_space_free(el_dim);
        FN(PW,free)(pw);
        isl_set_free(set);
        FN(EL,free)(el);
        return NULL;
}

/* Add a piece with domain "set" and base expression "el"
 * to the piecewise expression "pw", provided the domain
 * is not obviously empty and the base expression
 * is not equal to the default value.
 */
__isl_give PW *FN(PW,add_piece)(__isl_take PW *pw,
        __isl_take isl_set *set, __isl_take EL *el)
{
        isl_bool skip;

        skip = isl_set_plain_is_empty(set);
        if (skip >= 0 && !skip)
                skip = FN(EL,EL_IS_ZERO)(el);
        if (skip >= 0 && !skip)
                return FN(PW,add_dup_piece)(pw, set, el);

        isl_set_free(set);
        FN(EL,free)(el);
        if (skip < 0)
                return FN(PW,free)(pw);
        return pw;
}

/* Does the space of "set" correspond to that of the domain of "el".
 */
static isl_bool FN(PW,compatible_domain)(__isl_keep EL *el,
        __isl_keep isl_set *set)
{
        isl_bool ok;
        isl_space *el_space, *set_space;

        if (!set || !el)
                return isl_bool_error;
        set_space = isl_set_get_space(set);
        el_space = FN(EL,get_space)(el);
        ok = isl_space_is_domain_internal(set_space, el_space);
        isl_space_free(el_space);
        isl_space_free(set_space);
        return ok;
}

/* Check that the space of "set" corresponds to that of the domain of "el".
 */
static isl_stat FN(PW,check_compatible_domain)(__isl_keep EL *el,
        __isl_keep isl_set *set)
{
        isl_bool ok;

        ok = FN(PW,compatible_domain)(el, set);
        if (ok < 0)
                return isl_stat_error;
        if (!ok)
                isl_die(isl_set_get_ctx(set), isl_error_invalid,
                        "incompatible spaces", return isl_stat_error);

        return isl_stat_ok;
}

__isl_give PW *FN(PW,alloc)(OPT_TYPE_PARAM_FIRST
        __isl_take isl_set *set, __isl_take EL *el)
{
        PW *pw;

        if (FN(PW,check_compatible_domain)(el, set) < 0)
                goto error;

        pw = FN(PW,alloc_size)(FN(EL,get_space)(el) OPT_TYPE_ARG(NO_LOC), 1);

        return FN(PW,add_piece)(pw, set, el);
error:
        isl_set_free(set);
        FN(EL,free)(el);
        return NULL;
}

__isl_give PW *FN(PW,dup)(__isl_keep PW *pw)
{
        int i;
        PW *dup;

        if (!pw)
                return NULL;

        dup = FN(PW,alloc_size)(isl_space_copy(pw->dim)
                                OPT_TYPE_ARG(pw->), pw->n);
        if (!dup)
                return NULL;

        for (i = 0; i < pw->n; ++i)
                dup = FN(PW,add_dup_piece)(dup, isl_set_copy(pw->p[i].set),
                                            FN(EL,copy)(pw->p[i].FIELD));

        return dup;
}

__isl_give PW *FN(PW,cow)(__isl_take PW *pw)
{
        if (!pw)
                return NULL;

        if (pw->ref == 1)
                return pw;
        pw->ref--;
        return FN(PW,dup)(pw);
}

__isl_give PW *FN(PW,copy)(__isl_keep PW *pw)
{
        if (!pw)
                return NULL;

        pw->ref++;
        return pw;
}

__isl_null PW *FN(PW,free)(__isl_take PW *pw)
{
        int i;

        if (!pw)
                return NULL;
        if (--pw->ref > 0)
                return NULL;

        for (i = 0; i < pw->n; ++i) {
                isl_set_free(pw->p[i].set);
                FN(EL,free)(pw->p[i].FIELD);
        }
        isl_space_free(pw->dim);
        free(pw);

        return NULL;
}

/* Return the space of "pw".
 */
__isl_keep isl_space *FN(PW,peek_space)(__isl_keep PW *pw)
{
        return pw ? pw->dim : NULL;
}

__isl_give isl_space *FN(PW,get_space)(__isl_keep PW *pw)
{
        return isl_space_copy(FN(PW,peek_space)(pw));
}

/* Return the space of "pw".
 * This may be either a copy or the space itself
 * if there is only one reference to "pw".
 * This allows the space to be modified inplace
 * if both the piecewise expression and its space have only a single reference.
 * The caller is not allowed to modify "pw" between this call and
 * a subsequent call to isl_pw_*_restore_*.
 * The only exception is that isl_pw_*_free can be called instead.
 */
static __isl_give isl_space *FN(PW,take_space)(__isl_keep PW *pw)
{
        isl_space *space;

        if (!pw)
                return NULL;
        if (pw->ref != 1)
                return FN(PW,get_space)(pw);
        space = pw->dim;
        pw->dim = NULL;
        return space;
}

/* Set the space of "pw" to "space", where the space of "pw" may be missing
 * due to a preceding call to isl_pw_*_take_space.
 * However, in this case, "pw" only has a single reference and
 * then the call to isl_pw_*_cow has no effect.
 */
static __isl_give PW *FN(PW,restore_space)(__isl_take PW *pw,
        __isl_take isl_space *space)
{
        if (!pw || !space)
                goto error;

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

        pw = FN(PW,cow)(pw);
        if (!pw)
                goto error;
        isl_space_free(pw->dim);
        pw->dim = space;

        return pw;
error:
        FN(PW,free)(pw);
        isl_space_free(space);
        return NULL;
}

/* Check that "pos" is a valid position for a cell in "pw".
 */
static isl_stat FN(PW,check_pos)(__isl_keep PW *pw, int pos)
{
        if (!pw)
                return isl_stat_error;
        if (pos < 0 || pos >= pw->n)
                isl_die(FN(PW,get_ctx)(pw), isl_error_internal,
                        "position out of bounds", return isl_stat_error);
        return isl_stat_ok;
}

/* Return the cell at position "pos" in "pw".
 */
static __isl_keep isl_set *FN(PW,peek_domain_at)(__isl_keep PW *pw, int pos)
{
        if (FN(PW,check_pos)(pw, pos) < 0)
                return NULL;
        return pw->p[pos].set;
}

/* Return a copy of the cell at position "pos" in "pw".
 */
static __isl_give isl_set *FN(PW,get_domain_at)(__isl_keep PW *pw, int pos)
{
        return isl_set_copy(FN(PW,peek_domain_at)(pw, pos));
}

