add isl_point_get_dim

[platform/upstream/isl.git] / doc / user.pod

diff --git a/doc/user.pod b/doc/user.pod
index 95adf2b..3f0ac7f 100644 (file)
--- a/doc/user.pod
+++ b/doc/user.pod
@@ -473,6 +473,8 @@ specification of the original object.
        #include <isl/polynomial.h>
        __isl_give isl_dim *isl_qpolynomial_get_dim(
                __isl_keep isl_qpolynomial *qp);
        #include <isl/polynomial.h>
        __isl_give isl_dim *isl_qpolynomial_get_dim(
                __isl_keep isl_qpolynomial *qp);

+       __isl_give isl_dim *isl_qpolynomial_fold_get_dim(
+               __isl_keep isl_qpolynomial_fold *fold);

        __isl_give isl_dim *isl_pw_qpolynomial_get_dim(
                __isl_keep isl_pw_qpolynomial *pwqp);
        __isl_give isl_dim *isl_union_pw_qpolynomial_get_dim(
        __isl_give isl_dim *isl_pw_qpolynomial_get_dim(
                __isl_keep isl_pw_qpolynomial *pwqp);
        __isl_give isl_dim *isl_union_pw_qpolynomial_get_dim(


@@ -480,6 +482,14 @@ specification of the original object.
        __isl_give isl_dim *isl_union_pw_qpolynomial_fold_get_dim(
                __isl_keep isl_union_pw_qpolynomial_fold *upwf);
 
        __isl_give isl_dim *isl_union_pw_qpolynomial_fold_get_dim(
                __isl_keep isl_union_pw_qpolynomial_fold *upwf);
 

+       #include <isl/aff.h>
+       __isl_give isl_dim *isl_aff_get_dim(
+               __isl_keep isl_aff *aff);
+
+       #include <isl/point.h>
+       __isl_give isl_dim *isl_point_get_dim(
+               __isl_keep isl_point *pnt);
+

 The names of the individual dimensions may be set or read off
 using the following functions.
 
 The names of the individual dimensions may be set or read off
 using the following functions.
 


@@ -546,6 +556,8 @@ specifications using the following functions.
        __isl_give isl_dim *isl_dim_reverse(__isl_take isl_dim *dim);
        __isl_give isl_dim *isl_dim_join(__isl_take isl_dim *left,
                __isl_take isl_dim *right);
        __isl_give isl_dim *isl_dim_reverse(__isl_take isl_dim *dim);
        __isl_give isl_dim *isl_dim_join(__isl_take isl_dim *left,
                __isl_take isl_dim *right);

+       __isl_give isl_dim *isl_dim_align_params(
+               __isl_take isl_dim *dim1, __isl_take isl_dim *dim2)

        __isl_give isl_dim *isl_dim_insert(__isl_take isl_dim *dim,
                enum isl_dim_type type, unsigned pos, unsigned n);
        __isl_give isl_dim *isl_dim_add(__isl_take isl_dim *dim,
        __isl_give isl_dim *isl_dim_insert(__isl_take isl_dim *dim,
                enum isl_dim_type type, unsigned pos, unsigned n);
        __isl_give isl_dim *isl_dim_add(__isl_take isl_dim *dim,


@@ -559,6 +571,54 @@ specifications using the following functions.
 Note that if dimensions are added or removed from a space, then
 the name and the internal structure are lost.
 
 Note that if dimensions are added or removed from a space, then
 the name and the internal structure are lost.
 

