* Copyright 2011 Sven Verdoolaege
* Copyright 2012 Ecole Normale Superieure
*
- * Use of this software is governed by the GNU LGPLv2.1 license
+ * 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,
return aff;
}
+/* Add "v" to the numerator of the constant term of "aff".
+ */
+__isl_give isl_aff *isl_aff_add_constant_num(__isl_take isl_aff *aff, isl_int v)
+{
+ if (isl_int_is_zero(v))
+ return aff;
+
+ aff = isl_aff_cow(aff);
+ if (!aff)
+ return NULL;
+
+ aff->v = isl_vec_cow(aff->v);
+ if (!aff->v)
+ return isl_aff_free(aff);
+
+ isl_int_add(aff->v->el[1], aff->v->el[1], v);
+
+ return aff;
+}
+
+/* Add "v" to the numerator of the constant term of "aff".
+ */
+__isl_give isl_aff *isl_aff_add_constant_num_si(__isl_take isl_aff *aff, int v)
+{
+ isl_int t;
+
+ if (v == 0)
+ return aff;
+
+ isl_int_init(t);
+ isl_int_set_si(t, v);
+ aff = isl_aff_add_constant_num(aff, t);
+ isl_int_clear(t);
+
+ return aff;
+}
+
__isl_give isl_aff *isl_aff_set_constant_si(__isl_take isl_aff *aff, int v)
{
aff = isl_aff_cow(aff);
/* Given f, return floor(f).
* If f is an integer expression, then just return f.
+ * If f is a constant, then return the constant floor(f).
* Otherwise, if f = g/m, write g = q m + r,
* create a new div d = [r/m] and return the expression q + d.
* The coefficients in r are taken to lie between -m/2 and m/2.
return NULL;
aff->v = isl_vec_cow(aff->v);
+ if (!aff->v)
+ return isl_aff_free(aff);
+
+ if (isl_aff_is_cst(aff)) {
+ isl_int_fdiv_q(aff->v->el[1], aff->v->el[1], aff->v->el[0]);
+ isl_int_set_si(aff->v->el[0], 1);
+ return aff;
+ }
+
div = isl_vec_copy(aff->v);
div = isl_vec_cow(div);
if (!div)
aff = isl_aff_cow(aff);
if (!aff)
return NULL;
+
+ if (isl_int_is_zero(f))
+ isl_die(isl_aff_get_ctx(aff), isl_error_invalid,
+ "cannot scale down by zero", return isl_aff_free(aff));
+
aff->v = isl_vec_cow(aff->v);
if (!aff->v)
return isl_aff_free(aff);
return bset;
}
+/* Return a basic set containing those elements in the domain space
+ * of aff where it is negative.
+ */
+__isl_give isl_basic_set *isl_aff_neg_basic_set(__isl_take isl_aff *aff)
+{
+ aff = isl_aff_neg(aff);
+ aff = isl_aff_add_constant_num_si(aff, -1);
+ return isl_aff_nonneg_basic_set(aff);
+}
+
/* Return a basic set containing those elements in the space
* of aff where it is zero.
*/
return ma;
}
+/* Create an isl_multi_aff in the given space that maps each
+ * input dimension to the corresponding output dimension.
+ */
+__isl_give isl_multi_aff *isl_multi_aff_identity(__isl_take isl_space *space)
+{
+ int n;
+ isl_multi_aff *ma;
+
+ if (!space)
+ return NULL;
+
+ if (isl_space_is_set(space))
+ isl_die(isl_space_get_ctx(space), isl_error_invalid,
+ "expecting map space", goto error);
+
+ n = isl_space_dim(space, isl_dim_out);
+ if (n != isl_space_dim(space, isl_dim_in))
+ isl_die(isl_space_get_ctx(space), isl_error_invalid,
+ "number of input and output dimensions needs to be "
+ "the same", goto error);
+
+ ma = isl_multi_aff_alloc(isl_space_copy(space));
+
+ if (!n)
+ isl_space_free(space);
+ else {
+ int i;
+ isl_local_space *ls;
+ isl_aff *aff;
+
+ space = isl_space_domain(space);
+ ls = isl_local_space_from_space(space);
+ aff = isl_aff_zero_on_domain(ls);
+
+ for (i = 0; i < n; ++i) {
+ isl_aff *aff_i;
+ aff_i = isl_aff_copy(aff);
+ aff_i = isl_aff_add_coefficient_si(aff_i,
+ isl_dim_in, i, 1);
+ ma = isl_multi_aff_set_aff(ma, i, aff_i);
+ }
+
+ isl_aff_free(aff);
+ }
+
+ return ma;
+error:
+ isl_space_free(space);
+ return NULL;
+}
+
/* Create an isl_pw_multi_aff with the given isl_multi_aff on a universe
* domain.
