3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take the dimension specification
72 of a B<map> as input. An old call
73 C<isl_map_identity(dim)> can be rewritten to
74 C<isl_map_identity(isl_dim_map_from_set(dim))>.
76 =item * The function C<isl_map_power> no longer takes
77 a parameter position as input. Instead, the exponent
78 is now expressed as the domain of the resulting relation.
82 =head3 Changes since isl-0.06
86 =item * The format of C<isl_printer_print_qpolynomial>'s
87 C<ISL_FORMAT_ISL> output has changed.
88 Use C<ISL_FORMAT_C> to obtain the old output.
94 The source of C<isl> can be obtained either as a tarball
95 or from the git repository. Both are available from
96 L<http://freshmeat.net/projects/isl/>.
97 The installation process depends on how you obtained
100 =head2 Installation from the git repository
104 =item 1 Clone or update the repository
106 The first time the source is obtained, you need to clone
109 git clone git://repo.or.cz/isl.git
111 To obtain updates, you need to pull in the latest changes
115 =item 2 Generate C<configure>
121 After performing the above steps, continue
122 with the L<Common installation instructions>.
124 =head2 Common installation instructions
128 =item 1 Obtain C<GMP>
130 Building C<isl> requires C<GMP>, including its headers files.
131 Your distribution may not provide these header files by default
132 and you may need to install a package called C<gmp-devel> or something
133 similar. Alternatively, C<GMP> can be built from
134 source, available from L<http://gmplib.org/>.
138 C<isl> uses the standard C<autoconf> C<configure> script.
143 optionally followed by some configure options.
144 A complete list of options can be obtained by running
148 Below we discuss some of the more common options.
150 C<isl> can optionally use C<piplib>, but no
151 C<piplib> functionality is currently used by default.
152 The C<--with-piplib> option can
153 be used to specify which C<piplib>
154 library to use, either an installed version (C<system>),
155 an externally built version (C<build>)
156 or no version (C<no>). The option C<build> is mostly useful
157 in C<configure> scripts of larger projects that bundle both C<isl>
164 Installation prefix for C<isl>
166 =item C<--with-gmp-prefix>
168 Installation prefix for C<GMP> (architecture-independent files).
170 =item C<--with-gmp-exec-prefix>
172 Installation prefix for C<GMP> (architecture-dependent files).
174 =item C<--with-piplib>
176 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
178 =item C<--with-piplib-prefix>
180 Installation prefix for C<system> C<piplib> (architecture-independent files).
182 =item C<--with-piplib-exec-prefix>
184 Installation prefix for C<system> C<piplib> (architecture-dependent files).
186 =item C<--with-piplib-builddir>
188 Location where C<build> C<piplib> was built.
196 =item 4 Install (optional)
204 =head2 Initialization
206 All manipulations of integer sets and relations occur within
207 the context of an C<isl_ctx>.
208 A given C<isl_ctx> can only be used within a single thread.
209 All arguments of a function are required to have been allocated
210 within the same context.
211 There are currently no functions available for moving an object
212 from one C<isl_ctx> to another C<isl_ctx>. This means that
213 there is currently no way of safely moving an object from one
214 thread to another, unless the whole C<isl_ctx> is moved.
216 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
217 freed using C<isl_ctx_free>.
218 All objects allocated within an C<isl_ctx> should be freed
219 before the C<isl_ctx> itself is freed.
221 isl_ctx *isl_ctx_alloc();
222 void isl_ctx_free(isl_ctx *ctx);
226 All operations on integers, mainly the coefficients
227 of the constraints describing the sets and relations,
228 are performed in exact integer arithmetic using C<GMP>.
229 However, to allow future versions of C<isl> to optionally
230 support fixed integer arithmetic, all calls to C<GMP>
231 are wrapped inside C<isl> specific macros.
232 The basic type is C<isl_int> and the operations below
233 are available on this type.
234 The meanings of these operations are essentially the same
235 as their C<GMP> C<mpz_> counterparts.
236 As always with C<GMP> types, C<isl_int>s need to be
237 initialized with C<isl_int_init> before they can be used
238 and they need to be released with C<isl_int_clear>
240 The user should not assume that an C<isl_int> is represented
241 as a C<mpz_t>, but should instead explicitly convert between
242 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
243 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
247 =item isl_int_init(i)
249 =item isl_int_clear(i)
251 =item isl_int_set(r,i)
253 =item isl_int_set_si(r,i)
255 =item isl_int_set_gmp(r,g)
257 =item isl_int_get_gmp(i,g)
259 =item isl_int_abs(r,i)
261 =item isl_int_neg(r,i)
263 =item isl_int_swap(i,j)
265 =item isl_int_swap_or_set(i,j)
267 =item isl_int_add_ui(r,i,j)
269 =item isl_int_sub_ui(r,i,j)
271 =item isl_int_add(r,i,j)
273 =item isl_int_sub(r,i,j)
275 =item isl_int_mul(r,i,j)
277 =item isl_int_mul_ui(r,i,j)
279 =item isl_int_addmul(r,i,j)
281 =item isl_int_submul(r,i,j)
283 =item isl_int_gcd(r,i,j)
285 =item isl_int_lcm(r,i,j)
287 =item isl_int_divexact(r,i,j)
289 =item isl_int_cdiv_q(r,i,j)
291 =item isl_int_fdiv_q(r,i,j)
293 =item isl_int_fdiv_r(r,i,j)
295 =item isl_int_fdiv_q_ui(r,i,j)
297 =item isl_int_read(r,s)
299 =item isl_int_print(out,i,width)
303 =item isl_int_cmp(i,j)
305 =item isl_int_cmp_si(i,si)
307 =item isl_int_eq(i,j)
309 =item isl_int_ne(i,j)
311 =item isl_int_lt(i,j)
313 =item isl_int_le(i,j)
315 =item isl_int_gt(i,j)
317 =item isl_int_ge(i,j)
319 =item isl_int_abs_eq(i,j)
321 =item isl_int_abs_ne(i,j)
323 =item isl_int_abs_lt(i,j)
325 =item isl_int_abs_gt(i,j)
327 =item isl_int_abs_ge(i,j)
329 =item isl_int_is_zero(i)
331 =item isl_int_is_one(i)
333 =item isl_int_is_negone(i)
335 =item isl_int_is_pos(i)
337 =item isl_int_is_neg(i)
339 =item isl_int_is_nonpos(i)
341 =item isl_int_is_nonneg(i)
343 =item isl_int_is_divisible_by(i,j)
347 =head2 Sets and Relations
349 C<isl> uses six types of objects for representing sets and relations,
350 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
351 C<isl_union_set> and C<isl_union_map>.
352 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
353 can be described as a conjunction of affine constraints, while
354 C<isl_set> and C<isl_map> represent unions of
355 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
356 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
357 to have the same dimension. C<isl_union_set>s and C<isl_union_map>s
358 represent unions of C<isl_set>s or C<isl_map>s of I<different> dimensions,
359 where dimensions with different space names
360 (see L<Dimension Specifications>) are considered different as well.
361 The difference between sets and relations (maps) is that sets have
362 one set of variables, while relations have two sets of variables,
363 input variables and output variables.
365 =head2 Memory Management
367 Since a high-level operation on sets and/or relations usually involves
368 several substeps and since the user is usually not interested in
369 the intermediate results, most functions that return a new object
370 will also release all the objects passed as arguments.
371 If the user still wants to use one or more of these arguments
372 after the function call, she should pass along a copy of the
373 object rather than the object itself.
374 The user is then responsible for making sure that the original
375 object gets used somewhere else or is explicitly freed.
377 The arguments and return values of all documents functions are
378 annotated to make clear which arguments are released and which
379 arguments are preserved. In particular, the following annotations
386 C<__isl_give> means that a new object is returned.
387 The user should make sure that the returned pointer is
388 used exactly once as a value for an C<__isl_take> argument.
389 In between, it can be used as a value for as many
390 C<__isl_keep> arguments as the user likes.
391 There is one exception, and that is the case where the
392 pointer returned is C<NULL>. Is this case, the user
393 is free to use it as an C<__isl_take> argument or not.
397 C<__isl_take> means that the object the argument points to
398 is taken over by the function and may no longer be used
399 by the user as an argument to any other function.
400 The pointer value must be one returned by a function
401 returning an C<__isl_give> pointer.
402 If the user passes in a C<NULL> value, then this will
403 be treated as an error in the sense that the function will
404 not perform its usual operation. However, it will still
405 make sure that all the the other C<__isl_take> arguments
410 C<__isl_keep> means that the function will only use the object
411 temporarily. After the function has finished, the user
412 can still use it as an argument to other functions.
413 A C<NULL> value will be treated in the same way as
414 a C<NULL> value for an C<__isl_take> argument.
418 =head2 Dimension Specifications
420 Whenever a new set or relation is created from scratch,
421 its dimension needs to be specified using an C<isl_dim>.
424 __isl_give isl_dim *isl_dim_alloc(isl_ctx *ctx,
425 unsigned nparam, unsigned n_in, unsigned n_out);
426 __isl_give isl_dim *isl_dim_set_alloc(isl_ctx *ctx,
427 unsigned nparam, unsigned dim);
428 __isl_give isl_dim *isl_dim_copy(__isl_keep isl_dim *dim);
429 void isl_dim_free(__isl_take isl_dim *dim);
430 unsigned isl_dim_size(__isl_keep isl_dim *dim,
431 enum isl_dim_type type);
433 The dimension specification used for creating a set
434 needs to be created using C<isl_dim_set_alloc>, while
435 that for creating a relation
436 needs to be created using C<isl_dim_alloc>.
437 C<isl_dim_size> can be used
438 to find out the number of dimensions of each type in
439 a dimension specification, where type may be
440 C<isl_dim_param>, C<isl_dim_in> (only for relations),
441 C<isl_dim_out> (only for relations), C<isl_dim_set>
442 (only for sets) or C<isl_dim_all>.
444 It is often useful to create objects that live in the
445 same space as some other object. This can be accomplished
446 by creating the new objects
447 (see L<Creating New Sets and Relations> or
448 L<Creating New (Piecewise) Quasipolynomials>) based on the dimension
449 specification of the original object.
452 __isl_give isl_dim *isl_basic_set_get_dim(
453 __isl_keep isl_basic_set *bset);
454 __isl_give isl_dim *isl_set_get_dim(__isl_keep isl_set *set);
456 #include <isl/union_set.h>
457 __isl_give isl_dim *isl_union_set_get_dim(
458 __isl_keep isl_union_set *uset);
461 __isl_give isl_dim *isl_basic_map_get_dim(
462 __isl_keep isl_basic_map *bmap);
463 __isl_give isl_dim *isl_map_get_dim(__isl_keep isl_map *map);
465 #include <isl/union_map.h>
466 __isl_give isl_dim *isl_union_map_get_dim(
467 __isl_keep isl_union_map *umap);
469 #include <isl/constraint.h>
470 __isl_give isl_dim *isl_constraint_get_dim(
471 __isl_keep isl_constraint *constraint);
473 #include <isl/polynomial.h>
474 __isl_give isl_dim *isl_qpolynomial_get_dim(
475 __isl_keep isl_qpolynomial *qp);
476 __isl_give isl_dim *isl_qpolynomial_fold_get_dim(
477 __isl_keep isl_qpolynomial_fold *fold);
478 __isl_give isl_dim *isl_pw_qpolynomial_get_dim(
479 __isl_keep isl_pw_qpolynomial *pwqp);
480 __isl_give isl_dim *isl_union_pw_qpolynomial_get_dim(
481 __isl_keep isl_union_pw_qpolynomial *upwqp);
482 __isl_give isl_dim *isl_union_pw_qpolynomial_fold_get_dim(
483 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
486 __isl_give isl_dim *isl_aff_get_dim(
487 __isl_keep isl_aff *aff);
489 #include <isl/point.h>
490 __isl_give isl_dim *isl_point_get_dim(
491 __isl_keep isl_point *pnt);
493 The names of the individual dimensions may be set or read off
494 using the following functions.
497 __isl_give isl_dim *isl_dim_set_name(__isl_take isl_dim *dim,
498 enum isl_dim_type type, unsigned pos,
499 __isl_keep const char *name);
500 __isl_keep const char *isl_dim_get_name(__isl_keep isl_dim *dim,
501 enum isl_dim_type type, unsigned pos);
503 Note that C<isl_dim_get_name> returns a pointer to some internal
504 data structure, so the result can only be used while the
505 corresponding C<isl_dim> is alive.
506 Also note that every function that operates on two sets or relations
507 requires that both arguments have the same parameters. This also
508 means that if one of the arguments has named parameters, then the
509 other needs to have named parameters too and the names need to match.
510 Pairs of C<isl_union_set> and/or C<isl_union_map> arguments may
511 have different parameters (as long as they are named), in which case
512 the result will have as parameters the union of the parameters of
515 The names of entire spaces may be set or read off
516 using the following functions.
519 __isl_give isl_dim *isl_dim_set_tuple_name(
520 __isl_take isl_dim *dim,
521 enum isl_dim_type type, const char *s);
522 const char *isl_dim_get_tuple_name(__isl_keep isl_dim *dim,
523 enum isl_dim_type type);
525 The C<dim> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
526 or C<isl_dim_set>. As with C<isl_dim_get_name>,
527 the C<isl_dim_get_tuple_name> function returns a pointer to some internal
529 Binary operations require the corresponding spaces of their arguments
530 to have the same name.
532 Spaces can be nested. In particular, the domain of a set or
533 the domain or range of a relation can be a nested relation.
534 The following functions can be used to construct and deconstruct
535 such nested dimension specifications.
