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
Below we discuss some of the more common options.
-C<isl> can optionally use both C<PolyLib> and C<piplib>.
-C<PolyLib> is mainly used to convert between C<PolyLib> objects
-and C<isl> objects. No C<piplib> functionality is currently
-used by default.
-The C<--with-polylib> and C<--with-piplib> options can
-be used to specify which C<PolyLib> or C<piplib>
+C<isl> can optionally use C<piplib>, but no
+C<piplib> functionality is currently used by default.
+The C<--with-piplib> option can
+be used to specify which C<piplib>
library to use, either an installed version (C<system>),
-an externally built version (C<build>), a bundled version (C<bundled>)
+an externally built version (C<build>)
or no version (C<no>). The option C<build> is mostly useful
in C<configure> scripts of larger projects that bundle both C<isl>
-and
either C<PolyLib> or C<piplib>.
+and C<piplib>.
=over
Installation prefix for C<GMP> (architecture-dependent files).
-=item C<--with-polylib>
-
-Which copy of C<PolyLib> to use, either C<no> (default), C<system> or C<build>.
-
-=item C<--with-polylib-prefix>
-
-Installation prefix for C<system> C<PolyLib> (architecture-independent files).
-
-=item C<--with-polylib-exec-prefix>
-
-Installation prefix for C<system> C<PolyLib> (architecture-dependent files).
-
-=item C<--with-polylib-builddir>
-
-Location where C<build> C<PolyLib> was built.
-
=item C<--with-piplib>
-Which copy of C<piplib> to use, either C<no> (default), C<system>, C<build>
-or C<bundled>. Note that C<bundled> only works if you have obtained
-C<isl> and its submodules from the git repository.
+Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
=item C<--with-piplib-prefix>
are wrapped inside C<isl> specific macros.
The basic type is C<isl_int> and the following operations
are available on this type.
+The meanings of these operations are essentially the same
+as their C<GMP> C<mpz_> counterparts.
+As always with C<GMP> types, C<isl_int>s need to be
+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.
=over
=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.
C<isl_dim_out> (only for relations), C<isl_dim_set>
(only for sets) or C<isl_dim_all>.
+It is often useful to create objects that live in the
+same space as some other object. This can be accomplished
+by creating the new objects
+(see L<Creating New Sets and Relations> or
+L<Creating New (Piecewise) Quasipolynomials>) based on the dimension
+specification of the original object.
+
+ #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_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.
+
+ #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);
+ __isl_keep const char *isl_dim_get_name(__isl_keep isl_dim *dim,
+ enum isl_dim_type type, unsigned pos);
+
+Note that C<isl_dim_get_name> returns a pointer to some internal
+data structure, so the result can only be used while the
+corresponding C<isl_dim> is alive.
+Also note that every function that operates on two sets or relations
+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.
+
+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
-Proper input and output functions are still in development.
-However, some functions are provided to read and write
-to foreign file formats and to convert between
-C<isl> objects and C<PolyLib> objects (if C<PolyLib> is available).
+C<isl> supports its own input/output format, which is similar
+to the C<Omega> format, but also supports the C<PolyLib> format
+in some cases.
+
+=head3 C<isl> format
+
+The C<isl> format is similar to that of C<Omega>, but has a different
+syntax for describing the parameters and allows for the definition
+of an existentially quantified variable as the integer division
+of an affine expression.
+For example, the set of integers C<i> between C<0> and C<n>
+such that C<i % 10 <= 6> can be described as
+
+ [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
+ i - 10 a <= 6) }
+
+A set or relation can have several disjuncts, separated
+by the keyword C<or>. Each disjunct is either a conjunction
+of constraints or a projection (C<exists>) of a conjunction
+of constraints. The constraints are separated by the keyword
+C<and>.
+
+=head3 C<PolyLib> format
+
+If the represented set is a union, then the first line
+contains a single number representing the number of disjuncts.
+Otherwise, a line containing the number C<1> is optional.