*/
return NULL;
}
+/* Given two multi-affine expressions A -> B and C -> D,
+ * construct a multi-affine expression [A -> C] -> [B -> D].
+ */
+__isl_give isl_multi_aff *isl_multi_aff_product(
+ __isl_take isl_multi_aff *ma1, __isl_take isl_multi_aff *ma2)
+{
+ int i;
+ isl_aff *aff;
+ isl_space *space;
+ isl_multi_aff *res;
+ int in1, in2, out1, out2;
+
+ in1 = isl_multi_aff_dim(ma1, isl_dim_in);
+ in2 = isl_multi_aff_dim(ma2, isl_dim_in);
+ out1 = isl_multi_aff_dim(ma1, isl_dim_out);
+ out2 = isl_multi_aff_dim(ma2, isl_dim_out);
+ space = isl_space_product(isl_multi_aff_get_space(ma1),
+ isl_multi_aff_get_space(ma2));
+ res = isl_multi_aff_alloc(isl_space_copy(space));
+ space = isl_space_domain(space);
+
+ for (i = 0; i < out1; ++i) {
+ aff = isl_multi_aff_get_aff(ma1, i);
+ aff = isl_aff_insert_dims(aff, isl_dim_in, in1, in2);
+ aff = isl_aff_reset_domain_space(aff, isl_space_copy(space));
+ res = isl_multi_aff_set_aff(res, i, aff);
+ }
+
+ for (i = 0; i < out2; ++i) {
+ aff = isl_multi_aff_get_aff(ma2, i);
+ aff = isl_aff_insert_dims(aff, isl_dim_in, 0, in1);
+ aff = isl_aff_reset_domain_space(aff, isl_space_copy(space));
+ res = isl_multi_aff_set_aff(res, out1 + i, aff);
+ }
+
+ isl_space_free(space);
+ isl_multi_aff_free(ma1);
+ isl_multi_aff_free(ma2);
+ return res;
+}
+
/* Exploit the equalities in "eq" to simplify the affine expressions.
*/
static __isl_give isl_multi_aff *isl_multi_aff_substitute_equalities(
maff->space = isl_space_set_dim_name(maff->space, type, pos, s);
if (!maff->space)
return isl_multi_aff_free(maff);
+
+ if (type == isl_dim_out)
+ return maff;
for (i = 0; i < maff->n; ++i) {
maff->p[i] = isl_aff_set_dim_name(maff->p[i], type, pos, s);
if (!maff->p[i])
return maff;
}
+/* Return the set of domain elements where "ma1" is lexicographically
+ * smaller than or equal to "ma2".
+ */
+__isl_give isl_set *isl_multi_aff_lex_le_set(__isl_take isl_multi_aff *ma1,
+ __isl_take isl_multi_aff *ma2)
+{
+ return isl_multi_aff_lex_ge_set(ma2, ma1);
+}
+
+/* Return the set of domain elements where "ma1" is lexicographically
+ * greater than or equal to "ma2".
