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 a B<map> space as input. An old call
72 C<isl_map_identity(space)> can be rewritten to
73 C<isl_map_identity(isl_space_map_from_set(space))>.
75 =item * The function C<isl_map_power> no longer takes
76 a parameter position as input. Instead, the exponent
77 is now expressed as the domain of the resulting relation.
81 =head3 Changes since isl-0.06
85 =item * The format of C<isl_printer_print_qpolynomial>'s
86 C<ISL_FORMAT_ISL> output has changed.
87 Use C<ISL_FORMAT_C> to obtain the old output.
89 =item * The C<*_fast_*> functions have been renamed to C<*_plain_*>.
90 Some of the old names have been kept for backward compatibility,
91 but they will be removed in the future.
95 =head3 Changes since isl-0.07
99 =item * The function C<isl_pw_aff_max> has been renamed to
100 C<isl_pw_aff_union_max>.
102 =item * The C<isl_dim> type has been renamed to C<isl_space>
103 along with the associated functions.
104 Some of the old names have been kept for backward compatibility,
105 but they will be removed in the future.
111 The source of C<isl> can be obtained either as a tarball
112 or from the git repository. Both are available from
113 L<http://freshmeat.net/projects/isl/>.
114 The installation process depends on how you obtained
117 =head2 Installation from the git repository
121 =item 1 Clone or update the repository
123 The first time the source is obtained, you need to clone
126 git clone git://repo.or.cz/isl.git
128 To obtain updates, you need to pull in the latest changes
132 =item 2 Generate C<configure>
138 After performing the above steps, continue
139 with the L<Common installation instructions>.
141 =head2 Common installation instructions
145 =item 1 Obtain C<GMP>
147 Building C<isl> requires C<GMP>, including its headers files.
148 Your distribution may not provide these header files by default
149 and you may need to install a package called C<gmp-devel> or something
150 similar. Alternatively, C<GMP> can be built from
151 source, available from L<http://gmplib.org/>.
155 C<isl> uses the standard C<autoconf> C<configure> script.
160 optionally followed by some configure options.
161 A complete list of options can be obtained by running
165 Below we discuss some of the more common options.
167 C<isl> can optionally use C<piplib>, but no
168 C<piplib> functionality is currently used by default.
169 The C<--with-piplib> option can
170 be used to specify which C<piplib>
171 library to use, either an installed version (C<system>),
172 an externally built version (C<build>)
173 or no version (C<no>). The option C<build> is mostly useful
174 in C<configure> scripts of larger projects that bundle both C<isl>
181 Installation prefix for C<isl>
183 =item C<--with-gmp-prefix>
185 Installation prefix for C<GMP> (architecture-independent files).
187 =item C<--with-gmp-exec-prefix>
189 Installation prefix for C<GMP> (architecture-dependent files).
191 =item C<--with-piplib>
193 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
195 =item C<--with-piplib-prefix>
197 Installation prefix for C<system> C<piplib> (architecture-independent files).
199 =item C<--with-piplib-exec-prefix>
201 Installation prefix for C<system> C<piplib> (architecture-dependent files).
203 =item C<--with-piplib-builddir>
205 Location where C<build> C<piplib> was built.
213 =item 4 Install (optional)
221 =head2 Initialization
223 All manipulations of integer sets and relations occur within
224 the context of an C<isl_ctx>.
225 A given C<isl_ctx> can only be used within a single thread.
226 All arguments of a function are required to have been allocated
227 within the same context.
228 There are currently no functions available for moving an object
229 from one C<isl_ctx> to another C<isl_ctx>. This means that
230 there is currently no way of safely moving an object from one
231 thread to another, unless the whole C<isl_ctx> is moved.
233 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
234 freed using C<isl_ctx_free>.
235 All objects allocated within an C<isl_ctx> should be freed
236 before the C<isl_ctx> itself is freed.
238 isl_ctx *isl_ctx_alloc();
239 void isl_ctx_free(isl_ctx *ctx);
243 All operations on integers, mainly the coefficients
244 of the constraints describing the sets and relations,
245 are performed in exact integer arithmetic using C<GMP>.
246 However, to allow future versions of C<isl> to optionally
247 support fixed integer arithmetic, all calls to C<GMP>
248 are wrapped inside C<isl> specific macros.
249 The basic type is C<isl_int> and the operations below
250 are available on this type.
251 The meanings of these operations are essentially the same
252 as their C<GMP> C<mpz_> counterparts.
253 As always with C<GMP> types, C<isl_int>s need to be
254 initialized with C<isl_int_init> before they can be used
255 and they need to be released with C<isl_int_clear>
257 The user should not assume that an C<isl_int> is represented
258 as a C<mpz_t>, but should instead explicitly convert between
259 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
260 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
264 =item isl_int_init(i)
266 =item isl_int_clear(i)
268 =item isl_int_set(r,i)
270 =item isl_int_set_si(r,i)
272 =item isl_int_set_gmp(r,g)
274 =item isl_int_get_gmp(i,g)
276 =item isl_int_abs(r,i)
278 =item isl_int_neg(r,i)
280 =item isl_int_swap(i,j)
282 =item isl_int_swap_or_set(i,j)
284 =item isl_int_add_ui(r,i,j)
286 =item isl_int_sub_ui(r,i,j)
288 =item isl_int_add(r,i,j)
290 =item isl_int_sub(r,i,j)
292 =item isl_int_mul(r,i,j)
294 =item isl_int_mul_ui(r,i,j)
296 =item isl_int_addmul(r,i,j)
298 =item isl_int_submul(r,i,j)
300 =item isl_int_gcd(r,i,j)
302 =item isl_int_lcm(r,i,j)
304 =item isl_int_divexact(r,i,j)
306 =item isl_int_cdiv_q(r,i,j)
308 =item isl_int_fdiv_q(r,i,j)
310 =item isl_int_fdiv_r(r,i,j)
312 =item isl_int_fdiv_q_ui(r,i,j)
314 =item isl_int_read(r,s)
316 =item isl_int_print(out,i,width)
320 =item isl_int_cmp(i,j)
322 =item isl_int_cmp_si(i,si)
324 =item isl_int_eq(i,j)
326 =item isl_int_ne(i,j)
328 =item isl_int_lt(i,j)
330 =item isl_int_le(i,j)
332 =item isl_int_gt(i,j)
334 =item isl_int_ge(i,j)
336 =item isl_int_abs_eq(i,j)
338 =item isl_int_abs_ne(i,j)
340 =item isl_int_abs_lt(i,j)
342 =item isl_int_abs_gt(i,j)
344 =item isl_int_abs_ge(i,j)
346 =item isl_int_is_zero(i)
348 =item isl_int_is_one(i)
350 =item isl_int_is_negone(i)
352 =item isl_int_is_pos(i)
354 =item isl_int_is_neg(i)
356 =item isl_int_is_nonpos(i)
358 =item isl_int_is_nonneg(i)
360 =item isl_int_is_divisible_by(i,j)
364 =head2 Sets and Relations
366 C<isl> uses six types of objects for representing sets and relations,
367 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
368 C<isl_union_set> and C<isl_union_map>.
369 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
370 can be described as a conjunction of affine constraints, while
371 C<isl_set> and C<isl_map> represent unions of
372 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
373 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
374 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
375 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
376 where spaces are considered different if they have a different number
377 of dimensions and/or different names (see L<"Spaces">).
378 The difference between sets and relations (maps) is that sets have
379 one set of variables, while relations have two sets of variables,
380 input variables and output variables.
382 =head2 Memory Management
384 Since a high-level operation on sets and/or relations usually involves
385 several substeps and since the user is usually not interested in
386 the intermediate results, most functions that return a new object
387 will also release all the objects passed as arguments.
388 If the user still wants to use one or more of these arguments
389 after the function call, she should pass along a copy of the
390 object rather than the object itself.
391 The user is then responsible for making sure that the original
392 object gets used somewhere else or is explicitly freed.
394 The arguments and return values of all documented functions are
395 annotated to make clear which arguments are released and which
396 arguments are preserved. In particular, the following annotations
403 C<__isl_give> means that a new object is returned.
404 The user should make sure that the returned pointer is
405 used exactly once as a value for an C<__isl_take> argument.
406 In between, it can be used as a value for as many
407 C<__isl_keep> arguments as the user likes.
408 There is one exception, and that is the case where the
409 pointer returned is C<NULL>. Is this case, the user
410 is free to use it as an C<__isl_take> argument or not.
414 C<__isl_take> means that the object the argument points to
415 is taken over by the function and may no longer be used
416 by the user as an argument to any other function.
417 The pointer value must be one returned by a function
418 returning an C<__isl_give> pointer.
419 If the user passes in a C<NULL> value, then this will
420 be treated as an error in the sense that the function will
421 not perform its usual operation. However, it will still
422 make sure that all the other C<__isl_take> arguments
427 C<__isl_keep> means that the function will only use the object
428 temporarily. After the function has finished, the user
429 can still use it as an argument to other functions.
430 A C<NULL> value will be treated in the same way as
431 a C<NULL> value for an C<__isl_take> argument.
437 Identifiers are used to identify both individual dimensions
438 and tuples of dimensions. They consist of a name and an optional
439 pointer. Identifiers with the same name but different pointer values
440 are considered to be distinct.
441 Identifiers can be constructed, copied, freed, inspected and printed
442 using the following functions.
445 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
446 __isl_keep const char *name, void *user);
447 __isl_give isl_id *isl_id_copy(isl_id *id);
448 void *isl_id_free(__isl_take isl_id *id);
450 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
451 void *isl_id_get_user(__isl_keep isl_id *id);
452 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
454 __isl_give isl_printer *isl_printer_print_id(
455 __isl_take isl_printer *p, __isl_keep isl_id *id);
457 Note that C<isl_id_get_name> returns a pointer to some internal
458 data structure, so the result can only be used while the
459 corresponding C<isl_id> is alive.
463 Whenever a new set or relation is created from scratch,
464 the space in which it lives needs to be specified using an C<isl_space>.
466 #include <isl/space.h>
467 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
468 unsigned nparam, unsigned n_in, unsigned n_out);
469 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
470 unsigned nparam, unsigned dim);
471 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
472 void isl_space_free(__isl_take isl_space *space);
473 unsigned isl_space_dim(__isl_keep isl_space *space,
474 enum isl_dim_type type);
476 The space used for creating a set
477 needs to be created using C<isl_space_set_alloc>, while
478 that for creating a relation
479 needs to be created using C<isl_space_alloc>.
480 C<isl_space_dim> can be used
481 to find out the number of dimensions of each type in
482 a space, where type may be
483 C<isl_dim_param>, C<isl_dim_in> (only for relations),
484 C<isl_dim_out> (only for relations), C<isl_dim_set>
485 (only for sets) or C<isl_dim_all>.
487 It is often useful to create objects that live in the
488 same space as some other object. This can be accomplished
489 by creating the new objects
490 (see L<Creating New Sets and Relations> or
491 L<Creating New (Piecewise) Quasipolynomials>) based on the space
492 of the original object.
495 __isl_give isl_space *isl_basic_set_get_space(
496 __isl_keep isl_basic_set *bset);
497 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
499 #include <isl/union_set.h>
500 __isl_give isl_space *isl_union_set_get_space(
501 __isl_keep isl_union_set *uset);
504 __isl_give isl_space *isl_basic_map_get_space(
505 __isl_keep isl_basic_map *bmap);
506 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
508 #include <isl/union_map.h>
509 __isl_give isl_space *isl_union_map_get_space(
510 __isl_keep isl_union_map *umap);
512 #include <isl/constraint.h>
513 __isl_give isl_space *isl_constraint_get_space(
514 __isl_keep isl_constraint *constraint);
516 #include <isl/polynomial.h>
517 __isl_give isl_space *isl_qpolynomial_get_space(
518 __isl_keep isl_qpolynomial *qp);
519 __isl_give isl_space *isl_qpolynomial_fold_get_space(
520 __isl_keep isl_qpolynomial_fold *fold);
521 __isl_give isl_space *isl_pw_qpolynomial_get_space(
522 __isl_keep isl_pw_qpolynomial *pwqp);
523 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
524 __isl_keep isl_union_pw_qpolynomial *upwqp);
525 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
526 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
529 __isl_give isl_space *isl_aff_get_space(
530 __isl_keep isl_aff *aff);
531 __isl_give isl_space *isl_pw_aff_get_space(
532 __isl_keep isl_pw_aff *pwaff);
534 #include <isl/point.h>
535 __isl_give isl_space *isl_point_get_space(
536 __isl_keep isl_point *pnt);
538 The identifiers or names of the individual dimensions may be set or read off
539 using the following functions.
541 #include <isl/space.h>
542 __isl_give isl_space *isl_space_set_dim_id(
543 __isl_take isl_space *space,
544 enum isl_dim_type type, unsigned pos,
545 __isl_take isl_id *id);
546 int isl_space_has_dim_id(__isl_keep isl_space *space,
547 enum isl_dim_type type, unsigned pos);
548 __isl_give isl_id *isl_space_get_dim_id(
549 __isl_keep isl_space *space,
550 enum isl_dim_type type, unsigned pos);
551 __isl_give isl_space *isl_space_set_dim_name(__isl_take isl_space *space,
552 enum isl_dim_type type, unsigned pos,
553 __isl_keep const char *name);
554 __isl_keep const char *isl_space_get_dim_name(__isl_keep isl_space *space,
555 enum isl_dim_type type, unsigned pos);
557 Note that C<isl_space_get_name> returns a pointer to some internal
558 data structure, so the result can only be used while the
559 corresponding C<isl_space> is alive.
560 Also note that every function that operates on two sets or relations
561 requires that both arguments have the same parameters. This also
562 means that if one of the arguments has named parameters, then the
563 other needs to have named parameters too and the names need to match.
564 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
565 arguments may have different parameters (as long as they are named),
566 in which case the result will have as parameters the union of the parameters of
569 Given the identifier of a dimension (typically a parameter),
570 its position can be obtained from the following function.
572 #include <isl/space.h>
573 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
574 enum isl_dim_type type, __isl_keep isl_id *id);
576 The identifiers or names of entire spaces may be set or read off
577 using the following functions.
579 #include <isl/space.h>
580 __isl_give isl_space *isl_space_set_tuple_id(
581 __isl_take isl_space *space,
582 enum isl_dim_type type, __isl_take isl_id *id);
583 __isl_give isl_space *isl_space_reset_tuple_id(
584 __isl_take isl_space *space, enum isl_dim_type type);
585 int isl_space_has_tuple_id(__isl_keep isl_space *space,
586 enum isl_dim_type type);
587 __isl_give isl_id *isl_space_get_tuple_id(
588 __isl_keep isl_space *space, enum isl_dim_type type);
589 __isl_give isl_space *isl_space_set_tuple_name(
590 __isl_take isl_space *space,
591 enum isl_dim_type type, const char *s);
592 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
593 enum isl_dim_type type);
595 The C<dim> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
596 or C<isl_dim_set>. As with C<isl_space_get_name>,
597 the C<isl_space_get_tuple_name> function returns a pointer to some internal
599 Binary operations require the corresponding spaces of their arguments
600 to have the same name.
602 Spaces can be nested. In particular, the domain of a set or
603 the domain or range of a relation can be a nested relation.
604 The following functions can be used to construct and deconstruct
607 #include <isl/space.h>
608 int isl_space_is_wrapping(__isl_keep isl_space *space);
609 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
610 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
612 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
613 be the space of a set, while that of
614 C<isl_space_wrap> should be the space of a relation.
615 Conversely, the output of C<isl_space_unwrap> is the space
616 of a relation, while that of C<isl_space_wrap> is the space of a set.
618 Spaces can be created from other spaces
619 using the following functions.
621 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
622 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
623 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
624 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
625 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
626 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
627 __isl_take isl_space *right);
628 __isl_give isl_space *isl_space_align_params(
629 __isl_take isl_space *space1, __isl_take isl_space *space2)
630 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
631 enum isl_dim_type type, unsigned pos, unsigned n);
632 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
633 enum isl_dim_type type, unsigned n);
634 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
635 enum isl_dim_type type, unsigned first, unsigned n);
636 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
637 enum isl_dim_type dst_type, unsigned dst_pos,
638 enum isl_dim_type src_type, unsigned src_pos,
640 __isl_give isl_space *isl_space_map_from_set(
641 __isl_take isl_space *space);
642 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
644 Note that if dimensions are added or removed from a space, then
645 the name and the internal structure are lost.
