The C<--with-piplib> option can
be used to specify which C<piplib>
library to use, either an installed version (C<system>),
-an externally built version (C<build>), a bundled version (C<bundled>)
+an externally built version (C<build>)
or no version (C<no>). The option C<build> is mostly useful
in C<configure> scripts of larger projects that bundle both C<isl>
and C<piplib>.
=item C<--with-piplib>
-Which copy of C<piplib> to use, either C<no> (default), C<system>, C<build>
-or C<bundled>. Note that C<bundled> only works if you have obtained
-C<isl> and its submodules from the git repository.
+Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
=item C<--with-piplib-prefix>
are wrapped inside C<isl> specific macros.
The basic type is C<isl_int> and the following operations
are available on this type.
+The meanings of these operations are essentially the same
+as their C<GMP> C<mpz_> counterparts.
+As always with C<GMP> types, C<isl_int>s need to be
+initialized with C<isl_int_init> before they can be used
+and they need to be released with C<isl_int_clear>
+after the last use.
=over
=head2 Input and Output
-Proper input and output functions are still in development.
-However, some functions are provided to read and write
-to foreign file formats.
+C<isl> supports its own input/output format, which is similar
+to the C<Omega> format, but also supports the C<PolyLib> format
+in some cases.
+
+=head3 C<isl> format
+
+The C<isl> format is similar to that of C<Omega>, but has a different
+syntax for describing the parameters and allows for the definition
+of an existentially quantified variable as the integer division
+of an affine expression.
+For example, the set of integers C<i> between C<0> and C<n>
+such that C<i % 10 <= 6> can be described as
+
+ [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
+ i - 10 a <= 6) }
+
+A set or relation can have several disjuncts, separated
+by the keyword C<or>. Each disjunct is either a conjunction
+of constraints or a projection (C<exists>) of a conjunction
+of constraints. The constraints are separated by the keyword
+C<and>.
+
+=head3 C<PolyLib> format
+
+If the represented set is a union, then the first line
+contains a single number representing the number of disjuncts.
+Otherwise, a line containing the number C<1> is optional.
+
+Each disjunct is represented by a matrix of constraints.
+The first line contains two numbers representing
+the number of rows and columns,
+where the number of rows is equal to the number of constraints
+and the number of columns is equal to two plus the number of variables.
+The following lines contain the actual rows of the constraint matrix.
+In each row, the first column indicates whether the constraint
+is an equality (C<0>) or inequality (C<1>). The final column
+corresponds to the constant term.
+
+If the set is parametric, then the coefficients of the parameters
+appear in the last columns before the constant column.
+The coefficients of any existentially quantified variables appear
+between those of the set variables and those of the parameters.
=head3 Input
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_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
const char *str, int nparam);
-The input may be either in C<PolyLib> format or in the
-C<isl> format, which is similar to the C<Omega> format.
+The input format is autodetected and may be either the C<PolyLib> format
+or the C<isl> format.
C<nparam> specifies how many of the final columns in
the C<PolyLib> format correspond to parameters.
If input is given in the C<isl> format, then the number
void isl_set_print(__isl_keep struct isl_set *set,
FILE *out, int indent, unsigned output_format);
-C<input_format> must be C<ISL_FORMAT_POLYLIB>.
+ #include <isl_map.h>
+ void isl_basic_map_print(__isl_keep isl_basic_map *bmap,
+ FILE *out, int indent,
+ const char *prefix, const char *suffix,
+ unsigned output_format);
+ void isl_map_print(__isl_keep struct isl_map *map,
+ FILE *out, int indent, unsigned output_format);
+
+The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>
+or C<ISL_FORMAT_POLYLIB>.
Each line in the output is indented by C<indent> spaces,
prefixed by C<prefix> and suffixed by C<suffix>.
-The coefficients of the existentially quantified variables
+In the C<PolyLib> format output,
+the coefficients of the existentially quantified variables
appear between those of the set variables and those
of the parameters.
