used as a backend polyhedral library for the polyhedral
scanner C<CLooG> and as part of an equivalence checker of
static affine programs.
+For bug reports, feature requests and questions,
+visit the the discussion group at
+L<http://groups.google.com/group/isl-development>.
+
+=head2 Backward Incompatible Changes
+
+=head3 Changes since isl-0.02
+
+=over
+
+=item * The old printing functions have been deprecated
+and replaced by C<isl_printer> functions, see L<Input and Output>.
+
+=item * Most functions related to dependence analysis have acquired
+an extra C<must> argument. To obtain the old behavior, this argument
+should be given the value 1. See L<Dependence Analysis>.
+
+=back
=head1 Installation
git pull
-=item 2 Get submodule (optional)
-
-C<isl> can optionally use the C<piplib> library and provides
-this library as a submodule. If you want to use it, then
-after you have cloned C<isl>, you need to grab the submodules
-
- git submodule init
- git submodule update
-
-To obtain updates, you only need
-
- git submodule update
-
-Note that C<isl> currently does not use any C<piplib>
-functionality by default.
-
-=item 3 Generate C<configure>
+=item 2 Generate C<configure>
./autogen.sh
=head2 Sets and Relations
-C<isl> uses four types of objects for representing sets and relations,
-C<isl_basic_set>, C<isl_basic_map>, C<isl_set> and C<isl_map>.
+C<isl> uses six types of objects for representing sets and relations,
+C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
+C<isl_union_set> and C<isl_union_map>.
C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
can be described as a conjunction of affine constraints, while
C<isl_set> and C<isl_map> represent unions of
C<isl_basic_set>s and C<isl_basic_map>s, respectively.
+However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
+to have the same dimension. C<isl_union_set>s and C<isl_union_map>s
+represent unions of C<isl_set>s or C<isl_map>s of I<different> dimensions,
+where dimensions with different space names
+(see L<Dimension Specifications>) are considered different as well.
The difference between sets and relations (maps) is that sets have
one set of variables, while relations have two sets of variables,
input variables and output variables.
__isl_keep isl_basic_set *bset);
__isl_give isl_dim *isl_set_get_dim(__isl_keep isl_set *set);
+ #include <isl_union_set.h>
+ __isl_give isl_dim *isl_union_set_get_dim(
+ __isl_keep isl_union_set *uset);
+
#include <isl_map.h>
__isl_give isl_dim *isl_basic_map_get_dim(
__isl_keep isl_basic_map *bmap);
__isl_give isl_dim *isl_map_get_dim(__isl_keep isl_map *map);
+ #include <isl_union_map.h>
+ __isl_give isl_dim *isl_union_map_get_dim(
+ __isl_keep isl_union_map *umap);
+
#include <isl_polynomial.h>
__isl_give isl_dim *isl_qpolynomial_get_dim(
__isl_keep isl_qpolynomial *qp);
__isl_give isl_dim *isl_pw_qpolynomial_get_dim(
__isl_keep isl_pw_qpolynomial *pwqp);
+ __isl_give isl_dim *isl_union_pw_qpolynomial_get_dim(
+ __isl_keep isl_union_pw_qpolynomial *upwqp);
+ __isl_give isl_dim *isl_union_pw_qpolynomial_fold_get_dim(
+ __isl_keep isl_union_pw_qpolynomial_fold *upwf);
The names of the individual dimensions may be set or read off
using the following functions.
means that if one of the arguments has named parameters, then the
other needs to have named parameters too and the names need to match.
+The names of entire spaces may be set or read off
+using the following functions.
+
+ #include <isl_dim.h>
+ __isl_give isl_dim *isl_dim_set_tuple_name(
+ __isl_take isl_dim *dim,
+ enum isl_dim_type type, const char *s);
+ const char *isl_dim_get_tuple_name(__isl_keep isl_dim *dim,
+ enum isl_dim_type type);
+
+The C<dim> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
+or C<isl_dim_set>. As with C<isl_dim_get_name>,
+the C<isl_dim_get_tuple_name> function returns a pointer to some internal
+data structure.
+Binary operations require the corresponding spaces of their arguments
+to have the same name.
+
+Spaces can be nested. In particular, the domain of a set or
+the domain or range of a relation can be a nested relation.
+The following functions can be used to construct and deconstruct
+such nested dimension specifications.