+
+Each disjunct is represented by a matrix of constraints.
+The first line contains two numbers representing
+the number of rows and columns,
+where the number of rows is equal to the number of constraints
+and the number of columns is equal to two plus the number of variables.
+The following lines contain the actual rows of the constraint matrix.
+In each row, the first column indicates whether the constraint
+is an equality (C<0>) or inequality (C<1>). The final column
+corresponds to the constant term.
+
+If the set is parametric, then the coefficients of the parameters
+appear in the last columns before the constant column.
+The coefficients of any existentially quantified variables appear
+between those of the set variables and those of the parameters.
=head3 Input
#include <isl_set.h>
__isl_give isl_basic_set *isl_basic_set_read_from_file(
- isl_ctx *ctx, FILE *input, unsigned nparam,
- unsigned input_format);
+ isl_ctx *ctx, FILE *input, int nparam);
__isl_give isl_basic_set *isl_basic_set_read_from_str(
- isl_ctx *ctx, const char *str, unsigned nparam,
- unsigned input_format);
+ isl_ctx *ctx, const char *str, int nparam);
__isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
- FILE *input, unsigned nparam,
- unsigned input_format);
+ FILE *input, int nparam);
+ __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
+ const char *str, int nparam);
#include <isl_map.h>
__isl_give isl_basic_map *isl_basic_map_read_from_file(
- isl_ctx *ctx, FILE *input, unsigned nparam,
- unsigned input_format);
-
-C<input_format> may be either C<ISL_FORMAT_POLYLIB> or
-C<ISL_FORMAT_OMEGA>. However, not all combination are currently
-supported. Furthermore, only a very limited subset of
-the C<Omega> input format is currently supported.
-In particular, C<isl_basic_set_read_from_str> and
-C<isl_basic_map_read_from_file> only
-support C<ISL_FORMAT_OMEGA>, while C<isl_set_read_from_file>
-only supports C<ISL_FORMAT_POLYLIB>.
+ isl_ctx *ctx, FILE *input, int nparam);
+ __isl_give isl_basic_map *isl_basic_map_read_from_str(
+ isl_ctx *ctx, const char *str, int nparam);
+ __isl_give isl_map *isl_map_read_from_file(
+ struct isl_ctx *ctx, FILE *input, int nparam);
+ __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
+ const char *str, int nparam);
+
+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
-the C<PolyLib> format correspond to parameters. It should
-be zero when C<ISL_FORMAT_OMEGA> is used.
+the C<PolyLib> format correspond to parameters.
+If input is given in the C<isl> format, then the number
+of parameters needs to be equal to C<nparam>.
+If C<nparam> is negative, then any number of parameters
+is accepted in the C<isl> format and zero parameters
+are assumed in the C<PolyLib> format.
=head3 Output
- #include <isl_set.h>
- void isl_basic_set_print(__isl_keep isl_basic_set *bset,
- FILE *out, int indent,
- const char *prefix, const char *suffix,
- unsigned output_format);
- void isl_set_print(__isl_keep struct isl_set *set,
- FILE *out, int indent, unsigned output_format);
-
-C<input_format> must be C<ISL_FORMAT_POLYLIB>.
-Each line in the output is indented by C<indent> spaces,
-prefixed by C<prefix> and suffixed by C<suffix>.
-The coefficients of the existentially quantified variables
+Before anything can be printed, an C<isl_printer> needs to
+be created.
+
+ __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
+ FILE *file);
+ __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
+ void isl_printer_free(__isl_take isl_printer *printer);
+ __isl_give char *isl_printer_get_str(
+ __isl_keep isl_printer *printer);
+
+The behavior of the printer can be modified in various ways
+
+ __isl_give isl_printer *isl_printer_set_output_format(
+ __isl_take isl_printer *p, int output_format);
+ __isl_give isl_printer *isl_printer_set_indent(
+ __isl_take isl_printer *p, int indent);
+ __isl_give isl_printer *isl_printer_set_prefix(
+ __isl_take isl_printer *p, const char *prefix);
+ __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>.