+=head2 Local Spaces
+
+A local space is essentially a dimension specification with
+zero or more existentially quantified variables.
+The local space of a basic set or relation can be obtained
+using the following functions.
+
+       #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 dimension specification using
+
+       #include <isl/local_space.h>
+       __isl_give isl_local_space *isl_local_space_from_dim(
+               __isl_take isl_dim *dim);
+
+They can be inspected, 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_dim(__isl_keep isl_local_space *ls,
+               enum isl_dim_type type);
+       const char *isl_local_space_get_dim_name(
+               __isl_keep isl_local_space *ls,
+               enum isl_dim_type type, unsigned pos);
+       __isl_give isl_dim *isl_local_space_get_dim(
+               __isl_keep isl_local_space *ls);
+       __isl_give isl_div *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);
+
+Local spaces can be created from other local spaces
+using the following functions.
+
+       __isl_give isl_local_space *isl_local_space_from_domain(
+               __isl_take isl_local_space *ls);
+       __isl_give isl_local_space *isl_local_space_add_dim(
+               __isl_take isl_local_space *ls,
+               enum isl_dim_type type, unsigned n);
+

 =head2 Input and Output
 
 C<isl> supports its own input/output format, which is similar
 =head2 Input and Output
 
 C<isl> supports its own input/output format, which is similar


@@ -679,6 +739,8 @@ The behavior of the printer can be modified in various ways
                __isl_take isl_printer *p, int output_format);
        __isl_give isl_printer *isl_printer_set_indent(
                __isl_take isl_printer *p, int indent);
                __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_give isl_printer *isl_printer_set_prefix(
                __isl_take isl_printer *p, const char *prefix);
        __isl_give isl_printer *isl_printer_set_suffix(


@@ -687,12 +749,15 @@ The behavior of the printer can be modified in various ways
 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
 and defaults to C<ISL_FORMAT_ISL>.
 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
 and defaults to C<ISL_FORMAT_ISL>.

-Each line in the output is indented by C<indent> spaces
+Each line in the output is indented by C<indent> (set by
+C<isl_printer_set_indent>) spaces

 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
 In the C<PolyLib> format output,
 the coefficients of the existentially quantified variables
 appear between those of the set variables and those
 of the parameters.
 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
 In the C<PolyLib> format output,
 the coefficients of the existentially quantified variables
 appear between those of the set variables and those
 of the parameters.

+The function C<isl_printer_indent> increases the indentation
+by the specified amount (which may be negative).

 
 To actually print something, use
 
 
 To actually print something, use
 


@@ -865,7 +930,7 @@ 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
 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.
+added to (basic) sets and relations using the following functions.

 
        #include <isl/constraint.h>
        __isl_give isl_constraint *isl_equality_alloc(
 
        #include <isl/constraint.h>
        __isl_give isl_constraint *isl_equality_alloc(


@@ -883,6 +948,12 @@ added to basic sets and relations using the following functions.
        __isl_give isl_basic_set *isl_basic_set_add_constraint(
                __isl_take isl_basic_set *bset,
                __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);

 
 For example, to create a set containing the even integers
 between 10 and 42, you would use the following code.
 
 For example, to create a set containing the even integers
 between 10 and 42, you would use the following code.


@@ -950,6 +1021,19 @@ C<isl_dim_set> and C<isl_dim_div> for sets and
 of C<isl_dim_cst>, C<isl_dim_param>,
 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
 
 of C<isl_dim_cst>, C<isl_dim_param>,
 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
 

+A basic relation can also be constructed from an affine expression
+or a list of affine expressions (See L<"Quasi Affine Expressions">).
+
+       __isl_give isl_basic_map *isl_basic_map_from_aff(
+               __isl_take isl_aff *aff);
+       __isl_give isl_basic_map *isl_basic_map_from_aff_list(
+               __isl_take isl_dim *domain_dim,
+               __isl_take isl_aff_list *list);
+
+The C<domain_dim> argument describes the domain of the resulting
+basic relation.  It is required because the C<list> may consist
+of zero affine expressions.
+

 =head2 Inspecting Sets and Relations
 
 Usually, the user should not have to care about the actual constraints
 =head2 Inspecting Sets and Relations
 
 Usually, the user should not have to care about the actual constraints


@@ -1077,6 +1161,9 @@ the following functions.
        void isl_constraint_get_coefficient(
                __isl_keep isl_constraint *constraint,
                enum isl_dim_type type, int pos, isl_int *v);
        void isl_constraint_get_coefficient(
                __isl_keep isl_constraint *constraint,
                enum isl_dim_type type, int pos, isl_int *v);

+       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 functions.
 