+
+ #include <isl_dim.h>
+ int isl_dim_is_wrapping(__isl_keep isl_dim *dim);
+ __isl_give isl_dim *isl_dim_wrap(__isl_take isl_dim *dim);
+ __isl_give isl_dim *isl_dim_unwrap(__isl_take isl_dim *dim);
+
+The input to C<isl_dim_is_wrapping> and C<isl_dim_unwrap> should
+be the dimension specification of a set, while that of
+C<isl_dim_wrap> should be the dimension specification of a relation.
+Conversely, the output of C<isl_dim_unwrap> is the dimension specification
+of a relation, while that of C<isl_dim_wrap> is the dimension specification
+of a set.
+
=head2 Input and Output
C<isl> supports its own input/output format, which is similar
__isl_take isl_printer *printer,
__isl_keep isl_map *map);
+ #include <isl_union_set.h>
+ __isl_give isl_printer *isl_printer_print_union_set(
+ __isl_take isl_printer *p,
+ __isl_keep isl_union_set *uset);
+
+ #include <isl_union_map.h>
+ __isl_give isl_printer *isl_printer_print_union_map(
+ __isl_take isl_printer *p,
+ __isl_keep isl_union_map *umap);
+
When called on a file printer, the following function flushes
the file. When called on a string printer, the buffer is cleared.
__isl_take isl_dim *dim);
__isl_give isl_map *isl_map_empty(
__isl_take isl_dim *dim);
+ __isl_give isl_union_set *isl_union_set_empty(
+ __isl_take isl_dim *dim);
+ __isl_give isl_union_map *isl_union_map_empty(
+ __isl_take isl_dim *dim);
+
+For C<isl_union_set>s and C<isl_union_map>s, the dimensions specification
+is only used to specify the parameters.
=item * Universe sets and relations
__isl_give isl_map *isl_map_from_basic_map(
__isl_take isl_basic_map *bmap);
+Sets and relations can be converted to union sets and relations
+using the following functions.
+
+ __isl_give isl_union_map *isl_union_map_from_map(
+ __isl_take isl_map *map);
+ __isl_give isl_union_set *isl_union_set_from_set(
+ __isl_take isl_set *set);
+
Sets and relations can be copied and freed again using the following
functions.
__isl_give isl_basic_set *isl_basic_set_copy(
__isl_keep isl_basic_set *bset);
__isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
+ __isl_give isl_union_set *isl_union_set_copy(
+ __isl_keep isl_union_set *uset);
__isl_give isl_basic_map *isl_basic_map_copy(
__isl_keep isl_basic_map *bmap);
__isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
+ __isl_give isl_union_map *isl_union_map_copy(
+ __isl_keep isl_union_map *umap);
void isl_basic_set_free(__isl_take isl_basic_set *bset);
void isl_set_free(__isl_take isl_set *set);
+ void isl_union_set_free(__isl_take isl_union_set *uset);
void isl_basic_map_free(__isl_take isl_basic_map *bmap);
void isl_map_free(__isl_take isl_map *map);
+ void isl_union_map_free(__isl_take isl_union_map *umap);
Other sets and relations can be constructed by starting
from a universe set or relation, adding equality and/or
__isl_take isl_set *set);
__isl_give isl_map *isl_map_compute_divs(
__isl_take isl_map *map);
+ __isl_give isl_union_set *isl_union_set_compute_divs(
+ __isl_take isl_union_set *uset);
+ __isl_give isl_union_map *isl_union_map_compute_divs(
+ __isl_take isl_union_map *umap);
This explicit representation defines the existentially quantified
variables as integer divisions of the other variables, possibly
__isl_give isl_map *isl_map_align_divs(
__isl_take isl_map *map);
+To iterate over all the sets or maps in a union set or map, use
+
+ int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
+ int (*fn)(__isl_take isl_set *set, void *user),
+ void *user);
+ int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
+ int (*fn)(__isl_take isl_map *map, void *user),
+ void *user);
+
To iterate over all the basic sets or maps in a set or map, use
int isl_set_foreach_basic_set(__isl_keep isl_set *set,
Again, the callback function C<fn> should return 0 if successful and
-1 if an error occurs. In the latter case, or if any other error
occurs, the above functions will return -1.
+The constraint C<c> represents either an equality or an inequality.
+Use the following function to find out whether a constraint
+represents an equality. If not, it represents an inequality.