+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,
+the coefficients of the existentially quantified variables
appear between those of the set variables and those
of the parameters.
-=head3 Conversion from/to C<PolyLib>
+To actually print something, use
-The following functions are only available if C<isl> has
-been configured to use C<PolyLib>.
-
- #include <isl_set_polylib.h>
- __isl_give isl_basic_set *isl_basic_set_new_from_polylib(
- Polyhedron *P, __isl_take isl_dim *dim);
- Polyhedron *isl_basic_set_to_polylib(
+ #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_give isl_set *isl_set_new_from_polylib(Polyhedron *D,
- __isl_take isl_dim *dim);
- Polyhedron *isl_set_to_polylib(__isl_keep isl_set *set);
+ __isl_give isl_printer *isl_printer_print_set(
+ __isl_take isl_printer *printer,
+ __isl_keep isl_set *set);
- #include <isl_map_polylib.h>
- __isl_give isl_basic_map *isl_basic_map_new_from_polylib(
- Polyhedron *P, __isl_take isl_dim *dim);
- __isl_give isl_map *isl_map_new_from_polylib(Polyhedron *D,
- __isl_take isl_dim *dim);
- Polyhedron *isl_basic_map_to_polylib(
+ #include <isl_map.h>
+ __isl_give isl_printer *isl_printer_print_basic_map(
+ __isl_take isl_printer *printer,
__isl_keep isl_basic_map *bmap);
- Polyhedron *isl_map_to_polylib(__isl_keep isl_map *map);
+ __isl_give isl_printer *isl_printer_print_map(
+ __isl_take isl_printer *printer,
+ __isl_keep isl_map *map);
-=head3 Dumping the internal state
+ #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);
-For lack of proper output functions, the following functions
-can be used to dump the internal state of a set or relation.
-The user should not depend on the output format of these functions.
+ #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);
- void isl_basic_set_dump(__isl_keep isl_basic_set *bset,
- FILE *out, int indent);
- void isl_basic_map_dump(__isl_keep isl_basic_map *bmap,
- FILE *out, int indent);
- void isl_set_dump(__isl_keep isl_set *set,
- FILE *out, int indent);
- void isl_map_dump(__isl_keep isl_map *map,
- FILE *out, int indent);
+When called on a file printer, the following function flushes
+the file. When called on a string printer, the buffer is cleared.
+
+ __isl_give isl_printer *isl_printer_flush(
+ __isl_take isl_printer *p);
=head2 Creating New Sets and Relations
__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_take isl_dim *set_dim);
__isl_give isl_map *isl_map_lex_ge(
__isl_take isl_dim *set_dim);
-
-These functions take a dimension specification for a B<set>
+ __isl_give isl_map *isl_map_lex_lt_first(
+ __isl_take isl_dim *dim, unsigned n);
+ __isl_give isl_map *isl_map_lex_le_first(
+ __isl_take isl_dim *dim, unsigned n);
+ __isl_give isl_map *isl_map_lex_gt_first(
+ __isl_take isl_dim *dim, unsigned n);
+ __isl_give isl_map *isl_map_lex_ge_first(
+ __isl_take isl_dim *dim, unsigned n);
+
+The first four functions take a dimension specification for a B<set>
and return relations that express that the elements in the domain
-are lexicograhically less
+are lexicographically less
(C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
than the elements in the range.
+The last four functions take a dimension specification for a map
+and return relations that express that the first C<n> dimensions
+in the domain are lexicographically less
+(C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
+greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
+than the first C<n> dimensions in the range.
=back
__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_int_clear(v);
+Or, alternatively,
+
+ struct isl_basic_set *bset;
+ bset = isl_basic_set_read_from_str(ctx,
+ "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
+
+=head2 Inspecting Sets and Relations
+
+Usually, the user should not have to care about the actual constraints
+of the sets and maps, but should instead apply the abstract operations
+explained in the following sections.