+ */
+__isl_give isl_set *isl_multi_aff_lex_ge_set(__isl_take isl_multi_aff *ma1,
+ __isl_take isl_multi_aff *ma2)
+{
+ isl_space *space;
+ isl_map *map1, *map2;
+ isl_map *map, *ge;
+
+ map1 = isl_map_from_multi_aff(ma1);
+ map2 = isl_map_from_multi_aff(ma2);
+ map = isl_map_range_product(map1, map2);
+ space = isl_space_range(isl_map_get_space(map));
+ space = isl_space_domain(isl_space_unwrap(space));
+ ge = isl_map_lex_ge(space);
+ map = isl_map_intersect_range(map, isl_map_wrap(ge));
+
+ return isl_map_domain(map);
+}
+
#undef PW
#define PW isl_pw_multi_aff
#undef EL
#include <isl_union_templ.c>
+/* Given a function "cmp" that returns the set of elements where
+ * "ma1" is "better" than "ma2", return the intersection of this
+ * set with "dom1" and "dom2".
+ */
+static __isl_give isl_set *shared_and_better(__isl_keep isl_set *dom1,
+ __isl_keep isl_set *dom2, __isl_keep isl_multi_aff *ma1,
+ __isl_keep isl_multi_aff *ma2,
+ __isl_give isl_set *(*cmp)(__isl_take isl_multi_aff *ma1,
+ __isl_take isl_multi_aff *ma2))
+{
+ isl_set *common;
+ isl_set *better;
+ int is_empty;
+
+ common = isl_set_intersect(isl_set_copy(dom1), isl_set_copy(dom2));
+ is_empty = isl_set_plain_is_empty(common);
+ if (is_empty >= 0 && is_empty)
+ return common;
+ if (is_empty < 0)
+ return isl_set_free(common);
+ better = cmp(isl_multi_aff_copy(ma1), isl_multi_aff_copy(ma2));
+ better = isl_set_intersect(common, better);
+
+ return better;
+}
+
+/* Given a function "cmp" that returns the set of elements where
+ * "ma1" is "better" than "ma2", return a piecewise multi affine
+ * expression defined on the union of the definition domains
+ * of "pma1" and "pma2" that maps to the "best" of "pma1" and
+ * "pma2" on each cell. If only one of the two input functions
+ * is defined on a given cell, then it is considered the best.
+ */
+static __isl_give isl_pw_multi_aff *pw_multi_aff_union_opt(
+ __isl_take isl_pw_multi_aff *pma1,
+ __isl_take isl_pw_multi_aff *pma2,
+ __isl_give isl_set *(*cmp)(__isl_take isl_multi_aff *ma1,
+ __isl_take isl_multi_aff *ma2))
+{
+ int i, j, n;
+ isl_pw_multi_aff *res = NULL;
+ isl_ctx *ctx;
+ isl_set *set = NULL;
+
+ if (!pma1 || !pma2)
+ goto error;
+
+ ctx = isl_space_get_ctx(pma1->dim);
+ if (!isl_space_is_equal(pma1->dim, pma2->dim))
+ isl_die(ctx, isl_error_invalid,
+ "arguments should live in the same space", goto error);
+
+ if (isl_pw_multi_aff_is_empty(pma1)) {
+ isl_pw_multi_aff_free(pma1);
+ return pma2;
+ }
+
+ if (isl_pw_multi_aff_is_empty(pma2)) {
+ isl_pw_multi_aff_free(pma2);
+ return pma1;
+ }
+
+ n = 2 * (pma1->n + 1) * (pma2->n + 1);
+ res = isl_pw_multi_aff_alloc_size(isl_space_copy(pma1->dim), n);
+
+ for (i = 0; i < pma1->n; ++i) {
+ set = isl_set_copy(pma1->p[i].set);
+ for (j = 0; j < pma2->n; ++j) {
+ isl_set *better;
+ int is_empty;
+
+ better = shared_and_better(pma2->p[j].set,
+ pma1->p[i].set, pma2->p[j].maff,
+ pma1->p[i].maff, cmp);
+ is_empty = isl_set_plain_is_empty(better);
+ if (is_empty < 0 || is_empty) {
+ isl_set_free(better);
+ if (is_empty < 0)
+ goto error;
+ continue;
+ }
+ set = isl_set_subtract(set, isl_set_copy(better));
+
+ res = isl_pw_multi_aff_add_piece(res, better,
+ isl_multi_aff_copy(pma2->p[j].maff));
+ }
+ res = isl_pw_multi_aff_add_piece(res, set,
+ isl_multi_aff_copy(pma1->p[i].maff));
+ }
+
+ for (j = 0; j < pma2->n; ++j) {
+ set = isl_set_copy(pma2->p[j].set);
+ for (i = 0; i < pma1->n; ++i)
+ set = isl_set_subtract(set,
+ isl_set_copy(pma1->p[i].set));
+ res = isl_pw_multi_aff_add_piece(res, set,
+ isl_multi_aff_copy(pma2->p[j].maff));
