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_range(
787 __isl_take isl_local_space *ls);
788 __isl_give isl_local_space *isl_local_space_from_domain(
789 __isl_take isl_local_space *ls);
790 __isl_give isl_local_space *isl_local_space_intersect(
791 __isl_take isl_local_space *ls1,
792 __isl_take isl_local_space *ls2);
793 __isl_give isl_local_space *isl_local_space_add_dims(
794 __isl_take isl_local_space *ls,
795 enum isl_dim_type type, unsigned n);
796 __isl_give isl_local_space *isl_local_space_insert_dims(
797 __isl_take isl_local_space *ls,
798 enum isl_dim_type type, unsigned first, unsigned n);
799 __isl_give isl_local_space *isl_local_space_drop_dims(
800 __isl_take isl_local_space *ls,
801 enum isl_dim_type type, unsigned first, unsigned n);
803 =head2 Input and Output
805 C<isl> supports its own input/output format, which is similar
806 to the C<Omega> format, but also supports the C<PolyLib> format
811 The C<isl> format is similar to that of C<Omega>, but has a different
812 syntax for describing the parameters and allows for the definition
813 of an existentially quantified variable as the integer division
814 of an affine expression.
815 For example, the set of integers C<i> between C<0> and C<n>
816 such that C<i % 10 <= 6> can be described as
818 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
821 A set or relation can have several disjuncts, separated
822 by the keyword C<or>. Each disjunct is either a conjunction
823 of constraints or a projection (C<exists>) of a conjunction
824 of constraints. The constraints are separated by the keyword
827 =head3 C<PolyLib> format
829 If the represented set is a union, then the first line
830 contains a single number representing the number of disjuncts.
831 Otherwise, a line containing the number C<1> is optional.
833 Each disjunct is represented by a matrix of constraints.
834 The first line contains two numbers representing
835 the number of rows and columns,
836 where the number of rows is equal to the number of constraints
837 and the number of columns is equal to two plus the number of variables.
838 The following lines contain the actual rows of the constraint matrix.
839 In each row, the first column indicates whether the constraint
840 is an equality (C<0>) or inequality (C<1>). The final column
841 corresponds to the constant term.
843 If the set is parametric, then the coefficients of the parameters
844 appear in the last columns before the constant column.
845 The coefficients of any existentially quantified variables appear
846 between those of the set variables and those of the parameters.
848 =head3 Extended C<PolyLib> format
850 The extended C<PolyLib> format is nearly identical to the
851 C<PolyLib> format. The only difference is that the line
852 containing the number of rows and columns of a constraint matrix
853 also contains four additional numbers:
854 the number of output dimensions, the number of input dimensions,
855 the number of local dimensions (i.e., the number of existentially
856 quantified variables) and the number of parameters.
857 For sets, the number of ``output'' dimensions is equal
858 to the number of set dimensions, while the number of ``input''
864 __isl_give isl_basic_set *isl_basic_set_read_from_file(
865 isl_ctx *ctx, FILE *input);
866 __isl_give isl_basic_set *isl_basic_set_read_from_str(
867 isl_ctx *ctx, const char *str);
868 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
870 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
874 __isl_give isl_basic_map *isl_basic_map_read_from_file(
875 isl_ctx *ctx, FILE *input);
876 __isl_give isl_basic_map *isl_basic_map_read_from_str(
877 isl_ctx *ctx, const char *str);
878 __isl_give isl_map *isl_map_read_from_file(
879 isl_ctx *ctx, FILE *input);
880 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
883 #include <isl/union_set.h>
884 __isl_give isl_union_set *isl_union_set_read_from_file(
885 isl_ctx *ctx, FILE *input);
886 __isl_give isl_union_set *isl_union_set_read_from_str(
887 isl_ctx *ctx, const char *str);
889 #include <isl/union_map.h>
890 __isl_give isl_union_map *isl_union_map_read_from_file(
891 isl_ctx *ctx, FILE *input);
892 __isl_give isl_union_map *isl_union_map_read_from_str(
893 isl_ctx *ctx, const char *str);
895 The input format is autodetected and may be either the C<PolyLib> format
896 or the C<isl> format.
900 Before anything can be printed, an C<isl_printer> needs to
903 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
905 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
906 void isl_printer_free(__isl_take isl_printer *printer);
907 __isl_give char *isl_printer_get_str(
908 __isl_keep isl_printer *printer);
910 The behavior of the printer can be modified in various ways
912 __isl_give isl_printer *isl_printer_set_output_format(
913 __isl_take isl_printer *p, int output_format);
914 __isl_give isl_printer *isl_printer_set_indent(
915 __isl_take isl_printer *p, int indent);
916 __isl_give isl_printer *isl_printer_indent(
917 __isl_take isl_printer *p, int indent);
918 __isl_give isl_printer *isl_printer_set_prefix(
919 __isl_take isl_printer *p, const char *prefix);
920 __isl_give isl_printer *isl_printer_set_suffix(
921 __isl_take isl_printer *p, const char *suffix);
923 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
924 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
925 and defaults to C<ISL_FORMAT_ISL>.
926 Each line in the output is indented by C<indent> (set by
927 C<isl_printer_set_indent>) spaces
928 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
929 In the C<PolyLib> format output,
930 the coefficients of the existentially quantified variables
931 appear between those of the set variables and those
933 The function C<isl_printer_indent> increases the indentation
934 by the specified amount (which may be negative).
936 To actually print something, use
939 __isl_give isl_printer *isl_printer_print_basic_set(
940 __isl_take isl_printer *printer,
941 __isl_keep isl_basic_set *bset);
942 __isl_give isl_printer *isl_printer_print_set(
943 __isl_take isl_printer *printer,
944 __isl_keep isl_set *set);
947 __isl_give isl_printer *isl_printer_print_basic_map(
948 __isl_take isl_printer *printer,
949 __isl_keep isl_basic_map *bmap);
950 __isl_give isl_printer *isl_printer_print_map(
951 __isl_take isl_printer *printer,
952 __isl_keep isl_map *map);
954 #include <isl/union_set.h>
955 __isl_give isl_printer *isl_printer_print_union_set(
956 __isl_take isl_printer *p,
957 __isl_keep isl_union_set *uset);
959 #include <isl/union_map.h>
960 __isl_give isl_printer *isl_printer_print_union_map(
961 __isl_take isl_printer *p,
962 __isl_keep isl_union_map *umap);
964 When called on a file printer, the following function flushes
965 the file. When called on a string printer, the buffer is cleared.
967 __isl_give isl_printer *isl_printer_flush(
968 __isl_take isl_printer *p);
970 =head2 Creating New Sets and Relations
972 C<isl> has functions for creating some standard sets and relations.
976 =item * Empty sets and relations
978 __isl_give isl_basic_set *isl_basic_set_empty(
979 __isl_take isl_space *space);
980 __isl_give isl_basic_map *isl_basic_map_empty(
981 __isl_take isl_space *space);
982 __isl_give isl_set *isl_set_empty(
983 __isl_take isl_space *space);
984 __isl_give isl_map *isl_map_empty(
985 __isl_take isl_space *space);
986 __isl_give isl_union_set *isl_union_set_empty(
987 __isl_take isl_space *space);
988 __isl_give isl_union_map *isl_union_map_empty(
989 __isl_take isl_space *space);
991 For C<isl_union_set>s and C<isl_union_map>s, the space
992 is only used to specify the parameters.
