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>.
101 Similarly, the function C<isl_pw_aff_add> has been renamed to
102 C<isl_pw_aff_union_add>.
104 =item * The C<isl_dim> type has been renamed to C<isl_space>
105 along with the associated functions.
106 Some of the old names have been kept for backward compatibility,
107 but they will be removed in the future.
109 =item * Spaces of maps, sets and parameter domains are now
110 treated differently. The distinction between map spaces and set spaces
111 has always been made on a conceptual level, but proper use of such spaces
112 was never checked. Furthermore, up until isl-0.07 there was no way
113 of explicitly creating a parameter space. These can now be created
114 directly using C<isl_space_params_alloc> or from other spaces using
117 =item * The space in which C<isl_aff>, C<isl_pw_aff>, C<isl_qpolynomial>,
118 C<isl_pw_qpolynomial>, C<isl_qpolynomial_fold> and C<isl_pw_qpolynomial_fold>
119 objects live is now a map space
120 instead of a set space. This means, for example, that the dimensions
121 of the domain of an C<isl_aff> are now considered to be of type
122 C<isl_dim_in> instead of C<isl_dim_set>. Extra functions have been
123 added to obtain the domain space. Some of the constructors still
124 take a domain space and have therefore been renamed.
126 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
127 now take an C<isl_local_space> instead of an C<isl_space>.
128 An C<isl_local_space> can be created from an C<isl_space>
129 using C<isl_local_space_from_space>.
131 =item * The C<isl_div> type has been removed. Functions that used
132 to return an C<isl_div> now return an C<isl_aff>.
133 Note that the space of an C<isl_aff> is that of relation.
134 When replacing a call to C<isl_div_get_coefficient> by a call to
135 C<isl_aff_get_coefficient> any C<isl_dim_set> argument needs
136 to be replaced by C<isl_dim_in>.
137 A call to C<isl_aff_from_div> can be replaced by a call
139 A call to C<isl_qpolynomial_div(div)> call be replaced by
142 isl_qpolynomial_from_aff(isl_aff_floor(div))
144 The function C<isl_constraint_div> has also been renamed
145 to C<isl_constraint_get_div>.
147 =item * The C<nparam> argument has been removed from
148 C<isl_map_read_from_str> and similar functions.
149 When reading input in the original PolyLib format,
150 the result will have no parameters.
151 If parameters are expected, the caller may want to perform
152 dimension manipulation on the result.
158 The source of C<isl> can be obtained either as a tarball
159 or from the git repository. Both are available from
160 L<http://freshmeat.net/projects/isl/>.
161 The installation process depends on how you obtained
164 =head2 Installation from the git repository
168 =item 1 Clone or update the repository
170 The first time the source is obtained, you need to clone
173 git clone git://repo.or.cz/isl.git
175 To obtain updates, you need to pull in the latest changes
179 =item 2 Generate C<configure>
185 After performing the above steps, continue
186 with the L<Common installation instructions>.
188 =head2 Common installation instructions
192 =item 1 Obtain C<GMP>
194 Building C<isl> requires C<GMP>, including its headers files.
195 Your distribution may not provide these header files by default
196 and you may need to install a package called C<gmp-devel> or something
197 similar. Alternatively, C<GMP> can be built from
198 source, available from L<http://gmplib.org/>.
202 C<isl> uses the standard C<autoconf> C<configure> script.
207 optionally followed by some configure options.
208 A complete list of options can be obtained by running
212 Below we discuss some of the more common options.
214 C<isl> can optionally use C<piplib>, but no
215 C<piplib> functionality is currently used by default.
216 The C<--with-piplib> option can
217 be used to specify which C<piplib>
218 library to use, either an installed version (C<system>),
219 an externally built version (C<build>)
220 or no version (C<no>). The option C<build> is mostly useful
221 in C<configure> scripts of larger projects that bundle both C<isl>
228 Installation prefix for C<isl>
230 =item C<--with-gmp-prefix>
232 Installation prefix for C<GMP> (architecture-independent files).
234 =item C<--with-gmp-exec-prefix>
236 Installation prefix for C<GMP> (architecture-dependent files).
238 =item C<--with-piplib>
240 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
242 =item C<--with-piplib-prefix>
244 Installation prefix for C<system> C<piplib> (architecture-independent files).
246 =item C<--with-piplib-exec-prefix>
248 Installation prefix for C<system> C<piplib> (architecture-dependent files).
250 =item C<--with-piplib-builddir>
252 Location where C<build> C<piplib> was built.
260 =item 4 Install (optional)
268 =head2 Initialization
270 All manipulations of integer sets and relations occur within
271 the context of an C<isl_ctx>.
272 A given C<isl_ctx> can only be used within a single thread.
273 All arguments of a function are required to have been allocated
274 within the same context.
275 There are currently no functions available for moving an object
276 from one C<isl_ctx> to another C<isl_ctx>. This means that
277 there is currently no way of safely moving an object from one
278 thread to another, unless the whole C<isl_ctx> is moved.
280 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
281 freed using C<isl_ctx_free>.
282 All objects allocated within an C<isl_ctx> should be freed
283 before the C<isl_ctx> itself is freed.
285 isl_ctx *isl_ctx_alloc();
286 void isl_ctx_free(isl_ctx *ctx);
290 All operations on integers, mainly the coefficients
291 of the constraints describing the sets and relations,
292 are performed in exact integer arithmetic using C<GMP>.
293 However, to allow future versions of C<isl> to optionally
294 support fixed integer arithmetic, all calls to C<GMP>
295 are wrapped inside C<isl> specific macros.
296 The basic type is C<isl_int> and the operations below
297 are available on this type.
298 The meanings of these operations are essentially the same
299 as their C<GMP> C<mpz_> counterparts.
300 As always with C<GMP> types, C<isl_int>s need to be
301 initialized with C<isl_int_init> before they can be used
302 and they need to be released with C<isl_int_clear>
304 The user should not assume that an C<isl_int> is represented
305 as a C<mpz_t>, but should instead explicitly convert between
306 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
307 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
311 =item isl_int_init(i)
313 =item isl_int_clear(i)
315 =item isl_int_set(r,i)
317 =item isl_int_set_si(r,i)
319 =item isl_int_set_gmp(r,g)
321 =item isl_int_get_gmp(i,g)
323 =item isl_int_abs(r,i)
325 =item isl_int_neg(r,i)
327 =item isl_int_swap(i,j)
329 =item isl_int_swap_or_set(i,j)
331 =item isl_int_add_ui(r,i,j)
333 =item isl_int_sub_ui(r,i,j)
335 =item isl_int_add(r,i,j)
337 =item isl_int_sub(r,i,j)
339 =item isl_int_mul(r,i,j)
341 =item isl_int_mul_ui(r,i,j)
343 =item isl_int_addmul(r,i,j)
345 =item isl_int_submul(r,i,j)
347 =item isl_int_gcd(r,i,j)
349 =item isl_int_lcm(r,i,j)
351 =item isl_int_divexact(r,i,j)
353 =item isl_int_cdiv_q(r,i,j)
355 =item isl_int_fdiv_q(r,i,j)
357 =item isl_int_fdiv_r(r,i,j)
359 =item isl_int_fdiv_q_ui(r,i,j)
361 =item isl_int_read(r,s)
363 =item isl_int_print(out,i,width)
367 =item isl_int_cmp(i,j)
369 =item isl_int_cmp_si(i,si)
371 =item isl_int_eq(i,j)
373 =item isl_int_ne(i,j)
375 =item isl_int_lt(i,j)
377 =item isl_int_le(i,j)
379 =item isl_int_gt(i,j)
381 =item isl_int_ge(i,j)
383 =item isl_int_abs_eq(i,j)
385 =item isl_int_abs_ne(i,j)
387 =item isl_int_abs_lt(i,j)
389 =item isl_int_abs_gt(i,j)
391 =item isl_int_abs_ge(i,j)
393 =item isl_int_is_zero(i)
395 =item isl_int_is_one(i)
397 =item isl_int_is_negone(i)
399 =item isl_int_is_pos(i)
401 =item isl_int_is_neg(i)
403 =item isl_int_is_nonpos(i)
405 =item isl_int_is_nonneg(i)
407 =item isl_int_is_divisible_by(i,j)
411 =head2 Sets and Relations
413 C<isl> uses six types of objects for representing sets and relations,
414 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
415 C<isl_union_set> and C<isl_union_map>.
416 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
417 can be described as a conjunction of affine constraints, while
418 C<isl_set> and C<isl_map> represent unions of
419 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
420 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
421 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
422 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
423 where spaces are considered different if they have a different number
424 of dimensions and/or different names (see L<"Spaces">).
425 The difference between sets and relations (maps) is that sets have
426 one set of variables, while relations have two sets of variables,
427 input variables and output variables.
429 =head2 Memory Management
431 Since a high-level operation on sets and/or relations usually involves
432 several substeps and since the user is usually not interested in
433 the intermediate results, most functions that return a new object
434 will also release all the objects passed as arguments.
435 If the user still wants to use one or more of these arguments
436 after the function call, she should pass along a copy of the
437 object rather than the object itself.
438 The user is then responsible for making sure that the original
439 object gets used somewhere else or is explicitly freed.
441 The arguments and return values of all documented functions are
442 annotated to make clear which arguments are released and which
443 arguments are preserved. In particular, the following annotations
450 C<__isl_give> means that a new object is returned.
451 The user should make sure that the returned pointer is
452 used exactly once as a value for an C<__isl_take> argument.
453 In between, it can be used as a value for as many
454 C<__isl_keep> arguments as the user likes.
455 There is one exception, and that is the case where the
456 pointer returned is C<NULL>. Is this case, the user
457 is free to use it as an C<__isl_take> argument or not.
461 C<__isl_take> means that the object the argument points to
462 is taken over by the function and may no longer be used
463 by the user as an argument to any other function.
464 The pointer value must be one returned by a function
465 returning an C<__isl_give> pointer.
466 If the user passes in a C<NULL> value, then this will
467 be treated as an error in the sense that the function will
468 not perform its usual operation. However, it will still
469 make sure that all the other C<__isl_take> arguments
474 C<__isl_keep> means that the function will only use the object
475 temporarily. After the function has finished, the user
476 can still use it as an argument to other functions.
477 A C<NULL> value will be treated in the same way as
478 a C<NULL> value for an C<__isl_take> argument.
484 Identifiers are used to identify both individual dimensions
485 and tuples of dimensions. They consist of a name and an optional
486 pointer. Identifiers with the same name but different pointer values
487 are considered to be distinct.
488 Identifiers can be constructed, copied, freed, inspected and printed
489 using the following functions.
492 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
493 __isl_keep const char *name, void *user);
494 __isl_give isl_id *isl_id_copy(isl_id *id);
495 void *isl_id_free(__isl_take isl_id *id);
497 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
498 void *isl_id_get_user(__isl_keep isl_id *id);
499 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
501 __isl_give isl_printer *isl_printer_print_id(
502 __isl_take isl_printer *p, __isl_keep isl_id *id);
504 Note that C<isl_id_get_name> returns a pointer to some internal
505 data structure, so the result can only be used while the
506 corresponding C<isl_id> is alive.
510 Whenever a new set or relation is created from scratch,
511 the space in which it lives needs to be specified using an C<isl_space>.
513 #include <isl/space.h>
514 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
515 unsigned nparam, unsigned n_in, unsigned n_out);
516 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
518 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
519 unsigned nparam, unsigned dim);
520 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
521 void isl_space_free(__isl_take isl_space *space);
522 unsigned isl_space_dim(__isl_keep isl_space *space,
523 enum isl_dim_type type);
525 The space used for creating a parameter domain
526 needs to be created using C<isl_space_params_alloc>.
527 For other sets, the space
528 needs to be created using C<isl_space_set_alloc>, while
529 for a relation, the space
530 needs to be created using C<isl_space_alloc>.
531 C<isl_space_dim> can be used
532 to find out the number of dimensions of each type in
533 a space, where type may be
534 C<isl_dim_param>, C<isl_dim_in> (only for relations),
535 C<isl_dim_out> (only for relations), C<isl_dim_set>
536 (only for sets) or C<isl_dim_all>.
538 To check whether a given space is that of a set or a map
539 or whether it is a parameter space, use these functions:
541 #include <isl/space.h>
542 int isl_space_is_params(__isl_keep isl_space *space);
543 int isl_space_is_set(__isl_keep isl_space *space);
545 It is often useful to create objects that live in the
546 same space as some other object. This can be accomplished
547 by creating the new objects
548 (see L<Creating New Sets and Relations> or
549 L<Creating New (Piecewise) Quasipolynomials>) based on the space
550 of the original object.
553 __isl_give isl_space *isl_basic_set_get_space(
554 __isl_keep isl_basic_set *bset);
555 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
557 #include <isl/union_set.h>
558 __isl_give isl_space *isl_union_set_get_space(
559 __isl_keep isl_union_set *uset);
562 __isl_give isl_space *isl_basic_map_get_space(
563 __isl_keep isl_basic_map *bmap);
564 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
566 #include <isl/union_map.h>
567 __isl_give isl_space *isl_union_map_get_space(
568 __isl_keep isl_union_map *umap);
570 #include <isl/constraint.h>
571 __isl_give isl_space *isl_constraint_get_space(
572 __isl_keep isl_constraint *constraint);
574 #include <isl/polynomial.h>
575 __isl_give isl_space *isl_qpolynomial_get_domain_space(
576 __isl_keep isl_qpolynomial *qp);
577 __isl_give isl_space *isl_qpolynomial_get_space(
578 __isl_keep isl_qpolynomial *qp);
579 __isl_give isl_space *isl_qpolynomial_fold_get_space(
580 __isl_keep isl_qpolynomial_fold *fold);
581 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
582 __isl_keep isl_pw_qpolynomial *pwqp);
583 __isl_give isl_space *isl_pw_qpolynomial_get_space(
584 __isl_keep isl_pw_qpolynomial *pwqp);
585 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
586 __isl_keep isl_pw_qpolynomial_fold *pwf);
587 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
588 __isl_keep isl_pw_qpolynomial_fold *pwf);
589 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
590 __isl_keep isl_union_pw_qpolynomial *upwqp);
591 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
592 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
595 __isl_give isl_space *isl_aff_get_domain_space(
596 __isl_keep isl_aff *aff);
597 __isl_give isl_space *isl_aff_get_space(
598 __isl_keep isl_aff *aff);
599 __isl_give isl_space *isl_pw_aff_get_domain_space(
600 __isl_keep isl_pw_aff *pwaff);
601 __isl_give isl_space *isl_pw_aff_get_space(
602 __isl_keep isl_pw_aff *pwaff);
603 __isl_give isl_space *isl_multi_aff_get_space(
604 __isl_keep isl_multi_aff *maff);
605 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
606 __isl_keep isl_pw_multi_aff *pma);
607 __isl_give isl_space *isl_pw_multi_aff_get_space(
608 __isl_keep isl_pw_multi_aff *pma);
610 #include <isl/point.h>
611 __isl_give isl_space *isl_point_get_space(
612 __isl_keep isl_point *pnt);
614 The identifiers or names of the individual dimensions may be set or read off
615 using the following functions.
617 #include <isl/space.h>
618 __isl_give isl_space *isl_space_set_dim_id(
619 __isl_take isl_space *space,
620 enum isl_dim_type type, unsigned pos,
621 __isl_take isl_id *id);
622 int isl_space_has_dim_id(__isl_keep isl_space *space,
623 enum isl_dim_type type, unsigned pos);
624 __isl_give isl_id *isl_space_get_dim_id(
625 __isl_keep isl_space *space,
626 enum isl_dim_type type, unsigned pos);
627 __isl_give isl_space *isl_space_set_dim_name(__isl_take isl_space *space,
628 enum isl_dim_type type, unsigned pos,
629 __isl_keep const char *name);
630 __isl_keep const char *isl_space_get_dim_name(__isl_keep isl_space *space,
631 enum isl_dim_type type, unsigned pos);
633 Note that C<isl_space_get_name> returns a pointer to some internal
634 data structure, so the result can only be used while the
635 corresponding C<isl_space> is alive.
636 Also note that every function that operates on two sets or relations
637 requires that both arguments have the same parameters. This also
638 means that if one of the arguments has named parameters, then the
639 other needs to have named parameters too and the names need to match.
640 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
641 arguments may have different parameters (as long as they are named),
642 in which case the result will have as parameters the union of the parameters of
645 Given the identifier or name of a dimension (typically a parameter),
646 its position can be obtained from the following function.
648 #include <isl/space.h>
649 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
650 enum isl_dim_type type, __isl_keep isl_id *id);
651 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
652 enum isl_dim_type type, const char *name);
654 The identifiers or names of entire spaces may be set or read off
655 using the following functions.
657 #include <isl/space.h>
658 __isl_give isl_space *isl_space_set_tuple_id(
659 __isl_take isl_space *space,
660 enum isl_dim_type type, __isl_take isl_id *id);
661 __isl_give isl_space *isl_space_reset_tuple_id(
662 __isl_take isl_space *space, enum isl_dim_type type);
663 int isl_space_has_tuple_id(__isl_keep isl_space *space,
664 enum isl_dim_type type);
665 __isl_give isl_id *isl_space_get_tuple_id(
666 __isl_keep isl_space *space, enum isl_dim_type type);
667 __isl_give isl_space *isl_space_set_tuple_name(
668 __isl_take isl_space *space,
669 enum isl_dim_type type, const char *s);
670 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
671 enum isl_dim_type type);
673 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
674 or C<isl_dim_set>. As with C<isl_space_get_name>,
675 the C<isl_space_get_tuple_name> function returns a pointer to some internal
677 Binary operations require the corresponding spaces of their arguments
678 to have the same name.
680 Spaces can be nested. In particular, the domain of a set or
681 the domain or range of a relation can be a nested relation.
682 The following functions can be used to construct and deconstruct
685 #include <isl/space.h>
686 int isl_space_is_wrapping(__isl_keep isl_space *space);
687 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
688 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
690 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
691 be the space of a set, while that of
692 C<isl_space_wrap> should be the space of a relation.
693 Conversely, the output of C<isl_space_unwrap> is the space
694 of a relation, while that of C<isl_space_wrap> is the space of a set.