+
+ int isl_constraint_is_equality(
+ __isl_keep isl_constraint *constraint);
The coefficients of the constraints can be inspected using
the following functions.
int isl_basic_set_fast_is_empty(__isl_keep isl_basic_set *bset);
int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
int isl_set_is_empty(__isl_keep isl_set *set);
+ int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
int isl_basic_map_fast_is_empty(__isl_keep isl_basic_map *bmap);
int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
int isl_map_fast_is_empty(__isl_keep isl_map *map);
int isl_map_is_empty(__isl_keep isl_map *map);
+ int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
=item * Universality
int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
int isl_set_fast_is_universe(__isl_keep isl_set *set);
+=item * Single-valuedness
+
+ int isl_map_is_single_valued(__isl_keep isl_map *map);
+
+=item * Bijectivity
+
+ int isl_map_is_bijective(__isl_keep isl_map *map);
+
+=item * Wrapping
+
+The followning functions check whether the domain of the given
+(basic) set is a wrapped relation.
+
+ int isl_basic_set_is_wrapping(
+ __isl_keep isl_basic_set *bset);
+ int isl_set_is_wrapping(__isl_keep isl_set *set);
+
=back
=head3 Binary Properties
__isl_keep isl_set *set2);
int isl_set_is_equal(__isl_keep isl_set *set1,
__isl_keep isl_set *set2);
+ int isl_basic_map_is_equal(
+ __isl_keep isl_basic_map *bmap1,
+ __isl_keep isl_basic_map *bmap2);
int isl_map_is_equal(__isl_keep isl_map *map1,
__isl_keep isl_map *map2);
int isl_map_fast_is_equal(__isl_keep isl_map *map1,
__isl_keep isl_map *map2);
- int isl_basic_map_is_equal(
- __isl_keep isl_basic_map *bmap1,
- __isl_keep isl_basic_map *bmap2);
+ int isl_union_map_is_equal(
+ __isl_keep isl_union_map *umap1,
+ __isl_keep isl_union_map *umap2);
=item * Disjointness
int isl_map_is_strict_subset(
__isl_keep isl_map *map1,
__isl_keep isl_map *map2);
+ int isl_union_map_is_subset(
+ __isl_keep isl_union_map *umap1,
+ __isl_keep isl_union_map *umap2);
+ int isl_union_map_is_strict_subset(
+ __isl_keep isl_union_map *umap1,
+ __isl_keep isl_union_map *umap2);
=back
__isl_take isl_basic_map *bmap);
__isl_give isl_map *isl_map_reverse(
__isl_take isl_map *map);
+ __isl_give isl_union_map *isl_union_map_reverse(
+ __isl_take isl_union_map *umap);
=item * Projection
__isl_take isl_map *bmap);
__isl_give isl_set *isl_map_range(
__isl_take isl_map *map);
+ __isl_give isl_union_set *isl_union_map_domain(
+ __isl_take isl_union_map *umap);
+ __isl_give isl_union_set *isl_union_map_range(
+ __isl_take isl_union_map *umap);
+
+=item * Deltas
+
+ __isl_give isl_basic_set *isl_basic_map_deltas(
+ __isl_take isl_basic_map *bmap);
+ __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
+ __isl_give isl_union_set *isl_union_map_deltas(
+ __isl_take isl_union_map *umap);
+
+These functions return a (basic) set containing the differences
+between image elements and corresponding domain elements in the input.
=item * Coalescing
__isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
__isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
+ __isl_give isl_union_set *isl_union_set_coalesce(
+ __isl_take isl_union_set *uset);
+ __isl_give isl_union_map *isl_union_map_coalesce(
+ __isl_take isl_union_map *umap);
=item * Convex hull
__isl_take isl_basic_set *bset);
__isl_give isl_basic_set *isl_set_affine_hull(
__isl_take isl_set *set);
+ __isl_give isl_union_set *isl_union_set_affine_hull(
+ __isl_take isl_union_set *uset);
__isl_give isl_basic_map *isl_basic_map_affine_hull(
__isl_take isl_basic_map *bmap);
__isl_give isl_basic_map *isl_map_affine_hull(
__isl_take isl_map *map);
+ __isl_give isl_union_map *isl_union_map_affine_hull(
+ __isl_take isl_union_map *umap);
+
+In case of union sets and relations, the affine hull is computed
+per dimension.
=item * Power
__isl_give isl_map *isl_map_transitive_closure(
__isl_take isl_map *map, int *exact);
+ __isl_give isl_union_map *isl_union_map_transitive_closure(
+ __isl_take isl_union_map *umap, int *exact);
Compute the transitive closure of C<map>.
The result may be an overapproximation. If the result is known to be exact,
The current implementation only produces exact results for particular
cases of piecewise translations (i.e., piecewise uniform dependences).
+=item * Reaching path lengths
+
+ __isl_give isl_map *isl_map_reaching_path_lengths(
+ __isl_take isl_map *map, int *exact);
+
+Compute a relation that maps each element in the range of C<map>
+to the lengths of all paths composed of edges in C<map> that
+end up in the given element.