+ }
+
+ isl_pw_multi_aff_free(pma1);
+ isl_pw_multi_aff_free(pma2);
+
+ return res;
+error:
+ isl_pw_multi_aff_free(pma1);
+ isl_pw_multi_aff_free(pma2);
+ isl_set_free(set);
+ return isl_pw_multi_aff_free(res);
+}
+
+static __isl_give isl_pw_multi_aff *pw_multi_aff_union_lexmax(
+ __isl_take isl_pw_multi_aff *pma1,
+ __isl_take isl_pw_multi_aff *pma2)
+{
+ return pw_multi_aff_union_opt(pma1, pma2, &isl_multi_aff_lex_ge_set);
+}
+
+/* Given two piecewise multi affine expressions, return a piecewise
+ * multi-affine expression defined on the union of the definition domains
+ * of the inputs that is equal to the lexicographic maximum of the two
+ * inputs on each cell. If only one of the two inputs is defined on
+ * a given cell, then it is considered to be the maximum.
+ */
+__isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
+ __isl_take isl_pw_multi_aff *pma1,
+ __isl_take isl_pw_multi_aff *pma2)
+{
+ return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2,
+ &pw_multi_aff_union_lexmax);
+}
+
+static __isl_give isl_pw_multi_aff *pw_multi_aff_union_lexmin(
+ __isl_take isl_pw_multi_aff *pma1,
+ __isl_take isl_pw_multi_aff *pma2)
+{
+ return pw_multi_aff_union_opt(pma1, pma2, &isl_multi_aff_lex_le_set);
+}
+
+/* Given two piecewise multi affine expressions, return a piecewise
+ * multi-affine expression defined on the union of the definition domains
+ * of the inputs that is equal to the lexicographic minimum of the two
+ * inputs on each cell. If only one of the two inputs is defined on
+ * a given cell, then it is considered to be the minimum.
+ */
+__isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
+ __isl_take isl_pw_multi_aff *pma1,
+ __isl_take isl_pw_multi_aff *pma2)
+{
+ return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2,
+ &pw_multi_aff_union_lexmin);
+}
+
static __isl_give isl_pw_multi_aff *pw_multi_aff_add(
__isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
{
return isl_pw_multi_aff_union_add_(pma1, pma2);
}
-/* Construct a map mapping the domain the piecewise multi-affine expression
+/* Given two piecewise multi-affine expressions A -> B and C -> D,
+ * construct a piecewise multi-affine expression [A -> C] -> [B -> D].
+ */
+static __isl_give isl_pw_multi_aff *pw_multi_aff_product(
+ __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
+{
+ int i, j, n;
+ isl_space *space;
+ isl_pw_multi_aff *res;
+
+ if (!pma1 || !pma2)
+ goto error;
+
+ n = pma1->n * pma2->n;
+ space = isl_space_product(isl_space_copy(pma1->dim),
+ isl_space_copy(pma2->dim));
+ res = isl_pw_multi_aff_alloc_size(space, n);
+
+ for (i = 0; i < pma1->n; ++i) {
+ for (j = 0; j < pma2->n; ++j) {
+ isl_set *domain;
+ isl_multi_aff *ma;
+
+ domain = isl_set_product(isl_set_copy(pma1->p[i].set),
+ isl_set_copy(pma2->p[j].set));
+ ma = isl_multi_aff_product(
+ isl_multi_aff_copy(pma1->p[i].maff),
+ isl_multi_aff_copy(pma2->p[i].maff));
+ res = isl_pw_multi_aff_add_piece(res, domain, ma);
+ }
+ }
+
+ isl_pw_multi_aff_free(pma1);
+ isl_pw_multi_aff_free(pma2);
+ return res;
+error:
+ isl_pw_multi_aff_free(pma1);
+ isl_pw_multi_aff_free(pma2);
+ return NULL;
+}
+
+__isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
+ __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
+{
+ return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2,
+ &pw_multi_aff_product);
+}
+
+/* Construct a map mapping the domain of the piecewise multi-affine expression
* to its range, with each dimension in the range equated to the
* corresponding affine expression on its cell.