994 =item * Universe sets and relations
996 __isl_give isl_basic_set *isl_basic_set_universe(
997 __isl_take isl_space *space);
998 __isl_give isl_basic_map *isl_basic_map_universe(
999 __isl_take isl_space *space);
1000 __isl_give isl_set *isl_set_universe(
1001 __isl_take isl_space *space);
1002 __isl_give isl_map *isl_map_universe(
1003 __isl_take isl_space *space);
1004 __isl_give isl_union_set *isl_union_set_universe(
1005 __isl_take isl_union_set *uset);
1006 __isl_give isl_union_map *isl_union_map_universe(
1007 __isl_take isl_union_map *umap);
1009 The sets and relations constructed by the functions above
1010 contain all integer values, while those constructed by the
1011 functions below only contain non-negative values.
1013 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1014 __isl_take isl_space *space);
1015 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1016 __isl_take isl_space *space);
1017 __isl_give isl_set *isl_set_nat_universe(
1018 __isl_take isl_space *space);
1019 __isl_give isl_map *isl_map_nat_universe(
1020 __isl_take isl_space *space);
1022 =item * Identity relations
1024 __isl_give isl_basic_map *isl_basic_map_identity(
1025 __isl_take isl_space *space);
1026 __isl_give isl_map *isl_map_identity(
1027 __isl_take isl_space *space);
1029 The number of input and output dimensions in C<space> needs
1032 =item * Lexicographic order
1034 __isl_give isl_map *isl_map_lex_lt(
1035 __isl_take isl_space *set_space);
1036 __isl_give isl_map *isl_map_lex_le(
1037 __isl_take isl_space *set_space);
1038 __isl_give isl_map *isl_map_lex_gt(
1039 __isl_take isl_space *set_space);
1040 __isl_give isl_map *isl_map_lex_ge(
1041 __isl_take isl_space *set_space);
1042 __isl_give isl_map *isl_map_lex_lt_first(
1043 __isl_take isl_space *space, unsigned n);
1044 __isl_give isl_map *isl_map_lex_le_first(
1045 __isl_take isl_space *space, unsigned n);
1046 __isl_give isl_map *isl_map_lex_gt_first(
1047 __isl_take isl_space *space, unsigned n);
1048 __isl_give isl_map *isl_map_lex_ge_first(
1049 __isl_take isl_space *space, unsigned n);
1051 The first four functions take a space for a B<set>
1052 and return relations that express that the elements in the domain
1053 are lexicographically less
1054 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1055 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1056 than the elements in the range.
1057 The last four functions take a space for a map
1058 and return relations that express that the first C<n> dimensions
1059 in the domain are lexicographically less
1060 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1061 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1062 than the first C<n> dimensions in the range.
1066 A basic set or relation can be converted to a set or relation
1067 using the following functions.
1069 __isl_give isl_set *isl_set_from_basic_set(
1070 __isl_take isl_basic_set *bset);
1071 __isl_give isl_map *isl_map_from_basic_map(
1072 __isl_take isl_basic_map *bmap);
1074 Sets and relations can be converted to union sets and relations
1075 using the following functions.
1077 __isl_give isl_union_map *isl_union_map_from_map(
1078 __isl_take isl_map *map);
1079 __isl_give isl_union_set *isl_union_set_from_set(
1080 __isl_take isl_set *set);
1082 The inverse conversions below can only be used if the input
1083 union set or relation is known to contain elements in exactly one
1086 __isl_give isl_set *isl_set_from_union_set(
1087 __isl_take isl_union_set *uset);
1088 __isl_give isl_map *isl_map_from_union_map(
1089 __isl_take isl_union_map *umap);
1091 A zero-dimensional set can be constructed on a given parameter domain
1092 using the following function.
1094 __isl_give isl_set *isl_set_from_params(
1095 __isl_take isl_set *set);
1097 Sets and relations can be copied and freed again using the following
1100 __isl_give isl_basic_set *isl_basic_set_copy(
1101 __isl_keep isl_basic_set *bset);
1102 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1103 __isl_give isl_union_set *isl_union_set_copy(
1104 __isl_keep isl_union_set *uset);
1105 __isl_give isl_basic_map *isl_basic_map_copy(
1106 __isl_keep isl_basic_map *bmap);
1107 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1108 __isl_give isl_union_map *isl_union_map_copy(
1109 __isl_keep isl_union_map *umap);
1110 void isl_basic_set_free(__isl_take isl_basic_set *bset);
1111 void isl_set_free(__isl_take isl_set *set);
1112 void *isl_union_set_free(__isl_take isl_union_set *uset);
1113 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
1114 void isl_map_free(__isl_take isl_map *map);
1115 void *isl_union_map_free(__isl_take isl_union_map *umap);
1117 Other sets and relations can be constructed by starting
1118 from a universe set or relation, adding equality and/or
1119 inequality constraints and then projecting out the
1120 existentially quantified variables, if any.
1121 Constraints can be constructed, manipulated and
1122 added to (or removed from) (basic) sets and relations
1123 using the following functions.
1125 #include <isl/constraint.h>
1126 __isl_give isl_constraint *isl_equality_alloc(
1127 __isl_take isl_local_space *ls);
1128 __isl_give isl_constraint *isl_inequality_alloc(
1129 __isl_take isl_local_space *ls);
1130 __isl_give isl_constraint *isl_constraint_set_constant(
1131 __isl_take isl_constraint *constraint, isl_int v);
1132 __isl_give isl_constraint *isl_constraint_set_constant_si(
1133 __isl_take isl_constraint *constraint, int v);
1134 __isl_give isl_constraint *isl_constraint_set_coefficient(
1135 __isl_take isl_constraint *constraint,
1136 enum isl_dim_type type, int pos, isl_int v);
1137 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1138 __isl_take isl_constraint *constraint,
1139 enum isl_dim_type type, int pos, int v);
1140 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1141 __isl_take isl_basic_map *bmap,
1142 __isl_take isl_constraint *constraint);
1143 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1144 __isl_take isl_basic_set *bset,
1145 __isl_take isl_constraint *constraint);
1146 __isl_give isl_map *isl_map_add_constraint(
1147 __isl_take isl_map *map,
1148 __isl_take isl_constraint *constraint);
1149 __isl_give isl_set *isl_set_add_constraint(
1150 __isl_take isl_set *set,
1151 __isl_take isl_constraint *constraint);
1152 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1153 __isl_take isl_basic_set *bset,
1154 __isl_take isl_constraint *constraint);
1156 For example, to create a set containing the even integers
1157 between 10 and 42, you would use the following code.
1160 isl_local_space *ls;
1162 isl_basic_set *bset;
1164 space = isl_space_set_alloc(ctx, 0, 2);
1165 bset = isl_basic_set_universe(isl_space_copy(space));
1166 ls = isl_local_space_from_space(space);
1168 c = isl_equality_alloc(isl_local_space_copy(ls));
1169 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1170 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1171 bset = isl_basic_set_add_constraint(bset, c);
1173 c = isl_inequality_alloc(isl_local_space_copy(ls));
1174 c = isl_constraint_set_constant_si(c, -10);
1175 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1176 bset = isl_basic_set_add_constraint(bset, c);
1178 c = isl_inequality_alloc(ls);
1179 c = isl_constraint_set_constant_si(c, 42);
1180 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1181 bset = isl_basic_set_add_constraint(bset, c);
1183 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1187 isl_basic_set *bset;
1188 bset = isl_basic_set_read_from_str(ctx,
1189 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1191 A basic set or relation can also be constructed from two matrices
1192 describing the equalities and the inequalities.