+The result may be an overapproximation. If the result is known to be exact,
+then C<*exact> is set to C<1>.
+To compute the I<maximal> path length, the resulting relation
+should be postprocessed by C<isl_map_lexmax>.
+In particular, if the input relation is a dependence relation
+(mapping sources to sinks), then the maximal path length corresponds
+to the free schedule.
+Note, however, that C<isl_map_lexmax> expects the maximum to be
+finite, so if the path lengths are unbounded (possibly due to
+the overapproximation), then you will get an error message.
+
+=item * Wrapping
+
+ __isl_give isl_basic_set *isl_basic_map_wrap(
+ __isl_take isl_basic_map *bmap);
+ __isl_give isl_set *isl_map_wrap(
+ __isl_take isl_map *map);
+ __isl_give isl_union_set *isl_union_map_wrap(
+ __isl_take isl_union_map *umap);
+ __isl_give isl_basic_map *isl_basic_set_unwrap(
+ __isl_take isl_basic_set *bset);
+ __isl_give isl_map *isl_set_unwrap(
+ __isl_take isl_set *set);
+ __isl_give isl_union_map *isl_union_set_unwrap(
+ __isl_take isl_union_set *uset);
+
=back
=head2 Binary Operations
__isl_give isl_set *isl_set_intersect(
__isl_take isl_set *set1,
__isl_take isl_set *set2);
+ __isl_give isl_union_set *isl_union_set_intersect(
+ __isl_take isl_union_set *uset1,
+ __isl_take isl_union_set *uset2);
__isl_give isl_basic_map *isl_basic_map_intersect_domain(
__isl_take isl_basic_map *bmap,
__isl_take isl_basic_set *bset);
__isl_give isl_map *isl_map_intersect(
__isl_take isl_map *map1,
__isl_take isl_map *map2);
+ __isl_give isl_union_map *isl_union_map_intersect_domain(
+ __isl_take isl_union_map *umap,
+ __isl_take isl_union_set *uset);
+ __isl_give isl_union_map *isl_union_map_intersect(
+ __isl_take isl_union_map *umap1,
+ __isl_take isl_union_map *umap2);
=item * Union
__isl_give isl_map *isl_map_union(
__isl_take isl_map *map1,
__isl_take isl_map *map2);
+ __isl_give isl_union_set *isl_union_set_union(
+ __isl_take isl_union_set *uset1,
+ __isl_take isl_union_set *uset2);
+ __isl_give isl_union_map *isl_union_map_union(
+ __isl_take isl_union_map *umap1,
+ __isl_take isl_union_map *umap2);
=item * Set difference
__isl_give isl_map *isl_map_subtract(
__isl_take isl_map *map1,
__isl_take isl_map *map2);
+ __isl_give isl_union_set *isl_union_set_subtract(
+ __isl_take isl_union_set *uset1,
+ __isl_take isl_union_set *uset2);
+ __isl_give isl_union_map *isl_union_map_subtract(
+ __isl_take isl_union_map *umap1,
+ __isl_take isl_union_map *umap2);
=item * Application
__isl_give isl_set *isl_set_apply(
__isl_take isl_set *set,
__isl_take isl_map *map);
+ __isl_give isl_union_set *isl_union_set_apply(
+ __isl_take isl_union_set *uset,
+ __isl_take isl_union_map *umap);
__isl_give isl_basic_map *isl_basic_map_apply_domain(
__isl_take isl_basic_map *bmap1,
__isl_take isl_basic_map *bmap2);
__isl_give isl_map *isl_map_apply_range(
__isl_take isl_map *map1,
__isl_take isl_map *map2);
+ __isl_give isl_union_map *isl_union_map_apply_range(
+ __isl_take isl_union_map *umap1,
+ __isl_take isl_union_map *umap2);
+
+=item * Simplification
+
+ __isl_give isl_basic_set *isl_basic_set_gist(
+ __isl_take isl_basic_set *bset,
+ __isl_take isl_basic_set *context);
+ __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
+ __isl_take isl_set *context);
+ __isl_give isl_union_set *isl_union_set_gist(
+ __isl_take isl_union_set *uset,
+ __isl_take isl_union_set *context);
+ __isl_give isl_basic_map *isl_basic_map_gist(
+ __isl_take isl_basic_map *bmap,
+ __isl_take isl_basic_map *context);
+ __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
+ __isl_take isl_map *context);
+ __isl_give isl_union_map *isl_union_map_gist(
+ __isl_take isl_union_map *umap,
+ __isl_take isl_union_map *context);
+
+The gist operation returns a set or relation that has the
+same intersection with the context as the input set or relation.
