isl-polylib
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.
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
isl can optionally use the piplib library and provides
this library as a submodule. If you want to use it, then
after you have cloned isl, you need to grab the submodules
git submodule init
git submodule update
To obtain updates, you only need
git submodule update
Note that isl currently does not use any piplib
functionality by default.
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.
isl can optionally use piplib, but no
piplib functionality is currently used by default.
The --with-piplib option can
be used to specify which piplib
library to use, either an installed version (system),
an externally built version (build)
or no version (no). The option build is mostly useful
in configure scripts of larger projects that bundle both isl
and piplib.
--prefixInstallation prefix for isl
--with-gmp-prefixInstallation prefix for GMP (architecture-independent files).
--with-gmp-exec-prefixInstallation prefix for GMP (architecture-dependent files).
--with-piplibWhich copy of piplib to use, either no (default), system or build.
--with-piplib-prefixInstallation prefix for system piplib (architecture-independent files).
--with-piplib-exec-prefixInstallation prefix for system piplib (architecture-dependent files).
--with-piplib-builddirLocation where build piplib was built.
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);
All operations on integers, mainly the coefficients
of the constraints describing the sets and relations,
are performed in exact integer arithmetic using GMP.
However, to allow future versions of isl to optionally
support fixed integer arithmetic, all calls to GMP
are wrapped inside isl specific macros.
The basic type is isl_int and the following operations
are available on this type.
The meanings of these operations are essentially the same
as their GMP mpz_ counterparts.
As always with GMP types, isl_ints need to be
initialized with isl_int_init before they can be used
and they need to be released with isl_int_clear
after the last use.
isl uses four types of objects for representing sets and relations,
isl_basic_set, isl_basic_map, isl_set and isl_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.
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 make sure that the original object gets used somewhere else or is explicitly freed.
The arguments and return values of all documents 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 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.
Whenever a new set or relation is created from scratch,
its dimension needs to be specified using an isl_dim.
#include <isl_dim.h>
__isl_give isl_dim *isl_dim_alloc(isl_ctx *ctx,
unsigned nparam, unsigned n_in, unsigned n_out);
__isl_give isl_dim *isl_dim_set_alloc(isl_ctx *ctx,
unsigned nparam, unsigned dim);
__isl_give isl_dim *isl_dim_copy(__isl_keep isl_dim *dim);
void isl_dim_free(__isl_take isl_dim *dim);
unsigned isl_dim_size(__isl_keep isl_dim *dim,
enum isl_dim_type type);
The dimension specification used for creating a set
needs to be created using isl_dim_set_alloc, while
that for creating a relation
needs to be created using isl_dim_alloc.
isl_dim_size can be used
to find out the number of dimensions of each type in
a dimension specification, 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.
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 dimension specification of the original object.
#include <isl_set.h>
__isl_give isl_dim *isl_basic_set_get_dim(
__isl_keep isl_basic_set *bset);
__isl_give isl_dim *isl_set_get_dim(__isl_keep isl_set *set);
#include <isl_map.h>
__isl_give isl_dim *isl_basic_map_get_dim(
__isl_keep isl_basic_map *bmap);
__isl_give isl_dim *isl_map_get_dim(__isl_keep isl_map *map);
#include <isl_polynomial.h>
__isl_give isl_dim *isl_qpolynomial_get_dim(
__isl_keep isl_qpolynomial *qp);
__isl_give isl_dim *isl_pw_qpolynomial_get_dim(
__isl_keep isl_pw_qpolynomial *pwqp);
The names of the individual dimensions may be set or read off using the following functions.
#include <isl_dim.h>
__isl_give isl_dim *isl_dim_set_name(__isl_take isl_dim *dim,
enum isl_dim_type type, unsigned pos,
__isl_keep const char *name);
__isl_keep const char *isl_dim_get_name(__isl_keep isl_dim *dim,
enum isl_dim_type type, unsigned pos);
Note that isl_dim_get_name returns a pointer to some internal
data structure, so the result can only be used while the
corresponding isl_dim is alive.