/* Return the cell at position "pos" in "pw".
 * This may be either a copy or the cell itself
 * if there is only one reference to "pw".
 * This allows the cell to be modified inplace
 * if both the piecewise expression and this cell
 * have only a single reference.
 * The caller is not allowed to modify "pw" between this call and
 * the subsequent call to isl_pw_*_restore_domain_at.
 * The only exception is that isl_pw_*_free can be called instead.
 */
static __isl_give isl_set *FN(PW,take_domain_at)(__isl_keep PW *pw, int pos)
{
        isl_set *domain;

        if (!pw)
                return NULL;
        if (pw->ref != 1)
                return FN(PW,get_domain_at)(pw, pos);
        if (FN(PW,check_pos)(pw, pos) < 0)
                return NULL;
        domain = pw->p[pos].set;
        pw->p[pos].set = NULL;
        return domain;
}

/* Set the cell at position "pos" in "pw" to "el",
 * where this cell may be missing
 * due to a preceding call to isl_pw_*_take_domain_at.
 * However, in this case, "pw" only has a single reference and
 * then the call to isl_pw_*_cow has no effect.
 */
static __isl_give PW *FN(PW,restore_domain_at)(__isl_take PW *pw, int pos,
        __isl_take isl_set *domain)
{
        if (FN(PW,check_pos)(pw, pos) < 0 || !domain)
                goto error;

        if (pw->p[pos].set == domain) {
                isl_set_free(domain);
                return pw;
        }

        pw = FN(PW,cow)(pw);
        if (!pw)
                goto error;
        isl_set_free(pw->p[pos].set);
        pw->p[pos].set = domain;

        return pw;
error:
        FN(PW,free)(pw);
        isl_set_free(domain);
        return NULL;
}

/* Return the base expression associated to
 * the cell at position "pos" in "pw".
 */
__isl_keep EL *FN(PW,peek_base_at)(__isl_keep PW *pw, int pos)
{
        if (FN(PW,check_pos)(pw, pos) < 0)
                return NULL;
        return pw->p[pos].FIELD;
}

/* Return a copy of the base expression associated to
 * the cell at position "pos" in "pw".
 */
static __isl_give EL *FN(PW,get_base_at)(__isl_keep PW *pw, int pos)
{
        return FN(EL,copy)(FN(PW,peek_base_at)(pw, pos));
}

/* Return the base expression associated to
 * the cell at position "pos" in "pw".
 * This may be either a copy or the base expression itself
 * if there is only one reference to "pw".
 * This allows the base expression to be modified inplace
 * if both the piecewise expression and this base expression
 * have only a single reference.
 * The caller is not allowed to modify "pw" between this call and
 * a subsequent call to isl_pw_*_restore_*.
 * The only exception is that isl_pw_*_free can be called instead.
 */
static __isl_give EL *FN(PW,take_base_at)(__isl_keep PW *pw, int pos)
{
        EL *el;

        if (!pw)
                return NULL;
        if (pw->ref != 1)
                return FN(PW,get_base_at)(pw, pos);
        if (FN(PW,check_pos)(pw, pos) < 0)
                return NULL;
        el = pw->p[pos].FIELD;
        pw->p[pos].FIELD = NULL;
        return el;
}

/* Set the base expression associated to
 * the cell at position "pos" in "pw" to "el",
 * where this base expression may be missing
 * due to a preceding call to isl_pw_*_take_base_at.
 * However, in this case, "pw" only has a single reference and
 * then the call to isl_pw_*_cow has no effect.
 * If "inplace" is set, then replacing the base expression by "el"
 * is known not to change the meaning of "pw".  It can therefore be replaced
 * in all references to "pw".
 */
static __isl_give PW *FN(PW,restore_base_at_)(__isl_take PW *pw, int pos,
        __isl_take EL *el, int inplace)
{
        if (FN(PW,check_pos)(pw, pos) < 0 || !el)
                goto error;

        if (pw->p[pos].FIELD == el) {
                FN(EL,free)(el);
                return pw;
        }

        if (!inplace)
                pw = FN(PW,cow)(pw);
        if (!pw)
                goto error;
        FN(EL,free)(pw->p[pos].FIELD);
        pw->p[pos].FIELD = el;

        return pw;
error:
        FN(PW,free)(pw);
        FN(EL,free)(el);
        return NULL;
}

/* Set the base expression associated to
 * the cell at position "pos" in "pw" to "el",
 * where this base expression may be missing
 * due to a preceding call to isl_pw_*_take_base_at.
 */
static __isl_give PW *FN(PW,restore_base_at)(__isl_take PW *pw, int pos,
        __isl_take EL *el)
{
        return FN(PW,restore_base_at_)(pw, pos, el, 0);
}

/* Set the base expression associated to
 * the cell at position "pos" in "pw" to "el",
 * where this base expression may be missing
 * due to a preceding call to isl_pw_*_take_base_at.
 * Furthermore, replacing the base expression by "el"
 * is known not to change the meaning of "pw".
 */
static __isl_give PW *FN(PW,restore_base_at_inplace)(__isl_take PW *pw, int pos,
        __isl_take EL *el)
{
        return FN(PW,restore_base_at_)(pw, pos, el, 1);
}

/* Create a piecewise expression with the given base expression on a universe
 * domain.
 */
static __isl_give PW *FN(FN(FN(PW,from),BASE),type_base)(__isl_take EL *el
        OPT_TYPE_PARAM)
{
        isl_set *dom = isl_set_universe(FN(EL,get_domain_space)(el));
        return FN(PW,alloc)(OPT_TYPE_ARG_FIRST(NO_LOC) dom, el);
}

/* Create a piecewise expression with the given base expression on a universe
 * domain.
 *
 * If the default value of this piecewise type is zero and
 * if "el" is effectively zero, then create an empty piecewise expression
 * instead.
 */
static __isl_give PW *FN(FN(FN(PW,from),BASE),type)(__isl_take EL *el
        OPT_TYPE_PARAM)
{
        isl_bool is_zero;
        isl_space *space;

        if (!DEFAULT_IS_ZERO)
                return FN(FN(FN(PW,from),BASE),type_base)(el
                                                        OPT_TYPE_ARG(NO_LOC));
        is_zero = FN(EL,EL_IS_ZERO)(el);
        if (is_zero < 0)
                goto error;
        if (!is_zero)
                return FN(FN(FN(PW,from),BASE),type_base)(el
                                                        OPT_TYPE_ARG(NO_LOC));
        space = FN(EL,get_space)(el);
        FN(EL,free)(el);
        return FN(PW,ZERO)(space OPT_TYPE_ARG(NO_LOC));
error:
        FN(EL,free)(el);
        return NULL;
}

