isl is a thread-safe C library for manipulating
sets and relations of integer points bounded by affine constraints.
The descriptions of the sets and relations may involve
both parameters and existentially quantified variables.
All computations are performed in exact integer arithmetic
using GMP.
The isl library offers functionality that is similar
to that offered by the Omega and Omega+ libraries,
but the underlying algorithms are in most cases completely different.
The library is by no means complete and some fairly basic
functionality is still missing.
Still, even in its current form, the library has been successfully
used as a backend polyhedral library for the polyhedral
scanner 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
http://groups.google.com/group/isl-development.
isl_printer functions, see Input and Output.
must argument. To obtain the old behavior, this argument
should be given the value 1. See Dependence Analysis.
isl_printer_print_basic_set and
isl_printer_print_basic_map no longer print a newline.
isl_flow_get_no_source
and isl_union_map_compute_flow now return
the accesses for which no source could be found instead of
the iterations where those accesses occur.
isl_basic_map_identity and
isl_map_identity now take a map space as input. An old call
isl_map_identity(space) can be rewritten to
isl_map_identity(isl_space_map_from_set(space)).
isl_map_power no longer takes
a parameter position as input. Instead, the exponent
is now expressed as the domain of the resulting relation.
isl_printer_print_qpolynomial's
ISL_FORMAT_ISL output has changed.
Use ISL_FORMAT_C to obtain the old output.
*_fast_* functions have been renamed to *_plain_*.
Some of the old names have been kept for backward compatibility,
but they will be removed in the future.
isl_pw_aff_max has been renamed to
isl_pw_aff_union_max.
Similarly, the function isl_pw_aff_add has been renamed to
isl_pw_aff_union_add.
isl_dim type has been renamed to isl_space
along with the associated functions.
Some of the old names have been kept for backward compatibility,
but they will be removed in the future.
isl_space_params_alloc or from other spaces using
isl_space_params.
isl_aff, isl_pw_aff, isl_qpolynomial,
isl_pw_qpolynomial, isl_qpolynomial_fold and isl_pw_qpolynomial_fold
objects live is now a map space
instead of a set space. This means, for example, that the dimensions
of the domain of an isl_aff are now considered to be of type
isl_dim_in instead of isl_dim_set. Extra functions have been
added to obtain the domain space. Some of the constructors still
take a domain space and have therefore been renamed.
isl_equality_alloc and isl_inequality_alloc
now take an isl_local_space instead of an isl_space.
An isl_local_space can be created from an isl_space
using isl_local_space_from_space.
isl_div type has been removed. Functions that used
to return an isl_div now return an isl_aff.
Note that the space of an isl_aff is that of relation.
When replacing a call to isl_div_get_coefficient by a call to
isl_aff_get_coefficient any isl_dim_set argument needs
to be replaced by isl_dim_in.
A call to isl_aff_from_div can be replaced by a call
to isl_aff_floor.
A call to isl_qpolynomial_div(div) call be replaced by
the nested call
isl_qpolynomial_from_aff(isl_aff_floor(div))
The function isl_constraint_div has also been renamed
to isl_constraint_get_div.
nparam argument has been removed from
isl_map_read_from_str and similar functions.
When reading input in the original PolyLib format,
the result will have no parameters.
If parameters are expected, the caller may want to perform
dimension manipulation on the result.
schedule_split_parallel option has been replaced
by the schedule_split_scaled option.
isl_pw_aff_cond is now
an isl_pw_aff instead of an isl_set.
A call isl_pw_aff_cond(a, b, c) can be replaced by
isl_pw_aff_cond(isl_set_indicator_function(a), b, c)
isl_int has been replaced by isl_val.
Some of the old functions are still available in isl/deprecated/*.h
but they will be removed in the future.
isl_pw_qpolynomial_eval,
isl_union_pw_qpolynomial_eval, isl_pw_qpolynomial_fold_eval
and isl_union_pw_qpolynomial_fold_eval have been changed to return
an isl_val instead of an isl_qpolynomial.
isl is released under the MIT license.
Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
Note that isl currently requires GMP, which is released
under the GNU Lesser General Public License (LGPL). This means
that code linked against isl is also linked against LGPL code.
The source of isl can be obtained either as a tarball
or from the git repository. Both are available from
http://freshmeat.net/projects/isl/.
The installation process depends on how you obtained
the source.
The first time the source is obtained, you need to clone the repository.
git clone git://repo.or.cz/isl.git
To obtain updates, you need to pull in the latest changes
git pull
configure
./autogen.sh
After performing the above steps, continue with the Common installation instructions.
GMP
Building isl requires GMP, including its headers files.
Your distribution may not provide these header files by default
and you may need to install a package called gmp-devel or something
similar. Alternatively, GMP can be built from
source, available from http://gmplib.org/.
isl uses the standard autoconf configure script.
To run it, just type
./configure
optionally followed by some configure options. A complete list of options can be obtained by running
./configure --help
Below we discuss some of the more common options.
--prefixInstallation prefix for isl
--with-gmp-prefixInstallation prefix for GMP (architecture-independent files).
--with-gmp-exec-prefixInstallation prefix for GMP (architecture-dependent files).
make
make install
All manipulations of integer sets and relations occur within
the context of an isl_ctx.
A given isl_ctx can only be used within a single thread.
All arguments of a function are required to have been allocated
within the same context.
There are currently no functions available for moving an object
from one isl_ctx to another isl_ctx. This means that
there is currently no way of safely moving an object from one
thread to another, unless the whole isl_ctx is moved.
An isl_ctx can be allocated using isl_ctx_alloc and
freed using isl_ctx_free.
All objects allocated within an isl_ctx should be freed
before the isl_ctx itself is freed.
isl_ctx *isl_ctx_alloc();
void isl_ctx_free(isl_ctx *ctx);
An isl_val represents an integer value, a rational value
or one of three special values, infinity, negative infinity and NaN.
Some predefined values can be created using the following functions.
#include <isl/val.h>
__isl_give isl_val *isl_val_zero(isl_ctx *ctx);
__isl_give isl_val *isl_val_one(isl_ctx *ctx);
__isl_give isl_val *isl_val_nan(isl_ctx *ctx);
__isl_give isl_val *isl_val_infty(isl_ctx *ctx);
__isl_give isl_val *isl_val_neginfty(isl_ctx *ctx);
Specific integer values can be created using the following functions.
#include <isl/val.h>
__isl_give isl_val *isl_val_int_from_si(isl_ctx *ctx,
long i);
__isl_give isl_val *isl_val_int_from_ui(isl_ctx *ctx,
unsigned long u);
__isl_give isl_val *isl_val_int_from_chunks(isl_ctx *ctx,
size_t n, size_t size, const void *chunks);
The function isl_val_int_from_chunks constructs an isl_val
from the n digits, each consisting of size bytes, stored at chunks.
The least significant digit is assumed to be stored first.
Value objects can be copied and freed using the following functions.
#include <isl/val.h>
__isl_give isl_val *isl_val_copy(__isl_keep isl_val *v);
void *isl_val_free(__isl_take isl_val *v);
They can be inspected using the following functions.
#include <isl/val.h>
isl_ctx *isl_val_get_ctx(__isl_keep isl_val *val);
long isl_val_get_num_si(__isl_keep isl_val *v);
long isl_val_get_den_si(__isl_keep isl_val *v);
double isl_val_get_d(__isl_keep isl_val *v);
size_t isl_val_n_abs_num_chunks(__isl_keep isl_val *v,
size_t size);
int isl_val_get_abs_num_chunks(__isl_keep isl_val *v,
size_t size, void *chunks);
isl_val_n_abs_num_chunks returns the number of digits
of size bytes needed to store the absolute value of the
numerator of v.
isl_val_get_abs_num_chunks stores these digits at chunks,
which is assumed to have been preallocated by the caller.
The least significant digit is stored first.
Note that isl_val_get_num_si, isl_val_get_den_si,
isl_val_get_d, isl_val_n_abs_num_chunks
and isl_val_get_abs_num_chunks can only be applied to rational values.
An isl_val can be modified using the following function.
#include <isl/val.h>
__isl_give isl_val *isl_val_set_si(__isl_take isl_val *v,
long i);
The following unary properties are defined on isl_vals.
#include <isl/val.h>
int isl_val_sgn(__isl_keep isl_val *v);
int isl_val_is_zero(__isl_keep isl_val *v);
int isl_val_is_one(__isl_keep isl_val *v);
int isl_val_is_negone(__isl_keep isl_val *v);
int isl_val_is_nonneg(__isl_keep isl_val *v);
int isl_val_is_nonpos(__isl_keep isl_val *v);
int isl_val_is_pos(__isl_keep isl_val *v);
int isl_val_is_neg(__isl_keep isl_val *v);
int isl_val_is_int(__isl_keep isl_val *v);
int isl_val_is_rat(__isl_keep isl_val *v);
int isl_val_is_nan(__isl_keep isl_val *v);
int isl_val_is_infty(__isl_keep isl_val *v);
int isl_val_is_neginfty(__isl_keep isl_val *v);
Note that the sign of NaN is undefined.
The following binary properties are defined on pairs of isl_vals.
#include <isl/val.h>
int isl_val_lt(__isl_keep isl_val *v1,
__isl_keep isl_val *v2);
int isl_val_le(__isl_keep isl_val *v1,
__isl_keep isl_val *v2);
int isl_val_gt(__isl_keep isl_val *v1,
__isl_keep isl_val *v2);
int isl_val_ge(__isl_keep isl_val *v1,
__isl_keep isl_val *v2);
int isl_val_eq(__isl_keep isl_val *v1,
__isl_keep isl_val *v2);
int isl_val_ne(__isl_keep isl_val *v1,
__isl_keep isl_val *v2);
For integer isl_vals we additionally have the following binary property.
#include <isl/val.h>
int isl_val_is_divisible_by(__isl_keep isl_val *v1,
__isl_keep isl_val *v2);
An isl_val can also be compared to an integer using the following
function. The result is undefined for NaN.
#include <isl/val.h>
int isl_val_cmp_si(__isl_keep isl_val *v, long i);
The following unary operations are available on isl_vals.
#include <isl/val.h>
__isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
__isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
__isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
__isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
__isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
The following binary operations are available on isl_vals.
#include <isl/val.h>
__isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
__isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
__isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
__isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
__isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
__isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
__isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
__isl_take isl_val *v2);
__isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
__isl_take isl_val *v2);
__isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
__isl_take isl_val *v2);
__isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
unsigned long v2);
__isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
__isl_take isl_val *v2);
__isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
unsigned long v2);
__isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
__isl_take isl_val *v2);
__isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
unsigned long v2);
__isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
__isl_take isl_val *v2);
On integer values, we additionally have the following operations.
#include <isl/val.h>
__isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
__isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
__isl_take isl_val *v2);
__isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
__isl_take isl_val *v2);
__isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
__isl_take isl_val *v2, __isl_give isl_val **x,
__isl_give isl_val **y);
The function isl_val_gcdext returns the greatest common divisor g
of v1 and v2 as well as two integers *x and *y such
that *x * v1 + *y * v2 = g.
A value can be read from input using
#include <isl/val.h>
__isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
const char *str);
A value can be printed using
#include <isl/val.h>
__isl_give isl_printer *isl_printer_print_val(
__isl_take isl_printer *p, __isl_keep isl_val *v);
These functions are only available if isl has been compiled with GMP
support.
Specific integer and rational values can be created from GMP values using
the following functions.
#include <isl/val_gmp.h>
__isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
mpz_t z);
__isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
const mpz_t n, const mpz_t d);
The numerator and denominator of a rational value can be extracted as
GMP values using the following functions.
#include <isl/val_gmp.h>
int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
isl uses six types of objects for representing sets and relations,
isl_basic_set, isl_basic_map, isl_set, isl_map,
isl_union_set and isl_union_map.
isl_basic_set and isl_basic_map represent sets and relations that
can be described as a conjunction of affine constraints, while
isl_set and isl_map represent unions of
isl_basic_sets and isl_basic_maps, respectively.
However, all isl_basic_sets or isl_basic_maps in the union need
to live in the same space. isl_union_sets and isl_union_maps
represent unions of isl_sets or isl_maps in different spaces,
where spaces are considered different if they have a different number
of dimensions and/or different names (see Spaces).
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.
Since a high-level operation on sets and/or relations usually involves several substeps and since the user is usually not interested in the intermediate results, most functions that return a new object will also release all the objects passed as arguments. 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 making sure that the original object gets used somewhere else or is explicitly freed.
The arguments and return values of all documented functions are annotated to make clear which arguments are released and which arguments are preserved. In particular, the following annotations are used
__isl_give__isl_give means that a new object is returned.
The user should make sure that the returned pointer is
used exactly once as a value for an __isl_take argument.
In between, it can be used as a value for as many
__isl_keep arguments as the user likes.
There is one exception, and that is the case where the
pointer returned is NULL. Is this case, the user
is free to use it as an __isl_take argument or not.
__isl_take__isl_take means that the object the argument points to
is taken over by the function and may no longer be used
by the user as an argument to any other function.
The pointer value must be one returned by a function
returning an __isl_give pointer.
If the user passes in a NULL value, then this will
be treated as an error in the sense that the function will
not perform its usual operation. However, it will still
make sure that all the other __isl_take arguments
are released.
__isl_keep__isl_keep means that the function will only use the object
temporarily. After the function has finished, the user
can still use it as an argument to other functions.
A NULL value will be treated in the same way as
a NULL value for an __isl_take argument.
isl supports different ways to react in case a runtime error is triggered.
Runtime errors arise, e.g., if a function such as isl_map_intersect is called
with two maps that have incompatible spaces. There are three possible ways
to react on error: to warn, to continue or to abort.
The default behavior is to warn. In this mode, isl prints a warning, stores
the last error in the corresponding isl_ctx and the function in which the
error was triggered returns NULL. An error does not corrupt internal state,
such that isl can continue to be used. isl also provides functions to
read the last error and to reset the memory that stores the last error. The
last error is only stored for information purposes. Its presence does not
change the behavior of isl. Hence, resetting an error is not required to
continue to use isl, but only to observe new errors.
#include <isl/ctx.h>
enum isl_error isl_ctx_last_error(isl_ctx *ctx);
void isl_ctx_reset_error(isl_ctx *ctx);
Another option is to continue on error. This is similar to warn on error mode,
except that isl does not print any warning. This allows a program to
implement its own error reporting.
The last option is to directly abort the execution of the program from within the isl library. This makes it obviously impossible to recover from an error, but it allows to directly spot the error location. By aborting on error, debuggers break at the location the error occurred and can provide a stack trace. Other tools that automatically provide stack traces on abort or that do not want to continue execution after an error was triggered may also prefer to abort on error.
The on error behavior of isl can be specified by calling
isl_options_set_on_error or by setting the command line option
--isl-on-error. Valid arguments for the function call are
ISL_ON_ERROR_WARN, ISL_ON_ERROR_CONTINUE and ISL_ON_ERROR_ABORT. The
choices for the command line option are warn, continue and abort.
It is also possible to query the current error mode.
#include <isl/options.h>
int isl_options_set_on_error(isl_ctx *ctx, int val);
int isl_options_get_on_error(isl_ctx *ctx);
Identifiers are used to identify both individual dimensions
and tuples of dimensions. They consist of an optional name and an optional
user pointer. The name and the user pointer cannot both be NULL, however.
Identifiers with the same name but different pointer values
are considered to be distinct.
Similarly, identifiers with different names but the same pointer value
are also considered to be distinct.
Equal identifiers are represented using the same object.
Pairs of identifiers can therefore be tested for equality using the
== operator.
Identifiers can be constructed, copied, freed, inspected and printed
using the following functions.
#include <isl/id.h>
__isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
__isl_keep const char *name, void *user);
__isl_give isl_id *isl_id_set_free_user(
__isl_take isl_id *id,
__isl_give void (*free_user)(void *user));
__isl_give isl_id *isl_id_copy(isl_id *id);
void *isl_id_free(__isl_take isl_id *id);
isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
void *isl_id_get_user(__isl_keep isl_id *id);
__isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
__isl_give isl_printer *isl_printer_print_id(
__isl_take isl_printer *p, __isl_keep isl_id *id);
The callback set by isl_id_set_free_user is called on the user
pointer when the last reference to the isl_id is freed.
Note that isl_id_get_name returns a pointer to some internal
data structure, so the result can only be used while the
corresponding isl_id is alive.
Whenever a new set, relation or similiar object is created from scratch,
the space in which it lives needs to be specified using an isl_space.
Each space involves zero or more parameters and zero, one or two
tuples of set or input/output dimensions. The parameters and dimensions
are identified by an isl_dim_type and a position.
The type isl_dim_param refers to parameters,
the type isl_dim_set refers to set dimensions (for spaces
with a single tuple of dimensions) and the types isl_dim_in
and isl_dim_out refer to input and output dimensions
(for spaces with two tuples of dimensions).
Local spaces (see Local Spaces) also contain dimensions
of type isl_dim_div.
Note that parameters are only identified by their position within
a given object. Across different objects, parameters are (usually)
identified by their names or identifiers. Only unnamed parameters
are identified by their positions across objects. The use of unnamed
parameters is discouraged.
#include <isl/space.h>
__isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
unsigned nparam, unsigned n_in, unsigned n_out);
__isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
unsigned nparam);
__isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
unsigned nparam, unsigned dim);
__isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
void *isl_space_free(__isl_take isl_space *space);
unsigned isl_space_dim(__isl_keep isl_space *space,
enum isl_dim_type type);
The space used for creating a parameter domain
needs to be created using isl_space_params_alloc.
For other sets, the space
needs to be created using isl_space_set_alloc, while
for a relation, the space
needs to be created using isl_space_alloc.
isl_space_dim can be used
to find out the number of dimensions of each type in
a space, where type may be
isl_dim_param, isl_dim_in (only for relations),
isl_dim_out (only for relations), isl_dim_set
(only for sets) or isl_dim_all.
To check whether a given space is that of a set or a map or whether it is a parameter space, use these functions:
#include <isl/space.h>
int isl_space_is_params(__isl_keep isl_space *space);
int isl_space_is_set(__isl_keep isl_space *space);
int isl_space_is_map(__isl_keep isl_space *space);
Spaces can be compared using the following functions:
#include <isl/space.h>
int isl_space_is_equal(__isl_keep isl_space *space1,
__isl_keep isl_space *space2);
int isl_space_is_domain(__isl_keep isl_space *space1,
__isl_keep isl_space *space2);
int isl_space_is_range(__isl_keep isl_space *space1,
__isl_keep isl_space *space2);
isl_space_is_domain checks whether the first argument is equal
to the domain of the second argument. This requires in particular that
the first argument is a set space and that the second argument
is a map space.
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 Creating New Sets and Relations or Creating New (Piecewise) Quasipolynomials) based on the space of the original object.
#include <isl/set.h>
__isl_give isl_space *isl_basic_set_get_space(
__isl_keep isl_basic_set *bset);
__isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
#include <isl/union_set.h>
__isl_give isl_space *isl_union_set_get_space(
__isl_keep isl_union_set *uset);
#include <isl/map.h>
__isl_give isl_space *isl_basic_map_get_space(
__isl_keep isl_basic_map *bmap);
__isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
#include <isl/union_map.h>
__isl_give isl_space *isl_union_map_get_space(
__isl_keep isl_union_map *umap);
#include <isl/constraint.h>
__isl_give isl_space *isl_constraint_get_space(
__isl_keep isl_constraint *constraint);
#include <isl/polynomial.h>
__isl_give isl_space *isl_qpolynomial_get_domain_space(
__isl_keep isl_qpolynomial *qp);
__isl_give isl_space *isl_qpolynomial_get_space(
__isl_keep isl_qpolynomial *qp);
__isl_give isl_space *isl_qpolynomial_fold_get_space(
__isl_keep isl_qpolynomial_fold *fold);
__isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
__isl_keep isl_pw_qpolynomial *pwqp);
__isl_give isl_space *isl_pw_qpolynomial_get_space(
__isl_keep isl_pw_qpolynomial *pwqp);
__isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
__isl_keep isl_pw_qpolynomial_fold *pwf);
__isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
__isl_keep isl_pw_qpolynomial_fold *pwf);
__isl_give isl_space *isl_union_pw_qpolynomial_get_space(
__isl_keep isl_union_pw_qpolynomial *upwqp);
__isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
__isl_keep isl_union_pw_qpolynomial_fold *upwf);
#include <isl/val.h>
__isl_give isl_space *isl_multi_val_get_space(
__isl_keep isl_multi_val *mv);
#include <isl/aff.h>
__isl_give isl_space *isl_aff_get_domain_space(
__isl_keep isl_aff *aff);
__isl_give isl_space *isl_aff_get_space(
__isl_keep isl_aff *aff);
__isl_give isl_space *isl_pw_aff_get_domain_space(
__isl_keep isl_pw_aff *pwaff);
__isl_give isl_space *isl_pw_aff_get_space(
__isl_keep isl_pw_aff *pwaff);
__isl_give isl_space *isl_multi_aff_get_domain_space(
__isl_keep isl_multi_aff *maff);
__isl_give isl_space *isl_multi_aff_get_space(
__isl_keep isl_multi_aff *maff);
__isl_give isl_space *isl_pw_multi_aff_get_domain_space(
__isl_keep isl_pw_multi_aff *pma);
__isl_give isl_space *isl_pw_multi_aff_get_space(
__isl_keep isl_pw_multi_aff *pma);
__isl_give isl_space *isl_union_pw_multi_aff_get_space(
__isl_keep isl_union_pw_multi_aff *upma);
__isl_give isl_space *isl_multi_pw_aff_get_domain_space(
__isl_keep isl_multi_pw_aff *mpa);
__isl_give isl_space *isl_multi_pw_aff_get_space(
__isl_keep isl_multi_pw_aff *mpa);
#include <isl/point.h>
__isl_give isl_space *isl_point_get_space(
__isl_keep isl_point *pnt);
The identifiers or names of the individual dimensions may be set or read off using the following functions.
#include <isl/space.h>
__isl_give isl_space *isl_space_set_dim_id(
__isl_take isl_space *space,
enum isl_dim_type type, unsigned pos,
__isl_take isl_id *id);
int isl_space_has_dim_id(__isl_keep isl_space *space,
enum isl_dim_type type, unsigned pos);
__isl_give isl_id *isl_space_get_dim_id(
__isl_keep isl_space *space,
enum isl_dim_type type, unsigned pos);
__isl_give isl_space *isl_space_set_dim_name(
__isl_take isl_space *space,
enum isl_dim_type type, unsigned pos,
__isl_keep const char *name);
int isl_space_has_dim_name(__isl_keep isl_space *space,
enum isl_dim_type type, unsigned pos);
__isl_keep const char *isl_space_get_dim_name(
__isl_keep isl_space *space,
enum isl_dim_type type, unsigned pos);
Note that isl_space_get_name returns a pointer to some internal
data structure, so the result can only be used while the
corresponding isl_space 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.