*/
isl_union_pw_multi_aff_free(upma);
return NULL;
}
+
+/* Convert "pma" to an isl_map and add it to *umap.
+ */
+static int map_from_pw_multi_aff(__isl_take isl_pw_multi_aff *pma, void *user)
+{
+ isl_union_map **umap = user;
+ isl_map *map;
+
+ map = isl_map_from_pw_multi_aff(pma);
+ *umap = isl_union_map_add_map(*umap, map);
+
+ return 0;
+}
+
+/* Construct a union map mapping the domain of the union
+ * piecewise multi-affine expression to its range, with each dimension
+ * in the range equated to the corresponding affine expression on its cell.
+ */
+__isl_give isl_union_map *isl_union_map_from_union_pw_multi_aff(
+ __isl_take isl_union_pw_multi_aff *upma)
+{
+ isl_space *space;
+ isl_union_map *umap;
+
+ if (!upma)
+ return NULL;
+
+ space = isl_union_pw_multi_aff_get_space(upma);
+ umap = isl_union_map_empty(space);
+
+ if (isl_union_pw_multi_aff_foreach_pw_multi_aff(upma,
+ &map_from_pw_multi_aff, &umap) < 0)
+ goto error;
+
+ isl_union_pw_multi_aff_free(upma);
+ return umap;
+error:
+ isl_union_pw_multi_aff_free(upma);
+ isl_union_map_free(umap);
+ return NULL;
+}
+
+/* Local data for bin_entry and the callback "fn".
+ */
+struct isl_union_pw_multi_aff_bin_data {
+ isl_union_pw_multi_aff *upma2;
+ isl_union_pw_multi_aff *res;
+ isl_pw_multi_aff *pma;
+ int (*fn)(void **entry, void *user);
+};
+
+/* Given an isl_pw_multi_aff from upma1, store it in data->pma
+ * and call data->fn for each isl_pw_multi_aff in data->upma2.
+ */
+static int bin_entry(void **entry, void *user)
+{
+ struct isl_union_pw_multi_aff_bin_data *data = user;
+ isl_pw_multi_aff *pma = *entry;
+
+ data->pma = pma;
+ if (isl_hash_table_foreach(data->upma2->dim->ctx, &data->upma2->table,
+ data->fn, data) < 0)
+ return -1;
+
+ return 0;
+}
+
+/* Call "fn" on each pair of isl_pw_multi_affs in "upma1" and "upma2".
+ * The isl_pw_multi_aff from upma1 is stored in data->pma (where data is
+ * passed as user field) and the isl_pw_multi_aff from upma2 is available
+ * as *entry. The callback should adjust data->res if desired.
+ */
+static __isl_give isl_union_pw_multi_aff *bin_op(
+ __isl_take isl_union_pw_multi_aff *upma1,
+ __isl_take isl_union_pw_multi_aff *upma2,
+ int (*fn)(void **entry, void *user))
+{
+ isl_space *space;
+ struct isl_union_pw_multi_aff_bin_data data = { NULL, NULL, NULL, fn };
+
+ space = isl_union_pw_multi_aff_get_space(upma2);
+ upma1 = isl_union_pw_multi_aff_align_params(upma1, space);
+ space = isl_union_pw_multi_aff_get_space(upma1);
+ upma2 = isl_union_pw_multi_aff_align_params(upma2, space);
+
+ if (!upma1 || !upma2)
+ goto error;
+
+ data.upma2 = upma2;
+ data.res = isl_union_pw_multi_aff_alloc(isl_space_copy(upma1->dim),
+ upma1->table.n);
+ if (isl_hash_table_foreach(upma1->dim->ctx, &upma1->table,
+ &bin_entry, &data) < 0)
+ goto error;
+
+ isl_union_pw_multi_aff_free(upma1);
+ isl_union_pw_multi_aff_free(upma2);
+ return data.res;
+error:
+ isl_union_pw_multi_aff_free(upma1);
+ isl_union_pw_multi_aff_free(upma2);
+ isl_union_pw_multi_aff_free(data.res);
+ return NULL;
+}
+
+/* Given two isl_multi_affs A -> B and C -> D,
+ * construct an isl_multi_aff (A * C) -> (B, D).