#ifdef HAS_TYPE
/* Create a piecewise expression with the given base expression on a universe
 * domain.
 *
 * Pass along the type as an extra argument for improved uniformity
 * with piecewise types that do not have a fold type.
 */
__isl_give PW *FN(FN(PW,from),BASE)(__isl_take EL *el)
{
        enum isl_fold type = FN(EL,get_type)(el);
        return FN(FN(FN(PW,from),BASE),type)(el, type);
}
#else
__isl_give PW *FN(FN(PW,from),BASE)(__isl_take EL *el)
{
        return FN(FN(FN(PW,from),BASE),type)(el);
}
#endif

const char *FN(PW,get_dim_name)(__isl_keep PW *pw, enum isl_dim_type type,
        unsigned pos)
{
        return pw ? isl_space_get_dim_name(pw->dim, type, pos) : NULL;
}

isl_bool FN(PW,has_dim_id)(__isl_keep PW *pw, enum isl_dim_type type,
        unsigned pos)
{
        return pw ? isl_space_has_dim_id(pw->dim, type, pos) : isl_bool_error;
}

__isl_give isl_id *FN(PW,get_dim_id)(__isl_keep PW *pw, enum isl_dim_type type,
        unsigned pos)
{
        return pw ? isl_space_get_dim_id(pw->dim, type, pos) : NULL;
}

isl_bool FN(PW,has_tuple_name)(__isl_keep PW *pw, enum isl_dim_type type)
{
        return pw ? isl_space_has_tuple_name(pw->dim, type) : isl_bool_error;
}

const char *FN(PW,get_tuple_name)(__isl_keep PW *pw, enum isl_dim_type type)
{
        return pw ? isl_space_get_tuple_name(pw->dim, type) : NULL;
}

isl_bool FN(PW,has_tuple_id)(__isl_keep PW *pw, enum isl_dim_type type)
{
        return pw ? isl_space_has_tuple_id(pw->dim, type) : isl_bool_error;
}

__isl_give isl_id *FN(PW,get_tuple_id)(__isl_keep PW *pw, enum isl_dim_type type)
{
        return pw ? isl_space_get_tuple_id(pw->dim, type) : NULL;
}

isl_bool FN(PW,IS_ZERO)(__isl_keep PW *pw)
{
        if (!pw)
                return isl_bool_error;

        return isl_bool_ok(pw->n == 0);
}

static __isl_give PW *FN(PW,realign_domain)(__isl_take PW *pw,
        __isl_take isl_reordering *exp)
{
        int i;
        isl_size n;

        n = FN(PW,n_piece)(pw);
        if (n < 0 || !exp)
                goto error;

        for (i = 0; i < n; ++i) {
                isl_set *domain;
                EL *el;

                domain = FN(PW,take_domain_at)(pw, i);
                domain = isl_set_realign(domain, isl_reordering_copy(exp));
                pw = FN(PW,restore_domain_at)(pw, i, domain);

                el = FN(PW,take_base_at)(pw, i);
                el = FN(EL,realign_domain)(el, isl_reordering_copy(exp));
                pw = FN(PW,restore_base_at)(pw, i, el);
        }

        pw = FN(PW,reset_domain_space)(pw, isl_reordering_get_space(exp));

        isl_reordering_free(exp);
        return pw;
error:
        isl_reordering_free(exp);
        FN(PW,free)(pw);
        return NULL;
}

#undef TYPE
#define TYPE PW

#include "isl_check_named_params_templ.c"

/* Align the parameters of "pw" to those of "model".
 */
__isl_give PW *FN(PW,align_params)(__isl_take PW *pw, __isl_take isl_space *model)
{
        isl_ctx *ctx;
        isl_bool equal_params;

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

        ctx = isl_space_get_ctx(model);
        if (!isl_space_has_named_params(model))
                isl_die(ctx, isl_error_invalid,
                        "model has unnamed parameters", goto error);
        if (FN(PW,check_named_params)(pw) < 0)
                goto error;
        equal_params = isl_space_has_equal_params(pw->dim, model);
        if (equal_params < 0)
                goto error;
        if (!equal_params) {
                isl_space *space;
                isl_reordering *exp;

                space = FN(PW,get_domain_space)(pw);
                exp = isl_parameter_alignment_reordering(space, model);
                isl_space_free(space);
                pw = FN(PW,realign_domain)(pw, exp);
        }

        isl_space_free(model);
        return pw;
error:
        isl_space_free(model);
        FN(PW,free)(pw);
        return NULL;
}

#undef TYPE
#define TYPE    PW

static
#include "isl_align_params_bin_templ.c"

#undef SUFFIX
#define SUFFIX  set
#undef ARG1
#define ARG1    PW
#undef ARG2
#define ARG2    isl_set

static
#include "isl_align_params_templ.c"

#undef TYPE
#define TYPE    PW

#include "isl_type_has_equal_space_bin_templ.c"
#include "isl_type_check_equal_space_templ.c"

/* Private version of "union_add".  For isl_pw_qpolynomial and
 * isl_pw_qpolynomial_fold, we prefer to simply call it "add".
 */
static __isl_give PW *FN(PW,union_add_)(__isl_take PW *pw1, __isl_take PW *pw2)
{
        int i, j, n;
        struct PW *res;
        isl_ctx *ctx;
        isl_set *set;

        if (FN(PW,align_params_bin)(&pw1, &pw2) < 0)
                goto error;

        ctx = isl_space_get_ctx(pw1->dim);
        if (!OPT_EQUAL_TYPES(pw1->, pw2->))
                isl_die(ctx, isl_error_invalid,
                        "fold types don't match", goto error);
        if (FN(PW,check_equal_space)(pw1, pw2) < 0)
                goto error;

        if (FN(PW,IS_ZERO)(pw1)) {
                FN(PW,free)(pw1);
                return pw2;
        }

        if (FN(PW,IS_ZERO)(pw2)) {
                FN(PW,free)(pw2);
                return pw1;
        }

        n = (pw1->n + 1) * (pw2->n + 1);
        res = FN(PW,alloc_size)(isl_space_copy(pw1->dim)
                                OPT_TYPE_ARG(pw1->), 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;
                        EL *sum;
                        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;
                        }
                        set = isl_set_subtract(set,
                                        isl_set_copy(pw2->p[j].set));

                        sum = FN(EL,add_on_domain)(common,
                                                   FN(EL,copy)(pw1->p[i].FIELD),
                                                   FN(EL,copy)(pw2->p[j].FIELD));

                        res = FN(PW,add_piece)(res, common, sum);
                }
                res = FN(PW,add_piece)(res, set, FN(EL,copy)(pw1->p[i].FIELD));
        }

        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 = FN(PW,add_piece)(res, set, FN(EL,copy)(pw2->p[j].FIELD));
        }

        FN(PW,free)(pw1);
        FN(PW,free)(pw2);

        return res;
error:
        FN(PW,free)(pw1);
        FN(PW,free)(pw2);
        return NULL;
}

#if !DEFAULT_IS_ZERO

/* Compute the sum of "pw1" and "pw2 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 function is only defined for object types that do not have
 * a default zero value.  For other object types, this function
 * is simply called "add".
 */
__isl_give PW *FN(PW,union_add)(__isl_take PW *pw1, __isl_take PW *pw2)
{
        return FN(PW,union_add_)(pw1, pw2);
}