Pairs of isl_set, isl_map, isl_union_set and/or 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.
Given the identifier or name of a dimension (typically a parameter), its position can be obtained from the following function.
#include <isl/space.h>
int isl_space_find_dim_by_id(__isl_keep isl_space *space,
enum isl_dim_type type, __isl_keep isl_id *id);
int isl_space_find_dim_by_name(__isl_keep isl_space *space,
enum isl_dim_type type, const char *name);
The identifiers or names of entire spaces may be set or read off using the following functions.
#include <isl/space.h>
__isl_give isl_space *isl_space_set_tuple_id(
__isl_take isl_space *space,
enum isl_dim_type type, __isl_take isl_id *id);
__isl_give isl_space *isl_space_reset_tuple_id(
__isl_take isl_space *space, enum isl_dim_type type);
int isl_space_has_tuple_id(__isl_keep isl_space *space,
enum isl_dim_type type);
__isl_give isl_id *isl_space_get_tuple_id(
__isl_keep isl_space *space, enum isl_dim_type type);
__isl_give isl_space *isl_space_set_tuple_name(
__isl_take isl_space *space,
enum isl_dim_type type, const char *s);
int isl_space_has_tuple_name(__isl_keep isl_space *space,
enum isl_dim_type type);
const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
enum isl_dim_type type);
The type argument needs to be one of isl_dim_in, isl_dim_out
or isl_dim_set. As with isl_space_get_name,
the isl_space_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 spaces.
#include <isl/space.h>
int isl_space_is_wrapping(__isl_keep isl_space *space);
__isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
__isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
The input to isl_space_is_wrapping and isl_space_unwrap should
be the space of a set, while that of
isl_space_wrap should be the space of a relation.
Conversely, the output of isl_space_unwrap is the space
of a relation, while that of isl_space_wrap is the space of a set.
Spaces can be created from other spaces using the following functions.
__isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
__isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
__isl_give isl_space *isl_space_range(__isl_take isl_space *space);
__isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
__isl_give isl_space *isl_space_domain_map(
__isl_take isl_space *space);
__isl_give isl_space *isl_space_range_map(
__isl_take isl_space *space);
__isl_give isl_space *isl_space_params(
__isl_take isl_space *space);
__isl_give isl_space *isl_space_set_from_params(
__isl_take isl_space *space);
__isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
__isl_give isl_space *isl_space_join(__isl_take isl_space *left,
__isl_take isl_space *right);
__isl_give isl_space *isl_space_align_params(
__isl_take isl_space *space1, __isl_take isl_space *space2)
__isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
enum isl_dim_type type, unsigned pos, unsigned n);
__isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
enum isl_dim_type type, unsigned n);
__isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
enum isl_dim_type type, unsigned first, unsigned n);
__isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
enum isl_dim_type dst_type, unsigned dst_pos,
enum isl_dim_type src_type, unsigned src_pos,
unsigned n);
__isl_give isl_space *isl_space_map_from_set(
__isl_take isl_space *space);
__isl_give isl_space *isl_space_map_from_domain_and_range(
__isl_take isl_space *domain,
__isl_take isl_space *range);
__isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
__isl_give isl_space *isl_space_curry(
__isl_take isl_space *space);
__isl_give isl_space *isl_space_uncurry(
__isl_take isl_space *space);
Note that if dimensions are added or removed from a space, then the name and the internal structure are lost.
A local space is essentially a space with zero or more existentially quantified variables. The local space of a (constraint of a) basic set or relation can be obtained using the following functions.
#include <isl/constraint.h>
__isl_give isl_local_space *isl_constraint_get_local_space(
__isl_keep isl_constraint *constraint);
#include <isl/set.h>
__isl_give isl_local_space *isl_basic_set_get_local_space(
__isl_keep isl_basic_set *bset);
#include <isl/map.h>
__isl_give isl_local_space *isl_basic_map_get_local_space(
__isl_keep isl_basic_map *bmap);
A new local space can be created from a space using
#include <isl/local_space.h>
__isl_give isl_local_space *isl_local_space_from_space(
__isl_take isl_space *space);
They can be inspected, modified, copied and freed using the following functions.
#include <isl/local_space.h>
isl_ctx *isl_local_space_get_ctx(
__isl_keep isl_local_space *ls);
int isl_local_space_is_set(__isl_keep isl_local_space *ls);
int isl_local_space_dim(__isl_keep isl_local_space *ls,
enum isl_dim_type type);
int isl_local_space_has_dim_id(
__isl_keep isl_local_space *ls,
enum isl_dim_type type, unsigned pos);
__isl_give isl_id *isl_local_space_get_dim_id(
__isl_keep isl_local_space *ls,
enum isl_dim_type type, unsigned pos);
int isl_local_space_has_dim_name(
__isl_keep isl_local_space *ls,
enum isl_dim_type type, unsigned pos)
const char *isl_local_space_get_dim_name(
__isl_keep isl_local_space *ls,
enum isl_dim_type type, unsigned pos);
__isl_give isl_local_space *isl_local_space_set_dim_name(
__isl_take isl_local_space *ls,
enum isl_dim_type type, unsigned pos, const char *s);
__isl_give isl_local_space *isl_local_space_set_dim_id(
__isl_take isl_local_space *ls,
enum isl_dim_type type, unsigned pos,
__isl_take isl_id *id);
__isl_give isl_space *isl_local_space_get_space(
__isl_keep isl_local_space *ls);
__isl_give isl_aff *isl_local_space_get_div(
__isl_keep isl_local_space *ls, int pos);
__isl_give isl_local_space *isl_local_space_copy(
__isl_keep isl_local_space *ls);
void *isl_local_space_free(__isl_take isl_local_space *ls);
Note that isl_local_space_get_div can only be used on local spaces
of sets.
Two local spaces can be compared using
int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
__isl_keep isl_local_space *ls2);
Local spaces can be created from other local spaces using the following functions.
__isl_give isl_local_space *isl_local_space_domain(
__isl_take isl_local_space *ls);
__isl_give isl_local_space *isl_local_space_range(
__isl_take isl_local_space *ls);
__isl_give isl_local_space *isl_local_space_from_domain(
__isl_take isl_local_space *ls);
__isl_give isl_local_space *isl_local_space_intersect(
__isl_take isl_local_space *ls1,
__isl_take isl_local_space *ls2);
__isl_give isl_local_space *isl_local_space_add_dims(
__isl_take isl_local_space *ls,
enum isl_dim_type type, unsigned n);
__isl_give isl_local_space *isl_local_space_insert_dims(
__isl_take isl_local_space *ls,
enum isl_dim_type type, unsigned first, unsigned n);
__isl_give isl_local_space *isl_local_space_drop_dims(
__isl_take isl_local_space *ls,
enum isl_dim_type type, unsigned first, unsigned n);
isl supports its own input/output format, which is similar
to the Omega format, but also supports the PolyLib format
in some cases.
isl formatThe isl format is similar to that of 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 i between 0 and n
such that 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 or. Each disjunct is either a conjunction
of constraints or a projection (exists) of a conjunction
of constraints. The constraints are separated by the keyword
and.
PolyLib formatIf 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 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 (0) or inequality (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.
PolyLib formatThe extended PolyLib format is nearly identical to the
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.
#include <isl/set.h>
__isl_give isl_basic_set *isl_basic_set_read_from_file(
isl_ctx *ctx, FILE *input);
__isl_give isl_basic_set *isl_basic_set_read_from_str(
isl_ctx *ctx, const char *str);
__isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
FILE *input);
__isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
const char *str);
#include <isl/map.h>
__isl_give isl_basic_map *isl_basic_map_read_from_file(
isl_ctx *ctx, FILE *input);
__isl_give isl_basic_map *isl_basic_map_read_from_str(
isl_ctx *ctx, const char *str);
__isl_give isl_map *isl_map_read_from_file(
isl_ctx *ctx, FILE *input);
__isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
const char *str);
#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(
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(
isl_ctx *ctx, const char *str);
The input format is autodetected and may be either the PolyLib format
or the isl format.
Before anything can be printed, an 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 printer can be inspected using the following functions.
FILE *isl_printer_get_file(
__isl_keep isl_printer *printer);
int isl_printer_get_output_format(
__isl_keep isl_printer *p);
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_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 output_format may be either ISL_FORMAT_ISL, ISL_FORMAT_OMEGA,
ISL_FORMAT_POLYLIB, ISL_FORMAT_EXT_POLYLIB or ISL_FORMAT_LATEX
and defaults to ISL_FORMAT_ISL.
Each line in the output is indented by indent (set by
isl_printer_set_indent) spaces
(default: 0), prefixed by prefix and suffixed by suffix.
In the PolyLib format output,
the coefficients of the existentially quantified variables
appear between those of the set variables and those
of the parameters.
The function isl_printer_indent increases the indentation
by the specified amount (which may be negative).
To actually print something, use
#include <isl/printer.h>
__isl_give isl_printer *isl_printer_print_double(
__isl_take isl_printer *p, double d);
#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_printer *isl_printer_print_set(
__isl_take isl_printer *printer,
__isl_keep isl_set *set);
#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_give isl_printer *isl_printer_print_map(
__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_give isl_printer *isl_printer_flush(
__isl_take isl_printer *p);
isl has functions for creating some standard sets and relations.
__isl_give isl_basic_set *isl_basic_set_empty(
__isl_take isl_space *space);
__isl_give isl_basic_map *isl_basic_map_empty(
__isl_take isl_space *space);
__isl_give isl_set *isl_set_empty(
__isl_take isl_space *space);
__isl_give isl_map *isl_map_empty(
__isl_take isl_space *space);
__isl_give isl_union_set *isl_union_set_empty(
__isl_take isl_space *space);
__isl_give isl_union_map *isl_union_map_empty(
__isl_take isl_space *space);
For isl_union_sets and isl_union_maps, the space
is only used to specify the parameters.
__isl_give isl_basic_set *isl_basic_set_universe(
__isl_take isl_space *space);
__isl_give isl_basic_map *isl_basic_map_universe(
__isl_take isl_space *space);
__isl_give isl_set *isl_set_universe(
__isl_take isl_space *space);
__isl_give isl_map *isl_map_universe(
__isl_take isl_space *space);
__isl_give isl_union_set *isl_union_set_universe(
__isl_take isl_union_set *uset);
__isl_give isl_union_map *isl_union_map_universe(
__isl_take isl_union_map *umap);
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_space *space);
__isl_give isl_basic_map *isl_basic_map_nat_universe(
__isl_take isl_space *space);
__isl_give isl_set *isl_set_nat_universe(
__isl_take isl_space *space);
__isl_give isl_map *isl_map_nat_universe(
__isl_take isl_space *space);
__isl_give isl_basic_map *isl_basic_map_identity(
__isl_take isl_space *space);
__isl_give isl_map *isl_map_identity(
__isl_take isl_space *space);
The number of input and output dimensions in space needs
to be the same.
__isl_give isl_map *isl_map_lex_lt(
__isl_take isl_space *set_space);
__isl_give isl_map *isl_map_lex_le(
__isl_take isl_space *set_space);
__isl_give isl_map *isl_map_lex_gt(
__isl_take isl_space *set_space);
__isl_give isl_map *isl_map_lex_ge(
__isl_take isl_space *set_space);
__isl_give isl_map *isl_map_lex_lt_first(
__isl_take isl_space *space, unsigned n);
__isl_give isl_map *isl_map_lex_le_first(
__isl_take isl_space *space, unsigned n);
__isl_give isl_map *isl_map_lex_gt_first(
__isl_take isl_space *space, unsigned n);
__isl_give isl_map *isl_map_lex_ge_first(
__isl_take isl_space *space, unsigned n);
The first four functions take a space for a set
and return relations that express that the elements in the domain
are lexicographically less
(isl_map_lex_lt), less or equal (isl_map_lex_le),
greater (isl_map_lex_gt) or greater or equal (isl_map_lex_ge)
than the elements in the range.
The last four functions take a space for a map
and return relations that express that the first n dimensions
in the domain are lexicographically less
(isl_map_lex_lt_first), less or equal (isl_map_lex_le_first),
greater (isl_map_lex_gt_first) or greater or equal (isl_map_lex_ge_first)
than the first n dimensions in the range.
A basic set or relation can be converted to a set or relation using the following functions.
__isl_give isl_set *isl_set_from_basic_set(
__isl_take isl_basic_set *bset);
__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_set *isl_union_set_from_basic_set(
__isl_take isl_basic_set *bset);
__isl_give isl_union_map *isl_union_map_from_basic_map(
__isl_take isl_basic_map *bmap);
__isl_give isl_union_set *isl_union_set_from_set(
__isl_take isl_set *set);
__isl_give isl_union_map *isl_union_map_from_map(
__isl_take isl_map *map);
The inverse conversions below can only be used if the input union set or relation is known to contain elements in exactly one space.
__isl_give isl_set *isl_set_from_union_set(
__isl_take isl_union_set *uset);
__isl_give isl_map *isl_map_from_union_map(
__isl_take isl_union_map *umap);
A zero-dimensional (basic) set can be constructed on a given parameter domain using the following function.
__isl_give isl_basic_set *isl_basic_set_from_params(
__isl_take isl_basic_set *bset);
__isl_give isl_set *isl_set_from_params(
__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 inequality constraints and then projecting out the existentially quantified variables, if any. Constraints can be constructed, manipulated and added to (or removed from) (basic) sets and relations using the following functions.
#include <isl/constraint.h>
__isl_give isl_constraint *isl_equality_alloc(
__isl_take isl_local_space *ls);
__isl_give isl_constraint *isl_inequality_alloc(
__isl_take isl_local_space *ls);
__isl_give isl_constraint *isl_constraint_set_constant_si(
__isl_take isl_constraint *constraint, int v);
__isl_give isl_constraint *isl_constraint_set_constant_val(
__isl_take isl_constraint *constraint,
__isl_take isl_val *v);
__isl_give isl_constraint *isl_constraint_set_coefficient_si(
__isl_take isl_constraint *constraint,
enum isl_dim_type type, int pos, int v);
__isl_give isl_constraint *
isl_constraint_set_coefficient_val(
__isl_take isl_constraint *constraint,
enum isl_dim_type type, int pos, isl_val *v);
__isl_give isl_basic_map *isl_basic_map_add_constraint(
__isl_take isl_basic_map *bmap,
__isl_take isl_constraint *constraint);
__isl_give isl_basic_set *isl_basic_set_add_constraint(
__isl_take isl_basic_set *bset,
__isl_take isl_constraint *constraint);
__isl_give isl_map *isl_map_add_constraint(
__isl_take isl_map *map,
__isl_take isl_constraint *constraint);
__isl_give isl_set *isl_set_add_constraint(
__isl_take isl_set *set,
__isl_take isl_constraint *constraint);
__isl_give isl_basic_set *isl_basic_set_drop_constraint(
__isl_take isl_basic_set *bset,
__isl_take isl_constraint *constraint);
For example, to create a set containing the even integers between 10 and 42, you would use the following code.
isl_space *space;
isl_local_space *ls;
isl_constraint *c;
isl_basic_set *bset;
space = isl_space_set_alloc(ctx, 0, 2);
bset = isl_basic_set_universe(isl_space_copy(space));
ls = isl_local_space_from_space(space);
c = isl_equality_alloc(isl_local_space_copy(ls));
c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
bset = isl_basic_set_add_constraint(bset, c);
c = isl_inequality_alloc(isl_local_space_copy(ls));
c = isl_constraint_set_constant_si(c, -10);
c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
bset = isl_basic_set_add_constraint(bset, c);
c = isl_inequality_alloc(ls);
c = isl_constraint_set_constant_si(c, 42);
c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
bset = isl_basic_set_add_constraint(bset, c);
bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
Or, alternatively,
isl_basic_set *bset;
bset = isl_basic_set_read_from_str(ctx,
"{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
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_space *space,
__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_space *space,
__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 isl_dim_type arguments indicate the order in which
different kinds of variables appear in the input matrices
and should be a permutation of isl_dim_cst, isl_dim_param,
isl_dim_set and isl_dim_div for sets and
of isl_dim_cst, isl_dim_param,
isl_dim_in, isl_dim_out and isl_dim_div for relations.
A (basic or union) set or relation can also be constructed from a (union) (piecewise) (multiple) affine expression or a list of affine expressions (See Piecewise Quasi Affine Expressions and Piecewise Multiple Quasi Affine Expressions).
__isl_give isl_basic_map *isl_basic_map_from_aff(
__isl_take isl_aff *aff);
__isl_give isl_map *isl_map_from_aff(
__isl_take isl_aff *aff);
__isl_give isl_set *isl_set_from_pw_aff(
__isl_take isl_pw_aff *pwaff);
__isl_give isl_map *isl_map_from_pw_aff(
__isl_take isl_pw_aff *pwaff);
__isl_give isl_basic_map *isl_basic_map_from_aff_list(
__isl_take isl_space *domain_space,
__isl_take isl_aff_list *list);
__isl_give isl_basic_map *isl_basic_map_from_multi_aff(
__isl_take isl_multi_aff *maff)
__isl_give isl_map *isl_map_from_multi_aff(
__isl_take isl_multi_aff *maff)
__isl_give isl_set *isl_set_from_pw_multi_aff(
__isl_take isl_pw_multi_aff *pma);
__isl_give isl_map *isl_map_from_pw_multi_aff(
__isl_take isl_pw_multi_aff *pma);
__isl_give isl_set *isl_set_from_multi_pw_aff(
__isl_take isl_multi_pw_aff *mpa);
__isl_give isl_map *isl_map_from_multi_pw_aff(
__isl_take isl_multi_pw_aff *mpa);
__isl_give isl_union_map *
isl_union_map_from_union_pw_multi_aff(
__isl_take isl_union_pw_multi_aff *upma);
The domain_dim argument describes the domain of the resulting
basic relation. It is required because the list may consist
of zero affine expressions.
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 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);
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);
__isl_give isl_map *isl_map_remove_divs(
__isl_take isl_map *map);
It is also possible to only remove those divs that are defined in terms of a given range of dimensions or only those for which no explicit representation is known.
__isl_give isl_basic_set *
isl_basic_set_remove_divs_involving_dims(
__isl_take isl_basic_set *bset,
enum isl_dim_type type,
unsigned first, unsigned n);
__isl_give isl_basic_map *
isl_basic_map_remove_divs_involving_dims(
__isl_take isl_basic_map *bmap,
enum isl_dim_type type,
unsigned first, unsigned n);
__isl_give isl_set *isl_set_remove_divs_involving_dims(
__isl_take isl_set *set, enum isl_dim_type type,
unsigned first, unsigned n);
__isl_give isl_map *isl_map_remove_divs_involving_dims(
__isl_take isl_map *map, enum isl_dim_type type,
unsigned first, unsigned n);
__isl_give isl_basic_set *
isl_basic_set_remove_unknown_divs(
__isl_take isl_basic_set *bset);
__isl_give isl_set *isl_set_remove_unknown_divs(
__isl_take isl_set *set);
__isl_give isl_map *isl_map_remove_unknown_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);
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 in a given space from a union, use
__isl_give isl_set *isl_union_set_extract_set(
__isl_keep isl_union_set *uset,
__isl_take isl_space *space);
__isl_give isl_map *isl_union_map_extract_map(
__isl_keep isl_union_map *umap,
__isl_take isl_space *space);
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 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 isl does not guarantee that
the basic sets or maps passed to 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);
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>
int isl_basic_set_n_constraint(
__isl_keep isl_basic_set *bset);
int isl_basic_set_foreach_constraint(
__isl_keep isl_basic_set *bset,
int (*fn)(__isl_take isl_constraint *c, void *user),
void *user);
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(__isl_take isl_constraint *c);
Again, the callback function 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 represents either an equality or an inequality.
Use the following function to find out whether a constraint
represents an equality. If not, it represents an inequality.
int isl_constraint_is_equality(
__isl_keep isl_constraint *constraint);
The coefficients of the constraints can be inspected using the following functions.
int isl_constraint_is_lower_bound(
__isl_keep isl_constraint *constraint,
enum isl_dim_type type, unsigned pos);
int isl_constraint_is_upper_bound(
__isl_keep isl_constraint *constraint,
enum isl_dim_type type, unsigned pos);
__isl_give isl_val *isl_constraint_get_constant_val(
__isl_keep isl_constraint *constraint);
__isl_give isl_val *isl_constraint_get_coefficient_val(
__isl_keep isl_constraint *constraint,
enum isl_dim_type type, int pos);
int isl_constraint_involves_dims(
__isl_keep isl_constraint *constraint,
enum isl_dim_type type, unsigned first, unsigned n);
The explicit representations of the existentially quantified
variables can be inspected using the following function.
Note that the user is only allowed to use this function
if the inspected set or map is the result of a call
to isl_set_compute_divs or isl_map_compute_divs.
The existentially quantified variable is equal to the floor
of the returned affine expression. The affine expression
itself can be inspected using the functions in
Piecewise Quasi Affine Expressions.
__isl_give isl_aff *isl_constraint_get_div(
__isl_keep isl_constraint *constraint, int pos);
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 isl_dim_type arguments dictate the order in which
different kinds of variables appear in the resulting matrix
and should be a permutation of isl_dim_cst, isl_dim_param,
isl_dim_in, isl_dim_out and isl_dim_div.
The number of parameters, input, output or set dimensions can be obtained using the following functions.
unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
enum isl_dim_type type);
unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
enum isl_dim_type type);
unsigned isl_set_dim(__isl_keep isl_set *set,
enum isl_dim_type type);
unsigned isl_map_dim(__isl_keep isl_map *map,
enum isl_dim_type type);
To check whether the description of a set or relation depends on one or more given dimensions, it is not necessary to iterate over all constraints. Instead the following functions can be used.
int isl_basic_set_involves_dims(
__isl_keep isl_basic_set *bset,
enum isl_dim_type type, unsigned first, unsigned n);
int isl_set_involves_dims(__isl_keep isl_set *set,
enum isl_dim_type type, unsigned first, unsigned n);
int isl_basic_map_involves_dims(
__isl_keep isl_basic_map *bmap,
enum isl_dim_type type, unsigned first, unsigned n);
int isl_map_involves_dims(__isl_keep isl_map *map,
enum isl_dim_type type, unsigned first, unsigned n);
Similarly, the following functions can be used to check whether a given dimension is involved in any lower or upper bound.
int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
enum isl_dim_type type, unsigned pos);
int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
enum isl_dim_type type, unsigned pos);
Note that these functions return true even if there is a bound on
the dimension on only some of the basic sets of set.
To check if they have a bound for all of the basic sets in set,
use the following functions instead.
int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
enum isl_dim_type type, unsigned pos);
int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
enum isl_dim_type type, unsigned pos);
The identifiers or names of the domain and range spaces of a set or relation can be read off or set using the following functions.