1194 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1195 __isl_take isl_space *space,
1196 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1197 enum isl_dim_type c1,
1198 enum isl_dim_type c2, enum isl_dim_type c3,
1199 enum isl_dim_type c4);
1200 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1201 __isl_take isl_space *space,
1202 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1203 enum isl_dim_type c1,
1204 enum isl_dim_type c2, enum isl_dim_type c3,
1205 enum isl_dim_type c4, enum isl_dim_type c5);
1207 The C<isl_dim_type> arguments indicate the order in which
1208 different kinds of variables appear in the input matrices
1209 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1210 C<isl_dim_set> and C<isl_dim_div> for sets and
1211 of C<isl_dim_cst>, C<isl_dim_param>,
1212 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1214 A (basic) set or relation can also be constructed from a (piecewise)
1215 (multiple) affine expression
1216 or a list of affine expressions
1217 (See L<"Piecewise Quasi Affine Expressions"> and
1218 L<"Piecewise Multiple Quasi Affine Expressions">).
1220 __isl_give isl_basic_map *isl_basic_map_from_aff(
1221 __isl_take isl_aff *aff);
1222 __isl_give isl_set *isl_set_from_pw_aff(
1223 __isl_take isl_pw_aff *pwaff);
1224 __isl_give isl_map *isl_map_from_pw_aff(
1225 __isl_take isl_pw_aff *pwaff);
1226 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1227 __isl_take isl_space *domain_space,
1228 __isl_take isl_aff_list *list);
1229 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1230 __isl_take isl_multi_aff *maff)
1231 __isl_give isl_set *isl_set_from_pw_multi_aff(
1232 __isl_take isl_pw_multi_aff *pma);
1233 __isl_give isl_map *isl_map_from_pw_multi_aff(
1234 __isl_take isl_pw_multi_aff *pma);
1236 The C<domain_dim> argument describes the domain of the resulting
1237 basic relation. It is required because the C<list> may consist
1238 of zero affine expressions.
1240 =head2 Inspecting Sets and Relations
1242 Usually, the user should not have to care about the actual constraints
1243 of the sets and maps, but should instead apply the abstract operations
1244 explained in the following sections.
1245 Occasionally, however, it may be required to inspect the individual
1246 coefficients of the constraints. This section explains how to do so.
1247 In these cases, it may also be useful to have C<isl> compute
1248 an explicit representation of the existentially quantified variables.
1250 __isl_give isl_set *isl_set_compute_divs(
1251 __isl_take isl_set *set);
1252 __isl_give isl_map *isl_map_compute_divs(
1253 __isl_take isl_map *map);
1254 __isl_give isl_union_set *isl_union_set_compute_divs(
1255 __isl_take isl_union_set *uset);
1256 __isl_give isl_union_map *isl_union_map_compute_divs(
1257 __isl_take isl_union_map *umap);
1259 This explicit representation defines the existentially quantified
1260 variables as integer divisions of the other variables, possibly
1261 including earlier existentially quantified variables.
1262 An explicitly represented existentially quantified variable therefore
1263 has a unique value when the values of the other variables are known.
1264 If, furthermore, the same existentials, i.e., existentials
1265 with the same explicit representations, should appear in the
1266 same order in each of the disjuncts of a set or map, then the user should call
1267 either of the following functions.
1269 __isl_give isl_set *isl_set_align_divs(
1270 __isl_take isl_set *set);
1271 __isl_give isl_map *isl_map_align_divs(
1272 __isl_take isl_map *map);
1274 Alternatively, the existentially quantified variables can be removed
1275 using the following functions, which compute an overapproximation.
1277 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1278 __isl_take isl_basic_set *bset);
1279 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1280 __isl_take isl_basic_map *bmap);
1281 __isl_give isl_set *isl_set_remove_divs(
1282 __isl_take isl_set *set);
1283 __isl_give isl_map *isl_map_remove_divs(
1284 __isl_take isl_map *map);
1286 To iterate over all the sets or maps in a union set or map, use
1288 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1289 int (*fn)(__isl_take isl_set *set, void *user),
1291 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1292 int (*fn)(__isl_take isl_map *map, void *user),
1295 The number of sets or maps in a union set or map can be obtained
1298 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1299 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1301 To extract the set or map in a given space from a union, use
1303 __isl_give isl_set *isl_union_set_extract_set(
1304 __isl_keep isl_union_set *uset,
1305 __isl_take isl_space *space);
1306 __isl_give isl_map *isl_union_map_extract_map(
1307 __isl_keep isl_union_map *umap,
1308 __isl_take isl_space *space);
1310 To iterate over all the basic sets or maps in a set or map, use
1312 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1313 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1315 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1316 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1319 The callback function C<fn> should return 0 if successful and
1320 -1 if an error occurs. In the latter case, or if any other error
1321 occurs, the above functions will return -1.
1323 It should be noted that C<isl> does not guarantee that
1324 the basic sets or maps passed to C<fn> are disjoint.
1325 If this is required, then the user should call one of
1326 the following functions first.
1328 __isl_give isl_set *isl_set_make_disjoint(
1329 __isl_take isl_set *set);
1330 __isl_give isl_map *isl_map_make_disjoint(
1331 __isl_take isl_map *map);
1333 The number of basic sets in a set can be obtained
1336 int isl_set_n_basic_set(__isl_keep isl_set *set);
1338 To iterate over the constraints of a basic set or map, use
1340 #include <isl/constraint.h>
1342 int isl_basic_map_foreach_constraint(
1343 __isl_keep isl_basic_map *bmap,
1344 int (*fn)(__isl_take isl_constraint *c, void *user),
1346 void *isl_constraint_free(__isl_take isl_constraint *c);
1348 Again, the callback function C<fn> should return 0 if successful and
1349 -1 if an error occurs. In the latter case, or if any other error
1350 occurs, the above functions will return -1.
1351 The constraint C<c> represents either an equality or an inequality.
1352 Use the following function to find out whether a constraint
1353 represents an equality. If not, it represents an inequality.
1355 int isl_constraint_is_equality(
1356 __isl_keep isl_constraint *constraint);
1358 The coefficients of the constraints can be inspected using
1359 the following functions.
1361 void isl_constraint_get_constant(
1362 __isl_keep isl_constraint *constraint, isl_int *v);
1363 void isl_constraint_get_coefficient(
1364 __isl_keep isl_constraint *constraint,
1365 enum isl_dim_type type, int pos, isl_int *v);
1366 int isl_constraint_involves_dims(
1367 __isl_keep isl_constraint *constraint,
1368 enum isl_dim_type type, unsigned first, unsigned n);
1370 The explicit representations of the existentially quantified
1371 variables can be inspected using the following function.