696 Spaces can be created from other spaces
697 using the following functions.
699 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
700 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
701 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
702 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
703 __isl_give isl_space *isl_space_params(
704 __isl_take isl_space *space);
705 __isl_give isl_space *isl_space_set_from_params(
706 __isl_take isl_space *space);
707 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
708 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
709 __isl_take isl_space *right);
710 __isl_give isl_space *isl_space_align_params(
711 __isl_take isl_space *space1, __isl_take isl_space *space2)
712 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
713 enum isl_dim_type type, unsigned pos, unsigned n);
714 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
715 enum isl_dim_type type, unsigned n);
716 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
717 enum isl_dim_type type, unsigned first, unsigned n);
718 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
719 enum isl_dim_type dst_type, unsigned dst_pos,
720 enum isl_dim_type src_type, unsigned src_pos,
722 __isl_give isl_space *isl_space_map_from_set(
723 __isl_take isl_space *space);
724 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
726 Note that if dimensions are added or removed from a space, then
727 the name and the internal structure are lost.
731 A local space is essentially a space with
732 zero or more existentially quantified variables.
733 The local space of a basic set or relation can be obtained
734 using the following functions.
737 __isl_give isl_local_space *isl_basic_set_get_local_space(
738 __isl_keep isl_basic_set *bset);
741 __isl_give isl_local_space *isl_basic_map_get_local_space(
742 __isl_keep isl_basic_map *bmap);
744 A new local space can be created from a space using
746 #include <isl/local_space.h>
747 __isl_give isl_local_space *isl_local_space_from_space(
748 __isl_take isl_space *space);
750 They can be inspected, modified, copied and freed using the following functions.
752 #include <isl/local_space.h>
753 isl_ctx *isl_local_space_get_ctx(
754 __isl_keep isl_local_space *ls);
755 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
756 int isl_local_space_dim(__isl_keep isl_local_space *ls,
757 enum isl_dim_type type);
758 const char *isl_local_space_get_dim_name(
759 __isl_keep isl_local_space *ls,
760 enum isl_dim_type type, unsigned pos);
761 __isl_give isl_local_space *isl_local_space_set_dim_name(
762 __isl_take isl_local_space *ls,
763 enum isl_dim_type type, unsigned pos, const char *s);
764 __isl_give isl_local_space *isl_local_space_set_dim_id(
765 __isl_take isl_local_space *ls,
766 enum isl_dim_type type, unsigned pos,
767 __isl_take isl_id *id);
768 __isl_give isl_space *isl_local_space_get_space(
769 __isl_keep isl_local_space *ls);
770 __isl_give isl_aff *isl_local_space_get_div(
771 __isl_keep isl_local_space *ls, int pos);
772 __isl_give isl_local_space *isl_local_space_copy(
773 __isl_keep isl_local_space *ls);
774 void *isl_local_space_free(__isl_take isl_local_space *ls);
776 Two local spaces can be compared using
778 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
779 __isl_keep isl_local_space *ls2);
781 Local spaces can be created from other local spaces
782 using the following functions.
784 __isl_give isl_local_space *isl_local_space_domain(
785 __isl_take isl_local_space *ls);
786 __isl_give isl_local_space *isl_local_space_from_domain(
787 __isl_take isl_local_space *ls);
788 __isl_give isl_local_space *isl_local_space_intersect(
789 __isl_take isl_local_space *ls1,
790 __isl_take isl_local_space *ls2);
791 __isl_give isl_local_space *isl_local_space_add_dims(
792 __isl_take isl_local_space *ls,
793 enum isl_dim_type type, unsigned n);
794 __isl_give isl_local_space *isl_local_space_insert_dims(
795 __isl_take isl_local_space *ls,
796 enum isl_dim_type type, unsigned first, unsigned n);
797 __isl_give isl_local_space *isl_local_space_drop_dims(
798 __isl_take isl_local_space *ls,
799 enum isl_dim_type type, unsigned first, unsigned n);
801 =head2 Input and Output
803 C<isl> supports its own input/output format, which is similar
804 to the C<Omega> format, but also supports the C<PolyLib> format
809 The C<isl> format is similar to that of C<Omega>, but has a different
810 syntax for describing the parameters and allows for the definition
811 of an existentially quantified variable as the integer division
812 of an affine expression.
813 For example, the set of integers C<i> between C<0> and C<n>
814 such that C<i % 10 <= 6> can be described as
816 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
819 A set or relation can have several disjuncts, separated
820 by the keyword C<or>. Each disjunct is either a conjunction
821 of constraints or a projection (C<exists>) of a conjunction
822 of constraints. The constraints are separated by the keyword
825 =head3 C<PolyLib> format
827 If the represented set is a union, then the first line
828 contains a single number representing the number of disjuncts.
829 Otherwise, a line containing the number C<1> is optional.
831 Each disjunct is represented by a matrix of constraints.
832 The first line contains two numbers representing
833 the number of rows and columns,
834 where the number of rows is equal to the number of constraints
835 and the number of columns is equal to two plus the number of variables.
836 The following lines contain the actual rows of the constraint matrix.
837 In each row, the first column indicates whether the constraint
838 is an equality (C<0>) or inequality (C<1>). The final column
839 corresponds to the constant term.
841 If the set is parametric, then the coefficients of the parameters
842 appear in the last columns before the constant column.
843 The coefficients of any existentially quantified variables appear
844 between those of the set variables and those of the parameters.
846 =head3 Extended C<PolyLib> format
848 The extended C<PolyLib> format is nearly identical to the
849 C<PolyLib> format. The only difference is that the line
850 containing the number of rows and columns of a constraint matrix
851 also contains four additional numbers:
852 the number of output dimensions, the number of input dimensions,
853 the number of local dimensions (i.e., the number of existentially
854 quantified variables) and the number of parameters.
855 For sets, the number of ``output'' dimensions is equal
856 to the number of set dimensions, while the number of ``input''
862 __isl_give isl_basic_set *isl_basic_set_read_from_file(
863 isl_ctx *ctx, FILE *input);
864 __isl_give isl_basic_set *isl_basic_set_read_from_str(
865 isl_ctx *ctx, const char *str);
866 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
868 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
872 __isl_give isl_basic_map *isl_basic_map_read_from_file(
873 isl_ctx *ctx, FILE *input);
874 __isl_give isl_basic_map *isl_basic_map_read_from_str(
875 isl_ctx *ctx, const char *str);
876 __isl_give isl_map *isl_map_read_from_file(
877 isl_ctx *ctx, FILE *input);
878 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
881 #include <isl/union_set.h>
882 __isl_give isl_union_set *isl_union_set_read_from_file(
883 isl_ctx *ctx, FILE *input);
884 __isl_give isl_union_set *isl_union_set_read_from_str(
885 isl_ctx *ctx, const char *str);
887 #include <isl/union_map.h>
888 __isl_give isl_union_map *isl_union_map_read_from_file(
889 isl_ctx *ctx, FILE *input);
890 __isl_give isl_union_map *isl_union_map_read_from_str(
891 isl_ctx *ctx, const char *str);
893 The input format is autodetected and may be either the C<PolyLib> format
894 or the C<isl> format.
898 Before anything can be printed, an C<isl_printer> needs to
901 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
903 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
904 void isl_printer_free(__isl_take isl_printer *printer);
905 __isl_give char *isl_printer_get_str(
906 __isl_keep isl_printer *printer);
908 The behavior of the printer can be modified in various ways
910 __isl_give isl_printer *isl_printer_set_output_format(
911 __isl_take isl_printer *p, int output_format);
912 __isl_give isl_printer *isl_printer_set_indent(
913 __isl_take isl_printer *p, int indent);
914 __isl_give isl_printer *isl_printer_indent(
915 __isl_take isl_printer *p, int indent);
916 __isl_give isl_printer *isl_printer_set_prefix(
917 __isl_take isl_printer *p, const char *prefix);
918 __isl_give isl_printer *isl_printer_set_suffix(
919 __isl_take isl_printer *p, const char *suffix);
921 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
922 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
923 and defaults to C<ISL_FORMAT_ISL>.
924 Each line in the output is indented by C<indent> (set by
925 C<isl_printer_set_indent>) spaces
926 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
927 In the C<PolyLib> format output,
928 the coefficients of the existentially quantified variables
929 appear between those of the set variables and those
931 The function C<isl_printer_indent> increases the indentation
932 by the specified amount (which may be negative).
934 To actually print something, use
937 __isl_give isl_printer *isl_printer_print_basic_set(
938 __isl_take isl_printer *printer,
939 __isl_keep isl_basic_set *bset);
940 __isl_give isl_printer *isl_printer_print_set(
941 __isl_take isl_printer *printer,
942 __isl_keep isl_set *set);
945 __isl_give isl_printer *isl_printer_print_basic_map(
946 __isl_take isl_printer *printer,
947 __isl_keep isl_basic_map *bmap);
948 __isl_give isl_printer *isl_printer_print_map(
949 __isl_take isl_printer *printer,
950 __isl_keep isl_map *map);
952 #include <isl/union_set.h>
953 __isl_give isl_printer *isl_printer_print_union_set(
954 __isl_take isl_printer *p,
955 __isl_keep isl_union_set *uset);
957 #include <isl/union_map.h>
958 __isl_give isl_printer *isl_printer_print_union_map(
959 __isl_take isl_printer *p,
960 __isl_keep isl_union_map *umap);
962 When called on a file printer, the following function flushes
963 the file. When called on a string printer, the buffer is cleared.
965 __isl_give isl_printer *isl_printer_flush(
966 __isl_take isl_printer *p);
968 =head2 Creating New Sets and Relations
970 C<isl> has functions for creating some standard sets and relations.
974 =item * Empty sets and relations
976 __isl_give isl_basic_set *isl_basic_set_empty(
977 __isl_take isl_space *space);
978 __isl_give isl_basic_map *isl_basic_map_empty(
979 __isl_take isl_space *space);
980 __isl_give isl_set *isl_set_empty(
981 __isl_take isl_space *space);
982 __isl_give isl_map *isl_map_empty(
983 __isl_take isl_space *space);
984 __isl_give isl_union_set *isl_union_set_empty(
985 __isl_take isl_space *space);
986 __isl_give isl_union_map *isl_union_map_empty(
987 __isl_take isl_space *space);
989 For C<isl_union_set>s and C<isl_union_map>s, the space
990 is only used to specify the parameters.
992 =item * Universe sets and relations
994 __isl_give isl_basic_set *isl_basic_set_universe(
995 __isl_take isl_space *space);
996 __isl_give isl_basic_map *isl_basic_map_universe(
997 __isl_take isl_space *space);
998 __isl_give isl_set *isl_set_universe(
999 __isl_take isl_space *space);
1000 __isl_give isl_map *isl_map_universe(
1001 __isl_take isl_space *space);
1002 __isl_give isl_union_set *isl_union_set_universe(
1003 __isl_take isl_union_set *uset);
1004 __isl_give isl_union_map *isl_union_map_universe(
1005 __isl_take isl_union_map *umap);
1007 The sets and relations constructed by the functions above
1008 contain all integer values, while those constructed by the
1009 functions below only contain non-negative values.
1011 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1012 __isl_take isl_space *space);
1013 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1014 __isl_take isl_space *space);
1015 __isl_give isl_set *isl_set_nat_universe(
1016 __isl_take isl_space *space);
1017 __isl_give isl_map *isl_map_nat_universe(
1018 __isl_take isl_space *space);
1020 =item * Identity relations
1022 __isl_give isl_basic_map *isl_basic_map_identity(
1023 __isl_take isl_space *space);
1024 __isl_give isl_map *isl_map_identity(
1025 __isl_take isl_space *space);
1027 The number of input and output dimensions in C<space> needs
1030 =item * Lexicographic order
1032 __isl_give isl_map *isl_map_lex_lt(
1033 __isl_take isl_space *set_space);
1034 __isl_give isl_map *isl_map_lex_le(
1035 __isl_take isl_space *set_space);
1036 __isl_give isl_map *isl_map_lex_gt(
1037 __isl_take isl_space *set_space);
1038 __isl_give isl_map *isl_map_lex_ge(
1039 __isl_take isl_space *set_space);
1040 __isl_give isl_map *isl_map_lex_lt_first(
1041 __isl_take isl_space *space, unsigned n);
1042 __isl_give isl_map *isl_map_lex_le_first(
1043 __isl_take isl_space *space, unsigned n);
1044 __isl_give isl_map *isl_map_lex_gt_first(
1045 __isl_take isl_space *space, unsigned n);
1046 __isl_give isl_map *isl_map_lex_ge_first(
1047 __isl_take isl_space *space, unsigned n);
1049 The first four functions take a space for a B<set>
1050 and return relations that express that the elements in the domain
1051 are lexicographically less
1052 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1053 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1054 than the elements in the range.
1055 The last four functions take a space for a map
1056 and return relations that express that the first C<n> dimensions
1057 in the domain are lexicographically less
1058 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1059 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1060 than the first C<n> dimensions in the range.
1064 A basic set or relation can be converted to a set or relation
1065 using the following functions.
1067 __isl_give isl_set *isl_set_from_basic_set(
1068 __isl_take isl_basic_set *bset);
1069 __isl_give isl_map *isl_map_from_basic_map(
1070 __isl_take isl_basic_map *bmap);
1072 Sets and relations can be converted to union sets and relations
1073 using the following functions.
1075 __isl_give isl_union_map *isl_union_map_from_map(
1076 __isl_take isl_map *map);
1077 __isl_give isl_union_set *isl_union_set_from_set(
1078 __isl_take isl_set *set);
1080 The inverse conversions below can only be used if the input
1081 union set or relation is known to contain elements in exactly one
1084 __isl_give isl_set *isl_set_from_union_set(
1085 __isl_take isl_union_set *uset);
1086 __isl_give isl_map *isl_map_from_union_map(
1087 __isl_take isl_union_map *umap);
1089 A zero-dimensional set can be constructed on a given parameter domain
1090 using the following function.
1092 __isl_give isl_set *isl_set_from_params(
1093 __isl_take isl_set *set);
1095 Sets and relations can be copied and freed again using the following
1098 __isl_give isl_basic_set *isl_basic_set_copy(
1099 __isl_keep isl_basic_set *bset);
1100 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1101 __isl_give isl_union_set *isl_union_set_copy(
1102 __isl_keep isl_union_set *uset);
1103 __isl_give isl_basic_map *isl_basic_map_copy(
1104 __isl_keep isl_basic_map *bmap);
1105 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1106 __isl_give isl_union_map *isl_union_map_copy(
1107 __isl_keep isl_union_map *umap);
1108 void isl_basic_set_free(__isl_take isl_basic_set *bset);
1109 void isl_set_free(__isl_take isl_set *set);
1110 void *isl_union_set_free(__isl_take isl_union_set *uset);
1111 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
1112 void isl_map_free(__isl_take isl_map *map);
1113 void *isl_union_map_free(__isl_take isl_union_map *umap);
1115 Other sets and relations can be constructed by starting
1116 from a universe set or relation, adding equality and/or
1117 inequality constraints and then projecting out the
1118 existentially quantified variables, if any.
1119 Constraints can be constructed, manipulated and
1120 added to (or removed from) (basic) sets and relations
1121 using the following functions.
1123 #include <isl/constraint.h>
1124 __isl_give isl_constraint *isl_equality_alloc(
1125 __isl_take isl_local_space *ls);
1126 __isl_give isl_constraint *isl_inequality_alloc(
1127 __isl_take isl_local_space *ls);
1128 __isl_give isl_constraint *isl_constraint_set_constant(
1129 __isl_take isl_constraint *constraint, isl_int v);
1130 __isl_give isl_constraint *isl_constraint_set_constant_si(
1131 __isl_take isl_constraint *constraint, int v);
1132 __isl_give isl_constraint *isl_constraint_set_coefficient(
1133 __isl_take isl_constraint *constraint,
1134 enum isl_dim_type type, int pos, isl_int v);
1135 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1136 __isl_take isl_constraint *constraint,
1137 enum isl_dim_type type, int pos, int v);
1138 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1139 __isl_take isl_basic_map *bmap,
1140 __isl_take isl_constraint *constraint);
1141 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1142 __isl_take isl_basic_set *bset,
1143 __isl_take isl_constraint *constraint);
1144 __isl_give isl_map *isl_map_add_constraint(
1145 __isl_take isl_map *map,
1146 __isl_take isl_constraint *constraint);
1147 __isl_give isl_set *isl_set_add_constraint(
1148 __isl_take isl_set *set,
1149 __isl_take isl_constraint *constraint);
1150 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1151 __isl_take isl_basic_set *bset,
1152 __isl_take isl_constraint *constraint);
1154 For example, to create a set containing the even integers
1155 between 10 and 42, you would use the following code.
1158 isl_local_space *ls;
1160 isl_basic_set *bset;
1162 space = isl_space_set_alloc(ctx, 0, 2);
1163 bset = isl_basic_set_universe(isl_space_copy(space));
1164 ls = isl_local_space_from_space(space);
1166 c = isl_equality_alloc(isl_local_space_copy(ls));
1167 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1168 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1169 bset = isl_basic_set_add_constraint(bset, c);
1171 c = isl_inequality_alloc(isl_local_space_copy(ls));
1172 c = isl_constraint_set_constant_si(c, -10);
1173 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1174 bset = isl_basic_set_add_constraint(bset, c);
1176 c = isl_inequality_alloc(ls);
1177 c = isl_constraint_set_constant_si(c, 42);
1178 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1179 bset = isl_basic_set_add_constraint(bset, c);
1181 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1185 isl_basic_set *bset;
1186 bset = isl_basic_set_read_from_str(ctx,
1187 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1189 A basic set or relation can also be constructed from two matrices
1190 describing the equalities and the inequalities.