649 A local space is essentially a space with
650 zero or more existentially quantified variables.
651 The local space of a basic set or relation can be obtained
652 using the following functions.
655 __isl_give isl_local_space *isl_basic_set_get_local_space(
656 __isl_keep isl_basic_set *bset);
659 __isl_give isl_local_space *isl_basic_map_get_local_space(
660 __isl_keep isl_basic_map *bmap);
662 A new local space can be created from a space using
664 #include <isl/local_space.h>
665 __isl_give isl_local_space *isl_local_space_from_space(
666 __isl_take isl_space *space);
668 They can be inspected, copied and freed using the following functions.
670 #include <isl/local_space.h>
671 isl_ctx *isl_local_space_get_ctx(
672 __isl_keep isl_local_space *ls);
673 int isl_local_space_dim(__isl_keep isl_local_space *ls,
674 enum isl_dim_type type);
675 const char *isl_local_space_get_dim_name(
676 __isl_keep isl_local_space *ls,
677 enum isl_dim_type type, unsigned pos);
678 __isl_give isl_local_space *isl_local_space_set_dim_name(
679 __isl_take isl_local_space *ls,
680 enum isl_dim_type type, unsigned pos, const char *s);
681 __isl_give isl_space *isl_local_space_get_space(
682 __isl_keep isl_local_space *ls);
683 __isl_give isl_div *isl_local_space_get_div(
684 __isl_keep isl_local_space *ls, int pos);
685 __isl_give isl_local_space *isl_local_space_copy(
686 __isl_keep isl_local_space *ls);
687 void *isl_local_space_free(__isl_take isl_local_space *ls);
689 Two local spaces can be compared using
691 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
692 __isl_keep isl_local_space *ls2);
694 Local spaces can be created from other local spaces
695 using the following functions.
697 __isl_give isl_local_space *isl_local_space_from_domain(
698 __isl_take isl_local_space *ls);
699 __isl_give isl_local_space *isl_local_space_add_dims(
700 __isl_take isl_local_space *ls,
701 enum isl_dim_type type, unsigned n);
702 __isl_give isl_local_space *isl_local_space_insert_dims(
703 __isl_take isl_local_space *ls,
704 enum isl_dim_type type, unsigned first, unsigned n);
705 __isl_give isl_local_space *isl_local_space_drop_dims(
706 __isl_take isl_local_space *ls,
707 enum isl_dim_type type, unsigned first, unsigned n);
709 =head2 Input and Output
711 C<isl> supports its own input/output format, which is similar
712 to the C<Omega> format, but also supports the C<PolyLib> format
717 The C<isl> format is similar to that of C<Omega>, but has a different
718 syntax for describing the parameters and allows for the definition
719 of an existentially quantified variable as the integer division
720 of an affine expression.
721 For example, the set of integers C<i> between C<0> and C<n>
722 such that C<i % 10 <= 6> can be described as
724 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
727 A set or relation can have several disjuncts, separated
728 by the keyword C<or>. Each disjunct is either a conjunction
729 of constraints or a projection (C<exists>) of a conjunction
730 of constraints. The constraints are separated by the keyword
733 =head3 C<PolyLib> format
735 If the represented set is a union, then the first line
736 contains a single number representing the number of disjuncts.
737 Otherwise, a line containing the number C<1> is optional.
739 Each disjunct is represented by a matrix of constraints.
740 The first line contains two numbers representing
741 the number of rows and columns,
742 where the number of rows is equal to the number of constraints
743 and the number of columns is equal to two plus the number of variables.
744 The following lines contain the actual rows of the constraint matrix.
745 In each row, the first column indicates whether the constraint
746 is an equality (C<0>) or inequality (C<1>). The final column
747 corresponds to the constant term.
749 If the set is parametric, then the coefficients of the parameters
750 appear in the last columns before the constant column.
751 The coefficients of any existentially quantified variables appear
752 between those of the set variables and those of the parameters.
754 =head3 Extended C<PolyLib> format
756 The extended C<PolyLib> format is nearly identical to the
757 C<PolyLib> format. The only difference is that the line
758 containing the number of rows and columns of a constraint matrix
759 also contains four additional numbers:
760 the number of output dimensions, the number of input dimensions,
761 the number of local dimensions (i.e., the number of existentially
762 quantified variables) and the number of parameters.
763 For sets, the number of ``output'' dimensions is equal
764 to the number of set dimensions, while the number of ``input''
770 __isl_give isl_basic_set *isl_basic_set_read_from_file(
771 isl_ctx *ctx, FILE *input, int nparam);
772 __isl_give isl_basic_set *isl_basic_set_read_from_str(
773 isl_ctx *ctx, const char *str, int nparam);
774 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
775 FILE *input, int nparam);
776 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
777 const char *str, int nparam);
780 __isl_give isl_basic_map *isl_basic_map_read_from_file(
781 isl_ctx *ctx, FILE *input, int nparam);
782 __isl_give isl_basic_map *isl_basic_map_read_from_str(
783 isl_ctx *ctx, const char *str, int nparam);
784 __isl_give isl_map *isl_map_read_from_file(
785 isl_ctx *ctx, FILE *input, int nparam);
786 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
787 const char *str, int nparam);
789 #include <isl/union_set.h>
790 __isl_give isl_union_set *isl_union_set_read_from_file(
791 isl_ctx *ctx, FILE *input);
792 __isl_give isl_union_set *isl_union_set_read_from_str(
793 isl_ctx *ctx, const char *str);
795 #include <isl/union_map.h>
796 __isl_give isl_union_map *isl_union_map_read_from_file(
797 isl_ctx *ctx, FILE *input);
798 __isl_give isl_union_map *isl_union_map_read_from_str(
799 isl_ctx *ctx, const char *str);
801 The input format is autodetected and may be either the C<PolyLib> format
802 or the C<isl> format.
803 C<nparam> specifies how many of the final columns in
804 the C<PolyLib> format correspond to parameters.
805 If input is given in the C<isl> format, then the number
806 of parameters needs to be equal to C<nparam>.
807 If C<nparam> is negative, then any number of parameters
808 is accepted in the C<isl> format and zero parameters
809 are assumed in the C<PolyLib> format.
813 Before anything can be printed, an C<isl_printer> needs to
816 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
818 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
819 void isl_printer_free(__isl_take isl_printer *printer);
820 __isl_give char *isl_printer_get_str(
821 __isl_keep isl_printer *printer);
823 The behavior of the printer can be modified in various ways
825 __isl_give isl_printer *isl_printer_set_output_format(
826 __isl_take isl_printer *p, int output_format);
827 __isl_give isl_printer *isl_printer_set_indent(
828 __isl_take isl_printer *p, int indent);
829 __isl_give isl_printer *isl_printer_indent(
830 __isl_take isl_printer *p, int indent);
831 __isl_give isl_printer *isl_printer_set_prefix(
832 __isl_take isl_printer *p, const char *prefix);
833 __isl_give isl_printer *isl_printer_set_suffix(
834 __isl_take isl_printer *p, const char *suffix);
836 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
837 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
838 and defaults to C<ISL_FORMAT_ISL>.
839 Each line in the output is indented by C<indent> (set by
840 C<isl_printer_set_indent>) spaces
841 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
842 In the C<PolyLib> format output,
843 the coefficients of the existentially quantified variables
844 appear between those of the set variables and those
846 The function C<isl_printer_indent> increases the indentation
847 by the specified amount (which may be negative).
849 To actually print something, use
852 __isl_give isl_printer *isl_printer_print_basic_set(
853 __isl_take isl_printer *printer,
854 __isl_keep isl_basic_set *bset);
855 __isl_give isl_printer *isl_printer_print_set(
856 __isl_take isl_printer *printer,
857 __isl_keep isl_set *set);
860 __isl_give isl_printer *isl_printer_print_basic_map(
861 __isl_take isl_printer *printer,
862 __isl_keep isl_basic_map *bmap);
863 __isl_give isl_printer *isl_printer_print_map(
864 __isl_take isl_printer *printer,
865 __isl_keep isl_map *map);
867 #include <isl/union_set.h>
868 __isl_give isl_printer *isl_printer_print_union_set(
869 __isl_take isl_printer *p,
870 __isl_keep isl_union_set *uset);
872 #include <isl/union_map.h>
873 __isl_give isl_printer *isl_printer_print_union_map(
874 __isl_take isl_printer *p,
875 __isl_keep isl_union_map *umap);
877 When called on a file printer, the following function flushes
878 the file. When called on a string printer, the buffer is cleared.
880 __isl_give isl_printer *isl_printer_flush(
881 __isl_take isl_printer *p);
883 =head2 Creating New Sets and Relations
885 C<isl> has functions for creating some standard sets and relations.
889 =item * Empty sets and relations
891 __isl_give isl_basic_set *isl_basic_set_empty(
892 __isl_take isl_space *space);
893 __isl_give isl_basic_map *isl_basic_map_empty(
894 __isl_take isl_space *space);
895 __isl_give isl_set *isl_set_empty(
896 __isl_take isl_space *space);
897 __isl_give isl_map *isl_map_empty(
898 __isl_take isl_space *space);
899 __isl_give isl_union_set *isl_union_set_empty(
900 __isl_take isl_space *space);
901 __isl_give isl_union_map *isl_union_map_empty(
902 __isl_take isl_space *space);
904 For C<isl_union_set>s and C<isl_union_map>s, the space
905 is only used to specify the parameters.
907 =item * Universe sets and relations
909 __isl_give isl_basic_set *isl_basic_set_universe(
910 __isl_take isl_space *space);
911 __isl_give isl_basic_map *isl_basic_map_universe(
912 __isl_take isl_space *space);
913 __isl_give isl_set *isl_set_universe(
914 __isl_take isl_space *space);
915 __isl_give isl_map *isl_map_universe(
916 __isl_take isl_space *space);
917 __isl_give isl_union_set *isl_union_set_universe(
918 __isl_take isl_union_set *uset);
919 __isl_give isl_union_map *isl_union_map_universe(
920 __isl_take isl_union_map *umap);
922 The sets and relations constructed by the functions above
923 contain all integer values, while those constructed by the
924 functions below only contain non-negative values.
926 __isl_give isl_basic_set *isl_basic_set_nat_universe(
927 __isl_take isl_space *space);
928 __isl_give isl_basic_map *isl_basic_map_nat_universe(
929 __isl_take isl_space *space);
930 __isl_give isl_set *isl_set_nat_universe(
931 __isl_take isl_space *space);
932 __isl_give isl_map *isl_map_nat_universe(
933 __isl_take isl_space *space);
935 =item * Identity relations
937 __isl_give isl_basic_map *isl_basic_map_identity(
938 __isl_take isl_space *space);
939 __isl_give isl_map *isl_map_identity(
940 __isl_take isl_space *space);
942 The number of input and output dimensions in C<space> needs
945 =item * Lexicographic order
947 __isl_give isl_map *isl_map_lex_lt(
948 __isl_take isl_space *set_space);
949 __isl_give isl_map *isl_map_lex_le(
950 __isl_take isl_space *set_space);
951 __isl_give isl_map *isl_map_lex_gt(
952 __isl_take isl_space *set_space);
953 __isl_give isl_map *isl_map_lex_ge(
954 __isl_take isl_space *set_space);
955 __isl_give isl_map *isl_map_lex_lt_first(
956 __isl_take isl_space *space, unsigned n);
957 __isl_give isl_map *isl_map_lex_le_first(
958 __isl_take isl_space *space, unsigned n);
959 __isl_give isl_map *isl_map_lex_gt_first(
960 __isl_take isl_space *space, unsigned n);
961 __isl_give isl_map *isl_map_lex_ge_first(
962 __isl_take isl_space *space, unsigned n);
964 The first four functions take a space for a B<set>
965 and return relations that express that the elements in the domain
966 are lexicographically less
967 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
968 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
969 than the elements in the range.
970 The last four functions take a space for a map
971 and return relations that express that the first C<n> dimensions
972 in the domain are lexicographically less
973 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
974 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
975 than the first C<n> dimensions in the range.
979 A basic set or relation can be converted to a set or relation
980 using the following functions.
982 __isl_give isl_set *isl_set_from_basic_set(
983 __isl_take isl_basic_set *bset);
984 __isl_give isl_map *isl_map_from_basic_map(
985 __isl_take isl_basic_map *bmap);
987 Sets and relations can be converted to union sets and relations
988 using the following functions.
990 __isl_give isl_union_map *isl_union_map_from_map(
991 __isl_take isl_map *map);
992 __isl_give isl_union_set *isl_union_set_from_set(
993 __isl_take isl_set *set);
995 The inverse conversions below can only be used if the input
996 union set or relation is known to contain elements in exactly one
999 __isl_give isl_set *isl_set_from_union_set(
1000 __isl_take isl_union_set *uset);
1001 __isl_give isl_map *isl_map_from_union_map(
1002 __isl_take isl_union_map *umap);
1004 Sets and relations can be copied and freed again using the following
1007 __isl_give isl_basic_set *isl_basic_set_copy(
1008 __isl_keep isl_basic_set *bset);
1009 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1010 __isl_give isl_union_set *isl_union_set_copy(
1011 __isl_keep isl_union_set *uset);
1012 __isl_give isl_basic_map *isl_basic_map_copy(
1013 __isl_keep isl_basic_map *bmap);
1014 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1015 __isl_give isl_union_map *isl_union_map_copy(
1016 __isl_keep isl_union_map *umap);
1017 void isl_basic_set_free(__isl_take isl_basic_set *bset);
1018 void isl_set_free(__isl_take isl_set *set);
1019 void *isl_union_set_free(__isl_take isl_union_set *uset);
1020 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
1021 void isl_map_free(__isl_take isl_map *map);
1022 void *isl_union_map_free(__isl_take isl_union_map *umap);
1024 Other sets and relations can be constructed by starting
1025 from a universe set or relation, adding equality and/or
1026 inequality constraints and then projecting out the
1027 existentially quantified variables, if any.
1028 Constraints can be constructed, manipulated and
1029 added to (or removed from) (basic) sets and relations
1030 using the following functions.
1032 #include <isl/constraint.h>
1033 __isl_give isl_constraint *isl_equality_alloc(
1034 __isl_take isl_space *space);
1035 __isl_give isl_constraint *isl_inequality_alloc(
1036 __isl_take isl_space *space);
1037 __isl_give isl_constraint *isl_constraint_set_constant(
1038 __isl_take isl_constraint *constraint, isl_int v);
1039 __isl_give isl_constraint *isl_constraint_set_constant_si(
1040 __isl_take isl_constraint *constraint, int v);
1041 __isl_give isl_constraint *isl_constraint_set_coefficient(
1042 __isl_take isl_constraint *constraint,
1043 enum isl_dim_type type, int pos, isl_int v);
1044 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1045 __isl_take isl_constraint *constraint,
1046 enum isl_dim_type type, int pos, int v);
1047 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1048 __isl_take isl_basic_map *bmap,
1049 __isl_take isl_constraint *constraint);
1050 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1051 __isl_take isl_basic_set *bset,
1052 __isl_take isl_constraint *constraint);
1053 __isl_give isl_map *isl_map_add_constraint(
1054 __isl_take isl_map *map,
1055 __isl_take isl_constraint *constraint);
1056 __isl_give isl_set *isl_set_add_constraint(
1057 __isl_take isl_set *set,
1058 __isl_take isl_constraint *constraint);
1059 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1060 __isl_take isl_basic_set *bset,
1061 __isl_take isl_constraint *constraint);
1063 For example, to create a set containing the even integers
1064 between 10 and 42, you would use the following code.