1372 Note that the user is only allowed to use this function
1373 if the inspected set or map is the result of a call
1374 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1375 The existentially quantified variable is equal to the floor
1376 of the returned affine expression. The affine expression
1377 itself can be inspected using the functions in
1378 L<"Piecewise Quasi Affine Expressions">.
1380 __isl_give isl_aff *isl_constraint_get_div(
1381 __isl_keep isl_constraint *constraint, int pos);
1383 To obtain the constraints of a basic set or map in matrix
1384 form, use the following functions.
1386 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1387 __isl_keep isl_basic_set *bset,
1388 enum isl_dim_type c1, enum isl_dim_type c2,
1389 enum isl_dim_type c3, enum isl_dim_type c4);
1390 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1391 __isl_keep isl_basic_set *bset,
1392 enum isl_dim_type c1, enum isl_dim_type c2,
1393 enum isl_dim_type c3, enum isl_dim_type c4);
1394 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1395 __isl_keep isl_basic_map *bmap,
1396 enum isl_dim_type c1,
1397 enum isl_dim_type c2, enum isl_dim_type c3,
1398 enum isl_dim_type c4, enum isl_dim_type c5);
1399 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1400 __isl_keep isl_basic_map *bmap,
1401 enum isl_dim_type c1,
1402 enum isl_dim_type c2, enum isl_dim_type c3,
1403 enum isl_dim_type c4, enum isl_dim_type c5);
1405 The C<isl_dim_type> arguments dictate the order in which
1406 different kinds of variables appear in the resulting matrix
1407 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1408 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1410 The number of parameters, input, output or set dimensions can
1411 be obtained using the following functions.
1413 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1414 enum isl_dim_type type);
1415 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1416 enum isl_dim_type type);
1417 unsigned isl_set_dim(__isl_keep isl_set *set,
1418 enum isl_dim_type type);
1419 unsigned isl_map_dim(__isl_keep isl_map *map,
1420 enum isl_dim_type type);
1422 To check whether the description of a set or relation depends
1423 on one or more given dimensions, it is not necessary to iterate over all
1424 constraints. Instead the following functions can be used.
1426 int isl_basic_set_involves_dims(
1427 __isl_keep isl_basic_set *bset,
1428 enum isl_dim_type type, unsigned first, unsigned n);
1429 int isl_set_involves_dims(__isl_keep isl_set *set,
1430 enum isl_dim_type type, unsigned first, unsigned n);
1431 int isl_basic_map_involves_dims(
1432 __isl_keep isl_basic_map *bmap,
1433 enum isl_dim_type type, unsigned first, unsigned n);
1434 int isl_map_involves_dims(__isl_keep isl_map *map,
1435 enum isl_dim_type type, unsigned first, unsigned n);
1437 Similarly, the following functions can be used to check whether
1438 a given dimension is involved in any lower or upper bound.
1440 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1441 enum isl_dim_type type, unsigned pos);
1442 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1443 enum isl_dim_type type, unsigned pos);
1445 The identifiers or names of the domain and range spaces of a set
1446 or relation can be read off or set using the following functions.
1448 __isl_give isl_set *isl_set_set_tuple_id(
1449 __isl_take isl_set *set, __isl_take isl_id *id);
1450 __isl_give isl_set *isl_set_reset_tuple_id(
1451 __isl_take isl_set *set);
1452 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1453 __isl_give isl_id *isl_set_get_tuple_id(
1454 __isl_keep isl_set *set);
1455 __isl_give isl_map *isl_map_set_tuple_id(
1456 __isl_take isl_map *map, enum isl_dim_type type,
1457 __isl_take isl_id *id);
1458 __isl_give isl_map *isl_map_reset_tuple_id(
1459 __isl_take isl_map *map, enum isl_dim_type type);
1460 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1461 enum isl_dim_type type);
1462 __isl_give isl_id *isl_map_get_tuple_id(
1463 __isl_keep isl_map *map, enum isl_dim_type type);
1465 const char *isl_basic_set_get_tuple_name(
1466 __isl_keep isl_basic_set *bset);
1467 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1468 __isl_take isl_basic_set *set, const char *s);
1469 const char *isl_set_get_tuple_name(
1470 __isl_keep isl_set *set);
1471 const char *isl_basic_map_get_tuple_name(
1472 __isl_keep isl_basic_map *bmap,
1473 enum isl_dim_type type);
1474 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1475 __isl_take isl_basic_map *bmap,
1476 enum isl_dim_type type, const char *s);
1477 const char *isl_map_get_tuple_name(
1478 __isl_keep isl_map *map,
1479 enum isl_dim_type type);
1481 As with C<isl_space_get_tuple_name>, the value returned points to
1482 an internal data structure.
1483 The identifiers, positions or names of individual dimensions can be
1484 read off using the following functions.
1486 __isl_give isl_set *isl_set_set_dim_id(
1487 __isl_take isl_set *set, enum isl_dim_type type,
1488 unsigned pos, __isl_take isl_id *id);
1489 int isl_set_has_dim_id(__isl_keep isl_set *set,
1490 enum isl_dim_type type, unsigned pos);
1491 __isl_give isl_id *isl_set_get_dim_id(
1492 __isl_keep isl_set *set, enum isl_dim_type type,
1494 int isl_basic_map_has_dim_id(
1495 __isl_keep isl_basic_map *bmap,
1496 enum isl_dim_type type, unsigned pos);
1497 __isl_give isl_map *isl_map_set_dim_id(
1498 __isl_take isl_map *map, enum isl_dim_type type,
1499 unsigned pos, __isl_take isl_id *id);
1500 int isl_map_has_dim_id(__isl_keep isl_map *map,
1501 enum isl_dim_type type, unsigned pos);
1502 __isl_give isl_id *isl_map_get_dim_id(
1503 __isl_keep isl_map *map, enum isl_dim_type type,
1506 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1507 enum isl_dim_type type, __isl_keep isl_id *id);
1508 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1509 enum isl_dim_type type, __isl_keep isl_id *id);
1510 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1511 enum isl_dim_type type, const char *name);
1512 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1513 enum isl_dim_type type, const char *name);
1515 const char *isl_constraint_get_dim_name(
1516 __isl_keep isl_constraint *constraint,
1517 enum isl_dim_type type, unsigned pos);
1518 const char *isl_basic_set_get_dim_name(
1519 __isl_keep isl_basic_set *bset,
1520 enum isl_dim_type type, unsigned pos);
1521 const char *isl_set_get_dim_name(
1522 __isl_keep isl_set *set,
1523 enum isl_dim_type type, unsigned pos);
1524 const char *isl_basic_map_get_dim_name(
1525 __isl_keep isl_basic_map *bmap,
1526 enum isl_dim_type type, unsigned pos);
1527 const char *isl_map_get_dim_name(
1528 __isl_keep isl_map *map,
1529 enum isl_dim_type type, unsigned pos);
1531 These functions are mostly useful to obtain the identifiers, positions
1532 or names of the parameters. Identifiers of individual dimensions are
1533 essentially only useful for printing. They are ignored by all other
1534 operations and may not be preserved across those operations.
1538 =head3 Unary Properties
1544 The following functions test whether the given set or relation
1545 contains any integer points. The ``plain'' variants do not perform
1546 any computations, but simply check if the given set or relation
1547 is already known to be empty.