__isl_give isl_set *isl_set_set_tuple_id(
__isl_take isl_set *set, __isl_take isl_id *id);
__isl_give isl_set *isl_set_reset_tuple_id(
__isl_take isl_set *set);
int isl_set_has_tuple_id(__isl_keep isl_set *set);
__isl_give isl_id *isl_set_get_tuple_id(
__isl_keep isl_set *set);
__isl_give isl_map *isl_map_set_tuple_id(
__isl_take isl_map *map, enum isl_dim_type type,
__isl_take isl_id *id);
__isl_give isl_map *isl_map_reset_tuple_id(
__isl_take isl_map *map, enum isl_dim_type type);
int isl_map_has_tuple_id(__isl_keep isl_map *map,
enum isl_dim_type type);
__isl_give isl_id *isl_map_get_tuple_id(
__isl_keep isl_map *map, enum isl_dim_type type);
const char *isl_basic_set_get_tuple_name(
__isl_keep isl_basic_set *bset);
__isl_give isl_basic_set *isl_basic_set_set_tuple_name(
__isl_take isl_basic_set *set, const char *s);
int isl_set_has_tuple_name(__isl_keep isl_set *set);
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);
__isl_give isl_basic_map *isl_basic_map_set_tuple_name(
__isl_take isl_basic_map *bmap,
enum isl_dim_type type, const char *s);
int isl_map_has_tuple_name(__isl_keep isl_map *map,
enum isl_dim_type type);
const char *isl_map_get_tuple_name(
__isl_keep isl_map *map,
enum isl_dim_type type);
As with isl_space_get_tuple_name, the value returned points to
an internal data structure.
The identifiers, positions or names of individual dimensions can be
read off using the following functions.
__isl_give isl_id *isl_basic_set_get_dim_id(
__isl_keep isl_basic_set *bset,
enum isl_dim_type type, unsigned pos);
__isl_give isl_set *isl_set_set_dim_id(
__isl_take isl_set *set, enum isl_dim_type type,
unsigned pos, __isl_take isl_id *id);
int isl_set_has_dim_id(__isl_keep isl_set *set,
enum isl_dim_type type, unsigned pos);
__isl_give isl_id *isl_set_get_dim_id(
__isl_keep isl_set *set, enum isl_dim_type type,
unsigned pos);
int isl_basic_map_has_dim_id(
__isl_keep isl_basic_map *bmap,
enum isl_dim_type type, unsigned pos);
__isl_give isl_map *isl_map_set_dim_id(
__isl_take isl_map *map, enum isl_dim_type type,
unsigned pos, __isl_take isl_id *id);
int isl_map_has_dim_id(__isl_keep isl_map *map,
enum isl_dim_type type, unsigned pos);
__isl_give isl_id *isl_map_get_dim_id(
__isl_keep isl_map *map, enum isl_dim_type type,
unsigned pos);
int isl_set_find_dim_by_id(__isl_keep isl_set *set,
enum isl_dim_type type, __isl_keep isl_id *id);
int isl_map_find_dim_by_id(__isl_keep isl_map *map,
enum isl_dim_type type, __isl_keep isl_id *id);
int isl_set_find_dim_by_name(__isl_keep isl_set *set,
enum isl_dim_type type, const char *name);
int isl_map_find_dim_by_name(__isl_keep isl_map *map,
enum isl_dim_type type, const char *name);
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);
int isl_set_has_dim_name(__isl_keep isl_set *set,
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);
int isl_map_has_dim_name(__isl_keep isl_map *map,
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 identifiers, positions or names of the parameters. Identifiers of individual dimensions are essentially only useful for printing. They are ignored by all other operations and may not be preserved across those operations.
The following functions test whether the given set or relation contains any integer points. The ``plain'' variants do not perform any computations, but simply check if the given set or relation is already known to be empty.
int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
int isl_set_plain_is_empty(__isl_keep isl_set *set);
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_plain_is_empty(__isl_keep isl_basic_map *bmap);
int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
int isl_map_plain_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);
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_plain_is_universe(__isl_keep isl_set *set);
int isl_basic_map_is_single_valued(
__isl_keep isl_basic_map *bmap);
int isl_map_plain_is_single_valued(
__isl_keep isl_map *map);
int isl_map_is_single_valued(__isl_keep isl_map *map);
int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
int isl_map_plain_is_injective(__isl_keep isl_map *map);
int isl_map_is_injective(__isl_keep isl_map *map);
int isl_union_map_plain_is_injective(
__isl_keep isl_union_map *umap);
int isl_union_map_is_injective(
__isl_keep isl_union_map *umap);
int isl_map_is_bijective(__isl_keep isl_map *map);
int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
__isl_give isl_val *
isl_basic_map_plain_get_val_if_fixed(
__isl_keep isl_basic_map *bmap,
enum isl_dim_type type, unsigned pos);
__isl_give isl_val *isl_set_plain_get_val_if_fixed(
__isl_keep isl_set *set,
enum isl_dim_type type, unsigned pos);
__isl_give isl_val *isl_map_plain_get_val_if_fixed(
__isl_keep isl_map *map,
enum isl_dim_type type, unsigned pos);
If the set or relation obviously lies on a hyperplane where the given dimension has a fixed value, then return that value. Otherwise return NaN.
int isl_set_dim_residue_class_val(
__isl_keep isl_set *set,
int pos, __isl_give isl_val **modulo,
__isl_give isl_val **residue);
Check if the values of the given set dimension are equal to a fixed
value modulo some integer value. If so, assign the modulo to *modulo
and the fixed value to *residue. If the given dimension attains only
a single value, then assign 0 to *modulo and the fixed value to
*residue.
If the dimension does not attain only a single value and if no modulo
can be found then assign 1 to *modulo and 1 to *residue.
To check whether a set is a parameter domain, use this function:
int isl_set_is_params(__isl_keep isl_set *set);
int isl_union_set_is_params(
__isl_keep isl_union_set *uset);
The following 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);
int isl_basic_map_can_zip(
__isl_keep isl_basic_map *bmap);
int isl_map_can_zip(__isl_keep isl_map *map);
Check whether the product of domain and range of the given relation can be computed, i.e., whether both domain and range are nested relations.
int isl_basic_map_can_curry(
__isl_keep isl_basic_map *bmap);
int isl_map_can_curry(__isl_keep isl_map *map);
Check whether the domain of the (basic) relation is a wrapped relation.
int isl_basic_map_can_uncurry(
__isl_keep isl_basic_map *bmap);
int isl_map_can_uncurry(__isl_keep isl_map *map);
Check whether the range of the (basic) relation is a wrapped relation.
int isl_basic_set_plain_is_equal(
__isl_keep isl_basic_set *bset1,
__isl_keep isl_basic_set *bset2);
int isl_set_plain_is_equal(__isl_keep isl_set *set1,
__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_plain_is_equal(__isl_keep isl_map *map1,
__isl_keep isl_map *map2);
int isl_union_map_is_equal(
__isl_keep isl_union_map *umap1,
__isl_keep isl_union_map *umap2);
int isl_basic_set_is_disjoint(
__isl_keep isl_basic_set *bset1,
__isl_keep isl_basic_set *bset2);
int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
__isl_keep isl_set *set2);
int isl_set_is_disjoint(__isl_keep isl_set *set1,
__isl_keep isl_set *set2);
int isl_basic_map_is_disjoint(
__isl_keep isl_basic_map *bmap1,
__isl_keep isl_basic_map *bmap2);
int isl_map_is_disjoint(__isl_keep isl_map *map1,
__isl_keep isl_map *map2);
int isl_basic_set_is_subset(
__isl_keep isl_basic_set *bset1,
__isl_keep isl_basic_set *bset2);
int isl_set_is_subset(__isl_keep isl_set *set1,
__isl_keep isl_set *set2);
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_basic_map_is_strict_subset(
__isl_keep isl_basic_map *bmap1,
__isl_keep isl_basic_map *bmap2);
int isl_map_is_subset(
__isl_keep isl_map *map1,
__isl_keep isl_map *map2);
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);
Check whether the first argument is a (strict) subset of the second argument.
int isl_set_plain_cmp(__isl_keep isl_set *set1,
__isl_keep isl_set *set2);
This function is useful for sorting isl_sets.
The order depends on the internal representation of the inputs.
The order is fixed over different calls to the function (assuming
the internal representation of the inputs has not changed), but may
change over different versions of isl.
__isl_give isl_set *isl_set_complement(
__isl_take isl_set *set);
__isl_give isl_map *isl_map_complement(
__isl_take isl_map *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);
__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_set_params(
__isl_take isl_basic_set *bset);
__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_basic_map *bmap);
__isl_give isl_set *isl_set_params(__isl_take isl_set *set);
__isl_give isl_set *isl_map_params(__isl_take isl_map *map);
__isl_give isl_set *isl_map_domain(
__isl_take isl_map *bmap);
__isl_give isl_set *isl_map_range(
__isl_take isl_map *map);
__isl_give isl_set *isl_union_set_params(
__isl_take isl_union_set *uset);
__isl_give isl_set *isl_union_map_params(
__isl_take isl_union_map *umap);
__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.
__isl_give isl_basic_set *isl_basic_set_eliminate(
__isl_take isl_basic_set *bset,
enum isl_dim_type type,
unsigned first, unsigned n);
__isl_give isl_set *isl_set_eliminate(
__isl_take isl_set *set, enum isl_dim_type type,
unsigned first, unsigned n);
__isl_give isl_basic_map *isl_basic_map_eliminate(
__isl_take isl_basic_map *bmap,
enum isl_dim_type type,
unsigned first, unsigned n);
__isl_give isl_map *isl_map_eliminate(
__isl_take isl_map *map, enum isl_dim_type type,
unsigned first, unsigned n);
Eliminate the coefficients for the given dimensions from the constraints, without removing the dimensions.
__isl_give isl_basic_set *isl_basic_set_fix_si(
__isl_take isl_basic_set *bset,
enum isl_dim_type type, unsigned pos, int value);
__isl_give isl_basic_set *isl_basic_set_fix_val(
__isl_take isl_basic_set *bset,
enum isl_dim_type type, unsigned pos,
__isl_take isl_val *v);
__isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
enum isl_dim_type type, unsigned pos, int value);
__isl_give isl_set *isl_set_fix_val(
__isl_take isl_set *set,
enum isl_dim_type type, unsigned pos,
__isl_take isl_val *v);
__isl_give isl_basic_map *isl_basic_map_fix_si(
__isl_take isl_basic_map *bmap,
enum isl_dim_type type, unsigned pos, int value);
__isl_give isl_basic_map *isl_basic_map_fix_val(
__isl_take isl_basic_map *bmap,
enum isl_dim_type type, unsigned pos,
__isl_take isl_val *v);
__isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
enum isl_dim_type type, unsigned pos, int value);
__isl_give isl_map *isl_map_fix_val(
__isl_take isl_map *map,
enum isl_dim_type type, unsigned pos,
__isl_take isl_val *v);
Intersect the set or relation with the hyperplane where the given dimension has the fixed given value.
__isl_give isl_basic_map *isl_basic_map_lower_bound_si(
__isl_take isl_basic_map *bmap,
enum isl_dim_type type, unsigned pos, int value);
__isl_give isl_basic_map *isl_basic_map_upper_bound_si(
__isl_take isl_basic_map *bmap,
enum isl_dim_type type, unsigned pos, int value);
__isl_give isl_set *isl_set_lower_bound_si(
__isl_take isl_set *set,
enum isl_dim_type type, unsigned pos, int value);
__isl_give isl_set *isl_set_lower_bound_val(
__isl_take isl_set *set,
enum isl_dim_type type, unsigned pos,
__isl_take isl_val *value);
__isl_give isl_map *isl_map_lower_bound_si(
__isl_take isl_map *map,
enum isl_dim_type type, unsigned pos, int value);
__isl_give isl_set *isl_set_upper_bound_si(
__isl_take isl_set *set,
enum isl_dim_type type, unsigned pos, int value);
__isl_give isl_set *isl_set_upper_bound_val(
__isl_take isl_set *set,
enum isl_dim_type type, unsigned pos,
__isl_take isl_val *value);
__isl_give isl_map *isl_map_upper_bound_si(
__isl_take isl_map *map,
enum isl_dim_type type, unsigned pos, int value);
Intersect the set or relation with the half-space where the given dimension has a value bounded by the fixed given integer value.
__isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
enum isl_dim_type type1, int pos1,
enum isl_dim_type type2, int pos2);
__isl_give isl_basic_map *isl_basic_map_equate(
__isl_take isl_basic_map *bmap,
enum isl_dim_type type1, int pos1,
enum isl_dim_type type2, int pos2);
__isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
enum isl_dim_type type1, int pos1,
enum isl_dim_type type2, int pos2);
Intersect the set or relation with the hyperplane where the given dimensions are equal to each other.
__isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
enum isl_dim_type type1, int pos1,
enum isl_dim_type type2, int pos2);
Intersect the relation with the hyperplane where the given dimensions have opposite values.
__isl_give isl_basic_map *isl_basic_map_order_ge(
__isl_take isl_basic_map *bmap,
enum isl_dim_type type1, int pos1,
enum isl_dim_type type2, int pos2);
__isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
enum isl_dim_type type1, int pos1,
enum isl_dim_type type2, int pos2);
__isl_give isl_basic_map *isl_basic_map_order_gt(
__isl_take isl_basic_map *bmap,
enum isl_dim_type type1, int pos1,
enum isl_dim_type type2, int pos2);
__isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
enum isl_dim_type type1, int pos1,
enum isl_dim_type type2, int pos2);
Intersect the relation with the half-space where the given dimensions satisfy the given ordering.
__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.
__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.
__isl_give isl_basic_map *isl_basic_map_deltas_map(
__isl_take isl_basic_map *bmap);
__isl_give isl_map *isl_map_deltas_map(
__isl_take isl_map *map);
__isl_give isl_union_map *isl_union_map_deltas_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 delta set.
Simplify the representation of a set or relation by trying to combine pairs of basic sets or relations into a single basic set or relation.
__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);
One of the methods for combining pairs of basic sets or relations can result in coefficients that are much larger than those that appear in the constraints of the input. By default, the coefficients are not allowed to grow larger, but this can be changed by unsetting the following option.
int isl_options_set_coalesce_bounded_wrapping(
isl_ctx *ctx, int val);
int isl_options_get_coalesce_bounded_wrapping(
isl_ctx *ctx);
__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.
__isl_give isl_basic_set *isl_basic_set_remove_redundancies(
__isl_take isl_basic_set *bset);
__isl_give isl_set *isl_set_remove_redundancies(
__isl_take isl_set *set);
__isl_give isl_basic_map *isl_basic_map_remove_redundancies(
__isl_take isl_basic_map *bmap);
__isl_give isl_map *isl_map_remove_redundancies(
__isl_take isl_map *map);
__isl_give isl_basic_set *isl_set_convex_hull(
__isl_take isl_set *set);
__isl_give isl_basic_map *isl_map_convex_hull(
__isl_take isl_map *map);
If the input set or relation has any existentially quantified variables, then the result of these operations is currently undefined.
__isl_give isl_basic_set *
isl_set_unshifted_simple_hull(
__isl_take isl_set *set);
__isl_give isl_basic_map *
isl_map_unshifted_simple_hull(
__isl_take isl_map *map);
__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);
__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.
In particular, the output is described by translates
of the constraints describing the basic sets or relations in the input.
In case of isl_set_unshifted_simple_hull, only the original
constraints are used, without any translation.
__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 space.
__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.
__isl_give isl_basic_set *
isl_basic_set_drop_constraints_involving_dims(
__isl_take isl_basic_set *bset,
enum isl_dim_type type,
unsigned first, unsigned n);
__isl_give isl_basic_map *
isl_basic_map_drop_constraints_involving_dims(
__isl_take isl_basic_map *bmap,
enum isl_dim_type type,
unsigned first, unsigned n);
__isl_give isl_basic_set *
isl_basic_set_drop_constraints_not_involving_dims(
__isl_take isl_basic_set *bset,
enum isl_dim_type type,
unsigned first, unsigned n);
__isl_give isl_set *
isl_set_drop_constraints_involving_dims(
__isl_take isl_set *set,
enum isl_dim_type type,
unsigned first, unsigned n);
__isl_give isl_map *
isl_map_drop_constraints_involving_dims(
__isl_take isl_map *map,
enum isl_dim_type type,
unsigned first, unsigned n);
These functions drop any constraints (not) involving the specified dimensions. Note that the result depends on the representation of the input.
__isl_give isl_basic_set *isl_basic_set_sample(
__isl_take isl_basic_set *bset);
__isl_give isl_basic_set *isl_set_sample(
__isl_take isl_set *set);
__isl_give isl_basic_map *isl_basic_map_sample(
__isl_take isl_basic_map *bmap);
__isl_give isl_basic_map *isl_map_sample(
__isl_take isl_map *map);
If the input (basic) set or relation is non-empty, then return a singleton subset of the input. Otherwise, return an empty set.
#include <isl/ilp.h>
__isl_give isl_val *isl_basic_set_max_val(
__isl_keep isl_basic_set *bset,
__isl_keep isl_aff *obj);
__isl_give isl_val *isl_set_min_val(
__isl_keep isl_set *set,
__isl_keep isl_aff *obj);
__isl_give isl_val *isl_set_max_val(
__isl_keep isl_set *set,
__isl_keep isl_aff *obj);
Compute the minimum or maximum of the integer affine expression obj
over the points in set, returning the result in opt.
The result is NULL in case of an error, the optimal value in case
there is one, negative infinity or infinity if the problem is unbounded and
NaN if the problem is empty.
__isl_give isl_pw_aff *isl_set_dim_min(
__isl_take isl_set *set, int pos);
__isl_give isl_pw_aff *isl_set_dim_max(
__isl_take isl_set *set, int pos);
__isl_give isl_pw_aff *isl_map_dim_max(
__isl_take isl_map *map, int pos);
Compute the minimum or maximum of the given set or output dimension as a function of the parameters (and input dimensions), but independently of the other set or output dimensions. For lexicographic optimization, see Lexicographic Optimization.
The following functions compute either the set of (rational) coefficient values of valid constraints for the given set or the set of (rational) values satisfying the constraints with coefficients from the given set. Internally, these two sets of functions perform essentially the same operations, except that the set of coefficients is assumed to be a cone, while the set of values may be any polyhedron. The current implementation is based on the Farkas lemma and Fourier-Motzkin elimination, but this may change or be made optional in future. In particular, future implementations may use different dualization algorithms or skip the elimination step.
__isl_give isl_basic_set *isl_basic_set_coefficients(
__isl_take isl_basic_set *bset);
__isl_give isl_basic_set *isl_set_coefficients(
__isl_take isl_set *set);
__isl_give isl_union_set *isl_union_set_coefficients(
__isl_take isl_union_set *bset);
__isl_give isl_basic_set *isl_basic_set_solutions(
__isl_take isl_basic_set *bset);
__isl_give isl_basic_set *isl_set_solutions(
__isl_take isl_set *set);
__isl_give isl_union_set *isl_union_set_solutions(
__isl_take isl_union_set *bset);
__isl_give isl_map *isl_map_fixed_power_val(
__isl_take isl_map *map,
__isl_take isl_val *exp);
__isl_give isl_union_map *
isl_union_map_fixed_power_val(
__isl_take isl_union_map *umap,
__isl_take isl_val *exp);
Compute the given power of map, where exp is assumed to be non-zero.
If the exponent exp is negative, then the -exp th power of the inverse
of map is computed.
__isl_give isl_map *isl_map_power(__isl_take isl_map *map,
int *exact);
__isl_give isl_union_map *isl_union_map_power(
__isl_take isl_union_map *umap, int *exact);
Compute a parametric representation for all positive powers k of map.
The result maps k to a nested relation corresponding to the
kth power of map.
The result may be an overapproximation. If the result is known to be exact,
then *exact is set to 1.
__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 map.
The result may be an overapproximation. If the result is known to be exact,
then *exact is set to 1.
__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 map
to the lengths of all paths composed of edges in map that
end up in the given element.
The result may be an overapproximation. If the result is known to be exact,
then *exact is set to 1.
To compute the maximal path length, the resulting relation
should be postprocessed by 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 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.
__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);
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_domain(
__isl_take isl_basic_map *bmap);
__isl_give isl_basic_map *isl_basic_map_flatten_range(
__isl_take isl_basic_map *bmap);
__isl_give isl_map *isl_map_flatten_range(
__isl_take isl_map *map);
__isl_give isl_map *isl_map_flatten_domain(
__isl_take isl_map *map);
__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.
Lift the input set to a space with extra dimensions corresponding to the existentially quantified variables in the input. In particular, the result lives in a wrapped map where the domain is the original space and the range corresponds to the original existentially quantified variables.
__isl_give isl_basic_set *isl_basic_set_lift(
__isl_take isl_basic_set *bset);
__isl_give isl_set *isl_set_lift(
__isl_take isl_set *set);
__isl_give isl_union_set *isl_union_set_lift(
__isl_take isl_union_set *uset);
Given a local space that contains the existentially quantified
variables of a set, a basic relation that, when applied to
a basic set, has essentially the same effect as isl_basic_set_lift,
can be constructed using the following function.
#include <isl/local_space.h>
__isl_give isl_basic_map *isl_local_space_lifting(
__isl_take isl_local_space *ls);
__isl_give isl_basic_map *isl_basic_map_zip(
__isl_take isl_basic_map *bmap);
__isl_give isl_map *isl_map_zip(
__isl_take isl_map *map);
__isl_give isl_union_map *isl_union_map_zip(
__isl_take isl_union_map *umap);
Given a relation with nested relations for domain and range, interchange the range of the domain with the domain of the range.
__isl_give isl_basic_map *isl_basic_map_curry(
__isl_take isl_basic_map *bmap);
__isl_give isl_basic_map *isl_basic_map_uncurry(
__isl_take isl_basic_map *bmap);
__isl_give isl_map *isl_map_curry(
__isl_take isl_map *map);
__isl_give isl_map *isl_map_uncurry(
__isl_take isl_map *map);
__isl_give isl_union_map *isl_union_map_curry(
__isl_take isl_union_map *umap);
__isl_give isl_union_map *isl_union_map_uncurry(
__isl_take isl_union_map *umap);
Given a relation with a nested relation for domain,
the curry functions
move the range of the nested relation out of the domain
and use it as the domain of a nested relation in the range,
with the original range as range of this nested relation.
The uncurry functions perform the inverse operation.
__isl_give isl_basic_set *isl_basic_set_align_params(
__isl_take isl_basic_set *bset,
__isl_take isl_space *model);
__isl_give isl_set *isl_set_align_params(
__isl_take isl_set *set,
__isl_take isl_space *model);
__isl_give isl_basic_map *isl_basic_map_align_params(
__isl_take isl_basic_map *bmap,
__isl_take isl_space *model);
__isl_give isl_map *isl_map_align_params(
__isl_take isl_map *map,
__isl_take isl_space *model);
Change the order of the parameters of the given set or relation
such that the first parameters match those of model.
This may involve the introduction of extra parameters.
All parameters need to be named.