1192 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1193 __isl_take isl_space *space,
1194 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1195 enum isl_dim_type c1,
1196 enum isl_dim_type c2, enum isl_dim_type c3,
1197 enum isl_dim_type c4);
1198 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1199 __isl_take isl_space *space,
1200 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1201 enum isl_dim_type c1,
1202 enum isl_dim_type c2, enum isl_dim_type c3,
1203 enum isl_dim_type c4, enum isl_dim_type c5);
1205 The C<isl_dim_type> arguments indicate the order in which
1206 different kinds of variables appear in the input matrices
1207 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1208 C<isl_dim_set> and C<isl_dim_div> for sets and
1209 of C<isl_dim_cst>, C<isl_dim_param>,
1210 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1212 A (basic) set or relation can also be constructed from a (piecewise)
1213 (multiple) affine expression
1214 or a list of affine expressions
1215 (See L<"Piecewise Quasi Affine Expressions"> and
1216 L<"Piecewise Multiple Quasi Affine Expressions">).
1218 __isl_give isl_basic_map *isl_basic_map_from_aff(
1219 __isl_take isl_aff *aff);
1220 __isl_give isl_set *isl_set_from_pw_aff(
1221 __isl_take isl_pw_aff *pwaff);
1222 __isl_give isl_map *isl_map_from_pw_aff(
1223 __isl_take isl_pw_aff *pwaff);
1224 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1225 __isl_take isl_space *domain_space,
1226 __isl_take isl_aff_list *list);
1227 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1228 __isl_take isl_multi_aff *maff)
1229 __isl_give isl_set *isl_set_from_pw_multi_aff(
1230 __isl_take isl_pw_multi_aff *pma);
1231 __isl_give isl_map *isl_map_from_pw_multi_aff(
1232 __isl_take isl_pw_multi_aff *pma);
1234 The C<domain_dim> argument describes the domain of the resulting
1235 basic relation. It is required because the C<list> may consist
1236 of zero affine expressions.
1238 =head2 Inspecting Sets and Relations
1240 Usually, the user should not have to care about the actual constraints
1241 of the sets and maps, but should instead apply the abstract operations
1242 explained in the following sections.
1243 Occasionally, however, it may be required to inspect the individual
1244 coefficients of the constraints. This section explains how to do so.
1245 In these cases, it may also be useful to have C<isl> compute
1246 an explicit representation of the existentially quantified variables.
1248 __isl_give isl_set *isl_set_compute_divs(
1249 __isl_take isl_set *set);
1250 __isl_give isl_map *isl_map_compute_divs(
1251 __isl_take isl_map *map);
1252 __isl_give isl_union_set *isl_union_set_compute_divs(
1253 __isl_take isl_union_set *uset);
1254 __isl_give isl_union_map *isl_union_map_compute_divs(
1255 __isl_take isl_union_map *umap);
1257 This explicit representation defines the existentially quantified
1258 variables as integer divisions of the other variables, possibly
1259 including earlier existentially quantified variables.
1260 An explicitly represented existentially quantified variable therefore
1261 has a unique value when the values of the other variables are known.
1262 If, furthermore, the same existentials, i.e., existentials
1263 with the same explicit representations, should appear in the
1264 same order in each of the disjuncts of a set or map, then the user should call
1265 either of the following functions.
1267 __isl_give isl_set *isl_set_align_divs(
1268 __isl_take isl_set *set);
1269 __isl_give isl_map *isl_map_align_divs(
1270 __isl_take isl_map *map);
1272 Alternatively, the existentially quantified variables can be removed
1273 using the following functions, which compute an overapproximation.
1275 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1276 __isl_take isl_basic_set *bset);
1277 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1278 __isl_take isl_basic_map *bmap);
1279 __isl_give isl_set *isl_set_remove_divs(
1280 __isl_take isl_set *set);
1281 __isl_give isl_map *isl_map_remove_divs(
1282 __isl_take isl_map *map);
1284 To iterate over all the sets or maps in a union set or map, use
1286 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1287 int (*fn)(__isl_take isl_set *set, void *user),
1289 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1290 int (*fn)(__isl_take isl_map *map, void *user),
1293 The number of sets or maps in a union set or map can be obtained
1296 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1297 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1299 To extract the set or map in a given space from a union, use
1301 __isl_give isl_set *isl_union_set_extract_set(
1302 __isl_keep isl_union_set *uset,
1303 __isl_take isl_space *space);
1304 __isl_give isl_map *isl_union_map_extract_map(
1305 __isl_keep isl_union_map *umap,
1306 __isl_take isl_space *space);
1308 To iterate over all the basic sets or maps in a set or map, use
1310 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1311 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1313 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1314 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1317 The callback function C<fn> should return 0 if successful and
1318 -1 if an error occurs. In the latter case, or if any other error
1319 occurs, the above functions will return -1.
1321 It should be noted that C<isl> does not guarantee that
1322 the basic sets or maps passed to C<fn> are disjoint.
1323 If this is required, then the user should call one of
1324 the following functions first.
1326 __isl_give isl_set *isl_set_make_disjoint(
1327 __isl_take isl_set *set);
1328 __isl_give isl_map *isl_map_make_disjoint(
1329 __isl_take isl_map *map);
1331 The number of basic sets in a set can be obtained
1334 int isl_set_n_basic_set(__isl_keep isl_set *set);
1336 To iterate over the constraints of a basic set or map, use
1338 #include <isl/constraint.h>
1340 int isl_basic_map_foreach_constraint(
1341 __isl_keep isl_basic_map *bmap,
1342 int (*fn)(__isl_take isl_constraint *c, void *user),
1344 void *isl_constraint_free(__isl_take isl_constraint *c);
1346 Again, the callback function C<fn> should return 0 if successful and
1347 -1 if an error occurs. In the latter case, or if any other error
1348 occurs, the above functions will return -1.
1349 The constraint C<c> represents either an equality or an inequality.
1350 Use the following function to find out whether a constraint
1351 represents an equality. If not, it represents an inequality.
1353 int isl_constraint_is_equality(
1354 __isl_keep isl_constraint *constraint);
1356 The coefficients of the constraints can be inspected using
1357 the following functions.
1359 void isl_constraint_get_constant(
1360 __isl_keep isl_constraint *constraint, isl_int *v);
1361 void isl_constraint_get_coefficient(
1362 __isl_keep isl_constraint *constraint,
1363 enum isl_dim_type type, int pos, isl_int *v);
1364 int isl_constraint_involves_dims(
1365 __isl_keep isl_constraint *constraint,
1366 enum isl_dim_type type, unsigned first, unsigned n);
1368 The explicit representations of the existentially quantified
1369 variables can be inspected using the following function.
1370 Note that the user is only allowed to use this function
1371 if the inspected set or map is the result of a call
1372 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1373 The existentially quantified variable is equal to the floor
1374 of the returned affine expression. The affine expression
1375 itself can be inspected using the functions in
1376 L<"Piecewise Quasi Affine Expressions">.
1378 __isl_give isl_aff *isl_constraint_get_div(
1379 __isl_keep isl_constraint *constraint, int pos);
1381 To obtain the constraints of a basic set or map in matrix
1382 form, use the following functions.
1384 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1385 __isl_keep isl_basic_set *bset,
1386 enum isl_dim_type c1, enum isl_dim_type c2,
1387 enum isl_dim_type c3, enum isl_dim_type c4);
1388 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1389 __isl_keep isl_basic_set *bset,
1390 enum isl_dim_type c1, enum isl_dim_type c2,
1391 enum isl_dim_type c3, enum isl_dim_type c4);
1392 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1393 __isl_keep isl_basic_map *bmap,
1394 enum isl_dim_type c1,
1395 enum isl_dim_type c2, enum isl_dim_type c3,
1396 enum isl_dim_type c4, enum isl_dim_type c5);
1397 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1398 __isl_keep isl_basic_map *bmap,
1399 enum isl_dim_type c1,
1400 enum isl_dim_type c2, enum isl_dim_type c3,
1401 enum isl_dim_type c4, enum isl_dim_type c5);
1403 The C<isl_dim_type> arguments dictate the order in which
1404 different kinds of variables appear in the resulting matrix
1405 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1406 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1408 The number of parameters, input, output or set dimensions can
1409 be obtained using the following functions.
1411 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1412 enum isl_dim_type type);
1413 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1414 enum isl_dim_type type);
1415 unsigned isl_set_dim(__isl_keep isl_set *set,
1416 enum isl_dim_type type);
1417 unsigned isl_map_dim(__isl_keep isl_map *map,
1418 enum isl_dim_type type);
1420 To check whether the description of a set or relation depends
1421 on one or more given dimensions, it is not necessary to iterate over all
1422 constraints. Instead the following functions can be used.
1424 int isl_basic_set_involves_dims(
1425 __isl_keep isl_basic_set *bset,
1426 enum isl_dim_type type, unsigned first, unsigned n);
1427 int isl_set_involves_dims(__isl_keep isl_set *set,
1428 enum isl_dim_type type, unsigned first, unsigned n);
1429 int isl_basic_map_involves_dims(
1430 __isl_keep isl_basic_map *bmap,
1431 enum isl_dim_type type, unsigned first, unsigned n);
1432 int isl_map_involves_dims(__isl_keep isl_map *map,
1433 enum isl_dim_type type, unsigned first, unsigned n);
1435 Similarly, the following functions can be used to check whether
1436 a given dimension is involved in any lower or upper bound.
1438 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1439 enum isl_dim_type type, unsigned pos);
1440 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1441 enum isl_dim_type type, unsigned pos);
1443 The identifiers or names of the domain and range spaces of a set
1444 or relation can be read off or set using the following functions.
1446 __isl_give isl_set *isl_set_set_tuple_id(
1447 __isl_take isl_set *set, __isl_take isl_id *id);
1448 __isl_give isl_set *isl_set_reset_tuple_id(
1449 __isl_take isl_set *set);
1450 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1451 __isl_give isl_id *isl_set_get_tuple_id(
1452 __isl_keep isl_set *set);
1453 __isl_give isl_map *isl_map_set_tuple_id(
1454 __isl_take isl_map *map, enum isl_dim_type type,
1455 __isl_take isl_id *id);
1456 __isl_give isl_map *isl_map_reset_tuple_id(
1457 __isl_take isl_map *map, enum isl_dim_type type);
1458 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1459 enum isl_dim_type type);
1460 __isl_give isl_id *isl_map_get_tuple_id(
1461 __isl_keep isl_map *map, enum isl_dim_type type);
1463 const char *isl_basic_set_get_tuple_name(
1464 __isl_keep isl_basic_set *bset);
1465 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1466 __isl_take isl_basic_set *set, const char *s);
1467 const char *isl_set_get_tuple_name(
1468 __isl_keep isl_set *set);
1469 const char *isl_basic_map_get_tuple_name(
1470 __isl_keep isl_basic_map *bmap,
1471 enum isl_dim_type type);
1472 const char *isl_map_get_tuple_name(
1473 __isl_keep isl_map *map,
1474 enum isl_dim_type type);
1476 As with C<isl_space_get_tuple_name>, the value returned points to
1477 an internal data structure.
1478 The identifiers, positions or names of individual dimensions can be
1479 read off using the following functions.
1481 __isl_give isl_set *isl_set_set_dim_id(
1482 __isl_take isl_set *set, enum isl_dim_type type,
1483 unsigned pos, __isl_take isl_id *id);
1484 int isl_set_has_dim_id(__isl_keep isl_set *set,
1485 enum isl_dim_type type, unsigned pos);
1486 __isl_give isl_id *isl_set_get_dim_id(
1487 __isl_keep isl_set *set, enum isl_dim_type type,
1489 int isl_basic_map_has_dim_id(
1490 __isl_keep isl_basic_map *bmap,
1491 enum isl_dim_type type, unsigned pos);
1492 __isl_give isl_map *isl_map_set_dim_id(
1493 __isl_take isl_map *map, enum isl_dim_type type,
1494 unsigned pos, __isl_take isl_id *id);
1495 int isl_map_has_dim_id(__isl_keep isl_map *map,
1496 enum isl_dim_type type, unsigned pos);
1497 __isl_give isl_id *isl_map_get_dim_id(
1498 __isl_keep isl_map *map, enum isl_dim_type type,
1501 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1502 enum isl_dim_type type, __isl_keep isl_id *id);
1503 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1504 enum isl_dim_type type, __isl_keep isl_id *id);
1505 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1506 enum isl_dim_type type, const char *name);
1508 const char *isl_constraint_get_dim_name(
1509 __isl_keep isl_constraint *constraint,
1510 enum isl_dim_type type, unsigned pos);
1511 const char *isl_basic_set_get_dim_name(
1512 __isl_keep isl_basic_set *bset,
1513 enum isl_dim_type type, unsigned pos);
1514 const char *isl_set_get_dim_name(
1515 __isl_keep isl_set *set,
1516 enum isl_dim_type type, unsigned pos);
1517 const char *isl_basic_map_get_dim_name(
1518 __isl_keep isl_basic_map *bmap,
1519 enum isl_dim_type type, unsigned pos);
1520 const char *isl_map_get_dim_name(
1521 __isl_keep isl_map *map,
1522 enum isl_dim_type type, unsigned pos);
1524 These functions are mostly useful to obtain the identifiers, positions
1525 or names of the parameters. Identifiers of individual dimensions are
1526 essentially only useful for printing. They are ignored by all other
1527 operations and may not be preserved across those operations.
1531 =head3 Unary Properties
1537 The following functions test whether the given set or relation
1538 contains any integer points. The ``plain'' variants do not perform
1539 any computations, but simply check if the given set or relation
1540 is already known to be empty.
1542 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1543 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1544 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1545 int isl_set_is_empty(__isl_keep isl_set *set);
1546 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1547 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1548 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1549 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1550 int isl_map_is_empty(__isl_keep isl_map *map);
1551 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1553 =item * Universality
1555 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1556 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1557 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1559 =item * Single-valuedness
1561 int isl_map_is_single_valued(__isl_keep isl_map *map);
1562 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1566 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1567 int isl_map_is_injective(__isl_keep isl_map *map);
1568 int isl_union_map_plain_is_injective(
1569 __isl_keep isl_union_map *umap);
1570 int isl_union_map_is_injective(
1571 __isl_keep isl_union_map *umap);
1575 int isl_map_is_bijective(__isl_keep isl_map *map);
1576 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1580 int isl_basic_map_plain_is_fixed(
1581 __isl_keep isl_basic_map *bmap,
1582 enum isl_dim_type type, unsigned pos,
1584 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
1585 enum isl_dim_type type, unsigned pos,
1587 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1588 enum isl_dim_type type, unsigned pos,
1591 Check if the relation obviously lies on a hyperplane where the given dimension
1592 has a fixed value and if so, return that value in C<*val>.
1596 To check whether a set is a parameter domain, use this function:
1598 int isl_set_is_params(__isl_keep isl_set *set);
1599 int isl_union_set_is_params(
1600 __isl_keep isl_union_set *uset);
1604 The following functions check whether the domain of the given
1605 (basic) set is a wrapped relation.
1607 int isl_basic_set_is_wrapping(
1608 __isl_keep isl_basic_set *bset);
1609 int isl_set_is_wrapping(__isl_keep isl_set *set);
1611 =item * Internal Product
1613 int isl_basic_map_can_zip(
1614 __isl_keep isl_basic_map *bmap);
1615 int isl_map_can_zip(__isl_keep isl_map *map);
1617 Check whether the product of domain and range of the given relation
1619 i.e., whether both domain and range are nested relations.
1623 =head3 Binary Properties
1629 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1630 __isl_keep isl_set *set2);
1631 int isl_set_is_equal(__isl_keep isl_set *set1,
1632 __isl_keep isl_set *set2);
1633 int isl_union_set_is_equal(
1634 __isl_keep isl_union_set *uset1,
1635 __isl_keep isl_union_set *uset2);
1636 int isl_basic_map_is_equal(
1637 __isl_keep isl_basic_map *bmap1,
1638 __isl_keep isl_basic_map *bmap2);
1639 int isl_map_is_equal(__isl_keep isl_map *map1,
1640 __isl_keep isl_map *map2);
1641 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1642 __isl_keep isl_map *map2);
1643 int isl_union_map_is_equal(
1644 __isl_keep isl_union_map *umap1,
1645 __isl_keep isl_union_map *umap2);
1647 =item * Disjointness
1649 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1650 __isl_keep isl_set *set2);
1654 int isl_set_is_subset(__isl_keep isl_set *set1,
1655 __isl_keep isl_set *set2);
1656 int isl_set_is_strict_subset(
1657 __isl_keep isl_set *set1,
1658 __isl_keep isl_set *set2);
1659 int isl_union_set_is_subset(
1660 __isl_keep isl_union_set *uset1,
1661 __isl_keep isl_union_set *uset2);
1662 int isl_union_set_is_strict_subset(
1663 __isl_keep isl_union_set *uset1,
1664 __isl_keep isl_union_set *uset2);
1665 int isl_basic_map_is_subset(
1666 __isl_keep isl_basic_map *bmap1,
1667 __isl_keep isl_basic_map *bmap2);
1668 int isl_basic_map_is_strict_subset(
1669 __isl_keep isl_basic_map *bmap1,
1670 __isl_keep isl_basic_map *bmap2);
1671 int isl_map_is_subset(
1672 __isl_keep isl_map *map1,
1673 __isl_keep isl_map *map2);
1674 int isl_map_is_strict_subset(
1675 __isl_keep isl_map *map1,
1676 __isl_keep isl_map *map2);
1677 int isl_union_map_is_subset(
1678 __isl_keep isl_union_map *umap1,
1679 __isl_keep isl_union_map *umap2);
1680 int isl_union_map_is_strict_subset(
1681 __isl_keep isl_union_map *umap1,
1682 __isl_keep isl_union_map *umap2);
1686 =head2 Unary Operations
1692 __isl_give isl_set *isl_set_complement(
1693 __isl_take isl_set *set);
1697 __isl_give isl_basic_map *isl_basic_map_reverse(
1698 __isl_take isl_basic_map *bmap);
1699 __isl_give isl_map *isl_map_reverse(
1700 __isl_take isl_map *map);
1701 __isl_give isl_union_map *isl_union_map_reverse(
1702 __isl_take isl_union_map *umap);
1706 __isl_give isl_basic_set *isl_basic_set_project_out(
1707 __isl_take isl_basic_set *bset,
1708 enum isl_dim_type type, unsigned first, unsigned n);
1709 __isl_give isl_basic_map *isl_basic_map_project_out(
1710 __isl_take isl_basic_map *bmap,
1711 enum isl_dim_type type, unsigned first, unsigned n);
1712 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1713 enum isl_dim_type type, unsigned first, unsigned n);
1714 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1715 enum isl_dim_type type, unsigned first, unsigned n);
1716 __isl_give isl_basic_set *isl_basic_set_params(
1717 __isl_take isl_basic_set *bset);
1718 __isl_give isl_basic_set *isl_basic_map_domain(
1719 __isl_take isl_basic_map *bmap);
1720 __isl_give isl_basic_set *isl_basic_map_range(
1721 __isl_take isl_basic_map *bmap);
1722 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1723 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
1724 __isl_give isl_set *isl_map_domain(
1725 __isl_take isl_map *bmap);
1726 __isl_give isl_set *isl_map_range(
1727 __isl_take isl_map *map);
1728 __isl_give isl_set *isl_union_set_params(
1729 __isl_take isl_union_set *uset);
1730 __isl_give isl_set *isl_union_map_params(
1731 __isl_take isl_union_map *umap);
1732 __isl_give isl_union_set *isl_union_map_domain(
1733 __isl_take isl_union_map *umap);
1734 __isl_give isl_union_set *isl_union_map_range(
1735 __isl_take isl_union_map *umap);
1737 __isl_give isl_basic_map *isl_basic_map_domain_map(
1738 __isl_take isl_basic_map *bmap);
1739 __isl_give isl_basic_map *isl_basic_map_range_map(
1740 __isl_take isl_basic_map *bmap);
1741 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1742 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1743 __isl_give isl_union_map *isl_union_map_domain_map(
1744 __isl_take isl_union_map *umap);
1745 __isl_give isl_union_map *isl_union_map_range_map(
1746 __isl_take isl_union_map *umap);
1748 The functions above construct a (basic, regular or union) relation
1749 that maps (a wrapped version of) the input relation to its domain or range.
