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
+
+=head3 Changes since isl-0.03
+
+=over
+
+=item * The function C<isl_pw_qpolynomial_fold_add> has been
+renamed to C<isl_pw_qpolynomial_fold_fold>.
+Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
+renamed to C<isl_union_pw_qpolynomial_fold_fold>.
+
+=back
+
+=head3 Changes since isl-0.04
+
+=over
+
+=item * All header files have been renamed from C<isl_header.h>
+to C<isl/header.h>.
+
+=back
+
+=head3 Changes since isl-0.05
+
+=over
+
+=item * The functions C<isl_printer_print_basic_set> and
+C<isl_printer_print_basic_map> no longer print a newline.
+
+=item * The functions C<isl_flow_get_no_source>
+and C<isl_union_map_compute_flow> now return
+the accesses for which no source could be found instead of
+the iterations where those accesses occur.
+
+=item * The functions C<isl_basic_map_identity> and
+C<isl_map_identity> now take the dimension specification
+of a B<map> as input. An old call
+C<isl_map_identity(dim)> can be rewritten to
+C<isl_map_identity(isl_dim_map_from_set(dim))>.
+
+=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
However, to allow future versions of C<isl> to optionally
support fixed integer arithmetic, all calls to C<GMP>
are wrapped inside C<isl> specific macros.
-The basic type is C<isl_int> and the following operations
+The basic type is C<isl_int> and the operations below
are available on this type.
The meanings of these operations are essentially the same
as their C<GMP> C<mpz_> counterparts.
initialized with C<isl_int_init> before they can be used
and they need to be released with C<isl_int_clear>
after the last use.
+The user should not assume that an C<isl_int> is represented
+as a C<mpz_t>, but should instead explicitly convert between
+C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
+C<isl_int_get_gmp> whenever a C<mpz_t> is required.
=over
=item isl_int_set_si(r,i)
+=item isl_int_set_gmp(r,g)
+
+=item isl_int_get_gmp(i,g)
+
=item isl_int_abs(r,i)
=item isl_int_neg(r,i)
=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.
If the user still wants to use one or more of these arguments
after the function call, she should pass along a copy of the
object rather than the object itself.
-The user is then responsible for make sure that the original
+The user is then responsible for making sure that the original
object gets used somewhere else or is explicitly freed.
The arguments and return values of all documents functions are
Whenever a new set or relation is created from scratch,
its dimension needs to be specified using an C<isl_dim>.
- #include <isl_dim.h>
+ #include <isl/dim.h>
__isl_give isl_dim *isl_dim_alloc(isl_ctx *ctx,
unsigned nparam, unsigned n_in, unsigned n_out);
__isl_give isl_dim *isl_dim_set_alloc(isl_ctx *ctx,
L<Creating New (Piecewise) Quasipolynomials>) based on the dimension
specification of the original object.
- #include <isl_set.h>
+ #include <isl/set.h>
__isl_give isl_dim *isl_basic_set_get_dim(
__isl_keep isl_basic_set *bset);
__isl_give isl_dim *isl_set_get_dim(__isl_keep isl_set *set);
- #include <isl_map.h>
+ #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_polynomial.h>
+ #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.
- #include <isl_dim.h>
+ #include <isl/dim.h>
__isl_give isl_dim *isl_dim_set_name(__isl_take isl_dim *dim,
enum isl_dim_type type, unsigned pos,
__isl_keep const char *name);
requires that both arguments have the same parameters. This also
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.
+Pairs of C<isl_union_set> and/or C<isl_union_map> arguments may
+have different parameters (as long as they are named), in which case
+the result will have as parameters the union of the parameters of
+the arguments.
+
+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.
+
+Dimension specifications can be created from other dimension
+specifications using the following functions.
+
+ __isl_give isl_dim *isl_dim_domain(__isl_take isl_dim *dim);
+ __isl_give isl_dim *isl_dim_from_domain(__isl_take isl_dim *dim);
+ __isl_give isl_dim *isl_dim_range(__isl_take isl_dim *dim);
+ __isl_give isl_dim *isl_dim_from_range(__isl_take isl_dim *dim);
+ __isl_give isl_dim *isl_dim_reverse(__isl_take isl_dim *dim);
+ __isl_give isl_dim *isl_dim_join(__isl_take isl_dim *left,
+ __isl_take isl_dim *right);
+ __isl_give isl_dim *isl_dim_insert(__isl_take isl_dim *dim,
+ enum isl_dim_type type, unsigned pos, unsigned n);
+ __isl_give isl_dim *isl_dim_add(__isl_take isl_dim *dim,
+ enum isl_dim_type type, unsigned n);
+ __isl_give isl_dim *isl_dim_drop(__isl_take isl_dim *dim,
+ enum isl_dim_type type, unsigned first, unsigned n);
+ __isl_give isl_dim *isl_dim_map_from_set(
+ __isl_take isl_dim *dim);
+
+Note that if dimensions are added or removed from a space, then
+the name and the internal structure are lost.