538 int isl_dim_is_wrapping(__isl_keep isl_dim *dim);
539 __isl_give isl_dim *isl_dim_wrap(__isl_take isl_dim *dim);
540 __isl_give isl_dim *isl_dim_unwrap(__isl_take isl_dim *dim);
542 The input to C<isl_dim_is_wrapping> and C<isl_dim_unwrap> should
543 be the dimension specification of a set, while that of
544 C<isl_dim_wrap> should be the dimension specification of a relation.
545 Conversely, the output of C<isl_dim_unwrap> is the dimension specification
546 of a relation, while that of C<isl_dim_wrap> is the dimension specification
549 Dimension specifications can be created from other dimension
550 specifications using the following functions.
552 __isl_give isl_dim *isl_dim_domain(__isl_take isl_dim *dim);
553 __isl_give isl_dim *isl_dim_from_domain(__isl_take isl_dim *dim);
554 __isl_give isl_dim *isl_dim_range(__isl_take isl_dim *dim);
555 __isl_give isl_dim *isl_dim_from_range(__isl_take isl_dim *dim);
556 __isl_give isl_dim *isl_dim_reverse(__isl_take isl_dim *dim);
557 __isl_give isl_dim *isl_dim_join(__isl_take isl_dim *left,
558 __isl_take isl_dim *right);
559 __isl_give isl_dim *isl_dim_align_params(
560 __isl_take isl_dim *dim1, __isl_take isl_dim *dim2)
561 __isl_give isl_dim *isl_dim_insert(__isl_take isl_dim *dim,
562 enum isl_dim_type type, unsigned pos, unsigned n);
563 __isl_give isl_dim *isl_dim_add(__isl_take isl_dim *dim,
564 enum isl_dim_type type, unsigned n);
565 __isl_give isl_dim *isl_dim_drop(__isl_take isl_dim *dim,
566 enum isl_dim_type type, unsigned first, unsigned n);
567 __isl_give isl_dim *isl_dim_map_from_set(
568 __isl_take isl_dim *dim);
569 __isl_give isl_dim *isl_dim_zip(__isl_take isl_dim *dim);
571 Note that if dimensions are added or removed from a space, then
572 the name and the internal structure are lost.
576 A local space is essentially a dimension specification with
577 zero or more existentially quantified variables.
578 The local space of a basic set or relation can be obtained
579 using the following functions.
582 __isl_give isl_local_space *isl_basic_set_get_local_space(
583 __isl_keep isl_basic_set *bset);
586 __isl_give isl_local_space *isl_basic_map_get_local_space(
587 __isl_keep isl_basic_map *bmap);
589 A new local space can be created from a dimension specification using
591 #include <isl/local_space.h>
592 __isl_give isl_local_space *isl_local_space_from_dim(
593 __isl_take isl_dim *dim);
595 They can be inspected, copied and freed using the following functions.
597 #include <isl/local_space.h>
598 isl_ctx *isl_local_space_get_ctx(
599 __isl_keep isl_local_space *ls);
600 int isl_local_space_dim(__isl_keep isl_local_space *ls,
601 enum isl_dim_type type);
602 const char *isl_local_space_get_dim_name(
603 __isl_keep isl_local_space *ls,
604 enum isl_dim_type type, unsigned pos);
605 __isl_give isl_dim *isl_local_space_get_dim(
606 __isl_keep isl_local_space *ls);
607 __isl_give isl_div *isl_local_space_get_div(
608 __isl_keep isl_local_space *ls, int pos);
609 __isl_give isl_local_space *isl_local_space_copy(
610 __isl_keep isl_local_space *ls);
611 void *isl_local_space_free(__isl_take isl_local_space *ls);
613 Local spaces can be created from other local spaces
614 using the following functions.
616 __isl_give isl_local_space *isl_local_space_from_domain(
617 __isl_take isl_local_space *ls);
618 __isl_give isl_local_space *isl_local_space_add_dim(
619 __isl_take isl_local_space *ls,
620 enum isl_dim_type type, unsigned n);
622 =head2 Input and Output
624 C<isl> supports its own input/output format, which is similar
625 to the C<Omega> format, but also supports the C<PolyLib> format
630 The C<isl> format is similar to that of C<Omega>, but has a different
631 syntax for describing the parameters and allows for the definition
632 of an existentially quantified variable as the integer division
633 of an affine expression.
634 For example, the set of integers C<i> between C<0> and C<n>
635 such that C<i % 10 <= 6> can be described as
637 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
640 A set or relation can have several disjuncts, separated
641 by the keyword C<or>. Each disjunct is either a conjunction
642 of constraints or a projection (C<exists>) of a conjunction
643 of constraints. The constraints are separated by the keyword
646 =head3 C<PolyLib> format
648 If the represented set is a union, then the first line
649 contains a single number representing the number of disjuncts.
650 Otherwise, a line containing the number C<1> is optional.
652 Each disjunct is represented by a matrix of constraints.
653 The first line contains two numbers representing
654 the number of rows and columns,
655 where the number of rows is equal to the number of constraints
656 and the number of columns is equal to two plus the number of variables.
657 The following lines contain the actual rows of the constraint matrix.
658 In each row, the first column indicates whether the constraint
659 is an equality (C<0>) or inequality (C<1>). The final column
660 corresponds to the constant term.
662 If the set is parametric, then the coefficients of the parameters
663 appear in the last columns before the constant column.
664 The coefficients of any existentially quantified variables appear
665 between those of the set variables and those of the parameters.
667 =head3 Extended C<PolyLib> format
669 The extended C<PolyLib> format is nearly identical to the
670 C<PolyLib> format. The only difference is that the line
671 containing the number of rows and columns of a constraint matrix
672 also contains four additional numbers:
673 the number of output dimensions, the number of input dimensions,
674 the number of local dimensions (i.e., the number of existentially
675 quantified variables) and the number of parameters.
676 For sets, the number of ``output'' dimensions is equal
677 to the number of set dimensions, while the number of ``input''
683 __isl_give isl_basic_set *isl_basic_set_read_from_file(
684 isl_ctx *ctx, FILE *input, int nparam);
685 __isl_give isl_basic_set *isl_basic_set_read_from_str(
686 isl_ctx *ctx, const char *str, int nparam);
687 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
688 FILE *input, int nparam);
689 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
690 const char *str, int nparam);
693 __isl_give isl_basic_map *isl_basic_map_read_from_file(
694 isl_ctx *ctx, FILE *input, int nparam);
695 __isl_give isl_basic_map *isl_basic_map_read_from_str(
696 isl_ctx *ctx, const char *str, int nparam);
697 __isl_give isl_map *isl_map_read_from_file(
698 struct isl_ctx *ctx, FILE *input, int nparam);
699 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
700 const char *str, int nparam);
702 #include <isl/union_set.h>
703 __isl_give isl_union_set *isl_union_set_read_from_file(
704 isl_ctx *ctx, FILE *input);
705 __isl_give isl_union_set *isl_union_set_read_from_str(
706 struct isl_ctx *ctx, const char *str);
708 #include <isl/union_map.h>
709 __isl_give isl_union_map *isl_union_map_read_from_file(
710 isl_ctx *ctx, FILE *input);
711 __isl_give isl_union_map *isl_union_map_read_from_str(
712 struct isl_ctx *ctx, const char *str);
714 The input format is autodetected and may be either the C<PolyLib> format
715 or the C<isl> format.
716 C<nparam> specifies how many of the final columns in
717 the C<PolyLib> format correspond to parameters.
718 If input is given in the C<isl> format, then the number
719 of parameters needs to be equal to C<nparam>.
720 If C<nparam> is negative, then any number of parameters
721 is accepted in the C<isl> format and zero parameters
722 are assumed in the C<PolyLib> format.
726 Before anything can be printed, an C<isl_printer> needs to
729 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
731 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
732 void isl_printer_free(__isl_take isl_printer *printer);
733 __isl_give char *isl_printer_get_str(
734 __isl_keep isl_printer *printer);
736 The behavior of the printer can be modified in various ways
738 __isl_give isl_printer *isl_printer_set_output_format(
739 __isl_take isl_printer *p, int output_format);
740 __isl_give isl_printer *isl_printer_set_indent(
741 __isl_take isl_printer *p, int indent);
742 __isl_give isl_printer *isl_printer_indent(
743 __isl_take isl_printer *p, int indent);
744 __isl_give isl_printer *isl_printer_set_prefix(
745 __isl_take isl_printer *p, const char *prefix);
746 __isl_give isl_printer *isl_printer_set_suffix(
747 __isl_take isl_printer *p, const char *suffix);
749 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
750 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
751 and defaults to C<ISL_FORMAT_ISL>.
752 Each line in the output is indented by C<indent> (set by
753 C<isl_printer_set_indent>) spaces
754 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
755 In the C<PolyLib> format output,
756 the coefficients of the existentially quantified variables
757 appear between those of the set variables and those
759 The function C<isl_printer_indent> increases the indentation
760 by the specified amount (which may be negative).
762 To actually print something, use
765 __isl_give isl_printer *isl_printer_print_basic_set(
766 __isl_take isl_printer *printer,
767 __isl_keep isl_basic_set *bset);
768 __isl_give isl_printer *isl_printer_print_set(
769 __isl_take isl_printer *printer,
770 __isl_keep isl_set *set);
773 __isl_give isl_printer *isl_printer_print_basic_map(
774 __isl_take isl_printer *printer,
775 __isl_keep isl_basic_map *bmap);
776 __isl_give isl_printer *isl_printer_print_map(
777 __isl_take isl_printer *printer,
778 __isl_keep isl_map *map);
780 #include <isl/union_set.h>
781 __isl_give isl_printer *isl_printer_print_union_set(
782 __isl_take isl_printer *p,
783 __isl_keep isl_union_set *uset);
785 #include <isl/union_map.h>
786 __isl_give isl_printer *isl_printer_print_union_map(
787 __isl_take isl_printer *p,
788 __isl_keep isl_union_map *umap);
790 When called on a file printer, the following function flushes
791 the file. When called on a string printer, the buffer is cleared.
793 __isl_give isl_printer *isl_printer_flush(
794 __isl_take isl_printer *p);
796 =head2 Creating New Sets and Relations
798 C<isl> has functions for creating some standard sets and relations.
802 =item * Empty sets and relations
804 __isl_give isl_basic_set *isl_basic_set_empty(
805 __isl_take isl_dim *dim);
806 __isl_give isl_basic_map *isl_basic_map_empty(
807 __isl_take isl_dim *dim);
808 __isl_give isl_set *isl_set_empty(
809 __isl_take isl_dim *dim);
810 __isl_give isl_map *isl_map_empty(
811 __isl_take isl_dim *dim);
812 __isl_give isl_union_set *isl_union_set_empty(
813 __isl_take isl_dim *dim);
814 __isl_give isl_union_map *isl_union_map_empty(
815 __isl_take isl_dim *dim);
817 For C<isl_union_set>s and C<isl_union_map>s, the dimensions specification
818 is only used to specify the parameters.
820 =item * Universe sets and relations
822 __isl_give isl_basic_set *isl_basic_set_universe(
823 __isl_take isl_dim *dim);
824 __isl_give isl_basic_map *isl_basic_map_universe(
825 __isl_take isl_dim *dim);
826 __isl_give isl_set *isl_set_universe(
827 __isl_take isl_dim *dim);
828 __isl_give isl_map *isl_map_universe(
829 __isl_take isl_dim *dim);
830 __isl_give isl_union_set *isl_union_set_universe(
831 __isl_take isl_union_set *uset);
832 __isl_give isl_union_map *isl_union_map_universe(
833 __isl_take isl_union_map *umap);
835 The sets and relations constructed by the functions above
836 contain all integer values, while those constructed by the
837 functions below only contain non-negative values.
839 __isl_give isl_basic_set *isl_basic_set_nat_universe(
840 __isl_take isl_dim *dim);
841 __isl_give isl_basic_map *isl_basic_map_nat_universe(
842 __isl_take isl_dim *dim);
843 __isl_give isl_set *isl_set_nat_universe(
844 __isl_take isl_dim *dim);
845 __isl_give isl_map *isl_map_nat_universe(
846 __isl_take isl_dim *dim);
848 =item * Identity relations
850 __isl_give isl_basic_map *isl_basic_map_identity(
851 __isl_take isl_dim *dim);
852 __isl_give isl_map *isl_map_identity(
853 __isl_take isl_dim *dim);
855 The number of input and output dimensions in C<dim> needs
858 =item * Lexicographic order
860 __isl_give isl_map *isl_map_lex_lt(
861 __isl_take isl_dim *set_dim);
862 __isl_give isl_map *isl_map_lex_le(
863 __isl_take isl_dim *set_dim);
864 __isl_give isl_map *isl_map_lex_gt(
865 __isl_take isl_dim *set_dim);
866 __isl_give isl_map *isl_map_lex_ge(
867 __isl_take isl_dim *set_dim);
868 __isl_give isl_map *isl_map_lex_lt_first(
869 __isl_take isl_dim *dim, unsigned n);
870 __isl_give isl_map *isl_map_lex_le_first(
871 __isl_take isl_dim *dim, unsigned n);
872 __isl_give isl_map *isl_map_lex_gt_first(
873 __isl_take isl_dim *dim, unsigned n);
874 __isl_give isl_map *isl_map_lex_ge_first(
875 __isl_take isl_dim *dim, unsigned n);
877 The first four functions take a dimension specification for a B<set>
878 and return relations that express that the elements in the domain
879 are lexicographically less
880 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
881 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
882 than the elements in the range.
883 The last four functions take a dimension specification for a map
884 and return relations that express that the first C<n> dimensions
885 in the domain are lexicographically less
886 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
887 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
888 than the first C<n> dimensions in the range.
892 A basic set or relation can be converted to a set or relation
893 using the following functions.
895 __isl_give isl_set *isl_set_from_basic_set(
896 __isl_take isl_basic_set *bset);
897 __isl_give isl_map *isl_map_from_basic_map(
898 __isl_take isl_basic_map *bmap);
900 Sets and relations can be converted to union sets and relations
901 using the following functions.