1753 __isl_give isl_set *isl_set_eliminate(
1754 __isl_take isl_set *set, enum isl_dim_type type,
1755 unsigned first, unsigned n);
1756 __isl_give isl_basic_map *isl_basic_map_eliminate(
1757 __isl_take isl_basic_map *bmap,
1758 enum isl_dim_type type,
1759 unsigned first, unsigned n);
1761 Eliminate the coefficients for the given dimensions from the constraints,
1762 without removing the dimensions.
1766 __isl_give isl_basic_set *isl_basic_set_fix(
1767 __isl_take isl_basic_set *bset,
1768 enum isl_dim_type type, unsigned pos,
1770 __isl_give isl_basic_set *isl_basic_set_fix_si(
1771 __isl_take isl_basic_set *bset,
1772 enum isl_dim_type type, unsigned pos, int value);
1773 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1774 enum isl_dim_type type, unsigned pos,
1776 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1777 enum isl_dim_type type, unsigned pos, int value);
1778 __isl_give isl_basic_map *isl_basic_map_fix_si(
1779 __isl_take isl_basic_map *bmap,
1780 enum isl_dim_type type, unsigned pos, int value);
1781 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1782 enum isl_dim_type type, unsigned pos, int value);
1784 Intersect the set or relation with the hyperplane where the given
1785 dimension has the fixed given value.
1787 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1788 enum isl_dim_type type1, int pos1,
1789 enum isl_dim_type type2, int pos2);
1790 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1791 enum isl_dim_type type1, int pos1,
1792 enum isl_dim_type type2, int pos2);
1794 Intersect the set or relation with the hyperplane where the given
1795 dimensions are equal to each other.
1797 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
1798 enum isl_dim_type type1, int pos1,
1799 enum isl_dim_type type2, int pos2);
1801 Intersect the relation with the hyperplane where the given
1802 dimensions have opposite values.
1806 __isl_give isl_map *isl_set_identity(
1807 __isl_take isl_set *set);
1808 __isl_give isl_union_map *isl_union_set_identity(
1809 __isl_take isl_union_set *uset);
1811 Construct an identity relation on the given (union) set.
1815 __isl_give isl_basic_set *isl_basic_map_deltas(
1816 __isl_take isl_basic_map *bmap);
1817 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1818 __isl_give isl_union_set *isl_union_map_deltas(
1819 __isl_take isl_union_map *umap);
1821 These functions return a (basic) set containing the differences
1822 between image elements and corresponding domain elements in the input.
1824 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1825 __isl_take isl_basic_map *bmap);
1826 __isl_give isl_map *isl_map_deltas_map(
1827 __isl_take isl_map *map);
1828 __isl_give isl_union_map *isl_union_map_deltas_map(
1829 __isl_take isl_union_map *umap);
1831 The functions above construct a (basic, regular or union) relation
1832 that maps (a wrapped version of) the input relation to its delta set.
1836 Simplify the representation of a set or relation by trying
1837 to combine pairs of basic sets or relations into a single
1838 basic set or relation.
1840 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1841 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1842 __isl_give isl_union_set *isl_union_set_coalesce(
1843 __isl_take isl_union_set *uset);
1844 __isl_give isl_union_map *isl_union_map_coalesce(
1845 __isl_take isl_union_map *umap);
1847 =item * Detecting equalities
1849 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1850 __isl_take isl_basic_set *bset);
1851 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1852 __isl_take isl_basic_map *bmap);
1853 __isl_give isl_set *isl_set_detect_equalities(
1854 __isl_take isl_set *set);
1855 __isl_give isl_map *isl_map_detect_equalities(
1856 __isl_take isl_map *map);
1857 __isl_give isl_union_set *isl_union_set_detect_equalities(
1858 __isl_take isl_union_set *uset);
1859 __isl_give isl_union_map *isl_union_map_detect_equalities(
1860 __isl_take isl_union_map *umap);
1862 Simplify the representation of a set or relation by detecting implicit
1865 =item * Removing redundant constraints
1867 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1868 __isl_take isl_basic_set *bset);
1869 __isl_give isl_set *isl_set_remove_redundancies(
1870 __isl_take isl_set *set);
1871 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1872 __isl_take isl_basic_map *bmap);
1873 __isl_give isl_map *isl_map_remove_redundancies(
1874 __isl_take isl_map *map);
1878 __isl_give isl_basic_set *isl_set_convex_hull(
1879 __isl_take isl_set *set);
1880 __isl_give isl_basic_map *isl_map_convex_hull(
1881 __isl_take isl_map *map);
1883 If the input set or relation has any existentially quantified
1884 variables, then the result of these operations is currently undefined.
1888 __isl_give isl_basic_set *isl_set_simple_hull(
1889 __isl_take isl_set *set);
1890 __isl_give isl_basic_map *isl_map_simple_hull(
1891 __isl_take isl_map *map);
1892 __isl_give isl_union_map *isl_union_map_simple_hull(
1893 __isl_take isl_union_map *umap);
1895 These functions compute a single basic set or relation
1896 that contains the whole input set or relation.
1897 In particular, the output is described by translates
1898 of the constraints describing the basic sets or relations in the input.
1902 (See \autoref{s:simple hull}.)
1908 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1909 __isl_take isl_basic_set *bset);
1910 __isl_give isl_basic_set *isl_set_affine_hull(
1911 __isl_take isl_set *set);
1912 __isl_give isl_union_set *isl_union_set_affine_hull(
1913 __isl_take isl_union_set *uset);
1914 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1915 __isl_take isl_basic_map *bmap);
1916 __isl_give isl_basic_map *isl_map_affine_hull(
1917 __isl_take isl_map *map);
1918 __isl_give isl_union_map *isl_union_map_affine_hull(
1919 __isl_take isl_union_map *umap);
1921 In case of union sets and relations, the affine hull is computed
1924 =item * Polyhedral hull
1926 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1927 __isl_take isl_set *set);
1928 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1929 __isl_take isl_map *map);
1930 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1931 __isl_take isl_union_set *uset);
1932 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1933 __isl_take isl_union_map *umap);
1935 These functions compute a single basic set or relation
1936 not involving any existentially quantified variables
1937 that contains the whole input set or relation.
1938 In case of union sets and relations, the polyhedral hull is computed
1941 =item * Optimization
1943 #include <isl/ilp.h>
1944 enum isl_lp_result isl_basic_set_max(
1945 __isl_keep isl_basic_set *bset,
1946 __isl_keep isl_aff *obj, isl_int *opt)
1947 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
1948 __isl_keep isl_aff *obj, isl_int *opt);
1949 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
1950 __isl_keep isl_aff *obj, isl_int *opt);
1952 Compute the minimum or maximum of the integer affine expression C<obj>
1953 over the points in C<set>, returning the result in C<opt>.
1954 The return value may be one of C<isl_lp_error>,
1955 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
1957 =item * Parametric optimization
1959 __isl_give isl_pw_aff *isl_set_dim_min(
1960 __isl_take isl_set *set, int pos);
1961 __isl_give isl_pw_aff *isl_set_dim_max(
1962 __isl_take isl_set *set, int pos);
1963 __isl_give isl_pw_aff *isl_map_dim_max(
1964 __isl_take isl_map *map, int pos);
1966 Compute the minimum or maximum of the given set or output dimension
1967 as a function of the parameters (and input dimensions), but independently
1968 of the other set or output dimensions.
1969 For lexicographic optimization, see L<"Lexicographic Optimization">.
1973 The following functions compute either the set of (rational) coefficient
1974 values of valid constraints for the given set or the set of (rational)
1975 values satisfying the constraints with coefficients from the given set.
1976 Internally, these two sets of functions perform essentially the
1977 same operations, except that the set of coefficients is assumed to
1978 be a cone, while the set of values may be any polyhedron.
1979 The current implementation is based on the Farkas lemma and
1980 Fourier-Motzkin elimination, but this may change or be made optional
1981 in future. In particular, future implementations may use different
1982 dualization algorithms or skip the elimination step.
1984 __isl_give isl_basic_set *isl_basic_set_coefficients(
1985 __isl_take isl_basic_set *bset);
1986 __isl_give isl_basic_set *isl_set_coefficients(
1987 __isl_take isl_set *set);
1988 __isl_give isl_union_set *isl_union_set_coefficients(
1989 __isl_take isl_union_set *bset);
1990 __isl_give isl_basic_set *isl_basic_set_solutions(
1991 __isl_take isl_basic_set *bset);
1992 __isl_give isl_basic_set *isl_set_solutions(
1993 __isl_take isl_set *set);
1994 __isl_give isl_union_set *isl_union_set_solutions(
1995 __isl_take isl_union_set *bset);
1999 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2001 __isl_give isl_union_map *isl_union_map_power(
2002 __isl_take isl_union_map *umap, int *exact);
2004 Compute a parametric representation for all positive powers I<k> of C<map>.
2005 The result maps I<k> to a nested relation corresponding to the
2006 I<k>th power of C<map>.
2007 The result may be an overapproximation. If the result is known to be exact,
2008 then C<*exact> is set to C<1>.
2010 =item * Transitive closure
2012 __isl_give isl_map *isl_map_transitive_closure(
2013 __isl_take isl_map *map, int *exact);
2014 __isl_give isl_union_map *isl_union_map_transitive_closure(
2015 __isl_take isl_union_map *umap, int *exact);
2017 Compute the transitive closure of C<map>.
2018 The result may be an overapproximation. If the result is known to be exact,
2019 then C<*exact> is set to C<1>.
2021 =item * Reaching path lengths
2023 __isl_give isl_map *isl_map_reaching_path_lengths(
2024 __isl_take isl_map *map, int *exact);
2026 Compute a relation that maps each element in the range of C<map>
2027 to the lengths of all paths composed of edges in C<map> that
2028 end up in the given element.
2029 The result may be an overapproximation. If the result is known to be exact,
2030 then C<*exact> is set to C<1>.
2031 To compute the I<maximal> path length, the resulting relation
2032 should be postprocessed by C<isl_map_lexmax>.
2033 In particular, if the input relation is a dependence relation
2034 (mapping sources to sinks), then the maximal path length corresponds
2035 to the free schedule.
2036 Note, however, that C<isl_map_lexmax> expects the maximum to be
2037 finite, so if the path lengths are unbounded (possibly due to
2038 the overapproximation), then you will get an error message.
2042 __isl_give isl_basic_set *isl_basic_map_wrap(
2043 __isl_take isl_basic_map *bmap);
2044 __isl_give isl_set *isl_map_wrap(
2045 __isl_take isl_map *map);
2046 __isl_give isl_union_set *isl_union_map_wrap(
2047 __isl_take isl_union_map *umap);
2048 __isl_give isl_basic_map *isl_basic_set_unwrap(
2049 __isl_take isl_basic_set *bset);
2050 __isl_give isl_map *isl_set_unwrap(
2051 __isl_take isl_set *set);
2052 __isl_give isl_union_map *isl_union_set_unwrap(
2053 __isl_take isl_union_set *uset);
2057 Remove any internal structure of domain (and range) of the given
2058 set or relation. If there is any such internal structure in the input,
2059 then the name of the space is also removed.
2061 __isl_give isl_basic_set *isl_basic_set_flatten(
2062 __isl_take isl_basic_set *bset);
2063 __isl_give isl_set *isl_set_flatten(
2064 __isl_take isl_set *set);
2065 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2066 __isl_take isl_basic_map *bmap);
2067 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2068 __isl_take isl_basic_map *bmap);
2069 __isl_give isl_map *isl_map_flatten_range(
2070 __isl_take isl_map *map);
2071 __isl_give isl_map *isl_map_flatten_domain(
2072 __isl_take isl_map *map);
2073 __isl_give isl_basic_map *isl_basic_map_flatten(
2074 __isl_take isl_basic_map *bmap);
2075 __isl_give isl_map *isl_map_flatten(
2076 __isl_take isl_map *map);
2078 __isl_give isl_map *isl_set_flatten_map(
2079 __isl_take isl_set *set);
2081 The function above constructs a relation
2082 that maps the input set to a flattened version of the set.
2086 Lift the input set to a space with extra dimensions corresponding
2087 to the existentially quantified variables in the input.
2088 In particular, the result lives in a wrapped map where the domain
2089 is the original space and the range corresponds to the original
2090 existentially quantified variables.
2092 __isl_give isl_basic_set *isl_basic_set_lift(
2093 __isl_take isl_basic_set *bset);
2094 __isl_give isl_set *isl_set_lift(
2095 __isl_take isl_set *set);
2096 __isl_give isl_union_set *isl_union_set_lift(
2097 __isl_take isl_union_set *uset);
2099 Given a local space that contains the existentially quantified
2100 variables of a set, a basic relation that, when applied to
2101 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2102 can be constructed using the following function.
2104 #include <isl/local_space.h>
2105 __isl_give isl_basic_map *isl_local_space_lifting(
2106 __isl_take isl_local_space *ls);
2108 =item * Internal Product
2110 __isl_give isl_basic_map *isl_basic_map_zip(
2111 __isl_take isl_basic_map *bmap);
2112 __isl_give isl_map *isl_map_zip(
2113 __isl_take isl_map *map);
2114 __isl_give isl_union_map *isl_union_map_zip(
2115 __isl_take isl_union_map *umap);
2117 Given a relation with nested relations for domain and range,
2118 interchange the range of the domain with the domain of the range.
2120 =item * Aligning parameters
2122 __isl_give isl_set *isl_set_align_params(
2123 __isl_take isl_set *set,
2124 __isl_take isl_space *model);
2125 __isl_give isl_map *isl_map_align_params(
2126 __isl_take isl_map *map,
2127 __isl_take isl_space *model);
2129 Change the order of the parameters of the given set or relation
2130 such that the first parameters match those of C<model>.
2131 This may involve the introduction of extra parameters.
2132 All parameters need to be named.
2134 =item * Dimension manipulation
2136 __isl_give isl_set *isl_set_add_dims(
2137 __isl_take isl_set *set,
2138 enum isl_dim_type type, unsigned n);
2139 __isl_give isl_map *isl_map_add_dims(
2140 __isl_take isl_map *map,
2141 enum isl_dim_type type, unsigned n);
2142 __isl_give isl_set *isl_set_insert_dims(
2143 __isl_take isl_set *set,
2144 enum isl_dim_type type, unsigned pos, unsigned n);
2145 __isl_give isl_map *isl_map_insert_dims(
2146 __isl_take isl_map *map,
2147 enum isl_dim_type type, unsigned pos, unsigned n);
2148 __isl_give isl_basic_set *isl_basic_set_move_dims(
2149 __isl_take isl_basic_set *bset,
2150 enum isl_dim_type dst_type, unsigned dst_pos,
2151 enum isl_dim_type src_type, unsigned src_pos,
2153 __isl_give isl_basic_map *isl_basic_map_move_dims(
2154 __isl_take isl_basic_map *bmap,
2155 enum isl_dim_type dst_type, unsigned dst_pos,
2156 enum isl_dim_type src_type, unsigned src_pos,
2158 __isl_give isl_set *isl_set_move_dims(
2159 __isl_take isl_set *set,
2160 enum isl_dim_type dst_type, unsigned dst_pos,
2161 enum isl_dim_type src_type, unsigned src_pos,
2163 __isl_give isl_map *isl_map_move_dims(
2164 __isl_take isl_map *map,
2165 enum isl_dim_type dst_type, unsigned dst_pos,
2166 enum isl_dim_type src_type, unsigned src_pos,
2169 It is usually not advisable to directly change the (input or output)
2170 space of a set or a relation as this removes the name and the internal
2171 structure of the space. However, the above functions can be useful
2172 to add new parameters, assuming
2173 C<isl_set_align_params> and C<isl_map_align_params>
2178 =head2 Binary Operations
2180 The two arguments of a binary operation not only need to live
2181 in the same C<isl_ctx>, they currently also need to have
2182 the same (number of) parameters.