1069 isl_basic_set *bset;
1072 space = isl_space_set_alloc(ctx, 0, 2);
1073 bset = isl_basic_set_universe(isl_space_copy(space));
1075 c = isl_equality_alloc(isl_space_copy(space));
1076 isl_int_set_si(v, -1);
1077 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
1078 isl_int_set_si(v, 2);
1079 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
1080 bset = isl_basic_set_add_constraint(bset, c);
1082 c = isl_inequality_alloc(isl_space_copy(space));
1083 isl_int_set_si(v, -10);
1084 isl_constraint_set_constant(c, v);
1085 isl_int_set_si(v, 1);
1086 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
1087 bset = isl_basic_set_add_constraint(bset, c);
1089 c = isl_inequality_alloc(space);
1090 isl_int_set_si(v, 42);
1091 isl_constraint_set_constant(c, v);
1092 isl_int_set_si(v, -1);
1093 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
1094 bset = isl_basic_set_add_constraint(bset, c);
1096 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1102 isl_basic_set *bset;
1103 bset = isl_basic_set_read_from_str(ctx,
1104 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
1106 A basic set or relation can also be constructed from two matrices
1107 describing the equalities and the inequalities.
1109 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1110 __isl_take isl_space *space,
1111 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1112 enum isl_dim_type c1,
1113 enum isl_dim_type c2, enum isl_dim_type c3,
1114 enum isl_dim_type c4);
1115 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1116 __isl_take isl_space *space,
1117 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1118 enum isl_dim_type c1,
1119 enum isl_dim_type c2, enum isl_dim_type c3,
1120 enum isl_dim_type c4, enum isl_dim_type c5);
1122 The C<isl_dim_type> arguments indicate the order in which
1123 different kinds of variables appear in the input matrices
1124 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1125 C<isl_dim_set> and C<isl_dim_div> for sets and
1126 of C<isl_dim_cst>, C<isl_dim_param>,
1127 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1129 A (basic) relation can also be constructed from a (piecewise) affine expression
1130 or a list of affine expressions (See L<"Piecewise Quasi Affine Expressions">).
1132 __isl_give isl_basic_map *isl_basic_map_from_aff(
1133 __isl_take isl_aff *aff);
1134 __isl_give isl_map *isl_map_from_pw_aff(
1135 __isl_take isl_pw_aff *pwaff);
1136 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1137 __isl_take isl_space *domain_space,
1138 __isl_take isl_aff_list *list);
1140 The C<domain_dim> argument describes the domain of the resulting
1141 basic relation. It is required because the C<list> may consist
1142 of zero affine expressions.
1144 =head2 Inspecting Sets and Relations
1146 Usually, the user should not have to care about the actual constraints
1147 of the sets and maps, but should instead apply the abstract operations
1148 explained in the following sections.
1149 Occasionally, however, it may be required to inspect the individual
1150 coefficients of the constraints. This section explains how to do so.
1151 In these cases, it may also be useful to have C<isl> compute
1152 an explicit representation of the existentially quantified variables.
1154 __isl_give isl_set *isl_set_compute_divs(
1155 __isl_take isl_set *set);
1156 __isl_give isl_map *isl_map_compute_divs(
1157 __isl_take isl_map *map);
1158 __isl_give isl_union_set *isl_union_set_compute_divs(
1159 __isl_take isl_union_set *uset);
1160 __isl_give isl_union_map *isl_union_map_compute_divs(
1161 __isl_take isl_union_map *umap);
1163 This explicit representation defines the existentially quantified
1164 variables as integer divisions of the other variables, possibly
1165 including earlier existentially quantified variables.
1166 An explicitly represented existentially quantified variable therefore
1167 has a unique value when the values of the other variables are known.
1168 If, furthermore, the same existentials, i.e., existentials
1169 with the same explicit representations, should appear in the
1170 same order in each of the disjuncts of a set or map, then the user should call
1171 either of the following functions.
1173 __isl_give isl_set *isl_set_align_divs(
1174 __isl_take isl_set *set);
1175 __isl_give isl_map *isl_map_align_divs(
1176 __isl_take isl_map *map);
1178 Alternatively, the existentially quantified variables can be removed
1179 using the following functions, which compute an overapproximation.
1181 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1182 __isl_take isl_basic_set *bset);
1183 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1184 __isl_take isl_basic_map *bmap);
1185 __isl_give isl_set *isl_set_remove_divs(
1186 __isl_take isl_set *set);
1187 __isl_give isl_map *isl_map_remove_divs(
1188 __isl_take isl_map *map);
1190 To iterate over all the sets or maps in a union set or map, use
1192 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1193 int (*fn)(__isl_take isl_set *set, void *user),
1195 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1196 int (*fn)(__isl_take isl_map *map, void *user),
1199 The number of sets or maps in a union set or map can be obtained
1202 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1203 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1205 To extract the set or map in a given space from a union, use
1207 __isl_give isl_set *isl_union_set_extract_set(
1208 __isl_keep isl_union_set *uset,
1209 __isl_take isl_space *space);
1210 __isl_give isl_map *isl_union_map_extract_map(
1211 __isl_keep isl_union_map *umap,
1212 __isl_take isl_space *space);
1214 To iterate over all the basic sets or maps in a set or map, use
1216 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1217 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1219 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1220 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1223 The callback function C<fn> should return 0 if successful and
1224 -1 if an error occurs. In the latter case, or if any other error
1225 occurs, the above functions will return -1.
1227 It should be noted that C<isl> does not guarantee that
1228 the basic sets or maps passed to C<fn> are disjoint.
1229 If this is required, then the user should call one of
1230 the following functions first.
1232 __isl_give isl_set *isl_set_make_disjoint(
1233 __isl_take isl_set *set);
1234 __isl_give isl_map *isl_map_make_disjoint(
1235 __isl_take isl_map *map);
1237 The number of basic sets in a set can be obtained
1240 int isl_set_n_basic_set(__isl_keep isl_set *set);
1242 To iterate over the constraints of a basic set or map, use
1244 #include <isl/constraint.h>
1246 int isl_basic_map_foreach_constraint(
1247 __isl_keep isl_basic_map *bmap,
1248 int (*fn)(__isl_take isl_constraint *c, void *user),
1250 void *isl_constraint_free(__isl_take isl_constraint *c);
1252 Again, the callback function C<fn> should return 0 if successful and
1253 -1 if an error occurs. In the latter case, or if any other error
1254 occurs, the above functions will return -1.
1255 The constraint C<c> represents either an equality or an inequality.
1256 Use the following function to find out whether a constraint
1257 represents an equality. If not, it represents an inequality.
1259 int isl_constraint_is_equality(
1260 __isl_keep isl_constraint *constraint);
1262 The coefficients of the constraints can be inspected using
1263 the following functions.
1265 void isl_constraint_get_constant(
1266 __isl_keep isl_constraint *constraint, isl_int *v);
1267 void isl_constraint_get_coefficient(
1268 __isl_keep isl_constraint *constraint,
1269 enum isl_dim_type type, int pos, isl_int *v);
1270 int isl_constraint_involves_dims(
1271 __isl_keep isl_constraint *constraint,
1272 enum isl_dim_type type, unsigned first, unsigned n);
1274 The explicit representations of the existentially quantified
1275 variables can be inspected using the following functions.
1276 Note that the user is only allowed to use these functions
1277 if the inspected set or map is the result of a call
1278 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1280 __isl_give isl_div *isl_constraint_div(
1281 __isl_keep isl_constraint *constraint, int pos);
1282 isl_ctx *isl_div_get_ctx(__isl_keep isl_div *div);
1283 void isl_div_get_constant(__isl_keep isl_div *div,
1285 void isl_div_get_denominator(__isl_keep isl_div *div,
1287 void isl_div_get_coefficient(__isl_keep isl_div *div,
1288 enum isl_dim_type type, int pos, isl_int *v);
1290 To obtain the constraints of a basic set or map in matrix
1291 form, use the following functions.
1293 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1294 __isl_keep isl_basic_set *bset,
1295 enum isl_dim_type c1, enum isl_dim_type c2,
1296 enum isl_dim_type c3, enum isl_dim_type c4);
1297 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1298 __isl_keep isl_basic_set *bset,
1299 enum isl_dim_type c1, enum isl_dim_type c2,
1300 enum isl_dim_type c3, enum isl_dim_type c4);
1301 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1302 __isl_keep isl_basic_map *bmap,
1303 enum isl_dim_type c1,
1304 enum isl_dim_type c2, enum isl_dim_type c3,
1305 enum isl_dim_type c4, enum isl_dim_type c5);
1306 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1307 __isl_keep isl_basic_map *bmap,
1308 enum isl_dim_type c1,
1309 enum isl_dim_type c2, enum isl_dim_type c3,
1310 enum isl_dim_type c4, enum isl_dim_type c5);
1312 The C<isl_dim_type> arguments dictate the order in which
1313 different kinds of variables appear in the resulting matrix
1314 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1315 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1317 The number of parameters, input, output or set dimensions can
1318 be obtained using the following functions.
1320 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1321 enum isl_dim_type type);
1322 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1323 enum isl_dim_type type);
1324 unsigned isl_set_dim(__isl_keep isl_set *set,
1325 enum isl_dim_type type);
1326 unsigned isl_map_dim(__isl_keep isl_map *map,
1327 enum isl_dim_type type);
1329 To check whether the description of a set or relation depends
1330 on one or more given dimensions, it is not necessary to iterate over all
1331 constraints. Instead the following functions can be used.
1333 int isl_basic_set_involves_dims(
1334 __isl_keep isl_basic_set *bset,
1335 enum isl_dim_type type, unsigned first, unsigned n);
1336 int isl_set_involves_dims(__isl_keep isl_set *set,
1337 enum isl_dim_type type, unsigned first, unsigned n);
1338 int isl_basic_map_involves_dims(
1339 __isl_keep isl_basic_map *bmap,
1340 enum isl_dim_type type, unsigned first, unsigned n);
1341 int isl_map_involves_dims(__isl_keep isl_map *map,
1342 enum isl_dim_type type, unsigned first, unsigned n);
1344 Similarly, the following functions can be used to check whether
1345 a given dimension is involved in any lower or upper bound.
1347 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1348 enum isl_dim_type type, unsigned pos);
1349 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1350 enum isl_dim_type type, unsigned pos);
1352 The identifiers or names of the domain and range spaces of a set
1353 or relation can be read off or set using the following functions.
1355 __isl_give isl_set *isl_set_set_tuple_id(
1356 __isl_take isl_set *set, __isl_take isl_id *id);
1357 __isl_give isl_set *isl_set_reset_tuple_id(
1358 __isl_take isl_set *set);
1359 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1360 __isl_give isl_id *isl_set_get_tuple_id(
1361 __isl_keep isl_set *set);
1362 __isl_give isl_map *isl_map_set_tuple_id(
1363 __isl_take isl_map *map, enum isl_dim_type type,
1364 __isl_take isl_id *id);
1365 __isl_give isl_map *isl_map_reset_tuple_id(
1366 __isl_take isl_map *map, enum isl_dim_type type);
1367 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1368 enum isl_dim_type type);
1369 __isl_give isl_id *isl_map_get_tuple_id(
1370 __isl_keep isl_map *map, enum isl_dim_type type);
1372 const char *isl_basic_set_get_tuple_name(
1373 __isl_keep isl_basic_set *bset);
1374 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1375 __isl_take isl_basic_set *set, const char *s);
1376 const char *isl_set_get_tuple_name(
1377 __isl_keep isl_set *set);
1378 const char *isl_basic_map_get_tuple_name(
1379 __isl_keep isl_basic_map *bmap,
1380 enum isl_dim_type type);
1381 const char *isl_map_get_tuple_name(
1382 __isl_keep isl_map *map,
1383 enum isl_dim_type type);
1385 As with C<isl_space_get_tuple_name>, the value returned points to
1386 an internal data structure.
1387 The identifiers, positions or names of individual dimensions can be
1388 read off using the following functions.
1390 __isl_give isl_set *isl_set_set_dim_id(
1391 __isl_take isl_set *set, enum isl_dim_type type,
1392 unsigned pos, __isl_take isl_id *id);
1393 int isl_set_has_dim_id(__isl_keep isl_set *set,
1394 enum isl_dim_type type, unsigned pos);
1395 __isl_give isl_id *isl_set_get_dim_id(
1396 __isl_keep isl_set *set, enum isl_dim_type type,
1398 __isl_give isl_map *isl_map_set_dim_id(
1399 __isl_take isl_map *map, enum isl_dim_type type,
1400 unsigned pos, __isl_take isl_id *id);
1401 int isl_map_has_dim_id(__isl_keep isl_map *map,
1402 enum isl_dim_type type, unsigned pos);
1403 __isl_give isl_id *isl_map_get_dim_id(
1404 __isl_keep isl_map *map, enum isl_dim_type type,
1407 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1408 enum isl_dim_type type, __isl_keep isl_id *id);
1409 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1410 enum isl_dim_type type, __isl_keep isl_id *id);
1412 const char *isl_constraint_get_dim_name(
1413 __isl_keep isl_constraint *constraint,
1414 enum isl_dim_type type, unsigned pos);
1415 const char *isl_basic_set_get_dim_name(
1416 __isl_keep isl_basic_set *bset,
1417 enum isl_dim_type type, unsigned pos);
1418 const char *isl_set_get_dim_name(
1419 __isl_keep isl_set *set,
1420 enum isl_dim_type type, unsigned pos);
1421 const char *isl_basic_map_get_dim_name(
1422 __isl_keep isl_basic_map *bmap,
1423 enum isl_dim_type type, unsigned pos);
1424 const char *isl_map_get_dim_name(
1425 __isl_keep isl_map *map,
1426 enum isl_dim_type type, unsigned pos);
1428 These functions are mostly useful to obtain the identifiers, positions
1429 or names of the parameters. Identifiers of individual dimensions are
1430 essentially only useful for printing. They are ignored by all other
1431 operations and may not be preserved across those operations.
1435 =head3 Unary Properties
1441 The following functions test whether the given set or relation
1442 contains any integer points. The ``plain'' variants do not perform
1443 any computations, but simply check if the given set or relation
1444 is already known to be empty.
1446 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1447 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1448 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1449 int isl_set_is_empty(__isl_keep isl_set *set);
1450 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1451 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1452 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1453 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1454 int isl_map_is_empty(__isl_keep isl_map *map);
1455 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1457 =item * Universality
1459 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1460 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1461 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1463 =item * Single-valuedness
1465 int isl_map_is_single_valued(__isl_keep isl_map *map);
1466 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1470 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1471 int isl_map_is_injective(__isl_keep isl_map *map);
1472 int isl_union_map_plain_is_injective(
1473 __isl_keep isl_union_map *umap);
1474 int isl_union_map_is_injective(
1475 __isl_keep isl_union_map *umap);
1479 int isl_map_is_bijective(__isl_keep isl_map *map);
1480 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1484 int isl_basic_map_plain_is_fixed(
1485 __isl_keep isl_basic_map *bmap,
1486 enum isl_dim_type type, unsigned pos,
1488 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1489 enum isl_dim_type type, unsigned pos,
1492 Check if the relation obviously lies on a hyperplane where the given dimension
1493 has a fixed value and if so, return that value in C<*val>.
1497 The following functions check whether the domain of the given
1498 (basic) set is a wrapped relation.
1500 int isl_basic_set_is_wrapping(
1501 __isl_keep isl_basic_set *bset);
1502 int isl_set_is_wrapping(__isl_keep isl_set *set);
1504 =item * Internal Product
1506 int isl_basic_map_can_zip(
1507 __isl_keep isl_basic_map *bmap);
1508 int isl_map_can_zip(__isl_keep isl_map *map);
1510 Check whether the product of domain and range of the given relation
1512 i.e., whether both domain and range are nested relations.