1549 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1550 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1551 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1552 int isl_set_is_empty(__isl_keep isl_set *set);
1553 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1554 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1555 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1556 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1557 int isl_map_is_empty(__isl_keep isl_map *map);
1558 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1560 =item * Universality
1562 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1563 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1564 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1566 =item * Single-valuedness
1568 int isl_map_is_single_valued(__isl_keep isl_map *map);
1569 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1573 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1574 int isl_map_is_injective(__isl_keep isl_map *map);
1575 int isl_union_map_plain_is_injective(
1576 __isl_keep isl_union_map *umap);
1577 int isl_union_map_is_injective(
1578 __isl_keep isl_union_map *umap);
1582 int isl_map_is_bijective(__isl_keep isl_map *map);
1583 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1587 int isl_basic_map_plain_is_fixed(
1588 __isl_keep isl_basic_map *bmap,
1589 enum isl_dim_type type, unsigned pos,
1591 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
1592 enum isl_dim_type type, unsigned pos,
1594 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1595 enum isl_dim_type type, unsigned pos,
1598 Check if the relation obviously lies on a hyperplane where the given dimension
1599 has a fixed value and if so, return that value in C<*val>.
1603 To check whether a set is a parameter domain, use this function:
1605 int isl_set_is_params(__isl_keep isl_set *set);
1606 int isl_union_set_is_params(
1607 __isl_keep isl_union_set *uset);
1611 The following functions check whether the domain of the given
1612 (basic) set is a wrapped relation.
1614 int isl_basic_set_is_wrapping(
1615 __isl_keep isl_basic_set *bset);
1616 int isl_set_is_wrapping(__isl_keep isl_set *set);
1618 =item * Internal Product
1620 int isl_basic_map_can_zip(
1621 __isl_keep isl_basic_map *bmap);
1622 int isl_map_can_zip(__isl_keep isl_map *map);
1624 Check whether the product of domain and range of the given relation
1626 i.e., whether both domain and range are nested relations.
1630 =head3 Binary Properties
1636 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1637 __isl_keep isl_set *set2);
1638 int isl_set_is_equal(__isl_keep isl_set *set1,
1639 __isl_keep isl_set *set2);
1640 int isl_union_set_is_equal(
1641 __isl_keep isl_union_set *uset1,
1642 __isl_keep isl_union_set *uset2);
1643 int isl_basic_map_is_equal(
1644 __isl_keep isl_basic_map *bmap1,
1645 __isl_keep isl_basic_map *bmap2);
1646 int isl_map_is_equal(__isl_keep isl_map *map1,
1647 __isl_keep isl_map *map2);
1648 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1649 __isl_keep isl_map *map2);
1650 int isl_union_map_is_equal(
1651 __isl_keep isl_union_map *umap1,
1652 __isl_keep isl_union_map *umap2);
1654 =item * Disjointness
1656 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1657 __isl_keep isl_set *set2);
1661 int isl_set_is_subset(__isl_keep isl_set *set1,
1662 __isl_keep isl_set *set2);
1663 int isl_set_is_strict_subset(
1664 __isl_keep isl_set *set1,
1665 __isl_keep isl_set *set2);
1666 int isl_union_set_is_subset(
1667 __isl_keep isl_union_set *uset1,
1668 __isl_keep isl_union_set *uset2);
1669 int isl_union_set_is_strict_subset(
1670 __isl_keep isl_union_set *uset1,
1671 __isl_keep isl_union_set *uset2);
1672 int isl_basic_map_is_subset(
1673 __isl_keep isl_basic_map *bmap1,
1674 __isl_keep isl_basic_map *bmap2);
1675 int isl_basic_map_is_strict_subset(
1676 __isl_keep isl_basic_map *bmap1,
1677 __isl_keep isl_basic_map *bmap2);
1678 int isl_map_is_subset(
1679 __isl_keep isl_map *map1,
1680 __isl_keep isl_map *map2);
1681 int isl_map_is_strict_subset(
1682 __isl_keep isl_map *map1,
1683 __isl_keep isl_map *map2);
1684 int isl_union_map_is_subset(
1685 __isl_keep isl_union_map *umap1,
1686 __isl_keep isl_union_map *umap2);
1687 int isl_union_map_is_strict_subset(
1688 __isl_keep isl_union_map *umap1,
1689 __isl_keep isl_union_map *umap2);
1693 =head2 Unary Operations
1699 __isl_give isl_set *isl_set_complement(
1700 __isl_take isl_set *set);
1704 __isl_give isl_basic_map *isl_basic_map_reverse(
1705 __isl_take isl_basic_map *bmap);
1706 __isl_give isl_map *isl_map_reverse(
1707 __isl_take isl_map *map);
1708 __isl_give isl_union_map *isl_union_map_reverse(
1709 __isl_take isl_union_map *umap);
1713 __isl_give isl_basic_set *isl_basic_set_project_out(
1714 __isl_take isl_basic_set *bset,
1715 enum isl_dim_type type, unsigned first, unsigned n);
1716 __isl_give isl_basic_map *isl_basic_map_project_out(
1717 __isl_take isl_basic_map *bmap,
1718 enum isl_dim_type type, unsigned first, unsigned n);
1719 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1720 enum isl_dim_type type, unsigned first, unsigned n);
1721 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1722 enum isl_dim_type type, unsigned first, unsigned n);
1723 __isl_give isl_basic_set *isl_basic_set_params(
1724 __isl_take isl_basic_set *bset);
1725 __isl_give isl_basic_set *isl_basic_map_domain(
1726 __isl_take isl_basic_map *bmap);
1727 __isl_give isl_basic_set *isl_basic_map_range(
1728 __isl_take isl_basic_map *bmap);
1729 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1730 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
1731 __isl_give isl_set *isl_map_domain(
1732 __isl_take isl_map *bmap);
1733 __isl_give isl_set *isl_map_range(
1734 __isl_take isl_map *map);
1735 __isl_give isl_set *isl_union_set_params(
1736 __isl_take isl_union_set *uset);
1737 __isl_give isl_set *isl_union_map_params(
1738 __isl_take isl_union_map *umap);
1739 __isl_give isl_union_set *isl_union_map_domain(
1740 __isl_take isl_union_map *umap);
1741 __isl_give isl_union_set *isl_union_map_range(
1742 __isl_take isl_union_map *umap);
1744 __isl_give isl_basic_map *isl_basic_map_domain_map(
1745 __isl_take isl_basic_map *bmap);
1746 __isl_give isl_basic_map *isl_basic_map_range_map(
1747 __isl_take isl_basic_map *bmap);
1748 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1749 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1750 __isl_give isl_union_map *isl_union_map_domain_map(
1751 __isl_take isl_union_map *umap);
1752 __isl_give isl_union_map *isl_union_map_range_map(
1753 __isl_take isl_union_map *umap);
1755 The functions above construct a (basic, regular or union) relation
1756 that maps (a wrapped version of) the input relation to its domain or range.
1760 __isl_give isl_set *isl_set_eliminate(
1761 __isl_take isl_set *set, enum isl_dim_type type,
1762 unsigned first, unsigned n);
1763 __isl_give isl_basic_map *isl_basic_map_eliminate(
1764 __isl_take isl_basic_map *bmap,
1765 enum isl_dim_type type,
1766 unsigned first, unsigned n);
1768 Eliminate the coefficients for the given dimensions from the constraints,
1769 without removing the dimensions.