-=head3 Dumping the internal state
-
-For lack of proper output functions, the following functions
-can be used to dump the internal state of a set or relation.
-The user should not depend on the output format of these functions.
-
- void isl_basic_set_dump(__isl_keep isl_basic_set *bset,
- FILE *out, int indent);
- void isl_basic_map_dump(__isl_keep isl_basic_map *bmap,
- FILE *out, int indent);
- void isl_set_dump(__isl_keep isl_set *set,
- FILE *out, int indent);
- void isl_map_dump(__isl_keep isl_map *map,
- FILE *out, int indent);
-
=head2 Creating New Sets and Relations
C<isl> has functions for creating some standard sets and relations.
These functions take a dimension specification for a B<set>
and return relations that express that the elements in the domain
-are lexicograhically less
+are lexicographically less
(C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
than the elements in the range.
isl_int_clear(v);
+Or, alternatively,
+
+ struct isl_basic_set *bset;
+ bset = isl_basic_set_read_from_str(ctx,
+ "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
+
+=head2 Inspecting Sets and Relations
+
+Usually, the user should not have to care about the actual constraints
+of the sets and maps, but should instead apply the abstract operations
+explained in the following sections.
+Occasionally, however, it may be required to inspect the individual
+coefficients of the constraints. This section explains how to do so.
+In these cases, it may also be useful to have C<isl> compute
+an explicit representation of the existentially quantified variables.
+
+ __isl_give isl_set *isl_set_compute_divs(
+ __isl_take isl_set *set);
+ __isl_give isl_map *isl_map_compute_divs(
+ __isl_take isl_map *map);
+
+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 C<fn> should return 0 if successful and
+-1 if an error occurs. In the latter case, or if any other error
+occurs, the above functions will return -1.
+
+It should be noted that C<isl> does not guarantee that
+the basic sets or maps passed to C<fn> are disjoint.
+If this is required, then the user should call one of
+the following functions first.
+
+ __isl_give isl_set *isl_set_make_disjoint(
+ __isl_take isl_set *set);
+ __isl_give isl_map *isl_map_make_disjoint(
+ __isl_take isl_map *map);
+
+To iterate over the constraints of a basic set or map, use
+
+ #include <isl_constraint.h>
+
+ int isl_basic_map_foreach_constraint(
+ __isl_keep isl_basic_map *bmap,
+ int (*fn)(__isl_take isl_constraint *c, void *user),
+ void *user);
+ void isl_constraint_free(struct isl_constraint *c);
+
+Again, the callback function C<fn> should return 0 if successful and
+-1 if an error occurs. In the latter case, or if any other error
+occurs, the above functions will return -1.
+
+The coefficients of the constraints can be inspected using
+the following functions.
+
+ void isl_constraint_get_constant(
+ __isl_keep isl_constraint *constraint, isl_int *v);
+ void isl_constraint_get_coefficient(
+ __isl_keep isl_constraint *constraint,
+ enum isl_dim_type type, int pos, isl_int *v);
+
+The explicit representations of the existentially quantified
+variables can be inspected using the following functions.