1516 =head3 Binary Properties
1522 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1523 __isl_keep isl_set *set2);
1524 int isl_set_is_equal(__isl_keep isl_set *set1,
1525 __isl_keep isl_set *set2);
1526 int isl_union_set_is_equal(
1527 __isl_keep isl_union_set *uset1,
1528 __isl_keep isl_union_set *uset2);
1529 int isl_basic_map_is_equal(
1530 __isl_keep isl_basic_map *bmap1,
1531 __isl_keep isl_basic_map *bmap2);
1532 int isl_map_is_equal(__isl_keep isl_map *map1,
1533 __isl_keep isl_map *map2);
1534 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1535 __isl_keep isl_map *map2);
1536 int isl_union_map_is_equal(
1537 __isl_keep isl_union_map *umap1,
1538 __isl_keep isl_union_map *umap2);
1540 =item * Disjointness
1542 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1543 __isl_keep isl_set *set2);
1547 int isl_set_is_subset(__isl_keep isl_set *set1,
1548 __isl_keep isl_set *set2);
1549 int isl_set_is_strict_subset(
1550 __isl_keep isl_set *set1,
1551 __isl_keep isl_set *set2);
1552 int isl_union_set_is_subset(
1553 __isl_keep isl_union_set *uset1,
1554 __isl_keep isl_union_set *uset2);
1555 int isl_union_set_is_strict_subset(
1556 __isl_keep isl_union_set *uset1,
1557 __isl_keep isl_union_set *uset2);
1558 int isl_basic_map_is_subset(
1559 __isl_keep isl_basic_map *bmap1,
1560 __isl_keep isl_basic_map *bmap2);
1561 int isl_basic_map_is_strict_subset(
1562 __isl_keep isl_basic_map *bmap1,
1563 __isl_keep isl_basic_map *bmap2);
1564 int isl_map_is_subset(
1565 __isl_keep isl_map *map1,
1566 __isl_keep isl_map *map2);
1567 int isl_map_is_strict_subset(
1568 __isl_keep isl_map *map1,
1569 __isl_keep isl_map *map2);
1570 int isl_union_map_is_subset(
1571 __isl_keep isl_union_map *umap1,
1572 __isl_keep isl_union_map *umap2);
1573 int isl_union_map_is_strict_subset(
1574 __isl_keep isl_union_map *umap1,
1575 __isl_keep isl_union_map *umap2);
1579 =head2 Unary Operations
1585 __isl_give isl_set *isl_set_complement(
1586 __isl_take isl_set *set);
1590 __isl_give isl_basic_map *isl_basic_map_reverse(
1591 __isl_take isl_basic_map *bmap);
1592 __isl_give isl_map *isl_map_reverse(
1593 __isl_take isl_map *map);
1594 __isl_give isl_union_map *isl_union_map_reverse(
1595 __isl_take isl_union_map *umap);
1599 __isl_give isl_basic_set *isl_basic_set_project_out(
1600 __isl_take isl_basic_set *bset,
1601 enum isl_dim_type type, unsigned first, unsigned n);
1602 __isl_give isl_basic_map *isl_basic_map_project_out(
1603 __isl_take isl_basic_map *bmap,
1604 enum isl_dim_type type, unsigned first, unsigned n);
1605 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1606 enum isl_dim_type type, unsigned first, unsigned n);
1607 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1608 enum isl_dim_type type, unsigned first, unsigned n);
1609 __isl_give isl_basic_set *isl_basic_map_domain(
1610 __isl_take isl_basic_map *bmap);
1611 __isl_give isl_basic_set *isl_basic_map_range(
1612 __isl_take isl_basic_map *bmap);
1613 __isl_give isl_set *isl_map_domain(
1614 __isl_take isl_map *bmap);
1615 __isl_give isl_set *isl_map_range(
1616 __isl_take isl_map *map);
1617 __isl_give isl_union_set *isl_union_map_domain(
1618 __isl_take isl_union_map *umap);
1619 __isl_give isl_union_set *isl_union_map_range(
1620 __isl_take isl_union_map *umap);
1622 __isl_give isl_basic_map *isl_basic_map_domain_map(
1623 __isl_take isl_basic_map *bmap);
1624 __isl_give isl_basic_map *isl_basic_map_range_map(
1625 __isl_take isl_basic_map *bmap);
1626 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1627 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1628 __isl_give isl_union_map *isl_union_map_domain_map(
1629 __isl_take isl_union_map *umap);
1630 __isl_give isl_union_map *isl_union_map_range_map(
1631 __isl_take isl_union_map *umap);
1633 The functions above construct a (basic, regular or union) relation
1634 that maps (a wrapped version of) the input relation to its domain or range.
1638 __isl_give isl_set *isl_set_eliminate(
1639 __isl_take isl_set *set, enum isl_dim_type type,
1640 unsigned first, unsigned n);
1642 Eliminate the coefficients for the given dimensions from the constraints,
1643 without removing the dimensions.
1647 __isl_give isl_basic_set *isl_basic_set_fix(
1648 __isl_take isl_basic_set *bset,
1649 enum isl_dim_type type, unsigned pos,
1651 __isl_give isl_basic_set *isl_basic_set_fix_si(
1652 __isl_take isl_basic_set *bset,
1653 enum isl_dim_type type, unsigned pos, int value);
1654 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1655 enum isl_dim_type type, unsigned pos,
1657 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1658 enum isl_dim_type type, unsigned pos, int value);
1659 __isl_give isl_basic_map *isl_basic_map_fix_si(
1660 __isl_take isl_basic_map *bmap,
1661 enum isl_dim_type type, unsigned pos, int value);
1662 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1663 enum isl_dim_type type, unsigned pos, int value);
1665 Intersect the set or relation with the hyperplane where the given
1666 dimension has the fixed given value.
1668 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1669 enum isl_dim_type type1, int pos1,
1670 enum isl_dim_type type2, int pos2);
1671 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1672 enum isl_dim_type type1, int pos1,
1673 enum isl_dim_type type2, int pos2);
1675 Intersect the set or relation with the hyperplane where the given
1676 dimensions are equal to each other.
1678 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
1679 enum isl_dim_type type1, int pos1,
1680 enum isl_dim_type type2, int pos2);
1682 Intersect the relation with the hyperplane where the given
1683 dimensions have opposite values.
1687 __isl_give isl_map *isl_set_identity(
1688 __isl_take isl_set *set);
1689 __isl_give isl_union_map *isl_union_set_identity(
1690 __isl_take isl_union_set *uset);
1692 Construct an identity relation on the given (union) set.
1696 __isl_give isl_basic_set *isl_basic_map_deltas(
1697 __isl_take isl_basic_map *bmap);
1698 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1699 __isl_give isl_union_set *isl_union_map_deltas(
1700 __isl_take isl_union_map *umap);
1702 These functions return a (basic) set containing the differences
1703 between image elements and corresponding domain elements in the input.
1705 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1706 __isl_take isl_basic_map *bmap);
1707 __isl_give isl_map *isl_map_deltas_map(
1708 __isl_take isl_map *map);
1709 __isl_give isl_union_map *isl_union_map_deltas_map(
1710 __isl_take isl_union_map *umap);
1712 The functions above construct a (basic, regular or union) relation
1713 that maps (a wrapped version of) the input relation to its delta set.
1717 Simplify the representation of a set or relation by trying
1718 to combine pairs of basic sets or relations into a single
1719 basic set or relation.
1721 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1722 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1723 __isl_give isl_union_set *isl_union_set_coalesce(
1724 __isl_take isl_union_set *uset);
1725 __isl_give isl_union_map *isl_union_map_coalesce(
1726 __isl_take isl_union_map *umap);
1728 =item * Detecting equalities
1730 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1731 __isl_take isl_basic_set *bset);
1732 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1733 __isl_take isl_basic_map *bmap);
1734 __isl_give isl_set *isl_set_detect_equalities(
1735 __isl_take isl_set *set);
1736 __isl_give isl_map *isl_map_detect_equalities(
1737 __isl_take isl_map *map);
1738 __isl_give isl_union_set *isl_union_set_detect_equalities(
1739 __isl_take isl_union_set *uset);
1740 __isl_give isl_union_map *isl_union_map_detect_equalities(
1741 __isl_take isl_union_map *umap);
1743 Simplify the representation of a set or relation by detecting implicit
1746 =item * Removing redundant constraints
1748 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1749 __isl_take isl_basic_set *bset);
1750 __isl_give isl_set *isl_set_remove_redundancies(
1751 __isl_take isl_set *set);
1752 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1753 __isl_take isl_basic_map *bmap);
1754 __isl_give isl_map *isl_map_remove_redundancies(
1755 __isl_take isl_map *map);
1759 __isl_give isl_basic_set *isl_set_convex_hull(
1760 __isl_take isl_set *set);
1761 __isl_give isl_basic_map *isl_map_convex_hull(
1762 __isl_take isl_map *map);
1764 If the input set or relation has any existentially quantified
1765 variables, then the result of these operations is currently undefined.
1769 __isl_give isl_basic_set *isl_set_simple_hull(
1770 __isl_take isl_set *set);
1771 __isl_give isl_basic_map *isl_map_simple_hull(
1772 __isl_take isl_map *map);
1773 __isl_give isl_union_map *isl_union_map_simple_hull(
1774 __isl_take isl_union_map *umap);
1776 These functions compute a single basic set or relation
1777 that contains the whole input set or relation.
1778 In particular, the output is described by translates
1779 of the constraints describing the basic sets or relations in the input.
1783 (See \autoref{s:simple hull}.)
1789 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1790 __isl_take isl_basic_set *bset);
1791 __isl_give isl_basic_set *isl_set_affine_hull(
1792 __isl_take isl_set *set);
1793 __isl_give isl_union_set *isl_union_set_affine_hull(
1794 __isl_take isl_union_set *uset);
1795 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1796 __isl_take isl_basic_map *bmap);
1797 __isl_give isl_basic_map *isl_map_affine_hull(
1798 __isl_take isl_map *map);
1799 __isl_give isl_union_map *isl_union_map_affine_hull(
1800 __isl_take isl_union_map *umap);
1802 In case of union sets and relations, the affine hull is computed
1805 =item * Polyhedral hull
1807 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1808 __isl_take isl_set *set);
1809 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1810 __isl_take isl_map *map);
1811 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1812 __isl_take isl_union_set *uset);
1813 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1814 __isl_take isl_union_map *umap);
1816 These functions compute a single basic set or relation
1817 not involving any existentially quantified variables
1818 that contains the whole input set or relation.
1819 In case of union sets and relations, the polyhedral hull is computed
1822 =item * Optimization
1824 #include <isl/ilp.h>
1825 enum isl_lp_result isl_basic_set_max(
1826 __isl_keep isl_basic_set *bset,
1827 __isl_keep isl_aff *obj, isl_int *opt)
1828 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
1829 __isl_keep isl_aff *obj, isl_int *opt);
1830 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
1831 __isl_keep isl_aff *obj, isl_int *opt);
1833 Compute the minimum or maximum of the integer affine expression C<obj>
1834 over the points in C<set>, returning the result in C<opt>.
1835 The return value may be one of C<isl_lp_error>,
1836 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
1838 =item * Parametric optimization
1840 __isl_give isl_pw_aff *isl_set_dim_min(
1841 __isl_take isl_set *set, int pos);
1842 __isl_give isl_pw_aff *isl_set_dim_max(
1843 __isl_take isl_set *set, int pos);
1845 Compute the minimum or maximum of the given set dimension as a function of the
1846 parameters, but independently of the other set dimensions.
1847 For lexicographic optimization, see L<"Lexicographic Optimization">.
1851 The following functions compute either the set of (rational) coefficient
1852 values of valid constraints for the given set or the set of (rational)
1853 values satisfying the constraints with coefficients from the given set.
1854 Internally, these two sets of functions perform essentially the
1855 same operations, except that the set of coefficients is assumed to
1856 be a cone, while the set of values may be any polyhedron.
1857 The current implementation is based on the Farkas lemma and
1858 Fourier-Motzkin elimination, but this may change or be made optional
1859 in future. In particular, future implementations may use different
1860 dualization algorithms or skip the elimination step.
1862 __isl_give isl_basic_set *isl_basic_set_coefficients(
1863 __isl_take isl_basic_set *bset);
1864 __isl_give isl_basic_set *isl_set_coefficients(
1865 __isl_take isl_set *set);
1866 __isl_give isl_union_set *isl_union_set_coefficients(
1867 __isl_take isl_union_set *bset);
1868 __isl_give isl_basic_set *isl_basic_set_solutions(
1869 __isl_take isl_basic_set *bset);
1870 __isl_give isl_basic_set *isl_set_solutions(
1871 __isl_take isl_set *set);
1872 __isl_give isl_union_set *isl_union_set_solutions(
1873 __isl_take isl_union_set *bset);
1877 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1879 __isl_give isl_union_map *isl_union_map_power(
1880 __isl_take isl_union_map *umap, int *exact);
1882 Compute a parametric representation for all positive powers I<k> of C<map>.
1883 The result maps I<k> to a nested relation corresponding to the
1884 I<k>th power of C<map>.
1885 The result may be an overapproximation. If the result is known to be exact,
1886 then C<*exact> is set to C<1>.
1888 =item * Transitive closure
1890 __isl_give isl_map *isl_map_transitive_closure(
1891 __isl_take isl_map *map, int *exact);
1892 __isl_give isl_union_map *isl_union_map_transitive_closure(
1893 __isl_take isl_union_map *umap, int *exact);
1895 Compute the transitive closure of C<map>.
1896 The result may be an overapproximation. If the result is known to be exact,
1897 then C<*exact> is set to C<1>.
1899 =item * Reaching path lengths
1901 __isl_give isl_map *isl_map_reaching_path_lengths(
1902 __isl_take isl_map *map, int *exact);
1904 Compute a relation that maps each element in the range of C<map>
1905 to the lengths of all paths composed of edges in C<map> that
1906 end up in the given element.
1907 The result may be an overapproximation. If the result is known to be exact,
1908 then C<*exact> is set to C<1>.
1909 To compute the I<maximal> path length, the resulting relation
1910 should be postprocessed by C<isl_map_lexmax>.
1911 In particular, if the input relation is a dependence relation
1912 (mapping sources to sinks), then the maximal path length corresponds
1913 to the free schedule.
1914 Note, however, that C<isl_map_lexmax> expects the maximum to be
1915 finite, so if the path lengths are unbounded (possibly due to
1916 the overapproximation), then you will get an error message.
1920 __isl_give isl_basic_set *isl_basic_map_wrap(
1921 __isl_take isl_basic_map *bmap);
1922 __isl_give isl_set *isl_map_wrap(
1923 __isl_take isl_map *map);
1924 __isl_give isl_union_set *isl_union_map_wrap(
1925 __isl_take isl_union_map *umap);
1926 __isl_give isl_basic_map *isl_basic_set_unwrap(
1927 __isl_take isl_basic_set *bset);
1928 __isl_give isl_map *isl_set_unwrap(
1929 __isl_take isl_set *set);
1930 __isl_give isl_union_map *isl_union_set_unwrap(
1931 __isl_take isl_union_set *uset);
1935 Remove any internal structure of domain (and range) of the given
1936 set or relation. If there is any such internal structure in the input,
1937 then the name of the space is also removed.
1939 __isl_give isl_basic_set *isl_basic_set_flatten(
1940 __isl_take isl_basic_set *bset);
1941 __isl_give isl_set *isl_set_flatten(
1942 __isl_take isl_set *set);
1943 __isl_give isl_basic_map *isl_basic_map_flatten_range(
1944 __isl_take isl_basic_map *bmap);
1945 __isl_give isl_map *isl_map_flatten_range(
1946 __isl_take isl_map *map);
1947 __isl_give isl_basic_map *isl_basic_map_flatten(
1948 __isl_take isl_basic_map *bmap);
1949 __isl_give isl_map *isl_map_flatten(
1950 __isl_take isl_map *map);
1952 __isl_give isl_map *isl_set_flatten_map(
1953 __isl_take isl_set *set);
1955 The function above constructs a relation
1956 that maps the input set to a flattened version of the set.
1960 Lift the input set to a space with extra dimensions corresponding
1961 to the existentially quantified variables in the input.
1962 In particular, the result lives in a wrapped map where the domain
1963 is the original space and the range corresponds to the original
1964 existentially quantified variables.