903 __isl_give isl_union_map *isl_union_map_from_map(
904 __isl_take isl_map *map);
905 __isl_give isl_union_set *isl_union_set_from_set(
906 __isl_take isl_set *set);
908 Sets and relations can be copied and freed again using the following
911 __isl_give isl_basic_set *isl_basic_set_copy(
912 __isl_keep isl_basic_set *bset);
913 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
914 __isl_give isl_union_set *isl_union_set_copy(
915 __isl_keep isl_union_set *uset);
916 __isl_give isl_basic_map *isl_basic_map_copy(
917 __isl_keep isl_basic_map *bmap);
918 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
919 __isl_give isl_union_map *isl_union_map_copy(
920 __isl_keep isl_union_map *umap);
921 void isl_basic_set_free(__isl_take isl_basic_set *bset);
922 void isl_set_free(__isl_take isl_set *set);
923 void isl_union_set_free(__isl_take isl_union_set *uset);
924 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
925 void isl_map_free(__isl_take isl_map *map);
926 void isl_union_map_free(__isl_take isl_union_map *umap);
928 Other sets and relations can be constructed by starting
929 from a universe set or relation, adding equality and/or
930 inequality constraints and then projecting out the
931 existentially quantified variables, if any.
932 Constraints can be constructed, manipulated and
933 added to (basic) sets and relations using the following functions.
935 #include <isl/constraint.h>
936 __isl_give isl_constraint *isl_equality_alloc(
937 __isl_take isl_dim *dim);
938 __isl_give isl_constraint *isl_inequality_alloc(
939 __isl_take isl_dim *dim);
940 void isl_constraint_set_constant(
941 __isl_keep isl_constraint *constraint, isl_int v);
942 void isl_constraint_set_coefficient(
943 __isl_keep isl_constraint *constraint,
944 enum isl_dim_type type, int pos, isl_int v);
945 __isl_give isl_basic_map *isl_basic_map_add_constraint(
946 __isl_take isl_basic_map *bmap,
947 __isl_take isl_constraint *constraint);
948 __isl_give isl_basic_set *isl_basic_set_add_constraint(
949 __isl_take isl_basic_set *bset,
950 __isl_take isl_constraint *constraint);
951 __isl_give isl_map *isl_map_add_constraint(
952 __isl_take isl_map *map,
953 __isl_take isl_constraint *constraint);
954 __isl_give isl_set *isl_set_add_constraint(
955 __isl_take isl_set *set,
956 __isl_take isl_constraint *constraint);
958 For example, to create a set containing the even integers
959 between 10 and 42, you would use the following code.
963 struct isl_constraint *c;
964 struct isl_basic_set *bset;
967 dim = isl_dim_set_alloc(ctx, 0, 2);
968 bset = isl_basic_set_universe(isl_dim_copy(dim));
970 c = isl_equality_alloc(isl_dim_copy(dim));
971 isl_int_set_si(v, -1);
972 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
973 isl_int_set_si(v, 2);
974 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
975 bset = isl_basic_set_add_constraint(bset, c);
977 c = isl_inequality_alloc(isl_dim_copy(dim));
978 isl_int_set_si(v, -10);
979 isl_constraint_set_constant(c, v);
980 isl_int_set_si(v, 1);
981 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
982 bset = isl_basic_set_add_constraint(bset, c);
984 c = isl_inequality_alloc(dim);
985 isl_int_set_si(v, 42);
986 isl_constraint_set_constant(c, v);
987 isl_int_set_si(v, -1);
988 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
989 bset = isl_basic_set_add_constraint(bset, c);
991 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
997 struct isl_basic_set *bset;
998 bset = isl_basic_set_read_from_str(ctx,
999 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
1001 A basic set or relation can also be constructed from two matrices
1002 describing the equalities and the inequalities.
1004 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1005 __isl_take isl_dim *dim,
1006 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1007 enum isl_dim_type c1,
1008 enum isl_dim_type c2, enum isl_dim_type c3,
1009 enum isl_dim_type c4);
1010 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1011 __isl_take isl_dim *dim,
1012 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1013 enum isl_dim_type c1,
1014 enum isl_dim_type c2, enum isl_dim_type c3,
1015 enum isl_dim_type c4, enum isl_dim_type c5);
1017 The C<isl_dim_type> arguments indicate the order in which
1018 different kinds of variables appear in the input matrices
1019 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1020 C<isl_dim_set> and C<isl_dim_div> for sets and
1021 of C<isl_dim_cst>, C<isl_dim_param>,
1022 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1024 A basic relation can also be constructed from an affine expression
1025 or a list of affine expressions (See L<"Quasi Affine Expressions">).
1027 __isl_give isl_basic_map *isl_basic_map_from_aff(
1028 __isl_take isl_aff *aff);
1029 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1030 __isl_take isl_dim *domain_dim,
1031 __isl_take isl_aff_list *list);
1033 The C<domain_dim> argument describes the domain of the resulting
1034 basic relation. It is required because the C<list> may consist
1035 of zero affine expressions.
1037 =head2 Inspecting Sets and Relations
1039 Usually, the user should not have to care about the actual constraints
1040 of the sets and maps, but should instead apply the abstract operations
1041 explained in the following sections.
1042 Occasionally, however, it may be required to inspect the individual
1043 coefficients of the constraints. This section explains how to do so.
1044 In these cases, it may also be useful to have C<isl> compute
1045 an explicit representation of the existentially quantified variables.
1047 __isl_give isl_set *isl_set_compute_divs(
1048 __isl_take isl_set *set);
1049 __isl_give isl_map *isl_map_compute_divs(
1050 __isl_take isl_map *map);
1051 __isl_give isl_union_set *isl_union_set_compute_divs(
1052 __isl_take isl_union_set *uset);
1053 __isl_give isl_union_map *isl_union_map_compute_divs(
1054 __isl_take isl_union_map *umap);
1056 This explicit representation defines the existentially quantified
1057 variables as integer divisions of the other variables, possibly
1058 including earlier existentially quantified variables.
1059 An explicitly represented existentially quantified variable therefore
1060 has a unique value when the values of the other variables are known.
1061 If, furthermore, the same existentials, i.e., existentials
1062 with the same explicit representations, should appear in the
1063 same order in each of the disjuncts of a set or map, then the user should call
1064 either of the following functions.
1066 __isl_give isl_set *isl_set_align_divs(
1067 __isl_take isl_set *set);
1068 __isl_give isl_map *isl_map_align_divs(
1069 __isl_take isl_map *map);
1071 Alternatively, the existentially quantified variables can be removed
1072 using the following functions, which compute an overapproximation.
1074 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1075 __isl_take isl_basic_set *bset);
1076 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1077 __isl_take isl_basic_map *bmap);
1078 __isl_give isl_set *isl_set_remove_divs(
1079 __isl_take isl_set *set);
1080 __isl_give isl_map *isl_map_remove_divs(
1081 __isl_take isl_map *map);
1083 To iterate over all the sets or maps in a union set or map, use
1085 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1086 int (*fn)(__isl_take isl_set *set, void *user),
1088 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1089 int (*fn)(__isl_take isl_map *map, void *user),
1092 The number of sets or maps in a union set or map can be obtained
1095 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1096 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1098 To extract the set or map from a union with a given dimension
1101 __isl_give isl_set *isl_union_set_extract_set(
1102 __isl_keep isl_union_set *uset,
1103 __isl_take isl_dim *dim);
1104 __isl_give isl_map *isl_union_map_extract_map(
1105 __isl_keep isl_union_map *umap,
1106 __isl_take isl_dim *dim);
1108 To iterate over all the basic sets or maps in a set or map, use
1110 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1111 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1113 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1114 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1117 The callback function C<fn> should return 0 if successful and
1118 -1 if an error occurs. In the latter case, or if any other error
1119 occurs, the above functions will return -1.
1121 It should be noted that C<isl> does not guarantee that
1122 the basic sets or maps passed to C<fn> are disjoint.
1123 If this is required, then the user should call one of
1124 the following functions first.
1126 __isl_give isl_set *isl_set_make_disjoint(
1127 __isl_take isl_set *set);
1128 __isl_give isl_map *isl_map_make_disjoint(
1129 __isl_take isl_map *map);
1131 The number of basic sets in a set can be obtained
1134 int isl_set_n_basic_set(__isl_keep isl_set *set);
1136 To iterate over the constraints of a basic set or map, use
1138 #include <isl/constraint.h>
1140 int isl_basic_map_foreach_constraint(
1141 __isl_keep isl_basic_map *bmap,
1142 int (*fn)(__isl_take isl_constraint *c, void *user),
1144 void isl_constraint_free(struct isl_constraint *c);
1146 Again, the callback function C<fn> should return 0 if successful and
1147 -1 if an error occurs. In the latter case, or if any other error
1148 occurs, the above functions will return -1.
1149 The constraint C<c> represents either an equality or an inequality.
1150 Use the following function to find out whether a constraint
1151 represents an equality. If not, it represents an inequality.
1153 int isl_constraint_is_equality(
1154 __isl_keep isl_constraint *constraint);
1156 The coefficients of the constraints can be inspected using
1157 the following functions.
1159 void isl_constraint_get_constant(
1160 __isl_keep isl_constraint *constraint, isl_int *v);
1161 void isl_constraint_get_coefficient(
1162 __isl_keep isl_constraint *constraint,
1163 enum isl_dim_type type, int pos, isl_int *v);
1164 int isl_constraint_involves_dims(
1165 __isl_keep isl_constraint *constraint,
1166 enum isl_dim_type type, unsigned first, unsigned n);
1168 The explicit representations of the existentially quantified
1169 variables can be inspected using the following functions.
1170 Note that the user is only allowed to use these functions
1171 if the inspected set or map is the result of a call
1172 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1174 __isl_give isl_div *isl_constraint_div(
1175 __isl_keep isl_constraint *constraint, int pos);
1176 isl_ctx *isl_div_get_ctx(__isl_keep isl_div *div);
1177 void isl_div_get_constant(__isl_keep isl_div *div,
1179 void isl_div_get_denominator(__isl_keep isl_div *div,
1181 void isl_div_get_coefficient(__isl_keep isl_div *div,
1182 enum isl_dim_type type, int pos, isl_int *v);
1184 To obtain the constraints of a basic set or map in matrix
1185 form, use the following functions.
1187 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1188 __isl_keep isl_basic_set *bset,
1189 enum isl_dim_type c1, enum isl_dim_type c2,
1190 enum isl_dim_type c3, enum isl_dim_type c4);
1191 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1192 __isl_keep isl_basic_set *bset,
1193 enum isl_dim_type c1, enum isl_dim_type c2,
1194 enum isl_dim_type c3, enum isl_dim_type c4);
1195 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1196 __isl_keep isl_basic_map *bmap,
1197 enum isl_dim_type c1,
1198 enum isl_dim_type c2, enum isl_dim_type c3,
1199 enum isl_dim_type c4, enum isl_dim_type c5);
1200 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1201 __isl_keep isl_basic_map *bmap,
1202 enum isl_dim_type c1,
1203 enum isl_dim_type c2, enum isl_dim_type c3,
1204 enum isl_dim_type c4, enum isl_dim_type c5);
1206 The C<isl_dim_type> arguments dictate the order in which
1207 different kinds of variables appear in the resulting matrix
1208 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1209 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1211 The names of the domain and range spaces of a set or relation can be
1212 read off using the following functions.
1214 const char *isl_basic_set_get_tuple_name(
1215 __isl_keep isl_basic_set *bset);
1216 const char *isl_set_get_tuple_name(
1217 __isl_keep isl_set *set);
1218 const char *isl_basic_map_get_tuple_name(
1219 __isl_keep isl_basic_map *bmap,
1220 enum isl_dim_type type);
1221 const char *isl_map_get_tuple_name(
1222 __isl_keep isl_map *map,
1223 enum isl_dim_type type);
1225 As with C<isl_dim_get_tuple_name>, the value returned points to
1226 an internal data structure.
1227 The names of individual dimensions can be read off using
1228 the following functions.
1230 const char *isl_constraint_get_dim_name(
1231 __isl_keep isl_constraint *constraint,
1232 enum isl_dim_type type, unsigned pos);
1233 const char *isl_basic_set_get_dim_name(
1234 __isl_keep isl_basic_set *bset,
1235 enum isl_dim_type type, unsigned pos);
1236 const char *isl_set_get_dim_name(
1237 __isl_keep isl_set *set,
1238 enum isl_dim_type type, unsigned pos);
1239 const char *isl_basic_map_get_dim_name(
1240 __isl_keep isl_basic_map *bmap,
1241 enum isl_dim_type type, unsigned pos);
1242 const char *isl_map_get_dim_name(
1243 __isl_keep isl_map *map,
1244 enum isl_dim_type type, unsigned pos);
1246 These functions are mostly useful to obtain the names
1251 =head3 Unary Properties
1257 The following functions test whether the given set or relation
1258 contains any integer points. The ``plain'' variants do not perform
1259 any computations, but simply check if the given set or relation
1260 is already known to be empty.
1262 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1263 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1264 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1265 int isl_set_is_empty(__isl_keep isl_set *set);
1266 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1267 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1268 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1269 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1270 int isl_map_is_empty(__isl_keep isl_map *map);
1271 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1273 =item * Universality
1275 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1276 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1277 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1279 =item * Single-valuedness
1281 int isl_map_is_single_valued(__isl_keep isl_map *map);
1282 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1286 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1287 int isl_map_is_injective(__isl_keep isl_map *map);
1288 int isl_union_map_plain_is_injective(
1289 __isl_keep isl_union_map *umap);
1290 int isl_union_map_is_injective(
1291 __isl_keep isl_union_map *umap);
1295 int isl_map_is_bijective(__isl_keep isl_map *map);
1296 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1300 The following functions check whether the domain of the given
1301 (basic) set is a wrapped relation.