=head2 Input and Output
The coefficients of any existentially quantified variables appear
between those of the set variables and those of the parameters.
+=head3 Extended C<PolyLib> format
+
+The extended C<PolyLib> format is nearly identical to the
+C<PolyLib> format. The only difference is that the line
+containing the number of rows and columns of a constraint matrix
+also contains four additional numbers:
+the number of output dimensions, the number of input dimensions,
+the number of local dimensions (i.e., the number of existentially
+quantified variables) and the number of parameters.
+For sets, the number of ``output'' dimensions is equal
+to the number of set dimensions, while the number of ``input''
+dimensions is zero.
+
=head3 Input
- #include <isl_set.h>
+ #include <isl/set.h>
__isl_give isl_basic_set *isl_basic_set_read_from_file(
isl_ctx *ctx, FILE *input, int nparam);
__isl_give isl_basic_set *isl_basic_set_read_from_str(
__isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
const char *str, int nparam);
- #include <isl_map.h>
+ #include <isl/map.h>
__isl_give isl_basic_map *isl_basic_map_read_from_file(
isl_ctx *ctx, FILE *input, int nparam);
__isl_give isl_basic_map *isl_basic_map_read_from_str(
__isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
const char *str, int nparam);
+ #include <isl/union_set.h>
+ __isl_give isl_union_set *isl_union_set_read_from_file(
+ isl_ctx *ctx, FILE *input);
+ __isl_give isl_union_set *isl_union_set_read_from_str(
+ struct isl_ctx *ctx, const char *str);
+
+ #include <isl/union_map.h>
+ __isl_give isl_union_map *isl_union_map_read_from_file(
+ isl_ctx *ctx, FILE *input);
+ __isl_give isl_union_map *isl_union_map_read_from_str(
+ struct isl_ctx *ctx, const char *str);
+
The input format is autodetected and may be either the C<PolyLib> format
or the C<isl> format.
C<nparam> specifies how many of the final columns in
__isl_give isl_printer *isl_printer_set_suffix(
__isl_take isl_printer *p, const char *suffix);
-The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>
-or C<ISL_FORMAT_POLYLIB> and defaults to C<ISL_FORMAT_ISL>.
+The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
+C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
+and defaults to C<ISL_FORMAT_ISL>.
Each line in the output is indented by C<indent> spaces
(default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
In the C<PolyLib> format output,
To actually print something, use
- #include <isl_set.h>
+ #include <isl/set.h>
__isl_give isl_printer *isl_printer_print_basic_set(
__isl_take isl_printer *printer,
__isl_keep isl_basic_set *bset);
__isl_take isl_printer *printer,
__isl_keep isl_set *set);
- #include <isl_map.h>
+ #include <isl/map.h>
__isl_give isl_printer *isl_printer_print_basic_map(
__isl_take isl_printer *printer,
__isl_keep isl_basic_map *bmap);
__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_universe(
__isl_take isl_dim *dim);
+The sets and relations constructed by the functions above
+contain all integer values, while those constructed by the
+functions below only contain non-negative values.
+
+ __isl_give isl_basic_set *isl_basic_set_nat_universe(
+ __isl_take isl_dim *dim);
+ __isl_give isl_basic_map *isl_basic_map_nat_universe(
+ __isl_take isl_dim *dim);
+ __isl_give isl_set *isl_set_nat_universe(
+ __isl_take isl_dim *dim);
+ __isl_give isl_map *isl_map_nat_universe(
+ __isl_take isl_dim *dim);
+
=item * Identity relations
__isl_give isl_basic_map *isl_basic_map_identity(
- __isl_take isl_dim *set_dim);
+ __isl_take isl_dim *dim);
__isl_give isl_map *isl_map_identity(
- __isl_take isl_dim *set_dim);
+ __isl_take isl_dim *dim);
-These functions take a dimension specification for a B<set>
-and return an identity relation between two such sets.