Also note that every function that operates on two sets or relations
requires that both arguments have the same parameters. This also
means that if one of the arguments has named parameters, then the
other needs to have named parameters too and the names need to match.
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.
#include <isl_set.h>
__isl_give isl_basic_set *isl_basic_set_read_from_file(
isl_ctx *ctx, FILE *input, int nparam);
__isl_give isl_basic_set *isl_basic_set_read_from_str(
isl_ctx *ctx, const char *str, int nparam);
__isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
FILE *input, int nparam);
__isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
const char *str, int nparam);
#include <isl_map.h>
__isl_give isl_basic_map *isl_basic_map_read_from_file(
isl_ctx *ctx, FILE *input, int nparam);
__isl_give isl_basic_map *isl_basic_map_read_from_str(
isl_ctx *ctx, const char *str, int nparam);
__isl_give isl_map *isl_map_read_from_file(
struct isl_ctx *ctx, FILE *input, int nparam);
__isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
const char *str, int nparam);
The input format is autodetected and may be either the PolyLib format
or the isl format.
nparam specifies how many of the final columns in
the PolyLib format correspond to parameters.
If input is given in the isl format, then the number
of parameters needs to be equal to nparam.
If nparam is negative, then any number of parameters
is accepted in the isl format and zero parameters
are assumed in the PolyLib 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 behavior of the printer can be modified in various ways
__isl_give isl_printer *isl_printer_set_output_format(
__isl_take isl_printer *p, int output_format);
__isl_give isl_printer *isl_printer_set_indent(
__isl_take isl_printer *p, int indent);
__isl_give isl_printer *isl_printer_set_prefix(
__isl_take isl_printer *p, const char *prefix);
__isl_give isl_printer *isl_printer_set_suffix(
__isl_take isl_printer *p, const char *suffix);
The output_format may be either ISL_FORMAT_ISL, ISL_FORMAT_OMEGA
or ISL_FORMAT_POLYLIB and defaults to ISL_FORMAT_ISL.
Each line in the output is indented by 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.
To actually print something, use
#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);
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_dim *dim);
__isl_give isl_basic_map *isl_basic_map_empty(
__isl_take isl_dim *dim);
__isl_give isl_set *isl_set_empty(
__isl_take isl_dim *dim);
__isl_give isl_map *isl_map_empty(
__isl_take isl_dim *dim);
__isl_give isl_basic_set *isl_basic_set_universe(
__isl_take isl_dim *dim);
__isl_give isl_basic_map *isl_basic_map_universe(
__isl_take isl_dim *dim);
__isl_give isl_set *isl_set_universe(
__isl_take isl_dim *dim);
__isl_give isl_map *isl_map_universe(
__isl_take isl_dim *dim);
__isl_give isl_basic_map *isl_basic_map_identity(
__isl_take isl_dim *set_dim);
__isl_give isl_map *isl_map_identity(
__isl_take isl_dim *set_dim);
These functions take a dimension specification for a set and return an identity relation between two such sets.
__isl_give isl_map *isl_map_lex_lt(
__isl_take isl_dim *set_dim);
__isl_give isl_map *isl_map_lex_le(
__isl_take isl_dim *set_dim);
__isl_give isl_map *isl_map_lex_gt(
__isl_take isl_dim *set_dim);
__isl_give isl_map *isl_map_lex_ge(
__isl_take isl_dim *set_dim);
__isl_give isl_map *isl_map_lex_lt_first(
__isl_take isl_dim *dim, unsigned n);
__isl_give isl_map *isl_map_lex_le_first(
__isl_take isl_dim *dim, unsigned n);
__isl_give isl_map *isl_map_lex_gt_first(
__isl_take isl_dim *dim, unsigned n);
__isl_give isl_map *isl_map_lex_ge_first(
__isl_take isl_dim *dim, unsigned n);
The first four functions take a dimension specification for a 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 dimension specification 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 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_basic_map *isl_basic_map_copy(
__isl_keep isl_basic_map *bmap);
__isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
void isl_basic_set_free(__isl_take isl_basic_set *bset);
void isl_set_free(__isl_take isl_set *set);
void isl_basic_map_free(__isl_take isl_basic_map *bmap);
void isl_map_free(__isl_take isl_map *map);
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 basic sets and relations using the following functions.