__isl_give isl_basic_set *isl_basic_set_add_dims(
__isl_take isl_basic_set *bset,
enum isl_dim_type type, unsigned n);
__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);
__isl_give isl_basic_set *isl_basic_set_insert_dims(
__isl_take isl_basic_set *bset,
enum isl_dim_type type, unsigned pos,
unsigned n);
__isl_give isl_basic_map *isl_basic_map_insert_dims(
__isl_take isl_basic_map *bmap,
enum isl_dim_type type, unsigned pos,
unsigned n);
__isl_give isl_set *isl_set_insert_dims(
__isl_take isl_set *set,
enum isl_dim_type type, unsigned pos, unsigned n);
__isl_give isl_map *isl_map_insert_dims(
__isl_take isl_map *map,
enum isl_dim_type type, unsigned pos, unsigned n);
__isl_give isl_basic_set *isl_basic_set_move_dims(
__isl_take isl_basic_set *bset,
enum isl_dim_type dst_type, unsigned dst_pos,
enum isl_dim_type src_type, unsigned src_pos,
unsigned n);
__isl_give isl_basic_map *isl_basic_map_move_dims(
__isl_take isl_basic_map *bmap,
enum isl_dim_type dst_type, unsigned dst_pos,
enum isl_dim_type src_type, unsigned src_pos,
unsigned n);
__isl_give isl_set *isl_set_move_dims(
__isl_take isl_set *set,
enum isl_dim_type dst_type, unsigned dst_pos,
enum isl_dim_type src_type, unsigned src_pos,
unsigned n);
__isl_give isl_map *isl_map_move_dims(
__isl_take isl_map *map,
enum isl_dim_type dst_type, unsigned dst_pos,
enum isl_dim_type src_type, unsigned src_pos,
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, assuming
isl_set_align_params and isl_map_align_params
are not sufficient.
The two arguments of a binary operation not only need to live
in the same isl_ctx, they currently also need to have
the same (number of) parameters.
__isl_give isl_basic_set *isl_basic_set_intersect_params(
__isl_take isl_basic_set *bset1,
__isl_take isl_basic_set *bset2);
__isl_give isl_basic_set *isl_basic_set_intersect(
__isl_take isl_basic_set *bset1,
__isl_take isl_basic_set *bset2);
__isl_give isl_set *isl_set_intersect_params(
__isl_take isl_set *set,
__isl_take isl_set *params);
__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_params(
__isl_take isl_union_set *uset,
__isl_take isl_set *set);
__isl_give isl_union_map *isl_union_map_intersect_params(
__isl_take isl_union_map *umap,
__isl_take isl_set *set);
__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_basic_map *isl_basic_map_intersect_range(
__isl_take isl_basic_map *bmap,
__isl_take isl_basic_set *bset);
__isl_give isl_basic_map *isl_basic_map_intersect(
__isl_take isl_basic_map *bmap1,
__isl_take isl_basic_map *bmap2);
__isl_give isl_map *isl_map_intersect_params(
__isl_take isl_map *map,
__isl_take isl_set *params);
__isl_give isl_map *isl_map_intersect_domain(
__isl_take isl_map *map,
__isl_take isl_set *set);
__isl_give isl_map *isl_map_intersect_range(
__isl_take isl_map *map,
__isl_take isl_set *set);
__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);
The second argument to the _params functions needs to be
a parametric (basic) set. For the other functions, a parametric set
for either argument is only allowed if the other argument is
a parametric set as well.
__isl_give isl_set *isl_basic_set_union(
__isl_take isl_basic_set *bset1,
__isl_take isl_basic_set *bset2);
__isl_give isl_map *isl_basic_map_union(
__isl_take isl_basic_map *bmap1,
__isl_take isl_basic_map *bmap2);
__isl_give isl_set *isl_set_union(
__isl_take isl_set *set1,
__isl_take isl_set *set2);
__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);
__isl_give isl_set *isl_set_subtract(
__isl_take isl_set *set1,
__isl_take isl_set *set2);
__isl_give isl_map *isl_map_subtract(
__isl_take isl_map *map1,
__isl_take isl_map *map2);
__isl_give isl_map *isl_map_subtract_domain(
__isl_take isl_map *map,
__isl_take isl_set *dom);
__isl_give isl_map *isl_map_subtract_range(
__isl_take isl_map *map,
__isl_take isl_set *dom);
__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);
__isl_give isl_union_map *isl_union_map_subtract_domain(
__isl_take isl_union_map *umap,
__isl_take isl_union_set *dom);
__isl_give isl_union_map *isl_union_map_subtract_range(
__isl_take isl_union_map *umap,
__isl_take isl_union_set *dom);
__isl_give isl_basic_set *isl_basic_set_apply(
__isl_take isl_basic_set *bset,
__isl_take isl_basic_map *bmap);
__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_basic_map *isl_basic_map_apply_range(
__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);
__isl_give isl_basic_set *
isl_basic_set_preimage_multi_aff(
__isl_take isl_basic_set *bset,
__isl_take isl_multi_aff *ma);
__isl_give isl_set *isl_set_preimage_multi_aff(
__isl_take isl_set *set,
__isl_take isl_multi_aff *ma);
__isl_give isl_set *isl_set_preimage_pw_multi_aff(
__isl_take isl_set *set,
__isl_take isl_pw_multi_aff *pma);
__isl_give isl_set *isl_set_preimage_multi_pw_aff(
__isl_take isl_set *set,
__isl_take isl_multi_pw_aff *mpa);
__isl_give isl_basic_map *
isl_basic_map_preimage_domain_multi_aff(
__isl_take isl_basic_map *bmap,
__isl_take isl_multi_aff *ma);
__isl_give isl_map *isl_map_preimage_domain_multi_aff(
__isl_take isl_map *map,
__isl_take isl_multi_aff *ma);
__isl_give isl_map *
isl_map_preimage_domain_pw_multi_aff(
__isl_take isl_map *map,
__isl_take isl_pw_multi_aff *pma);
__isl_give isl_map *
isl_map_preimage_domain_multi_pw_aff(
__isl_take isl_map *map,
__isl_take isl_multi_pw_aff *mpa);
__isl_give isl_union_map *
isl_union_map_preimage_domain_multi_aff(
__isl_take isl_union_map *umap,
__isl_take isl_multi_aff *ma);
__isl_give isl_basic_map *
isl_basic_map_preimage_range_multi_aff(
__isl_take isl_basic_map *bmap,
__isl_take isl_multi_aff *ma);
These functions compute the preimage of the given set or map domain/range under
the given function. In other words, the expression is plugged
into the set description or into the domain/range of the map.
Objects of types isl_multi_aff and isl_pw_multi_aff are described in
Piecewise Multiple Quasi Affine Expressions.
__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_domain_product(
__isl_take isl_basic_map *bmap1,
__isl_take isl_basic_map *bmap2);
__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_basic_map *isl_basic_map_product(
__isl_take isl_basic_map *bmap1,
__isl_take isl_basic_map *bmap2);
__isl_give isl_map *isl_map_domain_product(
__isl_take isl_map *map1,
__isl_take isl_map *map2);
__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_domain_product(
__isl_take isl_union_map *umap1,
__isl_take isl_union_map *umap2);
__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_range_product(
__isl_take isl_basic_map *bmap1,
__isl_take isl_basic_map *bmap2);
__isl_give isl_map *isl_map_flat_domain_product(
__isl_take isl_map *map1,
__isl_take isl_map *map2);
__isl_give isl_map *isl_map_flat_range_product(
__isl_take isl_map *map1,
__isl_take isl_map *map2);
__isl_give isl_union_map *isl_union_map_flat_range_product(
__isl_take isl_union_map *umap1,
__isl_take isl_union_map *umap2);
__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);
__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_set *isl_set_gist_params(
__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_union_set *isl_union_set_gist_params(
__isl_take isl_union_set *uset,
__isl_take isl_set *set);
__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_map *isl_map_gist_params(
__isl_take isl_map *map,
__isl_take isl_set *context);
__isl_give isl_map *isl_map_gist_domain(
__isl_take isl_map *map,
__isl_take isl_set *context);
__isl_give isl_map *isl_map_gist_range(
__isl_take isl_map *map,
__isl_take isl_set *context);
__isl_give isl_union_map *isl_union_map_gist(
__isl_take isl_union_map *umap,
__isl_take isl_union_map *context);
__isl_give isl_union_map *isl_union_map_gist_params(
__isl_take isl_union_map *umap,
__isl_take isl_set *set);
__isl_give isl_union_map *isl_union_map_gist_domain(
__isl_take isl_union_map *umap,
__isl_take isl_union_set *uset);
__isl_give isl_union_map *isl_union_map_gist_range(
__isl_take isl_union_map *umap,
__isl_take isl_union_set *uset);
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.
Given a (basic) set set (or bset) and a zero-dimensional domain dom,
the following functions
compute a set that contains the lexicographic minimum or maximum
of the elements in set (or bset) for those values of the parameters
that satisfy dom.
If empty is not NULL, then *empty is assigned a set
that contains the parameter values in dom for which set (or bset)
has no elements.
In other words, the union of the parameter values
for which the result is non-empty and of *empty
is equal to dom.
__isl_give isl_set *isl_basic_set_partial_lexmin(
__isl_take isl_basic_set *bset,
__isl_take isl_basic_set *dom,
__isl_give isl_set **empty);
__isl_give isl_set *isl_basic_set_partial_lexmax(
__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 set (or bset), the following functions simply
return a set containing the lexicographic minimum or maximum
of the elements in set (or 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_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 map (or bmap) and a domain dom,
the following functions
compute a relation that maps each element of dom
to the single lexicographic minimum or maximum
of the elements that are associated to that same
element in map (or bmap).
If empty is not NULL, then *empty is assigned a set
that contains the elements in dom that do not map
to any elements in map (or bmap).
In other words, the union of the domain of the result and of *empty
is equal to dom.
__isl_give isl_map *isl_basic_map_partial_lexmax(
__isl_take isl_basic_map *bmap,
__isl_take isl_basic_set *dom,
__isl_give isl_set **empty);
__isl_give isl_map *isl_basic_map_partial_lexmin(
__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 map (or bmap), the following functions simply
return a map mapping each element in the domain of
map (or 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_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);
The following functions return their result in the form of a piecewise multi-affine expression (See Piecewise Multiple Quasi Affine Expressions), but are otherwise equivalent to the corresponding functions returning a basic set or relation.
__isl_give isl_pw_multi_aff *
isl_basic_map_lexmin_pw_multi_aff(
__isl_take isl_basic_map *bmap);
__isl_give isl_pw_multi_aff *
isl_basic_set_partial_lexmin_pw_multi_aff(
__isl_take isl_basic_set *bset,
__isl_take isl_basic_set *dom,
__isl_give isl_set **empty);
__isl_give isl_pw_multi_aff *
isl_basic_set_partial_lexmax_pw_multi_aff(
__isl_take isl_basic_set *bset,
__isl_take isl_basic_set *dom,
__isl_give isl_set **empty);
__isl_give isl_pw_multi_aff *
isl_basic_map_partial_lexmin_pw_multi_aff(
__isl_take isl_basic_map *bmap,
__isl_take isl_basic_set *dom,
__isl_give isl_set **empty);
__isl_give isl_pw_multi_aff *
isl_basic_map_partial_lexmax_pw_multi_aff(
__isl_take isl_basic_map *bmap,
__isl_take isl_basic_set *dom,
__isl_give isl_set **empty);
__isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
__isl_take isl_set *set);
__isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
__isl_take isl_set *set);
__isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
__isl_take isl_map *map);
__isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
__isl_take isl_map *map);
Lists are defined over several element types, including
isl_val, isl_id, isl_aff, isl_pw_aff, isl_constraint,
isl_basic_set, isl_set, isl_ast_expr and isl_ast_node.
Here we take lists of isl_sets as an example.
Lists can be created, copied, modified and freed using the following functions.
#include <isl/list.h>
__isl_give isl_set_list *isl_set_list_from_set(
__isl_take isl_set *el);
__isl_give isl_set_list *isl_set_list_alloc(
isl_ctx *ctx, int n);
__isl_give isl_set_list *isl_set_list_copy(
__isl_keep isl_set_list *list);
__isl_give isl_set_list *isl_set_list_insert(
__isl_take isl_set_list *list, unsigned pos,
__isl_take isl_set *el);
__isl_give isl_set_list *isl_set_list_add(
__isl_take isl_set_list *list,
__isl_take isl_set *el);
__isl_give isl_set_list *isl_set_list_drop(
__isl_take isl_set_list *list,
unsigned first, unsigned n);
__isl_give isl_set_list *isl_set_list_set_set(
__isl_take isl_set_list *list, int index,
__isl_take isl_set *set);
__isl_give isl_set_list *isl_set_list_concat(
__isl_take isl_set_list *list1,
__isl_take isl_set_list *list2);
__isl_give isl_set_list *isl_set_list_sort(
__isl_take isl_set_list *list,
int (*cmp)(__isl_keep isl_set *a,
__isl_keep isl_set *b, void *user),
void *user);
void *isl_set_list_free(__isl_take isl_set_list *list);
isl_set_list_alloc creates an empty list with a capacity for
n elements. isl_set_list_from_set creates a list with a single
element.
Lists can be inspected using the following functions.
#include <isl/list.h>
isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
int isl_set_list_n_set(__isl_keep isl_set_list *list);
__isl_give isl_set *isl_set_list_get_set(
__isl_keep isl_set_list *list, int index);
int isl_set_list_foreach(__isl_keep isl_set_list *list,
int (*fn)(__isl_take isl_set *el, void *user),
void *user);
int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
int (*follows)(__isl_keep isl_set *a,
__isl_keep isl_set *b, void *user),
void *follows_user
int (*fn)(__isl_take isl_set *el, void *user),
void *fn_user);
The function isl_set_list_foreach_scc calls fn on each of the
strongly connected components of the graph with as vertices the elements
of list and a directed edge from vertex b to vertex a
iff follows(a, b) returns 1. The callbacks follows and fn
should return -1 on error.
Lists can be printed using
#include <isl/list.h>
__isl_give isl_printer *isl_printer_print_set_list(
__isl_take isl_printer *p,
__isl_keep isl_set_list *list);
Associative arrays map isl objects of a specific type to isl objects
of some (other) specific type. They are defined for several pairs
of types, including (isl_map, isl_basic_set),
(isl_id, isl_ast_expr) and.
(isl_id, isl_pw_aff).
Here, we take associative arrays that map isl_ids to isl_ast_exprs
as an example.
Associative arrays can be created, copied and freed using the following functions.
#include <isl/id_to_ast_expr.h>
__isl_give id_to_ast_expr *isl_id_to_ast_expr_alloc(
isl_ctx *ctx, int min_size);
__isl_give id_to_ast_expr *isl_id_to_ast_expr_copy(
__isl_keep id_to_ast_expr *id2expr);
void *isl_id_to_ast_expr_free(
__isl_take id_to_ast_expr *id2expr);
The min_size argument to isl_id_to_ast_expr_alloc can be used
to specify the expected size of the associative array.
The associative array will be grown automatically as needed.
Associative arrays can be inspected using the following functions.
#include <isl/id_to_ast_expr.h>
isl_ctx *isl_id_to_ast_expr_get_ctx(
__isl_keep id_to_ast_expr *id2expr);
int isl_id_to_ast_expr_has(
__isl_keep id_to_ast_expr *id2expr,
__isl_keep isl_id *key);
__isl_give isl_ast_expr *isl_id_to_ast_expr_get(
__isl_keep id_to_ast_expr *id2expr,
__isl_take isl_id *key);
int isl_id_to_ast_expr_foreach(
__isl_keep id_to_ast_expr *id2expr,
int (*fn)(__isl_take isl_id *key,
__isl_take isl_ast_expr *val, void *user),
void *user);
They can be modified using the following function.
#include <isl/id_to_ast_expr.h>
__isl_give id_to_ast_expr *isl_id_to_ast_expr_set(
__isl_take id_to_ast_expr *id2expr,
__isl_take isl_id *key,
__isl_take isl_ast_expr *val);
Associative arrays can be printed using the following function.
#include <isl/id_to_ast_expr.h>
__isl_give isl_printer *isl_printer_print_id_to_ast_expr(
__isl_take isl_printer *p,
__isl_keep id_to_ast_expr *id2expr);
An isl_multi_val object represents a sequence of zero or more values,
living in a set space.
An isl_multi_val can be constructed from an isl_val_list
using the following function
#include <isl/val.h>
__isl_give isl_multi_val *isl_multi_val_from_val_list(
__isl_take isl_space *space,
__isl_take isl_val_list *list);
The zero multiple value (with value zero for each set dimension) can be created using the following function.
#include <isl/val.h>
__isl_give isl_multi_val *isl_multi_val_zero(
__isl_take isl_space *space);
Multiple values can be copied and freed using
#include <isl/val.h>
__isl_give isl_multi_val *isl_multi_val_copy(
__isl_keep isl_multi_val *mv);
void *isl_multi_val_free(__isl_take isl_multi_val *mv);
They can be inspected using
#include <isl/val.h>
isl_ctx *isl_multi_val_get_ctx(
__isl_keep isl_multi_val *mv);
unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
enum isl_dim_type type);
__isl_give isl_val *isl_multi_val_get_val(
__isl_keep isl_multi_val *mv, int pos);
int isl_multi_val_find_dim_by_id(
__isl_keep isl_multi_val *mv,
enum isl_dim_type type, __isl_keep isl_id *id);
__isl_give isl_id *isl_multi_val_get_dim_id(
__isl_keep isl_multi_val *mv,
enum isl_dim_type type, unsigned pos);
const char *isl_multi_val_get_tuple_name(
__isl_keep isl_multi_val *mv,
enum isl_dim_type type);
int isl_multi_val_has_tuple_id(__isl_keep isl_multi_val *mv,
enum isl_dim_type type);
__isl_give isl_id *isl_multi_val_get_tuple_id(
__isl_keep isl_multi_val *mv,
enum isl_dim_type type);
__isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
__isl_take isl_multi_val *mv,
enum isl_dim_type type);
They can be modified using
#include <isl/val.h>
__isl_give isl_multi_val *isl_multi_val_set_val(
__isl_take isl_multi_val *mv, int pos,
__isl_take isl_val *val);
__isl_give isl_multi_val *isl_multi_val_set_dim_name(
__isl_take isl_multi_val *mv,
enum isl_dim_type type, unsigned pos, const char *s);
__isl_give isl_multi_val *isl_multi_val_set_dim_id(
__isl_take isl_multi_val *mv,
enum isl_dim_type type, unsigned pos,
__isl_take isl_id *id);
__isl_give isl_multi_val *isl_multi_val_set_tuple_name(
__isl_take isl_multi_val *mv,
enum isl_dim_type type, const char *s);
__isl_give isl_multi_val *isl_multi_val_set_tuple_id(
__isl_take isl_multi_val *mv,
enum isl_dim_type type, __isl_take isl_id *id);
__isl_give isl_multi_val *isl_multi_val_insert_dims(
__isl_take isl_multi_val *mv,
enum isl_dim_type type, unsigned first, unsigned n);
__isl_give isl_multi_val *isl_multi_val_add_dims(
__isl_take isl_multi_val *mv,
enum isl_dim_type type, unsigned n);
__isl_give isl_multi_val *isl_multi_val_drop_dims(
__isl_take isl_multi_val *mv,
enum isl_dim_type type, unsigned first, unsigned n);
Operations include
#include <isl/val.h>
__isl_give isl_multi_val *isl_multi_val_align_params(
__isl_take isl_multi_val *mv,
__isl_take isl_space *model);
__isl_give isl_multi_val *isl_multi_val_from_range(
__isl_take isl_multi_val *mv);
__isl_give isl_multi_val *isl_multi_val_range_splice(
__isl_take isl_multi_val *mv1, unsigned pos,
__isl_take isl_multi_val *mv2);
__isl_give isl_multi_val *isl_multi_val_range_product(
__isl_take isl_multi_val *mv1,
__isl_take isl_multi_val *mv2);
__isl_give isl_multi_val *isl_multi_val_flat_range_product(
__isl_take isl_multi_val *mv1,
__isl_take isl_multi_aff *mv2);
__isl_give isl_multi_val *isl_multi_val_product(
__isl_take isl_multi_val *mv1,
__isl_take isl_multi_val *mv2);
__isl_give isl_multi_val *isl_multi_val_add_val(
__isl_take isl_multi_val *mv,
__isl_take isl_val *v);
__isl_give isl_multi_val *isl_multi_val_mod_val(
__isl_take isl_multi_val *mv,
__isl_take isl_val *v);
__isl_give isl_multi_val *isl_multi_val_scale_val(
__isl_take isl_multi_val *mv,
__isl_take isl_val *v);
__isl_give isl_multi_val *isl_multi_val_scale_multi_val(
__isl_take isl_multi_val *mv1,
__isl_take isl_multi_val *mv2);
__isl_give isl_multi_val *
isl_multi_val_scale_down_multi_val(
__isl_take isl_multi_val *mv1,
__isl_take isl_multi_val *mv2);
A multiple value can be printed using
__isl_give isl_printer *isl_printer_print_multi_val(
__isl_take isl_printer *p,
__isl_keep isl_multi_val *mv);
Vectors can be created, copied and freed using the following functions.
#include <isl/vec.h>
__isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
unsigned size);
__isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
void *isl_vec_free(__isl_take isl_vec *vec);
Note that the elements of a newly created vector may have arbitrary values. The elements can be changed and inspected using the following functions.
isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
int isl_vec_size(__isl_keep isl_vec *vec);
__isl_give isl_val *isl_vec_get_element_val(
__isl_keep isl_vec *vec, int pos);
__isl_give isl_vec *isl_vec_set_element_si(
__isl_take isl_vec *vec, int pos, int v);
__isl_give isl_vec *isl_vec_set_element_val(
__isl_take isl_vec *vec, int pos,
__isl_take isl_val *v);
__isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
int v);
__isl_give isl_vec *isl_vec_set_val(
__isl_take isl_vec *vec, __isl_take isl_val *v);
int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
__isl_keep isl_vec *vec2, int pos);
isl_vec_get_element will return a negative value if anything went wrong.
In that case, the value of *v is undefined.
The following function can be used to concatenate two vectors.
__isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
__isl_take isl_vec *vec2);
Matrices can be created, copied and freed using the following functions.
#include <isl/mat.h>
__isl_give isl_mat *isl_mat_alloc(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.
isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
int isl_mat_rows(__isl_keep isl_mat *mat);
int isl_mat_cols(__isl_keep isl_mat *mat);
__isl_give isl_val *isl_mat_get_element_val(
__isl_keep isl_mat *mat, int row, int col);
__isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
int row, int col, int v);
__isl_give isl_mat *isl_mat_set_element_val(
__isl_take isl_mat *mat, int row, int col,
__isl_take isl_val *v);
isl_mat_get_element will return a negative value if anything went wrong.
