/*
* Copyright 2011 INRIA Saclay
* Copyright 2011 Sven Verdoolaege
+ * Copyright 2012 Ecole Normale Superieure
*
* Use of this software is governed by the GNU LGPLv2.1 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_ctx_private.h>
+#define ISL_DIM_H
#include <isl_map_private.h>
+#include <isl_union_map_private.h>
#include <isl_aff_private.h>
#include <isl_space_private.h>
#include <isl_local_space_private.h>
#include <isl/constraint.h>
#include <isl/seq.h>
#include <isl/set.h>
+#include <isl_config.h>
__isl_give isl_aff *isl_aff_alloc_vec(__isl_take isl_local_space *ls,
__isl_take isl_vec *v)
return NULL;
}
+__isl_give isl_aff *isl_aff_align_params(__isl_take isl_aff *aff,
+ __isl_take isl_space *model)
+{
+ if (!aff || !model)
+ goto error;
+
+ if (!isl_space_match(aff->ls->dim, isl_dim_param,
+ model, isl_dim_param)) {
+ isl_reordering *exp;
+
+ model = isl_space_drop_dims(model, isl_dim_in,
+ 0, isl_space_dim(model, isl_dim_in));
+ model = isl_space_drop_dims(model, isl_dim_out,
+ 0, isl_space_dim(model, isl_dim_out));
+ exp = isl_parameter_alignment_reordering(aff->ls->dim, model);
+ exp = isl_reordering_extend_space(exp,
+ isl_aff_get_domain_space(aff));
+ aff = isl_aff_realign_domain(aff, exp);
+ }
+
+ isl_space_free(model);
+ return aff;
+error:
+ isl_space_free(model);
+ isl_aff_free(aff);
+ return NULL;
+}
+
int isl_aff_plain_is_zero(__isl_keep isl_aff *aff)
{
if (!aff)
return aff;
}
+/* Remove divs from the local space that do not appear in the affine
+ * expression.
+ * We currently only remove divs at the end.
+ * Some intermediate divs may also not appear directly in the affine
+ * expression, but we would also need to check that no other divs are
+ * defined in terms of them.
+ */
+__isl_give isl_aff *isl_aff_remove_unused_divs( __isl_take isl_aff *aff)
+{
+ int pos;
+ int off;
+ int n;
+
+ if (!aff)
+ return NULL;
+
+ n = isl_local_space_dim(aff->ls, isl_dim_div);
+ off = isl_local_space_offset(aff->ls, isl_dim_div);
+
+ pos = isl_seq_last_non_zero(aff->v->el + 1 + off, n) + 1;
+ if (pos == n)
+ return aff;
+
+ aff = isl_aff_cow(aff);
+ if (!aff)
+ return NULL;
+
+ aff->ls = isl_local_space_drop_dims(aff->ls, isl_dim_div, pos, n - pos);
+ aff->v = isl_vec_drop_els(aff->v, 1 + off + pos, n - pos);
+ if (!aff->ls || !aff->v)
+ return isl_aff_free(aff);
+
+ return aff;
+}
+
+__isl_give isl_aff *isl_aff_normalize(__isl_take isl_aff *aff)
+{
+ if (!aff)
+ return NULL;
+ aff->v = isl_vec_normalize(aff->v);
+ if (!aff->v)
+ return isl_aff_free(aff);
+ aff = isl_aff_remove_unused_divs(aff);
+ return aff;
+}
+
/* Given f, return floor(f).
* If f is an integer expression, then just return f.
* Otherwise, if f = g/m, write g = q m + r,
}
isl_basic_set_free(eq);
+ aff = isl_aff_normalize(aff);
return aff;
error:
isl_basic_set_free(eq);
return NULL;
}
+__isl_give isl_aff *isl_aff_gist_params(__isl_take isl_aff *aff,
+ __isl_take isl_set *context)
+{
+ isl_set *dom_context = isl_set_universe(isl_aff_get_domain_space(aff));
+ dom_context = isl_set_intersect_params(dom_context, context);
+ return isl_aff_gist(aff, dom_context);
+}
+
/* Return a basic set containing those elements in the space
* of aff where it is non-negative.
*/
__isl_give isl_basic_set *isl_aff_nonneg_basic_set(__isl_take isl_aff *aff)
{
isl_constraint *ineq;
+ isl_basic_set *bset;
ineq = isl_inequality_from_aff(aff);
- return isl_basic_set_from_constraint(ineq);
+ bset = isl_basic_set_from_constraint(ineq);
+ bset = isl_basic_set_simplify(bset);
+ return bset;
}
/* Return a basic set containing those elements in the space
__isl_give isl_basic_set *isl_aff_zero_basic_set(__isl_take isl_aff *aff)
{
isl_constraint *ineq;
+ isl_basic_set *bset;
ineq = isl_equality_from_aff(aff);
- return isl_basic_set_from_constraint(ineq);
+ bset = isl_basic_set_from_constraint(ineq);
+ bset = isl_basic_set_simplify(bset);
+ return bset;
}
/* Return a basic set containing those elements in the shared space
return aff;
}
+/* Project the domain of the affine expression onto its parameter space.
+ * The affine expression may not involve any of the domain dimensions.