1303 int isl_basic_set_is_wrapping(
1304 __isl_keep isl_basic_set *bset);
1305 int isl_set_is_wrapping(__isl_keep isl_set *set);
1307 =item * Internal Product
1309 int isl_basic_map_can_zip(
1310 __isl_keep isl_basic_map *bmap);
1311 int isl_map_can_zip(__isl_keep isl_map *map);
1313 Check whether the product of domain and range of the given relation
1315 i.e., whether both domain and range are nested relations.
1319 =head3 Binary Properties
1325 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1326 __isl_keep isl_set *set2);
1327 int isl_set_is_equal(__isl_keep isl_set *set1,
1328 __isl_keep isl_set *set2);
1329 int isl_union_set_is_equal(
1330 __isl_keep isl_union_set *uset1,
1331 __isl_keep isl_union_set *uset2);
1332 int isl_basic_map_is_equal(
1333 __isl_keep isl_basic_map *bmap1,
1334 __isl_keep isl_basic_map *bmap2);
1335 int isl_map_is_equal(__isl_keep isl_map *map1,
1336 __isl_keep isl_map *map2);
1337 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1338 __isl_keep isl_map *map2);
1339 int isl_union_map_is_equal(
1340 __isl_keep isl_union_map *umap1,
1341 __isl_keep isl_union_map *umap2);
1343 =item * Disjointness
1345 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1346 __isl_keep isl_set *set2);
1350 int isl_set_is_subset(__isl_keep isl_set *set1,
1351 __isl_keep isl_set *set2);
1352 int isl_set_is_strict_subset(
1353 __isl_keep isl_set *set1,
1354 __isl_keep isl_set *set2);
1355 int isl_union_set_is_subset(
1356 __isl_keep isl_union_set *uset1,
1357 __isl_keep isl_union_set *uset2);
1358 int isl_union_set_is_strict_subset(
1359 __isl_keep isl_union_set *uset1,
1360 __isl_keep isl_union_set *uset2);
1361 int isl_basic_map_is_subset(
1362 __isl_keep isl_basic_map *bmap1,
1363 __isl_keep isl_basic_map *bmap2);
1364 int isl_basic_map_is_strict_subset(
1365 __isl_keep isl_basic_map *bmap1,
1366 __isl_keep isl_basic_map *bmap2);
1367 int isl_map_is_subset(
1368 __isl_keep isl_map *map1,
1369 __isl_keep isl_map *map2);
1370 int isl_map_is_strict_subset(
1371 __isl_keep isl_map *map1,
1372 __isl_keep isl_map *map2);
1373 int isl_union_map_is_subset(
1374 __isl_keep isl_union_map *umap1,
1375 __isl_keep isl_union_map *umap2);
1376 int isl_union_map_is_strict_subset(
1377 __isl_keep isl_union_map *umap1,
1378 __isl_keep isl_union_map *umap2);
1382 =head2 Unary Operations
1388 __isl_give isl_set *isl_set_complement(
1389 __isl_take isl_set *set);
1393 __isl_give isl_basic_map *isl_basic_map_reverse(
1394 __isl_take isl_basic_map *bmap);
1395 __isl_give isl_map *isl_map_reverse(
1396 __isl_take isl_map *map);
1397 __isl_give isl_union_map *isl_union_map_reverse(
1398 __isl_take isl_union_map *umap);
1402 __isl_give isl_basic_set *isl_basic_set_project_out(
1403 __isl_take isl_basic_set *bset,
1404 enum isl_dim_type type, unsigned first, unsigned n);
1405 __isl_give isl_basic_map *isl_basic_map_project_out(
1406 __isl_take isl_basic_map *bmap,
1407 enum isl_dim_type type, unsigned first, unsigned n);
1408 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1409 enum isl_dim_type type, unsigned first, unsigned n);
1410 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1411 enum isl_dim_type type, unsigned first, unsigned n);
1412 __isl_give isl_basic_set *isl_basic_map_domain(
1413 __isl_take isl_basic_map *bmap);
1414 __isl_give isl_basic_set *isl_basic_map_range(
1415 __isl_take isl_basic_map *bmap);
1416 __isl_give isl_set *isl_map_domain(
1417 __isl_take isl_map *bmap);
1418 __isl_give isl_set *isl_map_range(
1419 __isl_take isl_map *map);
1420 __isl_give isl_union_set *isl_union_map_domain(
1421 __isl_take isl_union_map *umap);
1422 __isl_give isl_union_set *isl_union_map_range(
1423 __isl_take isl_union_map *umap);
1425 __isl_give isl_basic_map *isl_basic_map_domain_map(
1426 __isl_take isl_basic_map *bmap);
1427 __isl_give isl_basic_map *isl_basic_map_range_map(
1428 __isl_take isl_basic_map *bmap);
1429 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1430 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1431 __isl_give isl_union_map *isl_union_map_domain_map(
1432 __isl_take isl_union_map *umap);
1433 __isl_give isl_union_map *isl_union_map_range_map(
1434 __isl_take isl_union_map *umap);
1436 The functions above construct a (basic, regular or union) relation
1437 that maps (a wrapped version of) the input relation to its domain or range.
1441 __isl_give isl_set *isl_set_eliminate(
1442 __isl_take isl_set *set, enum isl_dim_type type,
1443 unsigned first, unsigned n);
1445 Eliminate the coefficients for the given dimensions from the constraints,
1446 without removing the dimensions.
1450 __isl_give isl_basic_set *isl_basic_set_fix(
1451 __isl_take isl_basic_set *bset,
1452 enum isl_dim_type type, unsigned pos,
1454 __isl_give isl_basic_set *isl_basic_set_fix_si(
1455 __isl_take isl_basic_set *bset,
1456 enum isl_dim_type type, unsigned pos, int value);
1457 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1458 enum isl_dim_type type, unsigned pos,
1460 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1461 enum isl_dim_type type, unsigned pos, int value);
1462 __isl_give isl_basic_map *isl_basic_map_fix_si(
1463 __isl_take isl_basic_map *bmap,
1464 enum isl_dim_type type, unsigned pos, int value);
1465 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1466 enum isl_dim_type type, unsigned pos, int value);
1468 Intersect the set or relation with the hyperplane where the given
1469 dimension has the fixed given value.
1473 __isl_give isl_map *isl_set_identity(
1474 __isl_take isl_set *set);
1475 __isl_give isl_union_map *isl_union_set_identity(
1476 __isl_take isl_union_set *uset);
1478 Construct an identity relation on the given (union) set.
1482 __isl_give isl_basic_set *isl_basic_map_deltas(
1483 __isl_take isl_basic_map *bmap);
1484 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1485 __isl_give isl_union_set *isl_union_map_deltas(
1486 __isl_take isl_union_map *umap);
1488 These functions return a (basic) set containing the differences
1489 between image elements and corresponding domain elements in the input.
1491 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1492 __isl_take isl_basic_map *bmap);
1493 __isl_give isl_map *isl_map_deltas_map(
1494 __isl_take isl_map *map);
1495 __isl_give isl_union_map *isl_union_map_deltas_map(
1496 __isl_take isl_union_map *umap);
1498 The functions above construct a (basic, regular or union) relation
1499 that maps (a wrapped version of) the input relation to its delta set.
1503 Simplify the representation of a set or relation by trying
1504 to combine pairs of basic sets or relations into a single
1505 basic set or relation.
1507 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1508 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1509 __isl_give isl_union_set *isl_union_set_coalesce(
1510 __isl_take isl_union_set *uset);
1511 __isl_give isl_union_map *isl_union_map_coalesce(
1512 __isl_take isl_union_map *umap);
1514 =item * Detecting equalities
1516 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1517 __isl_take isl_basic_set *bset);
1518 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1519 __isl_take isl_basic_map *bmap);
1520 __isl_give isl_set *isl_set_detect_equalities(
1521 __isl_take isl_set *set);
1522 __isl_give isl_map *isl_map_detect_equalities(
1523 __isl_take isl_map *map);
1524 __isl_give isl_union_set *isl_union_set_detect_equalities(
1525 __isl_take isl_union_set *uset);
1526 __isl_give isl_union_map *isl_union_map_detect_equalities(
1527 __isl_take isl_union_map *umap);
1529 Simplify the representation of a set or relation by detecting implicit
1532 =item * Removing redundant constraints
1534 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1535 __isl_take isl_basic_set *bset);
1536 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1537 __isl_take isl_basic_map *bmap);
1541 __isl_give isl_basic_set *isl_set_convex_hull(
1542 __isl_take isl_set *set);
1543 __isl_give isl_basic_map *isl_map_convex_hull(
1544 __isl_take isl_map *map);
1546 If the input set or relation has any existentially quantified
1547 variables, then the result of these operations is currently undefined.
1551 __isl_give isl_basic_set *isl_set_simple_hull(
1552 __isl_take isl_set *set);
1553 __isl_give isl_basic_map *isl_map_simple_hull(
1554 __isl_take isl_map *map);
1555 __isl_give isl_union_map *isl_union_map_simple_hull(
1556 __isl_take isl_union_map *umap);
1558 These functions compute a single basic set or relation
1559 that contains the whole input set or relation.
1560 In particular, the output is described by translates
1561 of the constraints describing the basic sets or relations in the input.
1565 (See \autoref{s:simple hull}.)
1571 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1572 __isl_take isl_basic_set *bset);
1573 __isl_give isl_basic_set *isl_set_affine_hull(
1574 __isl_take isl_set *set);
1575 __isl_give isl_union_set *isl_union_set_affine_hull(
1576 __isl_take isl_union_set *uset);
1577 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1578 __isl_take isl_basic_map *bmap);
1579 __isl_give isl_basic_map *isl_map_affine_hull(
1580 __isl_take isl_map *map);
1581 __isl_give isl_union_map *isl_union_map_affine_hull(
1582 __isl_take isl_union_map *umap);
1584 In case of union sets and relations, the affine hull is computed
1587 =item * Polyhedral hull
1589 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1590 __isl_take isl_set *set);
1591 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1592 __isl_take isl_map *map);
1593 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1594 __isl_take isl_union_set *uset);
1595 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1596 __isl_take isl_union_map *umap);
1598 These functions compute a single basic set or relation
1599 not involving any existentially quantified variables
1600 that contains the whole input set or relation.
1601 In case of union sets and relations, the polyhedral hull is computed
1604 =item * Optimization
1606 #include <isl/ilp.h>
1607 enum isl_lp_result isl_basic_set_max(
1608 __isl_keep isl_basic_set *bset,
1609 __isl_keep isl_aff *obj, isl_int *opt)
1610 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
1611 __isl_keep isl_aff *obj, isl_int *opt);
1613 Compute the maximum of the integer affine expression C<obj>
1614 over the points in C<set>, returning the result in C<opt>.
1615 The return value may be one of C<isl_lp_error>,
1616 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
1620 The following functions compute either the set of (rational) coefficient
1621 values of valid constraints for the given set or the set of (rational)
1622 values satisfying the constraints with coefficients from the given set.
1623 Internally, these two sets of functions perform essentially the
1624 same operations, except that the set of coefficients is assumed to
1625 be a cone, while the set of values may be any polyhedron.
1626 The current implementation is based on the Farkas lemma and
1627 Fourier-Motzkin elimination, but this may change or be made optional
1628 in future. In particular, future implementations may use different
1629 dualization algorithms or skip the elimination step.
1631 __isl_give isl_basic_set *isl_basic_set_coefficients(
1632 __isl_take isl_basic_set *bset);
1633 __isl_give isl_basic_set *isl_set_coefficients(
1634 __isl_take isl_set *set);
1635 __isl_give isl_union_set *isl_union_set_coefficients(
1636 __isl_take isl_union_set *bset);
1637 __isl_give isl_basic_set *isl_basic_set_solutions(
1638 __isl_take isl_basic_set *bset);
1639 __isl_give isl_basic_set *isl_set_solutions(
1640 __isl_take isl_set *set);
1641 __isl_give isl_union_set *isl_union_set_solutions(
1642 __isl_take isl_union_set *bset);
1646 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1648 __isl_give isl_union_map *isl_union_map_power(
1649 __isl_take isl_union_map *umap, int *exact);
1651 Compute a parametric representation for all positive powers I<k> of C<map>.
1652 The result maps I<k> to a nested relation corresponding to the
1653 I<k>th power of C<map>.
1654 The result may be an overapproximation. If the result is known to be exact,
1655 then C<*exact> is set to C<1>.
1657 =item * Transitive closure
1659 __isl_give isl_map *isl_map_transitive_closure(
1660 __isl_take isl_map *map, int *exact);
1661 __isl_give isl_union_map *isl_union_map_transitive_closure(
1662 __isl_take isl_union_map *umap, int *exact);
1664 Compute the transitive closure of C<map>.
1665 The result may be an overapproximation. If the result is known to be exact,
1666 then C<*exact> is set to C<1>.
1668 =item * Reaching path lengths
1670 __isl_give isl_map *isl_map_reaching_path_lengths(
1671 __isl_take isl_map *map, int *exact);
1673 Compute a relation that maps each element in the range of C<map>
1674 to the lengths of all paths composed of edges in C<map> that
1675 end up in the given element.
1676 The result may be an overapproximation. If the result is known to be exact,
1677 then C<*exact> is set to C<1>.
1678 To compute the I<maximal> path length, the resulting relation
1679 should be postprocessed by C<isl_map_lexmax>.
1680 In particular, if the input relation is a dependence relation
1681 (mapping sources to sinks), then the maximal path length corresponds
1682 to the free schedule.
1683 Note, however, that C<isl_map_lexmax> expects the maximum to be
1684 finite, so if the path lengths are unbounded (possibly due to
1685 the overapproximation), then you will get an error message.
1689 __isl_give isl_basic_set *isl_basic_map_wrap(
1690 __isl_take isl_basic_map *bmap);
1691 __isl_give isl_set *isl_map_wrap(
1692 __isl_take isl_map *map);
1693 __isl_give isl_union_set *isl_union_map_wrap(
1694 __isl_take isl_union_map *umap);
1695 __isl_give isl_basic_map *isl_basic_set_unwrap(
1696 __isl_take isl_basic_set *bset);
1697 __isl_give isl_map *isl_set_unwrap(
1698 __isl_take isl_set *set);
1699 __isl_give isl_union_map *isl_union_set_unwrap(
1700 __isl_take isl_union_set *uset);
1704 Remove any internal structure of domain (and range) of the given
1705 set or relation. If there is any such internal structure in the input,
1706 then the name of the space is also removed.