1773 __isl_give isl_basic_set *isl_basic_set_fix(
1774 __isl_take isl_basic_set *bset,
1775 enum isl_dim_type type, unsigned pos,
1777 __isl_give isl_basic_set *isl_basic_set_fix_si(
1778 __isl_take isl_basic_set *bset,
1779 enum isl_dim_type type, unsigned pos, int value);
1780 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1781 enum isl_dim_type type, unsigned pos,
1783 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1784 enum isl_dim_type type, unsigned pos, int value);
1785 __isl_give isl_basic_map *isl_basic_map_fix_si(
1786 __isl_take isl_basic_map *bmap,
1787 enum isl_dim_type type, unsigned pos, int value);
1788 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1789 enum isl_dim_type type, unsigned pos, int value);
1791 Intersect the set or relation with the hyperplane where the given
1792 dimension has the fixed given value.
1794 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
1795 __isl_take isl_basic_map *bmap,
1796 enum isl_dim_type type, unsigned pos, int value);
1797 __isl_give isl_set *isl_set_lower_bound_si(
1798 __isl_take isl_set *set,
1799 enum isl_dim_type type, unsigned pos, int value);
1800 __isl_give isl_map *isl_map_lower_bound_si(
1801 __isl_take isl_map *map,
1802 enum isl_dim_type type, unsigned pos, int value);
1803 __isl_give isl_set *isl_set_upper_bound_si(
1804 __isl_take isl_set *set,
1805 enum isl_dim_type type, unsigned pos, int value);
1806 __isl_give isl_map *isl_map_upper_bound_si(
1807 __isl_take isl_map *map,
1808 enum isl_dim_type type, unsigned pos, int value);
1810 Intersect the set or relation with the half-space where the given
1811 dimension has a value bounded the fixed given value.
1813 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1814 enum isl_dim_type type1, int pos1,
1815 enum isl_dim_type type2, int pos2);
1816 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1817 enum isl_dim_type type1, int pos1,
1818 enum isl_dim_type type2, int pos2);
1820 Intersect the set or relation with the hyperplane where the given
1821 dimensions are equal to each other.
1823 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
1824 enum isl_dim_type type1, int pos1,
1825 enum isl_dim_type type2, int pos2);
1827 Intersect the relation with the hyperplane where the given
1828 dimensions have opposite values.
1832 __isl_give isl_map *isl_set_identity(
1833 __isl_take isl_set *set);
1834 __isl_give isl_union_map *isl_union_set_identity(
1835 __isl_take isl_union_set *uset);
1837 Construct an identity relation on the given (union) set.
1841 __isl_give isl_basic_set *isl_basic_map_deltas(
1842 __isl_take isl_basic_map *bmap);
1843 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1844 __isl_give isl_union_set *isl_union_map_deltas(
1845 __isl_take isl_union_map *umap);
1847 These functions return a (basic) set containing the differences
1848 between image elements and corresponding domain elements in the input.
1850 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1851 __isl_take isl_basic_map *bmap);
1852 __isl_give isl_map *isl_map_deltas_map(
1853 __isl_take isl_map *map);
1854 __isl_give isl_union_map *isl_union_map_deltas_map(
1855 __isl_take isl_union_map *umap);
1857 The functions above construct a (basic, regular or union) relation
1858 that maps (a wrapped version of) the input relation to its delta set.
1862 Simplify the representation of a set or relation by trying
1863 to combine pairs of basic sets or relations into a single
1864 basic set or relation.
1866 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1867 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1868 __isl_give isl_union_set *isl_union_set_coalesce(
1869 __isl_take isl_union_set *uset);
1870 __isl_give isl_union_map *isl_union_map_coalesce(
1871 __isl_take isl_union_map *umap);
1873 =item * Detecting equalities
1875 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1876 __isl_take isl_basic_set *bset);
1877 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1878 __isl_take isl_basic_map *bmap);
1879 __isl_give isl_set *isl_set_detect_equalities(
1880 __isl_take isl_set *set);
1881 __isl_give isl_map *isl_map_detect_equalities(
1882 __isl_take isl_map *map);
1883 __isl_give isl_union_set *isl_union_set_detect_equalities(
1884 __isl_take isl_union_set *uset);
1885 __isl_give isl_union_map *isl_union_map_detect_equalities(
1886 __isl_take isl_union_map *umap);
1888 Simplify the representation of a set or relation by detecting implicit
1891 =item * Removing redundant constraints
1893 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1894 __isl_take isl_basic_set *bset);
1895 __isl_give isl_set *isl_set_remove_redundancies(
1896 __isl_take isl_set *set);
1897 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1898 __isl_take isl_basic_map *bmap);
1899 __isl_give isl_map *isl_map_remove_redundancies(
1900 __isl_take isl_map *map);
1904 __isl_give isl_basic_set *isl_set_convex_hull(
1905 __isl_take isl_set *set);
1906 __isl_give isl_basic_map *isl_map_convex_hull(
1907 __isl_take isl_map *map);
1909 If the input set or relation has any existentially quantified
1910 variables, then the result of these operations is currently undefined.
1914 __isl_give isl_basic_set *isl_set_simple_hull(
1915 __isl_take isl_set *set);
1916 __isl_give isl_basic_map *isl_map_simple_hull(
1917 __isl_take isl_map *map);
1918 __isl_give isl_union_map *isl_union_map_simple_hull(
1919 __isl_take isl_union_map *umap);
1921 These functions compute a single basic set or relation
1922 that contains the whole input set or relation.
1923 In particular, the output is described by translates
1924 of the constraints describing the basic sets or relations in the input.
1928 (See \autoref{s:simple hull}.)
1934 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1935 __isl_take isl_basic_set *bset);
1936 __isl_give isl_basic_set *isl_set_affine_hull(
1937 __isl_take isl_set *set);
1938 __isl_give isl_union_set *isl_union_set_affine_hull(
1939 __isl_take isl_union_set *uset);
1940 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1941 __isl_take isl_basic_map *bmap);
1942 __isl_give isl_basic_map *isl_map_affine_hull(
1943 __isl_take isl_map *map);
1944 __isl_give isl_union_map *isl_union_map_affine_hull(
1945 __isl_take isl_union_map *umap);
1947 In case of union sets and relations, the affine hull is computed
1950 =item * Polyhedral hull
1952 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1953 __isl_take isl_set *set);
1954 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1955 __isl_take isl_map *map);
1956 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1957 __isl_take isl_union_set *uset);
1958 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1959 __isl_take isl_union_map *umap);
1961 These functions compute a single basic set or relation
1962 not involving any existentially quantified variables
1963 that contains the whole input set or relation.
1964 In case of union sets and relations, the polyhedral hull is computed
1967 =item * Optimization
1969 #include <isl/ilp.h>
1970 enum isl_lp_result isl_basic_set_max(
1971 __isl_keep isl_basic_set *bset,
1972 __isl_keep isl_aff *obj, isl_int *opt)
1973 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
1974 __isl_keep isl_aff *obj, isl_int *opt);
1975 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
1976 __isl_keep isl_aff *obj, isl_int *opt);
1978 Compute the minimum or maximum of the integer affine expression C<obj>
1979 over the points in C<set>, returning the result in C<opt>.