+Any implicit equality in the intersection is made explicit in the result,
+while all inequalities that are redundant with respect to the intersection
+are removed.
+In case of union sets and relations, the gist operation is performed
+per dimension.
=back
Given a (basic) set C<set> (or C<bset>), the following functions simply
return a set containing the lexicographic minimum or maximum
of the elements in C<set> (or C<bset>).
+In case of union sets, the optimum is computed per dimension.
__isl_give isl_set *isl_basic_set_lexmin(
__isl_take isl_basic_set *bset);
__isl_take isl_set *set);
__isl_give isl_set *isl_set_lexmax(
__isl_take isl_set *set);
+ __isl_give isl_union_set *isl_union_set_lexmin(
+ __isl_take isl_union_set *uset);
+ __isl_give isl_union_set *isl_union_set_lexmax(
+ __isl_take isl_union_set *uset);
Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
the following functions
return a map mapping each element in the domain of
C<map> (or C<bmap>) to the lexicographic minimum or maximum
of all elements associated to that element.
+In case of union relations, the optimum is computed per dimension.
__isl_give isl_map *isl_basic_map_lexmin(
__isl_take isl_basic_map *bmap);
__isl_take isl_map *map);
__isl_give isl_map *isl_map_lexmax(
__isl_take isl_map *map);
+ __isl_give isl_union_map *isl_union_map_lexmin(
+ __isl_take isl_union_map *umap);
+ __isl_give isl_union_map *isl_union_map_lexmax(
+ __isl_take isl_union_map *umap);
=head2 Points
__isl_take isl_point *pnt1,
__isl_take isl_point *pnt2);
-All elements of a B<bounded> set can be enumerated using
-the following function.
+All elements of a B<bounded> (union) set can be enumerated using
+the following functions.
int isl_set_foreach_point(__isl_keep isl_set *set,
int (*fn)(__isl_take isl_point *pnt, void *user),
void *user);
+ int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
+ int (*fn)(__isl_take isl_point *pnt, void *user),
+ void *user);
The function C<fn> is called for each integer point in
C<set> with as second argument the last argument of
[n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
+A given piecewise quasipolynomial has a fixed domain dimension.
+Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
+defined over different domains.
Piecewise quasipolynomials are mainly used by the C<barvinok>
library for representing the number of elements in a parametric set or map.
For example, the piecewise quasipolynomial above represents
-the number of point in the map
+the number of points in the map
[n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
__isl_take isl_printer *p,
__isl_keep isl_pw_qpolynomial *pwqp);
+ __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
+ __isl_take isl_printer *p,
+ __isl_keep isl_union_pw_qpolynomial *upwqp);
+
The output format of the printer
needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
+For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
+is supported.
=head3 Creating New (Piecewise) Quasipolynomials
__isl_take isl_dim *dim);
__isl_give isl_qpolynomial *isl_qpolynomial_infty(
__isl_take isl_dim *dim);
+ __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
+ __isl_take isl_dim *dim);
__isl_give isl_qpolynomial *isl_qpolynomial_nan(
__isl_take isl_dim *dim);
__isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
__isl_take isl_set *set,
__isl_take isl_qpolynomial *qp);
+ __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
+ __isl_take isl_dim *dim);
+ __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
+ __isl_take isl_pw_qpolynomial *pwqp);
+ __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
+ __isl_take isl_union_pw_qpolynomial *upwqp,
+ __isl_take isl_pw_qpolynomial *pwqp);
+
Quasipolynomials can be copied and freed again using the following
functions.