#include <isl_constraint.h>
__isl_give isl_constraint *isl_equality_alloc(
__isl_take isl_dim *dim);
__isl_give isl_constraint *isl_inequality_alloc(
__isl_take isl_dim *dim);
void isl_constraint_set_constant(
__isl_keep isl_constraint *constraint, isl_int v);
void isl_constraint_set_coefficient(
__isl_keep isl_constraint *constraint,
enum isl_dim_type type, int pos, isl_int 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);
For example, to create a set containing the even integers between 10 and 42, you would use the following code.
isl_int v;
struct isl_dim *dim;
struct isl_constraint *c;
struct isl_basic_set *bset;
isl_int_init(v);
dim = isl_dim_set_alloc(ctx, 0, 2);
bset = isl_basic_set_universe(isl_dim_copy(dim));
c = isl_equality_alloc(isl_dim_copy(dim));
isl_int_set_si(v, -1);
isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
isl_int_set_si(v, 2);
isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
bset = isl_basic_set_add_constraint(bset, c);
c = isl_inequality_alloc(isl_dim_copy(dim));
isl_int_set_si(v, -10);
isl_constraint_set_constant(c, v);
isl_int_set_si(v, 1);
isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
bset = isl_basic_set_add_constraint(bset, c);
c = isl_inequality_alloc(dim);
isl_int_set_si(v, 42);
isl_constraint_set_constant(c, v);
isl_int_set_si(v, -1);
isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
bset = isl_basic_set_add_constraint(bset, c);
bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
isl_int_clear(v);
Or, alternatively,
struct isl_basic_set *bset;
bset = isl_basic_set_read_from_str(ctx,
"{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
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);
This explicit representation defines the existentially quantified variables as integer divisions of the other variables, possibly including earlier existentially quantified variables. An explicitly represented existentially quantified variable therefore has a unique value when the values of the other variables are known. If, furthermore, the same existentials, i.e., existentials with the same explicit representations, should appear in the same order in each of the disjuncts of a set or map, then the user should call either of the following functions.
__isl_give isl_set *isl_set_align_divs(
__isl_take isl_set *set);
__isl_give isl_map *isl_map_align_divs(
__isl_take isl_map *map);
To iterate over all the 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);
To iterate over the constraints of a basic set or map, use
#include <isl_constraint.h>
int isl_basic_map_foreach_constraint(
__isl_keep isl_basic_map *bmap,
int (*fn)(__isl_take isl_constraint *c, void *user),
void *user);
void isl_constraint_free(struct isl_constraint *c);
Again, the callback function 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.
void isl_constraint_get_constant(
__isl_keep isl_constraint *constraint, isl_int *v);
void isl_constraint_get_coefficient(
__isl_keep isl_constraint *constraint,
enum isl_dim_type type, int pos, isl_int *v);
The explicit representations of the existentially quantified
variables can be inspected using the following functions.
Note that the user is only allowed to use these functions
if the inspected set or map is the result of a call
to isl_set_compute_divs or isl_map_compute_divs.