In that case, the value of *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);
The zero quasi affine expression or the quasi affine expression that is equal to a given value or a specified dimension on a given domain can be created using
__isl_give isl_aff *isl_aff_zero_on_domain(
__isl_take isl_local_space *ls);
__isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
__isl_take isl_local_space *ls);
__isl_give isl_aff *isl_aff_val_on_domain(
__isl_take isl_local_space *ls,
__isl_take isl_val *val);
__isl_give isl_aff *isl_aff_var_on_domain(
__isl_take isl_local_space *ls,
enum isl_dim_type type, unsigned pos);
__isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
__isl_take isl_local_space *ls,
enum isl_dim_type type, unsigned pos);
Note that the space in which the resulting objects live is a map space with the given space as domain and a one-dimensional range.
An empty piecewise quasi affine expression (one with no cells) or a piecewise quasi affine expression with a single cell can be created using the following functions.
#include <isl/aff.h>
__isl_give isl_pw_aff *isl_pw_aff_empty(
__isl_take isl_space *space);
__isl_give isl_pw_aff *isl_pw_aff_alloc(
__isl_take isl_set *set, __isl_take isl_aff *aff);
__isl_give isl_pw_aff *isl_pw_aff_from_aff(
__isl_take isl_aff *aff);
A piecewise quasi affine expression that is equal to 1 on a set and 0 outside the set can be created using the following function.
#include <isl/aff.h>
__isl_give isl_pw_aff *isl_set_indicator_function(
__isl_take isl_set *set);
Quasi affine expressions can be copied and freed using
#include <isl/aff.h>
__isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
void *isl_aff_free(__isl_take isl_aff *aff);
__isl_give isl_pw_aff *isl_pw_aff_copy(
__isl_keep isl_pw_aff *pwaff);
void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
A (rational) bound on a dimension can be extracted from an isl_constraint
using the following function. The constraint is required to have
a non-zero coefficient for the specified dimension.
#include <isl/constraint.h>
__isl_give isl_aff *isl_constraint_get_bound(
__isl_keep isl_constraint *constraint,
enum isl_dim_type type, int pos);
The entire affine expression of the constraint can also be extracted using the following function.
#include <isl/constraint.h>
__isl_give isl_aff *isl_constraint_get_aff(
__isl_keep isl_constraint *constraint);
Conversely, an equality constraint equating the affine expression to zero or an inequality constraint enforcing the affine expression to be non-negative, can be constructed using
__isl_give isl_constraint *isl_equality_from_aff(
__isl_take isl_aff *aff);
__isl_give isl_constraint *isl_inequality_from_aff(
__isl_take isl_aff *aff);
The expression can be inspected using
#include <isl/aff.h>
isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
int isl_aff_dim(__isl_keep isl_aff *aff,
enum isl_dim_type type);
__isl_give isl_local_space *isl_aff_get_domain_local_space(
__isl_keep isl_aff *aff);
__isl_give isl_local_space *isl_aff_get_local_space(
__isl_keep isl_aff *aff);
const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
enum isl_dim_type type, unsigned pos);
const char *isl_pw_aff_get_dim_name(
__isl_keep isl_pw_aff *pa,
enum isl_dim_type type, unsigned pos);
int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
enum isl_dim_type type, unsigned pos);
__isl_give isl_id *isl_pw_aff_get_dim_id(
__isl_keep isl_pw_aff *pa,
enum isl_dim_type type, unsigned pos);
int isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
enum isl_dim_type type);
__isl_give isl_id *isl_pw_aff_get_tuple_id(
__isl_keep isl_pw_aff *pa,
enum isl_dim_type type);
__isl_give isl_val *isl_aff_get_constant_val(
__isl_keep isl_aff *aff);
__isl_give isl_val *isl_aff_get_coefficient_val(
__isl_keep isl_aff *aff,
enum isl_dim_type type, int pos);
__isl_give isl_val *isl_aff_get_denominator_val(
__isl_keep isl_aff *aff);
__isl_give isl_aff *isl_aff_get_div(
__isl_keep isl_aff *aff, int pos);
int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
int (*fn)(__isl_take isl_set *set,
__isl_take isl_aff *aff,
void *user), void *user);
int isl_aff_is_cst(__isl_keep isl_aff *aff);
int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
int isl_aff_involves_dims(__isl_keep isl_aff *aff,
enum isl_dim_type type, unsigned first, unsigned n);
int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
enum isl_dim_type type, unsigned first, unsigned n);
isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
enum isl_dim_type type);
int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
It can be modified using
#include <isl/aff.h>
__isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
__isl_take isl_pw_aff *pwaff,
enum isl_dim_type type, __isl_take isl_id *id);
__isl_give isl_aff *isl_aff_set_dim_name(
__isl_take isl_aff *aff, enum isl_dim_type type,
unsigned pos, const char *s);
__isl_give isl_aff *isl_aff_set_dim_id(
__isl_take isl_aff *aff, enum isl_dim_type type,
unsigned pos, __isl_take isl_id *id);
__isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
__isl_take isl_pw_aff *pma,
enum isl_dim_type type, unsigned pos,
__isl_take isl_id *id);
__isl_give isl_aff *isl_aff_set_constant_si(
__isl_take isl_aff *aff, int v);
__isl_give isl_aff *isl_aff_set_constant_val(
__isl_take isl_aff *aff, __isl_take isl_val *v);
__isl_give isl_aff *isl_aff_set_coefficient_si(
__isl_take isl_aff *aff,
enum isl_dim_type type, int pos, int v);
__isl_give isl_aff *isl_aff_set_coefficient_val(
__isl_take isl_aff *aff,
enum isl_dim_type type, int pos,
__isl_take isl_val *v);
__isl_give isl_aff *isl_aff_add_constant_si(
__isl_take isl_aff *aff, int v);
__isl_give isl_aff *isl_aff_add_constant_val(
__isl_take isl_aff *aff, __isl_take isl_val *v);
__isl_give isl_aff *isl_aff_add_constant_num_si(
__isl_take isl_aff *aff, int v);
__isl_give isl_aff *isl_aff_add_coefficient_si(
__isl_take isl_aff *aff,
enum isl_dim_type type, int pos, int v);
__isl_give isl_aff *isl_aff_add_coefficient_val(
__isl_take isl_aff *aff,
enum isl_dim_type type, int pos,
__isl_take isl_val *v);
__isl_give isl_aff *isl_aff_insert_dims(
__isl_take isl_aff *aff,
enum isl_dim_type type, unsigned first, unsigned n);
__isl_give isl_pw_aff *isl_pw_aff_insert_dims(
__isl_take isl_pw_aff *pwaff,
enum isl_dim_type type, unsigned first, unsigned n);
__isl_give isl_aff *isl_aff_add_dims(
__isl_take isl_aff *aff,
enum isl_dim_type type, unsigned n);
__isl_give isl_pw_aff *isl_pw_aff_add_dims(
__isl_take isl_pw_aff *pwaff,
enum isl_dim_type type, unsigned n);
__isl_give isl_aff *isl_aff_drop_dims(
__isl_take isl_aff *aff,
enum isl_dim_type type, unsigned first, unsigned n);
__isl_give isl_pw_aff *isl_pw_aff_drop_dims(
__isl_take isl_pw_aff *pwaff,
enum isl_dim_type type, unsigned first, unsigned n);
__isl_give isl_aff *isl_aff_move_dims(
__isl_take isl_aff *aff,
enum isl_dim_type dst_type, unsigned dst_pos,
enum isl_dim_type src_type, unsigned src_pos,
unsigned n);
__isl_give isl_pw_aff *isl_pw_aff_move_dims(
__isl_take isl_pw_aff *pa,
enum isl_dim_type dst_type, unsigned dst_pos,
enum isl_dim_type src_type, unsigned src_pos,
unsigned n);
Note that isl_aff_set_constant_si and isl_aff_set_coefficient_si
set the numerator of the constant or coefficient, while
isl_aff_set_constant_val and isl_aff_set_coefficient_val set
the constant or coefficient as a whole.
The add_constant and add_coefficient functions add an integer
or rational value to
the possibly rational constant or coefficient.
The add_constant_num functions add an integer value to
the numerator.
To check whether an affine expressions is obviously zero or (obviously) equal to some other affine expression, use
#include <isl/aff.h>
int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
__isl_keep isl_aff *aff2);
int isl_pw_aff_plain_is_equal(
__isl_keep isl_pw_aff *pwaff1,
__isl_keep isl_pw_aff *pwaff2);
int isl_pw_aff_is_equal(__isl_keep isl_pw_aff *pa1,
__isl_keep isl_pw_aff *pa2);
Operations include
#include <isl/aff.h>
__isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
__isl_take isl_aff *aff2);
__isl_give isl_pw_aff *isl_pw_aff_add(
__isl_take isl_pw_aff *pwaff1,
__isl_take isl_pw_aff *pwaff2);
__isl_give isl_pw_aff *isl_pw_aff_min(
__isl_take isl_pw_aff *pwaff1,
__isl_take isl_pw_aff *pwaff2);
__isl_give isl_pw_aff *isl_pw_aff_max(
__isl_take isl_pw_aff *pwaff1,
__isl_take isl_pw_aff *pwaff2);
__isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
__isl_take isl_aff *aff2);
__isl_give isl_pw_aff *isl_pw_aff_sub(
__isl_take isl_pw_aff *pwaff1,
__isl_take isl_pw_aff *pwaff2);
__isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
__isl_give isl_pw_aff *isl_pw_aff_neg(
__isl_take isl_pw_aff *pwaff);
__isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
__isl_give isl_pw_aff *isl_pw_aff_ceil(
__isl_take isl_pw_aff *pwaff);
__isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
__isl_give isl_pw_aff *isl_pw_aff_floor(
__isl_take isl_pw_aff *pwaff);
__isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
__isl_take isl_val *mod);
__isl_give isl_pw_aff *isl_pw_aff_mod_val(
__isl_take isl_pw_aff *pa,
__isl_take isl_val *mod);
__isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
__isl_take isl_val *v);
__isl_give isl_pw_aff *isl_pw_aff_scale_val(
__isl_take isl_pw_aff *pa, __isl_take isl_val *v);
__isl_give isl_aff *isl_aff_scale_down_ui(
__isl_take isl_aff *aff, unsigned f);
__isl_give isl_aff *isl_aff_scale_down_val(
__isl_take isl_aff *aff, __isl_take isl_val *v);
__isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
__isl_take isl_pw_aff *pa,
__isl_take isl_val *f);
__isl_give isl_pw_aff *isl_pw_aff_list_min(
__isl_take isl_pw_aff_list *list);
__isl_give isl_pw_aff *isl_pw_aff_list_max(
__isl_take isl_pw_aff_list *list);
__isl_give isl_pw_aff *isl_pw_aff_coalesce(
__isl_take isl_pw_aff *pwqp);
__isl_give isl_aff *isl_aff_align_params(
__isl_take isl_aff *aff,
__isl_take isl_space *model);
__isl_give isl_pw_aff *isl_pw_aff_align_params(
__isl_take isl_pw_aff *pwaff,
__isl_take isl_space *model);
__isl_give isl_aff *isl_aff_project_domain_on_params(
__isl_take isl_aff *aff);
__isl_give isl_pw_aff *isl_pw_aff_from_range(
__isl_take isl_pw_aff *pwa);
__isl_give isl_aff *isl_aff_gist_params(
__isl_take isl_aff *aff,
__isl_take isl_set *context);
__isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
__isl_take isl_set *context);
__isl_give isl_pw_aff *isl_pw_aff_gist_params(
__isl_take isl_pw_aff *pwaff,
__isl_take isl_set *context);
__isl_give isl_pw_aff *isl_pw_aff_gist(
__isl_take isl_pw_aff *pwaff,
__isl_take isl_set *context);
__isl_give isl_set *isl_pw_aff_domain(
__isl_take isl_pw_aff *pwaff);
__isl_give isl_set *isl_pw_aff_params(
__isl_take isl_pw_aff *pwa);
__isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
__isl_take isl_pw_aff *pa,
__isl_take isl_set *set);
__isl_give isl_pw_aff *isl_pw_aff_intersect_params(
__isl_take isl_pw_aff *pa,
__isl_take isl_set *set);
__isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
__isl_take isl_aff *aff2);
__isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
__isl_take isl_aff *aff2);
__isl_give isl_pw_aff *isl_pw_aff_mul(
__isl_take isl_pw_aff *pwaff1,
__isl_take isl_pw_aff *pwaff2);
__isl_give isl_pw_aff *isl_pw_aff_div(
__isl_take isl_pw_aff *pa1,
__isl_take isl_pw_aff *pa2);
__isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
__isl_take isl_pw_aff *pa1,
__isl_take isl_pw_aff *pa2);
__isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
__isl_take isl_pw_aff *pa1,
__isl_take isl_pw_aff *pa2);
When multiplying two affine expressions, at least one of the two needs
to be a constant. Similarly, when dividing an affine expression by another,
the second expression needs to be a constant.
isl_pw_aff_tdiv_q computes the quotient of an integer division with
rounding towards zero. isl_pw_aff_tdiv_r computes the corresponding
remainder.
#include <isl/aff.h>
__isl_give isl_aff *isl_aff_pullback_aff(
__isl_take isl_aff *aff1,
__isl_take isl_aff *aff2);
__isl_give isl_aff *isl_aff_pullback_multi_aff(
__isl_take isl_aff *aff,
__isl_take isl_multi_aff *ma);
__isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
__isl_take isl_pw_aff *pa,
__isl_take isl_multi_aff *ma);
__isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
__isl_take isl_pw_aff *pa,
__isl_take isl_pw_multi_aff *pma);
These functions precompose the input expression by the given
isl_aff, isl_multi_aff or isl_pw_multi_aff. In other words,
the isl_aff, isl_multi_aff or isl_pw_multi_aff is plugged
into the (piecewise) affine expression.
Objects of type isl_multi_aff are described in
Piecewise Multiple Quasi Affine Expressions.
#include <isl/aff.h>
__isl_give isl_basic_set *isl_aff_zero_basic_set(
__isl_take isl_aff *aff);
__isl_give isl_basic_set *isl_aff_neg_basic_set(
__isl_take isl_aff *aff);
__isl_give isl_basic_set *isl_aff_le_basic_set(
__isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
__isl_give isl_basic_set *isl_aff_ge_basic_set(
__isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
__isl_give isl_set *isl_pw_aff_eq_set(
__isl_take isl_pw_aff *pwaff1,
__isl_take isl_pw_aff *pwaff2);
__isl_give isl_set *isl_pw_aff_ne_set(
__isl_take isl_pw_aff *pwaff1,
__isl_take isl_pw_aff *pwaff2);
__isl_give isl_set *isl_pw_aff_le_set(
__isl_take isl_pw_aff *pwaff1,
__isl_take isl_pw_aff *pwaff2);
__isl_give isl_set *isl_pw_aff_lt_set(
__isl_take isl_pw_aff *pwaff1,
__isl_take isl_pw_aff *pwaff2);
__isl_give isl_set *isl_pw_aff_ge_set(
__isl_take isl_pw_aff *pwaff1,
__isl_take isl_pw_aff *pwaff2);
__isl_give isl_set *isl_pw_aff_gt_set(
__isl_take isl_pw_aff *pwaff1,
__isl_take isl_pw_aff *pwaff2);
__isl_give isl_set *isl_pw_aff_list_eq_set(
__isl_take isl_pw_aff_list *list1,
__isl_take isl_pw_aff_list *list2);
__isl_give isl_set *isl_pw_aff_list_ne_set(
__isl_take isl_pw_aff_list *list1,
__isl_take isl_pw_aff_list *list2);
__isl_give isl_set *isl_pw_aff_list_le_set(
__isl_take isl_pw_aff_list *list1,
__isl_take isl_pw_aff_list *list2);
__isl_give isl_set *isl_pw_aff_list_lt_set(
__isl_take isl_pw_aff_list *list1,
__isl_take isl_pw_aff_list *list2);
__isl_give isl_set *isl_pw_aff_list_ge_set(
__isl_take isl_pw_aff_list *list1,
__isl_take isl_pw_aff_list *list2);
__isl_give isl_set *isl_pw_aff_list_gt_set(
__isl_take isl_pw_aff_list *list1,
__isl_take isl_pw_aff_list *list2);
The function isl_aff_neg_basic_set returns a basic set
containing those elements in the domain space
of aff where aff is negative.
The function isl_aff_ge_basic_set returns a basic set
containing those elements in the shared space
of aff1 and aff2 where aff1 is greater than or equal to aff2.
The function isl_pw_aff_ge_set returns a set
containing those elements in the shared domain
of pwaff1 and pwaff2 where pwaff1 is greater than or equal to pwaff2.
The functions operating on isl_pw_aff_list apply the corresponding
isl_pw_aff function to each pair of elements in the two lists.
#include <isl/aff.h>
__isl_give isl_set *isl_pw_aff_nonneg_set(
__isl_take isl_pw_aff *pwaff);
__isl_give isl_set *isl_pw_aff_zero_set(
__isl_take isl_pw_aff *pwaff);
__isl_give isl_set *isl_pw_aff_non_zero_set(
__isl_take isl_pw_aff *pwaff);
The function isl_pw_aff_nonneg_set returns a set
containing those elements in the domain
of pwaff where pwaff is non-negative.
#include <isl/aff.h>
__isl_give isl_pw_aff *isl_pw_aff_cond(
__isl_take isl_pw_aff *cond,
__isl_take isl_pw_aff *pwaff_true,
__isl_take isl_pw_aff *pwaff_false);
The function isl_pw_aff_cond performs a conditional operator
and returns an expression that is equal to pwaff_true
for elements where cond is non-zero and equal to pwaff_false for elements
where cond is zero.
#include <isl/aff.h>
__isl_give isl_pw_aff *isl_pw_aff_union_min(
__isl_take isl_pw_aff *pwaff1,
__isl_take isl_pw_aff *pwaff2);
__isl_give isl_pw_aff *isl_pw_aff_union_max(
__isl_take isl_pw_aff *pwaff1,
__isl_take isl_pw_aff *pwaff2);
__isl_give isl_pw_aff *isl_pw_aff_union_add(
__isl_take isl_pw_aff *pwaff1,
__isl_take isl_pw_aff *pwaff2);
The function isl_pw_aff_union_max computes a piecewise quasi-affine
expression with a domain that is the union of those of pwaff1 and
pwaff2 and such that on each cell, the quasi-affine expression is
the maximum of those of pwaff1 and pwaff2. If only one of
pwaff1 or pwaff2 is defined on a given cell, then the
associated expression is the defined one.
An expression can be read from input using
#include <isl/aff.h>
__isl_give isl_aff *isl_aff_read_from_str(
isl_ctx *ctx, const char *str);
__isl_give isl_pw_aff *isl_pw_aff_read_from_str(
isl_ctx *ctx, const char *str);
An expression can be printed using
#include <isl/aff.h>
__isl_give isl_printer *isl_printer_print_aff(
__isl_take isl_printer *p, __isl_keep isl_aff *aff);
__isl_give isl_printer *isl_printer_print_pw_aff(
__isl_take isl_printer *p,
__isl_keep isl_pw_aff *pwaff);
An isl_multi_aff object represents a sequence of
zero or more affine expressions, all defined on the same domain space.
Similarly, an isl_multi_pw_aff object represents a sequence of
zero or more piecewise affine expressions.
An isl_multi_aff can be constructed from a single
isl_aff or an isl_aff_list using the
following functions. Similarly for isl_multi_pw_aff
and isl_pw_multi_aff.
#include <isl/aff.h>
__isl_give isl_multi_aff *isl_multi_aff_from_aff(
__isl_take isl_aff *aff);
__isl_give isl_multi_pw_aff *
isl_multi_pw_aff_from_multi_aff(
__isl_take isl_multi_aff *ma);
__isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
__isl_take isl_pw_aff *pa);
__isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
__isl_take isl_pw_aff *pa);
__isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
__isl_take isl_space *space,
__isl_take isl_aff_list *list);
An isl_multi_pw_aff can be converted to an isl_pw_multi_aff
using the function isl_pw_multi_aff_from_multi_pw_aff below.
Note however that the domain
of the result is the intersection of the domains of the input.
The reverse conversion is exact.
#include <isl/aff.h>
__isl_give isl_pw_multi_aff *
isl_pw_multi_aff_from_multi_pw_aff(
__isl_take isl_multi_pw_aff *mpa);
__isl_give isl_multi_pw_aff *
isl_multi_pw_aff_from_pw_multi_aff(
__isl_take isl_pw_multi_aff *pma);
An empty piecewise multiple quasi affine expression (one with no cells), the zero piecewise multiple quasi affine expression (with value zero for each output dimension), a piecewise multiple quasi affine expression with a single cell (with either a universe or a specified domain) or a zero-dimensional piecewise multiple quasi affine expression on a given domain can be created using the following functions.
#include <isl/aff.h>
__isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
__isl_take isl_space *space);
__isl_give isl_multi_aff *isl_multi_aff_zero(
__isl_take isl_space *space);
__isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
__isl_take isl_space *space);
__isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
__isl_take isl_space *space);
__isl_give isl_multi_aff *isl_multi_aff_identity(
__isl_take isl_space *space);
__isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
__isl_take isl_space *space);
__isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
__isl_take isl_space *space);
__isl_give isl_multi_aff *isl_multi_aff_domain_map(
__isl_take isl_space *space);
__isl_give isl_multi_aff *isl_multi_aff_range_map(
__isl_take isl_space *space);
__isl_give isl_multi_aff *isl_multi_aff_project_out_map(
__isl_take isl_space *space,
enum isl_dim_type type,
unsigned first, unsigned n);
__isl_give isl_pw_multi_aff *
isl_pw_multi_aff_project_out_map(
__isl_take isl_space *space,
enum isl_dim_type type,
unsigned first, unsigned n);
__isl_give isl_pw_multi_aff *
isl_pw_multi_aff_from_multi_aff(
__isl_take isl_multi_aff *ma);
__isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
__isl_take isl_set *set,
__isl_take isl_multi_aff *maff);
__isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
__isl_take isl_set *set);
__isl_give isl_union_pw_multi_aff *
isl_union_pw_multi_aff_empty(
__isl_take isl_space *space);
__isl_give isl_union_pw_multi_aff *
isl_union_pw_multi_aff_add_pw_multi_aff(
__isl_take isl_union_pw_multi_aff *upma,
__isl_take isl_pw_multi_aff *pma);
__isl_give isl_union_pw_multi_aff *
isl_union_pw_multi_aff_from_domain(
__isl_take isl_union_set *uset);
A piecewise multiple quasi affine expression can also be initialized
from an isl_set or isl_map, provided the isl_set is a singleton
and the isl_map is single-valued.
In case of a conversion from an isl_union_set or an isl_union_map
to an isl_union_pw_multi_aff, these properties need to hold in each space.
__isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
__isl_take isl_set *set);
__isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
__isl_take isl_map *map);
__isl_give isl_union_pw_multi_aff *
isl_union_pw_multi_aff_from_union_set(
__isl_take isl_union_set *uset);
__isl_give isl_union_pw_multi_aff *
isl_union_pw_multi_aff_from_union_map(
__isl_take isl_union_map *umap);
Multiple quasi affine expressions can be copied and freed using
#include <isl/aff.h>
__isl_give isl_multi_aff *isl_multi_aff_copy(
__isl_keep isl_multi_aff *maff);
void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
__isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
__isl_keep isl_pw_multi_aff *pma);
void *isl_pw_multi_aff_free(
__isl_take isl_pw_multi_aff *pma);
__isl_give isl_union_pw_multi_aff *
isl_union_pw_multi_aff_copy(
__isl_keep isl_union_pw_multi_aff *upma);
void *isl_union_pw_multi_aff_free(
__isl_take isl_union_pw_multi_aff *upma);
__isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
__isl_keep isl_multi_pw_aff *mpa);
void *isl_multi_pw_aff_free(
__isl_take isl_multi_pw_aff *mpa);
The expression can be inspected using
#include <isl/aff.h>
isl_ctx *isl_multi_aff_get_ctx(
__isl_keep isl_multi_aff *maff);
isl_ctx *isl_pw_multi_aff_get_ctx(
__isl_keep isl_pw_multi_aff *pma);
isl_ctx *isl_union_pw_multi_aff_get_ctx(
__isl_keep isl_union_pw_multi_aff *upma);
isl_ctx *isl_multi_pw_aff_get_ctx(
__isl_keep isl_multi_pw_aff *mpa);
unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
enum isl_dim_type type);
unsigned isl_pw_multi_aff_dim(
__isl_keep isl_pw_multi_aff *pma,
enum isl_dim_type type);
unsigned isl_multi_pw_aff_dim(
__isl_keep isl_multi_pw_aff *mpa,
enum isl_dim_type type);
__isl_give isl_aff *isl_multi_aff_get_aff(
__isl_keep isl_multi_aff *multi, int pos);
__isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
__isl_keep isl_pw_multi_aff *pma, int pos);
__isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
__isl_keep isl_multi_pw_aff *mpa, int pos);
int isl_multi_aff_find_dim_by_id(
__isl_keep isl_multi_aff *ma,
enum isl_dim_type type, __isl_keep isl_id *id);
int isl_multi_pw_aff_find_dim_by_id(
__isl_keep isl_multi_pw_aff *mpa,
enum isl_dim_type type, __isl_keep isl_id *id);
const char *isl_pw_multi_aff_get_dim_name(
__isl_keep isl_pw_multi_aff *pma,
enum isl_dim_type type, unsigned pos);
__isl_give isl_id *isl_multi_aff_get_dim_id(
__isl_keep isl_multi_aff *ma,
enum isl_dim_type type, unsigned pos);
__isl_give isl_id *isl_pw_multi_aff_get_dim_id(
__isl_keep isl_pw_multi_aff *pma,
enum isl_dim_type type, unsigned pos);
__isl_give isl_id *isl_multi_pw_aff_get_dim_id(
__isl_keep isl_multi_pw_aff *mpa,
enum isl_dim_type type, unsigned pos);
const char *isl_multi_aff_get_tuple_name(
__isl_keep isl_multi_aff *multi,
enum isl_dim_type type);
int isl_pw_multi_aff_has_tuple_name(
__isl_keep isl_pw_multi_aff *pma,
enum isl_dim_type type);
const char *isl_pw_multi_aff_get_tuple_name(
__isl_keep isl_pw_multi_aff *pma,
enum isl_dim_type type);
int isl_multi_aff_has_tuple_id(__isl_keep isl_multi_aff *ma,
enum isl_dim_type type);
int isl_pw_multi_aff_has_tuple_id(
__isl_keep isl_pw_multi_aff *pma,
enum isl_dim_type type);
int isl_multi_pw_aff_has_tuple_id(
__isl_keep isl_multi_pw_aff *mpa,
enum isl_dim_type type);
__isl_give isl_id *isl_multi_aff_get_tuple_id(
__isl_keep isl_multi_aff *ma,
enum isl_dim_type type);
__isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
__isl_keep isl_pw_multi_aff *pma,
enum isl_dim_type type);
__isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
__isl_keep isl_multi_pw_aff *mpa,
enum isl_dim_type type);
__isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
__isl_take isl_multi_aff *ma,
enum isl_dim_type type);
__isl_give isl_multi_pw_aff *
isl_multi_pw_aff_reset_tuple_id(
__isl_take isl_multi_pw_aff *mpa,
enum isl_dim_type type);
int isl_pw_multi_aff_foreach_piece(
__isl_keep isl_pw_multi_aff *pma,
int (*fn)(__isl_take isl_set *set,
__isl_take isl_multi_aff *maff,
void *user), void *user);
int isl_union_pw_multi_aff_foreach_pw_multi_aff(
__isl_keep isl_union_pw_multi_aff *upma,
int (*fn)(__isl_take isl_pw_multi_aff *pma,
void *user), void *user);
It can be modified using
#include <isl/aff.h>
__isl_give isl_multi_aff *isl_multi_aff_set_aff(
__isl_take isl_multi_aff *multi, int pos,
__isl_take isl_aff *aff);
__isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
__isl_take isl_pw_multi_aff *pma, unsigned pos,
__isl_take isl_pw_aff *pa);
__isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
__isl_take isl_multi_aff *maff,
enum isl_dim_type type, unsigned pos, const char *s);
__isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
__isl_take isl_multi_aff *maff,
enum isl_dim_type type, unsigned pos,
__isl_take isl_id *id);
__isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
__isl_take isl_multi_aff *maff,
enum isl_dim_type type, const char *s);
__isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
__isl_take isl_multi_aff *maff,
enum isl_dim_type type, __isl_take isl_id *id);
__isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
__isl_take isl_pw_multi_aff *pma,
enum isl_dim_type type, __isl_take isl_id *id);
__isl_give isl_multi_pw_aff *
isl_multi_pw_aff_set_dim_name(
__isl_take isl_multi_pw_aff *mpa,
enum isl_dim_type type, unsigned pos, const char *s);
__isl_give isl_multi_pw_aff *
isl_multi_pw_aff_set_dim_id(
__isl_take isl_multi_pw_aff *mpa,
enum isl_dim_type type, unsigned pos,
__isl_take isl_id *id);
__isl_give isl_multi_pw_aff *
isl_multi_pw_aff_set_tuple_name(
__isl_take isl_multi_pw_aff *mpa,
enum isl_dim_type type, const char *s);
__isl_give isl_multi_aff *isl_multi_aff_insert_dims(
__isl_take isl_multi_aff *ma,
enum isl_dim_type type, unsigned first, unsigned n);
__isl_give isl_multi_aff *isl_multi_aff_add_dims(
__isl_take isl_multi_aff *ma,
enum isl_dim_type type, unsigned n);
__isl_give isl_multi_aff *isl_multi_aff_drop_dims(
__isl_take isl_multi_aff *maff,
enum isl_dim_type type, unsigned first, unsigned n);
__isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
__isl_take isl_pw_multi_aff *pma,
enum isl_dim_type type, unsigned first, unsigned n);
__isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
__isl_take isl_multi_pw_aff *mpa,
enum isl_dim_type type, unsigned first, unsigned n);
__isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
__isl_take isl_multi_pw_aff *mpa,
enum isl_dim_type type, unsigned n);
__isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
__isl_take isl_multi_pw_aff *pma,
enum isl_dim_type dst_type, unsigned dst_pos,
enum isl_dim_type src_type, unsigned src_pos,
unsigned n);
To check whether two multiple affine expressions are (obviously) equal to each other, use
int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
__isl_keep isl_multi_aff *maff2);
int isl_pw_multi_aff_plain_is_equal(
__isl_keep isl_pw_multi_aff *pma1,
__isl_keep isl_pw_multi_aff *pma2);
int isl_multi_pw_aff_plain_is_equal(
__isl_keep isl_multi_pw_aff *mpa1,
__isl_keep isl_multi_pw_aff *mpa2);
int isl_multi_pw_aff_is_equal(
__isl_keep isl_multi_pw_aff *mpa1,
__isl_keep isl_multi_pw_aff *mpa2);
Operations include
#include <isl/aff.h>
__isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
__isl_take isl_pw_multi_aff *pma1,
__isl_take isl_pw_multi_aff *pma2);
__isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
__isl_take isl_pw_multi_aff *pma1,
__isl_take isl_pw_multi_aff *pma2);
__isl_give isl_multi_aff *isl_multi_aff_add(
__isl_take isl_multi_aff *maff1,
__isl_take isl_multi_aff *maff2);
__isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
__isl_take isl_pw_multi_aff *pma1,
__isl_take isl_pw_multi_aff *pma2);
__isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
__isl_take isl_union_pw_multi_aff *upma1,
__isl_take isl_union_pw_multi_aff *upma2);
__isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
__isl_take isl_pw_multi_aff *pma1,
__isl_take isl_pw_multi_aff *pma2);
__isl_give isl_multi_aff *isl_multi_aff_sub(
__isl_take isl_multi_aff *ma1,
__isl_take isl_multi_aff *ma2);
__isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
__isl_take isl_pw_multi_aff *pma1,
__isl_take isl_pw_multi_aff *pma2);
__isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
__isl_take isl_union_pw_multi_aff *upma1,
__isl_take isl_union_pw_multi_aff *upma2);
isl_multi_aff_sub subtracts the second argument from the first.
__isl_give isl_multi_aff *isl_multi_aff_scale_val(
__isl_take isl_multi_aff *ma,
__isl_take isl_val *v);
__isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
__isl_take isl_pw_multi_aff *pma,
__isl_take isl_val *v);
__isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
__isl_take isl_multi_pw_aff *mpa,
__isl_take isl_val *v);
__isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
__isl_take isl_multi_aff *ma,
__isl_take isl_multi_val *mv);
__isl_give isl_pw_multi_aff *
isl_pw_multi_aff_scale_multi_val(
__isl_take isl_pw_multi_aff *pma,
__isl_take isl_multi_val *mv);
__isl_give isl_multi_pw_aff *
isl_multi_pw_aff_scale_multi_val(
__isl_take isl_multi_pw_aff *mpa,
__isl_take isl_multi_val *mv);
__isl_give isl_union_pw_multi_aff *
isl_union_pw_multi_aff_scale_multi_val(
__isl_take isl_union_pw_multi_aff *upma,
__isl_take isl_multi_val *mv);
__isl_give isl_multi_aff *
isl_multi_aff_scale_down_multi_val(
__isl_take isl_multi_aff *ma,
__isl_take isl_multi_val *mv);
__isl_give isl_multi_pw_aff *
isl_multi_pw_aff_scale_down_multi_val(
__isl_take isl_multi_pw_aff *mpa,
__isl_take isl_multi_val *mv);
isl_multi_aff_scale_multi_val scales the elements of ma
by the corresponding elements of mv.
__isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
__isl_take isl_pw_multi_aff *pma,
enum isl_dim_type type, unsigned pos, int value);
__isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
__isl_take isl_pw_multi_aff *pma,
__isl_take isl_set *set);
__isl_give isl_set *isl_multi_pw_aff_domain(
__isl_take isl_multi_pw_aff *mpa);
__isl_give isl_multi_pw_aff *
isl_multi_pw_aff_intersect_params(
__isl_take isl_multi_pw_aff *mpa,
__isl_take isl_set *set);
__isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
__isl_take isl_pw_multi_aff *pma,
__isl_take isl_set *set);
__isl_give isl_multi_pw_aff *
isl_multi_pw_aff_intersect_domain(
__isl_take isl_multi_pw_aff *mpa,
__isl_take isl_set *domain);
__isl_give isl_union_pw_multi_aff *
isl_union_pw_multi_aff_intersect_domain(
__isl_take isl_union_pw_multi_aff *upma,
__isl_take isl_union_set *uset);
__isl_give isl_multi_aff *isl_multi_aff_lift(
__isl_take isl_multi_aff *maff,
__isl_give isl_local_space **ls);
__isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
__isl_take isl_pw_multi_aff *pma);
__isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
__isl_take isl_multi_pw_aff *mpa);
__isl_give isl_multi_aff *isl_multi_aff_align_params(
__isl_take isl_multi_aff *multi,
__isl_take isl_space *model);
__isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
__isl_take isl_pw_multi_aff *pma,
__isl_take isl_space *model);
__isl_give isl_pw_multi_aff *
isl_pw_multi_aff_project_domain_on_params(
__isl_take isl_pw_multi_aff *pma);
__isl_give isl_multi_aff *isl_multi_aff_gist_params(
__isl_take isl_multi_aff *maff,
__isl_take isl_set *context);
__isl_give isl_multi_aff *isl_multi_aff_gist(
__isl_take isl_multi_aff *maff,
__isl_take isl_set *context);
__isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
__isl_take isl_pw_multi_aff *pma,
__isl_take isl_set *set);
__isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
__isl_take isl_pw_multi_aff *pma,
__isl_take isl_set *set);
__isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
__isl_take isl_multi_pw_aff *mpa,
__isl_take isl_set *set);
__isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
__isl_take isl_multi_pw_aff *mpa,
__isl_take isl_set *set);
__isl_give isl_multi_aff *isl_multi_aff_from_range(
__isl_take isl_multi_aff *ma);
__isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
__isl_take isl_multi_pw_aff *mpa);
__isl_give isl_set *isl_pw_multi_aff_domain(
__isl_take isl_pw_multi_aff *pma);
__isl_give isl_union_set *isl_union_pw_multi_aff_domain(
__isl_take isl_union_pw_multi_aff *upma);
__isl_give isl_multi_aff *isl_multi_aff_range_splice(
__isl_take isl_multi_aff *ma1, unsigned pos,
__isl_take isl_multi_aff *ma2);
__isl_give isl_multi_aff *isl_multi_aff_splice(
__isl_take isl_multi_aff *ma1,
unsigned in_pos, unsigned out_pos,
__isl_take isl_multi_aff *ma2);
__isl_give isl_multi_aff *isl_multi_aff_range_product(
__isl_take isl_multi_aff *ma1,
__isl_take isl_multi_aff *ma2);
__isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
__isl_take isl_multi_aff *ma1,
__isl_take isl_multi_aff *ma2);
__isl_give isl_multi_aff *isl_multi_aff_product(
__isl_take isl_multi_aff *ma1,
__isl_take isl_multi_aff *ma2);
__isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
__isl_take isl_multi_pw_aff *mpa1,
__isl_take isl_multi_pw_aff *mpa2);
__isl_give isl_pw_multi_aff *
isl_pw_multi_aff_range_product(
__isl_take isl_pw_multi_aff *pma1,
__isl_take isl_pw_multi_aff *pma2);
__isl_give isl_pw_multi_aff *
isl_pw_multi_aff_flat_range_product(
__isl_take isl_pw_multi_aff *pma1,
__isl_take isl_pw_multi_aff *pma2);
__isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
__isl_take isl_pw_multi_aff *pma1,
__isl_take isl_pw_multi_aff *pma2);
__isl_give isl_union_pw_multi_aff *
isl_union_pw_multi_aff_flat_range_product(
__isl_take isl_union_pw_multi_aff *upma1,
__isl_take isl_union_pw_multi_aff *upma2);
__isl_give isl_multi_pw_aff *
isl_multi_pw_aff_range_splice(
__isl_take isl_multi_pw_aff *mpa1, unsigned pos,
__isl_take isl_multi_pw_aff *mpa2);
__isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
__isl_take isl_multi_pw_aff *mpa1,
unsigned in_pos, unsigned out_pos,
__isl_take isl_multi_pw_aff *mpa2);
__isl_give isl_multi_pw_aff *
isl_multi_pw_aff_range_product(
__isl_take isl_multi_pw_aff *mpa1,
__isl_take isl_multi_pw_aff *mpa2);
__isl_give isl_multi_pw_aff *
isl_multi_pw_aff_flat_range_product(
__isl_take isl_multi_pw_aff *mpa1,
__isl_take isl_multi_pw_aff *mpa2);
If the ls argument of isl_multi_aff_lift is not NULL,
then it is assigned the local space that lies at the basis of
the lifting applied.
#include <isl/aff.h>
__isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
__isl_take isl_multi_aff *ma1,
__isl_take isl_multi_aff *ma2);
__isl_give isl_pw_multi_aff *
isl_pw_multi_aff_pullback_multi_aff(
__isl_take isl_pw_multi_aff *pma,
__isl_take isl_multi_aff *ma);
__isl_give isl_multi_pw_aff *
isl_multi_pw_aff_pullback_multi_aff(
__isl_take isl_multi_pw_aff *mpa,
__isl_take isl_multi_aff *ma);
__isl_give isl_pw_multi_aff *
isl_pw_multi_aff_pullback_pw_multi_aff(
__isl_take isl_pw_multi_aff *pma1,
__isl_take isl_pw_multi_aff *pma2);
__isl_give isl_multi_pw_aff *
isl_multi_pw_aff_pullback_pw_multi_aff(
__isl_take isl_multi_pw_aff *mpa,
__isl_take isl_pw_multi_aff *pma);
__isl_give isl_multi_pw_aff *
isl_multi_pw_aff_pullback_multi_pw_aff(
__isl_take isl_multi_pw_aff *mpa1,
__isl_take isl_multi_pw_aff *mpa2);
The function isl_multi_aff_pullback_multi_aff precomposes ma1 by ma2.
In other words, ma2 is plugged
into ma1.
__isl_give isl_set *isl_multi_aff_lex_le_set(
__isl_take isl_multi_aff *ma1,
__isl_take isl_multi_aff *ma2);
__isl_give isl_set *isl_multi_aff_lex_ge_set(
__isl_take isl_multi_aff *ma1,
__isl_take isl_multi_aff *ma2);
The function isl_multi_aff_lex_le_set returns a set
containing those elements in the shared domain space
where ma1 is lexicographically smaller than or
equal to ma2.
An expression can be read from input using
#include <isl/aff.h>
__isl_give isl_multi_aff *isl_multi_aff_read_from_str(
isl_ctx *ctx, const char *str);
__isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
isl_ctx *ctx, const char *str);
__isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
isl_ctx *ctx, const char *str);
__isl_give isl_union_pw_multi_aff *
isl_union_pw_multi_aff_read_from_str(
isl_ctx *ctx, const char *str);
An expression can be printed using
#include <isl/aff.h>
__isl_give isl_printer *isl_printer_print_multi_aff(
__isl_take isl_printer *p,
__isl_keep isl_multi_aff *maff);
__isl_give isl_printer *isl_printer_print_pw_multi_aff(
__isl_take isl_printer *p,
__isl_keep isl_pw_multi_aff *pma);
__isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
__isl_take isl_printer *p,
__isl_keep isl_union_pw_multi_aff *upma);
__isl_give isl_printer *isl_printer_print_multi_pw_aff(
__isl_take isl_printer *p,
__isl_keep isl_multi_pw_aff *mpa);
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_space *space);
The coordinates of a point can be inspected, set and changed using
__isl_give isl_val *isl_point_get_coordinate_val(
__isl_keep isl_point *pnt,
enum isl_dim_type type, int pos);
__isl_give isl_point *isl_point_set_coordinate_val(
__isl_take isl_point *pnt,
enum isl_dim_type type, int pos,
__isl_take isl_val *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);
Other properties can be obtained using
isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
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_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 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 fn is called for each integer point in
set with as second argument the last argument of
the isl_set_foreach_point call. The function fn
should return 0 on success and -1 on failure.
In the latter case, isl_set_foreach_point will stop
enumerating and return -1 as well.
If the enumeration is performed successfully and to completion,
then isl_set_foreach_point returns 0.
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);
If 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);
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 x to 1 + n - x for values of x between 0 and 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 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 }
Piecewise quasipolynomials can be read from input using
__isl_give isl_union_pw_qpolynomial *
isl_union_pw_qpolynomial_read_from_str(
isl_ctx *ctx, const char *str);
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 ISL_FORMAT_ISL or ISL_FORMAT_C.
For isl_printer_print_union_pw_qpolynomial, only ISL_FORMAT_ISL
is supported.
In case of printing in 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);
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_on_domain(
__isl_take isl_space *domain);
__isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
__isl_take isl_space *domain);
__isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
__isl_take isl_space *domain);
__isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
__isl_take isl_space *domain);
__isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
__isl_take isl_space *domain);
__isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
__isl_take isl_space *domain,
__isl_take isl_val *val);
__isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
__isl_take isl_space *domain,
enum isl_dim_type type, unsigned pos);
__isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
__isl_take isl_aff *aff);
Note that the space in which a quasipolynomial lives is a map space
with a one-dimensional range. The domain argument in some of
the functions above corresponds to the domain of this map space.
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_space *space);
__isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
__isl_take isl_set *set,
__isl_take isl_qpolynomial *qp);
__isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
__isl_take isl_qpolynomial *qp);
__isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
__isl_take isl_pw_aff *pwaff);
__isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
__isl_take isl_space *space);
__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);
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 in a given space from a union, use
__isl_give isl_pw_qpolynomial *
isl_union_pw_qpolynomial_extract_pw_qpolynomial(
__isl_keep isl_union_pw_qpolynomial *upwqp,
__isl_take isl_space *space);
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 fn should return 0 on success
and -1 on failure. The difference between
isl_pw_qpolynomial_foreach_piece and
isl_pw_qpolynomial_foreach_lifted_piece is that
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 set passed to fn
will not have any existentially quantified variables, but that
the dimensions of the sets may be different for different
invocations of fn.
The constant term of a quasipolynomial can be extracted using
__isl_give isl_val *isl_qpolynomial_get_constant_val(
__isl_keep isl_qpolynomial *qp);
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);
__isl_give isl_val *isl_term_get_coefficient_val(
__isl_keep isl_term *term);
int isl_term_get_exp(__isl_keep isl_term *term,
enum isl_dim_type type, unsigned pos);
__isl_give isl_aff *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 isl_term_get_exp
returns the exponent of a given dimensions in the given term.