+Note that the user is only allowed to use these functions
+if the inspected set or map is the result of a call
+to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
+
+ __isl_give isl_div *isl_constraint_div(
+ __isl_keep isl_constraint *constraint, int pos);
+ void isl_div_get_constant(__isl_keep isl_div *div,
+ isl_int *v);
+ void isl_div_get_denominator(__isl_keep isl_div *div,
+ isl_int *v);
+ void isl_div_get_coefficient(__isl_keep isl_div *div,
+ enum isl_dim_type type, int pos, isl_int *v);
+
=head2 Properties
=head3 Unary Properties
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);
=back
=over
+=item * Complement
+
+ __isl_give isl_set *isl_set_complement(
+ __isl_take isl_set *set);
+
=item * Projection
__isl_give isl_basic_set *isl_basic_set_project_out(
__isl_take isl_basic_set *bset,
enum isl_dim_type type, unsigned first, unsigned n);
+ __isl_give isl_basic_map *isl_basic_map_project_out(
+ __isl_take isl_basic_map *bmap,
+ enum isl_dim_type type, unsigned first, unsigned n);
__isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
enum isl_dim_type type, unsigned first, unsigned n);
+ __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
+ enum isl_dim_type type, unsigned first, unsigned n);
__isl_give isl_basic_set *isl_basic_map_domain(
__isl_take isl_basic_map *bmap);
__isl_give isl_basic_set *isl_basic_map_range(
__isl_give isl_set *isl_map_range(
__isl_take isl_map *map);
-C<isl_basic_set_project_out> currently only supports projecting
-out the final C<isl_dim_set> dimensions.
-
=item * Coalescing
Simplify the representation of a set or relation by trying
__isl_give isl_basic_map *isl_map_affine_hull(
__isl_take isl_map *map);
+=item * Power
+
+ __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
+ unsigned param, int *exact);
+
+Compute a parametric representation for all positive powers I<k> of C<map>.
+The power I<k> is equated to the parameter at position C<param>.
+The result may be an overapproximation. If the result is exact,
+then C<*exact> is set to C<1>.
+The current implementation only produces exact results for particular
+cases of piecewise translations (i.e., piecewise uniform dependences).
+
+=item * Transitive closure
+
+ __isl_give isl_map *isl_map_transitive_closure(
+ __isl_take isl_map *map, int *exact);
+
+Compute the transitive closure of C<map>.
+The result may be an overapproximation. If the result is known to be exact,
+then C<*exact> is set to C<1>.
+The current implementation only produces exact results for particular
+cases of piecewise translations (i.e., piecewise uniform dependences).
+
=back
=head2 Binary Operations
=head3 Lexicographic Optimization
-Given a basic set C<bset> and a zero-dimensional domain C<dom>,
+Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
the following functions
compute a set that contains the lexicographic minimum or maximum
-of the elements in C<bset> for those values of the parameters
+of the elements in C<set> (or C<bset>) for those values of the parameters
that satisfy C<dom>.
If C<empty> is not C<NULL>, then C<*empty> is assigned a set
-that contains the parameter values in C<dom> for which C<bset>
+that contains the parameter values in C<dom> for which C<set> (or C<bset>)
has no elements.
In other words, the union of the parameter values
for which the result is non-empty and of C<*empty>
__isl_take isl_basic_set *bset,
__isl_take isl_basic_set *dom,
__isl_give isl_set **empty);
+ __isl_give isl_set *isl_set_partial_lexmin(
+ __isl_take isl_set *set, __isl_take isl_set *dom,
+ __isl_give isl_set **empty);
+ __isl_give isl_set *isl_set_partial_lexmax(
+ __isl_take isl_set *set, __isl_take isl_set *dom,
+ __isl_give isl_set **empty);
-Given a basic set C<bset>, the following functions simply
+Given a (basic) set C<set> (or C<bset>), the following functions simply
return a set containing the lexicographic minimum or maximum
-of the elements in C<bset>.
+of the elements in C<set> (or C<bset>).
__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 C<bmap> and a domain C<dom>,
+Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
the following functions
compute a relation that maps each element of C<dom>
to the single lexicographic minimum or maximum
of the elements that are associated to that same
-element in C<bmap>.
+element in C<map> (or C<bmap>).
If C<empty> is not C<NULL>, then C<*empty> is assigned a set
that contains the elements in C<dom> that do not map
-to any elements in C<bmap>.
+to any elements in C<map> (or C<bmap>).
In other words, the union of the domain of the result and of C<*empty>
is equal to C<dom>.