__isl_give isl_div *isl_constraint_div(
__isl_keep isl_constraint *constraint, int pos);
void isl_div_get_constant(__isl_keep isl_div *div,
isl_int *v);
void isl_div_get_denominator(__isl_keep isl_div *div,
isl_int *v);
void isl_div_get_coefficient(__isl_keep isl_div *div,
enum isl_dim_type type, int pos, isl_int *v);
The following functions test whether the given set or relation contains any integer points. The ``fast'' 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_fast_is_empty(__isl_keep isl_basic_set *bset);
int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
int isl_set_is_empty(__isl_keep isl_set *set);
int isl_basic_map_fast_is_empty(__isl_keep isl_basic_map *bmap);
int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
int isl_map_fast_is_empty(__isl_keep isl_map *map);
int isl_map_is_empty(__isl_keep isl_map *map);
int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
int isl_set_fast_is_universe(__isl_keep isl_set *set);
int isl_map_is_single_valued(__isl_keep isl_map *map);
int isl_map_is_bijective(__isl_keep isl_map *map);
int isl_set_fast_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_map_is_equal(__isl_keep isl_map *map1,
__isl_keep isl_map *map2);
int isl_map_fast_is_equal(__isl_keep isl_map *map1,
__isl_keep isl_map *map2);
int isl_basic_map_is_equal(
__isl_keep isl_basic_map *bmap1,
__isl_keep isl_basic_map *bmap2);
int isl_set_fast_is_disjoint(__isl_keep isl_set *set1,
__isl_keep isl_set *set2);
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_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);
__isl_give isl_set *isl_set_complement(
__isl_take isl_set *set);
__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_basic_set *isl_basic_set_project_out(
__isl_take isl_basic_set *bset,
enum isl_dim_type type, unsigned first, unsigned n);
__isl_give isl_basic_map *isl_basic_map_project_out(
__isl_take isl_basic_map *bmap,
enum isl_dim_type type, unsigned first, unsigned n);
__isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
enum isl_dim_type type, unsigned first, unsigned n);
__isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
enum isl_dim_type type, unsigned first, unsigned n);
__isl_give isl_basic_set *isl_basic_map_domain(
__isl_take isl_basic_map *bmap);
__isl_give isl_basic_set *isl_basic_map_range(
__isl_take isl_basic_map *bmap);
__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_basic_set *isl_basic_map_deltas(
__isl_take isl_basic_map *bmap);
__isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
These functions return a (basic) set containing the differences between image elements and corresponding domain elements in the input.
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_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_simple_hull(
__isl_take isl_set *set);
__isl_give isl_basic_map *isl_map_simple_hull(
__isl_take isl_map *map);
These functions compute a single basic set or relation that contains the whole input set or relation. In particular, the output is described by translates of the constraints describing the basic sets or relations in the input.
__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_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_map *isl_map_power(__isl_take isl_map *map,
unsigned param, int *exact);
Compute a parametric representation for all positive powers k of map.
The power k is equated to the parameter at position param.
The result may be an overapproximation. If the result is exact,
then *exact is set to 1.
The current implementation only produces exact results for particular
cases of piecewise translations (i.e., piecewise uniform dependences).
__isl_give isl_map *isl_map_transitive_closure(
__isl_take isl_map *map, 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.
The current implementation only produces exact results for particular
cases of piecewise translations (i.e., piecewise uniform dependences).
__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.
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(
__isl_take isl_basic_set *bset1,
__isl_take isl_basic_set *bset2);
__isl_give isl_set *isl_set_intersect(
__isl_take isl_set *set1,
__isl_take isl_set *set2);
__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_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_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_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_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_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_map *isl_map_apply_range(
__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_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);
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.
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).
__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);
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.