2184 =head3 Basic Operations
2188 =item * Intersection
2190 __isl_give isl_basic_set *isl_basic_set_intersect(
2191 __isl_take isl_basic_set *bset1,
2192 __isl_take isl_basic_set *bset2);
2193 __isl_give isl_set *isl_set_intersect_params(
2194 __isl_take isl_set *set,
2195 __isl_take isl_set *params);
2196 __isl_give isl_set *isl_set_intersect(
2197 __isl_take isl_set *set1,
2198 __isl_take isl_set *set2);
2199 __isl_give isl_union_set *isl_union_set_intersect_params(
2200 __isl_take isl_union_set *uset,
2201 __isl_take isl_set *set);
2202 __isl_give isl_union_map *isl_union_map_intersect_params(
2203 __isl_take isl_union_map *umap,
2204 __isl_take isl_set *set);
2205 __isl_give isl_union_set *isl_union_set_intersect(
2206 __isl_take isl_union_set *uset1,
2207 __isl_take isl_union_set *uset2);
2208 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2209 __isl_take isl_basic_map *bmap,
2210 __isl_take isl_basic_set *bset);
2211 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2212 __isl_take isl_basic_map *bmap,
2213 __isl_take isl_basic_set *bset);
2214 __isl_give isl_basic_map *isl_basic_map_intersect(
2215 __isl_take isl_basic_map *bmap1,
2216 __isl_take isl_basic_map *bmap2);
2217 __isl_give isl_map *isl_map_intersect_params(
2218 __isl_take isl_map *map,
2219 __isl_take isl_set *params);
2220 __isl_give isl_map *isl_map_intersect_domain(
2221 __isl_take isl_map *map,
2222 __isl_take isl_set *set);
2223 __isl_give isl_map *isl_map_intersect_range(
2224 __isl_take isl_map *map,
2225 __isl_take isl_set *set);
2226 __isl_give isl_map *isl_map_intersect(
2227 __isl_take isl_map *map1,
2228 __isl_take isl_map *map2);
2229 __isl_give isl_union_map *isl_union_map_intersect_domain(
2230 __isl_take isl_union_map *umap,
2231 __isl_take isl_union_set *uset);
2232 __isl_give isl_union_map *isl_union_map_intersect_range(
2233 __isl_take isl_union_map *umap,
2234 __isl_take isl_union_set *uset);
2235 __isl_give isl_union_map *isl_union_map_intersect(
2236 __isl_take isl_union_map *umap1,
2237 __isl_take isl_union_map *umap2);
2241 __isl_give isl_set *isl_basic_set_union(
2242 __isl_take isl_basic_set *bset1,
2243 __isl_take isl_basic_set *bset2);
2244 __isl_give isl_map *isl_basic_map_union(
2245 __isl_take isl_basic_map *bmap1,
2246 __isl_take isl_basic_map *bmap2);
2247 __isl_give isl_set *isl_set_union(
2248 __isl_take isl_set *set1,
2249 __isl_take isl_set *set2);
2250 __isl_give isl_map *isl_map_union(
2251 __isl_take isl_map *map1,
2252 __isl_take isl_map *map2);
2253 __isl_give isl_union_set *isl_union_set_union(
2254 __isl_take isl_union_set *uset1,
2255 __isl_take isl_union_set *uset2);
2256 __isl_give isl_union_map *isl_union_map_union(
2257 __isl_take isl_union_map *umap1,
2258 __isl_take isl_union_map *umap2);
2260 =item * Set difference
2262 __isl_give isl_set *isl_set_subtract(
2263 __isl_take isl_set *set1,
2264 __isl_take isl_set *set2);
2265 __isl_give isl_map *isl_map_subtract(
2266 __isl_take isl_map *map1,
2267 __isl_take isl_map *map2);
2268 __isl_give isl_union_set *isl_union_set_subtract(
2269 __isl_take isl_union_set *uset1,
2270 __isl_take isl_union_set *uset2);
2271 __isl_give isl_union_map *isl_union_map_subtract(
2272 __isl_take isl_union_map *umap1,
2273 __isl_take isl_union_map *umap2);
2277 __isl_give isl_basic_set *isl_basic_set_apply(
2278 __isl_take isl_basic_set *bset,
2279 __isl_take isl_basic_map *bmap);
2280 __isl_give isl_set *isl_set_apply(
2281 __isl_take isl_set *set,
2282 __isl_take isl_map *map);
2283 __isl_give isl_union_set *isl_union_set_apply(
2284 __isl_take isl_union_set *uset,
2285 __isl_take isl_union_map *umap);
2286 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2287 __isl_take isl_basic_map *bmap1,
2288 __isl_take isl_basic_map *bmap2);
2289 __isl_give isl_basic_map *isl_basic_map_apply_range(
2290 __isl_take isl_basic_map *bmap1,
2291 __isl_take isl_basic_map *bmap2);
2292 __isl_give isl_map *isl_map_apply_domain(
2293 __isl_take isl_map *map1,
2294 __isl_take isl_map *map2);
2295 __isl_give isl_union_map *isl_union_map_apply_domain(
2296 __isl_take isl_union_map *umap1,
2297 __isl_take isl_union_map *umap2);
2298 __isl_give isl_map *isl_map_apply_range(
2299 __isl_take isl_map *map1,
2300 __isl_take isl_map *map2);
2301 __isl_give isl_union_map *isl_union_map_apply_range(
2302 __isl_take isl_union_map *umap1,
2303 __isl_take isl_union_map *umap2);
2305 =item * Cartesian Product
2307 __isl_give isl_set *isl_set_product(
2308 __isl_take isl_set *set1,
2309 __isl_take isl_set *set2);
2310 __isl_give isl_union_set *isl_union_set_product(
2311 __isl_take isl_union_set *uset1,
2312 __isl_take isl_union_set *uset2);
2313 __isl_give isl_basic_map *isl_basic_map_domain_product(
2314 __isl_take isl_basic_map *bmap1,
2315 __isl_take isl_basic_map *bmap2);
2316 __isl_give isl_basic_map *isl_basic_map_range_product(
2317 __isl_take isl_basic_map *bmap1,
2318 __isl_take isl_basic_map *bmap2);
2319 __isl_give isl_map *isl_map_domain_product(
2320 __isl_take isl_map *map1,
2321 __isl_take isl_map *map2);
2322 __isl_give isl_map *isl_map_range_product(
2323 __isl_take isl_map *map1,
2324 __isl_take isl_map *map2);
2325 __isl_give isl_union_map *isl_union_map_range_product(
2326 __isl_take isl_union_map *umap1,
2327 __isl_take isl_union_map *umap2);
2328 __isl_give isl_map *isl_map_product(
2329 __isl_take isl_map *map1,
2330 __isl_take isl_map *map2);
2331 __isl_give isl_union_map *isl_union_map_product(
2332 __isl_take isl_union_map *umap1,
2333 __isl_take isl_union_map *umap2);
2335 The above functions compute the cross product of the given
2336 sets or relations. The domains and ranges of the results
2337 are wrapped maps between domains and ranges of the inputs.
2338 To obtain a ``flat'' product, use the following functions
2341 __isl_give isl_basic_set *isl_basic_set_flat_product(
2342 __isl_take isl_basic_set *bset1,
2343 __isl_take isl_basic_set *bset2);
2344 __isl_give isl_set *isl_set_flat_product(
2345 __isl_take isl_set *set1,
2346 __isl_take isl_set *set2);
2347 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2348 __isl_take isl_basic_map *bmap1,
2349 __isl_take isl_basic_map *bmap2);
2350 __isl_give isl_map *isl_map_flat_domain_product(
2351 __isl_take isl_map *map1,
2352 __isl_take isl_map *map2);
2353 __isl_give isl_map *isl_map_flat_range_product(
2354 __isl_take isl_map *map1,
2355 __isl_take isl_map *map2);
2356 __isl_give isl_union_map *isl_union_map_flat_range_product(
2357 __isl_take isl_union_map *umap1,
2358 __isl_take isl_union_map *umap2);
2359 __isl_give isl_basic_map *isl_basic_map_flat_product(
2360 __isl_take isl_basic_map *bmap1,
2361 __isl_take isl_basic_map *bmap2);
2362 __isl_give isl_map *isl_map_flat_product(
2363 __isl_take isl_map *map1,
2364 __isl_take isl_map *map2);
2366 =item * Simplification
2368 __isl_give isl_basic_set *isl_basic_set_gist(
2369 __isl_take isl_basic_set *bset,
2370 __isl_take isl_basic_set *context);
2371 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2372 __isl_take isl_set *context);
2373 __isl_give isl_set *isl_set_gist_params(
2374 __isl_take isl_set *set,
2375 __isl_take isl_set *context);
2376 __isl_give isl_union_set *isl_union_set_gist(
2377 __isl_take isl_union_set *uset,
2378 __isl_take isl_union_set *context);
2379 __isl_give isl_union_set *isl_union_set_gist_params(
2380 __isl_take isl_union_set *uset,
2381 __isl_take isl_set *set);
2382 __isl_give isl_basic_map *isl_basic_map_gist(
2383 __isl_take isl_basic_map *bmap,
2384 __isl_take isl_basic_map *context);
2385 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2386 __isl_take isl_map *context);
2387 __isl_give isl_map *isl_map_gist_params(
2388 __isl_take isl_map *map,
2389 __isl_take isl_set *context);
2390 __isl_give isl_map *isl_map_gist_domain(
2391 __isl_take isl_map *map,
2392 __isl_take isl_set *context);
2393 __isl_give isl_union_map *isl_union_map_gist(
2394 __isl_take isl_union_map *umap,
2395 __isl_take isl_union_map *context);
2396 __isl_give isl_union_map *isl_union_map_gist_params(
2397 __isl_take isl_union_map *umap,
2398 __isl_take isl_set *set);
2399 __isl_give isl_union_map *isl_union_map_gist_domain(
2400 __isl_take isl_union_map *umap,
2401 __isl_take isl_union_set *uset);
2403 The gist operation returns a set or relation that has the
2404 same intersection with the context as the input set or relation.
2405 Any implicit equality in the intersection is made explicit in the result,
2406 while all inequalities that are redundant with respect to the intersection
2408 In case of union sets and relations, the gist operation is performed
2413 =head3 Lexicographic Optimization
2415 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2416 the following functions
2417 compute a set that contains the lexicographic minimum or maximum
2418 of the elements in C<set> (or C<bset>) for those values of the parameters
2419 that satisfy C<dom>.
2420 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2421 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2423 In other words, the union of the parameter values
2424 for which the result is non-empty and of C<*empty>
2427 __isl_give isl_set *isl_basic_set_partial_lexmin(
2428 __isl_take isl_basic_set *bset,
2429 __isl_take isl_basic_set *dom,
2430 __isl_give isl_set **empty);
2431 __isl_give isl_set *isl_basic_set_partial_lexmax(
2432 __isl_take isl_basic_set *bset,
2433 __isl_take isl_basic_set *dom,
2434 __isl_give isl_set **empty);
2435 __isl_give isl_set *isl_set_partial_lexmin(
2436 __isl_take isl_set *set, __isl_take isl_set *dom,
2437 __isl_give isl_set **empty);
2438 __isl_give isl_set *isl_set_partial_lexmax(
2439 __isl_take isl_set *set, __isl_take isl_set *dom,
2440 __isl_give isl_set **empty);
2442 Given a (basic) set C<set> (or C<bset>), the following functions simply
2443 return a set containing the lexicographic minimum or maximum
2444 of the elements in C<set> (or C<bset>).
2445 In case of union sets, the optimum is computed per space.
2447 __isl_give isl_set *isl_basic_set_lexmin(
2448 __isl_take isl_basic_set *bset);
2449 __isl_give isl_set *isl_basic_set_lexmax(
2450 __isl_take isl_basic_set *bset);
2451 __isl_give isl_set *isl_set_lexmin(
2452 __isl_take isl_set *set);
2453 __isl_give isl_set *isl_set_lexmax(
2454 __isl_take isl_set *set);
2455 __isl_give isl_union_set *isl_union_set_lexmin(
2456 __isl_take isl_union_set *uset);
2457 __isl_give isl_union_set *isl_union_set_lexmax(
2458 __isl_take isl_union_set *uset);
2460 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2461 the following functions
2462 compute a relation that maps each element of C<dom>
2463 to the single lexicographic minimum or maximum
2464 of the elements that are associated to that same
2465 element in C<map> (or C<bmap>).
2466 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2467 that contains the elements in C<dom> that do not map
2468 to any elements in C<map> (or C<bmap>).
2469 In other words, the union of the domain of the result and of C<*empty>
2472 __isl_give isl_map *isl_basic_map_partial_lexmax(
2473 __isl_take isl_basic_map *bmap,
2474 __isl_take isl_basic_set *dom,
2475 __isl_give isl_set **empty);
2476 __isl_give isl_map *isl_basic_map_partial_lexmin(
2477 __isl_take isl_basic_map *bmap,
2478 __isl_take isl_basic_set *dom,
2479 __isl_give isl_set **empty);
2480 __isl_give isl_map *isl_map_partial_lexmax(
2481 __isl_take isl_map *map, __isl_take isl_set *dom,
2482 __isl_give isl_set **empty);
2483 __isl_give isl_map *isl_map_partial_lexmin(
2484 __isl_take isl_map *map, __isl_take isl_set *dom,
2485 __isl_give isl_set **empty);
2487 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2488 return a map mapping each element in the domain of
2489 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2490 of all elements associated to that element.
2491 In case of union relations, the optimum is computed per space.
2493 __isl_give isl_map *isl_basic_map_lexmin(
2494 __isl_take isl_basic_map *bmap);
2495 __isl_give isl_map *isl_basic_map_lexmax(
2496 __isl_take isl_basic_map *bmap);
2497 __isl_give isl_map *isl_map_lexmin(
2498 __isl_take isl_map *map);
2499 __isl_give isl_map *isl_map_lexmax(
2500 __isl_take isl_map *map);
2501 __isl_give isl_union_map *isl_union_map_lexmin(
2502 __isl_take isl_union_map *umap);
2503 __isl_give isl_union_map *isl_union_map_lexmax(
2504 __isl_take isl_union_map *umap);
2506 The following functions return their result in the form of
2507 a piecewise multi-affine expression
2508 (See L<"Piecewise Multiple Quasi Affine Expressions">),
2509 but are otherwise equivalent to the corresponding functions
2510 returning a basic set or relation.
2512 __isl_give isl_pw_multi_aff *
2513 isl_basic_map_lexmin_pw_multi_aff(
2514 __isl_take isl_basic_map *bmap);
2515 __isl_give isl_pw_multi_aff *
2516 isl_basic_set_partial_lexmin_pw_multi_aff(
2517 __isl_take isl_basic_set *bset,
2518 __isl_take isl_basic_set *dom,
2519 __isl_give isl_set **empty);
2520 __isl_give isl_pw_multi_aff *
2521 isl_basic_set_partial_lexmax_pw_multi_aff(
2522 __isl_take isl_basic_set *bset,
2523 __isl_take isl_basic_set *dom,
2524 __isl_give isl_set **empty);
2525 __isl_give isl_pw_multi_aff *
2526 isl_basic_map_partial_lexmin_pw_multi_aff(
2527 __isl_take isl_basic_map *bmap,
2528 __isl_take isl_basic_set *dom,
2529 __isl_give isl_set **empty);
2530 __isl_give isl_pw_multi_aff *
2531 isl_basic_map_partial_lexmax_pw_multi_aff(
2532 __isl_take isl_basic_map *bmap,
2533 __isl_take isl_basic_set *dom,
2534 __isl_give isl_set **empty);
2538 Lists are defined over several element types, including
2539 C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2540 Here we take lists of C<isl_set>s as an example.
2541 Lists can be created, copied and freed using the following functions.
2543 #include <isl/list.h>
2544 __isl_give isl_set_list *isl_set_list_from_set(
2545 __isl_take isl_set *el);
2546 __isl_give isl_set_list *isl_set_list_alloc(
2547 isl_ctx *ctx, int n);
2548 __isl_give isl_set_list *isl_set_list_copy(
2549 __isl_keep isl_set_list *list);
2550 __isl_give isl_set_list *isl_set_list_add(
2551 __isl_take isl_set_list *list,
2552 __isl_take isl_set *el);
2553 __isl_give isl_set_list *isl_set_list_concat(
2554 __isl_take isl_set_list *list1,
2555 __isl_take isl_set_list *list2);
2556 void *isl_set_list_free(__isl_take isl_set_list *list);
2558 C<isl_set_list_alloc> creates an empty list with a capacity for
2559 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2562 Lists can be inspected using the following functions.
2564 #include <isl/list.h>
2565 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2566 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2567 __isl_give isl_set *isl_set_list_get_set(
2568 __isl_keep isl_set_list *list, int index);
2569 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2570 int (*fn)(__isl_take isl_set *el, void *user),
2573 Lists can be printed using
2575 #include <isl/list.h>
2576 __isl_give isl_printer *isl_printer_print_set_list(
2577 __isl_take isl_printer *p,
2578 __isl_keep isl_set_list *list);
2582 Matrices can be created, copied and freed using the following functions.
2584 #include <isl/mat.h>
2585 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2586 unsigned n_row, unsigned n_col);
2587 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2588 void isl_mat_free(__isl_take isl_mat *mat);
2590 Note that the elements of a newly created matrix may have arbitrary values.
2591 The elements can be changed and inspected using the following functions.
2593 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2594 int isl_mat_rows(__isl_keep isl_mat *mat);
2595 int isl_mat_cols(__isl_keep isl_mat *mat);
2596 int isl_mat_get_element(__isl_keep isl_mat *mat,
2597 int row, int col, isl_int *v);
2598 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2599 int row, int col, isl_int v);
2600 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2601 int row, int col, int v);
2603 C<isl_mat_get_element> will return a negative value if anything went wrong.
2604 In that case, the value of C<*v> is undefined.
2606 The following function can be used to compute the (right) inverse
2607 of a matrix, i.e., a matrix such that the product of the original
2608 and the inverse (in that order) is a multiple of the identity matrix.
2609 The input matrix is assumed to be of full row-rank.
2611 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2613 The following function can be used to compute the (right) kernel
2614 (or null space) of a matrix, i.e., a matrix such that the product of
2615 the original and the kernel (in that order) is the zero matrix.
2617 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2619 =head2 Piecewise Quasi Affine Expressions
2621 The zero quasi affine expression on a given domain can be created using
2623 __isl_give isl_aff *isl_aff_zero_on_domain(
2624 __isl_take isl_local_space *ls);
2626 Note that the space in which the resulting object lives is a map space
2627 with the given space as domain and a one-dimensional range.
2629 An empty piecewise quasi affine expression (one with no cells)
2630 or a piecewise quasi affine expression with a single cell can
2631 be created using the following functions.