1980 The return value may be one of C<isl_lp_error>,
1981 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
1983 =item * Parametric optimization
1985 __isl_give isl_pw_aff *isl_set_dim_min(
1986 __isl_take isl_set *set, int pos);
1987 __isl_give isl_pw_aff *isl_set_dim_max(
1988 __isl_take isl_set *set, int pos);
1989 __isl_give isl_pw_aff *isl_map_dim_max(
1990 __isl_take isl_map *map, int pos);
1992 Compute the minimum or maximum of the given set or output dimension
1993 as a function of the parameters (and input dimensions), but independently
1994 of the other set or output dimensions.
1995 For lexicographic optimization, see L<"Lexicographic Optimization">.
1999 The following functions compute either the set of (rational) coefficient
2000 values of valid constraints for the given set or the set of (rational)
2001 values satisfying the constraints with coefficients from the given set.
2002 Internally, these two sets of functions perform essentially the
2003 same operations, except that the set of coefficients is assumed to
2004 be a cone, while the set of values may be any polyhedron.
2005 The current implementation is based on the Farkas lemma and
2006 Fourier-Motzkin elimination, but this may change or be made optional
2007 in future. In particular, future implementations may use different
2008 dualization algorithms or skip the elimination step.
2010 __isl_give isl_basic_set *isl_basic_set_coefficients(
2011 __isl_take isl_basic_set *bset);
2012 __isl_give isl_basic_set *isl_set_coefficients(
2013 __isl_take isl_set *set);
2014 __isl_give isl_union_set *isl_union_set_coefficients(
2015 __isl_take isl_union_set *bset);
2016 __isl_give isl_basic_set *isl_basic_set_solutions(
2017 __isl_take isl_basic_set *bset);
2018 __isl_give isl_basic_set *isl_set_solutions(
2019 __isl_take isl_set *set);
2020 __isl_give isl_union_set *isl_union_set_solutions(
2021 __isl_take isl_union_set *bset);
2025 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2027 __isl_give isl_union_map *isl_union_map_power(
2028 __isl_take isl_union_map *umap, int *exact);
2030 Compute a parametric representation for all positive powers I<k> of C<map>.
2031 The result maps I<k> to a nested relation corresponding to the
2032 I<k>th power of C<map>.
2033 The result may be an overapproximation. If the result is known to be exact,
2034 then C<*exact> is set to C<1>.
2036 =item * Transitive closure
2038 __isl_give isl_map *isl_map_transitive_closure(
2039 __isl_take isl_map *map, int *exact);
2040 __isl_give isl_union_map *isl_union_map_transitive_closure(
2041 __isl_take isl_union_map *umap, int *exact);
2043 Compute the transitive closure of C<map>.
2044 The result may be an overapproximation. If the result is known to be exact,
2045 then C<*exact> is set to C<1>.
2047 =item * Reaching path lengths
2049 __isl_give isl_map *isl_map_reaching_path_lengths(
2050 __isl_take isl_map *map, int *exact);
2052 Compute a relation that maps each element in the range of C<map>
2053 to the lengths of all paths composed of edges in C<map> that
2054 end up in the given element.
2055 The result may be an overapproximation. If the result is known to be exact,
2056 then C<*exact> is set to C<1>.
2057 To compute the I<maximal> path length, the resulting relation
2058 should be postprocessed by C<isl_map_lexmax>.
2059 In particular, if the input relation is a dependence relation
2060 (mapping sources to sinks), then the maximal path length corresponds
2061 to the free schedule.
2062 Note, however, that C<isl_map_lexmax> expects the maximum to be
2063 finite, so if the path lengths are unbounded (possibly due to
2064 the overapproximation), then you will get an error message.
2068 __isl_give isl_basic_set *isl_basic_map_wrap(
2069 __isl_take isl_basic_map *bmap);
2070 __isl_give isl_set *isl_map_wrap(
2071 __isl_take isl_map *map);
2072 __isl_give isl_union_set *isl_union_map_wrap(
2073 __isl_take isl_union_map *umap);
2074 __isl_give isl_basic_map *isl_basic_set_unwrap(
2075 __isl_take isl_basic_set *bset);
2076 __isl_give isl_map *isl_set_unwrap(
2077 __isl_take isl_set *set);
2078 __isl_give isl_union_map *isl_union_set_unwrap(
2079 __isl_take isl_union_set *uset);
2083 Remove any internal structure of domain (and range) of the given
2084 set or relation. If there is any such internal structure in the input,
2085 then the name of the space is also removed.
2087 __isl_give isl_basic_set *isl_basic_set_flatten(
2088 __isl_take isl_basic_set *bset);
2089 __isl_give isl_set *isl_set_flatten(
2090 __isl_take isl_set *set);
2091 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2092 __isl_take isl_basic_map *bmap);
2093 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2094 __isl_take isl_basic_map *bmap);
2095 __isl_give isl_map *isl_map_flatten_range(
2096 __isl_take isl_map *map);
2097 __isl_give isl_map *isl_map_flatten_domain(
2098 __isl_take isl_map *map);
2099 __isl_give isl_basic_map *isl_basic_map_flatten(
2100 __isl_take isl_basic_map *bmap);
2101 __isl_give isl_map *isl_map_flatten(
2102 __isl_take isl_map *map);
2104 __isl_give isl_map *isl_set_flatten_map(
2105 __isl_take isl_set *set);
2107 The function above constructs a relation
2108 that maps the input set to a flattened version of the set.
2112 Lift the input set to a space with extra dimensions corresponding
2113 to the existentially quantified variables in the input.
2114 In particular, the result lives in a wrapped map where the domain
2115 is the original space and the range corresponds to the original
2116 existentially quantified variables.
2118 __isl_give isl_basic_set *isl_basic_set_lift(
2119 __isl_take isl_basic_set *bset);
2120 __isl_give isl_set *isl_set_lift(
2121 __isl_take isl_set *set);
2122 __isl_give isl_union_set *isl_union_set_lift(
2123 __isl_take isl_union_set *uset);
2125 Given a local space that contains the existentially quantified
2126 variables of a set, a basic relation that, when applied to
2127 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2128 can be constructed using the following function.
2130 #include <isl/local_space.h>
2131 __isl_give isl_basic_map *isl_local_space_lifting(
2132 __isl_take isl_local_space *ls);
2134 =item * Internal Product
2136 __isl_give isl_basic_map *isl_basic_map_zip(
2137 __isl_take isl_basic_map *bmap);
2138 __isl_give isl_map *isl_map_zip(
2139 __isl_take isl_map *map);
2140 __isl_give isl_union_map *isl_union_map_zip(
2141 __isl_take isl_union_map *umap);
2143 Given a relation with nested relations for domain and range,
2144 interchange the range of the domain with the domain of the range.
2146 =item * Aligning parameters
2148 __isl_give isl_set *isl_set_align_params(
2149 __isl_take isl_set *set,
2150 __isl_take isl_space *model);
2151 __isl_give isl_map *isl_map_align_params(
2152 __isl_take isl_map *map,
2153 __isl_take isl_space *model);
2155 Change the order of the parameters of the given set or relation
2156 such that the first parameters match those of C<model>.