__isl_take isl_basic_map *bmap,
__isl_take isl_basic_set *dom,
__isl_give isl_set **empty);
+ __isl_give isl_map *isl_map_partial_lexmax(
+ __isl_take isl_map *map, __isl_take isl_set *dom,
+ __isl_give isl_set **empty);
+ __isl_give isl_map *isl_map_partial_lexmin(
+ __isl_take isl_map *map, __isl_take isl_set *dom,
+ __isl_give isl_set **empty);
-Given a basic map C<bmap>, the following functions simply
+Given a (basic) map C<map> (or C<bmap>), the following functions simply
return a map mapping each element in the domain of
-C<bmap> to the lexicographic minimum or maximum
+C<map> (or C<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);
+
+=head2 Points
+
+Points are elements of a set. They can be used to construct
+simple sets (boxes) or they can be used to represent the
+individual elements of a set.
+The zero point (the origin) can be created using
+
+ __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
+
+The coordinates of a point can be inspected, set and changed
+using
+
+ void isl_point_get_coordinate(__isl_keep isl_point *pnt,
+ enum isl_dim_type type, int pos, isl_int *v);
+ __isl_give isl_point *isl_point_set_coordinate(
+ __isl_take isl_point *pnt,
+ enum isl_dim_type type, int pos, isl_int v);
+
+ __isl_give isl_point *isl_point_add_ui(
+ __isl_take isl_point *pnt,
+ enum isl_dim_type type, int pos, unsigned val);
+ __isl_give isl_point *isl_point_sub_ui(
+ __isl_take isl_point *pnt,
+ enum isl_dim_type type, int pos, unsigned val);
+
+Points can be copied or freed using
+
+ __isl_give isl_point *isl_point_copy(
+ __isl_keep isl_point *pnt);
+ void isl_point_free(__isl_take isl_point *pnt);
+
+A singleton set can be created from a point using
+
+ __isl_give isl_set *isl_set_from_point(
+ __isl_take isl_point *pnt);
+
+and a box can be created from two opposite extremal points using
+
+ __isl_give isl_set *isl_set_box_from_points(
+ __isl_take isl_point *pnt1,
+ __isl_take isl_point *pnt2);
+
+All elements of a B<bounded> 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 C<fn> is called for each integer point in
+C<set> with as second argument the last argument of
+the C<isl_set_foreach_point> call. The function C<fn>
+should return C<0> on success and C<-1> on failure.
+In the latter case, C<isl_set_foreach_point> will stop
+enumerating and return C<-1> as well.
+If the enumeration is performed successfully and to completion,
+then C<isl_set_foreach_point> returns C<0>.
+
+To obtain a single point of a set, use
+
+ __isl_give isl_point *isl_set_sample_point(
+ __isl_take isl_set *set);
+
+If C<set> does not contain any (integer) points, then the
+resulting point will be ``void'', a property that can be
+tested using
+
+ int isl_point_is_void(__isl_keep isl_point *pnt);
+
+=head2 Piecewise Quasipolynomials
+
+A piecewise quasipolynomial is a particular kind of function that maps
+a parametric point to a rational value.
+More specifically, a quasipolynomial is a polynomial expression in greatest
+integer parts of affine expressions of parameters and variables.
+A piecewise quasipolynomial is a subdivision of a given parametric
+domain into disjoint cells with a quasipolynomial associated to
+each cell. The value of the piecewise quasipolynomial at a given
+point is the value of the quasipolynomial associated to the cell
+that contains the point. Outside of the union of cells,
+the value is assumed to be zero.
+For example, the piecewise quasipolynomial
+
+ [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
+
+maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
+Piecewise quasipolynomials are mainly used by the C<barvinok>
+library for representing the number of elements in a parametric set or map.
+For example, the piecewise quasipolynomial above represents
+the number of point in the map
+
+ [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
+
+=head3 Printing (Piecewise) Quasipolynomials
+
+Quasipolynomials and piecewise quasipolynomials can be printed
+using the following functions.