__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);
Points are elements of a set. They can be used to construct simple sets (boxes) or they can be used to represent the individual elements of a set. The zero point (the origin) can be created using
__isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
The coordinates of a point can be inspected, set and changed using
void isl_point_get_coordinate(__isl_keep isl_point *pnt,
enum isl_dim_type type, int pos, isl_int *v);
__isl_give isl_point *isl_point_set_coordinate(
__isl_take isl_point *pnt,
enum isl_dim_type type, int pos, isl_int v);
__isl_give isl_point *isl_point_add_ui(
__isl_take isl_point *pnt,
enum isl_dim_type type, int pos, unsigned val);
__isl_give isl_point *isl_point_sub_ui(
__isl_take isl_point *pnt,
enum isl_dim_type type, int pos, unsigned val);
Points can be copied or freed using
__isl_give isl_point *isl_point_copy(
__isl_keep isl_point *pnt);
void isl_point_free(__isl_take isl_point *pnt);
A singleton set can be created from a point using
__isl_give isl_set *isl_set_from_point(
__isl_take isl_point *pnt);
and a box can be created from two opposite extremal points using
__isl_give isl_set *isl_set_box_from_points(
__isl_take isl_point *pnt1,
__isl_take isl_point *pnt2);
All elements of a bounded set can be enumerated using the following function.
int isl_set_foreach_point(__isl_keep isl_set *set,
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 set, use
__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.
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 }
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);
The output format of the printer
needs to be set to either ISL_FORMAT_ISL or ISL_FORMAT_C.
Some simple quasipolynomials can be created using the following functions. More complicated quasipolynomials can be created by applying operations such as addition and multiplication on the resulting quasipolynomials
__isl_give isl_qpolynomial *isl_qpolynomial_zero(
__isl_take isl_dim *dim);
__isl_give isl_qpolynomial *isl_qpolynomial_infty(
__isl_take isl_dim *dim);
__isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
__isl_take isl_dim *dim);
__isl_give isl_qpolynomial *isl_qpolynomial_nan(
__isl_take isl_dim *dim);
__isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
__isl_take isl_dim *dim,
const isl_int n, const isl_int d);
__isl_give isl_qpolynomial *isl_qpolynomial_div(
__isl_take isl_div *div);
__isl_give isl_qpolynomial *isl_qpolynomial_var(
__isl_take isl_dim *dim,
enum isl_dim_type type, unsigned pos);
The zero piecewise quasipolynomial or a piecewise quasipolynomial with a single cell can be created using the following functions. Multiple of these single cell piecewise quasipolynomials can be combined to create more complicated piecewise quasipolynomials.
__isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
__isl_take isl_dim *dim);
__isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
__isl_take isl_set *set,
__isl_take isl_qpolynomial *qp);
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);
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.
To iterate over all terms in a quasipolynomial, use
int isl_qpolynomial_foreach_term(
__isl_keep isl_qpolynomial *qp,
int (*fn)(__isl_take isl_term *term,
void *user), void *user);
The terms themselves can be inspected and freed using these functions
unsigned isl_term_dim(__isl_keep isl_term *term,
enum isl_dim_type type);
void isl_term_get_num(__isl_keep isl_term *term,
isl_int *n);
void isl_term_get_den(__isl_keep isl_term *term,
isl_int *d);
int isl_term_get_exp(__isl_keep isl_term *term,
enum isl_dim_type type, unsigned pos);
__isl_give isl_div *isl_term_get_div(
__isl_keep isl_term *term, unsigned pos);
void isl_term_free(__isl_take isl_term *term);
Each term is a product of parameters, set variables and
integer divisions. The function isl_term_get_exp
returns the exponent of a given dimensions in the given term.
The isl_ints in the arguments of isl_term_get_num
and isl_term_get_den need to have been initialized
using isl_int_init before calling these functions.
To check whether a quasipolynomial is actually a constant, use the following function.
int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
isl_int *n, isl_int *d);
If qp is a constant and if n and d are not NULL
then the numerator and denominator of the constant
are returned in *n and *d, respectively.