+The number of input and output dimensions in C<dim> needs
+to be the same.
=item * Lexicographic order
__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
Constraints can be constructed, manipulated and
added to basic sets and relations using the following functions.
- #include <isl_constraint.h>
+ #include <isl/constraint.h>
__isl_give isl_constraint *isl_equality_alloc(
__isl_take isl_dim *dim);
__isl_give isl_constraint *isl_inequality_alloc(
bset = isl_basic_set_read_from_str(ctx,
"{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
+A basic set or relation can also be constructed from two matrices
+describing the equalities and the inequalities.
+
+ __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
+ __isl_take isl_dim *dim,
+ __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
+ enum isl_dim_type c1,
+ enum isl_dim_type c2, enum isl_dim_type c3,
+ enum isl_dim_type c4);
+ __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
+ __isl_take isl_dim *dim,
+ __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
+ enum isl_dim_type c1,
+ enum isl_dim_type c2, enum isl_dim_type c3,
+ enum isl_dim_type c4, enum isl_dim_type c5);
+
+The C<isl_dim_type> arguments indicate the order in which
+different kinds of variables appear in the input matrices
+and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
+C<isl_dim_set> and C<isl_dim_div> for sets and
+of C<isl_dim_cst>, C<isl_dim_param>,
+C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
+
=head2 Inspecting Sets and Relations
Usually, the user should not have to care about the actual constraints
__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);
+Alternatively, the existentially quantified variables can be removed
+using the following functions, which compute an overapproximation.
+
+ __isl_give isl_basic_set *isl_basic_set_remove_divs(
+ __isl_take isl_basic_set *bset);
+ __isl_give isl_basic_map *isl_basic_map_remove_divs(
+ __isl_take isl_basic_map *bmap);
+ __isl_give isl_set *isl_set_remove_divs(
+ __isl_take isl_set *set);
+
+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);
+
+The number of sets or maps in a union set or map can be obtained
+from
+
+ int isl_union_set_n_set(__isl_keep isl_union_set *uset);
+ int isl_union_map_n_map(__isl_keep isl_union_map *umap);
+
+To extract the set or map from a union with a given dimension
+specification, use
+
+ __isl_give isl_set *isl_union_set_extract_set(
+ __isl_keep isl_union_set *uset,
+ __isl_take isl_dim *dim);
+ __isl_give isl_map *isl_union_map_extract_map(
+ __isl_keep isl_union_map *umap,
+ __isl_take isl_dim *dim);
+
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,
__isl_give isl_map *isl_map_make_disjoint(
__isl_take isl_map *map);
+The number of basic sets in a set can be obtained
+from
+
+ int isl_set_n_basic_set(__isl_keep isl_set *set);
+
To iterate over the constraints of a basic set or map, use
- #include <isl_constraint.h>
+ #include <isl/constraint.h>
int isl_basic_map_foreach_constraint(
__isl_keep isl_basic_map *bmap,
void isl_div_get_coefficient(__isl_keep isl_div *div,
enum isl_dim_type type, int pos, isl_int *v);
+To obtain the constraints of a basic set or map in matrix
+form, use the following functions.
+
+ __isl_give isl_mat *isl_basic_set_equalities_matrix(
+ __isl_keep isl_basic_set *bset,
+ enum isl_dim_type c1, enum isl_dim_type c2,
+ enum isl_dim_type c3, enum isl_dim_type c4);
+ __isl_give isl_mat *isl_basic_set_inequalities_matrix(
+ __isl_keep isl_basic_set *bset,
+ enum isl_dim_type c1, enum isl_dim_type c2,
+ enum isl_dim_type c3, enum isl_dim_type c4);
+ __isl_give isl_mat *isl_basic_map_equalities_matrix(
+ __isl_keep isl_basic_map *bmap,
+ enum isl_dim_type c1,
+ enum isl_dim_type c2, enum isl_dim_type c3,
+ enum isl_dim_type c4, enum isl_dim_type c5);
+ __isl_give isl_mat *isl_basic_map_inequalities_matrix(
+ __isl_keep isl_basic_map *bmap,
+ enum isl_dim_type c1,
+ enum isl_dim_type c2, enum isl_dim_type c3,
+ enum isl_dim_type c4, enum isl_dim_type c5);
+
+The C<isl_dim_type> arguments dictate the order in which
+different kinds of variables appear in the resulting matrix
+and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
+C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
+
+The names of the domain and range spaces of a set or relation can be
+read off using the following functions.