2633 #include <isl/aff.h>
2634 __isl_give isl_pw_aff *isl_pw_aff_empty(
2635 __isl_take isl_space *space);
2636 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2637 __isl_take isl_set *set, __isl_take isl_aff *aff);
2638 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2639 __isl_take isl_aff *aff);
2641 Quasi affine expressions can be copied and freed using
2643 #include <isl/aff.h>
2644 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2645 void *isl_aff_free(__isl_take isl_aff *aff);
2647 __isl_give isl_pw_aff *isl_pw_aff_copy(
2648 __isl_keep isl_pw_aff *pwaff);
2649 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2651 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2652 using the following function. The constraint is required to have
2653 a non-zero coefficient for the specified dimension.
2655 #include <isl/constraint.h>
2656 __isl_give isl_aff *isl_constraint_get_bound(
2657 __isl_keep isl_constraint *constraint,
2658 enum isl_dim_type type, int pos);
2660 The entire affine expression of the constraint can also be extracted
2661 using the following function.
2663 #include <isl/constraint.h>
2664 __isl_give isl_aff *isl_constraint_get_aff(
2665 __isl_keep isl_constraint *constraint);
2667 Conversely, an equality constraint equating
2668 the affine expression to zero or an inequality constraint enforcing
2669 the affine expression to be non-negative, can be constructed using
2671 __isl_give isl_constraint *isl_equality_from_aff(
2672 __isl_take isl_aff *aff);
2673 __isl_give isl_constraint *isl_inequality_from_aff(
2674 __isl_take isl_aff *aff);
2676 The expression can be inspected using
2678 #include <isl/aff.h>
2679 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2680 int isl_aff_dim(__isl_keep isl_aff *aff,
2681 enum isl_dim_type type);
2682 __isl_give isl_local_space *isl_aff_get_domain_local_space(
2683 __isl_keep isl_aff *aff);
2684 __isl_give isl_local_space *isl_aff_get_local_space(
2685 __isl_keep isl_aff *aff);
2686 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2687 enum isl_dim_type type, unsigned pos);
2688 const char *isl_pw_aff_get_dim_name(
2689 __isl_keep isl_pw_aff *pa,
2690 enum isl_dim_type type, unsigned pos);
2691 __isl_give isl_id *isl_pw_aff_get_dim_id(
2692 __isl_keep isl_pw_aff *pa,
2693 enum isl_dim_type type, unsigned pos);
2694 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2696 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2697 enum isl_dim_type type, int pos, isl_int *v);
2698 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2700 __isl_give isl_aff *isl_aff_get_div(
2701 __isl_keep isl_aff *aff, int pos);
2703 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2704 int (*fn)(__isl_take isl_set *set,
2705 __isl_take isl_aff *aff,
2706 void *user), void *user);
2708 int isl_aff_is_cst(__isl_keep isl_aff *aff);
2709 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
2711 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
2712 enum isl_dim_type type, unsigned first, unsigned n);
2713 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
2714 enum isl_dim_type type, unsigned first, unsigned n);
2716 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2717 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2718 enum isl_dim_type type);
2719 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2721 It can be modified using
2723 #include <isl/aff.h>
2724 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
2725 __isl_take isl_pw_aff *pwaff,
2726 enum isl_dim_type type, __isl_take isl_id *id);
2727 __isl_give isl_aff *isl_aff_set_dim_name(
2728 __isl_take isl_aff *aff, enum isl_dim_type type,
2729 unsigned pos, const char *s);
2730 __isl_give isl_aff *isl_aff_set_dim_id(
2731 __isl_take isl_aff *aff, enum isl_dim_type type,
2732 unsigned pos, __isl_take isl_id *id);
2733 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
2734 __isl_take isl_pw_aff *pma,
2735 enum isl_dim_type type, unsigned pos,
2736 __isl_take isl_id *id);
2737 __isl_give isl_aff *isl_aff_set_constant(
2738 __isl_take isl_aff *aff, isl_int v);
2739 __isl_give isl_aff *isl_aff_set_constant_si(
2740 __isl_take isl_aff *aff, int v);
2741 __isl_give isl_aff *isl_aff_set_coefficient(
2742 __isl_take isl_aff *aff,
2743 enum isl_dim_type type, int pos, isl_int v);
2744 __isl_give isl_aff *isl_aff_set_coefficient_si(
2745 __isl_take isl_aff *aff,
2746 enum isl_dim_type type, int pos, int v);
2747 __isl_give isl_aff *isl_aff_set_denominator(
2748 __isl_take isl_aff *aff, isl_int v);
2750 __isl_give isl_aff *isl_aff_add_constant(
2751 __isl_take isl_aff *aff, isl_int v);
2752 __isl_give isl_aff *isl_aff_add_constant_si(
2753 __isl_take isl_aff *aff, int v);
2754 __isl_give isl_aff *isl_aff_add_coefficient(
2755 __isl_take isl_aff *aff,
2756 enum isl_dim_type type, int pos, isl_int v);
2757 __isl_give isl_aff *isl_aff_add_coefficient_si(
2758 __isl_take isl_aff *aff,
2759 enum isl_dim_type type, int pos, int v);
2761 __isl_give isl_aff *isl_aff_insert_dims(
2762 __isl_take isl_aff *aff,
2763 enum isl_dim_type type, unsigned first, unsigned n);
2764 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
2765 __isl_take isl_pw_aff *pwaff,
2766 enum isl_dim_type type, unsigned first, unsigned n);
2767 __isl_give isl_aff *isl_aff_add_dims(
2768 __isl_take isl_aff *aff,
2769 enum isl_dim_type type, unsigned n);
2770 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
2771 __isl_take isl_pw_aff *pwaff,
2772 enum isl_dim_type type, unsigned n);
2773 __isl_give isl_aff *isl_aff_drop_dims(
2774 __isl_take isl_aff *aff,
2775 enum isl_dim_type type, unsigned first, unsigned n);
2776 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
2777 __isl_take isl_pw_aff *pwaff,
2778 enum isl_dim_type type, unsigned first, unsigned n);
2780 Note that the C<set_constant> and C<set_coefficient> functions
2781 set the I<numerator> of the constant or coefficient, while
2782 C<add_constant> and C<add_coefficient> add an integer value to
2783 the possibly rational constant or coefficient.
2785 To check whether an affine expressions is obviously zero
2786 or obviously equal to some other affine expression, use
2788 #include <isl/aff.h>
2789 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
2790 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
2791 __isl_keep isl_aff *aff2);
2792 int isl_pw_aff_plain_is_equal(
2793 __isl_keep isl_pw_aff *pwaff1,
2794 __isl_keep isl_pw_aff *pwaff2);
2798 #include <isl/aff.h>
2799 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2800 __isl_take isl_aff *aff2);
2801 __isl_give isl_pw_aff *isl_pw_aff_add(
2802 __isl_take isl_pw_aff *pwaff1,
2803 __isl_take isl_pw_aff *pwaff2);
2804 __isl_give isl_pw_aff *isl_pw_aff_min(
2805 __isl_take isl_pw_aff *pwaff1,
2806 __isl_take isl_pw_aff *pwaff2);
2807 __isl_give isl_pw_aff *isl_pw_aff_max(
2808 __isl_take isl_pw_aff *pwaff1,
2809 __isl_take isl_pw_aff *pwaff2);
2810 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2811 __isl_take isl_aff *aff2);
2812 __isl_give isl_pw_aff *isl_pw_aff_sub(
2813 __isl_take isl_pw_aff *pwaff1,
2814 __isl_take isl_pw_aff *pwaff2);
2815 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2816 __isl_give isl_pw_aff *isl_pw_aff_neg(
2817 __isl_take isl_pw_aff *pwaff);
2818 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2819 __isl_give isl_pw_aff *isl_pw_aff_ceil(
2820 __isl_take isl_pw_aff *pwaff);
2821 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
2822 __isl_give isl_pw_aff *isl_pw_aff_floor(
2823 __isl_take isl_pw_aff *pwaff);
2824 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
2826 __isl_give isl_pw_aff *isl_pw_aff_mod(
2827 __isl_take isl_pw_aff *pwaff, isl_int mod);
2828 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2830 __isl_give isl_pw_aff *isl_pw_aff_scale(
2831 __isl_take isl_pw_aff *pwaff, isl_int f);
2832 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2834 __isl_give isl_aff *isl_aff_scale_down_ui(
2835 __isl_take isl_aff *aff, unsigned f);
2836 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
2837 __isl_take isl_pw_aff *pwaff, isl_int f);
2839 __isl_give isl_pw_aff *isl_pw_aff_list_min(
2840 __isl_take isl_pw_aff_list *list);
2841 __isl_give isl_pw_aff *isl_pw_aff_list_max(
2842 __isl_take isl_pw_aff_list *list);
2844 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
2845 __isl_take isl_pw_aff *pwqp);
2847 __isl_give isl_pw_aff *isl_pw_aff_align_params(
2848 __isl_take isl_pw_aff *pwaff,
2849 __isl_take isl_space *model);
2851 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
2852 __isl_take isl_set *context);
2853 __isl_give isl_pw_aff *isl_pw_aff_gist(
2854 __isl_take isl_pw_aff *pwaff,
2855 __isl_take isl_set *context);
2857 __isl_give isl_set *isl_pw_aff_domain(
2858 __isl_take isl_pw_aff *pwaff);
2859 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
2860 __isl_take isl_pw_aff *pa,
2861 __isl_take isl_set *set);
2863 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
2864 __isl_take isl_aff *aff2);
2865 __isl_give isl_pw_aff *isl_pw_aff_mul(
2866 __isl_take isl_pw_aff *pwaff1,
2867 __isl_take isl_pw_aff *pwaff2);
2869 When multiplying two affine expressions, at least one of the two needs
2872 #include <isl/aff.h>
2873 __isl_give isl_basic_set *isl_aff_le_basic_set(
2874 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2875 __isl_give isl_basic_set *isl_aff_ge_basic_set(
2876 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2877 __isl_give isl_set *isl_pw_aff_eq_set(
2878 __isl_take isl_pw_aff *pwaff1,
2879 __isl_take isl_pw_aff *pwaff2);
2880 __isl_give isl_set *isl_pw_aff_ne_set(
2881 __isl_take isl_pw_aff *pwaff1,
2882 __isl_take isl_pw_aff *pwaff2);
2883 __isl_give isl_set *isl_pw_aff_le_set(
2884 __isl_take isl_pw_aff *pwaff1,
2885 __isl_take isl_pw_aff *pwaff2);
2886 __isl_give isl_set *isl_pw_aff_lt_set(
2887 __isl_take isl_pw_aff *pwaff1,
2888 __isl_take isl_pw_aff *pwaff2);
2889 __isl_give isl_set *isl_pw_aff_ge_set(
2890 __isl_take isl_pw_aff *pwaff1,
2891 __isl_take isl_pw_aff *pwaff2);
2892 __isl_give isl_set *isl_pw_aff_gt_set(
2893 __isl_take isl_pw_aff *pwaff1,
2894 __isl_take isl_pw_aff *pwaff2);
2896 __isl_give isl_set *isl_pw_aff_list_eq_set(
2897 __isl_take isl_pw_aff_list *list1,
2898 __isl_take isl_pw_aff_list *list2);
2899 __isl_give isl_set *isl_pw_aff_list_ne_set(
2900 __isl_take isl_pw_aff_list *list1,
2901 __isl_take isl_pw_aff_list *list2);
2902 __isl_give isl_set *isl_pw_aff_list_le_set(
2903 __isl_take isl_pw_aff_list *list1,
2904 __isl_take isl_pw_aff_list *list2);
2905 __isl_give isl_set *isl_pw_aff_list_lt_set(
2906 __isl_take isl_pw_aff_list *list1,
2907 __isl_take isl_pw_aff_list *list2);
2908 __isl_give isl_set *isl_pw_aff_list_ge_set(
2909 __isl_take isl_pw_aff_list *list1,
2910 __isl_take isl_pw_aff_list *list2);
2911 __isl_give isl_set *isl_pw_aff_list_gt_set(
2912 __isl_take isl_pw_aff_list *list1,
2913 __isl_take isl_pw_aff_list *list2);
2915 The function C<isl_aff_ge_basic_set> returns a basic set
2916 containing those elements in the shared space
2917 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
2918 The function C<isl_aff_ge_set> returns a set
2919 containing those elements in the shared domain
2920 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
2921 The functions operating on C<isl_pw_aff_list> apply the corresponding
2922 C<isl_pw_aff> function to each pair of elements in the two lists.
2924 #include <isl/aff.h>
2925 __isl_give isl_set *isl_pw_aff_nonneg_set(
2926 __isl_take isl_pw_aff *pwaff);
2927 __isl_give isl_set *isl_pw_aff_zero_set(
2928 __isl_take isl_pw_aff *pwaff);
2929 __isl_give isl_set *isl_pw_aff_non_zero_set(
2930 __isl_take isl_pw_aff *pwaff);
2932 The function C<isl_pw_aff_nonneg_set> returns a set
2933 containing those elements in the domain
2934 of C<pwaff> where C<pwaff> is non-negative.
2936 #include <isl/aff.h>
2937 __isl_give isl_pw_aff *isl_pw_aff_cond(
2938 __isl_take isl_set *cond,
2939 __isl_take isl_pw_aff *pwaff_true,
2940 __isl_take isl_pw_aff *pwaff_false);
2942 The function C<isl_pw_aff_cond> performs a conditional operator
2943 and returns an expression that is equal to C<pwaff_true>
2944 for elements in C<cond> and equal to C<pwaff_false> for elements
2947 #include <isl/aff.h>
2948 __isl_give isl_pw_aff *isl_pw_aff_union_min(
2949 __isl_take isl_pw_aff *pwaff1,
2950 __isl_take isl_pw_aff *pwaff2);
2951 __isl_give isl_pw_aff *isl_pw_aff_union_max(
2952 __isl_take isl_pw_aff *pwaff1,
2953 __isl_take isl_pw_aff *pwaff2);
2954 __isl_give isl_pw_aff *isl_pw_aff_union_add(
2955 __isl_take isl_pw_aff *pwaff1,
2956 __isl_take isl_pw_aff *pwaff2);
2958 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
2959 expression with a domain that is the union of those of C<pwaff1> and
2960 C<pwaff2> and such that on each cell, the quasi-affine expression is
2961 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
2962 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
2963 associated expression is the defined one.
2965 An expression can be read from input using
2967 #include <isl/aff.h>
2968 __isl_give isl_aff *isl_aff_read_from_str(
2969 isl_ctx *ctx, const char *str);
2970 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
2971 isl_ctx *ctx, const char *str);
2973 An expression can be printed using
2975 #include <isl/aff.h>
2976 __isl_give isl_printer *isl_printer_print_aff(
2977 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
2979 __isl_give isl_printer *isl_printer_print_pw_aff(
2980 __isl_take isl_printer *p,
2981 __isl_keep isl_pw_aff *pwaff);
2983 =head2 Piecewise Multiple Quasi Affine Expressions
2985 An C<isl_multi_aff> object represents a sequence of
2986 zero or more affine expressions, all defined on the same domain space.
2988 An C<isl_multi_aff> can be constructed from a C<isl_aff_list> using the
2991 #include <isl/aff.h>
2992 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
2993 __isl_take isl_space *space,
2994 __isl_take isl_aff_list *list);
2996 An empty piecewise multiple quasi affine expression (one with no cells) or
2997 a piecewise multiple quasi affine expression with a single cell can
2998 be created using the following functions.
3000 #include <isl/aff.h>
3001 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3002 __isl_take isl_space *space);
3003 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3004 __isl_take isl_set *set,
3005 __isl_take isl_multi_aff *maff);
3007 A piecewise multiple quasi affine expression can also be initialized
3008 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3009 and the C<isl_map> is single-valued.
3011 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3012 __isl_take isl_set *set);
3013 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3014 __isl_take isl_map *map);
3016 Multiple quasi affine expressions can be copied and freed using
3018 #include <isl/aff.h>
3019 __isl_give isl_multi_aff *isl_multi_aff_copy(
3020 __isl_keep isl_multi_aff *maff);
3021 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
3023 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3024 __isl_keep isl_pw_multi_aff *pma);
3025 void *isl_pw_multi_aff_free(
3026 __isl_take isl_pw_multi_aff *pma);
3028 The expression can be inspected using
3030 #include <isl/aff.h>
3031 isl_ctx *isl_multi_aff_get_ctx(
3032 __isl_keep isl_multi_aff *maff);
3033 isl_ctx *isl_pw_multi_aff_get_ctx(
3034 __isl_keep isl_pw_multi_aff *pma);
3035 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
3036 enum isl_dim_type type);
3037 unsigned isl_pw_multi_aff_dim(
3038 __isl_keep isl_pw_multi_aff *pma,
3039 enum isl_dim_type type);
3040 __isl_give isl_aff *isl_multi_aff_get_aff(
3041 __isl_keep isl_multi_aff *multi, int pos);
3042 const char *isl_pw_multi_aff_get_dim_name(
3043 __isl_keep isl_pw_multi_aff *pma,
3044 enum isl_dim_type type, unsigned pos);
3045 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
3046 __isl_keep isl_pw_multi_aff *pma,
3047 enum isl_dim_type type, unsigned pos);
3048 const char *isl_multi_aff_get_tuple_name(
3049 __isl_keep isl_multi_aff *multi,
3050 enum isl_dim_type type);
3051 const char *isl_pw_multi_aff_get_tuple_name(
3052 __isl_keep isl_pw_multi_aff *pma,
3053 enum isl_dim_type type);
3054 int isl_pw_multi_aff_has_tuple_id(
3055 __isl_keep isl_pw_multi_aff *pma,
3056 enum isl_dim_type type);
3057 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
3058 __isl_keep isl_pw_multi_aff *pma,
3059 enum isl_dim_type type);
3061 int isl_pw_multi_aff_foreach_piece(
3062 __isl_keep isl_pw_multi_aff *pma,
3063 int (*fn)(__isl_take isl_set *set,
3064 __isl_take isl_multi_aff *maff,
3065 void *user), void *user);
3067 It can be modified using
3069 #include <isl/aff.h>
3070 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
3071 __isl_take isl_multi_aff *maff,
3072 enum isl_dim_type type, unsigned pos, const char *s);
3073 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
3074 __isl_take isl_pw_multi_aff *pma,
3075 enum isl_dim_type type, __isl_take isl_id *id);
3077 To check whether two multiple affine expressions are
3078 obviously equal to each other, use
3080 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
3081 __isl_keep isl_multi_aff *maff2);
3082 int isl_pw_multi_aff_plain_is_equal(
3083 __isl_keep isl_pw_multi_aff *pma1,
3084 __isl_keep isl_pw_multi_aff *pma2);
3088 #include <isl/aff.h>
3089 __isl_give isl_multi_aff *isl_multi_aff_add(
3090 __isl_take isl_multi_aff *maff1,
3091 __isl_take isl_multi_aff *maff2);
3092 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
3093 __isl_take isl_pw_multi_aff *pma1,
3094 __isl_take isl_pw_multi_aff *pma2);
3095 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
3096 __isl_take isl_pw_multi_aff *pma1,
3097 __isl_take isl_pw_multi_aff *pma2);
3098 __isl_give isl_multi_aff *isl_multi_aff_scale(
3099 __isl_take isl_multi_aff *maff,
3101 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
3102 __isl_take isl_pw_multi_aff *pma,
3103 __isl_take isl_set *set);
3104 __isl_give isl_multi_aff *isl_multi_aff_lift(
3105 __isl_take isl_multi_aff *maff,
3106 __isl_give isl_local_space **ls);
3107 __isl_give isl_multi_aff *isl_multi_aff_gist(
3108 __isl_take isl_multi_aff *maff,
3109 __isl_take isl_set *context);
3111 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
3112 then it is assigned the local space that lies at the basis of
3113 the lifting applied.