1966 __isl_give isl_basic_set *isl_basic_set_lift(
1967 __isl_take isl_basic_set *bset);
1968 __isl_give isl_set *isl_set_lift(
1969 __isl_take isl_set *set);
1970 __isl_give isl_union_set *isl_union_set_lift(
1971 __isl_take isl_union_set *uset);
1973 =item * Internal Product
1975 __isl_give isl_basic_map *isl_basic_map_zip(
1976 __isl_take isl_basic_map *bmap);
1977 __isl_give isl_map *isl_map_zip(
1978 __isl_take isl_map *map);
1979 __isl_give isl_union_map *isl_union_map_zip(
1980 __isl_take isl_union_map *umap);
1982 Given a relation with nested relations for domain and range,
1983 interchange the range of the domain with the domain of the range.
1985 =item * Aligning parameters
1987 __isl_give isl_set *isl_set_align_params(
1988 __isl_take isl_set *set,
1989 __isl_take isl_space *model);
1990 __isl_give isl_map *isl_map_align_params(
1991 __isl_take isl_map *map,
1992 __isl_take isl_space *model);
1994 Change the order of the parameters of the given set or relation
1995 such that the first parameters match those of C<model>.
1996 This may involve the introduction of extra parameters.
1997 All parameters need to be named.
1999 =item * Dimension manipulation
2001 __isl_give isl_set *isl_set_add_dims(
2002 __isl_take isl_set *set,
2003 enum isl_dim_type type, unsigned n);
2004 __isl_give isl_map *isl_map_add_dims(
2005 __isl_take isl_map *map,
2006 enum isl_dim_type type, unsigned n);
2007 __isl_give isl_set *isl_set_insert_dims(
2008 __isl_take isl_set *set,
2009 enum isl_dim_type type, unsigned pos, unsigned n);
2010 __isl_give isl_map *isl_map_insert_dims(
2011 __isl_take isl_map *map,
2012 enum isl_dim_type type, unsigned pos, unsigned n);
2014 It is usually not advisable to directly change the (input or output)
2015 space of a set or a relation as this removes the name and the internal
2016 structure of the space. However, the above functions can be useful
2017 to add new parameters, assuming
2018 C<isl_set_align_params> and C<isl_map_align_params>
2023 =head2 Binary Operations
2025 The two arguments of a binary operation not only need to live
2026 in the same C<isl_ctx>, they currently also need to have
2027 the same (number of) parameters.
2029 =head3 Basic Operations
2033 =item * Intersection
2035 __isl_give isl_basic_set *isl_basic_set_intersect(
2036 __isl_take isl_basic_set *bset1,
2037 __isl_take isl_basic_set *bset2);
2038 __isl_give isl_set *isl_set_intersect_params(
2039 __isl_take isl_set *set,
2040 __isl_take isl_set *params);
2041 __isl_give isl_set *isl_set_intersect(
2042 __isl_take isl_set *set1,
2043 __isl_take isl_set *set2);
2044 __isl_give isl_union_set *isl_union_set_intersect(
2045 __isl_take isl_union_set *uset1,
2046 __isl_take isl_union_set *uset2);
2047 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2048 __isl_take isl_basic_map *bmap,
2049 __isl_take isl_basic_set *bset);
2050 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2051 __isl_take isl_basic_map *bmap,
2052 __isl_take isl_basic_set *bset);
2053 __isl_give isl_basic_map *isl_basic_map_intersect(
2054 __isl_take isl_basic_map *bmap1,
2055 __isl_take isl_basic_map *bmap2);
2056 __isl_give isl_map *isl_map_intersect_params(
2057 __isl_take isl_map *map,
2058 __isl_take isl_set *params);
2059 __isl_give isl_map *isl_map_intersect_domain(
2060 __isl_take isl_map *map,
2061 __isl_take isl_set *set);
2062 __isl_give isl_map *isl_map_intersect_range(
2063 __isl_take isl_map *map,
2064 __isl_take isl_set *set);
2065 __isl_give isl_map *isl_map_intersect(
2066 __isl_take isl_map *map1,
2067 __isl_take isl_map *map2);
2068 __isl_give isl_union_map *isl_union_map_intersect_domain(
2069 __isl_take isl_union_map *umap,
2070 __isl_take isl_union_set *uset);
2071 __isl_give isl_union_map *isl_union_map_intersect_range(
2072 __isl_take isl_union_map *umap,
2073 __isl_take isl_union_set *uset);
2074 __isl_give isl_union_map *isl_union_map_intersect(
2075 __isl_take isl_union_map *umap1,
2076 __isl_take isl_union_map *umap2);
2080 __isl_give isl_set *isl_basic_set_union(
2081 __isl_take isl_basic_set *bset1,
2082 __isl_take isl_basic_set *bset2);
2083 __isl_give isl_map *isl_basic_map_union(
2084 __isl_take isl_basic_map *bmap1,
2085 __isl_take isl_basic_map *bmap2);
2086 __isl_give isl_set *isl_set_union(
2087 __isl_take isl_set *set1,
2088 __isl_take isl_set *set2);
2089 __isl_give isl_map *isl_map_union(
2090 __isl_take isl_map *map1,
2091 __isl_take isl_map *map2);
2092 __isl_give isl_union_set *isl_union_set_union(
2093 __isl_take isl_union_set *uset1,
2094 __isl_take isl_union_set *uset2);
2095 __isl_give isl_union_map *isl_union_map_union(
2096 __isl_take isl_union_map *umap1,
2097 __isl_take isl_union_map *umap2);
2099 =item * Set difference
2101 __isl_give isl_set *isl_set_subtract(
2102 __isl_take isl_set *set1,
2103 __isl_take isl_set *set2);
2104 __isl_give isl_map *isl_map_subtract(
2105 __isl_take isl_map *map1,
2106 __isl_take isl_map *map2);
2107 __isl_give isl_union_set *isl_union_set_subtract(
2108 __isl_take isl_union_set *uset1,
2109 __isl_take isl_union_set *uset2);
2110 __isl_give isl_union_map *isl_union_map_subtract(
2111 __isl_take isl_union_map *umap1,
2112 __isl_take isl_union_map *umap2);
2116 __isl_give isl_basic_set *isl_basic_set_apply(
2117 __isl_take isl_basic_set *bset,
2118 __isl_take isl_basic_map *bmap);
2119 __isl_give isl_set *isl_set_apply(
2120 __isl_take isl_set *set,
2121 __isl_take isl_map *map);
2122 __isl_give isl_union_set *isl_union_set_apply(
2123 __isl_take isl_union_set *uset,
2124 __isl_take isl_union_map *umap);
2125 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2126 __isl_take isl_basic_map *bmap1,
2127 __isl_take isl_basic_map *bmap2);
2128 __isl_give isl_basic_map *isl_basic_map_apply_range(
2129 __isl_take isl_basic_map *bmap1,
2130 __isl_take isl_basic_map *bmap2);
2131 __isl_give isl_map *isl_map_apply_domain(
2132 __isl_take isl_map *map1,
2133 __isl_take isl_map *map2);
2134 __isl_give isl_union_map *isl_union_map_apply_domain(
2135 __isl_take isl_union_map *umap1,
2136 __isl_take isl_union_map *umap2);
2137 __isl_give isl_map *isl_map_apply_range(
2138 __isl_take isl_map *map1,
2139 __isl_take isl_map *map2);
2140 __isl_give isl_union_map *isl_union_map_apply_range(
2141 __isl_take isl_union_map *umap1,
2142 __isl_take isl_union_map *umap2);
2144 =item * Cartesian Product
2146 __isl_give isl_set *isl_set_product(
2147 __isl_take isl_set *set1,
2148 __isl_take isl_set *set2);
2149 __isl_give isl_union_set *isl_union_set_product(
2150 __isl_take isl_union_set *uset1,
2151 __isl_take isl_union_set *uset2);
2152 __isl_give isl_basic_map *isl_basic_map_range_product(
2153 __isl_take isl_basic_map *bmap1,
2154 __isl_take isl_basic_map *bmap2);
2155 __isl_give isl_map *isl_map_range_product(
2156 __isl_take isl_map *map1,
2157 __isl_take isl_map *map2);
2158 __isl_give isl_union_map *isl_union_map_range_product(
2159 __isl_take isl_union_map *umap1,
2160 __isl_take isl_union_map *umap2);
2161 __isl_give isl_map *isl_map_product(
2162 __isl_take isl_map *map1,
2163 __isl_take isl_map *map2);
2164 __isl_give isl_union_map *isl_union_map_product(
2165 __isl_take isl_union_map *umap1,
2166 __isl_take isl_union_map *umap2);
2168 The above functions compute the cross product of the given
2169 sets or relations. The domains and ranges of the results
2170 are wrapped maps between domains and ranges of the inputs.
2171 To obtain a ``flat'' product, use the following functions
2174 __isl_give isl_basic_set *isl_basic_set_flat_product(
2175 __isl_take isl_basic_set *bset1,
2176 __isl_take isl_basic_set *bset2);
2177 __isl_give isl_set *isl_set_flat_product(
2178 __isl_take isl_set *set1,
2179 __isl_take isl_set *set2);
2180 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2181 __isl_take isl_basic_map *bmap1,
2182 __isl_take isl_basic_map *bmap2);
2183 __isl_give isl_map *isl_map_flat_range_product(
2184 __isl_take isl_map *map1,
2185 __isl_take isl_map *map2);
2186 __isl_give isl_union_map *isl_union_map_flat_range_product(
2187 __isl_take isl_union_map *umap1,
2188 __isl_take isl_union_map *umap2);
2189 __isl_give isl_basic_map *isl_basic_map_flat_product(
2190 __isl_take isl_basic_map *bmap1,
2191 __isl_take isl_basic_map *bmap2);
2192 __isl_give isl_map *isl_map_flat_product(
2193 __isl_take isl_map *map1,
2194 __isl_take isl_map *map2);
2196 =item * Simplification
2198 __isl_give isl_basic_set *isl_basic_set_gist(
2199 __isl_take isl_basic_set *bset,
2200 __isl_take isl_basic_set *context);
2201 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2202 __isl_take isl_set *context);
2203 __isl_give isl_union_set *isl_union_set_gist(
2204 __isl_take isl_union_set *uset,
2205 __isl_take isl_union_set *context);
2206 __isl_give isl_basic_map *isl_basic_map_gist(
2207 __isl_take isl_basic_map *bmap,
2208 __isl_take isl_basic_map *context);
2209 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2210 __isl_take isl_map *context);
2211 __isl_give isl_union_map *isl_union_map_gist(
2212 __isl_take isl_union_map *umap,
2213 __isl_take isl_union_map *context);
2215 The gist operation returns a set or relation that has the
2216 same intersection with the context as the input set or relation.
2217 Any implicit equality in the intersection is made explicit in the result,
2218 while all inequalities that are redundant with respect to the intersection
2220 In case of union sets and relations, the gist operation is performed
2225 =head3 Lexicographic Optimization
2227 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2228 the following functions
2229 compute a set that contains the lexicographic minimum or maximum
2230 of the elements in C<set> (or C<bset>) for those values of the parameters
2231 that satisfy C<dom>.
2232 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2233 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2235 In other words, the union of the parameter values
2236 for which the result is non-empty and of C<*empty>
2239 __isl_give isl_set *isl_basic_set_partial_lexmin(
2240 __isl_take isl_basic_set *bset,
2241 __isl_take isl_basic_set *dom,
2242 __isl_give isl_set **empty);
2243 __isl_give isl_set *isl_basic_set_partial_lexmax(
2244 __isl_take isl_basic_set *bset,
2245 __isl_take isl_basic_set *dom,
2246 __isl_give isl_set **empty);
2247 __isl_give isl_set *isl_set_partial_lexmin(
2248 __isl_take isl_set *set, __isl_take isl_set *dom,
2249 __isl_give isl_set **empty);
2250 __isl_give isl_set *isl_set_partial_lexmax(
2251 __isl_take isl_set *set, __isl_take isl_set *dom,
2252 __isl_give isl_set **empty);
2254 Given a (basic) set C<set> (or C<bset>), the following functions simply
2255 return a set containing the lexicographic minimum or maximum
2256 of the elements in C<set> (or C<bset>).
2257 In case of union sets, the optimum is computed per space.
2259 __isl_give isl_set *isl_basic_set_lexmin(
2260 __isl_take isl_basic_set *bset);
2261 __isl_give isl_set *isl_basic_set_lexmax(
2262 __isl_take isl_basic_set *bset);
2263 __isl_give isl_set *isl_set_lexmin(
2264 __isl_take isl_set *set);
2265 __isl_give isl_set *isl_set_lexmax(
2266 __isl_take isl_set *set);
2267 __isl_give isl_union_set *isl_union_set_lexmin(
2268 __isl_take isl_union_set *uset);
2269 __isl_give isl_union_set *isl_union_set_lexmax(
2270 __isl_take isl_union_set *uset);
2272 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2273 the following functions
2274 compute a relation that maps each element of C<dom>
2275 to the single lexicographic minimum or maximum
2276 of the elements that are associated to that same
2277 element in C<map> (or C<bmap>).
2278 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2279 that contains the elements in C<dom> that do not map
2280 to any elements in C<map> (or C<bmap>).
2281 In other words, the union of the domain of the result and of C<*empty>
2284 __isl_give isl_map *isl_basic_map_partial_lexmax(
2285 __isl_take isl_basic_map *bmap,
2286 __isl_take isl_basic_set *dom,
2287 __isl_give isl_set **empty);
2288 __isl_give isl_map *isl_basic_map_partial_lexmin(
2289 __isl_take isl_basic_map *bmap,
2290 __isl_take isl_basic_set *dom,
2291 __isl_give isl_set **empty);
2292 __isl_give isl_map *isl_map_partial_lexmax(
2293 __isl_take isl_map *map, __isl_take isl_set *dom,
2294 __isl_give isl_set **empty);
2295 __isl_give isl_map *isl_map_partial_lexmin(
2296 __isl_take isl_map *map, __isl_take isl_set *dom,
2297 __isl_give isl_set **empty);
2299 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2300 return a map mapping each element in the domain of
2301 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2302 of all elements associated to that element.
2303 In case of union relations, the optimum is computed per space.
2305 __isl_give isl_map *isl_basic_map_lexmin(
2306 __isl_take isl_basic_map *bmap);
2307 __isl_give isl_map *isl_basic_map_lexmax(
2308 __isl_take isl_basic_map *bmap);
2309 __isl_give isl_map *isl_map_lexmin(
2310 __isl_take isl_map *map);
2311 __isl_give isl_map *isl_map_lexmax(
2312 __isl_take isl_map *map);
2313 __isl_give isl_union_map *isl_union_map_lexmin(
2314 __isl_take isl_union_map *umap);
2315 __isl_give isl_union_map *isl_union_map_lexmax(
2316 __isl_take isl_union_map *umap);
2320 Lists are defined over several element types, including
2321 C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2322 Here we take lists of C<isl_set>s as an example.
2323 Lists can be created, copied and freed using the following functions.
2325 #include <isl/list.h>
2326 __isl_give isl_set_list *isl_set_list_from_set(
2327 __isl_take isl_set *el);
2328 __isl_give isl_set_list *isl_set_list_alloc(
2329 isl_ctx *ctx, int n);
2330 __isl_give isl_set_list *isl_set_list_copy(
2331 __isl_keep isl_set_list *list);
2332 __isl_give isl_set_list *isl_set_list_add(
2333 __isl_take isl_set_list *list,
2334 __isl_take isl_set *el);
2335 __isl_give isl_set_list *isl_set_list_concat(
2336 __isl_take isl_set_list *list1,
2337 __isl_take isl_set_list *list2);
2338 void *isl_set_list_free(__isl_take isl_set_list *list);
2340 C<isl_set_list_alloc> creates an empty list with a capacity for
2341 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2344 Lists can be inspected using the following functions.