 The explicit representations of the existentially quantified
 variables can be inspected using the following functions.


@@ -1358,6 +1445,29 @@ that maps (a wrapped version of) the input relation to its domain or range.
 Eliminate the coefficients for the given dimensions from the constraints,
 without removing the dimensions.
 
 Eliminate the coefficients for the given dimensions from the constraints,
 without removing the dimensions.
 

+=item * Slicing
+
+       __isl_give isl_basic_set *isl_basic_set_fix(
+               __isl_take isl_basic_set *bset,
+               enum isl_dim_type type, unsigned pos,
+               isl_int value);
+       __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_set *isl_set_fix(__isl_take isl_set *set,
+               enum isl_dim_type type, unsigned pos,
+               isl_int value);
+       __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_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_map *isl_map_fix_si(__isl_take isl_map *map,
+               enum isl_dim_type type, unsigned pos, int value);
+
+Intersect the set or relation with the hyperplane where the given
+dimension has the fixed given value.
+

 =item * Identity
 
        __isl_give isl_map *isl_set_identity(
 =item * Identity
 
        __isl_give isl_map *isl_set_identity(


@@ -1491,6 +1601,20 @@ that contains the whole input set or relation.
 In case of union sets and relations, the polyhedral hull is computed
 per space.
 
 In case of union sets and relations, the polyhedral hull is computed
 per space.
 

+=item * Optimization
+
+       #include <isl/ilp.h>
+       enum isl_lp_result isl_basic_set_max(
+               __isl_keep isl_basic_set *bset,
+               __isl_keep isl_aff *obj, isl_int *opt)
+       enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
+               __isl_keep isl_aff *obj, isl_int *opt);
+
+Compute the maximum of the integer affine expression C<obj>
+over the points in C<set>, returning the result in C<opt>.
+The return value may be one of C<isl_lp_error>,
+C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
+

 =item * Dual
 
 The following functions compute either the set of (rational) coefficient
 =item * Dual
 
 The following functions compute either the set of (rational) coefficient


@@ -1585,6 +1709,10 @@ then the name of the space is also removed.
                __isl_take isl_basic_set *bset);
        __isl_give isl_set *isl_set_flatten(
                __isl_take isl_set *set);
                __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_range(
+               __isl_take isl_basic_map *bmap);
+       __isl_give isl_map *isl_map_flatten_range(
+               __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_give isl_basic_map *isl_basic_map_flatten(
                __isl_take isl_basic_map *bmap);
        __isl_give isl_map *isl_map_flatten(


@@ -1806,6 +1934,15 @@ instead.
        __isl_give isl_set *isl_set_flat_product(
                __isl_take isl_set *set1,
                __isl_take isl_set *set2);
        __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_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_basic_map *isl_basic_map_flat_product(
                __isl_take isl_basic_map *bmap1,
                __isl_take isl_basic_map *bmap2);


@@ -1935,6 +2072,44 @@ In case of union relations, the optimum is computed per space.
        __isl_give isl_union_map *isl_union_map_lexmax(
                __isl_take isl_union_map *umap);
 
        __isl_give isl_union_map *isl_union_map_lexmax(
                __isl_take isl_union_map *umap);
 

+=head2 Lists
+
+Lists are defined over several element types, including
+C<isl_aff>, C<isl_basic_set> and C<isl_set>.
+Here we take lists of C<isl_set>s as an example.
+Lists can be created, copied and freed using the following functions.
+
+       #include <isl/list.h>
+       __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_add(
+               __isl_take isl_set_list *list,
+               __isl_take isl_set *el);
+       void isl_set_list_free(__isl_take isl_set_list *list);
+
+C<isl_set_list_alloc> creates an empty list with a capacity for
+C<n> elements.
+
+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 struct 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 struct isl_set *el, void *user),
+               void *user);
+
+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);
+

 =head2 Matrices
 
 Matrices can be created, copied and freed using the following functions.
 =head2 Matrices
 
 Matrices can be created, copied and freed using the following functions.