#endif

/* This function is currently only used from isl_aff.c
 */
static __isl_give PW *FN(PW,on_shared_domain_in)(__isl_take PW *pw1,
        __isl_take PW *pw2, __isl_take isl_space *space,
        __isl_give EL *(*fn)(__isl_take EL *el1, __isl_take EL *el2))
        __attribute__ ((unused));

/* Apply "fn" to pairs of elements from pw1 and pw2 on shared domains.
 * The result of "fn" (and therefore also of this function) lives in "space".
 */
static __isl_give PW *FN(PW,on_shared_domain_in)(__isl_take PW *pw1,
        __isl_take PW *pw2, __isl_take isl_space *space,
        __isl_give EL *(*fn)(__isl_take EL *el1, __isl_take EL *el2))
{
        int i, j, n;
        PW *res = NULL;

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

        n = pw1->n * pw2->n;
        res = FN(PW,alloc_size)(isl_space_copy(space) OPT_TYPE_ARG(pw1->), n);

        for (i = 0; i < pw1->n; ++i) {
                for (j = 0; j < pw2->n; ++j) {
                        isl_set *common;
                        EL *res_ij;
                        int empty;

                        common = isl_set_intersect(
                                        isl_set_copy(pw1->p[i].set),
                                        isl_set_copy(pw2->p[j].set));
                        empty = isl_set_plain_is_empty(common);
                        if (empty < 0 || empty) {
                                isl_set_free(common);
                                if (empty < 0)
                                        goto error;
                                continue;
                        }

                        res_ij = fn(FN(EL,copy)(pw1->p[i].FIELD),
                                    FN(EL,copy)(pw2->p[j].FIELD));
                        res_ij = FN(EL,gist)(res_ij, isl_set_copy(common));

                        res = FN(PW,add_piece)(res, common, res_ij);
                }
        }

        isl_space_free(space);
        FN(PW,free)(pw1);
        FN(PW,free)(pw2);
        return res;
error:
        isl_space_free(space);
        FN(PW,free)(pw1);
        FN(PW,free)(pw2);
        FN(PW,free)(res);
        return NULL;
}

/* This function is currently only used from isl_aff.c
 */
static __isl_give PW *FN(PW,on_shared_domain)(__isl_take PW *pw1,
        __isl_take PW *pw2,
        __isl_give EL *(*fn)(__isl_take EL *el1, __isl_take EL *el2))
        __attribute__ ((unused));

/* Apply "fn" to pairs of elements from pw1 and pw2 on shared domains.
 * The result of "fn" is assumed to live in the same space as "pw1" and "pw2".
 */
static __isl_give PW *FN(PW,on_shared_domain)(__isl_take PW *pw1,
        __isl_take PW *pw2,
        __isl_give EL *(*fn)(__isl_take EL *el1, __isl_take EL *el2))
{
        isl_space *space;

        if (FN(PW,check_equal_space)(pw1, pw2) < 0)
                goto error;

        space = isl_space_copy(pw1->dim);
        return FN(PW,on_shared_domain_in)(pw1, pw2, space, fn);
error:
        FN(PW,free)(pw1);
        FN(PW,free)(pw2);
        return NULL;
}

/* Return the parameter domain of "pw".
 */
__isl_give isl_set *FN(PW,params)(__isl_take PW *pw)
{
        return isl_set_params(FN(PW,domain)(pw));
}

__isl_give isl_set *FN(PW,domain)(__isl_take PW *pw)
{
        int i;
        isl_set *dom;

        if (!pw)
                return NULL;

        dom = isl_set_empty(FN(PW,get_domain_space)(pw));
        for (i = 0; i < pw->n; ++i)
                dom = isl_set_union_disjoint(dom, isl_set_copy(pw->p[i].set));

        FN(PW,free)(pw);

        return dom;
}

/* Exploit the equalities in the domain of piece "i" of "pw"
 * to simplify the associated function.
 * If the domain of piece "i" is empty, then remove it entirely,
 * replacing it with the final piece.
 */
static __isl_give PW *FN(PW,exploit_equalities_and_remove_if_empty)(
        __isl_take PW *pw, int i)
{
        EL *el;
        isl_set *domain;
        isl_basic_set *aff;
        int empty;

        domain = FN(PW,peek_domain_at)(pw, i);
        empty = isl_set_plain_is_empty(domain);
        if (empty < 0)
                return FN(PW,free)(pw);
        if (empty) {
                isl_set_free(pw->p[i].set);
                FN(EL,free)(pw->p[i].FIELD);
                if (i != pw->n - 1)
                        pw->p[i] = pw->p[pw->n - 1];
                pw->n--;

                return pw;
        }

        aff = isl_set_affine_hull(FN(PW,get_domain_at)(pw, i));
        el = FN(PW,take_base_at)(pw, i);
        el = FN(EL,substitute_equalities)(el, aff);
        pw = FN(PW,restore_base_at_inplace)(pw, i, el);

        return pw;
}

/* Restrict the domain of "pw" by combining each cell
 * with "set" through a call to "fn", where "fn" may be
 * isl_set_intersect, isl_set_intersect_params, isl_set_intersect_factor_domain,
 * isl_set_intersect_factor_range or isl_set_subtract.
 */
static __isl_give PW *FN(PW,restrict_domain)(__isl_take PW *pw,
        __isl_take isl_set *set,
        __isl_give isl_set *(*fn)(__isl_take isl_set *set1,
                                    __isl_take isl_set *set2))
{
        int i;
        isl_size n;

        FN(PW,align_params_set)(&pw, &set);
        n = FN(PW,n_piece)(pw);
        if (n < 0 || !set)
                goto error;

        for (i = n - 1; i >= 0; --i) {
                isl_set *domain;

                domain = FN(PW,take_domain_at)(pw, i);
                domain = fn(domain, isl_set_copy(set));
                pw = FN(PW,restore_domain_at)(pw, i, domain);
                pw = FN(PW,exploit_equalities_and_remove_if_empty)(pw, i);
        }
        
        isl_set_free(set);
        return pw;
error:
        isl_set_free(set);
        FN(PW,free)(pw);
        return NULL;
}

__isl_give PW *FN(PW,intersect_domain)(__isl_take PW *pw,
        __isl_take isl_set *context)
{
        return FN(PW,restrict_domain)(pw, context, &isl_set_intersect);
}

/* Intersect the domain of "pw" with the parameter domain "context".
 */
__isl_give PW *FN(PW,intersect_params)(__isl_take PW *pw,
        __isl_take isl_set *context)
{
        return FN(PW,restrict_domain)(pw, context, &isl_set_intersect_params);
}