+Occasionally, however, it may be required to inspect the individual
+coefficients of the constraints. This section explains how to do so.
+In these cases, it may also be useful to have C<isl> compute
+an explicit representation of the existentially quantified variables.
+
+ __isl_give isl_set *isl_set_compute_divs(
+ __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
+including earlier existentially quantified variables.
+An explicitly represented existentially quantified variable therefore
+has a unique value when the values of the other variables are known.
+If, furthermore, the same existentials, i.e., existentials
+with the same explicit representations, should appear in the
+same order in each of the disjuncts of a set or map, then the user should call
+either of the following functions.
+
+ __isl_give isl_set *isl_set_align_divs(
+ __isl_take isl_set *set);
+ __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,
+ int (*fn)(__isl_take isl_basic_set *bset, void *user),
+ void *user);
+ int isl_map_foreach_basic_map(__isl_keep isl_map *map,
+ int (*fn)(__isl_take isl_basic_map *bmap, void *user),
+ void *user);
+
+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.
+
+It should be noted that C<isl> does not guarantee that
+the basic sets or maps passed to C<fn> are disjoint.
+If this is required, then the user should call one of
+the following functions first.
+
+ __isl_give isl_set *isl_set_make_disjoint(
+ __isl_take isl_set *set);
+ __isl_give isl_map *isl_map_make_disjoint(
+ __isl_take isl_map *map);
+
+To iterate over the constraints of a basic set or map, use
+
+ #include <isl_constraint.h>
+
+ int isl_basic_map_foreach_constraint(
+ __isl_keep isl_basic_map *bmap,
+ int (*fn)(__isl_take isl_constraint *c, void *user),
+ void *user);
+ void isl_constraint_free(struct isl_constraint *c);
+
+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.
+
+ void isl_constraint_get_constant(
+ __isl_keep isl_constraint *constraint, isl_int *v);
+ void isl_constraint_get_coefficient(
+ __isl_keep isl_constraint *constraint,
+ enum isl_dim_type type, int pos, isl_int *v);
+
+The explicit representations of the existentially quantified
+variables can be inspected using the following functions.
+Note that the user is only allowed to use these functions
+if the inspected set or map is the result of a call
+to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
+
+ __isl_give isl_div *isl_constraint_div(
+ __isl_keep isl_constraint *constraint, int pos);
+ void isl_div_get_constant(__isl_keep isl_div *div,
+ isl_int *v);
+ void isl_div_get_denominator(__isl_keep isl_div *div,
+ isl_int *v);
+ void isl_div_get_coefficient(__isl_keep isl_div *div,
+ enum isl_dim_type type, int pos, isl_int *v);
+
=head2 Properties
=head3 Unary Properties
=over
-=item Emptiness
+=item * Emptiness
The following functions test whether the given set or relation
contains any integer points. The ``fast'' variants do not perform
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_set_is_universe(__isl_keep isl_basic_set *bset);
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
__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
=over
+=item * Complement
+
+ __isl_give isl_set *isl_set_complement(
+ __isl_take isl_set *set);
+
+=item * Inverse map
+
+ __isl_give isl_basic_map *isl_basic_map_reverse(
+ __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_give isl_basic_set *isl_basic_set_project_out(
__isl_take isl_basic_set *bset,
enum isl_dim_type type, unsigned first, unsigned n);
+ __isl_give isl_basic_map *isl_basic_map_project_out(
+ __isl_take isl_basic_map *bmap,
+ enum isl_dim_type type, unsigned first, unsigned n);
__isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
enum isl_dim_type type, unsigned first, unsigned n);
+ __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
+ enum isl_dim_type type, unsigned first, unsigned n);
__isl_give isl_basic_set *isl_basic_map_domain(
__isl_take isl_basic_map *bmap);
__isl_give isl_basic_set *isl_basic_map_range(
__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);
-C<isl_basic_set_project_out> currently only supports projecting
-out the final C<isl_dim_set> dimensions.