+ */
+__isl_give isl_aff *isl_aff_project_domain_on_params(__isl_take isl_aff *aff)
+{
+ isl_space *space;
+ unsigned n;
+ int involves;
+
+ n = isl_aff_dim(aff, isl_dim_in);
+ involves = isl_aff_involves_dims(aff, isl_dim_in, 0, n);
+ if (involves < 0)
+ return isl_aff_free(aff);
+ if (involves)
+ isl_die(isl_aff_get_ctx(aff), isl_error_invalid,
+ "affine expression involves some of the domain dimensions",
+ return isl_aff_free(aff));
+ aff = isl_aff_drop_dims(aff, isl_dim_in, 0, n);
+ space = isl_aff_get_domain_space(aff);
+ space = isl_space_params(space);
+ aff = isl_aff_reset_domain_space(aff, space);
+ return aff;
+}
+
__isl_give isl_aff *isl_aff_insert_dims(__isl_take isl_aff *aff,
enum isl_dim_type type, unsigned first, unsigned n)
{
#define IS_ZERO is_empty
#undef FIELD
#define FIELD aff
+#undef DEFAULT_IS_ZERO
+#define DEFAULT_IS_ZERO 0
#define NO_EVAL
#define NO_OPT
__isl_give isl_pw_aff *isl_pw_aff_union_max(__isl_take isl_pw_aff *pwaff1,
__isl_take isl_pw_aff *pwaff2)
{
- return align_params_pw_pw_and(pwaff1, pwaff2, &pw_aff_union_max);
+ return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2,
+ &pw_aff_union_max);
}
/* Compute a piecewise quasi-affine expression with a domain that
__isl_give isl_pw_aff *isl_pw_aff_union_min(__isl_take isl_pw_aff *pwaff1,
__isl_take isl_pw_aff *pwaff2)
{
- return align_params_pw_pw_and(pwaff1, pwaff2, &pw_aff_union_min);
+ return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2,
+ &pw_aff_union_min);
}
__isl_give isl_pw_aff *isl_pw_aff_union_opt(__isl_take isl_pw_aff *pwaff1,
*/
__isl_give isl_map *isl_map_from_pw_aff(__isl_take isl_pw_aff *pwaff)
{
+ if (!pwaff)
+ return NULL;
if (isl_space_is_set(pwaff->dim))
isl_die(isl_pw_aff_get_ctx(pwaff), isl_error_invalid,
"space of input is not a map",
*/
__isl_give isl_set *isl_set_from_pw_aff(__isl_take isl_pw_aff *pwaff)
{
+ if (!pwaff)
+ return NULL;
if (!isl_space_is_set(pwaff->dim))
isl_die(isl_pw_aff_get_ctx(pwaff), isl_error_invalid,
"space of input is not a set",
}
/* Return a set containing those elements in the domain
- * of pwaff where it is zero.
+ * of pwaff where it is zero (if complement is 0) or not zero
+ * (if complement is 1).
*/
-__isl_give isl_set *isl_pw_aff_zero_set(__isl_take isl_pw_aff *pwaff)
+static __isl_give isl_set *pw_aff_zero_set(__isl_take isl_pw_aff *pwaff,
+ int complement)
{
int i;
isl_set *set;
for (i = 0; i < pwaff->n; ++i) {
isl_basic_set *bset;
- isl_set *set_i;
+ isl_set *set_i, *zero;
bset = isl_aff_zero_basic_set(isl_aff_copy(pwaff->p[i].aff));
- set_i = isl_set_from_basic_set(bset);
- set_i = isl_set_intersect(set_i, isl_set_copy(pwaff->p[i].set));
+ zero = isl_set_from_basic_set(bset);
+ set_i = isl_set_copy(pwaff->p[i].set);
+ if (complement)
+ set_i = isl_set_subtract(set_i, zero);
+ else
+ set_i = isl_set_intersect(set_i, zero);
set = isl_set_union_disjoint(set, set_i);
}
}
/* Return a set containing those elements in the domain
+ * of pwaff where it is zero.
+ */
+__isl_give isl_set *isl_pw_aff_zero_set(__isl_take isl_pw_aff *pwaff)
+{
+ return pw_aff_zero_set(pwaff, 0);
+}
+
+/* Return a set containing those elements in the domain
* of pwaff where it is not zero.
*/
__isl_give isl_set *isl_pw_aff_non_zero_set(__isl_take isl_pw_aff *pwaff)
{
- return isl_set_complement(isl_pw_aff_zero_set(pwaff));
+ return pw_aff_zero_set(pwaff, 1);
}
/* Return a set containing those elements in the shared domain
return pwaff;
}
+/* Assuming that "cond1" and "cond2" are disjoint,
+ * return an affine expression that is equal to pwaff1 on cond1
+ * and to pwaff2 on cond2.
+ */
+static __isl_give isl_pw_aff *isl_pw_aff_select(
+ __isl_take isl_set *cond1, __isl_take isl_pw_aff *pwaff1,
+ __isl_take isl_set *cond2, __isl_take isl_pw_aff *pwaff2)
+{
+ pwaff1 = isl_pw_aff_intersect_domain(pwaff1, cond1);
+ pwaff2 = isl_pw_aff_intersect_domain(pwaff2, cond2);
+
+ return isl_pw_aff_add_disjoint(pwaff1, pwaff2);
+}
+
/* Return an affine expression that is equal to pwaff_true for elements
- * in "cond" and to pwaff_false for elements not in "cond".
+ * where "cond" is non-zero and to pwaff_false for elements where "cond"
+ * is zero.