To check whether two union piecewise quasipolynomials are obviously equal, use
int isl_union_pw_qpolynomial_plain_is_equal(
__isl_keep isl_union_pw_qpolynomial *upwqp1,
__isl_keep isl_union_pw_qpolynomial *upwqp2);
__isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
__isl_take isl_qpolynomial *qp,
__isl_take isl_val *v);
__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_qpolynomial *isl_qpolynomial_pow(
__isl_take isl_qpolynomial *qp, unsigned exponent);
__isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
__isl_take isl_pw_qpolynomial *pwqp,
enum isl_dim_type type, unsigned n,
__isl_take isl_val *v);
__isl_give isl_pw_qpolynomial *
isl_pw_qpolynomial_scale_val(
__isl_take isl_pw_qpolynomial *pwqp,
__isl_take isl_val *v);
__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_pw_qpolynomial *isl_pw_qpolynomial_pow(
__isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
__isl_give isl_union_pw_qpolynomial *
isl_union_pw_qpolynomial_scale_val(
__isl_take isl_union_pw_qpolynomial *upwqp,
__isl_take isl_val *v);
__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_val *isl_pw_qpolynomial_eval(
__isl_take isl_pw_qpolynomial *pwqp,
__isl_take isl_point *pnt);
__isl_give isl_val *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_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
__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_intersect_params(
__isl_take isl_union_pw_qpolynomial *upwpq,
__isl_take isl_set *set);
__isl_give isl_qpolynomial *isl_qpolynomial_align_params(
__isl_take isl_qpolynomial *qp,
__isl_take isl_space *model);
__isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
__isl_take isl_qpolynomial *qp);
__isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
__isl_take isl_pw_qpolynomial *pwqp);
__isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
__isl_take isl_union_pw_qpolynomial *upwqp);
__isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
__isl_take isl_qpolynomial *qp,
__isl_take isl_set *context);
__isl_give isl_qpolynomial *isl_qpolynomial_gist(
__isl_take isl_qpolynomial *qp,
__isl_take isl_set *context);
__isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
__isl_take isl_pw_qpolynomial *pwqp,
__isl_take isl_set *context);
__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_params(
__isl_take isl_union_pw_qpolynomial *upwqp,
__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 sign is positive,
the polynomial will be an overapproximation. If sign is negative,
it will be an underapproximation. If sign is zero, the approximation
will lie somewhere in between.
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 type argument may be either isl_fold_min or isl_fold_max.
If tight is not NULL, then *tight is set to 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 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 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);
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 isl_printer_print_pw_qpolynomial_fold,
output format of the printer
needs to be set to either ISL_FORMAT_ISL or ISL_FORMAT_C.
For isl_printer_print_union_pw_qpolynomial_fold,
output format of the printer
needs to be set to ISL_FORMAT_ISL.
In case of printing in 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);
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 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);
To check whether two union piecewise quasipolynomial reductions are obviously equal, use
int isl_union_pw_qpolynomial_fold_plain_is_equal(
__isl_keep isl_union_pw_qpolynomial_fold *upwf1,
__isl_keep isl_union_pw_qpolynomial_fold *upwf2);
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale_val(
__isl_take isl_qpolynomial_fold *fold,
__isl_take isl_val *v);
__isl_give isl_pw_qpolynomial_fold *
isl_pw_qpolynomial_fold_scale_val(
__isl_take isl_pw_qpolynomial_fold *pwf,
__isl_take isl_val *v);
__isl_give isl_union_pw_qpolynomial_fold *
isl_union_pw_qpolynomial_fold_scale_val(
__isl_take isl_union_pw_qpolynomial_fold *upwf,
__isl_take isl_val *v);
__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_val *isl_pw_qpolynomial_fold_eval(
__isl_take isl_pw_qpolynomial_fold *pwf,
__isl_take isl_point *pnt);
__isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
__isl_take isl_union_pw_qpolynomial_fold *upwf,
__isl_take isl_point *pnt);
__isl_give isl_pw_qpolynomial_fold *
isl_pw_qpolynomial_fold_intersect_params(
__isl_take isl_pw_qpolynomial_fold *pwf,
__isl_take isl_set *set);
__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_union_pw_qpolynomial_fold *
isl_union_pw_qpolynomial_fold_intersect_params(
__isl_take isl_union_pw_qpolynomial_fold *upwf,
__isl_take isl_set *set);
__isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
__isl_take isl_pw_qpolynomial_fold *pwf);
__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_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
__isl_take isl_qpolynomial_fold *fold,
__isl_take isl_set *context);
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
__isl_take isl_qpolynomial_fold *fold,
__isl_take isl_set *context);
__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_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
__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);
__isl_give isl_union_pw_qpolynomial_fold *
isl_union_pw_qpolynomial_fold_gist_params(
__isl_take isl_union_pw_qpolynomial_fold *upwf,
__isl_take isl_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 pwf or 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.
The parametric vertex enumeration described in this section
is mainly intended to be used internally and by the barvinok
library.
#include <isl/vertices.h>
__isl_give isl_vertices *isl_basic_set_compute_vertices(
__isl_keep isl_basic_set *bset);
The function isl_basic_set_compute_vertices performs the
actual computation of the parametric vertices and the chamber
decomposition and store the result in an 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 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);
isl_vertex_get_expr returns a singleton parametric set describing
the vertex, while isl_vertex_get_domain returns the activity domain
of the vertex.
Note that isl_vertex_get_domain and isl_vertex_get_expr return
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);
This section collects functionality in isl that has been specifically
designed for use during polyhedral compilation.
isl contains specialized functionality for performing
array dataflow analysis. That is, given a sink access relation
and a collection of possible source access relations,
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.
The resulting dependence relations map source iterations
to the corresponding sink iterations.
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 may
accesses, then there will be a dependence from the last
must access and from any may access that follows
this last must access.
In particular, if all sources are may accesses,
then memory based dependence analysis is performed.
If, on the other hand, all sources are must accesses,
then value based dependence analysis is performed.
#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,
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);
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 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_map *isl_flow_get_no_source(
__isl_keep isl_flow *deps, int must);
void isl_flow_free(__isl_take isl_flow *deps);
The function 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 isl_access_info, which can
be created through a call to isl_access_info_alloc.
The arguments to this functions are the sink access relation
sink, a token 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 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 n be the number of loops shared by
the two accesses. If first precedes second textually,
then the function should return 2 * n + 1; otherwise,
it should return 2 * n.
The sources can be added to the isl_access_info by performing
(at most) max_source calls to isl_access_info_add_source.
must indicates whether the source is a must access
or a may access. Note that a multi-valued access relation
should only be marked must if every iteration in the domain
of the relation accesses all elements in its image.
The source_user token is again used to identify
the source access. The range of the source access relation
source should have the same dimension as the range
of the sink access relation.
The isl_access_info_free function should usually not be
called explicitly, because it is called implicitly by
isl_access_info_compute_flow.
The result of the dependence analysis is collected in an
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 may accesses.
The relations containing these elements can be obtained through
calls to isl_flow_get_no_source, the first with must set
and the second with must unset.
In the case of standard flow dependence analysis,
with the sink a read and the sources must writes,
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
isl_flow_foreach. This function will call the user-specified
callback function fn for each 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 must or may dependence, a token
identifying the source and an additional void * with value
equal to the third argument of the isl_flow_foreach call.
A dependence is marked must if it originates from a must
source and if it is not followed by any may sources.
After finishing with an isl_flow, the user should call
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 must_no_source
and may_no_source are subsets of sink.
Any of must_dep, may_dep, must_no_source
or may_no_source may be NULL, but a NULL value for
any of the other arguments is treated as an error.
During the dependence analysis, we frequently need to perform
the following operation. Given a relation between sink iterations
and potential source iterations from a particular source domain,
what is the last potential source iteration corresponding to each
sink iteration. It can sometimes be convenient to adjust
the set of potential source iterations before or after each such operation.
The prototypical example is fuzzy array dataflow analysis,
where we need to analyze if, based on data-dependent constraints,
the sink iteration can ever be executed without one or more of
the corresponding potential source iterations being executed.
If so, we can introduce extra parameters and select an unknown
but fixed source iteration from the potential source iterations.
To be able to perform such manipulations, isl provides the following
function.
#include <isl/flow.h>
typedef __isl_give isl_restriction *(*isl_access_restrict)(
__isl_keep isl_map *source_map,
__isl_keep isl_set *sink, void *source_user,
void *user);
__isl_give isl_access_info *isl_access_info_set_restrict(
__isl_take isl_access_info *acc,
isl_access_restrict fn, void *user);
The function isl_access_info_set_restrict should be called
before calling isl_access_info_compute_flow and registers a callback function
that will be called any time isl is about to compute the last
potential source. The first argument is the (reverse) proto-dependence,
mapping sink iterations to potential source iterations.
The second argument represents the sink iterations for which
we want to compute the last source iteration.
The third argument is the token corresponding to the source
and the final argument is the token passed to isl_access_info_set_restrict.
The callback is expected to return a restriction on either the input or
the output of the operation computing the last potential source.
If the input needs to be restricted then restrictions are needed
for both the source and the sink iterations. The sink iterations
and the potential source iterations will be intersected with these sets.
If the output needs to be restricted then only a restriction on the source
iterations is required.
If any error occurs, the callback should return NULL.
An isl_restriction object can be created, freed and inspected
using the following functions.
#include <isl/flow.h>
__isl_give isl_restriction *isl_restriction_input(
__isl_take isl_set *source_restr,
__isl_take isl_set *sink_restr);
__isl_give isl_restriction *isl_restriction_output(
__isl_take isl_set *source_restr);
__isl_give isl_restriction *isl_restriction_none(
__isl_take isl_map *source_map);
__isl_give isl_restriction *isl_restriction_empty(
__isl_take isl_map *source_map);
void *isl_restriction_free(
__isl_take isl_restriction *restr);
isl_ctx *isl_restriction_get_ctx(
__isl_keep isl_restriction *restr);
isl_restriction_none and isl_restriction_empty are special
cases of isl_restriction_input. isl_restriction_none
is essentially equivalent to
isl_restriction_input(isl_set_universe(
isl_space_range(isl_map_get_space(source_map))),
isl_set_universe(
isl_space_domain(isl_map_get_space(source_map))));
whereas isl_restriction_empty is essentially equivalent to
isl_restriction_input(isl_set_empty(
isl_space_range(isl_map_get_space(source_map))),
isl_set_universe(
isl_space_domain(isl_map_get_space(source_map))));
The functionality described in this section is fairly new and may be subject to change.
The following function can be used to compute a schedule
for a union of domains.
By default, the algorithm used to construct the schedule is similar
to that of Pluto.
Alternatively, Feautrier's multi-dimensional scheduling algorithm can
be selected.
The generated schedule respects all validity dependences.
That is, all dependence distances over these dependences in the
scheduled space are lexicographically positive.
The default algorithm tries to minimize the dependence distances over
proximity dependences.
Moreover, it tries to obtain sequences (bands) of schedule dimensions
for groups of domains where the dependence distances have only
non-negative values.
When using Feautrier's algorithm, the proximity dependence
distances are only minimized during the extension to a
full-dimensional schedule.
#include <isl/schedule.h>
__isl_give isl_schedule *isl_union_set_compute_schedule(
__isl_take isl_union_set *domain,
__isl_take isl_union_map *validity,
__isl_take isl_union_map *proximity);
void *isl_schedule_free(__isl_take isl_schedule *sched);
A mapping from the domains to the scheduled space can be obtained
from an isl_schedule using the following function.
__isl_give isl_union_map *isl_schedule_get_map(
__isl_keep isl_schedule *sched);
A representation of the schedule can be printed using
__isl_give isl_printer *isl_printer_print_schedule(
__isl_take isl_printer *p,
__isl_keep isl_schedule *schedule);
A representation of the schedule as a forest of bands can be obtained using the following function.
__isl_give isl_band_list *isl_schedule_get_band_forest(
__isl_keep isl_schedule *schedule);
The individual bands can be visited in depth-first post-order using the following function.
#include <isl/schedule.h>
int isl_schedule_foreach_band(
__isl_keep isl_schedule *sched,
int (*fn)(__isl_keep isl_band *band, void *user),
void *user);
The list can be manipulated as explained in Lists. The bands inside the list can be copied and freed using the following functions.
#include <isl/band.h>
__isl_give isl_band *isl_band_copy(
__isl_keep isl_band *band);
void *isl_band_free(__isl_take isl_band *band);
Each band contains zero or more scheduling dimensions. These are referred to as the members of the band. The section of the schedule that corresponds to the band is referred to as the partial schedule of the band. For those nodes that participate in a band, the outer scheduling dimensions form the prefix schedule, while the inner scheduling dimensions form the suffix schedule. That is, if we take a cut of the band forest, then the union of the concatenations of the prefix, partial and suffix schedules of each band in the cut is equal to the entire schedule (modulo some possible padding at the end with zero scheduling dimensions). The properties of a band can be inspected using the following functions.
#include <isl/band.h>
isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
int isl_band_has_children(__isl_keep isl_band *band);
__isl_give isl_band_list *isl_band_get_children(
__isl_keep isl_band *band);
__isl_give isl_union_map *isl_band_get_prefix_schedule(
__isl_keep isl_band *band);
__isl_give isl_union_map *isl_band_get_partial_schedule(
__isl_keep isl_band *band);
__isl_give isl_union_map *isl_band_get_suffix_schedule(
__isl_keep isl_band *band);
int isl_band_n_member(__isl_keep isl_band *band);
int isl_band_member_is_zero_distance(
__isl_keep isl_band *band, int pos);
int isl_band_list_foreach_band(
__isl_keep isl_band_list *list,
int (*fn)(__isl_keep isl_band *band, void *user),
void *user);
Note that a scheduling dimension is considered to be ``zero
distance'' if it does not carry any proximity dependences
within its band.
That is, if the dependence distances of the proximity
dependences are all zero in that direction (for fixed
iterations of outer bands).
Like isl_schedule_foreach_band,
the function isl_band_list_foreach_band calls fn on the bands
in depth-first post-order.
A band can be tiled using the following function.
#include <isl/band.h>
int isl_band_tile(__isl_keep isl_band *band,
__isl_take isl_vec *sizes);
int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
int val);
int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
int val);
int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
The isl_band_tile function tiles the band using the given tile sizes
inside its schedule.
A new child band is created to represent the point loops and it is
inserted between the modified band and its children.
The tile_scale_tile_loops option specifies whether the tile
loops iterators should be scaled by the tile sizes.
If the tile_shift_point_loops option is set, then the point loops
are shifted to start at zero.
A band can be split into two nested bands using the following function.
int isl_band_split(__isl_keep isl_band *band, int pos);
The resulting outer band contains the first pos dimensions of band
while the inner band contains the remaining dimensions.
A representation of the band can be printed using
#include <isl/band.h>
__isl_give isl_printer *isl_printer_print_band(
__isl_take isl_printer *p,
__isl_keep isl_band *band);
#include <isl/schedule.h>
int isl_options_set_schedule_max_coefficient(
isl_ctx *ctx, int val);
int isl_options_get_schedule_max_coefficient(
isl_ctx *ctx);
int isl_options_set_schedule_max_constant_term(
isl_ctx *ctx, int val);
int isl_options_get_schedule_max_constant_term(
isl_ctx *ctx);
int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
int isl_options_get_schedule_fuse(isl_ctx *ctx);
int isl_options_set_schedule_maximize_band_depth(
isl_ctx *ctx, int val);
int isl_options_get_schedule_maximize_band_depth(
isl_ctx *ctx);
int isl_options_set_schedule_outer_zero_distance(
isl_ctx *ctx, int val);
int isl_options_get_schedule_outer_zero_distance(
isl_ctx *ctx);
int isl_options_set_schedule_split_scaled(
isl_ctx *ctx, int val);
int isl_options_get_schedule_split_scaled(
isl_ctx *ctx);
int isl_options_set_schedule_algorithm(
isl_ctx *ctx, int val);
int isl_options_get_schedule_algorithm(
isl_ctx *ctx);
int isl_options_set_schedule_separate_components(
isl_ctx *ctx, int val);
int isl_options_get_schedule_separate_components(
isl_ctx *ctx);
This option enforces that the coefficients for variable and parameter dimensions in the calculated schedule are not larger than the specified value. This option can significantly increase the speed of the scheduling calculation and may also prevent fusing of unrelated dimensions. A value of -1 means that this option does not introduce bounds on the variable or parameter coefficients.
This option enforces that the constant coefficients in the calculated schedule are not larger than the maximal constant term. This option can significantly increase the speed of the scheduling calculation and may also prevent fusing of unrelated dimensions. A value of -1 means that this option does not introduce bounds on the constant coefficients.
This option controls the level of fusion.
If this option is set to ISL_SCHEDULE_FUSE_MIN, then loops in the
resulting schedule will be distributed as much as possible.
If this option is set to ISL_SCHEDULE_FUSE_MAX, then isl will
try to fuse loops in the resulting schedule.
If this option is set, we do not split bands at the point
where we detect splitting is necessary. Instead, we
backtrack and split bands as early as possible. This
reduces the number of splits and maximizes the width of
the bands. Wider bands give more possibilities for tiling.
Note that if the schedule_fuse option is set to ISL_SCHEDULE_FUSE_MIN,
then bands will be split as early as possible, even if there is no need.
The schedule_maximize_band_depth option therefore has no effect in this case.
If this option is set, then we try to construct schedules where the outermost scheduling dimension in each band results in a zero dependence distance over the proximity dependences.
If this option is set, then we try to construct schedules in which the constant term is split off from the linear part if the linear parts of the scheduling rows for all nodes in the graphs have a common non-trivial divisor. The constant term is then placed in a separate band and the linear part is reduced.
Selects the scheduling algorithm to be used.
Available scheduling algorithms are ISL_SCHEDULE_ALGORITHM_ISL
and ISL_SCHEDULE_ALGORITHM_FEAUTRIER.
If at any point the dependence graph contains any (weakly connected) components, then these components are scheduled separately. If this option is not set, then some iterations of the domains in these components may be scheduled together. If this option is set, then the components are given consecutive schedules.
This section describes the isl functionality for generating
ASTs that visit all the elements
in a domain in an order specified by a schedule.
In particular, given a isl_union_map, an AST is generated
that visits all the elements in the domain of the isl_union_map
according to the lexicographic order of the corresponding image
element(s). If the range of the isl_union_map consists of
elements in more than one space, then each of these spaces is handled
separately in an arbitrary order.
It should be noted that the image elements only specify the order
in which the corresponding domain elements should be visited.
No direct relation between the image elements and the loop iterators
in the generated AST should be assumed.
Each AST is generated within a build. The initial build simply specifies the constraints on the parameters (if any) and can be created, inspected, copied and freed using the following functions.
#include <isl/ast_build.h>
__isl_give isl_ast_build *isl_ast_build_from_context(
__isl_take isl_set *set);
isl_ctx *isl_ast_build_get_ctx(
__isl_keep isl_ast_build *build);
__isl_give isl_ast_build *isl_ast_build_copy(
__isl_keep isl_ast_build *build);
void *isl_ast_build_free(
__isl_take isl_ast_build *build);
The set argument is usually a parameter set with zero or more parameters.
More isl_ast_build functions are described in Nested AST Generation
and Fine-grained Control over AST Generation.
Finally, the AST itself can be constructed using the following
function.
#include <isl/ast_build.h>
__isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
__isl_keep isl_ast_build *build,
__isl_take isl_union_map *schedule);
The basic properties of an AST node can be obtained as follows.
#include <isl/ast.h>
isl_ctx *isl_ast_node_get_ctx(
__isl_keep isl_ast_node *node);
enum isl_ast_node_type isl_ast_node_get_type(
__isl_keep isl_ast_node *node);
The type of an AST node is one of
isl_ast_node_for,
isl_ast_node_if,
isl_ast_node_block or
isl_ast_node_user.
An isl_ast_node_for represents a for node.
An isl_ast_node_if represents an if node.
An isl_ast_node_block represents a compound node.
An isl_ast_node_user represents an expression statement.
An expression statement typically corresponds to a domain element, i.e.,
one of the elements that is visited by the AST.
Each type of node has its own additional properties.
#include <isl/ast.h>
__isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
__isl_keep isl_ast_node *node);
__isl_give isl_ast_expr *isl_ast_node_for_get_init(
__isl_keep isl_ast_node *node);
__isl_give isl_ast_expr *isl_ast_node_for_get_cond(
__isl_keep isl_ast_node *node);
__isl_give isl_ast_expr *isl_ast_node_for_get_inc(
__isl_keep isl_ast_node *node);
__isl_give isl_ast_node *isl_ast_node_for_get_body(
__isl_keep isl_ast_node *node);
int isl_ast_node_for_is_degenerate(
__isl_keep isl_ast_node *node);
An isl_ast_for is considered degenerate if it is known to execute
exactly once.
#include <isl/ast.h>
__isl_give isl_ast_expr *isl_ast_node_if_get_cond(
__isl_keep isl_ast_node *node);
__isl_give isl_ast_node *isl_ast_node_if_get_then(
__isl_keep isl_ast_node *node);
int isl_ast_node_if_has_else(
__isl_keep isl_ast_node *node);
__isl_give isl_ast_node *isl_ast_node_if_get_else(
__isl_keep isl_ast_node *node);
__isl_give isl_ast_node_list *
isl_ast_node_block_get_children(
__isl_keep isl_ast_node *node);
__isl_give isl_ast_expr *isl_ast_node_user_get_expr(
__isl_keep isl_ast_node *node);
Each of the returned isl_ast_exprs can in turn be inspected using
the following functions.
#include <isl/ast.h>
isl_ctx *isl_ast_expr_get_ctx(
__isl_keep isl_ast_expr *expr);
enum isl_ast_expr_type isl_ast_expr_get_type(
__isl_keep isl_ast_expr *expr);
The type of an AST expression is one of
isl_ast_expr_op,
isl_ast_expr_id or
isl_ast_expr_int.
An isl_ast_expr_op represents the result of an operation.
An isl_ast_expr_id represents an identifier.
An isl_ast_expr_int represents an integer value.
Each type of expression has its own additional properties.
#include <isl/ast.h>
enum isl_ast_op_type isl_ast_expr_get_op_type(
__isl_keep isl_ast_expr *expr);
int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
__isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
__isl_keep isl_ast_expr *expr, int pos);
int isl_ast_node_foreach_ast_op_type(
__isl_keep isl_ast_node *node,
int (*fn)(enum isl_ast_op_type type, void *user),
void *user);
isl_ast_expr_get_op_type returns the type of the operation
performed. isl_ast_expr_get_op_n_arg returns the number of
arguments. isl_ast_expr_get_op_arg returns the specified
argument.
isl_ast_node_foreach_ast_op_type calls fn for each distinct
isl_ast_op_type that appears in node.
The operation type is one of the following.
isl_ast_op_andLogical and of two arguments. Both arguments can be evaluated.
isl_ast_op_and_thenLogical and of two arguments. The second argument can only be evaluated if the first evaluates to true.
isl_ast_op_orLogical or of two arguments. Both arguments can be evaluated.
isl_ast_op_or_elseLogical or of two arguments. The second argument can only be evaluated if the first evaluates to false.
isl_ast_op_maxMaximum of two or more arguments.
isl_ast_op_minMinimum of two or more arguments.
isl_ast_op_minusChange sign.
isl_ast_op_addSum of two arguments.
isl_ast_op_subDifference of two arguments.
isl_ast_op_mulProduct of two arguments.
isl_ast_op_divExact division. That is, the result is known to be an integer.
isl_ast_op_fdiv_qResult of integer division, rounded towards negative infinity.
isl_ast_op_pdiv_qResult of integer division, where dividend is known to be non-negative.
isl_ast_op_pdiv_rRemainder of integer division, where dividend is known to be non-negative.
isl_ast_op_condConditional operator defined on three arguments.
If the first argument evaluates to true, then the result
is equal to the second argument. Otherwise, the result
is equal to the third argument.
The second and third argument may only be evaluated if
the first argument evaluates to true and false, respectively.