+=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
If the input set or relation has any existentially quantified
variables, then the result of these operations is currently undefined.
+=item * Simple hull
+
+ __isl_give isl_basic_set *isl_set_simple_hull(
+ __isl_take isl_set *set);
+ __isl_give isl_basic_map *isl_map_simple_hull(
+ __isl_take isl_map *map);
+
+These functions compute a single basic set or relation
+that contains the whole input set or relation.
+In particular, the output is described by translates
+of the constraints describing the basic sets or relations in the input.
+
+=begin latex
+
+(See \autoref{s:simple hull}.)
+
+=end latex
+
=item * Affine hull
__isl_give isl_basic_set *isl_basic_set_affine_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_power(__isl_take isl_map *map,
+ unsigned param, int *exact);
+
+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,
+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);
=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(
+ __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
=head3 Lexicographic Optimization
-Given a basic set C<bset> and a zero-dimensional domain C<dom>,
+Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
the following functions
compute a set that contains the lexicographic minimum or maximum
-of the elements in C<bset> for those values of the parameters
+of the elements in C<set> (or C<bset>) for those values of the parameters
that satisfy C<dom>.
If C<empty> is not C<NULL>, then C<*empty> is assigned a set
-that contains the parameter values in C<dom> for which C<bset>
+that contains the parameter values in C<dom> for which C<set> (or C<bset>)
has no elements.
In other words, the union of the parameter values
for which the result is non-empty and of C<*empty>
__isl_take isl_basic_set *bset,
__isl_take isl_basic_set *dom,
__isl_give isl_set **empty);
+ __isl_give isl_set *isl_set_partial_lexmin(
+ __isl_take isl_set *set, __isl_take isl_set *dom,
+ __isl_give isl_set **empty);
+ __isl_give isl_set *isl_set_partial_lexmax(
+ __isl_take isl_set *set, __isl_take isl_set *dom,
+ __isl_give isl_set **empty);
-Given a basic set C<bset>, the following functions simply
+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<bset>.
+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_give isl_set *isl_basic_set_lexmax(
__isl_take isl_basic_set *bset);
+ __isl_give isl_set *isl_set_lexmin(
+ __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<bmap> and a domain C<dom>,
+Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
the following functions
compute a relation that maps each element of C<dom>
to the single lexicographic minimum or maximum
of the elements that are associated to that same
-element in C<bmap>.
+element in C<map> (or C<bmap>).
If C<empty> is not C<NULL>, then C<*empty> is assigned a set
that contains the elements in C<dom> that do not map
-to any elements in C<bmap>.
+to any elements in C<map> (or C<bmap>).
In other words, the union of the domain of the result and of C<*empty>
is equal to C<dom>.
__isl_take isl_basic_map *bmap,
__isl_take isl_basic_set *dom,
__isl_give isl_set **empty);
+ __isl_give isl_map *isl_map_partial_lexmax(
+ __isl_take isl_map *map, __isl_take isl_set *dom,
+ __isl_give isl_set **empty);
+ __isl_give isl_map *isl_map_partial_lexmin(
+ __isl_take isl_map *map, __isl_take isl_set *dom,
+ __isl_give isl_set **empty);
-Given a basic map C<bmap>, the following function simply
-returns a map mapping each element in the domain of
-C<bmap> to the lexicographic minimum of all elements associated
-to that element.
+Given a (basic) map C<map> (or C<bmap>), the following functions simply
+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_give isl_map *isl_basic_map_lexmax(
+ __isl_take isl_basic_map *bmap);
+ __isl_give isl_map *isl_map_lexmin(
+ __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
+
+Points are elements of a set. They can be used to construct
+simple sets (boxes) or they can be used to represent the
+individual elements of a set.