* That is, return cond ? pwaff_true : pwaff_false;
*/
-__isl_give isl_pw_aff *isl_pw_aff_cond(__isl_take isl_set *cond,
+__isl_give isl_pw_aff *isl_pw_aff_cond(__isl_take isl_pw_aff *cond,
__isl_take isl_pw_aff *pwaff_true, __isl_take isl_pw_aff *pwaff_false)
{
- isl_set *comp;
-
- comp = isl_set_complement(isl_set_copy(cond));
- pwaff_true = isl_pw_aff_intersect_domain(pwaff_true, cond);
- pwaff_false = isl_pw_aff_intersect_domain(pwaff_false, comp);
+ isl_set *cond_true, *cond_false;
- return isl_pw_aff_add_disjoint(pwaff_true, pwaff_false);
+ cond_true = isl_pw_aff_non_zero_set(isl_pw_aff_copy(cond));
+ cond_false = isl_pw_aff_zero_set(cond);
+ return isl_pw_aff_select(cond_true, pwaff_true,
+ cond_false, pwaff_false);
}
int isl_aff_is_cst(__isl_keep isl_aff *aff)
return NULL;
}
-static __isl_give isl_pw_aff *pw_aff_mul(__isl_take isl_pw_aff *pwaff1,
+static __isl_give isl_pw_aff *pw_aff_add(__isl_take isl_pw_aff *pwaff1,
__isl_take isl_pw_aff *pwaff2)
{
- int i, j, n;
- isl_pw_aff *res;
-
- if (!pwaff1 || !pwaff2)
- goto error;
-
- n = pwaff1->n * pwaff2->n;
- res = isl_pw_aff_alloc_size(isl_space_copy(pwaff1->dim), n);
-
- for (i = 0; i < pwaff1->n; ++i) {
- for (j = 0; j < pwaff2->n; ++j) {
- isl_set *common;
- isl_aff *prod;
- common = isl_set_intersect(
- isl_set_copy(pwaff1->p[i].set),
- isl_set_copy(pwaff2->p[j].set));
- if (isl_set_plain_is_empty(common)) {
- isl_set_free(common);
- continue;
- }
+ return isl_pw_aff_on_shared_domain(pwaff1, pwaff2, &isl_aff_add);
+}
- prod = isl_aff_mul(isl_aff_copy(pwaff1->p[i].aff),
- isl_aff_copy(pwaff2->p[j].aff));
+__isl_give isl_pw_aff *isl_pw_aff_add(__isl_take isl_pw_aff *pwaff1,
+ __isl_take isl_pw_aff *pwaff2)
+{
+ return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2, &pw_aff_add);
+}
- res = isl_pw_aff_add_piece(res, common, prod);
- }
- }
+__isl_give isl_pw_aff *isl_pw_aff_union_add(__isl_take isl_pw_aff *pwaff1,
+ __isl_take isl_pw_aff *pwaff2)
+{
+ return isl_pw_aff_union_add_(pwaff1, pwaff2);
+}
- isl_pw_aff_free(pwaff1);
- isl_pw_aff_free(pwaff2);
- return res;
-error:
- isl_pw_aff_free(pwaff1);
- isl_pw_aff_free(pwaff2);
- return NULL;
+static __isl_give isl_pw_aff *pw_aff_mul(__isl_take isl_pw_aff *pwaff1,
+ __isl_take isl_pw_aff *pwaff2)
+{
+ return isl_pw_aff_on_shared_domain(pwaff1, pwaff2, &isl_aff_mul);
}
__isl_give isl_pw_aff *isl_pw_aff_mul(__isl_take isl_pw_aff *pwaff1,
__isl_take isl_pw_aff *pwaff2)
{
- return align_params_pw_pw_and(pwaff1, pwaff2, &pw_aff_mul);
+ return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2, &pw_aff_mul);
}
static __isl_give isl_pw_aff *pw_aff_min(__isl_take isl_pw_aff *pwaff1,
__isl_take isl_pw_aff *pwaff2)
{
isl_set *le;
+ isl_set *dom;
+ dom = isl_set_intersect(isl_pw_aff_domain(isl_pw_aff_copy(pwaff1)),
+ isl_pw_aff_domain(isl_pw_aff_copy(pwaff2)));
le = isl_pw_aff_le_set(isl_pw_aff_copy(pwaff1),
isl_pw_aff_copy(pwaff2));
- return isl_pw_aff_cond(le, pwaff1, pwaff2);
+ dom = isl_set_subtract(dom, isl_set_copy(le));
+ return isl_pw_aff_select(le, pwaff1, dom, pwaff2);
}
__isl_give isl_pw_aff *isl_pw_aff_min(__isl_take isl_pw_aff *pwaff1,
__isl_take isl_pw_aff *pwaff2)
{
- return align_params_pw_pw_and(pwaff1, pwaff2, &pw_aff_min);
+ return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2, &pw_aff_min);
}
static __isl_give isl_pw_aff *pw_aff_max(__isl_take isl_pw_aff *pwaff1,
__isl_take isl_pw_aff *pwaff2)
{
- isl_set *le;
+ isl_set *ge;
+ isl_set *dom;
- le = isl_pw_aff_ge_set(isl_pw_aff_copy(pwaff1),
+ dom = isl_set_intersect(isl_pw_aff_domain(isl_pw_aff_copy(pwaff1)),
+ isl_pw_aff_domain(isl_pw_aff_copy(pwaff2)));
+ ge = isl_pw_aff_ge_set(isl_pw_aff_copy(pwaff1),
isl_pw_aff_copy(pwaff2));
- return isl_pw_aff_cond(le, pwaff1, pwaff2);
+ dom = isl_set_subtract(dom, isl_set_copy(ge));
+ return isl_pw_aff_select(ge, pwaff1, dom, pwaff2);
}
__isl_give isl_pw_aff *isl_pw_aff_max(__isl_take isl_pw_aff *pwaff1,
__isl_take isl_pw_aff *pwaff2)
{
- return align_params_pw_pw_and(pwaff1, pwaff2, &pw_aff_max);
+ return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2, &pw_aff_max);
}
static __isl_give isl_pw_aff *pw_aff_list_reduce(
{
return pw_aff_list_reduce(list, &isl_pw_aff_max);
}
+
+#undef BASE
+#define BASE aff
+
+#include <isl_multi_templ.c>
+
+/* Construct an isl_multi_aff in the given space with value zero in
+ * each of the output dimensions.