1708 __isl_give isl_basic_set *isl_basic_set_flatten(
1709 __isl_take isl_basic_set *bset);
1710 __isl_give isl_set *isl_set_flatten(
1711 __isl_take isl_set *set);
1712 __isl_give isl_basic_map *isl_basic_map_flatten_range(
1713 __isl_take isl_basic_map *bmap);
1714 __isl_give isl_map *isl_map_flatten_range(
1715 __isl_take isl_map *map);
1716 __isl_give isl_basic_map *isl_basic_map_flatten(
1717 __isl_take isl_basic_map *bmap);
1718 __isl_give isl_map *isl_map_flatten(
1719 __isl_take isl_map *map);
1721 __isl_give isl_map *isl_set_flatten_map(
1722 __isl_take isl_set *set);
1724 The function above constructs a relation
1725 that maps the input set to a flattened version of the set.
1729 Lift the input set to a space with extra dimensions corresponding
1730 to the existentially quantified variables in the input.
1731 In particular, the result lives in a wrapped map where the domain
1732 is the original space and the range corresponds to the original
1733 existentially quantified variables.
1735 __isl_give isl_basic_set *isl_basic_set_lift(
1736 __isl_take isl_basic_set *bset);
1737 __isl_give isl_set *isl_set_lift(
1738 __isl_take isl_set *set);
1739 __isl_give isl_union_set *isl_union_set_lift(
1740 __isl_take isl_union_set *uset);
1742 =item * Internal Product
1744 __isl_give isl_basic_map *isl_basic_map_zip(
1745 __isl_take isl_basic_map *bmap);
1746 __isl_give isl_map *isl_map_zip(
1747 __isl_take isl_map *map);
1748 __isl_give isl_union_map *isl_union_map_zip(
1749 __isl_take isl_union_map *umap);
1751 Given a relation with nested relations for domain and range,
1752 interchange the range of the domain with the domain of the range.
1754 =item * Aligning parameters
1756 __isl_give isl_set *isl_set_align_params(
1757 __isl_take isl_set *set,
1758 __isl_take isl_dim *model);
1759 __isl_give isl_map *isl_map_align_params(
1760 __isl_take isl_map *map,
1761 __isl_take isl_dim *model);
1763 Change the order of the parameters of the given set or relation
1764 such that the first parameters match those of C<model>.
1765 This may involve the introduction of extra parameters.
1766 All parameters need to be named.
1768 =item * Dimension manipulation
1770 __isl_give isl_set *isl_set_add_dims(
1771 __isl_take isl_set *set,
1772 enum isl_dim_type type, unsigned n);
1773 __isl_give isl_map *isl_map_add_dims(
1774 __isl_take isl_map *map,
1775 enum isl_dim_type type, unsigned n);
1777 It is usually not advisable to directly change the (input or output)
1778 space of a set or a relation as this removes the name and the internal
1779 structure of the space. However, the above functions can be useful
1780 to add new parameters, assuming
1781 C<isl_set_align_params> and C<isl_map_align_params>
1786 =head2 Binary Operations
1788 The two arguments of a binary operation not only need to live
1789 in the same C<isl_ctx>, they currently also need to have
1790 the same (number of) parameters.
1792 =head3 Basic Operations
1796 =item * Intersection
1798 __isl_give isl_basic_set *isl_basic_set_intersect(
1799 __isl_take isl_basic_set *bset1,
1800 __isl_take isl_basic_set *bset2);
1801 __isl_give isl_set *isl_set_intersect(
1802 __isl_take isl_set *set1,
1803 __isl_take isl_set *set2);
1804 __isl_give isl_union_set *isl_union_set_intersect(
1805 __isl_take isl_union_set *uset1,
1806 __isl_take isl_union_set *uset2);
1807 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
1808 __isl_take isl_basic_map *bmap,
1809 __isl_take isl_basic_set *bset);
1810 __isl_give isl_basic_map *isl_basic_map_intersect_range(
1811 __isl_take isl_basic_map *bmap,
1812 __isl_take isl_basic_set *bset);
1813 __isl_give isl_basic_map *isl_basic_map_intersect(
1814 __isl_take isl_basic_map *bmap1,
1815 __isl_take isl_basic_map *bmap2);
1816 __isl_give isl_map *isl_map_intersect_domain(
1817 __isl_take isl_map *map,
1818 __isl_take isl_set *set);
1819 __isl_give isl_map *isl_map_intersect_range(
1820 __isl_take isl_map *map,
1821 __isl_take isl_set *set);
1822 __isl_give isl_map *isl_map_intersect(
1823 __isl_take isl_map *map1,
1824 __isl_take isl_map *map2);
1825 __isl_give isl_union_map *isl_union_map_intersect_domain(
1826 __isl_take isl_union_map *umap,
1827 __isl_take isl_union_set *uset);
1828 __isl_give isl_union_map *isl_union_map_intersect_range(
1829 __isl_take isl_union_map *umap,
1830 __isl_take isl_union_set *uset);
1831 __isl_give isl_union_map *isl_union_map_intersect(
1832 __isl_take isl_union_map *umap1,
1833 __isl_take isl_union_map *umap2);
1837 __isl_give isl_set *isl_basic_set_union(
1838 __isl_take isl_basic_set *bset1,
1839 __isl_take isl_basic_set *bset2);
1840 __isl_give isl_map *isl_basic_map_union(
1841 __isl_take isl_basic_map *bmap1,
1842 __isl_take isl_basic_map *bmap2);
1843 __isl_give isl_set *isl_set_union(
1844 __isl_take isl_set *set1,
1845 __isl_take isl_set *set2);
1846 __isl_give isl_map *isl_map_union(
1847 __isl_take isl_map *map1,
1848 __isl_take isl_map *map2);
1849 __isl_give isl_union_set *isl_union_set_union(
1850 __isl_take isl_union_set *uset1,
1851 __isl_take isl_union_set *uset2);
1852 __isl_give isl_union_map *isl_union_map_union(
1853 __isl_take isl_union_map *umap1,
1854 __isl_take isl_union_map *umap2);
1856 =item * Set difference
1858 __isl_give isl_set *isl_set_subtract(
1859 __isl_take isl_set *set1,
1860 __isl_take isl_set *set2);
1861 __isl_give isl_map *isl_map_subtract(
1862 __isl_take isl_map *map1,
1863 __isl_take isl_map *map2);
1864 __isl_give isl_union_set *isl_union_set_subtract(
1865 __isl_take isl_union_set *uset1,
1866 __isl_take isl_union_set *uset2);
1867 __isl_give isl_union_map *isl_union_map_subtract(
1868 __isl_take isl_union_map *umap1,
1869 __isl_take isl_union_map *umap2);
1873 __isl_give isl_basic_set *isl_basic_set_apply(
1874 __isl_take isl_basic_set *bset,
1875 __isl_take isl_basic_map *bmap);
1876 __isl_give isl_set *isl_set_apply(
1877 __isl_take isl_set *set,
1878 __isl_take isl_map *map);
1879 __isl_give isl_union_set *isl_union_set_apply(
1880 __isl_take isl_union_set *uset,
1881 __isl_take isl_union_map *umap);
1882 __isl_give isl_basic_map *isl_basic_map_apply_domain(
1883 __isl_take isl_basic_map *bmap1,
1884 __isl_take isl_basic_map *bmap2);
1885 __isl_give isl_basic_map *isl_basic_map_apply_range(
1886 __isl_take isl_basic_map *bmap1,
1887 __isl_take isl_basic_map *bmap2);
1888 __isl_give isl_map *isl_map_apply_domain(
1889 __isl_take isl_map *map1,
1890 __isl_take isl_map *map2);
1891 __isl_give isl_union_map *isl_union_map_apply_domain(
1892 __isl_take isl_union_map *umap1,
1893 __isl_take isl_union_map *umap2);
1894 __isl_give isl_map *isl_map_apply_range(
1895 __isl_take isl_map *map1,
1896 __isl_take isl_map *map2);
1897 __isl_give isl_union_map *isl_union_map_apply_range(
1898 __isl_take isl_union_map *umap1,
1899 __isl_take isl_union_map *umap2);
1901 =item * Cartesian Product
1903 __isl_give isl_set *isl_set_product(
1904 __isl_take isl_set *set1,
1905 __isl_take isl_set *set2);
1906 __isl_give isl_union_set *isl_union_set_product(
1907 __isl_take isl_union_set *uset1,
1908 __isl_take isl_union_set *uset2);
1909 __isl_give isl_basic_map *isl_basic_map_range_product(
1910 __isl_take isl_basic_map *bmap1,
1911 __isl_take isl_basic_map *bmap2);
1912 __isl_give isl_map *isl_map_range_product(
1913 __isl_take isl_map *map1,
1914 __isl_take isl_map *map2);
1915 __isl_give isl_union_map *isl_union_map_range_product(
1916 __isl_take isl_union_map *umap1,
1917 __isl_take isl_union_map *umap2);
1918 __isl_give isl_map *isl_map_product(
1919 __isl_take isl_map *map1,
1920 __isl_take isl_map *map2);
1921 __isl_give isl_union_map *isl_union_map_product(
1922 __isl_take isl_union_map *umap1,
1923 __isl_take isl_union_map *umap2);
1925 The above functions compute the cross product of the given
1926 sets or relations. The domains and ranges of the results
1927 are wrapped maps between domains and ranges of the inputs.
1928 To obtain a ``flat'' product, use the following functions
1931 __isl_give isl_basic_set *isl_basic_set_flat_product(
1932 __isl_take isl_basic_set *bset1,
1933 __isl_take isl_basic_set *bset2);
1934 __isl_give isl_set *isl_set_flat_product(
1935 __isl_take isl_set *set1,
1936 __isl_take isl_set *set2);
1937 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
1938 __isl_take isl_basic_map *bmap1,
1939 __isl_take isl_basic_map *bmap2);
1940 __isl_give isl_map *isl_map_flat_range_product(
1941 __isl_take isl_map *map1,
1942 __isl_take isl_map *map2);
1943 __isl_give isl_union_map *isl_union_map_flat_range_product(
1944 __isl_take isl_union_map *umap1,
1945 __isl_take isl_union_map *umap2);
1946 __isl_give isl_basic_map *isl_basic_map_flat_product(
1947 __isl_take isl_basic_map *bmap1,
1948 __isl_take isl_basic_map *bmap2);
1949 __isl_give isl_map *isl_map_flat_product(
1950 __isl_take isl_map *map1,
1951 __isl_take isl_map *map2);
1953 =item * Simplification
1955 __isl_give isl_basic_set *isl_basic_set_gist(
1956 __isl_take isl_basic_set *bset,
1957 __isl_take isl_basic_set *context);
1958 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1959 __isl_take isl_set *context);
1960 __isl_give isl_union_set *isl_union_set_gist(
1961 __isl_take isl_union_set *uset,
1962 __isl_take isl_union_set *context);
1963 __isl_give isl_basic_map *isl_basic_map_gist(
1964 __isl_take isl_basic_map *bmap,
1965 __isl_take isl_basic_map *context);
1966 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1967 __isl_take isl_map *context);
1968 __isl_give isl_union_map *isl_union_map_gist(
1969 __isl_take isl_union_map *umap,
1970 __isl_take isl_union_map *context);
1972 The gist operation returns a set or relation that has the
1973 same intersection with the context as the input set or relation.
1974 Any implicit equality in the intersection is made explicit in the result,
1975 while all inequalities that are redundant with respect to the intersection
1977 In case of union sets and relations, the gist operation is performed
1982 =head3 Lexicographic Optimization
1984 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
1985 the following functions
1986 compute a set that contains the lexicographic minimum or maximum
1987 of the elements in C<set> (or C<bset>) for those values of the parameters
1988 that satisfy C<dom>.
1989 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1990 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
1992 In other words, the union of the parameter values
1993 for which the result is non-empty and of C<*empty>
1996 __isl_give isl_set *isl_basic_set_partial_lexmin(
1997 __isl_take isl_basic_set *bset,
1998 __isl_take isl_basic_set *dom,
1999 __isl_give isl_set **empty);
2000 __isl_give isl_set *isl_basic_set_partial_lexmax(
2001 __isl_take isl_basic_set *bset,
2002 __isl_take isl_basic_set *dom,
2003 __isl_give isl_set **empty);
2004 __isl_give isl_set *isl_set_partial_lexmin(
2005 __isl_take isl_set *set, __isl_take isl_set *dom,
2006 __isl_give isl_set **empty);
2007 __isl_give isl_set *isl_set_partial_lexmax(
2008 __isl_take isl_set *set, __isl_take isl_set *dom,
2009 __isl_give isl_set **empty);
2011 Given a (basic) set C<set> (or C<bset>), the following functions simply
2012 return a set containing the lexicographic minimum or maximum
2013 of the elements in C<set> (or C<bset>).
2014 In case of union sets, the optimum is computed per space.
2016 __isl_give isl_set *isl_basic_set_lexmin(
2017 __isl_take isl_basic_set *bset);
2018 __isl_give isl_set *isl_basic_set_lexmax(
2019 __isl_take isl_basic_set *bset);
2020 __isl_give isl_set *isl_set_lexmin(
2021 __isl_take isl_set *set);
2022 __isl_give isl_set *isl_set_lexmax(
2023 __isl_take isl_set *set);
2024 __isl_give isl_union_set *isl_union_set_lexmin(
2025 __isl_take isl_union_set *uset);
2026 __isl_give isl_union_set *isl_union_set_lexmax(
2027 __isl_take isl_union_set *uset);
2029 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2030 the following functions
2031 compute a relation that maps each element of C<dom>
2032 to the single lexicographic minimum or maximum
2033 of the elements that are associated to that same
2034 element in C<map> (or C<bmap>).