void isl_pw_qpolynomial_free(
__isl_take isl_pw_qpolynomial *pwqp);
+ __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
+ __isl_keep isl_union_pw_qpolynomial *upwqp);
+ void isl_union_pw_qpolynomial_free(
+ __isl_take isl_union_pw_qpolynomial *upwqp);
+
=head3 Inspecting (Piecewise) Quasipolynomials
+To iterate over all piecewise quasipolynomials in a union
+piecewise quasipolynomial, use the following function
+
+ int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
+ __isl_keep isl_union_pw_qpolynomial *upwqp,
+ int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
+ void *user);
+
To iterate over the cells in a piecewise quasipolynomial,
use either of the following two functions
__isl_give isl_qpolynomial *isl_qpolynomial_add(
__isl_take isl_qpolynomial *qp1,
__isl_take isl_qpolynomial *qp2);
+ __isl_give isl_qpolynomial *isl_qpolynomial_sub(
+ __isl_take isl_qpolynomial *qp1,
+ __isl_take isl_qpolynomial *qp2);
__isl_give isl_qpolynomial *isl_qpolynomial_mul(
__isl_take isl_qpolynomial *qp1,
__isl_take isl_qpolynomial *qp2);
__isl_take isl_pw_qpolynomial *pwqp1,
__isl_take isl_pw_qpolynomial *pwqp2);
+ __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
+ __isl_take isl_union_pw_qpolynomial *upwqp1,
+ __isl_take isl_union_pw_qpolynomial *upwqp2);
+ __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
+ __isl_take isl_union_pw_qpolynomial *upwqp1,
+ __isl_take isl_union_pw_qpolynomial *upwqp2);
+ __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
+ __isl_take isl_union_pw_qpolynomial *upwqp1,
+ __isl_take isl_union_pw_qpolynomial *upwqp2);
+
__isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
__isl_take isl_pw_qpolynomial *pwqp,
__isl_take isl_point *pnt);
+ __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
+ __isl_take isl_union_pw_qpolynomial *upwqp,
+ __isl_take isl_point *pnt);
+
__isl_give isl_set *isl_pw_qpolynomial_domain(
__isl_take isl_pw_qpolynomial *pwqp);
__isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
__isl_take isl_pw_qpolynomial *pwpq,
__isl_take isl_set *set);
+ __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
+ __isl_take isl_union_pw_qpolynomial *upwqp);
+ __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
+ __isl_take isl_union_pw_qpolynomial *upwpq,
+ __isl_take isl_union_set *uset);
+
+ __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
+ __isl_take isl_union_pw_qpolynomial *upwqp);
+
+ __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
+ __isl_take isl_pw_qpolynomial *pwqp,
+ __isl_take isl_set *context);
+
+ __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
+ __isl_take isl_union_pw_qpolynomial *upwqp,
+ __isl_take isl_union_set *context);
+
+The gist operation applies the gist operation to each of
+the cells in the domain of the input piecewise quasipolynomial.
+In future, the operation will also exploit the context
+to simplify the quasipolynomials associated to each cell.
+
+=head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
+
+A piecewise quasipolynomial reduction is a piecewise
+reduction (or fold) of quasipolynomials.
+In particular, the reduction can be maximum or a minimum.
+The objects are mainly used to represent the result of
+an upper or lower bound on a quasipolynomial over its domain,
+i.e., as the result of the following function.
+
+ __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
+ __isl_take isl_pw_qpolynomial *pwqp,
+ enum isl_fold type, int *tight);
+
+ __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
+ __isl_take isl_union_pw_qpolynomial *upwqp,
+ enum isl_fold type, int *tight);
+
+The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
+If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
+is the returned bound is known be tight, i.e., for each value
+of the parameters there is at least
+one element in the domain that reaches the bound.
+If the domain of C<pwqp> is not wrapping, then the bound is computed
+over all elements in that domain and the result has a purely parametric
+domain. If the domain of C<pwqp> is wrapping, then the bound is
+computed over the range of the wrapped relation. The domain of the
+wrapped relation becomes the domain of the result.
+
+A (piecewise) quasipolynomial reduction can be copied or freed using the
+following functions.
+
+ __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
+ __isl_keep isl_qpolynomial_fold *fold);
+ __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
+ __isl_keep isl_pw_qpolynomial_fold *pwf);
+ __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
+ __isl_keep isl_union_pw_qpolynomial_fold *upwf);
+ void isl_qpolynomial_fold_free(
+ __isl_take isl_qpolynomial_fold *fold);
+ void isl_pw_qpolynomial_fold_free(
+ __isl_take isl_pw_qpolynomial_fold *pwf);
+ void isl_union_pw_qpolynomial_fold_free(
+ __isl_take isl_union_pw_qpolynomial_fold *upwf);
+
+=head3 Printing Piecewise Quasipolynomial Reductions
+
+Piecewise quasipolynomial reductions can be printed
+using the following function.
+
+ __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
+ __isl_take isl_printer *p,
+ __isl_keep isl_pw_qpolynomial_fold *pwf);
+ __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
+ __isl_take isl_printer *p,
+ __isl_keep isl_union_pw_qpolynomial_fold *upwf);
+
+For C<isl_printer_print_pw_qpolynomial_fold>,
+output format of the printer
+needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
+For C<isl_printer_print_union_pw_qpolynomial_fold>,
+output format of the printer
+needs to be set to either C<ISL_FORMAT_ISL>.