/* Given a piecewise expression "pw" with domain in a space [A -> B] and
 * a set in the space A, intersect the domain with the set.
 */
__isl_give PW *FN(PW,intersect_domain_wrapped_domain)(__isl_take PW *pw,
        __isl_take isl_set *set)
{
        return FN(PW,restrict_domain)(pw, set,
                                            &isl_set_intersect_factor_domain);
}

/* Given a piecewise expression "pw" with domain in a space [A -> B] and
 * a set in the space B, intersect the domain with the set.
 */
__isl_give PW *FN(PW,intersect_domain_wrapped_range)(__isl_take PW *pw,
        __isl_take isl_set *set)
{
        return FN(PW,restrict_domain)(pw, set, &isl_set_intersect_factor_range);
}

/* Subtract "domain' from the domain of "pw".
 */
__isl_give PW *FN(PW,subtract_domain)(__isl_take PW *pw,
        __isl_take isl_set *domain)
{
        return FN(PW,restrict_domain)(pw, domain, &isl_set_subtract);
}

/* Return -1 if the piece "p1" should be sorted before "p2"
 * and 1 if it should be sorted after "p2".
 * Return 0 if they do not need to be sorted in a specific order.
 *
 * The two pieces are compared on the basis of their function value expressions.
 */
static int FN(PW,sort_field_cmp)(const void *p1, const void *p2, void *arg)
{
        struct FN(PW,piece) const *pc1 = p1;
        struct FN(PW,piece) const *pc2 = p2;

        return FN(EL,plain_cmp)(pc1->FIELD, pc2->FIELD);
}

/* Sort the pieces of "pw" according to their function value
 * expressions and then combine pairs of adjacent pieces with
 * the same such expression.
 *
 * The sorting is performed in place because it does not
 * change the meaning of "pw", but care needs to be
 * taken not to change any possible other copies of "pw"
 * in case anything goes wrong.
 */
static __isl_give PW *FN(PW,sort_unique)(__isl_take PW *pw)
{
        int i, j;
        isl_set *set;

        if (!pw)
                return NULL;
        if (pw->n <= 1)
                return pw;
        if (isl_sort(pw->p, pw->n, sizeof(pw->p[0]),
                    &FN(PW,sort_field_cmp), NULL) < 0)
                return FN(PW,free)(pw);
        for (i = pw->n - 1; i >= 1; --i) {
                isl_bool equal;
                EL *el, *el_prev;
                isl_set *set_prev;

                el = FN(PW,peek_base_at)(pw, i);
                el_prev = FN(PW,peek_base_at)(pw, i - 1);
                equal = FN(EL,plain_is_equal)(el, el_prev);
                if (equal < 0)
                        return FN(PW,free)(pw);
                if (!equal)
                        continue;
                set = FN(PW,get_domain_at)(pw, i);
                set_prev = FN(PW,get_domain_at)(pw, i - 1);
                set = isl_set_union(set_prev, set);
                if (!set)
                        return FN(PW,free)(pw);
                isl_set_free(pw->p[i].set);
                FN(EL,free)(pw->p[i].FIELD);
                isl_set_free(pw->p[i - 1].set);
                pw->p[i - 1].set = set;
                for (j = i + 1; j < pw->n; ++j)
                        pw->p[j - 1] = pw->p[j];
                pw->n--;
        }

        return pw;
}

/* Compute the gist of "pw" with respect to the domain constraints
 * of "context" for the case where the domain of the last element
 * of "pw" is equal to "context".
 * Compute the gist of this element, replace
 * its domain by the universe and drop all other elements
 * as their domains are necessarily disjoint from "context".
 */
static __isl_give PW *FN(PW,gist_last)(__isl_take PW *pw,
        __isl_take isl_set *context)
{
        int i;
        isl_space *space;
        EL *el;

        for (i = 0; i < pw->n - 1; ++i) {
                isl_set_free(pw->p[i].set);
                FN(EL,free)(pw->p[i].FIELD);
        }
        pw->p[0].FIELD = pw->p[pw->n - 1].FIELD;
        pw->p[0].set = pw->p[pw->n - 1].set;
        pw->n = 1;

        space = isl_set_get_space(context);
        el = FN(PW,take_base_at)(pw, 0);
        el = FN(EL,gist)(el, context);
        pw = FN(PW,restore_base_at)(pw, 0, el);
        context = isl_set_universe(space);
        pw = FN(PW,restore_domain_at)(pw, 0, context);

        return pw;
}

/* Compute the gist of "pw" with respect to the domain constraints
 * of "context".
 * Call "fn_dom" to compute the gist of the domains and
 * "intersect_context" to intersect the domain with the context.
 *
 * If the piecewise expression is empty or the context is the universe,
 * then nothing can be simplified.
 * If "pw" has a single domain and it is equal to "context",
 * then simply replace the domain by the universe.
 * Combine duplicate function value expressions first
 * to increase the chance of "pw" having a single domain.
 */
static __isl_give PW *FN(PW,gist_fn)(__isl_take PW *pw,
        __isl_take isl_set *context,
        __isl_give isl_set *(*fn_dom)(__isl_take isl_set *set,
                                    __isl_take isl_set *context),
        __isl_give isl_set *intersect_context(__isl_take isl_set *set,
                __isl_take isl_set *context))
{
        int i;
        int is_universe;

        pw = FN(PW,sort_unique)(pw);
        if (!pw || !context)
                goto error;

        if (pw->n == 0) {
                isl_set_free(context);
                return pw;
        }

        is_universe = isl_set_plain_is_universe(context);
        if (is_universe < 0)
                goto error;
        if (is_universe) {
                isl_set_free(context);
                return pw;
        }

        FN(PW,align_params_set)(&pw, &context);

        pw = FN(PW,cow)(pw);
        if (!pw)
                goto error;

        if (pw->n == 1) {
                int equal;

                equal = isl_set_plain_is_equal(pw->p[0].set, context);
                if (equal < 0)
                        goto error;
                if (equal)
                        return FN(PW,gist_last)(pw, context);
        }

        context = isl_set_compute_divs(context);

        for (i = pw->n - 1; i >= 0; --i) {
                isl_set *set_i;
                EL *el;
                int empty;

                if (i == pw->n - 1) {
                        int equal;
                        equal = isl_set_plain_is_equal(pw->p[i].set, context);
                        if (equal < 0)
                                goto error;
                        if (equal)
                                return FN(PW,gist_last)(pw, context);
                }
                set_i = FN(PW,get_domain_at)(pw, i);
                set_i = intersect_context(set_i, isl_set_copy(context));
                empty = isl_set_plain_is_empty(set_i);
                el = FN(PW,take_base_at)(pw, i);
                el = FN(EL,gist)(el, set_i);
                pw = FN(PW,restore_base_at)(pw, i, el);
                set_i = FN(PW,take_domain_at)(pw, i);
                set_i = fn_dom(set_i, isl_set_copy(context));
                pw = FN(PW,restore_domain_at)(pw, i, set_i);
                if (empty < 0 || !pw)
                        goto error;
                if (empty) {
                        isl_set_free(pw->p[i].set);
                        FN(EL,free)(pw->p[i].FIELD);
                        if (i != pw->n - 1)
                                pw->p[i] = pw->p[pw->n - 1];
                        pw->n--;
                }
        }

        isl_set_free(context);

        return pw;
error:
        FN(PW,free)(pw);
        isl_set_free(context);
        return NULL;
}