+
+ const char *isl_basic_set_get_tuple_name(
+ __isl_keep isl_basic_set *bset);
+ const char *isl_set_get_tuple_name(
+ __isl_keep isl_set *set);
+ const char *isl_basic_map_get_tuple_name(
+ __isl_keep isl_basic_map *bmap,
+ enum isl_dim_type type);
+ const char *isl_map_get_tuple_name(
+ __isl_keep isl_map *map,
+ enum isl_dim_type type);
+
+As with C<isl_dim_get_tuple_name>, the value returned points to
+an internal data structure.
+The names of individual dimensions can be read off using
+the following functions.
+
+ const char *isl_constraint_get_dim_name(
+ __isl_keep isl_constraint *constraint,
+ enum isl_dim_type type, unsigned pos);
+ const char *isl_basic_set_get_dim_name(
+ __isl_keep isl_basic_set *bset,
+ enum isl_dim_type type, unsigned pos);
+ const char *isl_set_get_dim_name(
+ __isl_keep isl_set *set,
+ enum isl_dim_type type, unsigned pos);
+ const char *isl_basic_map_get_dim_name(
+ __isl_keep isl_basic_map *bmap,
+ enum isl_dim_type type, unsigned pos);
+ const char *isl_map_get_dim_name(
+ __isl_keep isl_map *map,
+ enum isl_dim_type type, unsigned pos);
+
+These functions are mostly useful to obtain the names
+of the parameters.
+
=head2 Properties
=head3 Unary Properties
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_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_union_set_is_equal(
+ __isl_keep isl_union_set *uset1,
+ __isl_keep isl_union_set *uset2);
+ 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_set_is_strict_subset(
__isl_keep isl_set *set1,
__isl_keep isl_set *set2);
+ int isl_union_set_is_subset(
+ __isl_keep isl_union_set *uset1,
+ __isl_keep isl_union_set *uset2);
+ int isl_union_set_is_strict_subset(
+ __isl_keep isl_union_set *uset1,
+ __isl_keep isl_union_set *uset2);
int isl_basic_map_is_subset(
__isl_keep isl_basic_map *bmap1,
__isl_keep isl_basic_map *bmap2);
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);
+
+ __isl_give isl_basic_map *isl_basic_map_domain_map(
+ __isl_take isl_basic_map *bmap);
+ __isl_give isl_basic_map *isl_basic_map_range_map(
+ __isl_take isl_basic_map *bmap);
+ __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
+ __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
+ __isl_give isl_union_map *isl_union_map_domain_map(
+ __isl_take isl_union_map *umap);
+ __isl_give isl_union_map *isl_union_map_range_map(
+ __isl_take isl_union_map *umap);
+
+The functions above construct a (basic, regular or union) relation
+that maps (a wrapped version of) the input relation to its domain or range.
+
+=item * Identity
+
+ __isl_give isl_map *isl_set_identity(
+ __isl_take isl_set *set);
+ __isl_give isl_union_map *isl_union_set_identity(
+ __isl_take isl_union_set *uset);
+
+Construct an identity relation on the given (union) set.
+
+=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 * Detecting equalities
+
+ __isl_give isl_basic_set *isl_basic_set_detect_equalities(
+ __isl_take isl_basic_set *bset);
+ __isl_give isl_basic_map *isl_basic_map_detect_equalities(
+ __isl_take isl_basic_map *bmap);
+ __isl_give isl_set *isl_set_detect_equalities(
+ __isl_take isl_set *set);
+ __isl_give isl_map *isl_map_detect_equalities(
+ __isl_take isl_map *map);
+ __isl_give isl_union_set *isl_union_set_detect_equalities(
+ __isl_take isl_union_set *uset);
+ __isl_give isl_union_map *isl_union_map_detect_equalities(
+ __isl_take isl_union_map *umap);
+
+Simplify the representation of a set or relation by detecting implicit
+equalities.
=item * Convex hull
__isl_take isl_set *set);
__isl_give isl_basic_map *isl_map_simple_hull(
__isl_take isl_map *map);
+ __isl_give isl_union_map *isl_union_map_simple_hull(
+ __isl_take isl_union_map *umap);
These functions compute a single basic set or relation
that contains the whole input set or relation.