+The zero point (the origin) can be created using
+
+ __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
+
+The coordinates of a point can be inspected, set and changed
+using
+
+ void isl_point_get_coordinate(__isl_keep isl_point *pnt,
+ enum isl_dim_type type, int pos, isl_int *v);
+ __isl_give isl_point *isl_point_set_coordinate(
+ __isl_take isl_point *pnt,
+ enum isl_dim_type type, int pos, isl_int v);
+
+ __isl_give isl_point *isl_point_add_ui(
+ __isl_take isl_point *pnt,
+ enum isl_dim_type type, int pos, unsigned val);
+ __isl_give isl_point *isl_point_sub_ui(
+ __isl_take isl_point *pnt,
+ enum isl_dim_type type, int pos, unsigned val);
+
+Points can be copied or freed using
+
+ __isl_give isl_point *isl_point_copy(
+ __isl_keep isl_point *pnt);
+ void isl_point_free(__isl_take isl_point *pnt);
+
+A singleton set can be created from a point using
+
+ __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_set *isl_set_box_from_points(
+ __isl_take isl_point *pnt1,
+ __isl_take isl_point *pnt2);
+
+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
+the C<isl_set_foreach_point> call. The function C<fn>
+should return C<0> on success and C<-1> on failure.
+In the latter case, C<isl_set_foreach_point> will stop
+enumerating and return C<-1> as well.
+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
+
+ __isl_give isl_point *isl_set_sample_point(
+ __isl_take isl_set *set);
+
+If C<set> does not contain any (integer) points, then the
+resulting point will be ``void'', a property that can be
+tested using
+
+ int isl_point_is_void(__isl_keep isl_point *pnt);
+
+=head2 Piecewise Quasipolynomials
+
+A piecewise quasipolynomial is a particular kind of function that maps
+a parametric point to a rational value.
+More specifically, a quasipolynomial is a polynomial expression in greatest
+integer parts of affine expressions of parameters and variables.
+A piecewise quasipolynomial is a subdivision of a given parametric
+domain into disjoint cells with a quasipolynomial associated to
+each cell. The value of the piecewise quasipolynomial at a given
+point is the value of the quasipolynomial associated to the cell
+that contains the point. Outside of the union of cells,
+the value is assumed to be zero.
+For example, the piecewise quasipolynomial
+
+ [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 points in the map
+
+ [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
+
+=head3 Printing (Piecewise) Quasipolynomials
+
+Quasipolynomials and piecewise quasipolynomials can be printed
+using the following functions.
+
+ __isl_give isl_printer *isl_printer_print_qpolynomial(
+ __isl_take isl_printer *p,
+ __isl_keep isl_qpolynomial *qp);
+
+ __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
+ __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
+
+Some simple quasipolynomials can be created using the following functions.
+More complicated quasipolynomials can be created by applying
+operations such as addition and multiplication
+on the resulting quasipolynomials
+
+ __isl_give isl_qpolynomial *isl_qpolynomial_zero(
+ __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_dim *dim,
+ const isl_int n, const isl_int d);
+ __isl_give isl_qpolynomial *isl_qpolynomial_div(
+ __isl_take isl_div *div);
+ __isl_give isl_qpolynomial *isl_qpolynomial_var(
+ __isl_take isl_dim *dim,
+ enum isl_dim_type type, unsigned pos);
+
+The zero piecewise quasipolynomial or a piecewise quasipolynomial
+with a single cell can be created using the following functions.
+Multiple of these single cell piecewise quasipolynomials can
+be combined to create more complicated piecewise quasipolynomials.
+
+ __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
+ __isl_take isl_dim *dim);
+ __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
+ __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.