+
+ void isl_qpolynomial_print(__isl_keep isl_qpolynomial *qp,
+ FILE *out, unsigned output_format);
+
+ void isl_pw_qpolynomial_print(
+ __isl_keep isl_pw_qpolynomial *pwqp, FILE *out,
+ unsigned output_format);
+
+=head3 Creating New (Piecewise) Quasipolynomials
+
+Some simple quasipolynomials can be created using the following functions.
+More complicated quasipolynomials can be created by applying
+operations such as addition and multiplication
+on the resulting quasipolynomials
+
+ __isl_give isl_qpolynomial *isl_qpolynomial_zero(
+ __isl_take isl_dim *dim);
+ __isl_give isl_qpolynomial *isl_qpolynomial_infty(
+ __isl_take isl_dim *dim);
+ __isl_give isl_qpolynomial *isl_qpolynomial_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);
+
+=head3 Inspecting (Piecewise) Quasipolynomials
+
+To iterate over the cells in a piecewise quasipolynomial,
+use the following function
+
+ 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);
+
+As usual, the function C<fn> should return C<0> on success
+and C<-1> on failure.
+
+To iterate over all terms in a quasipolynomial,
+use
+
+ int isl_qpolynomial_foreach_term(
+ __isl_keep isl_qpolynomial *qp,
+ int (*fn)(__isl_take isl_term *term,
+ void *user), void *user);
+
+The terms themselves can be inspected and freed using
+these functions
+
+ unsigned isl_term_dim(__isl_keep isl_term *term,
+ enum isl_dim_type type);
+ void isl_term_get_num(__isl_keep isl_term *term,
+ isl_int *n);
+ void isl_term_get_den(__isl_keep isl_term *term,
+ isl_int *d);
+ int isl_term_get_exp(__isl_keep isl_term *term,
+ enum isl_dim_type type, unsigned pos);
+ __isl_give isl_div *isl_term_get_div(
+ __isl_keep isl_term *term, unsigned pos);
+ void isl_term_free(__isl_take isl_term *term);
+
+Each term is a product of parameters, set variables and
+integer divisions. The function C<isl_term_get_exp>
+returns the exponent of a given dimensions in the given term.
+The C<isl_int>s in the arguments of C<isl_term_get_num>
+and C<isl_term_get_den> need to have been initialized
+using C<isl_int_init> before calling these functions.
+
+=head3 Properties of (Piecewise) Quasipolynomials
+
+To check whether a quasipolynomial is actually a constant,
+use the following function.
+
+ int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
+ isl_int *n, isl_int *d);
+
+If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
+then the numerator and denominator of the constant
+are returned in C<*n> and C<*d>, respectively.
+
+=head3 Operations on (Piecewise) Quasipolynomials
+
+ __isl_give isl_qpolynomial *isl_qpolynomial_neg(
+ __isl_take isl_qpolynomial *qp);
+ __isl_give isl_qpolynomial *isl_qpolynomial_add(
+ __isl_take isl_qpolynomial *qp1,
+ __isl_take isl_qpolynomial *qp2);
+ __isl_give isl_qpolynomial *isl_qpolynomial_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);
+
+=head2 Dependence Analysis
+
+C<isl> contains specialized functionality for performing
+array dataflow analysis. That is, given a I<sink> access relation
+and a collection of possible I<source> access relations,
+C<isl> can compute relations that describe
+for each iteration of the sink access, which iteration
+of which of the source access relations was the last
+to access the same data element before the given iteration
+of the sink access.
+To compute standard flow dependences, the sink should be
+a read, while the sources should be writes.
+
+ #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, void *source_user);
+
+ __isl_give isl_flow *isl_access_info_compute_flow(
+ __isl_take isl_access_info *acc);
+
+ int isl_flow_foreach(__isl_keep isl_flow *deps,
+ int (*fn)(__isl_take isl_map *dep, void *dep_user,
+ void *user),
+ void *user);
+ __isl_give isl_set *isl_flow_get_no_source(
+ __isl_keep isl_flow *deps);
+ void isl_flow_free(__isl_take isl_flow *deps);
+
+The function C<isl_access_info_compute_flow> performs the actual
+dependence analysis. The other functions are used to construct
+the input for this function or to read off the output.