2346 #include <isl/list.h>
2347 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2348 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2349 __isl_give isl_set *isl_set_list_get_set(
2350 __isl_keep isl_set_list *list, int index);
2351 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2352 int (*fn)(__isl_take isl_set *el, void *user),
2355 Lists can be printed using
2357 #include <isl/list.h>
2358 __isl_give isl_printer *isl_printer_print_set_list(
2359 __isl_take isl_printer *p,
2360 __isl_keep isl_set_list *list);
2364 Matrices can be created, copied and freed using the following functions.
2366 #include <isl/mat.h>
2367 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2368 unsigned n_row, unsigned n_col);
2369 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2370 void isl_mat_free(__isl_take isl_mat *mat);
2372 Note that the elements of a newly created matrix may have arbitrary values.
2373 The elements can be changed and inspected using the following functions.
2375 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2376 int isl_mat_rows(__isl_keep isl_mat *mat);
2377 int isl_mat_cols(__isl_keep isl_mat *mat);
2378 int isl_mat_get_element(__isl_keep isl_mat *mat,
2379 int row, int col, isl_int *v);
2380 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2381 int row, int col, isl_int v);
2382 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2383 int row, int col, int v);
2385 C<isl_mat_get_element> will return a negative value if anything went wrong.
2386 In that case, the value of C<*v> is undefined.
2388 The following function can be used to compute the (right) inverse
2389 of a matrix, i.e., a matrix such that the product of the original
2390 and the inverse (in that order) is a multiple of the identity matrix.
2391 The input matrix is assumed to be of full row-rank.
2393 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2395 The following function can be used to compute the (right) kernel
2396 (or null space) of a matrix, i.e., a matrix such that the product of
2397 the original and the kernel (in that order) is the zero matrix.
2399 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2401 =head2 Piecewise Quasi Affine Expressions
2403 The zero quasi affine expression can be created using
2405 __isl_give isl_aff *isl_aff_zero(
2406 __isl_take isl_local_space *ls);
2408 A quasi affine expression can also be initialized from an C<isl_div>:
2410 #include <isl/div.h>
2411 __isl_give isl_aff *isl_aff_from_div(__isl_take isl_div *div);
2413 An empty piecewise quasi affine expression (one with no cells)
2414 or a piecewise quasi affine expression with a single cell can
2415 be created using the following functions.
2417 #include <isl/aff.h>
2418 __isl_give isl_pw_aff *isl_pw_aff_empty(
2419 __isl_take isl_space *space);
2420 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2421 __isl_take isl_set *set, __isl_take isl_aff *aff);
2422 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2423 __isl_take isl_aff *aff);
2425 Quasi affine expressions can be copied and freed using
2427 #include <isl/aff.h>
2428 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2429 void *isl_aff_free(__isl_take isl_aff *aff);
2431 __isl_give isl_pw_aff *isl_pw_aff_copy(
2432 __isl_keep isl_pw_aff *pwaff);
2433 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2435 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2436 using the following function. The constraint is required to have
2437 a non-zero coefficient for the specified dimension.
2439 #include <isl/constraint.h>
2440 __isl_give isl_aff *isl_constraint_get_bound(
2441 __isl_keep isl_constraint *constraint,
2442 enum isl_dim_type type, int pos);
2444 The entire affine expression of the constraint can also be extracted
2445 using the following function.
2447 #include <isl/constraint.h>
2448 __isl_give isl_aff *isl_constraint_get_aff(
2449 __isl_keep isl_constraint *constraint);
2451 Conversely, an equality constraint equating
2452 the affine expression to zero or an inequality constraint enforcing
2453 the affine expression to be non-negative, can be constructed using
2455 __isl_give isl_constraint *isl_equality_from_aff(
2456 __isl_take isl_aff *aff);
2457 __isl_give isl_constraint *isl_inequality_from_aff(
2458 __isl_take isl_aff *aff);
2460 The expression can be inspected using
2462 #include <isl/aff.h>
2463 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2464 int isl_aff_dim(__isl_keep isl_aff *aff,
2465 enum isl_dim_type type);
2466 __isl_give isl_local_space *isl_aff_get_local_space(
2467 __isl_keep isl_aff *aff);
2468 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2469 enum isl_dim_type type, unsigned pos);
2470 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2472 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2473 enum isl_dim_type type, int pos, isl_int *v);
2474 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2476 __isl_give isl_div *isl_aff_get_div(
2477 __isl_keep isl_aff *aff, int pos);
2479 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2480 int (*fn)(__isl_take isl_set *set,
2481 __isl_take isl_aff *aff,
2482 void *user), void *user);
2484 int isl_aff_is_cst(__isl_keep isl_aff *aff);
2485 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
2487 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
2488 enum isl_dim_type type, unsigned first, unsigned n);
2489 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
2490 enum isl_dim_type type, unsigned first, unsigned n);
2492 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2493 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2494 enum isl_dim_type type);
2495 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2497 It can be modified using
2499 #include <isl/aff.h>
2500 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
2501 __isl_take isl_pw_aff *pwaff,
2502 __isl_take isl_id *id);
2503 __isl_give isl_aff *isl_aff_set_dim_name(
2504 __isl_take isl_aff *aff, enum isl_dim_type type,
2505 unsigned pos, const char *s);
2506 __isl_give isl_aff *isl_aff_set_constant(
2507 __isl_take isl_aff *aff, isl_int v);
2508 __isl_give isl_aff *isl_aff_set_constant_si(
2509 __isl_take isl_aff *aff, int v);
2510 __isl_give isl_aff *isl_aff_set_coefficient(
2511 __isl_take isl_aff *aff,
2512 enum isl_dim_type type, int pos, isl_int v);
2513 __isl_give isl_aff *isl_aff_set_coefficient_si(
2514 __isl_take isl_aff *aff,
2515 enum isl_dim_type type, int pos, int v);
2516 __isl_give isl_aff *isl_aff_set_denominator(
2517 __isl_take isl_aff *aff, isl_int v);
2519 __isl_give isl_aff *isl_aff_add_constant(
2520 __isl_take isl_aff *aff, isl_int v);
2521 __isl_give isl_aff *isl_aff_add_constant_si(
2522 __isl_take isl_aff *aff, int v);
2523 __isl_give isl_aff *isl_aff_add_coefficient(
2524 __isl_take isl_aff *aff,
2525 enum isl_dim_type type, int pos, isl_int v);
2526 __isl_give isl_aff *isl_aff_add_coefficient_si(
2527 __isl_take isl_aff *aff,
2528 enum isl_dim_type type, int pos, int v);
2530 __isl_give isl_aff *isl_aff_insert_dims(
2531 __isl_take isl_aff *aff,
2532 enum isl_dim_type type, unsigned first, unsigned n);
2533 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
2534 __isl_take isl_pw_aff *pwaff,
2535 enum isl_dim_type type, unsigned first, unsigned n);
2536 __isl_give isl_aff *isl_aff_add_dims(
2537 __isl_take isl_aff *aff,
2538 enum isl_dim_type type, unsigned n);
2539 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
2540 __isl_take isl_pw_aff *pwaff,
2541 enum isl_dim_type type, unsigned n);
2542 __isl_give isl_aff *isl_aff_drop_dims(
2543 __isl_take isl_aff *aff,
2544 enum isl_dim_type type, unsigned first, unsigned n);
2545 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
2546 __isl_take isl_pw_aff *pwaff,
2547 enum isl_dim_type type, unsigned first, unsigned n);
2549 Note that the C<set_constant> and C<set_coefficient> functions
2550 set the I<numerator> of the constant or coefficient, while
2551 C<add_constant> and C<add_coefficient> add an integer value to
2552 the possibly rational constant or coefficient.
2554 To check whether an affine expressions is obviously zero
2555 or obviously equal to some other affine expression, use
2557 #include <isl/aff.h>
2558 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
2559 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
2560 __isl_keep isl_aff *aff2);
2564 #include <isl/aff.h>
2565 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2566 __isl_take isl_aff *aff2);
2567 __isl_give isl_pw_aff *isl_pw_aff_add(
2568 __isl_take isl_pw_aff *pwaff1,
2569 __isl_take isl_pw_aff *pwaff2);
2570 __isl_give isl_pw_aff *isl_pw_aff_min(
2571 __isl_take isl_pw_aff *pwaff1,
2572 __isl_take isl_pw_aff *pwaff2);
2573 __isl_give isl_pw_aff *isl_pw_aff_max(
2574 __isl_take isl_pw_aff *pwaff1,
2575 __isl_take isl_pw_aff *pwaff2);
2576 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2577 __isl_take isl_aff *aff2);
2578 __isl_give isl_pw_aff *isl_pw_aff_sub(
2579 __isl_take isl_pw_aff *pwaff1,
2580 __isl_take isl_pw_aff *pwaff2);
2581 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2582 __isl_give isl_pw_aff *isl_pw_aff_neg(
2583 __isl_take isl_pw_aff *pwaff);
2584 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2585 __isl_give isl_pw_aff *isl_pw_aff_ceil(
2586 __isl_take isl_pw_aff *pwaff);
2587 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
2588 __isl_give isl_pw_aff *isl_pw_aff_floor(
2589 __isl_take isl_pw_aff *pwaff);
2590 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
2592 __isl_give isl_pw_aff *isl_pw_aff_mod(
2593 __isl_take isl_pw_aff *pwaff, isl_int mod);
2594 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2596 __isl_give isl_pw_aff *isl_pw_aff_scale(
2597 __isl_take isl_pw_aff *pwaff, isl_int f);
2598 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2600 __isl_give isl_aff *isl_aff_scale_down_ui(
2601 __isl_take isl_aff *aff, unsigned f);
2602 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
2603 __isl_take isl_pw_aff *pwaff, isl_int f);
2605 __isl_give isl_pw_aff *isl_pw_aff_list_min(
2606 __isl_take isl_pw_aff_list *list);
2607 __isl_give isl_pw_aff *isl_pw_aff_list_max(
2608 __isl_take isl_pw_aff_list *list);
2610 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
2611 __isl_take isl_pw_aff *pwqp);
2613 __isl_give isl_pw_aff *isl_pw_aff_align_params(
2614 __isl_take isl_pw_aff *pwaff,
2615 __isl_take isl_space *model);
2617 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
2618 __isl_take isl_set *context);
2619 __isl_give isl_pw_aff *isl_pw_aff_gist(
2620 __isl_take isl_pw_aff *pwaff,
2621 __isl_take isl_set *context);
2623 __isl_give isl_set *isl_pw_aff_domain(
2624 __isl_take isl_pw_aff *pwaff);
2626 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
2627 __isl_take isl_aff *aff2);
2628 __isl_give isl_pw_aff *isl_pw_aff_mul(
2629 __isl_take isl_pw_aff *pwaff1,
2630 __isl_take isl_pw_aff *pwaff2);
2632 When multiplying two affine expressions, at least one of the two needs
2635 #include <isl/aff.h>
2636 __isl_give isl_basic_set *isl_aff_le_basic_set(
2637 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2638 __isl_give isl_basic_set *isl_aff_ge_basic_set(
2639 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2640 __isl_give isl_set *isl_pw_aff_eq_set(
2641 __isl_take isl_pw_aff *pwaff1,
2642 __isl_take isl_pw_aff *pwaff2);
2643 __isl_give isl_set *isl_pw_aff_ne_set(
2644 __isl_take isl_pw_aff *pwaff1,
2645 __isl_take isl_pw_aff *pwaff2);
2646 __isl_give isl_set *isl_pw_aff_le_set(
2647 __isl_take isl_pw_aff *pwaff1,
2648 __isl_take isl_pw_aff *pwaff2);
2649 __isl_give isl_set *isl_pw_aff_lt_set(
2650 __isl_take isl_pw_aff *pwaff1,
2651 __isl_take isl_pw_aff *pwaff2);
2652 __isl_give isl_set *isl_pw_aff_ge_set(
2653 __isl_take isl_pw_aff *pwaff1,
2654 __isl_take isl_pw_aff *pwaff2);
2655 __isl_give isl_set *isl_pw_aff_gt_set(
2656 __isl_take isl_pw_aff *pwaff1,
2657 __isl_take isl_pw_aff *pwaff2);
2659 __isl_give isl_set *isl_pw_aff_list_eq_set(
2660 __isl_take isl_pw_aff_list *list1,
2661 __isl_take isl_pw_aff_list *list2);
2662 __isl_give isl_set *isl_pw_aff_list_ne_set(
2663 __isl_take isl_pw_aff_list *list1,
2664 __isl_take isl_pw_aff_list *list2);
2665 __isl_give isl_set *isl_pw_aff_list_le_set(
2666 __isl_take isl_pw_aff_list *list1,
2667 __isl_take isl_pw_aff_list *list2);
2668 __isl_give isl_set *isl_pw_aff_list_lt_set(
2669 __isl_take isl_pw_aff_list *list1,
2670 __isl_take isl_pw_aff_list *list2);
2671 __isl_give isl_set *isl_pw_aff_list_ge_set(
2672 __isl_take isl_pw_aff_list *list1,
2673 __isl_take isl_pw_aff_list *list2);
2674 __isl_give isl_set *isl_pw_aff_list_gt_set(
2675 __isl_take isl_pw_aff_list *list1,
2676 __isl_take isl_pw_aff_list *list2);
2678 The function C<isl_aff_ge_basic_set> returns a basic set
2679 containing those elements in the shared space
2680 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
2681 The function C<isl_aff_ge_set> returns a set
2682 containing those elements in the shared domain
2683 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
2684 The functions operating on C<isl_pw_aff_list> apply the corresponding
2685 C<isl_pw_aff> function to each pair of elements in the two lists.
2687 #include <isl/aff.h>
2688 __isl_give isl_set *isl_pw_aff_nonneg_set(
2689 __isl_take isl_pw_aff *pwaff);
2690 __isl_give isl_set *isl_pw_aff_zero_set(
2691 __isl_take isl_pw_aff *pwaff);
2692 __isl_give isl_set *isl_pw_aff_non_zero_set(
2693 __isl_take isl_pw_aff *pwaff);
2695 The function C<isl_pw_aff_nonneg_set> returns a set
2696 containing those elements in the domain
2697 of C<pwaff> where C<pwaff> is non-negative.
2699 #include <isl/aff.h>
2700 __isl_give isl_pw_aff *isl_pw_aff_cond(
2701 __isl_take isl_set *cond,
2702 __isl_take isl_pw_aff *pwaff_true,
2703 __isl_take isl_pw_aff *pwaff_false);
2705 The function C<isl_pw_aff_cond> performs a conditional operator
2706 and returns an expression that is equal to C<pwaff_true>
2707 for elements in C<cond> and equal to C<pwaff_false> for elements
2710 #include <isl/aff.h>
2711 __isl_give isl_pw_aff *isl_pw_aff_union_min(
2712 __isl_take isl_pw_aff *pwaff1,
2713 __isl_take isl_pw_aff *pwaff2);
2714 __isl_give isl_pw_aff *isl_pw_aff_union_max(
2715 __isl_take isl_pw_aff *pwaff1,
2716 __isl_take isl_pw_aff *pwaff2);
2718 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
2719 expression with a domain that is the union of those of C<pwaff1> and
2720 C<pwaff2> and such that on each cell, the quasi-affine expression is
2721 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
2722 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
2723 associated expression is the defined one.
2725 An expression can be printed using
2727 #include <isl/aff.h>
2728 __isl_give isl_printer *isl_printer_print_aff(
2729 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
2731 __isl_give isl_printer *isl_printer_print_pw_aff(
2732 __isl_take isl_printer *p,
2733 __isl_keep isl_pw_aff *pwaff);
2737 Points are elements of a set. They can be used to construct
2738 simple sets (boxes) or they can be used to represent the
2739 individual elements of a set.
2740 The zero point (the origin) can be created using
2742 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2744 The coordinates of a point can be inspected, set and changed
2747 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
2748 enum isl_dim_type type, int pos, isl_int *v);
2749 __isl_give isl_point *isl_point_set_coordinate(
2750 __isl_take isl_point *pnt,
2751 enum isl_dim_type type, int pos, isl_int v);
2753 __isl_give isl_point *isl_point_add_ui(
2754 __isl_take isl_point *pnt,
2755 enum isl_dim_type type, int pos, unsigned val);
2756 __isl_give isl_point *isl_point_sub_ui(
2757 __isl_take isl_point *pnt,
2758 enum isl_dim_type type, int pos, unsigned val);
2760 Other properties can be obtained using
2762 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
2764 Points can be copied or freed using
2766 __isl_give isl_point *isl_point_copy(
2767 __isl_keep isl_point *pnt);
2768 void isl_point_free(__isl_take isl_point *pnt);
2770 A singleton set can be created from a point using
2772 __isl_give isl_basic_set *isl_basic_set_from_point(
2773 __isl_take isl_point *pnt);
2774 __isl_give isl_set *isl_set_from_point(
2775 __isl_take isl_point *pnt);
2777 and a box can be created from two opposite extremal points using
2779 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2780 __isl_take isl_point *pnt1,
2781 __isl_take isl_point *pnt2);
2782 __isl_give isl_set *isl_set_box_from_points(
2783 __isl_take isl_point *pnt1,
2784 __isl_take isl_point *pnt2);
2786 All elements of a B<bounded> (union) set can be enumerated using
2787 the following functions.