+ */
+__isl_give isl_multi_aff *isl_multi_aff_zero(__isl_take isl_space *space)
+{
+ int n;
+ isl_multi_aff *ma;
+
+ if (!space)
+ return NULL;
+
+ n = isl_space_dim(space , isl_dim_out);
+ 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)
+ ma = isl_multi_aff_set_aff(ma, i, isl_aff_copy(aff));
+
+ isl_aff_free(aff);
+ }
+
+ return ma;
+}
+
+/* Create an isl_pw_multi_aff with the given isl_multi_aff on a universe
+ * domain.
+ */
+__isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_multi_aff(
+ __isl_take isl_multi_aff *ma)
+{
+ isl_set *dom = isl_set_universe(isl_multi_aff_get_domain_space(ma));
+ return isl_pw_multi_aff_alloc(dom, ma);
+}
+
+__isl_give isl_multi_aff *isl_multi_aff_add(__isl_take isl_multi_aff *maff1,
+ __isl_take isl_multi_aff *maff2)
+{
+ int i;
+ isl_ctx *ctx;
+
+ maff1 = isl_multi_aff_cow(maff1);
+ if (!maff1 || !maff2)
+ goto error;
+
+ ctx = isl_multi_aff_get_ctx(maff1);
+ if (!isl_space_is_equal(maff1->space, maff2->space))
+ isl_die(ctx, isl_error_invalid,
+ "spaces don't match", goto error);
+
+ for (i = 0; i < maff1->n; ++i) {
+ maff1->p[i] = isl_aff_add(maff1->p[i],
+ isl_aff_copy(maff2->p[i]));
+ if (!maff1->p[i])
+ goto error;
+ }
+
+ isl_multi_aff_free(maff2);
+ return maff1;
+error:
+ isl_multi_aff_free(maff1);
+ isl_multi_aff_free(maff2);
+ return NULL;
+}
+
+/* Exploit the equalities in "eq" to simplify the affine expressions.
+ */
+static __isl_give isl_multi_aff *isl_multi_aff_substitute_equalities(
+ __isl_take isl_multi_aff *maff, __isl_take isl_basic_set *eq)
+{
+ int i;
+
+ maff = isl_multi_aff_cow(maff);
+ if (!maff || !eq)
+ goto error;
+
+ for (i = 0; i < maff->n; ++i) {
+ maff->p[i] = isl_aff_substitute_equalities(maff->p[i],
+ isl_basic_set_copy(eq));
+ if (!maff->p[i])
+ goto error;
+ }
+
+ isl_basic_set_free(eq);
+ return maff;
+error:
+ isl_basic_set_free(eq);
+ isl_multi_aff_free(maff);
+ return NULL;
+}
+
+__isl_give isl_multi_aff *isl_multi_aff_scale(__isl_take isl_multi_aff *maff,
+ isl_int f)
+{
+ int i;
+
+ maff = isl_multi_aff_cow(maff);
+ if (!maff)
+ return NULL;
+
+ for (i = 0; i < maff->n; ++i) {
+ maff->p[i] = isl_aff_scale(maff->p[i], f);
+ if (!maff->p[i])
+ return isl_multi_aff_free(maff);
+ }
+
+ return maff;
+}
+
+__isl_give isl_multi_aff *isl_multi_aff_add_on_domain(__isl_keep isl_set *dom,
+ __isl_take isl_multi_aff *maff1, __isl_take isl_multi_aff *maff2)
+{
+ maff1 = isl_multi_aff_add(maff1, maff2);
+ maff1 = isl_multi_aff_gist(maff1, isl_set_copy(dom));
+ return maff1;
+}
+
+int isl_multi_aff_is_empty(__isl_keep isl_multi_aff *maff)
+{
+ if (!maff)
+ return -1;
+
+ return 0;
+}
+
+int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
+ __isl_keep isl_multi_aff *maff2)
+{
+ int i;
+ int equal;
+
+ if (!maff1 || !maff2)
+ return -1;
+ if (maff1->n != maff2->n)
+ return 0;
+ equal = isl_space_is_equal(maff1->space, maff2->space);
+ if (equal < 0 || !equal)
+ return equal;
+
+ for (i = 0; i < maff1->n; ++i) {
+ equal = isl_aff_plain_is_equal(maff1->p[i], maff2->p[i]);
+ if (equal < 0 || !equal)
+ return equal;
+ }
+
+ return 1;
+}
+
+__isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
+ __isl_take isl_multi_aff *maff,
+ enum isl_dim_type type, unsigned pos, const char *s)
+{
+ int i;
+
+ maff = isl_multi_aff_cow(maff);
+ if (!maff)
+ return NULL;
+
+ maff->space = isl_space_set_dim_name(maff->space, type, pos, s);
+ if (!maff->space)
+ return isl_multi_aff_free(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 isl_multi_aff_free(maff);
+ }
+
+ return maff;
+}
+
+__isl_give isl_multi_aff *isl_multi_aff_drop_dims(__isl_take isl_multi_aff *maff,
+ enum isl_dim_type type, unsigned first, unsigned n)
+{
+ int i;
+
+ maff = isl_multi_aff_cow(maff);
+ if (!maff)
+ return NULL;
+
+ maff->space = isl_space_drop_dims(maff->space, type, first, n);
+ if (!maff->space)
+ return isl_multi_aff_free(maff);
+
+ if (type == isl_dim_out) {
+ for (i = 0; i < n; ++i)
+ isl_aff_free(maff->p[first + i]);
+ for (i = first; i + n < maff->n; ++i)
+ maff->p[i] = maff->p[i + n];
+ maff->n -= n;
+ return maff;
+ }
+
+ for (i = 0; i < maff->n; ++i) {
+ maff->p[i] = isl_aff_drop_dims(maff->p[i], type, first, n);
+ if (!maff->p[i])
+ return isl_multi_aff_free(maff);
+ }
+
+ return maff;
+}
+
+#undef PW
+#define PW isl_pw_multi_aff