3115 An expression can be read from input using
3117 #include <isl/aff.h>
3118 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3119 isl_ctx *ctx, const char *str);
3120 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3121 isl_ctx *ctx, const char *str);
3123 An expression can be printed using
3125 #include <isl/aff.h>
3126 __isl_give isl_printer *isl_printer_print_multi_aff(
3127 __isl_take isl_printer *p,
3128 __isl_keep isl_multi_aff *maff);
3129 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3130 __isl_take isl_printer *p,
3131 __isl_keep isl_pw_multi_aff *pma);
3135 Points are elements of a set. They can be used to construct
3136 simple sets (boxes) or they can be used to represent the
3137 individual elements of a set.
3138 The zero point (the origin) can be created using
3140 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
3142 The coordinates of a point can be inspected, set and changed
3145 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
3146 enum isl_dim_type type, int pos, isl_int *v);
3147 __isl_give isl_point *isl_point_set_coordinate(
3148 __isl_take isl_point *pnt,
3149 enum isl_dim_type type, int pos, isl_int v);
3151 __isl_give isl_point *isl_point_add_ui(
3152 __isl_take isl_point *pnt,
3153 enum isl_dim_type type, int pos, unsigned val);
3154 __isl_give isl_point *isl_point_sub_ui(
3155 __isl_take isl_point *pnt,
3156 enum isl_dim_type type, int pos, unsigned val);
3158 Other properties can be obtained using
3160 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
3162 Points can be copied or freed using
3164 __isl_give isl_point *isl_point_copy(
3165 __isl_keep isl_point *pnt);
3166 void isl_point_free(__isl_take isl_point *pnt);
3168 A singleton set can be created from a point using
3170 __isl_give isl_basic_set *isl_basic_set_from_point(
3171 __isl_take isl_point *pnt);
3172 __isl_give isl_set *isl_set_from_point(
3173 __isl_take isl_point *pnt);
3175 and a box can be created from two opposite extremal points using
3177 __isl_give isl_basic_set *isl_basic_set_box_from_points(
3178 __isl_take isl_point *pnt1,
3179 __isl_take isl_point *pnt2);
3180 __isl_give isl_set *isl_set_box_from_points(
3181 __isl_take isl_point *pnt1,
3182 __isl_take isl_point *pnt2);
3184 All elements of a B<bounded> (union) set can be enumerated using
3185 the following functions.
3187 int isl_set_foreach_point(__isl_keep isl_set *set,
3188 int (*fn)(__isl_take isl_point *pnt, void *user),
3190 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
3191 int (*fn)(__isl_take isl_point *pnt, void *user),
3194 The function C<fn> is called for each integer point in
3195 C<set> with as second argument the last argument of
3196 the C<isl_set_foreach_point> call. The function C<fn>
3197 should return C<0> on success and C<-1> on failure.
3198 In the latter case, C<isl_set_foreach_point> will stop
3199 enumerating and return C<-1> as well.
3200 If the enumeration is performed successfully and to completion,
3201 then C<isl_set_foreach_point> returns C<0>.
3203 To obtain a single point of a (basic) set, use
3205 __isl_give isl_point *isl_basic_set_sample_point(
3206 __isl_take isl_basic_set *bset);
3207 __isl_give isl_point *isl_set_sample_point(
3208 __isl_take isl_set *set);
3210 If C<set> does not contain any (integer) points, then the
3211 resulting point will be ``void'', a property that can be
3214 int isl_point_is_void(__isl_keep isl_point *pnt);
3216 =head2 Piecewise Quasipolynomials
3218 A piecewise quasipolynomial is a particular kind of function that maps
3219 a parametric point to a rational value.
3220 More specifically, a quasipolynomial is a polynomial expression in greatest
3221 integer parts of affine expressions of parameters and variables.
3222 A piecewise quasipolynomial is a subdivision of a given parametric
3223 domain into disjoint cells with a quasipolynomial associated to
3224 each cell. The value of the piecewise quasipolynomial at a given
3225 point is the value of the quasipolynomial associated to the cell
3226 that contains the point. Outside of the union of cells,
3227 the value is assumed to be zero.
3228 For example, the piecewise quasipolynomial
3230 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3232 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
3233 A given piecewise quasipolynomial has a fixed domain dimension.
3234 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
3235 defined over different domains.
3236 Piecewise quasipolynomials are mainly used by the C<barvinok>
3237 library for representing the number of elements in a parametric set or map.
3238 For example, the piecewise quasipolynomial above represents
3239 the number of points in the map
3241 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3243 =head3 Input and Output
3245 Piecewise quasipolynomials can be read from input using
3247 __isl_give isl_union_pw_qpolynomial *
3248 isl_union_pw_qpolynomial_read_from_str(
3249 isl_ctx *ctx, const char *str);
3251 Quasipolynomials and piecewise quasipolynomials can be printed
3252 using the following functions.
3254 __isl_give isl_printer *isl_printer_print_qpolynomial(
3255 __isl_take isl_printer *p,
3256 __isl_keep isl_qpolynomial *qp);
3258 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3259 __isl_take isl_printer *p,
3260 __isl_keep isl_pw_qpolynomial *pwqp);
3262 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3263 __isl_take isl_printer *p,
3264 __isl_keep isl_union_pw_qpolynomial *upwqp);
3266 The output format of the printer
3267 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3268 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
3270 In case of printing in C<ISL_FORMAT_C>, the user may want
3271 to set the names of all dimensions
3273 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
3274 __isl_take isl_qpolynomial *qp,
3275 enum isl_dim_type type, unsigned pos,
3277 __isl_give isl_pw_qpolynomial *
3278 isl_pw_qpolynomial_set_dim_name(
3279 __isl_take isl_pw_qpolynomial *pwqp,
3280 enum isl_dim_type type, unsigned pos,
3283 =head3 Creating New (Piecewise) Quasipolynomials
3285 Some simple quasipolynomials can be created using the following functions.
3286 More complicated quasipolynomials can be created by applying
3287 operations such as addition and multiplication
3288 on the resulting quasipolynomials
3290 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3291 __isl_take isl_space *domain);
3292 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3293 __isl_take isl_space *domain);
3294 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3295 __isl_take isl_space *domain);
3296 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3297 __isl_take isl_space *domain);
3298 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3299 __isl_take isl_space *domain);
3300 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
3301 __isl_take isl_space *domain,
3302 const isl_int n, const isl_int d);
3303 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3304 __isl_take isl_space *domain,
3305 enum isl_dim_type type, unsigned pos);
3306 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3307 __isl_take isl_aff *aff);
3309 Note that the space in which a quasipolynomial lives is a map space
3310 with a one-dimensional range. The C<domain> argument in some of
3311 the functions above corresponds to the domain of this map space.
3313 The zero piecewise quasipolynomial or a piecewise quasipolynomial
3314 with a single cell can be created using the following functions.
3315 Multiple of these single cell piecewise quasipolynomials can
3316 be combined to create more complicated piecewise quasipolynomials.
3318 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3319 __isl_take isl_space *space);
3320 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3321 __isl_take isl_set *set,
3322 __isl_take isl_qpolynomial *qp);
3323 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3324 __isl_take isl_qpolynomial *qp);
3325 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3326 __isl_take isl_pw_aff *pwaff);
3328 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3329 __isl_take isl_space *space);
3330 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3331 __isl_take isl_pw_qpolynomial *pwqp);
3332 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3333 __isl_take isl_union_pw_qpolynomial *upwqp,
3334 __isl_take isl_pw_qpolynomial *pwqp);
3336 Quasipolynomials can be copied and freed again using the following
3339 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3340 __isl_keep isl_qpolynomial *qp);
3341 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3343 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3344 __isl_keep isl_pw_qpolynomial *pwqp);
3345 void *isl_pw_qpolynomial_free(
3346 __isl_take isl_pw_qpolynomial *pwqp);
3348 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3349 __isl_keep isl_union_pw_qpolynomial *upwqp);
3350 void isl_union_pw_qpolynomial_free(
3351 __isl_take isl_union_pw_qpolynomial *upwqp);
3353 =head3 Inspecting (Piecewise) Quasipolynomials
3355 To iterate over all piecewise quasipolynomials in a union
3356 piecewise quasipolynomial, use the following function
3358 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3359 __isl_keep isl_union_pw_qpolynomial *upwqp,
3360 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3363 To extract the piecewise quasipolynomial in a given space from a union, use
3365 __isl_give isl_pw_qpolynomial *
3366 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3367 __isl_keep isl_union_pw_qpolynomial *upwqp,
3368 __isl_take isl_space *space);
3370 To iterate over the cells in a piecewise quasipolynomial,
3371 use either of the following two functions
3373 int isl_pw_qpolynomial_foreach_piece(
3374 __isl_keep isl_pw_qpolynomial *pwqp,
3375 int (*fn)(__isl_take isl_set *set,
3376 __isl_take isl_qpolynomial *qp,
3377 void *user), void *user);
3378 int isl_pw_qpolynomial_foreach_lifted_piece(
3379 __isl_keep isl_pw_qpolynomial *pwqp,
3380 int (*fn)(__isl_take isl_set *set,
3381 __isl_take isl_qpolynomial *qp,
3382 void *user), void *user);
3384 As usual, the function C<fn> should return C<0> on success
3385 and C<-1> on failure. The difference between
3386 C<isl_pw_qpolynomial_foreach_piece> and
3387 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3388 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3389 compute unique representations for all existentially quantified
3390 variables and then turn these existentially quantified variables
3391 into extra set variables, adapting the associated quasipolynomial
3392 accordingly. This means that the C<set> passed to C<fn>
3393 will not have any existentially quantified variables, but that
3394 the dimensions of the sets may be different for different
3395 invocations of C<fn>.
3397 To iterate over all terms in a quasipolynomial,
3400 int isl_qpolynomial_foreach_term(
3401 __isl_keep isl_qpolynomial *qp,
3402 int (*fn)(__isl_take isl_term *term,
3403 void *user), void *user);
3405 The terms themselves can be inspected and freed using
3408 unsigned isl_term_dim(__isl_keep isl_term *term,
3409 enum isl_dim_type type);
3410 void isl_term_get_num(__isl_keep isl_term *term,
3412 void isl_term_get_den(__isl_keep isl_term *term,
3414 int isl_term_get_exp(__isl_keep isl_term *term,
3415 enum isl_dim_type type, unsigned pos);
3416 __isl_give isl_aff *isl_term_get_div(
3417 __isl_keep isl_term *term, unsigned pos);
3418 void isl_term_free(__isl_take isl_term *term);
3420 Each term is a product of parameters, set variables and
3421 integer divisions. The function C<isl_term_get_exp>
3422 returns the exponent of a given dimensions in the given term.
3423 The C<isl_int>s in the arguments of C<isl_term_get_num>
3424 and C<isl_term_get_den> need to have been initialized
3425 using C<isl_int_init> before calling these functions.
3427 =head3 Properties of (Piecewise) Quasipolynomials
3429 To check whether a quasipolynomial is actually a constant,
3430 use the following function.
3432 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3433 isl_int *n, isl_int *d);
3435 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3436 then the numerator and denominator of the constant
3437 are returned in C<*n> and C<*d>, respectively.
3439 To check whether two union piecewise quasipolynomials are
3440 obviously equal, use
3442 int isl_union_pw_qpolynomial_plain_is_equal(
3443 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3444 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3446 =head3 Operations on (Piecewise) Quasipolynomials
3448 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3449 __isl_take isl_qpolynomial *qp, isl_int v);
3450 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3451 __isl_take isl_qpolynomial *qp);
3452 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3453 __isl_take isl_qpolynomial *qp1,
3454 __isl_take isl_qpolynomial *qp2);
3455 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3456 __isl_take isl_qpolynomial *qp1,
3457 __isl_take isl_qpolynomial *qp2);
3458 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3459 __isl_take isl_qpolynomial *qp1,
3460 __isl_take isl_qpolynomial *qp2);
3461 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3462 __isl_take isl_qpolynomial *qp, unsigned exponent);
3464 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3465 __isl_take isl_pw_qpolynomial *pwqp1,
3466 __isl_take isl_pw_qpolynomial *pwqp2);
3467 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3468 __isl_take isl_pw_qpolynomial *pwqp1,
3469 __isl_take isl_pw_qpolynomial *pwqp2);
3470 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3471 __isl_take isl_pw_qpolynomial *pwqp1,
3472 __isl_take isl_pw_qpolynomial *pwqp2);
3473 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3474 __isl_take isl_pw_qpolynomial *pwqp);
3475 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3476 __isl_take isl_pw_qpolynomial *pwqp1,
3477 __isl_take isl_pw_qpolynomial *pwqp2);
3478 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3479 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3481 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3482 __isl_take isl_union_pw_qpolynomial *upwqp1,
3483 __isl_take isl_union_pw_qpolynomial *upwqp2);
3484 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3485 __isl_take isl_union_pw_qpolynomial *upwqp1,
3486 __isl_take isl_union_pw_qpolynomial *upwqp2);
3487 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3488 __isl_take isl_union_pw_qpolynomial *upwqp1,
3489 __isl_take isl_union_pw_qpolynomial *upwqp2);
3491 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
3492 __isl_take isl_pw_qpolynomial *pwqp,
3493 __isl_take isl_point *pnt);
3495 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
3496 __isl_take isl_union_pw_qpolynomial *upwqp,
3497 __isl_take isl_point *pnt);
3499 __isl_give isl_set *isl_pw_qpolynomial_domain(
3500 __isl_take isl_pw_qpolynomial *pwqp);
3501 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
3502 __isl_take isl_pw_qpolynomial *pwpq,
3503 __isl_take isl_set *set);
3505 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3506 __isl_take isl_union_pw_qpolynomial *upwqp);
3507 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
3508 __isl_take isl_union_pw_qpolynomial *upwpq,
3509 __isl_take isl_union_set *uset);
3511 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3512 __isl_take isl_qpolynomial *qp,
3513 __isl_take isl_space *model);
3515 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
3516 __isl_take isl_qpolynomial *qp);
3517 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
3518 __isl_take isl_pw_qpolynomial *pwqp);
3520 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
3521 __isl_take isl_union_pw_qpolynomial *upwqp);
3523 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
3524 __isl_take isl_qpolynomial *qp,
3525 __isl_take isl_set *context);
3527 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
3528 __isl_take isl_pw_qpolynomial *pwqp,
3529 __isl_take isl_set *context);
3531 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
3532 __isl_take isl_union_pw_qpolynomial *upwqp,
3533 __isl_take isl_union_set *context);
3535 The gist operation applies the gist operation to each of
3536 the cells in the domain of the input piecewise quasipolynomial.
3537 The context is also exploited
3538 to simplify the quasipolynomials associated to each cell.
3540 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
3541 __isl_take isl_pw_qpolynomial *pwqp, int sign);
3542 __isl_give isl_union_pw_qpolynomial *
3543 isl_union_pw_qpolynomial_to_polynomial(
3544 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
3546 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
3547 the polynomial will be an overapproximation. If C<sign> is negative,
3548 it will be an underapproximation. If C<sign> is zero, the approximation
3549 will lie somewhere in between.
3551 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
3553 A piecewise quasipolynomial reduction is a piecewise
3554 reduction (or fold) of quasipolynomials.
3555 In particular, the reduction can be maximum or a minimum.
3556 The objects are mainly used to represent the result of
3557 an upper or lower bound on a quasipolynomial over its domain,
3558 i.e., as the result of the following function.
3560 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
3561 __isl_take isl_pw_qpolynomial *pwqp,
3562 enum isl_fold type, int *tight);
3564 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
3565 __isl_take isl_union_pw_qpolynomial *upwqp,
3566 enum isl_fold type, int *tight);
3568 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
3569 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
3570 is the returned bound is known be tight, i.e., for each value
3571 of the parameters there is at least
3572 one element in the domain that reaches the bound.
3573 If the domain of C<pwqp> is not wrapping, then the bound is computed
3574 over all elements in that domain and the result has a purely parametric
3575 domain. If the domain of C<pwqp> is wrapping, then the bound is
3576 computed over the range of the wrapped relation. The domain of the
3577 wrapped relation becomes the domain of the result.
3579 A (piecewise) quasipolynomial reduction can be copied or freed using the
3580 following functions.
