* 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;
}
+/* Normalize the representation of "aff".
+ *
+ * This function should only be called of "new" isl_affs, i.e.,
+ * with only a single reference. We therefore do not need to
+ * worry about affecting other instances.
+ */
__isl_give isl_aff *isl_aff_normalize(__isl_take isl_aff *aff)
{
if (!aff)
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 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(
#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);
}
+/* 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.
*
* The result is
*
- * floor((a f + d g')/(m d))
+ * (a f + d g')/(m d)
*
* where g' is the result of plugging in "subs" in each of the integer
* divisions in g.
projects / platform / upstream / isl.git / blobdiff