+#undef EL
+#define EL isl_multi_aff
+#undef EL_IS_ZERO
+#define EL_IS_ZERO is_empty
+#undef ZERO
+#define ZERO empty
+#undef IS_ZERO
+#define IS_ZERO is_empty
+#undef FIELD
+#define FIELD maff
+#undef DEFAULT_IS_ZERO
+#define DEFAULT_IS_ZERO 0
+
+#define NO_NEG
+#define NO_EVAL
+#define NO_OPT
+#define NO_INVOLVES_DIMS
+#define NO_MOVE_DIMS
+#define NO_INSERT_DIMS
+#define NO_LIFT
+#define NO_MORPH
+
+#include <isl_pw_templ.c>
+
+#undef UNION
+#define UNION isl_union_pw_multi_aff
+#undef PART
+#define PART isl_pw_multi_aff
+#undef PARTS
+#define PARTS pw_multi_aff
+#define ALIGN_DOMAIN
+
+#define NO_EVAL
+
+#include <isl_union_templ.c>
+
+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_on_shared_domain(pma1, pma2,
+ &isl_multi_aff_add);
+}
+
+__isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
+ __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_add);
+}
+
+__isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_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
+ * to its range, with each dimension in the range equated to the
+ * corresponding affine expression on its cell.
+ */
+__isl_give isl_map *isl_map_from_pw_multi_aff(__isl_take isl_pw_multi_aff *pma)
+{
+ int i;
+ isl_map *map;
+
+ if (!pma)
+ return NULL;
+
+ map = isl_map_empty(isl_pw_multi_aff_get_space(pma));
+
+ for (i = 0; i < pma->n; ++i) {
+ isl_multi_aff *maff;
+ isl_basic_map *bmap;
+ isl_map *map_i;
+
+ maff = isl_multi_aff_copy(pma->p[i].maff);
+ bmap = isl_basic_map_from_multi_aff(maff);
+ map_i = isl_map_from_basic_map(bmap);
+ map_i = isl_map_intersect_domain(map_i,
+ isl_set_copy(pma->p[i].set));
+ map = isl_map_union_disjoint(map, map_i);
+ }
+
+ isl_pw_multi_aff_free(pma);
+ return map;
+}
+
+__isl_give isl_set *isl_set_from_pw_multi_aff(__isl_take isl_pw_multi_aff *pma)
+{
+ if (!isl_space_is_set(pma->dim))
+ isl_die(isl_pw_multi_aff_get_ctx(pma), isl_error_invalid,
+ "isl_pw_multi_aff cannot be converted into an isl_set",
+ return isl_pw_multi_aff_free(pma));
+
+ return isl_map_from_pw_multi_aff(pma);
+}
+
+/* Given a basic map with a single output dimension that is defined
+ * in terms of the parameters and input dimensions using an equality,
+ * extract an isl_aff that expresses the output dimension in terms
+ * of the parameters and input dimensions.
+ *
+ * Since some applications expect the result of isl_pw_multi_aff_from_map
+ * to only contain integer affine expressions, we compute the floor
+ * of the expression before returning.
+ *
+ * This function shares some similarities with
+ * isl_basic_map_has_defining_equality and isl_constraint_get_bound.
+ */
+static __isl_give isl_aff *extract_isl_aff_from_basic_map(
+ __isl_take isl_basic_map *bmap)
+{
+ int i;
+ unsigned offset;
+ unsigned total;
+ isl_local_space *ls;
+ isl_aff *aff;
+
+ if (!bmap)
+ return NULL;
+ if (isl_basic_map_dim(bmap, isl_dim_out) != 1)
+ isl_die(isl_basic_map_get_ctx(bmap), isl_error_invalid,
+ "basic map should have a single output dimension",
+ goto error);
+ offset = isl_basic_map_offset(bmap, isl_dim_out);
+ total = isl_basic_map_total_dim(bmap);
+ for (i = 0; i < bmap->n_eq; ++i) {
+ if (isl_int_is_zero(bmap->eq[i][offset]))
+ continue;
+ if (isl_seq_first_non_zero(bmap->eq[i] + offset + 1,
+ 1 + total - (offset + 1)) != -1)
+ continue;
+ break;
+ }
+ if (i >= bmap->n_eq)
+ isl_die(isl_basic_map_get_ctx(bmap), isl_error_invalid,
+ "unable to find suitable equality", goto error);
+ ls = isl_basic_map_get_local_space(bmap);
+ aff = isl_aff_alloc(isl_local_space_domain(ls));
+ if (!aff)
+ goto error;
+ if (isl_int_is_neg(bmap->eq[i][offset]))
+ isl_seq_cpy(aff->v->el + 1, bmap->eq[i], offset);
+ else
+ isl_seq_neg(aff->v->el + 1, bmap->eq[i], offset);
+ isl_seq_clr(aff->v->el + 1 + offset, aff->v->size - (1 + offset));
+ isl_int_abs(aff->v->el[0], bmap->eq[i][offset]);
+ isl_basic_map_free(bmap);
+
+ aff = isl_aff_remove_unused_divs(aff);
+ aff = isl_aff_floor(aff);
+ return aff;
+error:
+ isl_basic_map_free(bmap);
+ return NULL;
+}
+
+/* Given a basic map where each output dimension is defined
+ * in terms of the parameters and input dimensions using an equality,
+ * extract an isl_multi_aff that expresses the output dimensions in terms
+ * of the parameters and input dimensions.