2789 int isl_set_foreach_point(__isl_keep isl_set *set,
2790 int (*fn)(__isl_take isl_point *pnt, void *user),
2792 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2793 int (*fn)(__isl_take isl_point *pnt, void *user),
2796 The function C<fn> is called for each integer point in
2797 C<set> with as second argument the last argument of
2798 the C<isl_set_foreach_point> call. The function C<fn>
2799 should return C<0> on success and C<-1> on failure.
2800 In the latter case, C<isl_set_foreach_point> will stop
2801 enumerating and return C<-1> as well.
2802 If the enumeration is performed successfully and to completion,
2803 then C<isl_set_foreach_point> returns C<0>.
2805 To obtain a single point of a (basic) set, use
2807 __isl_give isl_point *isl_basic_set_sample_point(
2808 __isl_take isl_basic_set *bset);
2809 __isl_give isl_point *isl_set_sample_point(
2810 __isl_take isl_set *set);
2812 If C<set> does not contain any (integer) points, then the
2813 resulting point will be ``void'', a property that can be
2816 int isl_point_is_void(__isl_keep isl_point *pnt);
2818 =head2 Piecewise Quasipolynomials
2820 A piecewise quasipolynomial is a particular kind of function that maps
2821 a parametric point to a rational value.
2822 More specifically, a quasipolynomial is a polynomial expression in greatest
2823 integer parts of affine expressions of parameters and variables.
2824 A piecewise quasipolynomial is a subdivision of a given parametric
2825 domain into disjoint cells with a quasipolynomial associated to
2826 each cell. The value of the piecewise quasipolynomial at a given
2827 point is the value of the quasipolynomial associated to the cell
2828 that contains the point. Outside of the union of cells,
2829 the value is assumed to be zero.
2830 For example, the piecewise quasipolynomial
2832 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2834 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
2835 A given piecewise quasipolynomial has a fixed domain dimension.
2836 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
2837 defined over different domains.
2838 Piecewise quasipolynomials are mainly used by the C<barvinok>
2839 library for representing the number of elements in a parametric set or map.
2840 For example, the piecewise quasipolynomial above represents
2841 the number of points in the map
2843 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2845 =head3 Printing (Piecewise) Quasipolynomials
2847 Quasipolynomials and piecewise quasipolynomials can be printed
2848 using the following functions.
2850 __isl_give isl_printer *isl_printer_print_qpolynomial(
2851 __isl_take isl_printer *p,
2852 __isl_keep isl_qpolynomial *qp);
2854 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
2855 __isl_take isl_printer *p,
2856 __isl_keep isl_pw_qpolynomial *pwqp);
2858 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
2859 __isl_take isl_printer *p,
2860 __isl_keep isl_union_pw_qpolynomial *upwqp);
2862 The output format of the printer
2863 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2864 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
2866 In case of printing in C<ISL_FORMAT_C>, the user may want
2867 to set the names of all dimensions
2869 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2870 __isl_take isl_qpolynomial *qp,
2871 enum isl_dim_type type, unsigned pos,
2873 __isl_give isl_pw_qpolynomial *
2874 isl_pw_qpolynomial_set_dim_name(
2875 __isl_take isl_pw_qpolynomial *pwqp,
2876 enum isl_dim_type type, unsigned pos,
2879 =head3 Creating New (Piecewise) Quasipolynomials
2881 Some simple quasipolynomials can be created using the following functions.
2882 More complicated quasipolynomials can be created by applying
2883 operations such as addition and multiplication
2884 on the resulting quasipolynomials
2886 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
2887 __isl_take isl_space *dim);
2888 __isl_give isl_qpolynomial *isl_qpolynomial_one(
2889 __isl_take isl_space *dim);
2890 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
2891 __isl_take isl_space *dim);
2892 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
2893 __isl_take isl_space *dim);
2894 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
2895 __isl_take isl_space *dim);
2896 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
2897 __isl_take isl_space *dim,
2898 const isl_int n, const isl_int d);
2899 __isl_give isl_qpolynomial *isl_qpolynomial_div(
2900 __isl_take isl_div *div);
2901 __isl_give isl_qpolynomial *isl_qpolynomial_var(
2902 __isl_take isl_space *dim,
2903 enum isl_dim_type type, unsigned pos);
2904 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2905 __isl_take isl_aff *aff);
2907 The zero piecewise quasipolynomial or a piecewise quasipolynomial
2908 with a single cell can be created using the following functions.
2909 Multiple of these single cell piecewise quasipolynomials can
2910 be combined to create more complicated piecewise quasipolynomials.
2912 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2913 __isl_take isl_space *space);
2914 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2915 __isl_take isl_set *set,
2916 __isl_take isl_qpolynomial *qp);
2917 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
2918 __isl_take isl_qpolynomial *qp);
2919 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
2920 __isl_take isl_pw_aff *pwaff);
2922 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
2923 __isl_take isl_space *space);
2924 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
2925 __isl_take isl_pw_qpolynomial *pwqp);
2926 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
2927 __isl_take isl_union_pw_qpolynomial *upwqp,
2928 __isl_take isl_pw_qpolynomial *pwqp);
2930 Quasipolynomials can be copied and freed again using the following
2933 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2934 __isl_keep isl_qpolynomial *qp);
2935 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
2937 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2938 __isl_keep isl_pw_qpolynomial *pwqp);
2939 void *isl_pw_qpolynomial_free(
2940 __isl_take isl_pw_qpolynomial *pwqp);
2942 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
2943 __isl_keep isl_union_pw_qpolynomial *upwqp);
2944 void isl_union_pw_qpolynomial_free(
2945 __isl_take isl_union_pw_qpolynomial *upwqp);
2947 =head3 Inspecting (Piecewise) Quasipolynomials
2949 To iterate over all piecewise quasipolynomials in a union
2950 piecewise quasipolynomial, use the following function
2952 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
2953 __isl_keep isl_union_pw_qpolynomial *upwqp,
2954 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
2957 To extract the piecewise quasipolynomial in a given space from a union, use
2959 __isl_give isl_pw_qpolynomial *
2960 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
2961 __isl_keep isl_union_pw_qpolynomial *upwqp,
2962 __isl_take isl_space *space);
2964 To iterate over the cells in a piecewise quasipolynomial,
2965 use either of the following two functions
2967 int isl_pw_qpolynomial_foreach_piece(
2968 __isl_keep isl_pw_qpolynomial *pwqp,
2969 int (*fn)(__isl_take isl_set *set,
2970 __isl_take isl_qpolynomial *qp,
2971 void *user), void *user);
2972 int isl_pw_qpolynomial_foreach_lifted_piece(
2973 __isl_keep isl_pw_qpolynomial *pwqp,
2974 int (*fn)(__isl_take isl_set *set,
2975 __isl_take isl_qpolynomial *qp,
2976 void *user), void *user);
2978 As usual, the function C<fn> should return C<0> on success
2979 and C<-1> on failure. The difference between
2980 C<isl_pw_qpolynomial_foreach_piece> and
2981 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
2982 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
2983 compute unique representations for all existentially quantified
2984 variables and then turn these existentially quantified variables
2985 into extra set variables, adapting the associated quasipolynomial
2986 accordingly. This means that the C<set> passed to C<fn>
2987 will not have any existentially quantified variables, but that
2988 the dimensions of the sets may be different for different
2989 invocations of C<fn>.
2991 To iterate over all terms in a quasipolynomial,
2994 int isl_qpolynomial_foreach_term(
2995 __isl_keep isl_qpolynomial *qp,
2996 int (*fn)(__isl_take isl_term *term,
2997 void *user), void *user);
2999 The terms themselves can be inspected and freed using
3002 unsigned isl_term_dim(__isl_keep isl_term *term,
3003 enum isl_dim_type type);
3004 void isl_term_get_num(__isl_keep isl_term *term,
3006 void isl_term_get_den(__isl_keep isl_term *term,
3008 int isl_term_get_exp(__isl_keep isl_term *term,
3009 enum isl_dim_type type, unsigned pos);
3010 __isl_give isl_div *isl_term_get_div(
3011 __isl_keep isl_term *term, unsigned pos);
3012 void isl_term_free(__isl_take isl_term *term);
3014 Each term is a product of parameters, set variables and
3015 integer divisions. The function C<isl_term_get_exp>
3016 returns the exponent of a given dimensions in the given term.
3017 The C<isl_int>s in the arguments of C<isl_term_get_num>
3018 and C<isl_term_get_den> need to have been initialized
3019 using C<isl_int_init> before calling these functions.
3021 =head3 Properties of (Piecewise) Quasipolynomials
3023 To check whether a quasipolynomial is actually a constant,
3024 use the following function.
3026 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3027 isl_int *n, isl_int *d);
3029 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3030 then the numerator and denominator of the constant
3031 are returned in C<*n> and C<*d>, respectively.
3033 =head3 Operations on (Piecewise) Quasipolynomials
3035 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3036 __isl_take isl_qpolynomial *qp, isl_int v);
3037 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3038 __isl_take isl_qpolynomial *qp);
3039 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3040 __isl_take isl_qpolynomial *qp1,
3041 __isl_take isl_qpolynomial *qp2);
3042 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3043 __isl_take isl_qpolynomial *qp1,
3044 __isl_take isl_qpolynomial *qp2);
3045 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3046 __isl_take isl_qpolynomial *qp1,
3047 __isl_take isl_qpolynomial *qp2);
3048 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3049 __isl_take isl_qpolynomial *qp, unsigned exponent);
3051 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3052 __isl_take isl_pw_qpolynomial *pwqp1,
3053 __isl_take isl_pw_qpolynomial *pwqp2);
3054 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3055 __isl_take isl_pw_qpolynomial *pwqp1,
3056 __isl_take isl_pw_qpolynomial *pwqp2);
3057 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3058 __isl_take isl_pw_qpolynomial *pwqp1,
3059 __isl_take isl_pw_qpolynomial *pwqp2);
3060 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3061 __isl_take isl_pw_qpolynomial *pwqp);
3062 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3063 __isl_take isl_pw_qpolynomial *pwqp1,
3064 __isl_take isl_pw_qpolynomial *pwqp2);
3065 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3066 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3068 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3069 __isl_take isl_union_pw_qpolynomial *upwqp1,
3070 __isl_take isl_union_pw_qpolynomial *upwqp2);
3071 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3072 __isl_take isl_union_pw_qpolynomial *upwqp1,
3073 __isl_take isl_union_pw_qpolynomial *upwqp2);
3074 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3075 __isl_take isl_union_pw_qpolynomial *upwqp1,
3076 __isl_take isl_union_pw_qpolynomial *upwqp2);
3078 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
3079 __isl_take isl_pw_qpolynomial *pwqp,
3080 __isl_take isl_point *pnt);
3082 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
3083 __isl_take isl_union_pw_qpolynomial *upwqp,
3084 __isl_take isl_point *pnt);
3086 __isl_give isl_set *isl_pw_qpolynomial_domain(
3087 __isl_take isl_pw_qpolynomial *pwqp);
3088 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
3089 __isl_take isl_pw_qpolynomial *pwpq,
3090 __isl_take isl_set *set);
3092 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3093 __isl_take isl_union_pw_qpolynomial *upwqp);
3094 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
3095 __isl_take isl_union_pw_qpolynomial *upwpq,
3096 __isl_take isl_union_set *uset);
3098 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3099 __isl_take isl_qpolynomial *qp,
3100 __isl_take isl_space *model);
3102 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
3103 __isl_take isl_union_pw_qpolynomial *upwqp);
3105 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
3106 __isl_take isl_qpolynomial *qp,
3107 __isl_take isl_set *context);
3109 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
3110 __isl_take isl_pw_qpolynomial *pwqp,
3111 __isl_take isl_set *context);
3113 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
3114 __isl_take isl_union_pw_qpolynomial *upwqp,
3115 __isl_take isl_union_set *context);
3117 The gist operation applies the gist operation to each of
3118 the cells in the domain of the input piecewise quasipolynomial.
3119 The context is also exploited
3120 to simplify the quasipolynomials associated to each cell.
3122 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
3123 __isl_take isl_pw_qpolynomial *pwqp, int sign);
3124 __isl_give isl_union_pw_qpolynomial *
3125 isl_union_pw_qpolynomial_to_polynomial(
3126 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
3128 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
3129 the polynomial will be an overapproximation. If C<sign> is negative,
3130 it will be an underapproximation. If C<sign> is zero, the approximation
3131 will lie somewhere in between.
3133 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
3135 A piecewise quasipolynomial reduction is a piecewise
3136 reduction (or fold) of quasipolynomials.
3137 In particular, the reduction can be maximum or a minimum.
3138 The objects are mainly used to represent the result of
3139 an upper or lower bound on a quasipolynomial over its domain,
3140 i.e., as the result of the following function.
3142 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
3143 __isl_take isl_pw_qpolynomial *pwqp,
3144 enum isl_fold type, int *tight);
3146 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
3147 __isl_take isl_union_pw_qpolynomial *upwqp,
3148 enum isl_fold type, int *tight);
3150 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
3151 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
3152 is the returned bound is known be tight, i.e., for each value
3153 of the parameters there is at least
3154 one element in the domain that reaches the bound.
3155 If the domain of C<pwqp> is not wrapping, then the bound is computed
3156 over all elements in that domain and the result has a purely parametric
3157 domain. If the domain of C<pwqp> is wrapping, then the bound is
3158 computed over the range of the wrapped relation. The domain of the
3159 wrapped relation becomes the domain of the result.
3161 A (piecewise) quasipolynomial reduction can be copied or freed using the
3162 following functions.
3164 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
3165 __isl_keep isl_qpolynomial_fold *fold);
3166 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
3167 __isl_keep isl_pw_qpolynomial_fold *pwf);
3168 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
3169 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3170 void isl_qpolynomial_fold_free(
3171 __isl_take isl_qpolynomial_fold *fold);
3172 void *isl_pw_qpolynomial_fold_free(
3173 __isl_take isl_pw_qpolynomial_fold *pwf);
3174 void isl_union_pw_qpolynomial_fold_free(
3175 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3177 =head3 Printing Piecewise Quasipolynomial Reductions
3179 Piecewise quasipolynomial reductions can be printed
3180 using the following function.
3182 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
3183 __isl_take isl_printer *p,
3184 __isl_keep isl_pw_qpolynomial_fold *pwf);
3185 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
3186 __isl_take isl_printer *p,
3187 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3189 For C<isl_printer_print_pw_qpolynomial_fold>,
3190 output format of the printer
3191 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3192 For C<isl_printer_print_union_pw_qpolynomial_fold>,
3193 output format of the printer
3194 needs to be set to C<ISL_FORMAT_ISL>.
3195 In case of printing in C<ISL_FORMAT_C>, the user may want
3196 to set the names of all dimensions
3198 __isl_give isl_pw_qpolynomial_fold *
3199 isl_pw_qpolynomial_fold_set_dim_name(
3200 __isl_take isl_pw_qpolynomial_fold *pwf,
3201 enum isl_dim_type type, unsigned pos,
3204 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
3206 To iterate over all piecewise quasipolynomial reductions in a union
3207 piecewise quasipolynomial reduction, use the following function
3209 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3210 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3211 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3212 void *user), void *user);
3214 To iterate over the cells in a piecewise quasipolynomial reduction,
3215 use either of the following two functions
3217 int isl_pw_qpolynomial_fold_foreach_piece(
3218 __isl_keep isl_pw_qpolynomial_fold *pwf,
3219 int (*fn)(__isl_take isl_set *set,
3220 __isl_take isl_qpolynomial_fold *fold,
3221 void *user), void *user);
3222 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
3223 __isl_keep isl_pw_qpolynomial_fold *pwf,
3224 int (*fn)(__isl_take isl_set *set,
3225 __isl_take isl_qpolynomial_fold *fold,
3226 void *user), void *user);
3228 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
3229 of the difference between these two functions.