Corresponds to a ? b : c in C.
isl_ast_op_selectConditional operator defined on three arguments.
If the first argument evaluates to true, then the result
is equal to the second argument. Otherwise, the result
is equal to the third argument.
The second and third argument may be evaluated independently
of the value of the first argument.
Corresponds to a * b + (1 - a) * c in C.
isl_ast_op_eqEquality relation.
isl_ast_op_leLess than or equal relation.
isl_ast_op_ltLess than relation.
isl_ast_op_geGreater than or equal relation.
isl_ast_op_gtGreater than relation.
isl_ast_op_callA function call.
The number of arguments of the isl_ast_expr is one more than
the number of arguments in the function call, the first argument
representing the function being called.
isl_ast_op_accessAn array access.
The number of arguments of the isl_ast_expr is one more than
the number of index expressions in the array access, the first argument
representing the array being accessed.
#include <isl/ast.h>
__isl_give isl_id *isl_ast_expr_get_id(
__isl_keep isl_ast_expr *expr);
Return the identifier represented by the AST expression.
#include <isl/ast.h>
__isl_give isl_val *isl_ast_expr_get_val(
__isl_keep isl_ast_expr *expr);
Return the integer represented by the AST expression.
#include <isl/ast.h>
int isl_ast_expr_is_equal(__isl_keep isl_ast_expr *expr1,
__isl_keep isl_ast_expr *expr2);
Check if two isl_ast_exprs are equal to each other.
AST nodes can be copied and freed using the following functions.
#include <isl/ast.h>
__isl_give isl_ast_node *isl_ast_node_copy(
__isl_keep isl_ast_node *node);
void *isl_ast_node_free(__isl_take isl_ast_node *node);
AST expressions can be copied and freed using the following functions.
#include <isl/ast.h>
__isl_give isl_ast_expr *isl_ast_expr_copy(
__isl_keep isl_ast_expr *expr);
void *isl_ast_expr_free(__isl_take isl_ast_expr *expr);
New AST expressions can be created either directly or within
the context of an isl_ast_build.
#include <isl/ast.h>
__isl_give isl_ast_expr *isl_ast_expr_from_val(
__isl_take isl_val *v);
__isl_give isl_ast_expr *isl_ast_expr_from_id(
__isl_take isl_id *id);
__isl_give isl_ast_expr *isl_ast_expr_neg(
__isl_take isl_ast_expr *expr);
__isl_give isl_ast_expr *isl_ast_expr_add(
__isl_take isl_ast_expr *expr1,
__isl_take isl_ast_expr *expr2);
__isl_give isl_ast_expr *isl_ast_expr_sub(
__isl_take isl_ast_expr *expr1,
__isl_take isl_ast_expr *expr2);
__isl_give isl_ast_expr *isl_ast_expr_mul(
__isl_take isl_ast_expr *expr1,
__isl_take isl_ast_expr *expr2);
__isl_give isl_ast_expr *isl_ast_expr_div(
__isl_take isl_ast_expr *expr1,
__isl_take isl_ast_expr *expr2);
__isl_give isl_ast_expr *isl_ast_expr_and(
__isl_take isl_ast_expr *expr1,
__isl_take isl_ast_expr *expr2)
__isl_give isl_ast_expr *isl_ast_expr_or(
__isl_take isl_ast_expr *expr1,
__isl_take isl_ast_expr *expr2)
__isl_give isl_ast_expr *isl_ast_expr_access(
__isl_take isl_ast_expr *array,
__isl_take isl_ast_expr_list *indices);
__isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
__isl_take isl_ast_expr *expr,
__isl_take isl_id_to_ast_expr *id2expr);
The function isl_ast_expr_substitute_ids replaces the
subexpressions of expr of type isl_ast_expr_id
by the corresponding expression in id2expr, if there is any.
#include <isl/ast_build.h>
__isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
__isl_keep isl_ast_build *build,
__isl_take isl_pw_aff *pa);
__isl_give isl_ast_expr *
isl_ast_build_access_from_pw_multi_aff(
__isl_keep isl_ast_build *build,
__isl_take isl_pw_multi_aff *pma);
__isl_give isl_ast_expr *
isl_ast_build_access_from_multi_pw_aff(
__isl_keep isl_ast_build *build,
__isl_take isl_multi_pw_aff *mpa);
__isl_give isl_ast_expr *
isl_ast_build_call_from_pw_multi_aff(
__isl_keep isl_ast_build *build,
__isl_take isl_pw_multi_aff *pma);
__isl_give isl_ast_expr *
isl_ast_build_call_from_multi_pw_aff(
__isl_keep isl_ast_build *build,
__isl_take isl_multi_pw_aff *mpa);
The domains of pa, mpa and pma should correspond
to the schedule space of build.
The tuple id of mpa or pma is used as the array being accessed or
the function being called.
User specified data can be attached to an isl_ast_node and obtained
from the same isl_ast_node using the following functions.
#include <isl/ast.h>
__isl_give isl_ast_node *isl_ast_node_set_annotation(
__isl_take isl_ast_node *node,
__isl_take isl_id *annotation);
__isl_give isl_id *isl_ast_node_get_annotation(
__isl_keep isl_ast_node *node);
Basic printing can be performed using the following functions.
#include <isl/ast.h>
__isl_give isl_printer *isl_printer_print_ast_expr(
__isl_take isl_printer *p,
__isl_keep isl_ast_expr *expr);
__isl_give isl_printer *isl_printer_print_ast_node(
__isl_take isl_printer *p,
__isl_keep isl_ast_node *node);
More advanced printing can be performed using the following functions.
#include <isl/ast.h>
__isl_give isl_printer *isl_ast_op_type_print_macro(
enum isl_ast_op_type type,
__isl_take isl_printer *p);
__isl_give isl_printer *isl_ast_node_print_macros(
__isl_keep isl_ast_node *node,
__isl_take isl_printer *p);
__isl_give isl_printer *isl_ast_node_print(
__isl_keep isl_ast_node *node,
__isl_take isl_printer *p,
__isl_take isl_ast_print_options *options);
__isl_give isl_printer *isl_ast_node_for_print(
__isl_keep isl_ast_node *node,
__isl_take isl_printer *p,
__isl_take isl_ast_print_options *options);
__isl_give isl_printer *isl_ast_node_if_print(
__isl_keep isl_ast_node *node,
__isl_take isl_printer *p,
__isl_take isl_ast_print_options *options);
While printing an isl_ast_node in ISL_FORMAT_C,
isl may print out an AST that makes use of macros such
as floord, min and max.
isl_ast_op_type_print_macro prints out the macro
corresponding to a specific isl_ast_op_type.
isl_ast_node_print_macros scans the isl_ast_node
for expressions where these macros would be used and prints
out the required macro definitions.
Essentially, isl_ast_node_print_macros calls
isl_ast_node_foreach_ast_op_type with isl_ast_op_type_print_macro
as function argument.
isl_ast_node_print, isl_ast_node_for_print and
isl_ast_node_if_print print an isl_ast_node
in ISL_FORMAT_C, but allow for some extra control
through an isl_ast_print_options object.
This object can be created using the following functions.
#include <isl/ast.h>
__isl_give isl_ast_print_options *
isl_ast_print_options_alloc(isl_ctx *ctx);
__isl_give isl_ast_print_options *
isl_ast_print_options_copy(
__isl_keep isl_ast_print_options *options);
void *isl_ast_print_options_free(
__isl_take isl_ast_print_options *options);
__isl_give isl_ast_print_options *
isl_ast_print_options_set_print_user(
__isl_take isl_ast_print_options *options,
__isl_give isl_printer *(*print_user)(
__isl_take isl_printer *p,
__isl_take isl_ast_print_options *options,
__isl_keep isl_ast_node *node, void *user),
void *user);
__isl_give isl_ast_print_options *
isl_ast_print_options_set_print_for(
__isl_take isl_ast_print_options *options,
__isl_give isl_printer *(*print_for)(
__isl_take isl_printer *p,
__isl_take isl_ast_print_options *options,
__isl_keep isl_ast_node *node, void *user),
void *user);
The callback set by isl_ast_print_options_set_print_user
is called whenever a node of type isl_ast_node_user needs to
be printed.
The callback set by isl_ast_print_options_set_print_for
is called whenever a node of type isl_ast_node_for needs to
be printed.
Note that isl_ast_node_for_print will not call the
callback set by isl_ast_print_options_set_print_for on the node
on which isl_ast_node_for_print is called, but only on nested
nodes of type isl_ast_node_for. It is therefore safe to
call isl_ast_node_for_print from within the callback set by
isl_ast_print_options_set_print_for.
The following option determines the type to be used for iterators while printing the AST.
int isl_options_set_ast_iterator_type(
isl_ctx *ctx, const char *val);
const char *isl_options_get_ast_iterator_type(
isl_ctx *ctx);
#include <isl/ast_build.h>
int isl_options_set_ast_build_atomic_upper_bound(
isl_ctx *ctx, int val);
int isl_options_get_ast_build_atomic_upper_bound(
isl_ctx *ctx);
int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
int val);
int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
int isl_options_set_ast_build_exploit_nested_bounds(
isl_ctx *ctx, int val);
int isl_options_get_ast_build_exploit_nested_bounds(
isl_ctx *ctx);
int isl_options_set_ast_build_group_coscheduled(
isl_ctx *ctx, int val);
int isl_options_get_ast_build_group_coscheduled(
isl_ctx *ctx);
int isl_options_set_ast_build_scale_strides(
isl_ctx *ctx, int val);
int isl_options_get_ast_build_scale_strides(
isl_ctx *ctx);
int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
int val);
int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
int val);
int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
Generate loop upper bounds that consist of the current loop iterator, an operator and an expression not involving the iterator. If this option is not set, then the current loop iterator may appear several times in the upper bound. For example, when this option is turned off, AST generation for the schedule
[n] -> { A[i] -> [i] : 0 <= i <= 100, n }
produces
for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
A(c0);
When the option is turned on, the following AST is generated
for (int c0 = 0; c0 <= min(100, n); c0 += 1)
A(c0);
If this option is turned off, then the AST generation will
produce ASTs that may only contain isl_ast_op_fdiv_q
operators, but no isl_ast_op_pdiv_q or
isl_ast_op_pdiv_r operators.
If this options is turned on, then isl will try to convert
some of the isl_ast_op_fdiv_q operators to (expressions containing)
isl_ast_op_pdiv_q or isl_ast_op_pdiv_r operators.
Simplify conditions based on bounds of nested for loops. In particular, remove conditions that are implied by the fact that one or more nested loops have at least one iteration, meaning that the upper bound is at least as large as the lower bound. For example, when this option is turned off, AST generation for the schedule
[N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
0 <= j <= M }
produces
if (M >= 0)
for (int c0 = 0; c0 <= N; c0 += 1)
for (int c1 = 0; c1 <= M; c1 += 1)
A(c0, c1);
When the option is turned on, the following AST is generated
for (int c0 = 0; c0 <= N; c0 += 1)
for (int c1 = 0; c1 <= M; c1 += 1)
A(c0, c1);
If two domain elements are assigned the same schedule point, then they may be executed in any order and they may even appear in different loops. If this options is set, then the AST generator will make sure that coscheduled domain elements do not appear in separate parts of the AST. This is useful in case of nested AST generation if the outer AST generation is given only part of a schedule and the inner AST generation should handle the domains that are coscheduled by this initial part of the schedule together. For example if an AST is generated for a schedule
{ A[i] -> [0]; B[i] -> [0] }
then the isl_ast_build_set_create_leaf callback described
below may get called twice, once for each domain.
Setting this option ensures that the callback is only called once
on both domains together.
This option specifies which bounds to use during separation.
If this option is set to ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT
then all (possibly implicit) bounds on the current dimension will
be used during separation.
If this option is set to ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT
then only those bounds that are explicitly available will
be used during separation.
This option specifies whether the AST generator is allowed to scale down iterators of strided loops.
This option specifies whether the AST generator is allowed to construct if statements with else branches.
This option specifies whether the AST generator is allowed to construct if conditions with disjunctions.
Besides specifying the constraints on the parameters,
an isl_ast_build object can be used to control
various aspects of the AST generation process.
The most prominent way of control is through ``options'',
which can be set using the following function.
#include <isl/ast_build.h>
__isl_give isl_ast_build *
isl_ast_build_set_options(
__isl_take isl_ast_build *control,
__isl_take isl_union_map *options);
The options are encoded in an <isl_union_map>.
The domain of this union relation refers to the schedule domain,
i.e., the range of the schedule passed to isl_ast_build_ast_from_schedule.
In the case of nested AST generation (see Nested AST Generation),
the domain of options should refer to the extra piece of the schedule.
That is, it should be equal to the range of the wrapped relation in the
range of the schedule.
The range of the options can consist of elements in one or more spaces,
the names of which determine the effect of the option.
The values of the range typically also refer to the schedule dimension
to which the option applies. In case of nested AST generation
(see Nested AST Generation), these values refer to the position
of the schedule dimension within the innermost AST generation.
The constraints on the domain elements of
the option should only refer to this dimension and earlier dimensions.
We consider the following spaces.
separation_classThis space is a wrapped relation between two one dimensional spaces. The input space represents the schedule dimension to which the option applies and the output space represents the separation class. While constructing a loop corresponding to the specified schedule dimension(s), the AST generator will try to generate separate loops for domain elements that are assigned different classes. If only some of the elements are assigned a class, then those elements that are not assigned any class will be treated as belonging to a class that is separate from the explicitly assigned classes. The typical use case for this option is to separate full tiles from partial tiles. The other options, described below, are applied after the separation into classes.
As an example, consider the separation into full and partial tiles of a tiling of a triangular domain. Take, for example, the domain
{ A[i,j] : 0 <= i,j and i + j <= 100 }
and a tiling into tiles of 10 by 10. The input to the AST generator is then the schedule
{ A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
i + j <= 100 }
Without any options, the following AST is generated
for (int c0 = 0; c0 <= 10; c0 += 1)
for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
for (int c2 = 10 * c0;
c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
c2 += 1)
for (int c3 = 10 * c1;
c3 <= min(10 * c1 + 9, -c2 + 100);
c3 += 1)
A(c2, c3);
Separation into full and partial tiles can be obtained by assigning
a class, say 0, to the full tiles. The full tiles are represented by those
values of the first and second schedule dimensions for which there are
values of the third and fourth dimensions to cover an entire tile.
That is, we need to specify the following option
{ [a,b,c,d] -> separation_class[[0]->[0]] :
exists b': 0 <= 10a,10b' and
10a+9+10b'+9 <= 100;
[a,b,c,d] -> separation_class[[1]->[0]] :
0 <= 10a,10b and 10a+9+10b+9 <= 100 }
which simplifies to
{ [a, b, c, d] -> separation_class[[1] -> [0]] :
a >= 0 and b >= 0 and b <= 8 - a;
[a, b, c, d] -> separation_class[[0] -> [0]] :
a >= 0 and a <= 8 }
With this option, the generated AST is as follows
{
for (int c0 = 0; c0 <= 8; c0 += 1) {
for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
for (int c2 = 10 * c0;
c2 <= 10 * c0 + 9; c2 += 1)
for (int c3 = 10 * c1;
c3 <= 10 * c1 + 9; c3 += 1)
A(c2, c3);
for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
for (int c2 = 10 * c0;
c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
c2 += 1)
for (int c3 = 10 * c1;
c3 <= min(-c2 + 100, 10 * c1 + 9);
c3 += 1)
A(c2, c3);
}
for (int c0 = 9; c0 <= 10; c0 += 1)
for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
for (int c2 = 10 * c0;
c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
c2 += 1)
for (int c3 = 10 * c1;
c3 <= min(10 * c1 + 9, -c2 + 100);
c3 += 1)
A(c2, c3);
}
separateThis is a single-dimensional space representing the schedule dimension(s)
to which ``separation'' should be applied. Separation tries to split
a loop into several pieces if this can avoid the generation of guards
inside the loop.
See also the atomic option.
atomicThis is a single-dimensional space representing the schedule dimension(s) for which the domains should be considered ``atomic''. That is, the AST generator will make sure that any given domain space will only appear in a single loop at the specified level.
Consider the following schedule
{ a[i] -> [i] : 0 <= i < 10;
b[i] -> [i+1] : 0 <= i < 10 }
If the following option is specified
{ [i] -> separate[x] }
then the following AST will be generated
{
a(0);
for (int c0 = 1; c0 <= 9; c0 += 1) {
a(c0);
b(c0 - 1);
}
b(9);
}
If, on the other hand, the following option is specified
{ [i] -> atomic[x] }
then the following AST will be generated
for (int c0 = 0; c0 <= 10; c0 += 1) {
if (c0 <= 9)
a(c0);
if (c0 >= 1)
b(c0 - 1);
}
If neither atomic nor separate is specified, then the AST generator
may produce either of these two results or some intermediate form.
unrollThis is a single-dimensional space representing the schedule dimension(s) that should be completely unrolled. To obtain a partial unrolling, the user should apply an additional strip-mining to the schedule and fully unroll the inner loop.
Additional control is available through the following functions.
#include <isl/ast_build.h>
__isl_give isl_ast_build *
isl_ast_build_set_iterators(
__isl_take isl_ast_build *control,
__isl_take isl_id_list *iterators);
The function isl_ast_build_set_iterators allows the user to
specify a list of iterator isl_ids to be used as iterators.
If the input schedule is injective, then
the number of elements in this list should be as large as the dimension
of the schedule space, but no direct correspondence should be assumed
between dimensions and elements.
If the input schedule is not injective, then an additional number
of isl_ids equal to the largest dimension of the input domains
may be required.
If the number of provided isl_ids is insufficient, then additional
names are automatically generated.
#include <isl/ast_build.h>
__isl_give isl_ast_build *
isl_ast_build_set_create_leaf(
__isl_take isl_ast_build *control,
__isl_give isl_ast_node *(*fn)(
__isl_take isl_ast_build *build,
void *user), void *user);
The
isl_ast_build_set_create_leaf function allows for the
specification of a callback that should be called whenever the AST
generator arrives at an element of the schedule domain.
The callback should return an AST node that should be inserted
at the corresponding position of the AST. The default action (when
the callback is not set) is to continue generating parts of the AST to scan
all the domain elements associated to the schedule domain element
and to insert user nodes, ``calling'' the domain element, for each of them.
The build argument contains the current state of the isl_ast_build.
To ease nested AST generation (see Nested AST Generation),
all control information that is
specific to the current AST generation such as the options and
the callbacks has been removed from this isl_ast_build.
The callback would typically return the result of a nested
AST generation or a
user defined node created using the following function.
#include <isl/ast.h>
__isl_give isl_ast_node *isl_ast_node_alloc_user(
__isl_take isl_ast_expr *expr);
#include <isl/ast_build.h>
__isl_give isl_ast_build *
isl_ast_build_set_at_each_domain(
__isl_take isl_ast_build *build,
__isl_give isl_ast_node *(*fn)(
__isl_take isl_ast_node *node,
__isl_keep isl_ast_build *build,
void *user), void *user);
__isl_give isl_ast_build *
isl_ast_build_set_before_each_for(
__isl_take isl_ast_build *build,
__isl_give isl_id *(*fn)(
__isl_keep isl_ast_build *build,
void *user), void *user);
__isl_give isl_ast_build *
isl_ast_build_set_after_each_for(
__isl_take isl_ast_build *build,
__isl_give isl_ast_node *(*fn)(
__isl_take isl_ast_node *node,
__isl_keep isl_ast_build *build,
void *user), void *user);
The callback set by isl_ast_build_set_at_each_domain will
be called for each domain AST node.
The callbacks set by isl_ast_build_set_before_each_for
and isl_ast_build_set_after_each_for will be called
for each for AST node. The first will be called in depth-first
pre-order, while the second will be called in depth-first post-order.
Since isl_ast_build_set_before_each_for is called before the for
node is actually constructed, it is only passed an isl_ast_build.
The returned isl_id will be added as an annotation (using
isl_ast_node_set_annotation) to the constructed for node.
In particular, if the user has also specified an after_each_for
callback, then the annotation can be retrieved from the node passed to
that callback using isl_ast_node_get_annotation.
All callbacks should NULL on failure.
The given isl_ast_build can be used to create new
isl_ast_expr objects using isl_ast_build_expr_from_pw_aff
or isl_ast_build_call_from_pw_multi_aff.
isl allows the user to create an AST within the context
of another AST. These nested ASTs are created using the
same isl_ast_build_ast_from_schedule function that is used to create the
outer AST. The build argument should be an isl_ast_build
passed to a callback set by
isl_ast_build_set_create_leaf.
The space of the range of the schedule argument should refer
to this build. In particular, the space should be a wrapped
relation and the domain of this wrapped relation should be the
same as that of the range of the schedule returned by
isl_ast_build_get_schedule below.
In practice, the new schedule is typically
created by calling isl_union_map_range_product on the old schedule
and some extra piece of the schedule.
The space of the schedule domain is also available from
the isl_ast_build.
#include <isl/ast_build.h>
__isl_give isl_union_map *isl_ast_build_get_schedule(
__isl_keep isl_ast_build *build);
__isl_give isl_space *isl_ast_build_get_schedule_space(
__isl_keep isl_ast_build *build);
__isl_give isl_ast_build *isl_ast_build_restrict(
__isl_take isl_ast_build *build,
__isl_take isl_set *set);
The isl_ast_build_get_schedule function returns a (partial)
schedule for the domains elements for which part of the AST still needs to
be generated in the current build.
In particular, the domain elements are mapped to those iterations of the loops
enclosing the current point of the AST generation inside which
the domain elements are executed.
No direct correspondence between
the input schedule and this schedule should be assumed.
The space obtained from isl_ast_build_get_schedule_space can be used
to create a set for isl_ast_build_restrict to intersect
with the current build. In particular, the set passed to
isl_ast_build_restrict can have additional parameters.
The ids of the set dimensions in the space returned by
isl_ast_build_get_schedule_space correspond to the
iterators of the already generated loops.
The user should not rely on the ids of the output dimensions
of the relations in the union relation returned by
isl_ast_build_get_schedule having any particular value.
Although isl is mainly meant to be used as a library,
it also contains some basic applications that use some
of the functionality of isl.
The input may be specified in either the isl format
or the PolyLib format.
isl_polyhedron_sampleisl_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,
then a vector of length zero is printed.
isl_pipisl_pip takes the same input as the example program
from the piplib distribution, i.e., a set of constraints
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.
As isl currently does not have its own output format, the output
is just a dump of the internal state.
isl_polyhedron_minimizeisl_polyhedron_minimize computes the minimum of some linear
or affine objective function over the integer points in a polyhedron.
If an affine objective function
is given, then the constant should appear in the last column.
isl_polytope_scanGiven a polytope, isl_polytope_scan prints
all integer points in the polytope.
isl_codegenGiven a schedule, a context set and an options relation,
isl_codegen prints out an AST that scans the domain elements
of the schedule in the order of their image(s) taking into account
the constraints in the context set.