+ */
+static __isl_give isl_multi_aff *extract_isl_multi_aff_from_basic_map(
+ __isl_take isl_basic_map *bmap)
+{
+ int i;
+ unsigned n_out;
+ isl_multi_aff *ma;
+
+ if (!bmap)
+ return NULL;
+
+ ma = isl_multi_aff_alloc(isl_basic_map_get_space(bmap));
+ n_out = isl_basic_map_dim(bmap, isl_dim_out);
+
+ for (i = 0; i < n_out; ++i) {
+ isl_basic_map *bmap_i;
+ isl_aff *aff;
+
+ bmap_i = isl_basic_map_copy(bmap);
+ bmap_i = isl_basic_map_project_out(bmap_i, isl_dim_out,
+ i + 1, n_out - (1 + i));
+ bmap_i = isl_basic_map_project_out(bmap_i, isl_dim_out, 0, i);
+ aff = extract_isl_aff_from_basic_map(bmap_i);
+ ma = isl_multi_aff_set_aff(ma, i, aff);
+ }
+
+ isl_basic_map_free(bmap);
+
+ return ma;
+}
+
+/* Create an isl_pw_multi_aff that is equivalent to
+ * isl_map_intersect_domain(isl_map_from_basic_map(bmap), domain).
+ * The given basic map is such that each output dimension is defined
+ * in terms of the parameters and input dimensions using an equality.
+ */
+static __isl_give isl_pw_multi_aff *plain_pw_multi_aff_from_map(
+ __isl_take isl_set *domain, __isl_take isl_basic_map *bmap)
+{
+ isl_multi_aff *ma;
+
+ ma = extract_isl_multi_aff_from_basic_map(bmap);
+ return isl_pw_multi_aff_alloc(domain, ma);
+}
+
+/* Try and create an isl_pw_multi_aff that is equivalent to the given isl_map.
+ * This obivously only works if the input "map" is single-valued.
+ * If so, we compute the lexicographic minimum of the image in the form
+ * of an isl_pw_multi_aff. Since the image is unique, it is equal
+ * to its lexicographic minimum.
+ * If the input is not single-valued, we produce an error.
+ *
+ * As a special case, we first check if all output dimensions are uniquely
+ * defined in terms of the parameters and input dimensions over the entire
+ * domain. If so, we extract the desired isl_pw_multi_aff directly
+ * from the affine hull of "map" and its domain.
+ */
+__isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(__isl_take isl_map *map)
+{
+ int i;
+ int sv;
+ isl_pw_multi_aff *pma;
+ isl_basic_map *hull;
+
+ if (!map)
+ return NULL;
+
+ hull = isl_map_affine_hull(isl_map_copy(map));
+ sv = isl_basic_map_plain_is_single_valued(hull);
+ if (sv >= 0 && sv)
+ return plain_pw_multi_aff_from_map(isl_map_domain(map), hull);
+ isl_basic_map_free(hull);
+ if (sv < 0)
+ goto error;
+
+ sv = isl_map_is_single_valued(map);
+ if (sv < 0)
+ goto error;
+ if (!sv)
+ isl_die(isl_map_get_ctx(map), isl_error_invalid,
+ "map is not single-valued", goto error);
+ map = isl_map_make_disjoint(map);
+ if (!map)
+ return NULL;
+
+ pma = isl_pw_multi_aff_empty(isl_map_get_space(map));
+
+ for (i = 0; i < map->n; ++i) {
+ isl_pw_multi_aff *pma_i;
+ isl_basic_map *bmap;
+ bmap = isl_basic_map_copy(map->p[i]);
+ pma_i = isl_basic_map_lexmin_pw_multi_aff(bmap);
+ pma = isl_pw_multi_aff_add_disjoint(pma, pma_i);
+ }
+
+ isl_map_free(map);
+ return pma;
+error:
+ isl_map_free(map);
+ return NULL;
+}
+
+__isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(__isl_take isl_set *set)
+{
+ return isl_pw_multi_aff_from_map(set);
+}
+
+/* Return the piecewise affine expression "set ? 1 : 0".
+ */
+__isl_give isl_pw_aff *isl_set_indicator_function(__isl_take isl_set *set)
+{
+ isl_pw_aff *pa;
+ isl_space *space = isl_set_get_space(set);
+ isl_local_space *ls = isl_local_space_from_space(space);
+ isl_aff *zero = isl_aff_zero_on_domain(isl_local_space_copy(ls));
+ isl_aff *one = isl_aff_zero_on_domain(ls);
+
+ one = isl_aff_add_constant_si(one, 1);
+ pa = isl_pw_aff_alloc(isl_set_copy(set), one);
+ set = isl_set_complement(set);
+ pa = isl_pw_aff_add_disjoint(pa, isl_pw_aff_alloc(set, zero));
+
+ return pa;
+}
+
+/* Plug in "subs" for dimension "type", "pos" of "aff".