__isl_give isl_qpolynomial *isl_qpolynomial_neg(
__isl_take isl_qpolynomial *qp);
__isl_give isl_qpolynomial *isl_qpolynomial_add(
__isl_take isl_qpolynomial *qp1,
__isl_take isl_qpolynomial *qp2);
__isl_give isl_qpolynomial *isl_qpolynomial_sub(
__isl_take isl_qpolynomial *qp1,
__isl_take isl_qpolynomial *qp2);
__isl_give isl_qpolynomial *isl_qpolynomial_mul(
__isl_take isl_qpolynomial *qp1,
__isl_take isl_qpolynomial *qp2);
__isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
__isl_take isl_pw_qpolynomial *pwqp1,
__isl_take isl_pw_qpolynomial *pwqp2);
__isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
__isl_take isl_pw_qpolynomial *pwqp1,
__isl_take isl_pw_qpolynomial *pwqp2);
__isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
__isl_take isl_pw_qpolynomial *pwqp1,
__isl_take isl_pw_qpolynomial *pwqp2);
__isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
__isl_take isl_pw_qpolynomial *pwqp);
__isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
__isl_take isl_pw_qpolynomial *pwqp1,
__isl_take isl_pw_qpolynomial *pwqp2);
__isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
__isl_take isl_pw_qpolynomial *pwqp,
__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_gist(
__isl_take isl_pw_qpolynomial *pwqp,
__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. In future, the operation will also exploit the context to simplify the quasipolynomials associated to each cell.
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);
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.
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);
void isl_qpolynomial_fold_free(
__isl_take isl_qpolynomial_fold *fold);
void isl_pw_qpolynomial_fold_free(
__isl_take isl_pw_qpolynomial_fold *pwf);
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);
The output format of the printer
needs to be set to either ISL_FORMAT_ISL or ISL_FORMAT_C.
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);
__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_qpolynomial *isl_pw_qpolynomial_fold_eval(
__isl_take isl_pw_qpolynomial_fold *pwf,
__isl_take isl_point *pnt);
__isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
__isl_take isl_pw_qpolynomial_fold *pwf);
__isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
__isl_take isl_pw_qpolynomial_fold *pwf,
__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 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.
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 to the last
must access and to 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>
__isl_give isl_access_info *isl_access_info_alloc(
__isl_take isl_map *sink,
void *sink_user, isl_access_level_before fn,
int max_source);
__isl_give isl_access_info *isl_access_info_add_source(
__isl_take isl_access_info *acc,
__isl_take isl_map *source, int must,
void *source_user);
__isl_give isl_flow *isl_access_info_compute_flow(
__isl_take isl_access_info *acc);
int isl_flow_foreach(__isl_keep isl_flow *deps,
int (*fn)(__isl_take isl_map *dep, int must,
void *dep_user, void *user),
void *user);
__isl_give isl_set *isl_flow_get_no_source(
__isl_keep isl_flow *deps, int must);
void isl_flow_free(__isl_take isl_flow *deps);
The function 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 result of the dependence analysis is collected in an
isl_flow. There may be elements in the domain of
the sink access for which no preceding source access could be
found or for which all preceding sources are may accesses.
The sets of 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 set corresponds to the reads from uninitialized
array elements and the second set 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.
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);
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 contains 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-polylibThe isl-polylib library provides the following functions for converting
between isl objects and PolyLib objects.
The library is distributed separately for licensing reasons.
#include <isl_set_polylib.h>
__isl_give isl_basic_set *isl_basic_set_new_from_polylib(
Polyhedron *P, __isl_take isl_dim *dim);
Polyhedron *isl_basic_set_to_polylib(
__isl_keep isl_basic_set *bset);
__isl_give isl_set *isl_set_new_from_polylib(Polyhedron *D,
__isl_take isl_dim *dim);
Polyhedron *isl_set_to_polylib(__isl_keep isl_set *set);
#include <isl_map_polylib.h>
__isl_give isl_basic_map *isl_basic_map_new_from_polylib(
Polyhedron *P, __isl_take isl_dim *dim);
__isl_give isl_map *isl_map_new_from_polylib(Polyhedron *D,
__isl_take isl_dim *dim);
Polyhedron *isl_basic_map_to_polylib(
__isl_keep isl_basic_map *bmap);
Polyhedron *isl_map_to_polylib(__isl_keep isl_map *map);