__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 space.
+
+=item * Polyhedral hull
+
+ __isl_give isl_basic_set *isl_set_polyhedral_hull(
+ __isl_take isl_set *set);
+ __isl_give isl_basic_map *isl_map_polyhedral_hull(
+ __isl_take isl_map *map);
+ __isl_give isl_union_set *isl_union_set_polyhedral_hull(
+ __isl_take isl_union_set *uset);
+ __isl_give isl_union_map *isl_union_map_polyhedral_hull(
+ __isl_take isl_union_map *umap);
+
+These functions compute a single basic set or relation
+not involving any existentially quantified variables
+that contains the whole input set or relation.
+In case of union sets and relations, the polyhedral hull is computed
+per space.
=item * Power
Compute a parametric representation for all positive powers I<k> of C<map>.
The power I<k> is equated to the parameter at position C<param>.
-The result may be an overapproximation. If the result is exact,
+The result may be an overapproximation. If the result is known to be exact,
then C<*exact> is set to C<1>.
-The current implementation only produces exact results for particular
-cases of piecewise translations (i.e., piecewise uniform dependences).
=item * Transitive closure
__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,
then C<*exact> is set to C<1>.
-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);
+
+=item * Flattening
+
+Remove any internal structure of domain (and range) of the given
+set or relation. If there is any such internal structure in the input,
+then the name of the space is also removed.
+
+ __isl_give isl_basic_set *isl_basic_set_flatten(
+ __isl_take isl_basic_set *bset);
+ __isl_give isl_set *isl_set_flatten(
+ __isl_take isl_set *set);
+ __isl_give isl_basic_map *isl_basic_map_flatten(
+ __isl_take isl_basic_map *bmap);
+ __isl_give isl_map *isl_map_flatten(
+ __isl_take isl_map *map);
+
+ __isl_give isl_map *isl_set_flatten_map(
+ __isl_take isl_set *set);
+
+The function above constructs a relation
+that maps the input set to a flattened version of the set.
+
+=item * Dimension manipulation
+
+ __isl_give isl_set *isl_set_add_dims(
+ __isl_take isl_set *set,
+ enum isl_dim_type type, unsigned n);
+ __isl_give isl_map *isl_map_add_dims(
+ __isl_take isl_map *map,
+ enum isl_dim_type type, unsigned n);
+
+It is usually not advisable to directly change the (input or output)
+space of a set or a relation as this removes the name and the internal
+structure of the space. However, the above functions can be useful
+to add new parameters.
=back
__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_range(
+ __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_domain(
__isl_take isl_map *map1,
__isl_take isl_map *map2);
+ __isl_give isl_union_map *isl_union_map_apply_domain(
+ __isl_take isl_union_map *umap1,
+ __isl_take isl_union_map *umap2);
__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 * Cartesian Product
+
+ __isl_give isl_set *isl_set_product(
+ __isl_take isl_set *set1,
+ __isl_take isl_set *set2);
+ __isl_give isl_union_set *isl_union_set_product(
+ __isl_take isl_union_set *uset1,
+ __isl_take isl_union_set *uset2);
+ __isl_give isl_basic_map *isl_basic_map_range_product(
+ __isl_take isl_basic_map *bmap1,
+ __isl_take isl_basic_map *bmap2);
+ __isl_give isl_map *isl_map_range_product(
+ __isl_take isl_map *map1,
+ __isl_take isl_map *map2);
+ __isl_give isl_union_map *isl_union_map_range_product(
+ __isl_take isl_union_map *umap1,
+ __isl_take isl_union_map *umap2);
+ __isl_give isl_map *isl_map_product(
+ __isl_take isl_map *map1,
+ __isl_take isl_map *map2);
+ __isl_give isl_union_map *isl_union_map_product(
+ __isl_take isl_union_map *umap1,
+ __isl_take isl_union_map *umap2);
+
+The above functions compute the cross product of the given
+sets or relations. The domains and ranges of the results
+are wrapped maps between domains and ranges of the inputs.
+To obtain a ``flat'' product, use the following functions
+instead.
+
+ __isl_give isl_basic_set *isl_basic_set_flat_product(
+ __isl_take isl_basic_set *bset1,
+ __isl_take isl_basic_set *bset2);
+ __isl_give isl_set *isl_set_flat_product(
+ __isl_take isl_set *set1,
+ __isl_take isl_set *set2);
+ __isl_give isl_basic_map *isl_basic_map_flat_product(
+ __isl_take isl_basic_map *bmap1,
+ __isl_take isl_basic_map *bmap2);
+ __isl_give isl_map *isl_map_flat_product(
+ __isl_take isl_map *map1,
+ __isl_take isl_map *map2);
+
+=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 space.