+
+ __isl_give isl_qpolynomial *isl_qpolynomial_copy(
+ __isl_keep isl_qpolynomial *qp);
+ void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
+
+ __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
+ __isl_keep isl_pw_qpolynomial *pwqp);
+ 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
+
+ int isl_pw_qpolynomial_foreach_piece(
+ __isl_keep isl_pw_qpolynomial *pwqp,
+ int (*fn)(__isl_take isl_set *set,
+ __isl_take isl_qpolynomial *qp,
+ void *user), void *user);
+ int isl_pw_qpolynomial_foreach_lifted_piece(
+ __isl_keep isl_pw_qpolynomial *pwqp,
+ int (*fn)(__isl_take isl_set *set,
+ __isl_take isl_qpolynomial *qp,
+ void *user), void *user);
+
+As usual, the function C<fn> should return C<0> on success
+and C<-1> on failure. The difference between
+C<isl_pw_qpolynomial_foreach_piece> and
+C<isl_pw_qpolynomial_foreach_lifted_piece> is that
+C<isl_pw_qpolynomial_foreach_lifted_piece> will first
+compute unique representations for all existentially quantified
+variables and then turn these existentially quantified variables
+into extra set variables, adapting the associated quasipolynomial
+accordingly. This means that the C<set> passed to C<fn>
+will not have any existentially quantified variables, but that
+the dimensions of the sets may be different for different
+invocations of C<fn>.
+
+To iterate over all terms in a quasipolynomial,
+use
+
+ int isl_qpolynomial_foreach_term(
+ __isl_keep isl_qpolynomial *qp,
+ int (*fn)(__isl_take isl_term *term,
+ void *user), void *user);
+
+The terms themselves can be inspected and freed using
+these functions
+
+ unsigned isl_term_dim(__isl_keep isl_term *term,
+ enum isl_dim_type type);
+ void isl_term_get_num(__isl_keep isl_term *term,
+ isl_int *n);
+ void isl_term_get_den(__isl_keep isl_term *term,
+ isl_int *d);
+ int isl_term_get_exp(__isl_keep isl_term *term,
+ enum isl_dim_type type, unsigned pos);
+ __isl_give isl_div *isl_term_get_div(
+ __isl_keep isl_term *term, unsigned pos);
+ void isl_term_free(__isl_take isl_term *term);
+
+Each term is a product of parameters, set variables and
+integer divisions. The function C<isl_term_get_exp>
+returns the exponent of a given dimensions in the given term.
+The C<isl_int>s in the arguments of C<isl_term_get_num>
+and C<isl_term_get_den> need to have been initialized
+using C<isl_int_init> before calling these functions.
+
+=head3 Properties of (Piecewise) Quasipolynomials
+
+To check whether a quasipolynomial is actually a constant,
+use the following function.
+
+ int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
+ isl_int *n, isl_int *d);
+
+If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
+then the numerator and denominator of the constant
+are returned in C<*n> and C<*d>, respectively.
+
+=head3 Operations on (Piecewise) Quasipolynomials
+
+ __isl_give isl_qpolynomial *isl_qpolynomial_neg(
+ __isl_take isl_qpolynomial *qp);
+ __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_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
+ __isl_take isl_pw_qpolynomial *pwqp1,
+ __isl_take isl_pw_qpolynomial *pwqp2);
+ __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
+ __isl_take isl_pw_qpolynomial *pwqp1,
+ __isl_take isl_pw_qpolynomial *pwqp2);
+ __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
+ __isl_take isl_pw_qpolynomial *pwqp1,
+ __isl_take isl_pw_qpolynomial *pwqp2);
+ __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
+ __isl_take isl_pw_qpolynomial *pwqp);
+ __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
+ __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
+array dataflow analysis. That is, given a I<sink> access relation
+and a collection of possible I<source> access relations,
+C<isl> can compute relations that describe
+for each iteration of the sink access, which iteration
+of which of the source access relations was the last
+to access the same data element before the given iteration
+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>
+
+ __isl_give isl_access_info *isl_access_info_alloc(
+ __isl_take isl_map *sink,
+ void *sink_user, isl_access_level_before fn,
+ int max_source);
+ __isl_give isl_access_info *isl_access_info_add_source(
+ __isl_take isl_access_info *acc,
+ __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, int must,
+ void *dep_user, void *user),
+ void *user);
+ __isl_give isl_set *isl_flow_get_no_source(
+ __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
+dependence analysis. The other functions are used to construct
+the input for this function or to read off the output.