__isl_give PW *FN(PW,gist)(__isl_take PW *pw, __isl_take isl_set *context)
{
        return FN(PW,gist_fn)(pw, context, &isl_set_gist,
                                        &isl_set_intersect);
}

__isl_give PW *FN(PW,gist_params)(__isl_take PW *pw,
        __isl_take isl_set *context)
{
        return FN(PW,gist_fn)(pw, context, &isl_set_gist_params,
                                        &isl_set_intersect_params);
}

/* Coalesce the domains of "pw".
 *
 * Prior to the actual coalescing, first sort the pieces such that
 * pieces with the same function value expression are combined
 * into a single piece, the combined domain of which can then
 * be coalesced.
 */
__isl_give PW *FN(PW,coalesce)(__isl_take PW *pw)
{
        int i;
        isl_size n;

        pw = FN(PW,sort_unique)(pw);
        n = FN(PW,n_piece)(pw);
        if (n < 0)
                return FN(PW,free)(pw);

        for (i = 0; i < n; ++i) {
                pw->p[i].set = isl_set_coalesce(pw->p[i].set);
                if (!pw->p[i].set)
                        goto error;
        }

        return pw;
error:
        FN(PW,free)(pw);
        return NULL;
}

isl_ctx *FN(PW,get_ctx)(__isl_keep PW *pw)
{
        return pw ? isl_space_get_ctx(pw->dim) : NULL;
}

isl_bool FN(PW,involves_dims)(__isl_keep PW *pw, enum isl_dim_type type,
        unsigned first, unsigned n)
{
        int i;
        enum isl_dim_type set_type;

        if (!pw)
                return isl_bool_error;
        if (pw->n == 0 || n == 0)
                return isl_bool_false;

        set_type = type == isl_dim_in ? isl_dim_set : type;

        for (i = 0; i < pw->n; ++i) {
                isl_bool involves = FN(EL,involves_dims)(pw->p[i].FIELD,
                                                        type, first, n);
                if (involves < 0 || involves)
                        return involves;
                involves = isl_set_involves_dims(pw->p[i].set,
                                                        set_type, first, n);
                if (involves < 0 || involves)
                        return involves;
        }
        return isl_bool_false;
}

__isl_give PW *FN(PW,set_dim_name)(__isl_take PW *pw,
        enum isl_dim_type type, unsigned pos, const char *s)
{
        isl_space *space;

        space = FN(PW,get_space)(pw);
        space = isl_space_set_dim_name(space, type, pos, s);
        return FN(PW,reset_space)(pw, space);
}

__isl_give PW *FN(PW,drop_dims)(__isl_take PW *pw,
        enum isl_dim_type type, unsigned first, unsigned n)
{
        int i;
        isl_size n_piece;
        enum isl_dim_type set_type;
        isl_space *space;

        n_piece = FN(PW,n_piece)(pw);
        if (n_piece < 0)
                return FN(PW,free)(pw);
        if (n == 0 && !isl_space_get_tuple_name(pw->dim, type))
                return pw;

        set_type = type == isl_dim_in ? isl_dim_set : type;

        space = FN(PW,take_space)(pw);
        space = isl_space_drop_dims(space, type, first, n);
        pw = FN(PW,restore_space)(pw, space);
        for (i = 0; i < n_piece; ++i) {
                isl_set *domain;
                EL *el;

                el = FN(PW,take_base_at)(pw, i);
                el = FN(EL,drop_dims)(el, type, first, n);
                pw = FN(PW,restore_base_at)(pw, i, el);
                if (type == isl_dim_out)
                        continue;
                domain = FN(PW,take_domain_at)(pw, i);
                domain = isl_set_drop(domain, set_type, first, n);
                pw = FN(PW,restore_domain_at)(pw, i, domain);
        }

        return pw;
}

/* This function is very similar to drop_dims.
 * The only difference is that the cells may still involve
 * the specified dimensions.  They are removed using
 * isl_set_project_out instead of isl_set_drop.
 */
__isl_give PW *FN(PW,project_out)(__isl_take PW *pw,
        enum isl_dim_type type, unsigned first, unsigned n)
{
        int i;
        isl_size n_piece;
        enum isl_dim_type set_type;
        isl_space *space;

        n_piece = FN(PW,n_piece)(pw);
        if (n_piece < 0)
                return FN(PW,free)(pw);
        if (n == 0 && !isl_space_get_tuple_name(pw->dim, type))
                return pw;

        set_type = type == isl_dim_in ? isl_dim_set : type;

        space = FN(PW,take_space)(pw);
        space = isl_space_drop_dims(space, type, first, n);
        pw = FN(PW,restore_space)(pw, space);
        for (i = 0; i < n_piece; ++i) {
                isl_set *domain;
                EL *el;

                domain = FN(PW,take_domain_at)(pw, i);
                domain = isl_set_project_out(domain, set_type, first, n);
                pw = FN(PW,restore_domain_at)(pw, i, domain);
                el = FN(PW,take_base_at)(pw, i);
                el = FN(EL,drop_dims)(el, type, first, n);
                pw = FN(PW,restore_base_at)(pw, i, el);
        }

        return pw;
}

/* Project the domain of pw onto its parameter space.
 */
__isl_give PW *FN(PW,project_domain_on_params)(__isl_take PW *pw)
{
        isl_space *space;
        isl_size n;

        n = FN(PW,dim)(pw, isl_dim_in);
        if (n < 0)
                return FN(PW,free)(pw);
        pw = FN(PW,project_out)(pw, isl_dim_in, 0, n);
        space = FN(PW,get_domain_space)(pw);
        space = isl_space_params(space);
        pw = FN(PW,reset_domain_space)(pw, space);
        return pw;
}

#undef TYPE
#define TYPE    PW
#include "isl_drop_unused_params_templ.c"

isl_size FN(PW,dim)(__isl_keep PW *pw, enum isl_dim_type type)
{
        return isl_space_dim(FN(PW,peek_space)(pw), type);
}

__isl_give isl_space *FN(PW,get_domain_space)(__isl_keep PW *pw)
{
        return pw ? isl_space_domain(isl_space_copy(pw->dim)) : NULL;
}