=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 space.
__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 space.
__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 Matrices
+
+Matrices can be created, copied and freed using the following functions.
+
+ #include <isl/mat.h>
+ __isl_give isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
+ unsigned n_row, unsigned n_col);
+ __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
+ void isl_mat_free(__isl_take isl_mat *mat);
+
+Note that the elements of a newly created matrix may have arbitrary values.
+The elements can be changed and inspected using the following functions.
+
+ int isl_mat_rows(__isl_keep isl_mat *mat);
+ int isl_mat_cols(__isl_keep isl_mat *mat);
+ int isl_mat_get_element(__isl_keep isl_mat *mat,
+ int row, int col, isl_int *v);
+ __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
+ int row, int col, isl_int v);
+
+C<isl_mat_get_element> will return a negative value if anything went wrong.
+In that case, the value of C<*v> is undefined.
+
+The following function can be used to compute the (right) inverse
+of a matrix, i.e., a matrix such that the product of the original
+and the inverse (in that order) is a multiple of the identity matrix.
+The input matrix is assumed to be of full row-rank.
+
+ __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
+
+The following function can be used to compute the (right) kernel
+(or null space) of a matrix, i.e., a matrix such that the product of
+the original and the kernel (in that order) is the zero matrix.
+
+ __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
=head2 Points
A singleton set can be created from a point using
+ __isl_give isl_basic_set *isl_basic_set_from_point(
+ __isl_take isl_point *pnt);
__isl_give isl_set *isl_set_from_point(
__isl_take isl_point *pnt);
and a box can be created from two opposite extremal points using
+ __isl_give isl_basic_set *isl_basic_set_box_from_points(
+ __isl_take isl_point *pnt1,
+ __isl_take isl_point *pnt2);
__isl_give isl_set *isl_set_box_from_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
If the enumeration is performed successfully and to completion,
then C<isl_set_foreach_point> returns C<0>.
-To obtain a single point of a set, use
+To obtain a single point of a (basic) set, use
+ __isl_give isl_point *isl_basic_set_sample_point(
+ __isl_take isl_basic_set *bset);
__isl_give isl_point *isl_set_sample_point(
__isl_take isl_set *set);
[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.
+In case of printing in C<ISL_FORMAT_C>, the user may want
+to set the names of all dimensions
+
+ __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
+ __isl_take isl_qpolynomial *qp,
+ enum isl_dim_type type, unsigned pos,
+ const char *s);
+ __isl_give isl_pw_qpolynomial *
+ isl_pw_qpolynomial_set_dim_name(
+ __isl_take isl_pw_qpolynomial *pwqp,
+ enum isl_dim_type type, unsigned pos,
+ const char *s);
=head3 Creating New (Piecewise) Quasipolynomials
__isl_give isl_qpolynomial *isl_qpolynomial_zero(
__isl_take isl_dim *dim);
+ __isl_give isl_qpolynomial *isl_qpolynomial_one(
+ __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_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 extract the piecewise quasipolynomial from a union with a given dimension
+specification, use
+
+ __isl_give isl_pw_qpolynomial *
+ isl_union_pw_qpolynomial_extract_pw_qpolynomial(
+ __isl_keep isl_union_pw_qpolynomial *upwqp,
+ __isl_take isl_dim *dim);
+
To iterate over the cells in a piecewise quasipolynomial,
use either of the following two functions
__isl_give isl_qpolynomial *isl_qpolynomial_mul(
__isl_take isl_qpolynomial *qp1,
__isl_take isl_qpolynomial *qp2);
+ __isl_give isl_qpolynomial *isl_qpolynomial_pow(
+ __isl_take isl_qpolynomial *qp, unsigned exponent);
__isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
__isl_take isl_pw_qpolynomial *pwqp1,
__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.
+The context is also exploited
+to simplify the quasipolynomials associated to each cell.
+
+ __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
+ __isl_take isl_pw_qpolynomial *pwqp, int sign);
+ __isl_give isl_union_pw_qpolynomial *
+ isl_union_pw_qpolynomial_to_polynomial(
+ __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
+
+Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
+the polynomial will be an overapproximation. If C<sign> is negative,
+it will be an underapproximation. If C<sign> is zero, the approximation
+will lie somewhere in between.