+ *
+ * Let i be the dimension to replace and let "subs" be of the form
+ *
+ * f/d
+ *
+ * and "aff" of the form
+ *
+ * (a i + g)/m
+ *
+ * The result is
+ *
+ * floor((a f + d g')/(m d))
+ *
+ * where g' is the result of plugging in "subs" in each of the integer
+ * divisions in g.
+ */
+__isl_give isl_aff *isl_aff_substitute(__isl_take isl_aff *aff,
+ enum isl_dim_type type, unsigned pos, __isl_keep isl_aff *subs)
+{
+ isl_ctx *ctx;
+ isl_int v;
+
+ aff = isl_aff_cow(aff);
+ if (!aff || !subs)
+ return isl_aff_free(aff);
+
+ ctx = isl_aff_get_ctx(aff);
+ if (!isl_space_is_equal(aff->ls->dim, subs->ls->dim))
+ isl_die(ctx, isl_error_invalid,
+ "spaces don't match", return isl_aff_free(aff));
+ if (isl_local_space_dim(subs->ls, isl_dim_div) != 0)
+ isl_die(ctx, isl_error_unsupported,
+ "cannot handle divs yet", return isl_aff_free(aff));
+
+ aff->ls = isl_local_space_substitute(aff->ls, type, pos, subs);
+ if (!aff->ls)
+ return isl_aff_free(aff);
+
+ aff->v = isl_vec_cow(aff->v);
+ if (!aff->v)
+ return isl_aff_free(aff);
+
+ pos += isl_local_space_offset(aff->ls, type);
+
+ isl_int_init(v);
+ isl_int_set(v, aff->v->el[1 + pos]);
+ isl_int_set_si(aff->v->el[1 + pos], 0);
+ isl_seq_combine(aff->v->el + 1, subs->v->el[0], aff->v->el + 1,
+ v, subs->v->el + 1, subs->v->size - 1);
+ isl_int_mul(aff->v->el[0], aff->v->el[0], subs->v->el[0]);
+ isl_int_clear(v);
+
+ return aff;
+}
+
+/* Plug in "subs" for dimension "type", "pos" in each of the affine
+ * expressions in "maff".
+ */
+__isl_give isl_multi_aff *isl_multi_aff_substitute(
+ __isl_take isl_multi_aff *maff, enum isl_dim_type type, unsigned pos,
+ __isl_keep isl_aff *subs)
+{
+ int i;
+
+ maff = isl_multi_aff_cow(maff);
+ if (!maff || !subs)
+ return isl_multi_aff_free(maff);
+
+ if (type == isl_dim_in)
+ type = isl_dim_set;
+
+ for (i = 0; i < maff->n; ++i) {
+ maff->p[i] = isl_aff_substitute(maff->p[i], type, pos, subs);
+ if (!maff->p[i])
+ return isl_multi_aff_free(maff);
+ }
+
+ return maff;
+}
+
+/* Plug in "subs" for dimension "type", "pos" of "pma".
+ *
+ * pma is of the form
+ *
+ * A_i(v) -> M_i(v)
+ *
+ * while subs is of the form
+ *
+ * v' = B_j(v) -> S_j
+ *
+ * Each pair i,j such that C_ij = A_i \cap B_i is non-empty
+ * has a contribution in the result, in particular
+ *
+ * C_ij(S_j) -> M_i(S_j)
+ *
+ * Note that plugging in S_j in C_ij may also result in an empty set
+ * and this contribution should simply be discarded.
+ */
+__isl_give isl_pw_multi_aff *isl_pw_multi_aff_substitute(
+ __isl_take isl_pw_multi_aff *pma, enum isl_dim_type type, unsigned pos,
+ __isl_keep isl_pw_aff *subs)
+{
+ int i, j, n;
+ isl_pw_multi_aff *res;
+
+ if (!pma || !subs)
+ return isl_pw_multi_aff_free(pma);
+
+ n = pma->n * subs->n;
+ res = isl_pw_multi_aff_alloc_size(isl_space_copy(pma->dim), n);
+
+ for (i = 0; i < pma->n; ++i) {
+ for (j = 0; j < subs->n; ++j) {
+ isl_set *common;
+ isl_multi_aff *res_ij;
+ common = isl_set_intersect(
+ isl_set_copy(pma->p[i].set),
+ isl_set_copy(subs->p[j].set));
+ common = isl_set_substitute(common,
+ type, pos, subs->p[j].aff);
+ if (isl_set_plain_is_empty(common)) {
+ isl_set_free(common);
+ continue;
+ }
+
+ res_ij = isl_multi_aff_substitute(
+ isl_multi_aff_copy(pma->p[i].maff),
+ type, pos, subs->p[j].aff);
+
+ res = isl_pw_multi_aff_add_piece(res, common, res_ij);
+ }
+ }
+
+ isl_pw_multi_aff_free(pma);
+ return res;
+}
+
+/* Extend the local space of "dst" to include the divs
+ * in the local space of "src".