+ */
+__isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
+ __isl_take isl_multi_aff *ma1, __isl_take isl_multi_aff *ma2)
+{
+ int i, n1, n2;
+ isl_aff *aff;
+ isl_space *space;
+ isl_multi_aff *res;
+
+ if (!ma1 || !ma2)
+ goto error;
+
+ space = isl_space_range_product(isl_multi_aff_get_space(ma1),
+ isl_multi_aff_get_space(ma2));
+ space = isl_space_flatten_range(space);
+ res = isl_multi_aff_alloc(space);
+
+ n1 = isl_multi_aff_dim(ma1, isl_dim_out);
+ n2 = isl_multi_aff_dim(ma2, isl_dim_out);
+
+ for (i = 0; i < n1; ++i) {
+ aff = isl_multi_aff_get_aff(ma1, i);
+ res = isl_multi_aff_set_aff(res, i, aff);
+ }
+
+ for (i = 0; i < n2; ++i) {
+ aff = isl_multi_aff_get_aff(ma2, i);
+ res = isl_multi_aff_set_aff(res, n1 + i, aff);
+ }
+
+ isl_multi_aff_free(ma1);
+ isl_multi_aff_free(ma2);
+ return res;
+error:
+ isl_multi_aff_free(ma1);
+ isl_multi_aff_free(ma2);
+ return NULL;
+}
+
+/* Given two aligned isl_pw_multi_affs A -> B and C -> D,
+ * construct an isl_pw_multi_aff (A * C) -> (B, D).
+ */
+static __isl_give isl_pw_multi_aff *pw_multi_aff_flat_range_product(
+ __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
+{
+ isl_space *space;
+
+ space = isl_space_range_product(isl_pw_multi_aff_get_space(pma1),
+ isl_pw_multi_aff_get_space(pma2));
+ space = isl_space_flatten_range(space);
+ return isl_pw_multi_aff_on_shared_domain_in(pma1, pma2, space,
+ &isl_multi_aff_flat_range_product);
+}
+
+/* Given two isl_pw_multi_affs A -> B and C -> D,
+ * construct an isl_pw_multi_aff (A * C) -> (B, D).
+ */
+__isl_give isl_pw_multi_aff *isl_pw_multi_aff_flat_range_product(
+ __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
+{
+ return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2,
+ &pw_multi_aff_flat_range_product);
+}
+
+/* If data->pma and *entry have the same domain space, then compute
+ * their flat range product and the result to data->res.
+ */
+static int flat_range_product_entry(void **entry, void *user)
+{
+ struct isl_union_pw_multi_aff_bin_data *data = user;
+ isl_pw_multi_aff *pma2 = *entry;
+
+ if (!isl_space_tuple_match(data->pma->dim, isl_dim_in,
+ pma2->dim, isl_dim_in))
+ return 0;
+
+ pma2 = isl_pw_multi_aff_flat_range_product(
+ isl_pw_multi_aff_copy(data->pma),
+ isl_pw_multi_aff_copy(pma2));
+
+ data->res = isl_union_pw_multi_aff_add_pw_multi_aff(data->res, pma2);
+
+ return 0;
+}
+
+/* Given two isl_union_pw_multi_affs A -> B and C -> D,
+ * construct an isl_union_pw_multi_aff (A * C) -> (B, D).
+ */
+__isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_flat_range_product(
+ __isl_take isl_union_pw_multi_aff *upma1,
+ __isl_take isl_union_pw_multi_aff *upma2)
+{
+ return bin_op(upma1, upma2, &flat_range_product_entry);
+}