+
+The input is collected in an C<isl_access_info>, which can
+be created through a call to C<isl_access_info_alloc>.
+The arguments to this functions are the sink access relation
+C<sink>, a token C<sink_user> used to identify the sink
+access to the user, a callback function for specifying the
+relative order of source and sink accesses, and the number
+of source access relations that will be added.
+The callback function has type C<int (*)(void *first, void *second)>.
+The function is called with two user supplied tokens identifying
+either a source or the sink and it should return the shared nesting
+level and the relative order of the two accesses.
+In particular, let I<n> be the number of loops shared by
+the two accesses. If C<first> precedes C<second> textually,
+then the function should return I<2 * n + 1>; otherwise,
+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
+of the sink access relation.
+
+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
+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,
+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 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,
it also contains some basic applications that use some
of the functionality of C<isl>.
-Since C<isl> does not have its own input format yet, these
-applications currently take input in C<PolyLib> style.
-That is, a line with the number of rows and columns,
-where the number of rows is equal to the number of constraints
-and the number of columns is equal to two plus the number of variables,
-followed by the actual rows.
-In each row, the first column indicates whether the constraint
-is an equality (C<0>) or inequality (C<1>). The final column
-corresponds to the constant term.
+The input may be specified in either the L<isl format>
+or the L<PolyLib format>.
=head2 C<isl_polyhedron_sample>
-C<isl_polyhedron_sample>
-takes a polyhedron in C<PolyLib> format as input and prints
+C<isl_polyhedron_sample> takes a polyhedron as input and prints
an integer element of the polyhedron, if there is any.
The first column in the output is the denominator and is always
equal to 1. If the polyhedron contains no integer points,
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 in C<PolyLib> format,
-a line contains only -1 and finally a set
-of constraints on a parametric polyhedron, again in C<PolyLib> format.
+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).
The output is the lexicographic minimum of the parametric polyhedron.
C<isl_polyhedron_minimize> computes the minimum of some linear
or affine objective function over the integer points in a polyhedron.
-The input is in C<PolyLib> format. If an affine objective function
+If an affine objective function
is given, then the constant should appear in the last column.
=head2 C<isl_polytope_scan>
-Given a polytope in C<PolyLib> format, C<isl_polytope_scan> prints
+Given a polytope, C<isl_polytope_scan> prints
all integer points in the polytope.
+
+=head1 C<isl-polylib>
+
+The C<isl-polylib> library provides the following functions for converting
+between C<isl> objects and C<PolyLib> objects.
+The library is distributed separately for licensing reasons.
+
+ #include <isl_set_polylib.h>
+ __isl_give isl_basic_set *isl_basic_set_new_from_polylib(
+ Polyhedron *P, __isl_take isl_dim *dim);
+ Polyhedron *isl_basic_set_to_polylib(
+ __isl_keep isl_basic_set *bset);
+ __isl_give isl_set *isl_set_new_from_polylib(Polyhedron *D,
+ __isl_take isl_dim *dim);
+ Polyhedron *isl_set_to_polylib(__isl_keep isl_set *set);
+
+ #include <isl_map_polylib.h>
+ __isl_give isl_basic_map *isl_basic_map_new_from_polylib(
+ Polyhedron *P, __isl_take isl_dim *dim);
+ __isl_give isl_map *isl_map_new_from_polylib(Polyhedron *D,
+ __isl_take isl_dim *dim);
+ Polyhedron *isl_basic_map_to_polylib(
+ __isl_keep isl_basic_map *bmap);
+ Polyhedron *isl_map_to_polylib(__isl_keep isl_map *map);
projects / platform / upstream / isl.git / blobdiff