3231 To iterate over all quasipolynomials in a reduction, use
3233 int isl_qpolynomial_fold_foreach_qpolynomial(
3234 __isl_keep isl_qpolynomial_fold *fold,
3235 int (*fn)(__isl_take isl_qpolynomial *qp,
3236 void *user), void *user);
3238 =head3 Operations on Piecewise Quasipolynomial Reductions
3240 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
3241 __isl_take isl_qpolynomial_fold *fold, isl_int v);
3243 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
3244 __isl_take isl_pw_qpolynomial_fold *pwf1,
3245 __isl_take isl_pw_qpolynomial_fold *pwf2);
3247 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
3248 __isl_take isl_pw_qpolynomial_fold *pwf1,
3249 __isl_take isl_pw_qpolynomial_fold *pwf2);
3251 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
3252 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
3253 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
3255 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
3256 __isl_take isl_pw_qpolynomial_fold *pwf,
3257 __isl_take isl_point *pnt);
3259 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
3260 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3261 __isl_take isl_point *pnt);
3263 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
3264 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3265 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
3266 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3267 __isl_take isl_union_set *uset);
3269 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
3270 __isl_take isl_pw_qpolynomial_fold *pwf);
3272 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
3273 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3275 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
3276 __isl_take isl_pw_qpolynomial_fold *pwf,
3277 __isl_take isl_set *context);
3279 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
3280 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3281 __isl_take isl_union_set *context);
3283 The gist operation applies the gist operation to each of
3284 the cells in the domain of the input piecewise quasipolynomial reduction.
3285 In future, the operation will also exploit the context
3286 to simplify the quasipolynomial reductions associated to each cell.
3288 __isl_give isl_pw_qpolynomial_fold *
3289 isl_set_apply_pw_qpolynomial_fold(
3290 __isl_take isl_set *set,
3291 __isl_take isl_pw_qpolynomial_fold *pwf,
3293 __isl_give isl_pw_qpolynomial_fold *
3294 isl_map_apply_pw_qpolynomial_fold(
3295 __isl_take isl_map *map,
3296 __isl_take isl_pw_qpolynomial_fold *pwf,
3298 __isl_give isl_union_pw_qpolynomial_fold *
3299 isl_union_set_apply_union_pw_qpolynomial_fold(
3300 __isl_take isl_union_set *uset,
3301 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3303 __isl_give isl_union_pw_qpolynomial_fold *
3304 isl_union_map_apply_union_pw_qpolynomial_fold(
3305 __isl_take isl_union_map *umap,
3306 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3309 The functions taking a map
3310 compose the given map with the given piecewise quasipolynomial reduction.
3311 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
3312 over all elements in the intersection of the range of the map
3313 and the domain of the piecewise quasipolynomial reduction
3314 as a function of an element in the domain of the map.
3315 The functions taking a set compute a bound over all elements in the
3316 intersection of the set and the domain of the
3317 piecewise quasipolynomial reduction.
3319 =head2 Dependence Analysis
3321 C<isl> contains specialized functionality for performing
3322 array dataflow analysis. That is, given a I<sink> access relation
3323 and a collection of possible I<source> access relations,
3324 C<isl> can compute relations that describe
3325 for each iteration of the sink access, which iteration
3326 of which of the source access relations was the last
3327 to access the same data element before the given iteration
3329 To compute standard flow dependences, the sink should be
3330 a read, while the sources should be writes.
3331 If any of the source accesses are marked as being I<may>
3332 accesses, then there will be a dependence to the last
3333 I<must> access B<and> to any I<may> access that follows
3334 this last I<must> access.
3335 In particular, if I<all> sources are I<may> accesses,
3336 then memory based dependence analysis is performed.
3337 If, on the other hand, all sources are I<must> accesses,
3338 then value based dependence analysis is performed.
3340 #include <isl/flow.h>
3342 typedef int (*isl_access_level_before)(void *first, void *second);
3344 __isl_give isl_access_info *isl_access_info_alloc(
3345 __isl_take isl_map *sink,
3346 void *sink_user, isl_access_level_before fn,
3348 __isl_give isl_access_info *isl_access_info_add_source(
3349 __isl_take isl_access_info *acc,
3350 __isl_take isl_map *source, int must,
3352 void isl_access_info_free(__isl_take isl_access_info *acc);
3354 __isl_give isl_flow *isl_access_info_compute_flow(
3355 __isl_take isl_access_info *acc);
3357 int isl_flow_foreach(__isl_keep isl_flow *deps,
3358 int (*fn)(__isl_take isl_map *dep, int must,
3359 void *dep_user, void *user),
3361 __isl_give isl_map *isl_flow_get_no_source(
3362 __isl_keep isl_flow *deps, int must);
3363 void isl_flow_free(__isl_take isl_flow *deps);
3365 The function C<isl_access_info_compute_flow> performs the actual
3366 dependence analysis. The other functions are used to construct
3367 the input for this function or to read off the output.
3369 The input is collected in an C<isl_access_info>, which can
3370 be created through a call to C<isl_access_info_alloc>.
3371 The arguments to this functions are the sink access relation
3372 C<sink>, a token C<sink_user> used to identify the sink
3373 access to the user, a callback function for specifying the
3374 relative order of source and sink accesses, and the number
3375 of source access relations that will be added.
3376 The callback function has type C<int (*)(void *first, void *second)>.
3377 The function is called with two user supplied tokens identifying
3378 either a source or the sink and it should return the shared nesting
3379 level and the relative order of the two accesses.
3380 In particular, let I<n> be the number of loops shared by
3381 the two accesses. If C<first> precedes C<second> textually,
3382 then the function should return I<2 * n + 1>; otherwise,
3383 it should return I<2 * n>.
3384 The sources can be added to the C<isl_access_info> by performing
3385 (at most) C<max_source> calls to C<isl_access_info_add_source>.
3386 C<must> indicates whether the source is a I<must> access
3387 or a I<may> access. Note that a multi-valued access relation
3388 should only be marked I<must> if every iteration in the domain
3389 of the relation accesses I<all> elements in its image.
3390 The C<source_user> token is again used to identify
3391 the source access. The range of the source access relation
3392 C<source> should have the same dimension as the range
3393 of the sink access relation.
3394 The C<isl_access_info_free> function should usually not be
3395 called explicitly, because it is called implicitly by
3396 C<isl_access_info_compute_flow>.
3398 The result of the dependence analysis is collected in an
3399 C<isl_flow>. There may be elements of
3400 the sink access for which no preceding source access could be
3401 found or for which all preceding sources are I<may> accesses.
3402 The relations containing these elements can be obtained through
3403 calls to C<isl_flow_get_no_source>, the first with C<must> set
3404 and the second with C<must> unset.
3405 In the case of standard flow dependence analysis,
3406 with the sink a read and the sources I<must> writes,
3407 the first relation corresponds to the reads from uninitialized
3408 array elements and the second relation is empty.
3409 The actual flow dependences can be extracted using
3410 C<isl_flow_foreach>. This function will call the user-specified
3411 callback function C<fn> for each B<non-empty> dependence between
3412 a source and the sink. The callback function is called
3413 with four arguments, the actual flow dependence relation
3414 mapping source iterations to sink iterations, a boolean that
3415 indicates whether it is a I<must> or I<may> dependence, a token
3416 identifying the source and an additional C<void *> with value
3417 equal to the third argument of the C<isl_flow_foreach> call.
3418 A dependence is marked I<must> if it originates from a I<must>
3419 source and if it is not followed by any I<may> sources.
3421 After finishing with an C<isl_flow>, the user should call
3422 C<isl_flow_free> to free all associated memory.
3424 A higher-level interface to dependence analysis is provided
3425 by the following function.
3427 #include <isl/flow.h>
3429 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
3430 __isl_take isl_union_map *must_source,
3431 __isl_take isl_union_map *may_source,
3432 __isl_take isl_union_map *schedule,
3433 __isl_give isl_union_map **must_dep,
3434 __isl_give isl_union_map **may_dep,
3435 __isl_give isl_union_map **must_no_source,
3436 __isl_give isl_union_map **may_no_source);
3438 The arrays are identified by the tuple names of the ranges
3439 of the accesses. The iteration domains by the tuple names
3440 of the domains of the accesses and of the schedule.
3441 The relative order of the iteration domains is given by the
3442 schedule. The relations returned through C<must_no_source>
3443 and C<may_no_source> are subsets of C<sink>.
3444 Any of C<must_dep>, C<may_dep>, C<must_no_source>
3445 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
3446 any of the other arguments is treated as an error.
3450 B<The functionality described in this section is fairly new
3451 and may be subject to change.>
3453 The following function can be used to compute a schedule
3454 for a union of domains. The generated schedule respects
3455 all C<validity> dependences. That is, all dependence distances
3456 over these dependences in the scheduled space are lexicographically
3457 positive. The generated schedule schedule also tries to minimize
3458 the dependence distances over C<proximity> dependences.
3459 Moreover, it tries to obtain sequences (bands) of schedule dimensions
3460 for groups of domains where the dependence distances have only
3461 non-negative values.
3462 The algorithm used to construct the schedule is similar to that
3465 #include <isl/schedule.h>
3466 __isl_give isl_schedule *isl_union_set_compute_schedule(
3467 __isl_take isl_union_set *domain,
3468 __isl_take isl_union_map *validity,
3469 __isl_take isl_union_map *proximity);
3470 void *isl_schedule_free(__isl_take isl_schedule *sched);
3472 A mapping from the domains to the scheduled space can be obtained
3473 from an C<isl_schedule> using the following function.
3475 __isl_give isl_union_map *isl_schedule_get_map(
3476 __isl_keep isl_schedule *sched);
3478 A representation of the schedule can be printed using
3480 __isl_give isl_printer *isl_printer_print_schedule(
3481 __isl_take isl_printer *p,
3482 __isl_keep isl_schedule *schedule);
3484 A representation of the schedule as a forest of bands can be obtained
3485 using the following function.
3487 __isl_give isl_band_list *isl_schedule_get_band_forest(
3488 __isl_keep isl_schedule *schedule);
3490 The list can be manipulated as explained in L<"Lists">.
3491 The bands inside the list can be copied and freed using the following
3494 #include <isl/band.h>
3495 __isl_give isl_band *isl_band_copy(
3496 __isl_keep isl_band *band);
3497 void *isl_band_free(__isl_take isl_band *band);
3499 Each band contains zero or more scheduling dimensions.
3500 These are referred to as the members of the band.
3501 The section of the schedule that corresponds to the band is
3502 referred to as the partial schedule of the band.
3503 For those nodes that participate in a band, the outer scheduling
3504 dimensions form the prefix schedule, while the inner scheduling
3505 dimensions form the suffix schedule.
3506 That is, if we take a cut of the band forest, then the union of
3507 the concatenations of the prefix, partial and suffix schedules of
3508 each band in the cut is equal to the entire schedule (modulo
3509 some possible padding at the end with zero scheduling dimensions).
3510 The properties of a band can be inspected using the following functions.
3512 #include <isl/band.h>
3513 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
3515 int isl_band_has_children(__isl_keep isl_band *band);
3516 __isl_give isl_band_list *isl_band_get_children(
3517 __isl_keep isl_band *band);
3519 __isl_give isl_union_map *isl_band_get_prefix_schedule(
3520 __isl_keep isl_band *band);
3521 __isl_give isl_union_map *isl_band_get_partial_schedule(
3522 __isl_keep isl_band *band);
3523 __isl_give isl_union_map *isl_band_get_suffix_schedule(
3524 __isl_keep isl_band *band);
3526 int isl_band_n_member(__isl_keep isl_band *band);
3527 int isl_band_member_is_zero_distance(
3528 __isl_keep isl_band *band, int pos);
3530 Note that a scheduling dimension is considered to be ``zero
3531 distance'' if it does not carry any proximity dependences
3533 That is, if the dependence distances of the proximity
3534 dependences are all zero in that direction (for fixed
3535 iterations of outer bands).
3537 A representation of the band can be printed using
3539 #include <isl/band.h>
3540 __isl_give isl_printer *isl_printer_print_band(
3541 __isl_take isl_printer *p,
3542 __isl_keep isl_band *band);
3544 =head2 Parametric Vertex Enumeration
3546 The parametric vertex enumeration described in this section
3547 is mainly intended to be used internally and by the C<barvinok>
3550 #include <isl/vertices.h>
3551 __isl_give isl_vertices *isl_basic_set_compute_vertices(
3552 __isl_keep isl_basic_set *bset);
3554 The function C<isl_basic_set_compute_vertices> performs the
3555 actual computation of the parametric vertices and the chamber
3556 decomposition and store the result in an C<isl_vertices> object.
3557 This information can be queried by either iterating over all
3558 the vertices or iterating over all the chambers or cells
3559 and then iterating over all vertices that are active on the chamber.
3561 int isl_vertices_foreach_vertex(
3562 __isl_keep isl_vertices *vertices,
3563 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3566 int isl_vertices_foreach_cell(
3567 __isl_keep isl_vertices *vertices,
3568 int (*fn)(__isl_take isl_cell *cell, void *user),
3570 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
3571 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3574 Other operations that can be performed on an C<isl_vertices> object are
3577 isl_ctx *isl_vertices_get_ctx(
3578 __isl_keep isl_vertices *vertices);
3579 int isl_vertices_get_n_vertices(
3580 __isl_keep isl_vertices *vertices);
3581 void isl_vertices_free(__isl_take isl_vertices *vertices);
3583 Vertices can be inspected and destroyed using the following functions.
3585 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
3586 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
3587 __isl_give isl_basic_set *isl_vertex_get_domain(
3588 __isl_keep isl_vertex *vertex);
3589 __isl_give isl_basic_set *isl_vertex_get_expr(
3590 __isl_keep isl_vertex *vertex);
3591 void isl_vertex_free(__isl_take isl_vertex *vertex);
3593 C<isl_vertex_get_expr> returns a singleton parametric set describing
3594 the vertex, while C<isl_vertex_get_domain> returns the activity domain
3596 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
3597 B<rational> basic sets, so they should mainly be used for inspection
3598 and should not be mixed with integer sets.
3600 Chambers can be inspected and destroyed using the following functions.
3602 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
3603 __isl_give isl_basic_set *isl_cell_get_domain(
3604 __isl_keep isl_cell *cell);
3605 void isl_cell_free(__isl_take isl_cell *cell);
3609 Although C<isl> is mainly meant to be used as a library,
3610 it also contains some basic applications that use some
3611 of the functionality of C<isl>.
3612 The input may be specified in either the L<isl format>
3613 or the L<PolyLib format>.
3615 =head2 C<isl_polyhedron_sample>
3617 C<isl_polyhedron_sample> takes a polyhedron as input and prints
3618 an integer element of the polyhedron, if there is any.
3619 The first column in the output is the denominator and is always
3620 equal to 1. If the polyhedron contains no integer points,
3621 then a vector of length zero is printed.
3625 C<isl_pip> takes the same input as the C<example> program
3626 from the C<piplib> distribution, i.e., a set of constraints
3627 on the parameters, a line containing only -1 and finally a set
3628 of constraints on a parametric polyhedron.
3629 The coefficients of the parameters appear in the last columns
3630 (but before the final constant column).
3631 The output is the lexicographic minimum of the parametric polyhedron.
3632 As C<isl> currently does not have its own output format, the output
3633 is just a dump of the internal state.
3635 =head2 C<isl_polyhedron_minimize>
3637 C<isl_polyhedron_minimize> computes the minimum of some linear
3638 or affine objective function over the integer points in a polyhedron.
3639 If an affine objective function
3640 is given, then the constant should appear in the last column.
3642 =head2 C<isl_polytope_scan>
3644 Given a polytope, C<isl_polytope_scan> prints
3645 all integer points in the polytope.