3582 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
3583 __isl_keep isl_qpolynomial_fold *fold);
3584 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
3585 __isl_keep isl_pw_qpolynomial_fold *pwf);
3586 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
3587 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3588 void isl_qpolynomial_fold_free(
3589 __isl_take isl_qpolynomial_fold *fold);
3590 void *isl_pw_qpolynomial_fold_free(
3591 __isl_take isl_pw_qpolynomial_fold *pwf);
3592 void isl_union_pw_qpolynomial_fold_free(
3593 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3595 =head3 Printing Piecewise Quasipolynomial Reductions
3597 Piecewise quasipolynomial reductions can be printed
3598 using the following function.
3600 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
3601 __isl_take isl_printer *p,
3602 __isl_keep isl_pw_qpolynomial_fold *pwf);
3603 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
3604 __isl_take isl_printer *p,
3605 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3607 For C<isl_printer_print_pw_qpolynomial_fold>,
3608 output format of the printer
3609 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3610 For C<isl_printer_print_union_pw_qpolynomial_fold>,
3611 output format of the printer
3612 needs to be set to C<ISL_FORMAT_ISL>.
3613 In case of printing in C<ISL_FORMAT_C>, the user may want
3614 to set the names of all dimensions
3616 __isl_give isl_pw_qpolynomial_fold *
3617 isl_pw_qpolynomial_fold_set_dim_name(
3618 __isl_take isl_pw_qpolynomial_fold *pwf,
3619 enum isl_dim_type type, unsigned pos,
3622 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
3624 To iterate over all piecewise quasipolynomial reductions in a union
3625 piecewise quasipolynomial reduction, use the following function
3627 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3628 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3629 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3630 void *user), void *user);
3632 To iterate over the cells in a piecewise quasipolynomial reduction,
3633 use either of the following two functions
3635 int isl_pw_qpolynomial_fold_foreach_piece(
3636 __isl_keep isl_pw_qpolynomial_fold *pwf,
3637 int (*fn)(__isl_take isl_set *set,
3638 __isl_take isl_qpolynomial_fold *fold,
3639 void *user), void *user);
3640 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
3641 __isl_keep isl_pw_qpolynomial_fold *pwf,
3642 int (*fn)(__isl_take isl_set *set,
3643 __isl_take isl_qpolynomial_fold *fold,
3644 void *user), void *user);
3646 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
3647 of the difference between these two functions.
3649 To iterate over all quasipolynomials in a reduction, use
3651 int isl_qpolynomial_fold_foreach_qpolynomial(
3652 __isl_keep isl_qpolynomial_fold *fold,
3653 int (*fn)(__isl_take isl_qpolynomial *qp,
3654 void *user), void *user);
3656 =head3 Properties of Piecewise Quasipolynomial Reductions
3658 To check whether two union piecewise quasipolynomial reductions are
3659 obviously equal, use
3661 int isl_union_pw_qpolynomial_fold_plain_is_equal(
3662 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
3663 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
3665 =head3 Operations on Piecewise Quasipolynomial Reductions
3667 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
3668 __isl_take isl_qpolynomial_fold *fold, isl_int v);
3670 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
3671 __isl_take isl_pw_qpolynomial_fold *pwf1,
3672 __isl_take isl_pw_qpolynomial_fold *pwf2);
3674 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
3675 __isl_take isl_pw_qpolynomial_fold *pwf1,
3676 __isl_take isl_pw_qpolynomial_fold *pwf2);
3678 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
3679 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
3680 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
3682 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
3683 __isl_take isl_pw_qpolynomial_fold *pwf,
3684 __isl_take isl_point *pnt);
3686 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
3687 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3688 __isl_take isl_point *pnt);
3690 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
3691 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3692 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
3693 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3694 __isl_take isl_union_set *uset);
3696 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
3697 __isl_take isl_pw_qpolynomial_fold *pwf);
3699 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
3700 __isl_take isl_pw_qpolynomial_fold *pwf);
3702 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
3703 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3705 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
3706 __isl_take isl_pw_qpolynomial_fold *pwf,
3707 __isl_take isl_set *context);
3709 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
3710 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3711 __isl_take isl_union_set *context);
3713 The gist operation applies the gist operation to each of
3714 the cells in the domain of the input piecewise quasipolynomial reduction.
3715 In future, the operation will also exploit the context
3716 to simplify the quasipolynomial reductions associated to each cell.
3718 __isl_give isl_pw_qpolynomial_fold *
3719 isl_set_apply_pw_qpolynomial_fold(
3720 __isl_take isl_set *set,
3721 __isl_take isl_pw_qpolynomial_fold *pwf,
3723 __isl_give isl_pw_qpolynomial_fold *
3724 isl_map_apply_pw_qpolynomial_fold(
3725 __isl_take isl_map *map,
3726 __isl_take isl_pw_qpolynomial_fold *pwf,
3728 __isl_give isl_union_pw_qpolynomial_fold *
3729 isl_union_set_apply_union_pw_qpolynomial_fold(
3730 __isl_take isl_union_set *uset,
3731 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3733 __isl_give isl_union_pw_qpolynomial_fold *
3734 isl_union_map_apply_union_pw_qpolynomial_fold(
3735 __isl_take isl_union_map *umap,
3736 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3739 The functions taking a map
3740 compose the given map with the given piecewise quasipolynomial reduction.
3741 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
3742 over all elements in the intersection of the range of the map
3743 and the domain of the piecewise quasipolynomial reduction
3744 as a function of an element in the domain of the map.
3745 The functions taking a set compute a bound over all elements in the
3746 intersection of the set and the domain of the
3747 piecewise quasipolynomial reduction.
3749 =head2 Dependence Analysis
3751 C<isl> contains specialized functionality for performing
3752 array dataflow analysis. That is, given a I<sink> access relation
3753 and a collection of possible I<source> access relations,
3754 C<isl> can compute relations that describe
3755 for each iteration of the sink access, which iteration
3756 of which of the source access relations was the last
3757 to access the same data element before the given iteration
3759 The resulting dependence relations map source iterations
3760 to the corresponding sink iterations.
3761 To compute standard flow dependences, the sink should be
3762 a read, while the sources should be writes.
3763 If any of the source accesses are marked as being I<may>
3764 accesses, then there will be a dependence from the last
3765 I<must> access B<and> from any I<may> access that follows
3766 this last I<must> access.
3767 In particular, if I<all> sources are I<may> accesses,
3768 then memory based dependence analysis is performed.
3769 If, on the other hand, all sources are I<must> accesses,
3770 then value based dependence analysis is performed.
3772 #include <isl/flow.h>
3774 typedef int (*isl_access_level_before)(void *first, void *second);
3776 __isl_give isl_access_info *isl_access_info_alloc(
3777 __isl_take isl_map *sink,
3778 void *sink_user, isl_access_level_before fn,
3780 __isl_give isl_access_info *isl_access_info_add_source(
3781 __isl_take isl_access_info *acc,
3782 __isl_take isl_map *source, int must,
3784 void isl_access_info_free(__isl_take isl_access_info *acc);
3786 __isl_give isl_flow *isl_access_info_compute_flow(
3787 __isl_take isl_access_info *acc);
3789 int isl_flow_foreach(__isl_keep isl_flow *deps,
3790 int (*fn)(__isl_take isl_map *dep, int must,
3791 void *dep_user, void *user),
3793 __isl_give isl_map *isl_flow_get_no_source(
3794 __isl_keep isl_flow *deps, int must);
3795 void isl_flow_free(__isl_take isl_flow *deps);
3797 The function C<isl_access_info_compute_flow> performs the actual
3798 dependence analysis. The other functions are used to construct
3799 the input for this function or to read off the output.
3801 The input is collected in an C<isl_access_info>, which can
3802 be created through a call to C<isl_access_info_alloc>.
3803 The arguments to this functions are the sink access relation
3804 C<sink>, a token C<sink_user> used to identify the sink
3805 access to the user, a callback function for specifying the
3806 relative order of source and sink accesses, and the number
3807 of source access relations that will be added.
3808 The callback function has type C<int (*)(void *first, void *second)>.
3809 The function is called with two user supplied tokens identifying
3810 either a source or the sink and it should return the shared nesting
3811 level and the relative order of the two accesses.
3812 In particular, let I<n> be the number of loops shared by
3813 the two accesses. If C<first> precedes C<second> textually,
3814 then the function should return I<2 * n + 1>; otherwise,
3815 it should return I<2 * n>.
3816 The sources can be added to the C<isl_access_info> by performing
3817 (at most) C<max_source> calls to C<isl_access_info_add_source>.
3818 C<must> indicates whether the source is a I<must> access
3819 or a I<may> access. Note that a multi-valued access relation
3820 should only be marked I<must> if every iteration in the domain
3821 of the relation accesses I<all> elements in its image.
3822 The C<source_user> token is again used to identify
3823 the source access. The range of the source access relation
3824 C<source> should have the same dimension as the range
3825 of the sink access relation.
3826 The C<isl_access_info_free> function should usually not be
3827 called explicitly, because it is called implicitly by
3828 C<isl_access_info_compute_flow>.
3830 The result of the dependence analysis is collected in an
3831 C<isl_flow>. There may be elements of
3832 the sink access for which no preceding source access could be
3833 found or for which all preceding sources are I<may> accesses.
3834 The relations containing these elements can be obtained through
3835 calls to C<isl_flow_get_no_source>, the first with C<must> set
3836 and the second with C<must> unset.
3837 In the case of standard flow dependence analysis,
3838 with the sink a read and the sources I<must> writes,
3839 the first relation corresponds to the reads from uninitialized
3840 array elements and the second relation is empty.
3841 The actual flow dependences can be extracted using
3842 C<isl_flow_foreach>. This function will call the user-specified
3843 callback function C<fn> for each B<non-empty> dependence between
3844 a source and the sink. The callback function is called
3845 with four arguments, the actual flow dependence relation
3846 mapping source iterations to sink iterations, a boolean that
3847 indicates whether it is a I<must> or I<may> dependence, a token
3848 identifying the source and an additional C<void *> with value
3849 equal to the third argument of the C<isl_flow_foreach> call.
3850 A dependence is marked I<must> if it originates from a I<must>
3851 source and if it is not followed by any I<may> sources.
3853 After finishing with an C<isl_flow>, the user should call
3854 C<isl_flow_free> to free all associated memory.
3856 A higher-level interface to dependence analysis is provided
3857 by the following function.
3859 #include <isl/flow.h>
3861 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
3862 __isl_take isl_union_map *must_source,
3863 __isl_take isl_union_map *may_source,
3864 __isl_take isl_union_map *schedule,
3865 __isl_give isl_union_map **must_dep,
3866 __isl_give isl_union_map **may_dep,
3867 __isl_give isl_union_map **must_no_source,
3868 __isl_give isl_union_map **may_no_source);
3870 The arrays are identified by the tuple names of the ranges
3871 of the accesses. The iteration domains by the tuple names
3872 of the domains of the accesses and of the schedule.
3873 The relative order of the iteration domains is given by the
3874 schedule. The relations returned through C<must_no_source>
3875 and C<may_no_source> are subsets of C<sink>.
3876 Any of C<must_dep>, C<may_dep>, C<must_no_source>
3877 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
3878 any of the other arguments is treated as an error.
3882 B<The functionality described in this section is fairly new
3883 and may be subject to change.>
3885 The following function can be used to compute a schedule
3886 for a union of domains. The generated schedule respects
3887 all C<validity> dependences. That is, all dependence distances
3888 over these dependences in the scheduled space are lexicographically
3889 positive. The generated schedule schedule also tries to minimize
3890 the dependence distances over C<proximity> dependences.
3891 Moreover, it tries to obtain sequences (bands) of schedule dimensions
3892 for groups of domains where the dependence distances have only
3893 non-negative values.
3894 The algorithm used to construct the schedule is similar to that
3897 #include <isl/schedule.h>
3898 __isl_give isl_schedule *isl_union_set_compute_schedule(
3899 __isl_take isl_union_set *domain,
3900 __isl_take isl_union_map *validity,
3901 __isl_take isl_union_map *proximity);
3902 void *isl_schedule_free(__isl_take isl_schedule *sched);
3904 A mapping from the domains to the scheduled space can be obtained
3905 from an C<isl_schedule> using the following function.
3907 __isl_give isl_union_map *isl_schedule_get_map(
3908 __isl_keep isl_schedule *sched);
3910 A representation of the schedule can be printed using
3912 __isl_give isl_printer *isl_printer_print_schedule(
3913 __isl_take isl_printer *p,
3914 __isl_keep isl_schedule *schedule);
3916 A representation of the schedule as a forest of bands can be obtained
3917 using the following function.
3919 __isl_give isl_band_list *isl_schedule_get_band_forest(
3920 __isl_keep isl_schedule *schedule);
3922 The list can be manipulated as explained in L<"Lists">.
3923 The bands inside the list can be copied and freed using the following
3926 #include <isl/band.h>
3927 __isl_give isl_band *isl_band_copy(
3928 __isl_keep isl_band *band);
3929 void *isl_band_free(__isl_take isl_band *band);
3931 Each band contains zero or more scheduling dimensions.
3932 These are referred to as the members of the band.
3933 The section of the schedule that corresponds to the band is
3934 referred to as the partial schedule of the band.
3935 For those nodes that participate in a band, the outer scheduling
3936 dimensions form the prefix schedule, while the inner scheduling
3937 dimensions form the suffix schedule.
3938 That is, if we take a cut of the band forest, then the union of
3939 the concatenations of the prefix, partial and suffix schedules of
3940 each band in the cut is equal to the entire schedule (modulo
3941 some possible padding at the end with zero scheduling dimensions).
3942 The properties of a band can be inspected using the following functions.
3944 #include <isl/band.h>
3945 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
3947 int isl_band_has_children(__isl_keep isl_band *band);
3948 __isl_give isl_band_list *isl_band_get_children(
3949 __isl_keep isl_band *band);
3951 __isl_give isl_union_map *isl_band_get_prefix_schedule(
3952 __isl_keep isl_band *band);
3953 __isl_give isl_union_map *isl_band_get_partial_schedule(
3954 __isl_keep isl_band *band);
3955 __isl_give isl_union_map *isl_band_get_suffix_schedule(
3956 __isl_keep isl_band *band);
3958 int isl_band_n_member(__isl_keep isl_band *band);
3959 int isl_band_member_is_zero_distance(
3960 __isl_keep isl_band *band, int pos);
3962 Note that a scheduling dimension is considered to be ``zero
3963 distance'' if it does not carry any proximity dependences
3965 That is, if the dependence distances of the proximity
3966 dependences are all zero in that direction (for fixed
3967 iterations of outer bands).
3969 A representation of the band can be printed using
3971 #include <isl/band.h>
3972 __isl_give isl_printer *isl_printer_print_band(
3973 __isl_take isl_printer *p,
3974 __isl_keep isl_band *band);
3976 =head2 Parametric Vertex Enumeration
3978 The parametric vertex enumeration described in this section
3979 is mainly intended to be used internally and by the C<barvinok>
3982 #include <isl/vertices.h>
3983 __isl_give isl_vertices *isl_basic_set_compute_vertices(
3984 __isl_keep isl_basic_set *bset);
3986 The function C<isl_basic_set_compute_vertices> performs the
3987 actual computation of the parametric vertices and the chamber
3988 decomposition and store the result in an C<isl_vertices> object.
3989 This information can be queried by either iterating over all
3990 the vertices or iterating over all the chambers or cells
3991 and then iterating over all vertices that are active on the chamber.
3993 int isl_vertices_foreach_vertex(
3994 __isl_keep isl_vertices *vertices,
3995 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3998 int isl_vertices_foreach_cell(
3999 __isl_keep isl_vertices *vertices,
4000 int (*fn)(__isl_take isl_cell *cell, void *user),
4002 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
4003 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4006 Other operations that can be performed on an C<isl_vertices> object are
4009 isl_ctx *isl_vertices_get_ctx(
4010 __isl_keep isl_vertices *vertices);
4011 int isl_vertices_get_n_vertices(
4012 __isl_keep isl_vertices *vertices);
4013 void isl_vertices_free(__isl_take isl_vertices *vertices);
4015 Vertices can be inspected and destroyed using the following functions.
4017 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
4018 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
4019 __isl_give isl_basic_set *isl_vertex_get_domain(
4020 __isl_keep isl_vertex *vertex);
4021 __isl_give isl_basic_set *isl_vertex_get_expr(
4022 __isl_keep isl_vertex *vertex);
4023 void isl_vertex_free(__isl_take isl_vertex *vertex);
4025 C<isl_vertex_get_expr> returns a singleton parametric set describing
4026 the vertex, while C<isl_vertex_get_domain> returns the activity domain
4028 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
4029 B<rational> basic sets, so they should mainly be used for inspection
4030 and should not be mixed with integer sets.
4032 Chambers can be inspected and destroyed using the following functions.
4034 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
4035 __isl_give isl_basic_set *isl_cell_get_domain(
4036 __isl_keep isl_cell *cell);
4037 void isl_cell_free(__isl_take isl_cell *cell);
4041 Although C<isl> is mainly meant to be used as a library,
4042 it also contains some basic applications that use some
4043 of the functionality of C<isl>.
4044 The input may be specified in either the L<isl format>
4045 or the L<PolyLib format>.
4047 =head2 C<isl_polyhedron_sample>
4049 C<isl_polyhedron_sample> takes a polyhedron as input and prints
4050 an integer element of the polyhedron, if there is any.
4051 The first column in the output is the denominator and is always
4052 equal to 1. If the polyhedron contains no integer points,
4053 then a vector of length zero is printed.
4057 C<isl_pip> takes the same input as the C<example> program
4058 from the C<piplib> distribution, i.e., a set of constraints
4059 on the parameters, a line containing only -1 and finally a set
4060 of constraints on a parametric polyhedron.
4061 The coefficients of the parameters appear in the last columns
4062 (but before the final constant column).
4063 The output is the lexicographic minimum of the parametric polyhedron.
4064 As C<isl> currently does not have its own output format, the output
4065 is just a dump of the internal state.
4067 =head2 C<isl_polyhedron_minimize>
4069 C<isl_polyhedron_minimize> computes the minimum of some linear
4070 or affine objective function over the integer points in a polyhedron.
4071 If an affine objective function
4072 is given, then the constant should appear in the last column.
4074 =head2 C<isl_polytope_scan>
4076 Given a polytope, C<isl_polytope_scan> prints
4077 all integer points in the polytope.