@@ -1974,6 +2149,103 @@ 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);
 
 
        __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
 

+=head2 Quasi Affine Expressions
+
+The zero quasi affine expression can be created using
+
+       __isl_give isl_aff *isl_aff_zero(
+               __isl_take isl_local_space *ls);
+
+Quasi affine expressions can be copied and free 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);
+
+A (rational) bound on a dimension can be extracted from an C<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);
+
+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_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);
+       int isl_aff_get_constant(__isl_keep isl_aff *aff,
+               isl_int *v);
+       int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
+               enum isl_dim_type type, int pos, isl_int *v);
+       int isl_aff_get_denominator(__isl_keep isl_aff *aff,
+               isl_int *v);
+       __isl_give isl_div *isl_aff_get_div(
+               __isl_keep isl_aff *aff, int pos);
+
+It can be modified using
+
+       #include <isl/aff.h>
+       __isl_give isl_aff *isl_aff_set_constant(
+               __isl_take isl_aff *aff, isl_int v);
+       __isl_give isl_aff *isl_aff_set_constant_si(
+               __isl_take isl_aff *aff, int v);
+       __isl_give isl_aff *isl_aff_set_coefficient(
+               __isl_take isl_aff *aff,
+               enum isl_dim_type type, int pos, isl_int 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_denominator(
+               __isl_take isl_aff *aff, isl_int v);
+
+       __isl_give isl_aff *isl_aff_add_constant(
+               __isl_take isl_aff *aff, isl_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);
+
+Note that the C<set_constant> and C<set_coefficient> functions
+set the I<numerator> of the constant or coefficient, while
+C<add_constant> and C<add_coefficient> add an integer value to
+the possibly rational constant or coefficient.
+
+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_aff *isl_aff_sub(__isl_take isl_aff *aff1,
+               __isl_take isl_aff *aff2);
+       __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
+       __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
+       __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
+               isl_int f);
+       __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
+               isl_int f);
+
+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);
+

 =head2 Points
 
 Points are elements of a set.  They can be used to construct
 =head2 Points
 
 Points are elements of a set.  They can be used to construct


@@ -1999,6 +2271,10 @@ using
                __isl_take isl_point *pnt,
                enum isl_dim_type type, int pos, unsigned val);
 
                __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(
 Points can be copied or freed using
 
        __isl_give isl_point *isl_point_copy(


@@ -2139,6 +2415,8 @@ on the resulting quasipolynomials
        __isl_give isl_qpolynomial *isl_qpolynomial_var(
                __isl_take isl_dim *dim,
                enum isl_dim_type type, unsigned pos);
        __isl_give isl_qpolynomial *isl_qpolynomial_var(
                __isl_take isl_dim *dim,
                enum isl_dim_type type, unsigned pos);

+       __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
+               __isl_take isl_aff *aff);

 
 The zero piecewise quasipolynomial or a piecewise quasipolynomial
 with a single cell can be created using the following functions.
 
 The zero piecewise quasipolynomial or a piecewise quasipolynomial
 with a single cell can be created using the following functions.


@@ -2701,7 +2979,74 @@ from an C<isl_schedule> using the following function.
        __isl_give isl_union_map *isl_schedule_get_map(
                __isl_keep isl_schedule *sched);
 
        __isl_give isl_union_map *isl_schedule_get_map(
                __isl_keep isl_schedule *sched);
 

-This mapping can also be obtained in pieces using the following functions.
+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 list can be manipulated as explained in L<"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);
+
+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).
+
+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);
+
+Alternatively, the schedule mapping
+can also be obtained in pieces using the following functions.

 
        int isl_schedule_n_band(__isl_keep isl_schedule *sched);
        __isl_give isl_union_map *isl_schedule_get_band(
 
        int isl_schedule_n_band(__isl_keep isl_schedule *sched);
        __isl_give isl_union_map *isl_schedule_get_band(