2035 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2036 that contains the elements in C<dom> that do not map
2037 to any elements in C<map> (or C<bmap>).
2038 In other words, the union of the domain of the result and of C<*empty>
2041 __isl_give isl_map *isl_basic_map_partial_lexmax(
2042 __isl_take isl_basic_map *bmap,
2043 __isl_take isl_basic_set *dom,
2044 __isl_give isl_set **empty);
2045 __isl_give isl_map *isl_basic_map_partial_lexmin(
2046 __isl_take isl_basic_map *bmap,
2047 __isl_take isl_basic_set *dom,
2048 __isl_give isl_set **empty);
2049 __isl_give isl_map *isl_map_partial_lexmax(
2050 __isl_take isl_map *map, __isl_take isl_set *dom,
2051 __isl_give isl_set **empty);
2052 __isl_give isl_map *isl_map_partial_lexmin(
2053 __isl_take isl_map *map, __isl_take isl_set *dom,
2054 __isl_give isl_set **empty);
2056 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2057 return a map mapping each element in the domain of
2058 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2059 of all elements associated to that element.
2060 In case of union relations, the optimum is computed per space.
2062 __isl_give isl_map *isl_basic_map_lexmin(
2063 __isl_take isl_basic_map *bmap);
2064 __isl_give isl_map *isl_basic_map_lexmax(
2065 __isl_take isl_basic_map *bmap);
2066 __isl_give isl_map *isl_map_lexmin(
2067 __isl_take isl_map *map);
2068 __isl_give isl_map *isl_map_lexmax(
2069 __isl_take isl_map *map);
2070 __isl_give isl_union_map *isl_union_map_lexmin(
2071 __isl_take isl_union_map *umap);
2072 __isl_give isl_union_map *isl_union_map_lexmax(
2073 __isl_take isl_union_map *umap);
2077 Lists are defined over several element types, including
2078 C<isl_aff>, C<isl_basic_set> and C<isl_set>.
2079 Here we take lists of C<isl_set>s as an example.
2080 Lists can be created, copied and freed using the following functions.
2082 #include <isl/list.h>
2083 __isl_give isl_set_list *isl_set_list_alloc(
2084 isl_ctx *ctx, int n);
2085 __isl_give isl_set_list *isl_set_list_copy(
2086 __isl_keep isl_set_list *list);
2087 __isl_give isl_set_list *isl_set_list_add(
2088 __isl_take isl_set_list *list,
2089 __isl_take isl_set *el);
2090 void isl_set_list_free(__isl_take isl_set_list *list);
2092 C<isl_set_list_alloc> creates an empty list with a capacity for
2095 Lists can be inspected using the following functions.
2097 #include <isl/list.h>
2098 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2099 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2100 __isl_give struct isl_set *isl_set_list_get_set(
2101 __isl_keep isl_set_list *list, int index);
2102 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2103 int (*fn)(__isl_take struct isl_set *el, void *user),
2106 Lists can be printed using
2108 #include <isl/list.h>
2109 __isl_give isl_printer *isl_printer_print_set_list(
2110 __isl_take isl_printer *p,
2111 __isl_keep isl_set_list *list);
2115 Matrices can be created, copied and freed using the following functions.
2117 #include <isl/mat.h>
2118 __isl_give isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
2119 unsigned n_row, unsigned n_col);
2120 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2121 void isl_mat_free(__isl_take isl_mat *mat);
2123 Note that the elements of a newly created matrix may have arbitrary values.
2124 The elements can be changed and inspected using the following functions.
2126 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2127 int isl_mat_rows(__isl_keep isl_mat *mat);
2128 int isl_mat_cols(__isl_keep isl_mat *mat);
2129 int isl_mat_get_element(__isl_keep isl_mat *mat,
2130 int row, int col, isl_int *v);
2131 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2132 int row, int col, isl_int v);
2133 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2134 int row, int col, int v);
2136 C<isl_mat_get_element> will return a negative value if anything went wrong.
2137 In that case, the value of C<*v> is undefined.
2139 The following function can be used to compute the (right) inverse
2140 of a matrix, i.e., a matrix such that the product of the original
2141 and the inverse (in that order) is a multiple of the identity matrix.
2142 The input matrix is assumed to be of full row-rank.
2144 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2146 The following function can be used to compute the (right) kernel
2147 (or null space) of a matrix, i.e., a matrix such that the product of
2148 the original and the kernel (in that order) is the zero matrix.
2150 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2152 =head2 Quasi Affine Expressions
2154 The zero quasi affine expression can be created using
2156 __isl_give isl_aff *isl_aff_zero(
2157 __isl_take isl_local_space *ls);
2159 Quasi affine expressions can be copied and free using
2161 #include <isl/aff.h>
2162 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2163 void *isl_aff_free(__isl_take isl_aff *aff);
2165 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2166 using the following function. The constraint is required to have
2167 a non-zero coefficient for the specified dimension.
2169 #include <isl/constraint.h>
2170 __isl_give isl_aff *isl_constraint_get_bound(
2171 __isl_keep isl_constraint *constraint,
2172 enum isl_dim_type type, int pos);
2174 Conversely, an equality constraint equating
2175 the affine expression to zero or an inequality constraint enforcing
2176 the affine expression to be non-negative, can be constructed using
2178 __isl_give isl_constraint *isl_equality_from_aff(
2179 __isl_take isl_aff *aff);
2180 __isl_give isl_constraint *isl_inequality_from_aff(
2181 __isl_take isl_aff *aff);
2183 The expression can be inspected using
2185 #include <isl/aff.h>
2186 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2187 int isl_aff_dim(__isl_keep isl_aff *aff,
2188 enum isl_dim_type type);
2189 __isl_give isl_local_space *isl_aff_get_local_space(
2190 __isl_keep isl_aff *aff);
2191 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2192 enum isl_dim_type type, unsigned pos);
2193 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2195 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2196 enum isl_dim_type type, int pos, isl_int *v);
2197 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2199 __isl_give isl_div *isl_aff_get_div(
2200 __isl_keep isl_aff *aff, int pos);
2202 It can be modified using
2204 #include <isl/aff.h>
2205 __isl_give isl_aff *isl_aff_set_constant(
2206 __isl_take isl_aff *aff, isl_int v);
2207 __isl_give isl_aff *isl_aff_set_constant_si(
2208 __isl_take isl_aff *aff, int v);
2209 __isl_give isl_aff *isl_aff_set_coefficient(
2210 __isl_take isl_aff *aff,
2211 enum isl_dim_type type, int pos, isl_int v);
2212 __isl_give isl_aff *isl_aff_set_coefficient_si(
2213 __isl_take isl_aff *aff,
2214 enum isl_dim_type type, int pos, int v);
2215 __isl_give isl_aff *isl_aff_set_denominator(
2216 __isl_take isl_aff *aff, isl_int v);
2218 __isl_give isl_aff *isl_aff_add_constant(
2219 __isl_take isl_aff *aff, isl_int v);
2220 __isl_give isl_aff *isl_aff_add_coefficient_si(
2221 __isl_take isl_aff *aff,
2222 enum isl_dim_type type, int pos, int v);
2224 Note that the C<set_constant> and C<set_coefficient> functions
2225 set the I<numerator> of the constant or coefficient, while
2226 C<add_constant> and C<add_coefficient> add an integer value to
2227 the possibly rational constant or coefficient.
2231 #include <isl/aff.h>
2232 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2233 __isl_take isl_aff *aff2);
2234 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2235 __isl_take isl_aff *aff2);
2236 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2237 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2238 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2240 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2243 An expression can be printed using
2245 #include <isl/aff.h>
2246 __isl_give isl_printer *isl_printer_print_aff(
2247 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
2251 Points are elements of a set. They can be used to construct
2252 simple sets (boxes) or they can be used to represent the
2253 individual elements of a set.
2254 The zero point (the origin) can be created using
2256 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
2258 The coordinates of a point can be inspected, set and changed
2261 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
2262 enum isl_dim_type type, int pos, isl_int *v);
2263 __isl_give isl_point *isl_point_set_coordinate(
2264 __isl_take isl_point *pnt,
2265 enum isl_dim_type type, int pos, isl_int v);
2267 __isl_give isl_point *isl_point_add_ui(
2268 __isl_take isl_point *pnt,
2269 enum isl_dim_type type, int pos, unsigned val);
2270 __isl_give isl_point *isl_point_sub_ui(
2271 __isl_take isl_point *pnt,
2272 enum isl_dim_type type, int pos, unsigned val);
2274 Other properties can be obtained using
2276 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
2278 Points can be copied or freed using
2280 __isl_give isl_point *isl_point_copy(
2281 __isl_keep isl_point *pnt);
2282 void isl_point_free(__isl_take isl_point *pnt);
2284 A singleton set can be created from a point using
2286 __isl_give isl_basic_set *isl_basic_set_from_point(
2287 __isl_take isl_point *pnt);
2288 __isl_give isl_set *isl_set_from_point(
2289 __isl_take isl_point *pnt);
2291 and a box can be created from two opposite extremal points using
2293 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2294 __isl_take isl_point *pnt1,
2295 __isl_take isl_point *pnt2);
2296 __isl_give isl_set *isl_set_box_from_points(
2297 __isl_take isl_point *pnt1,
2298 __isl_take isl_point *pnt2);
2300 All elements of a B<bounded> (union) set can be enumerated using
2301 the following functions.
2303 int isl_set_foreach_point(__isl_keep isl_set *set,
2304 int (*fn)(__isl_take isl_point *pnt, void *user),
2306 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2307 int (*fn)(__isl_take isl_point *pnt, void *user),
2310 The function C<fn> is called for each integer point in
2311 C<set> with as second argument the last argument of
2312 the C<isl_set_foreach_point> call. The function C<fn>
2313 should return C<0> on success and C<-1> on failure.
2314 In the latter case, C<isl_set_foreach_point> will stop
2315 enumerating and return C<-1> as well.
2316 If the enumeration is performed successfully and to completion,
2317 then C<isl_set_foreach_point> returns C<0>.
2319 To obtain a single point of a (basic) set, use
2321 __isl_give isl_point *isl_basic_set_sample_point(
2322 __isl_take isl_basic_set *bset);
2323 __isl_give isl_point *isl_set_sample_point(
2324 __isl_take isl_set *set);
2326 If C<set> does not contain any (integer) points, then the
2327 resulting point will be ``void'', a property that can be
2330 int isl_point_is_void(__isl_keep isl_point *pnt);
2332 =head2 Piecewise Quasipolynomials
2334 A piecewise quasipolynomial is a particular kind of function that maps
2335 a parametric point to a rational value.
2336 More specifically, a quasipolynomial is a polynomial expression in greatest
2337 integer parts of affine expressions of parameters and variables.
2338 A piecewise quasipolynomial is a subdivision of a given parametric
2339 domain into disjoint cells with a quasipolynomial associated to
2340 each cell. The value of the piecewise quasipolynomial at a given
2341 point is the value of the quasipolynomial associated to the cell
2342 that contains the point. Outside of the union of cells,
2343 the value is assumed to be zero.
2344 For example, the piecewise quasipolynomial
2346 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2348 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
2349 A given piecewise quasipolynomial has a fixed domain dimension.
2350 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
2351 defined over different domains.
2352 Piecewise quasipolynomials are mainly used by the C<barvinok>
2353 library for representing the number of elements in a parametric set or map.
2354 For example, the piecewise quasipolynomial above represents
2355 the number of points in the map
2357 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2359 =head3 Printing (Piecewise) Quasipolynomials
2361 Quasipolynomials and piecewise quasipolynomials can be printed
2362 using the following functions.
2364 __isl_give isl_printer *isl_printer_print_qpolynomial(
2365 __isl_take isl_printer *p,
2366 __isl_keep isl_qpolynomial *qp);
2368 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
2369 __isl_take isl_printer *p,
2370 __isl_keep isl_pw_qpolynomial *pwqp);
2372 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
2373 __isl_take isl_printer *p,
2374 __isl_keep isl_union_pw_qpolynomial *upwqp);
2376 The output format of the printer
2377 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2378 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
2380 In case of printing in C<ISL_FORMAT_C>, the user may want
2381 to set the names of all dimensions
2383 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2384 __isl_take isl_qpolynomial *qp,
2385 enum isl_dim_type type, unsigned pos,
2387 __isl_give isl_pw_qpolynomial *
2388 isl_pw_qpolynomial_set_dim_name(
2389 __isl_take isl_pw_qpolynomial *pwqp,
2390 enum isl_dim_type type, unsigned pos,
2393 =head3 Creating New (Piecewise) Quasipolynomials
2395 Some simple quasipolynomials can be created using the following functions.
2396 More complicated quasipolynomials can be created by applying
2397 operations such as addition and multiplication
2398 on the resulting quasipolynomials
2400 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
2401 __isl_take isl_dim *dim);
2402 __isl_give isl_qpolynomial *isl_qpolynomial_one(
2403 __isl_take isl_dim *dim);
2404 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
2405 __isl_take isl_dim *dim);
2406 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
2407 __isl_take isl_dim *dim);
2408 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
2409 __isl_take isl_dim *dim);
2410 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
2411 __isl_take isl_dim *dim,
2412 const isl_int n, const isl_int d);
2413 __isl_give isl_qpolynomial *isl_qpolynomial_div(
2414 __isl_take isl_div *div);
2415 __isl_give isl_qpolynomial *isl_qpolynomial_var(
2416 __isl_take isl_dim *dim,
2417 enum isl_dim_type type, unsigned pos);
2418 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2419 __isl_take isl_aff *aff);
2421 The zero piecewise quasipolynomial or a piecewise quasipolynomial
2422 with a single cell can be created using the following functions.