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

/* Return the position of the dimension of the given type and identifier
 * in "pw".
 * Return -1 if no such dimension can be found.
 */
static int FN(PW,find_dim_by_id)(__isl_keep PW *pw,
        enum isl_dim_type type, __isl_keep isl_id *id)
{
        isl_space *space;

        space = FN(PW,peek_space)(pw);
        return isl_space_find_dim_by_id(space, type, id);
}

/* Does the piecewise expression "pw" depend in any way
 * on the parameter with identifier "id"?
 */
isl_bool FN(PW,involves_param_id)(__isl_keep PW *pw, __isl_keep isl_id *id)
{
        int pos;

        if (!pw || !id)
                return isl_bool_error;
        if (pw->n == 0)
                return isl_bool_false;

        pos = FN(PW,find_dim_by_id)(pw, isl_dim_param, id);
        if (pos < 0)
                return isl_bool_false;
        return FN(PW,involves_dims)(pw, isl_dim_param, pos, 1);
}

/* Reset the space of "pw".  Since we don't know if the elements
 * represent the spaces themselves or their domains, we pass along
 * both when we call their reset_space_and_domain.
 */
static __isl_give PW *FN(PW,reset_space_and_domain)(__isl_take PW *pw,
        __isl_take isl_space *space, __isl_take isl_space *domain)
{
        int i;
        isl_size n;

        n = FN(PW,n_piece)(pw);
        if (n < 0 || !space || !domain)
                goto error;

        for (i = 0; i < n; ++i) {
                isl_set *set;
                EL *el;

                set = FN(PW,take_domain_at)(pw, i);
                set = isl_set_reset_space(set, isl_space_copy(domain));
                pw = FN(PW,restore_domain_at)(pw, i, set);
                el = FN(PW,take_base_at)(pw, i);
                el = FN(EL,reset_space_and_domain)(el,
                              isl_space_copy(space), isl_space_copy(domain));
                pw = FN(PW,restore_base_at)(pw, i, el);
        }

        isl_space_free(domain);

        pw = FN(PW,restore_space)(pw, space);

        return pw;
error:
        isl_space_free(domain);
        isl_space_free(space);
        FN(PW,free)(pw);
        return NULL;
}

__isl_give PW *FN(PW,reset_domain_space)(__isl_take PW *pw,
        __isl_take isl_space *domain)
{
        isl_space *space;

        space = isl_space_extend_domain_with_range(isl_space_copy(domain),
                                                   FN(PW,get_space)(pw));
        return FN(PW,reset_space_and_domain)(pw, space, domain);
}

__isl_give PW *FN(PW,reset_space)(__isl_take PW *pw,
        __isl_take isl_space *space)
{
        isl_space *domain;

        domain = isl_space_domain(isl_space_copy(space));
        return FN(PW,reset_space_and_domain)(pw, space, domain);
}

__isl_give PW *FN(PW,set_tuple_id)(__isl_take PW *pw, enum isl_dim_type type,
        __isl_take isl_id *id)
{
        isl_space *space;

        pw = FN(PW,cow)(pw);
        if (!pw)
                goto error;

        space = FN(PW,get_space)(pw);
        space = isl_space_set_tuple_id(space, type, id);

        return FN(PW,reset_space)(pw, space);
error:
        isl_id_free(id);
        return FN(PW,free)(pw);
}

/* Drop the id on the specified tuple.
 */
__isl_give PW *FN(PW,reset_tuple_id)(__isl_take PW *pw, enum isl_dim_type type)
{
        isl_space *space;

        if (!pw)
                return NULL;
        if (!FN(PW,has_tuple_id)(pw, type))
                return pw;

        pw = FN(PW,cow)(pw);
        if (!pw)
                return NULL;

        space = FN(PW,get_space)(pw);
        space = isl_space_reset_tuple_id(space, type);

        return FN(PW,reset_space)(pw, space);
}

__isl_give PW *FN(PW,set_dim_id)(__isl_take PW *pw,
        enum isl_dim_type type, unsigned pos, __isl_take isl_id *id)
{
        isl_space *space;

        space = FN(PW,get_space)(pw);
        space = isl_space_set_dim_id(space, type, pos, id);
        return FN(PW,reset_space)(pw, space);
}

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

        space = FN(PW,get_space)(pw);
        space = isl_space_reset_user(space);

        return FN(PW,reset_space)(pw, space);
}

isl_size FN(PW,n_piece)(__isl_keep PW *pw)
{
        return pw ? pw->n : isl_size_error;
}

isl_stat FN(PW,foreach_piece)(__isl_keep PW *pw,
        isl_stat (*fn)(__isl_take isl_set *set, __isl_take EL *el, void *user),
        void *user)
{
        int i;

        if (!pw)
                return isl_stat_error;

        for (i = 0; i < pw->n; ++i)
                if (fn(isl_set_copy(pw->p[i].set),
                                FN(EL,copy)(pw->p[i].FIELD), user) < 0)
                        return isl_stat_error;

        return isl_stat_ok;
}

/* Does "test" succeed on every cell of "pw"?
 */
isl_bool FN(PW,every_piece)(__isl_keep PW *pw,
        isl_bool (*test)(__isl_keep isl_set *set,
                __isl_keep EL *el, void *user), void *user)
{
        int i;

        if (!pw)
                return isl_bool_error;

        for (i = 0; i < pw->n; ++i) {
                isl_bool r;

                r = test(pw->p[i].set, pw->p[i].FIELD, user);
                if (r < 0 || !r)
                        return r;
        }

        return isl_bool_true;
}

/* Is "pw" defined over a single universe domain?
 *
 * If the default value of this piecewise type is zero,
 * then a "pw" with a zero number of cells is also accepted
 * as it represents the default zero value.
 */
isl_bool FN(FN(PW,isa),BASE)(__isl_keep PW *pw)
{
        isl_size n;

        n = FN(PW,n_piece)(pw);
        if (n < 0)
                return isl_bool_error;
        if (DEFAULT_IS_ZERO && n == 0)
                return isl_bool_true;
        if (n != 1)
                return isl_bool_false;
        return isl_set_plain_is_universe(FN(PW,peek_domain_at)(pw, 0));
}

/* Return a zero base expression in the same space (and of the same type)
 * as "pw".
 */
static __isl_give EL *FN(EL,zero_like_type)(__isl_take PW *pw OPT_TYPE_PARAM)
{
        isl_space *space;

        space = FN(PW,get_space)(pw);
        FN(PW,free)(pw);
        return FN(EL,zero_in_space)(space OPT_TYPE_ARG(NO_LOC));
}

#ifndef HAS_TYPE
/* Return a zero base expression in the same space as "pw".
 */
static __isl_give EL *FN(EL,zero_like)(__isl_take PW *pw)
{
        return FN(EL,zero_like_type)(pw);
}
#else
/* Return a zero base expression in the same space and of the same type
 * as "pw".
 *
 * Pass along the type as an explicit argument for uniform handling
 * in isl_*_zero_like_type.
 */
static __isl_give EL *FN(EL,zero_like)(__isl_take PW *pw)
{
        enum isl_fold type;

        type = FN(PW,get_type)(pw);
        if (type < 0)
                goto error;
        return FN(EL,zero_like_type)(pw, type);
error:
        FN(PW,free)(pw);
        return NULL;
}
#endif