+
+=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 C<ISL_FORMAT_ISL>.
+In case of printing in C<ISL_FORMAT_C>, the user may want
+to set the names of all dimensions
+
+ __isl_give isl_pw_qpolynomial_fold *
+ isl_pw_qpolynomial_fold_set_dim_name(
+ __isl_take isl_pw_qpolynomial_fold *pwf,
+ enum isl_dim_type type, unsigned pos,
+ const char *s);
+
+=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_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
+ __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_fold(
+ __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.
+
+ __isl_give isl_pw_qpolynomial_fold *
+ isl_set_apply_pw_qpolynomial_fold(
+ __isl_take isl_set *set,
+ __isl_take isl_pw_qpolynomial_fold *pwf,
+ int *tight);
+ __isl_give isl_pw_qpolynomial_fold *
+ isl_map_apply_pw_qpolynomial_fold(
+ __isl_take isl_map *map,
+ __isl_take isl_pw_qpolynomial_fold *pwf,
+ int *tight);
+ __isl_give isl_union_pw_qpolynomial_fold *
+ isl_union_set_apply_union_pw_qpolynomial_fold(
+ __isl_take isl_union_set *uset,
+ __isl_take isl_union_pw_qpolynomial_fold *upwf,
+ int *tight);
+ __isl_give isl_union_pw_qpolynomial_fold *
+ isl_union_map_apply_union_pw_qpolynomial_fold(
+ __isl_take isl_union_map *umap,
+ __isl_take isl_union_pw_qpolynomial_fold *upwf,
+ int *tight);
+
+The functions taking a map
+compose the given map with the given piecewise quasipolynomial reduction.
+That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
+over all elements in the intersection of the range of the map
+and the domain of the piecewise quasipolynomial reduction
+as a function of an element in the domain of the map.
+The functions taking a set compute a bound over all elements in the
+intersection of the set and the domain of the
+piecewise quasipolynomial reduction.
+
=head2 Dependence Analysis
C<isl> contains specialized functionality for performing
If, on the other hand, all sources are I<must> accesses,
then value based dependence analysis is performed.
- #include <isl_flow.h>
+ #include <isl/flow.h>
+
+ typedef int (*isl_access_level_before)(void *first, void *second);
__isl_give isl_access_info *isl_access_info_alloc(
__isl_take isl_map *sink,
__isl_take isl_access_info *acc,
__isl_take isl_map *source, int must,
void *source_user);
+ void isl_access_info_free(__isl_take isl_access_info *acc);
__isl_give isl_flow *isl_access_info_compute_flow(
__isl_take isl_access_info *acc);
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_give isl_map *isl_flow_get_no_source(
__isl_keep isl_flow *deps, int must);
void isl_flow_free(__isl_take isl_flow *deps);
the source access. The range of the source access relation
C<source> should have the same dimension as the range
of the sink access relation.
+The C<isl_access_info_free> function should usually not be
+called explicitly, because it is called implicitly by
+C<isl_access_info_compute_flow>.
The result of the dependence analysis is collected in an
-C<isl_flow>. There may be elements in the domain of
+C<isl_flow>. There may be elements of
the sink access for which no preceding source access could be
found or for which all preceding sources are I<may> accesses.
-The sets of these elements can be obtained through
+The relations containing 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,
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 first relation corresponds to the reads from uninitialized
+array elements and the second relation 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
After finishing with an C<isl_flow>, the user should call
C<isl_flow_free> to free all associated memory.
+A higher-level interface to dependence analysis is provided
+by the following function.
+
+ #include <isl/flow.h>
+
+ int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
+ __isl_take isl_union_map *must_source,
+ __isl_take isl_union_map *may_source,
+ __isl_take isl_union_map *schedule,
+ __isl_give isl_union_map **must_dep,
+ __isl_give isl_union_map **may_dep,
+ __isl_give isl_union_map **must_no_source,
+ __isl_give isl_union_map **may_no_source);
+
+The arrays are identified by the tuple names of the ranges
+of the accesses. The iteration domains by the tuple names
+of the domains of the accesses and of the schedule.
+The relative order of the iteration domains is given by the
+schedule. The relations returned through C<must_no_source>
+and C<may_no_source> are subsets of C<sink>.
+Any of C<must_dep>, C<may_dep>, C<must_no_source>
+or C<may_no_source> may be C<NULL>, but a C<NULL> value for
+any of the other arguments is treated as an error.
+
+=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