+
+The input is collected in an C<isl_access_info>, which can
+be created through a call to C<isl_access_info_alloc>.
+The arguments to this functions are the sink access relation
+C<sink>, a token C<sink_user> used to identify the sink
+access to the user, a callback function for specifying the
+relative order of source and sink accesses, and the number
+of source access relations that will be added.
+The callback function has type C<int (*)(void *first, void *second)>.
+The function is called with two user supplied tokens identifying
+either a source or the sink and it should return the shared nesting
+level and the relative order of the two accesses.
+In particular, let I<n> be the number of loops shared by
+the two accesses. If C<first> precedes C<second> textually,
+then the function should return I<2 * n + 1>; otherwise,
+it should return I<2 * n>.
+The sources can be added to the C<isl_access_info> by performing
+(at most) C<max_source> calls to C<isl_access_info_add_source>.
+The C<source_user> token is again used to identify
+the source access. The range of the source access relation
+C<source> should have the same dimension as the range
+of the sink access relation.
+
+The result of the dependence analysis is collected in an
+C<isl_flow>. There may be elements in the domain of
+the sink access for which no preceding source access could be
+find. The set of these elements can be obtained through
+a call to C<isl_flow_get_no_source>.
+In the case of standard flow dependence analysis,
+this set corresponds to the reads from uninitialized
+array elements.
+The actual flow dependences can be extracted using
+C<isl_flow_foreach>. This function will call the user-specified
+callback function C<fn> for each B<non-empty> dependence between
+a source and the sink. The callback function is called
+with three arguments, the actual flow dependence relation
+mapping source iterations to sink iterations, a token
+identifying the source and an additional C<void *> with value
+equal to the third argument of the C<isl_flow_foreach> call.
+
+After finishing with an C<isl_flow>, the user should call
+C<isl_flow_free> to free all associated memory.
=head1 Applications
Although C<isl> is mainly meant to be used as a library,
it also contains some basic applications that use some
of the functionality of C<isl>.
-Since C<isl> does not have its own input format yet, these
-applications currently take input in C<PolyLib> style.
-That is, a line with the number of rows and columns,
-where the number of rows is equal to the number of constraints
-and the number of columns is equal to two plus the number of variables,
-followed by the actual rows.
-In each row, the first column indicates whether the constraint
-is an equality (C<0>) or inequality (C<1>). The final column
-corresponds to the constant term.
+The input may be specified in either the L<isl format>
+or the L<PolyLib format>.
=head2 C<isl_polyhedron_sample>
-C<isl_polyhedron_sample>
-takes a polyhedron in C<PolyLib> format as input and prints
+C<isl_polyhedron_sample> takes a polyhedron as input and prints
an integer element of the polyhedron, if there is any.
The first column in the output is the denominator and is always
equal to 1. If the polyhedron contains no integer points,
C<isl_pip> takes the same input as the C<example> program
from the C<piplib> distribution, i.e., a set of constraints
-on the parameters in C<PolyLib> format,
-a line contains only -1 and finally a set
-of constraints on a parametric polyhedron, again in C<PolyLib> format.
+on the parameters, a line 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.
C<isl_polyhedron_minimize> computes the minimum of some linear
or affine objective function over the integer points in a polyhedron.
-The input is in C<PolyLib> format. If an affine objective function
+If an affine objective function
is given, then the constant should appear in the last column.
=head2 C<isl_polytope_scan>
-Given a polytope in C<PolyLib> format, C<isl_polytope_scan> prints
+Given a polytope, C<isl_polytope_scan> prints
all integer points in the polytope.
=head1 C<isl-polylib>
projects / platform / upstream / isl.git / blobdiff