2423 Multiple of these single cell piecewise quasipolynomials can
2424 be combined to create more complicated piecewise quasipolynomials.
2426 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2427 __isl_take isl_dim *dim);
2428 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2429 __isl_take isl_set *set,
2430 __isl_take isl_qpolynomial *qp);
2432 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
2433 __isl_take isl_dim *dim);
2434 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
2435 __isl_take isl_pw_qpolynomial *pwqp);
2436 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
2437 __isl_take isl_union_pw_qpolynomial *upwqp,
2438 __isl_take isl_pw_qpolynomial *pwqp);
2440 Quasipolynomials can be copied and freed again using the following
2443 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2444 __isl_keep isl_qpolynomial *qp);
2445 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
2447 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2448 __isl_keep isl_pw_qpolynomial *pwqp);
2449 void isl_pw_qpolynomial_free(
2450 __isl_take isl_pw_qpolynomial *pwqp);
2452 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
2453 __isl_keep isl_union_pw_qpolynomial *upwqp);
2454 void isl_union_pw_qpolynomial_free(
2455 __isl_take isl_union_pw_qpolynomial *upwqp);
2457 =head3 Inspecting (Piecewise) Quasipolynomials
2459 To iterate over all piecewise quasipolynomials in a union
2460 piecewise quasipolynomial, use the following function
2462 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
2463 __isl_keep isl_union_pw_qpolynomial *upwqp,
2464 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
2467 To extract the piecewise quasipolynomial from a union with a given dimension
2470 __isl_give isl_pw_qpolynomial *
2471 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
2472 __isl_keep isl_union_pw_qpolynomial *upwqp,
2473 __isl_take isl_dim *dim);
2475 To iterate over the cells in a piecewise quasipolynomial,
2476 use either of the following two functions
2478 int isl_pw_qpolynomial_foreach_piece(
2479 __isl_keep isl_pw_qpolynomial *pwqp,
2480 int (*fn)(__isl_take isl_set *set,
2481 __isl_take isl_qpolynomial *qp,
2482 void *user), void *user);
2483 int isl_pw_qpolynomial_foreach_lifted_piece(
2484 __isl_keep isl_pw_qpolynomial *pwqp,
2485 int (*fn)(__isl_take isl_set *set,
2486 __isl_take isl_qpolynomial *qp,
2487 void *user), void *user);
2489 As usual, the function C<fn> should return C<0> on success
2490 and C<-1> on failure. The difference between
2491 C<isl_pw_qpolynomial_foreach_piece> and
2492 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
2493 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
2494 compute unique representations for all existentially quantified
2495 variables and then turn these existentially quantified variables
2496 into extra set variables, adapting the associated quasipolynomial
2497 accordingly. This means that the C<set> passed to C<fn>
2498 will not have any existentially quantified variables, but that
2499 the dimensions of the sets may be different for different
2500 invocations of C<fn>.
2502 To iterate over all terms in a quasipolynomial,
2505 int isl_qpolynomial_foreach_term(
2506 __isl_keep isl_qpolynomial *qp,
2507 int (*fn)(__isl_take isl_term *term,
2508 void *user), void *user);
2510 The terms themselves can be inspected and freed using
2513 unsigned isl_term_dim(__isl_keep isl_term *term,
2514 enum isl_dim_type type);
2515 void isl_term_get_num(__isl_keep isl_term *term,
2517 void isl_term_get_den(__isl_keep isl_term *term,
2519 int isl_term_get_exp(__isl_keep isl_term *term,
2520 enum isl_dim_type type, unsigned pos);
2521 __isl_give isl_div *isl_term_get_div(
2522 __isl_keep isl_term *term, unsigned pos);
2523 void isl_term_free(__isl_take isl_term *term);
2525 Each term is a product of parameters, set variables and
2526 integer divisions. The function C<isl_term_get_exp>
2527 returns the exponent of a given dimensions in the given term.
2528 The C<isl_int>s in the arguments of C<isl_term_get_num>
2529 and C<isl_term_get_den> need to have been initialized
2530 using C<isl_int_init> before calling these functions.
2532 =head3 Properties of (Piecewise) Quasipolynomials
2534 To check whether a quasipolynomial is actually a constant,
2535 use the following function.
2537 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
2538 isl_int *n, isl_int *d);
2540 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
2541 then the numerator and denominator of the constant
2542 are returned in C<*n> and C<*d>, respectively.
2544 =head3 Operations on (Piecewise) Quasipolynomials
2546 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
2547 __isl_take isl_qpolynomial *qp);
2548 __isl_give isl_qpolynomial *isl_qpolynomial_add(
2549 __isl_take isl_qpolynomial *qp1,
2550 __isl_take isl_qpolynomial *qp2);
2551 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
2552 __isl_take isl_qpolynomial *qp1,
2553 __isl_take isl_qpolynomial *qp2);
2554 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
2555 __isl_take isl_qpolynomial *qp1,
2556 __isl_take isl_qpolynomial *qp2);
2557 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
2558 __isl_take isl_qpolynomial *qp, unsigned exponent);
2560 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
2561 __isl_take isl_pw_qpolynomial *pwqp1,
2562 __isl_take isl_pw_qpolynomial *pwqp2);
2563 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2564 __isl_take isl_pw_qpolynomial *pwqp1,
2565 __isl_take isl_pw_qpolynomial *pwqp2);
2566 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
2567 __isl_take isl_pw_qpolynomial *pwqp1,
2568 __isl_take isl_pw_qpolynomial *pwqp2);
2569 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2570 __isl_take isl_pw_qpolynomial *pwqp);
2571 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2572 __isl_take isl_pw_qpolynomial *pwqp1,
2573 __isl_take isl_pw_qpolynomial *pwqp2);
2575 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
2576 __isl_take isl_union_pw_qpolynomial *upwqp1,
2577 __isl_take isl_union_pw_qpolynomial *upwqp2);
2578 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
2579 __isl_take isl_union_pw_qpolynomial *upwqp1,
2580 __isl_take isl_union_pw_qpolynomial *upwqp2);
2581 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
2582 __isl_take isl_union_pw_qpolynomial *upwqp1,
2583 __isl_take isl_union_pw_qpolynomial *upwqp2);
2585 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
2586 __isl_take isl_pw_qpolynomial *pwqp,
2587 __isl_take isl_point *pnt);
2589 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
2590 __isl_take isl_union_pw_qpolynomial *upwqp,
2591 __isl_take isl_point *pnt);
2593 __isl_give isl_set *isl_pw_qpolynomial_domain(
2594 __isl_take isl_pw_qpolynomial *pwqp);
2595 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
2596 __isl_take isl_pw_qpolynomial *pwpq,
2597 __isl_take isl_set *set);
2599 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
2600 __isl_take isl_union_pw_qpolynomial *upwqp);
2601 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
2602 __isl_take isl_union_pw_qpolynomial *upwpq,
2603 __isl_take isl_union_set *uset);
2605 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
2606 __isl_take isl_qpolynomial *qp,
2607 __isl_take isl_dim *model);
2609 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
2610 __isl_take isl_union_pw_qpolynomial *upwqp);
2612 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2613 __isl_take isl_qpolynomial *qp,
2614 __isl_take isl_set *context);
2616 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
2617 __isl_take isl_pw_qpolynomial *pwqp,
2618 __isl_take isl_set *context);
2620 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
2621 __isl_take isl_union_pw_qpolynomial *upwqp,
2622 __isl_take isl_union_set *context);
2624 The gist operation applies the gist operation to each of
2625 the cells in the domain of the input piecewise quasipolynomial.
2626 The context is also exploited
2627 to simplify the quasipolynomials associated to each cell.
2629 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
2630 __isl_take isl_pw_qpolynomial *pwqp, int sign);
2631 __isl_give isl_union_pw_qpolynomial *
2632 isl_union_pw_qpolynomial_to_polynomial(
2633 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
2635 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
2636 the polynomial will be an overapproximation. If C<sign> is negative,
2637 it will be an underapproximation. If C<sign> is zero, the approximation
2638 will lie somewhere in between.
2640 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
2642 A piecewise quasipolynomial reduction is a piecewise
2643 reduction (or fold) of quasipolynomials.
2644 In particular, the reduction can be maximum or a minimum.
2645 The objects are mainly used to represent the result of
2646 an upper or lower bound on a quasipolynomial over its domain,
2647 i.e., as the result of the following function.
2649 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
2650 __isl_take isl_pw_qpolynomial *pwqp,
2651 enum isl_fold type, int *tight);
2653 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
2654 __isl_take isl_union_pw_qpolynomial *upwqp,
2655 enum isl_fold type, int *tight);
2657 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
2658 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
2659 is the returned bound is known be tight, i.e., for each value
2660 of the parameters there is at least
2661 one element in the domain that reaches the bound.
2662 If the domain of C<pwqp> is not wrapping, then the bound is computed
2663 over all elements in that domain and the result has a purely parametric
2664 domain. If the domain of C<pwqp> is wrapping, then the bound is
2665 computed over the range of the wrapped relation. The domain of the
2666 wrapped relation becomes the domain of the result.
2668 A (piecewise) quasipolynomial reduction can be copied or freed using the
2669 following functions.
2671 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
2672 __isl_keep isl_qpolynomial_fold *fold);
2673 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
2674 __isl_keep isl_pw_qpolynomial_fold *pwf);
2675 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
2676 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2677 void isl_qpolynomial_fold_free(
2678 __isl_take isl_qpolynomial_fold *fold);
2679 void isl_pw_qpolynomial_fold_free(
2680 __isl_take isl_pw_qpolynomial_fold *pwf);
2681 void isl_union_pw_qpolynomial_fold_free(
2682 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2684 =head3 Printing Piecewise Quasipolynomial Reductions
2686 Piecewise quasipolynomial reductions can be printed
2687 using the following function.
2689 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
2690 __isl_take isl_printer *p,
2691 __isl_keep isl_pw_qpolynomial_fold *pwf);
2692 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
2693 __isl_take isl_printer *p,
2694 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2696 For C<isl_printer_print_pw_qpolynomial_fold>,
2697 output format of the printer
2698 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2699 For C<isl_printer_print_union_pw_qpolynomial_fold>,
2700 output format of the printer
2701 needs to be set to C<ISL_FORMAT_ISL>.
2702 In case of printing in C<ISL_FORMAT_C>, the user may want
2703 to set the names of all dimensions
2705 __isl_give isl_pw_qpolynomial_fold *
2706 isl_pw_qpolynomial_fold_set_dim_name(
2707 __isl_take isl_pw_qpolynomial_fold *pwf,
2708 enum isl_dim_type type, unsigned pos,
2711 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
2713 To iterate over all piecewise quasipolynomial reductions in a union
2714 piecewise quasipolynomial reduction, use the following function
2716 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
2717 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
2718 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
2719 void *user), void *user);
2721 To iterate over the cells in a piecewise quasipolynomial reduction,
2722 use either of the following two functions
2724 int isl_pw_qpolynomial_fold_foreach_piece(
2725 __isl_keep isl_pw_qpolynomial_fold *pwf,
2726 int (*fn)(__isl_take isl_set *set,
2727 __isl_take isl_qpolynomial_fold *fold,
2728 void *user), void *user);
2729 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
2730 __isl_keep isl_pw_qpolynomial_fold *pwf,
2731 int (*fn)(__isl_take isl_set *set,
2732 __isl_take isl_qpolynomial_fold *fold,
2733 void *user), void *user);
2735 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
2736 of the difference between these two functions.
2738 To iterate over all quasipolynomials in a reduction, use
2740 int isl_qpolynomial_fold_foreach_qpolynomial(
2741 __isl_keep isl_qpolynomial_fold *fold,
2742 int (*fn)(__isl_take isl_qpolynomial *qp,
2743 void *user), void *user);
2745 =head3 Operations on Piecewise Quasipolynomial Reductions
2747 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
2748 __isl_take isl_pw_qpolynomial_fold *pwf1,
2749 __isl_take isl_pw_qpolynomial_fold *pwf2);
2751 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
2752 __isl_take isl_pw_qpolynomial_fold *pwf1,
2753 __isl_take isl_pw_qpolynomial_fold *pwf2);
2755 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
2756 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
2757 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
2759 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
2760 __isl_take isl_pw_qpolynomial_fold *pwf,
2761 __isl_take isl_point *pnt);
2763 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
2764 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2765 __isl_take isl_point *pnt);
2767 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
2768 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2769 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
2770 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2771 __isl_take isl_union_set *uset);
2773 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
2774 __isl_take isl_pw_qpolynomial_fold *pwf);
2776 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
2777 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2779 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
2780 __isl_take isl_pw_qpolynomial_fold *pwf,
2781 __isl_take isl_set *context);
2783 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
2784 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2785 __isl_take isl_union_set *context);
2787 The gist operation applies the gist operation to each of
2788 the cells in the domain of the input piecewise quasipolynomial reduction.
2789 In future, the operation will also exploit the context
2790 to simplify the quasipolynomial reductions associated to each cell.
2792 __isl_give isl_pw_qpolynomial_fold *
2793 isl_set_apply_pw_qpolynomial_fold(
2794 __isl_take isl_set *set,
2795 __isl_take isl_pw_qpolynomial_fold *pwf,
2797 __isl_give isl_pw_qpolynomial_fold *
2798 isl_map_apply_pw_qpolynomial_fold(
2799 __isl_take isl_map *map,
2800 __isl_take isl_pw_qpolynomial_fold *pwf,
2802 __isl_give isl_union_pw_qpolynomial_fold *
2803 isl_union_set_apply_union_pw_qpolynomial_fold(
2804 __isl_take isl_union_set *uset,
2805 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2807 __isl_give isl_union_pw_qpolynomial_fold *
2808 isl_union_map_apply_union_pw_qpolynomial_fold(
2809 __isl_take isl_union_map *umap,
2810 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2813 The functions taking a map
2814 compose the given map with the given piecewise quasipolynomial reduction.