+
+=head3 Inspecting (Piecewise) Quasipolynomial Reductions
+
+To iterate over all piecewise quasipolynomial reductions in a union
+piecewise quasipolynomial reduction, use the following function
+
+ int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
+ __isl_keep isl_union_pw_qpolynomial_fold *upwf,
+ int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
+ void *user), void *user);
+
+To iterate over the cells in a piecewise quasipolynomial reduction,
+use either of the following two functions
+
+ int isl_pw_qpolynomial_fold_foreach_piece(
+ __isl_keep isl_pw_qpolynomial_fold *pwf,
+ int (*fn)(__isl_take isl_set *set,
+ __isl_take isl_qpolynomial_fold *fold,
+ void *user), void *user);
+ int isl_pw_qpolynomial_fold_foreach_lifted_piece(
+ __isl_keep isl_pw_qpolynomial_fold *pwf,
+ int (*fn)(__isl_take isl_set *set,
+ __isl_take isl_qpolynomial_fold *fold,
+ void *user), void *user);
+
+See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
+of the difference between these two functions.
+
+To iterate over all quasipolynomials in a reduction, use
+
+ int isl_qpolynomial_fold_foreach_qpolynomial(
+ __isl_keep isl_qpolynomial_fold *fold,
+ int (*fn)(__isl_take isl_qpolynomial *qp,
+ void *user), void *user);
+
+=head3 Operations on Piecewise Quasipolynomial Reductions
+
+ __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
+ __isl_take isl_pw_qpolynomial_fold *pwf1,
+ __isl_take isl_pw_qpolynomial_fold *pwf2);
+
+ __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_add(
+ __isl_take isl_union_pw_qpolynomial_fold *upwf1,
+ __isl_take isl_union_pw_qpolynomial_fold *upwf2);
+
+ __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
+ __isl_take isl_pw_qpolynomial_fold *pwf,
+ __isl_take isl_point *pnt);
+
+ __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
+ __isl_take isl_union_pw_qpolynomial_fold *upwf,
+ __isl_take isl_point *pnt);
+
+ __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
+ __isl_take isl_union_pw_qpolynomial_fold *upwf);
+ __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
+ __isl_take isl_union_pw_qpolynomial_fold *upwf,
+ __isl_take isl_union_set *uset);
+
+ __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
+ __isl_take isl_pw_qpolynomial_fold *pwf);
+
+ __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
+ __isl_take isl_union_pw_qpolynomial_fold *upwf);
+
+ __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
+ __isl_take isl_pw_qpolynomial_fold *pwf,
+ __isl_take isl_set *context);
+
+ __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
+ __isl_take isl_union_pw_qpolynomial_fold *upwf,
+ __isl_take isl_union_set *context);
+
+The gist operation applies the gist operation to each of
+the cells in the domain of the input piecewise quasipolynomial reduction.
+In future, the operation will also exploit the context
+to simplify the quasipolynomial reductions associated to each cell.
+
=head2 Dependence Analysis
C<isl> contains specialized functionality for performing
of the sink access.
To compute standard flow dependences, the sink should be
a read, while the sources should be writes.
+If any of the source accesses are marked as being I<may>
+accesses, then there will be a dependence to the last
+I<must> access B<and> to any I<may> access that follows
+this last I<must> access.
+In particular, if I<all> sources are I<may> accesses,
+then memory based dependence analysis is performed.
+If, on the other hand, all sources are I<must> accesses,
+then value based dependence analysis is performed.
#include <isl_flow.h>
int max_source);
__isl_give isl_access_info *isl_access_info_add_source(
__isl_take isl_access_info *acc,
- __isl_take isl_map *source, void *source_user);
+ __isl_take isl_map *source, int must,
+ void *source_user);
__isl_give isl_flow *isl_access_info_compute_flow(
__isl_take isl_access_info *acc);
int isl_flow_foreach(__isl_keep isl_flow *deps,
- int (*fn)(__isl_take isl_map *dep, void *dep_user,
- void *user),
+ int (*fn)(__isl_take isl_map *dep, int must,
+ void *dep_user, void *user),
void *user);
__isl_give isl_set *isl_flow_get_no_source(
- __isl_keep isl_flow *deps);
+ __isl_keep isl_flow *deps, int must);
void isl_flow_free(__isl_take isl_flow *deps);
The function C<isl_access_info_compute_flow> performs the actual
it should return I<2 * n>.
The sources can be added to the C<isl_access_info> by performing
(at most) C<max_source> calls to C<isl_access_info_add_source>.