/* Given that "pw" is defined over a single universe domain,
 * return the base expression associated to this domain.
 *
 * If the number of cells is zero, then "pw" is of a piecewise type
 * with a default zero value and effectively represents zero.
 * In this case, create a zero base expression in the same space
 * (and with the same type).
 * Otherwise, simply extract the associated base expression.
 */
__isl_give EL *FN(FN(PW,as),BASE)(__isl_take PW *pw)
{
        isl_bool is_total;
        isl_size n;
        EL *el;

        is_total = FN(FN(PW,isa),BASE)(pw);
        if (is_total < 0)
                goto error;
        if (!is_total)
                isl_die(FN(PW,get_ctx)(pw), isl_error_invalid,
                        "expecting single total function", goto error);
        n = FN(PW,n_piece)(pw);
        if (n < 0)
                goto error;
        if (n == 0)
                return FN(EL,zero_like)(pw);
        el = FN(PW,take_base_at)(pw, 0);
        FN(PW,free)(pw);
        return el;
error:
        FN(PW,free)(pw);
        return NULL;
}

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

/* Multiply the pieces of "pw" by "v" and return the result.
 */
__isl_give PW *FN(PW,scale_val)(__isl_take PW *pw, __isl_take isl_val *v)
{
        int i;
        isl_size n;

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

        if (isl_val_is_one(v)) {
                isl_val_free(v);
                return pw;
        }
        if (pw && DEFAULT_IS_ZERO && isl_val_is_zero(v)) {
                PW *zero;
                isl_space *space = FN(PW,get_space)(pw);
                zero = FN(PW,ZERO)(space OPT_TYPE_ARG(pw->));
                FN(PW,free)(pw);
                isl_val_free(v);
                return zero;
        }
        if (isl_val_is_neg(v))
                pw = FN(PW,negate_type)(pw);
        n = FN(PW,n_piece)(pw);
        if (n < 0)
                goto error;

        for (i = 0; i < n; ++i) {
                EL *el;

                el = FN(PW,take_base_at)(pw, i);
                el = FN(EL,scale_val)(el, isl_val_copy(v));
                pw = FN(PW,restore_base_at)(pw, i, el);
        }

        isl_val_free(v);
        return pw;
error:
        isl_val_free(v);
        FN(PW,free)(pw);
        return NULL;
}

/* Divide the pieces of "pw" by "v" and return the result.
 */
__isl_give PW *FN(PW,scale_down_val)(__isl_take PW *pw, __isl_take isl_val *v)
{
        int i;
        isl_size n;

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

        if (isl_val_is_one(v)) {
                isl_val_free(v);
                return pw;
        }

        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);

        if (isl_val_is_neg(v))
                pw = FN(PW,negate_type)(pw);
        n = FN(PW,n_piece)(pw);
        if (n < 0)
                goto error;

        for (i = 0; i < n; ++i) {
                EL *el;

                el = FN(PW,take_base_at)(pw, i);
                el = FN(EL,scale_down_val)(el, isl_val_copy(v));
                pw = FN(PW,restore_base_at)(pw, i, el);
        }

        isl_val_free(v);
        return pw;
error:
        isl_val_free(v);
        FN(PW,free)(pw);
        return NULL;
}

/* Apply some normalization to "pw".
 * In particular, sort the pieces according to their function value
 * expressions, combining pairs of adjacent pieces with
 * the same such expression, and then normalize the domains of the pieces.
 *
 * We normalize in place, but if anything goes wrong we need
 * to return NULL, so we need to make sure we don't change the
 * meaning of any possible other copies of "pw".
 */
static __isl_give PW *FN(PW,normalize)(__isl_take PW *pw)
{
        int i;
        isl_set *set;

        pw = FN(PW,sort_unique)(pw);
        if (!pw)
                return NULL;
        for (i = 0; i < pw->n; ++i) {
                set = isl_set_normalize(isl_set_copy(pw->p[i].set));
                if (!set)
                        return FN(PW,free)(pw);
                isl_set_free(pw->p[i].set);
                pw->p[i].set = set;
        }

        return pw;
}

/* Is pw1 obviously equal to pw2?
 * That is, do they have obviously identical cells and obviously identical
 * elements on each cell?
 *
 * If "pw1" or "pw2" contain any NaNs, then they are considered
 * not to be the same.  A NaN is not equal to anything, not even
 * to another NaN.
 */
isl_bool FN(PW,plain_is_equal)(__isl_keep PW *pw1, __isl_keep PW *pw2)
{
        int i;
        isl_bool equal, has_nan;

        if (!pw1 || !pw2)
                return isl_bool_error;

        has_nan = FN(PW,involves_nan)(pw1);
        if (has_nan >= 0 && !has_nan)
                has_nan = FN(PW,involves_nan)(pw2);
        if (has_nan < 0 || has_nan)
                return isl_bool_not(has_nan);

        if (pw1 == pw2)
                return isl_bool_true;
        equal = FN(PW,has_equal_space)(pw1, pw2);
        if (equal < 0 || !equal)
                return equal;

        pw1 = FN(PW,copy)(pw1);
        pw2 = FN(PW,copy)(pw2);
        pw1 = FN(PW,normalize)(pw1);
        pw2 = FN(PW,normalize)(pw2);
        if (!pw1 || !pw2)
                goto error;

        equal = isl_bool_ok(pw1->n == pw2->n);
        for (i = 0; equal && i < pw1->n; ++i) {
                equal = isl_set_plain_is_equal(pw1->p[i].set, pw2->p[i].set);
                if (equal < 0)
                        goto error;
                if (!equal)
                        break;
                equal = FN(EL,plain_is_equal)(pw1->p[i].FIELD, pw2->p[i].FIELD);
                if (equal < 0)
                        goto error;
        }

        FN(PW,free)(pw1);
        FN(PW,free)(pw2);
        return equal;
error:
        FN(PW,free)(pw1);
        FN(PW,free)(pw2);
        return isl_bool_error;
}

/* Does "pw" involve any NaNs?
 */
isl_bool FN(PW,involves_nan)(__isl_keep PW *pw)
{
        int i;

        if (!pw)
                return isl_bool_error;
        if (pw->n == 0)
                return isl_bool_false;

        for (i = 0; i < pw->n; ++i) {
                isl_bool has_nan = FN(EL,involves_nan)(pw->p[i].FIELD);
                if (has_nan < 0 || has_nan)
                        return has_nan;
        }

        return isl_bool_false;
}