2815 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
2816 over all elements in the intersection of the range of the map
2817 and the domain of the piecewise quasipolynomial reduction
2818 as a function of an element in the domain of the map.
2819 The functions taking a set compute a bound over all elements in the
2820 intersection of the set and the domain of the
2821 piecewise quasipolynomial reduction.
2823 =head2 Dependence Analysis
2825 C<isl> contains specialized functionality for performing
2826 array dataflow analysis. That is, given a I<sink> access relation
2827 and a collection of possible I<source> access relations,
2828 C<isl> can compute relations that describe
2829 for each iteration of the sink access, which iteration
2830 of which of the source access relations was the last
2831 to access the same data element before the given iteration
2833 To compute standard flow dependences, the sink should be
2834 a read, while the sources should be writes.
2835 If any of the source accesses are marked as being I<may>
2836 accesses, then there will be a dependence to the last
2837 I<must> access B<and> to any I<may> access that follows
2838 this last I<must> access.
2839 In particular, if I<all> sources are I<may> accesses,
2840 then memory based dependence analysis is performed.
2841 If, on the other hand, all sources are I<must> accesses,
2842 then value based dependence analysis is performed.
2844 #include <isl/flow.h>
2846 typedef int (*isl_access_level_before)(void *first, void *second);
2848 __isl_give isl_access_info *isl_access_info_alloc(
2849 __isl_take isl_map *sink,
2850 void *sink_user, isl_access_level_before fn,
2852 __isl_give isl_access_info *isl_access_info_add_source(
2853 __isl_take isl_access_info *acc,
2854 __isl_take isl_map *source, int must,
2856 void isl_access_info_free(__isl_take isl_access_info *acc);
2858 __isl_give isl_flow *isl_access_info_compute_flow(
2859 __isl_take isl_access_info *acc);
2861 int isl_flow_foreach(__isl_keep isl_flow *deps,
2862 int (*fn)(__isl_take isl_map *dep, int must,
2863 void *dep_user, void *user),
2865 __isl_give isl_map *isl_flow_get_no_source(
2866 __isl_keep isl_flow *deps, int must);
2867 void isl_flow_free(__isl_take isl_flow *deps);
2869 The function C<isl_access_info_compute_flow> performs the actual
2870 dependence analysis. The other functions are used to construct
2871 the input for this function or to read off the output.
2873 The input is collected in an C<isl_access_info>, which can
2874 be created through a call to C<isl_access_info_alloc>.
2875 The arguments to this functions are the sink access relation
2876 C<sink>, a token C<sink_user> used to identify the sink
2877 access to the user, a callback function for specifying the
2878 relative order of source and sink accesses, and the number
2879 of source access relations that will be added.
2880 The callback function has type C<int (*)(void *first, void *second)>.
2881 The function is called with two user supplied tokens identifying
2882 either a source or the sink and it should return the shared nesting
2883 level and the relative order of the two accesses.
2884 In particular, let I<n> be the number of loops shared by
2885 the two accesses. If C<first> precedes C<second> textually,
2886 then the function should return I<2 * n + 1>; otherwise,
2887 it should return I<2 * n>.
2888 The sources can be added to the C<isl_access_info> by performing
2889 (at most) C<max_source> calls to C<isl_access_info_add_source>.
2890 C<must> indicates whether the source is a I<must> access
2891 or a I<may> access. Note that a multi-valued access relation
2892 should only be marked I<must> if every iteration in the domain
2893 of the relation accesses I<all> elements in its image.
2894 The C<source_user> token is again used to identify
2895 the source access. The range of the source access relation
2896 C<source> should have the same dimension as the range
2897 of the sink access relation.
2898 The C<isl_access_info_free> function should usually not be
2899 called explicitly, because it is called implicitly by
2900 C<isl_access_info_compute_flow>.
2902 The result of the dependence analysis is collected in an
2903 C<isl_flow>. There may be elements of
2904 the sink access for which no preceding source access could be
2905 found or for which all preceding sources are I<may> accesses.
2906 The relations containing these elements can be obtained through
2907 calls to C<isl_flow_get_no_source>, the first with C<must> set
2908 and the second with C<must> unset.
2909 In the case of standard flow dependence analysis,
2910 with the sink a read and the sources I<must> writes,
2911 the first relation corresponds to the reads from uninitialized
2912 array elements and the second relation is empty.
2913 The actual flow dependences can be extracted using
2914 C<isl_flow_foreach>. This function will call the user-specified
2915 callback function C<fn> for each B<non-empty> dependence between
2916 a source and the sink. The callback function is called
2917 with four arguments, the actual flow dependence relation
2918 mapping source iterations to sink iterations, a boolean that
2919 indicates whether it is a I<must> or I<may> dependence, a token
2920 identifying the source and an additional C<void *> with value
2921 equal to the third argument of the C<isl_flow_foreach> call.
2922 A dependence is marked I<must> if it originates from a I<must>
2923 source and if it is not followed by any I<may> sources.
2925 After finishing with an C<isl_flow>, the user should call
2926 C<isl_flow_free> to free all associated memory.
2928 A higher-level interface to dependence analysis is provided
2929 by the following function.
2931 #include <isl/flow.h>
2933 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
2934 __isl_take isl_union_map *must_source,
2935 __isl_take isl_union_map *may_source,
2936 __isl_take isl_union_map *schedule,
2937 __isl_give isl_union_map **must_dep,
2938 __isl_give isl_union_map **may_dep,
2939 __isl_give isl_union_map **must_no_source,
2940 __isl_give isl_union_map **may_no_source);
2942 The arrays are identified by the tuple names of the ranges
2943 of the accesses. The iteration domains by the tuple names
2944 of the domains of the accesses and of the schedule.
2945 The relative order of the iteration domains is given by the
2946 schedule. The relations returned through C<must_no_source>
2947 and C<may_no_source> are subsets of C<sink>.
2948 Any of C<must_dep>, C<may_dep>, C<must_no_source>
2949 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
2950 any of the other arguments is treated as an error.
2954 B<The functionality described in this section is fairly new
2955 and may be subject to change.>
2957 The following function can be used to compute a schedule
2958 for a union of domains. The generated schedule respects
2959 all C<validity> dependences. That is, all dependence distances
2960 over these dependences in the scheduled space are lexicographically
2961 positive. The generated schedule schedule also tries to minimize
2962 the dependence distances over C<proximity> dependences.
2963 Moreover, it tries to obtain sequences (bands) of schedule dimensions
2964 for groups of domains where the dependence distances have only
2965 non-negative values.
2966 The algorithm used to construct the schedule is similar to that
2969 #include <isl/schedule.h>
2970 __isl_give isl_schedule *isl_union_set_compute_schedule(
2971 __isl_take isl_union_set *domain,
2972 __isl_take isl_union_map *validity,
2973 __isl_take isl_union_map *proximity);
2974 void *isl_schedule_free(__isl_take isl_schedule *sched);
2976 A mapping from the domains to the scheduled space can be obtained
2977 from an C<isl_schedule> using the following function.
2979 __isl_give isl_union_map *isl_schedule_get_map(
2980 __isl_keep isl_schedule *sched);
2982 A representation of the schedule can be printed using
2984 __isl_give isl_printer *isl_printer_print_schedule(
2985 __isl_take isl_printer *p,
2986 __isl_keep isl_schedule *schedule);
2988 A representation of the schedule as a forest of bands can be obtained
2989 using the following function.
2991 __isl_give isl_band_list *isl_schedule_get_band_forest(
2992 __isl_keep isl_schedule *schedule);
2994 The list can be manipulated as explained in L<"Lists">.
2995 The bands inside the list can be copied and freed using the following
2998 #include <isl/band.h>
2999 __isl_give isl_band *isl_band_copy(
3000 __isl_keep isl_band *band);
3001 void *isl_band_free(__isl_take isl_band *band);
3003 Each band contains zero or more scheduling dimensions.
3004 These are referred to as the members of the band.
3005 The section of the schedule that corresponds to the band is
3006 referred to as the partial schedule of the band.
3007 For those nodes that participate in a band, the outer scheduling
3008 dimensions form the prefix schedule, while the inner scheduling
3009 dimensions form the suffix schedule.
3010 That is, if we take a cut of the band forest, then the union of
3011 the concatenations of the prefix, partial and suffix schedules of
3012 each band in the cut is equal to the entire schedule (modulo
3013 some possible padding at the end with zero scheduling dimensions).
3014 The properties of a band can be inspected using the following functions.
3016 #include <isl/band.h>
3017 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
3019 int isl_band_has_children(__isl_keep isl_band *band);
3020 __isl_give isl_band_list *isl_band_get_children(
3021 __isl_keep isl_band *band);
3023 __isl_give isl_union_map *isl_band_get_prefix_schedule(
3024 __isl_keep isl_band *band);
3025 __isl_give isl_union_map *isl_band_get_partial_schedule(
3026 __isl_keep isl_band *band);
3027 __isl_give isl_union_map *isl_band_get_suffix_schedule(
3028 __isl_keep isl_band *band);
3030 int isl_band_n_member(__isl_keep isl_band *band);
3031 int isl_band_member_is_zero_distance(
3032 __isl_keep isl_band *band, int pos);
3034 Note that a scheduling dimension is considered to be ``zero
3035 distance'' if it does not carry any proximity dependences
3037 That is, if the dependence distances of the proximity
3038 dependences are all zero in that direction (for fixed
3039 iterations of outer bands).
3041 A representation of the band can be printed using
3043 #include <isl/band.h>
3044 __isl_give isl_printer *isl_printer_print_band(
3045 __isl_take isl_printer *p,
3046 __isl_keep isl_band *band);
3048 Alternatively, the schedule mapping
3049 can also be obtained in pieces using the following functions.
3051 int isl_schedule_n_band(__isl_keep isl_schedule *sched);
3052 __isl_give isl_union_map *isl_schedule_get_band(
3053 __isl_keep isl_schedule *sched, unsigned band);
3055 C<isl_schedule_n_band> returns the maximal number of bands.
3056 C<isl_schedule_get_band> returns a union of mappings from a domain to
3057 the band of consecutive schedule dimensions with the given sequence
3058 number for that domain. Bands with the same sequence number but for
3059 different domains may be completely unrelated.
3060 Within a band, the corresponding coordinates of the distance vectors
3061 are all non-negative, assuming that the coordinates for all previous
3064 =head2 Parametric Vertex Enumeration
3066 The parametric vertex enumeration described in this section
3067 is mainly intended to be used internally and by the C<barvinok>
3070 #include <isl/vertices.h>
3071 __isl_give isl_vertices *isl_basic_set_compute_vertices(
3072 __isl_keep isl_basic_set *bset);
3074 The function C<isl_basic_set_compute_vertices> performs the
3075 actual computation of the parametric vertices and the chamber
3076 decomposition and store the result in an C<isl_vertices> object.
3077 This information can be queried by either iterating over all
3078 the vertices or iterating over all the chambers or cells
3079 and then iterating over all vertices that are active on the chamber.
3081 int isl_vertices_foreach_vertex(
3082 __isl_keep isl_vertices *vertices,
3083 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3086 int isl_vertices_foreach_cell(
3087 __isl_keep isl_vertices *vertices,
3088 int (*fn)(__isl_take isl_cell *cell, void *user),
3090 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
3091 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3094 Other operations that can be performed on an C<isl_vertices> object are
3097 isl_ctx *isl_vertices_get_ctx(
3098 __isl_keep isl_vertices *vertices);
3099 int isl_vertices_get_n_vertices(
3100 __isl_keep isl_vertices *vertices);
3101 void isl_vertices_free(__isl_take isl_vertices *vertices);
3103 Vertices can be inspected and destroyed using the following functions.
3105 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
3106 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
3107 __isl_give isl_basic_set *isl_vertex_get_domain(
3108 __isl_keep isl_vertex *vertex);
3109 __isl_give isl_basic_set *isl_vertex_get_expr(
3110 __isl_keep isl_vertex *vertex);
3111 void isl_vertex_free(__isl_take isl_vertex *vertex);
3113 C<isl_vertex_get_expr> returns a singleton parametric set describing
3114 the vertex, while C<isl_vertex_get_domain> returns the activity domain
3116 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
3117 B<rational> basic sets, so they should mainly be used for inspection
3118 and should not be mixed with integer sets.
3120 Chambers can be inspected and destroyed using the following functions.
3122 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
3123 __isl_give isl_basic_set *isl_cell_get_domain(
3124 __isl_keep isl_cell *cell);
3125 void isl_cell_free(__isl_take isl_cell *cell);
3129 Although C<isl> is mainly meant to be used as a library,
3130 it also contains some basic applications that use some
3131 of the functionality of C<isl>.
3132 The input may be specified in either the L<isl format>
3133 or the L<PolyLib format>.
3135 =head2 C<isl_polyhedron_sample>
3137 C<isl_polyhedron_sample> takes a polyhedron as input and prints
3138 an integer element of the polyhedron, if there is any.
3139 The first column in the output is the denominator and is always
3140 equal to 1. If the polyhedron contains no integer points,
3141 then a vector of length zero is printed.
3145 C<isl_pip> takes the same input as the C<example> program
3146 from the C<piplib> distribution, i.e., a set of constraints
3147 on the parameters, a line containing only -1 and finally a set
3148 of constraints on a parametric polyhedron.
3149 The coefficients of the parameters appear in the last columns
3150 (but before the final constant column).
3151 The output is the lexicographic minimum of the parametric polyhedron.
3152 As C<isl> currently does not have its own output format, the output
3153 is just a dump of the internal state.
3155 =head2 C<isl_polyhedron_minimize>
3157 C<isl_polyhedron_minimize> computes the minimum of some linear
3158 or affine objective function over the integer points in a polyhedron.
3159 If an affine objective function
3160 is given, then the constant should appear in the last column.
3162 =head2 C<isl_polytope_scan>
3164 Given a polytope, C<isl_polytope_scan> prints
3165 all integer points in the polytope.