+C<must> indicates whether the source is a I<must> access
+or a I<may> access. Note that a multi-valued access relation
+should only be marked I<must> if every iteration in the domain
+of the relation accesses I<all> elements in its image.
The C<source_user> token is again used to identify
the source access. The range of the source access relation
C<source> should have the same dimension as the range
The result of the dependence analysis is collected in an
C<isl_flow>. There may be elements in the domain of
the sink access for which no preceding source access could be
-find. The set of these elements can be obtained through
-a call to C<isl_flow_get_no_source>.
+found or for which all preceding sources are I<may> accesses.
+The sets of these elements can be obtained through
+calls to C<isl_flow_get_no_source>, the first with C<must> set
+and the second with C<must> unset.
In the case of standard flow dependence analysis,
-this set corresponds to the reads from uninitialized
-array elements.
+with the sink a read and the sources I<must> writes,
+the first set corresponds to the reads from uninitialized
+array elements and the second set is empty.
The actual flow dependences can be extracted using
C<isl_flow_foreach>. This function will call the user-specified
callback function C<fn> for each B<non-empty> dependence between
a source and the sink. The callback function is called
-with three arguments, the actual flow dependence relation
-mapping source iterations to sink iterations, a token
+with four arguments, the actual flow dependence relation
+mapping source iterations to sink iterations, a boolean that
+indicates whether it is a I<must> or I<may> dependence, a token
identifying the source and an additional C<void *> with value
equal to the third argument of the C<isl_flow_foreach> call.
+A dependence is marked I<must> if it originates from a I<must>
+source and if it is not followed by any I<may> sources.
After finishing with an C<isl_flow>, the user should call
C<isl_flow_free> to free all associated memory.
+=head2 Parametric Vertex Enumeration
+
+The parametric vertex enumeration described in this section
+is mainly intended to be used internally and by the C<barvinok>
+library.
+
+ #include <isl_vertices.h>
+ __isl_give isl_vertices *isl_basic_set_compute_vertices(
+ __isl_keep isl_basic_set *bset);
+
+The function C<isl_basic_set_compute_vertices> performs the
+actual computation of the parametric vertices and the chamber
+decomposition and store the result in an C<isl_vertices> object.
+This information can be queried by either iterating over all
+the vertices or iterating over all the chambers or cells
+and then iterating over all vertices that are active on the chamber.
+
+ int isl_vertices_foreach_vertex(
+ __isl_keep isl_vertices *vertices,
+ int (*fn)(__isl_take isl_vertex *vertex, void *user),
+ void *user);
+
+ int isl_vertices_foreach_cell(
+ __isl_keep isl_vertices *vertices,
+ int (*fn)(__isl_take isl_cell *cell, void *user),
+ void *user);
+ int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
+ int (*fn)(__isl_take isl_vertex *vertex, void *user),
+ void *user);
+
+Other operations that can be performed on an C<isl_vertices> object are
+the following.
+
+ isl_ctx *isl_vertices_get_ctx(
+ __isl_keep isl_vertices *vertices);
+ int isl_vertices_get_n_vertices(
+ __isl_keep isl_vertices *vertices);
+ void isl_vertices_free(__isl_take isl_vertices *vertices);
+
+Vertices can be inspected and destroyed using the following functions.
+
+ isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
+ int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
+ __isl_give isl_basic_set *isl_vertex_get_domain(
+ __isl_keep isl_vertex *vertex);
+ __isl_give isl_basic_set *isl_vertex_get_expr(
+ __isl_keep isl_vertex *vertex);
+ void isl_vertex_free(__isl_take isl_vertex *vertex);
+
+C<isl_vertex_get_expr> returns a singleton parametric set describing
+the vertex, while C<isl_vertex_get_domain> returns the activity domain
+of the vertex.
+Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
+B<rational> basic sets, so they should mainly be used for inspection
+and should not be mixed with integer sets.
+
+Chambers can be inspected and destroyed using the following functions.
+
+ isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
+ __isl_give isl_basic_set *isl_cell_get_domain(
+ __isl_keep isl_cell *cell);
+ void isl_cell_free(__isl_take isl_cell *cell);
+
=head1 Applications
Although C<isl> is mainly meant to be used as a library,
C<isl_pip> takes the same input as the C<example> program
from the C<piplib> distribution, i.e., a set of constraints
-on the parameters, a line contains only -1 and finally a set
+on the parameters, a line containing only -1 and finally a set
of constraints on a parametric polyhedron.
The coefficients of the parameters appear in the last columns
(but before the final constant column).
projects / platform / upstream / isl.git / blobdiff