+ */
+__isl_give isl_aff *isl_aff_align_divs(__isl_take isl_aff *dst,
+ __isl_keep isl_aff *src)
+{
+ isl_ctx *ctx;
+ int *exp1 = NULL;
+ int *exp2 = NULL;
+ isl_mat *div;
+
+ if (!src || !dst)
+ return isl_aff_free(dst);
+
+ ctx = isl_aff_get_ctx(src);
+ if (!isl_space_is_equal(src->ls->dim, dst->ls->dim))
+ isl_die(ctx, isl_error_invalid,
+ "spaces don't match", goto error);
+
+ if (src->ls->div->n_row == 0)
+ return dst;
+
+ exp1 = isl_alloc_array(ctx, int, src->ls->div->n_row);
+ exp2 = isl_alloc_array(ctx, int, dst->ls->div->n_row);
+ if (!exp1 || !exp2)
+ goto error;
+
+ div = isl_merge_divs(src->ls->div, dst->ls->div, exp1, exp2);
+ dst = isl_aff_expand_divs(dst, div, exp2);
+ free(exp1);
+ free(exp2);
+
+ return dst;
+error:
+ free(exp1);
+ free(exp2);
+ return isl_aff_free(dst);
+}
+
+/* Adjust the local spaces of the affine expressions in "maff"
+ * such that they all have the save divs.
+ */
+__isl_give isl_multi_aff *isl_multi_aff_align_divs(
+ __isl_take isl_multi_aff *maff)
+{
+ int i;
+
+ if (!maff)
+ return NULL;
+ if (maff->n == 0)
+ return maff;
+ maff = isl_multi_aff_cow(maff);
+ if (!maff)
+ return NULL;
+
+ for (i = 1; i < maff->n; ++i)
+ maff->p[0] = isl_aff_align_divs(maff->p[0], maff->p[i]);
+ for (i = 1; i < maff->n; ++i) {
+ maff->p[i] = isl_aff_align_divs(maff->p[i], maff->p[0]);
+ if (!maff->p[i])
+ return isl_multi_aff_free(maff);
+ }
+
+ return maff;
+}
+
+__isl_give isl_aff *isl_aff_lift(__isl_take isl_aff *aff)
+{
+ aff = isl_aff_cow(aff);
+ if (!aff)
+ return NULL;
+
+ aff->ls = isl_local_space_lift(aff->ls);
+ if (!aff->ls)
+ return isl_aff_free(aff);
+
+ return aff;
+}
+
+/* Lift "maff" to a space with extra dimensions such that the result
+ * has no more existentially quantified variables.
+ * If "ls" is not NULL, then *ls is assigned the local space that lies
+ * at the basis of the lifting applied to "maff".
+ */
+__isl_give isl_multi_aff *isl_multi_aff_lift(__isl_take isl_multi_aff *maff,
+ __isl_give isl_local_space **ls)
+{
+ int i;
+ isl_space *space;
+ unsigned n_div;
+
+ if (ls)
+ *ls = NULL;
+
+ if (!maff)
+ return NULL;
+
+ if (maff->n == 0) {
+ if (ls) {
+ isl_space *space = isl_multi_aff_get_domain_space(maff);
+ *ls = isl_local_space_from_space(space);
+ if (!*ls)
+ return isl_multi_aff_free(maff);
+ }
+ return maff;
+ }
+
+ maff = isl_multi_aff_cow(maff);
+ maff = isl_multi_aff_align_divs(maff);
+ if (!maff)
+ return NULL;
+
+ n_div = isl_aff_dim(maff->p[0], isl_dim_div);
+ space = isl_multi_aff_get_space(maff);
+ space = isl_space_lift(isl_space_domain(space), n_div);
+ space = isl_space_extend_domain_with_range(space,
+ isl_multi_aff_get_space(maff));
+ if (!space)
+ return isl_multi_aff_free(maff);
+ isl_space_free(maff->space);
+ maff->space = space;
+
+ if (ls) {
+ *ls = isl_aff_get_domain_local_space(maff->p[0]);
+ if (!*ls)
+ return isl_multi_aff_free(maff);
+ }
+
+ for (i = 0; i < maff->n; ++i) {
+ maff->p[i] = isl_aff_lift(maff->p[i]);
+ if (!maff->p[i])
+ goto error;
+ }
+
+ return maff;
+error:
+ if (ls)
+ isl_local_space_free(*ls);
+ return isl_multi_aff_free(maff);
+}
+
+
+/* Extract an isl_pw_aff corresponding to output dimension "pos" of "pma".
+ */
+__isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
+ __isl_keep isl_pw_multi_aff *pma, int pos)
+{
+ int i;
+ int n_out;
+ isl_space *space;
+ isl_pw_aff *pa;
+
+ if (!pma)
+ return NULL;
+
+ n_out = isl_pw_multi_aff_dim(pma, isl_dim_out);
+ if (pos < 0 || pos >= n_out)
+ isl_die(isl_pw_multi_aff_get_ctx(pma), isl_error_invalid,
+ "index out of bounds", return NULL);
+
+ space = isl_pw_multi_aff_get_space(pma);
+ space = isl_space_drop_dims(space, isl_dim_out,
+ pos + 1, n_out - pos - 1);
+ space = isl_space_drop_dims(space, isl_dim_out, 0, pos);
+
+ pa = isl_pw_aff_alloc_size(space, pma->n);
+ for (i = 0; i < pma->n; ++i) {
+ isl_aff *aff;
+ aff = isl_multi_aff_get_aff(pma->p[i].maff, pos);
+ pa = isl_pw_aff_add_piece(pa, isl_set_copy(pma->p[i].set), aff);
+ }
+
+ return pa;
+}
projects / platform / upstream / isl.git / blobdiff