2157 This may involve the introduction of extra parameters.
2158 All parameters need to be named.
2160 =item * Dimension manipulation
2162 __isl_give isl_set *isl_set_add_dims(
2163 __isl_take isl_set *set,
2164 enum isl_dim_type type, unsigned n);
2165 __isl_give isl_map *isl_map_add_dims(
2166 __isl_take isl_map *map,
2167 enum isl_dim_type type, unsigned n);
2168 __isl_give isl_set *isl_set_insert_dims(
2169 __isl_take isl_set *set,
2170 enum isl_dim_type type, unsigned pos, unsigned n);
2171 __isl_give isl_map *isl_map_insert_dims(
2172 __isl_take isl_map *map,
2173 enum isl_dim_type type, unsigned pos, unsigned n);
2174 __isl_give isl_basic_set *isl_basic_set_move_dims(
2175 __isl_take isl_basic_set *bset,
2176 enum isl_dim_type dst_type, unsigned dst_pos,
2177 enum isl_dim_type src_type, unsigned src_pos,
2179 __isl_give isl_basic_map *isl_basic_map_move_dims(
2180 __isl_take isl_basic_map *bmap,
2181 enum isl_dim_type dst_type, unsigned dst_pos,
2182 enum isl_dim_type src_type, unsigned src_pos,
2184 __isl_give isl_set *isl_set_move_dims(
2185 __isl_take isl_set *set,
2186 enum isl_dim_type dst_type, unsigned dst_pos,
2187 enum isl_dim_type src_type, unsigned src_pos,
2189 __isl_give isl_map *isl_map_move_dims(
2190 __isl_take isl_map *map,
2191 enum isl_dim_type dst_type, unsigned dst_pos,
2192 enum isl_dim_type src_type, unsigned src_pos,
2195 It is usually not advisable to directly change the (input or output)
2196 space of a set or a relation as this removes the name and the internal
2197 structure of the space. However, the above functions can be useful
2198 to add new parameters, assuming
2199 C<isl_set_align_params> and C<isl_map_align_params>
2204 =head2 Binary Operations
2206 The two arguments of a binary operation not only need to live
2207 in the same C<isl_ctx>, they currently also need to have
2208 the same (number of) parameters.
2210 =head3 Basic Operations
2214 =item * Intersection
2216 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2217 __isl_take isl_basic_set *bset1,
2218 __isl_take isl_basic_set *bset2);
2219 __isl_give isl_basic_set *isl_basic_set_intersect(
2220 __isl_take isl_basic_set *bset1,
2221 __isl_take isl_basic_set *bset2);
2222 __isl_give isl_set *isl_set_intersect_params(
2223 __isl_take isl_set *set,
2224 __isl_take isl_set *params);
2225 __isl_give isl_set *isl_set_intersect(
2226 __isl_take isl_set *set1,
2227 __isl_take isl_set *set2);
2228 __isl_give isl_union_set *isl_union_set_intersect_params(
2229 __isl_take isl_union_set *uset,
2230 __isl_take isl_set *set);
2231 __isl_give isl_union_map *isl_union_map_intersect_params(
2232 __isl_take isl_union_map *umap,
2233 __isl_take isl_set *set);
2234 __isl_give isl_union_set *isl_union_set_intersect(
2235 __isl_take isl_union_set *uset1,
2236 __isl_take isl_union_set *uset2);
2237 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2238 __isl_take isl_basic_map *bmap,
2239 __isl_take isl_basic_set *bset);
2240 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2241 __isl_take isl_basic_map *bmap,
2242 __isl_take isl_basic_set *bset);
2243 __isl_give isl_basic_map *isl_basic_map_intersect(
2244 __isl_take isl_basic_map *bmap1,
2245 __isl_take isl_basic_map *bmap2);
2246 __isl_give isl_map *isl_map_intersect_params(
2247 __isl_take isl_map *map,
2248 __isl_take isl_set *params);
2249 __isl_give isl_map *isl_map_intersect_domain(
2250 __isl_take isl_map *map,
2251 __isl_take isl_set *set);
2252 __isl_give isl_map *isl_map_intersect_range(
2253 __isl_take isl_map *map,
2254 __isl_take isl_set *set);
2255 __isl_give isl_map *isl_map_intersect(
2256 __isl_take isl_map *map1,
2257 __isl_take isl_map *map2);
2258 __isl_give isl_union_map *isl_union_map_intersect_domain(
2259 __isl_take isl_union_map *umap,
2260 __isl_take isl_union_set *uset);
2261 __isl_give isl_union_map *isl_union_map_intersect_range(
2262 __isl_take isl_union_map *umap,
2263 __isl_take isl_union_set *uset);
2264 __isl_give isl_union_map *isl_union_map_intersect(
2265 __isl_take isl_union_map *umap1,
2266 __isl_take isl_union_map *umap2);
2270 __isl_give isl_set *isl_basic_set_union(
2271 __isl_take isl_basic_set *bset1,
2272 __isl_take isl_basic_set *bset2);
2273 __isl_give isl_map *isl_basic_map_union(
2274 __isl_take isl_basic_map *bmap1,
2275 __isl_take isl_basic_map *bmap2);
2276 __isl_give isl_set *isl_set_union(
2277 __isl_take isl_set *set1,
2278 __isl_take isl_set *set2);
2279 __isl_give isl_map *isl_map_union(
2280 __isl_take isl_map *map1,
2281 __isl_take isl_map *map2);
2282 __isl_give isl_union_set *isl_union_set_union(
2283 __isl_take isl_union_set *uset1,
2284 __isl_take isl_union_set *uset2);
2285 __isl_give isl_union_map *isl_union_map_union(
2286 __isl_take isl_union_map *umap1,
2287 __isl_take isl_union_map *umap2);
2289 =item * Set difference
2291 __isl_give isl_set *isl_set_subtract(
2292 __isl_take isl_set *set1,
2293 __isl_take isl_set *set2);
2294 __isl_give isl_map *isl_map_subtract(
2295 __isl_take isl_map *map1,
2296 __isl_take isl_map *map2);
2297 __isl_give isl_map *isl_map_subtract_domain(
2298 __isl_take isl_map *map,
2299 __isl_take isl_set *dom);
2300 __isl_give isl_map *isl_map_subtract_range(
2301 __isl_take isl_map *map,
2302 __isl_take isl_set *dom);
2303 __isl_give isl_union_set *isl_union_set_subtract(
2304 __isl_take isl_union_set *uset1,
2305 __isl_take isl_union_set *uset2);
2306 __isl_give isl_union_map *isl_union_map_subtract(
2307 __isl_take isl_union_map *umap1,
2308 __isl_take isl_union_map *umap2);
2312 __isl_give isl_basic_set *isl_basic_set_apply(
2313 __isl_take isl_basic_set *bset,
2314 __isl_take isl_basic_map *bmap);
2315 __isl_give isl_set *isl_set_apply(
2316 __isl_take isl_set *set,
2317 __isl_take isl_map *map);
2318 __isl_give isl_union_set *isl_union_set_apply(
2319 __isl_take isl_union_set *uset,
2320 __isl_take isl_union_map *umap);
2321 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2322 __isl_take isl_basic_map *bmap1,
2323 __isl_take isl_basic_map *bmap2);
2324 __isl_give isl_basic_map *isl_basic_map_apply_range(
2325 __isl_take isl_basic_map *bmap1,
2326 __isl_take isl_basic_map *bmap2);
2327 __isl_give isl_map *isl_map_apply_domain(
2328 __isl_take isl_map *map1,
2329 __isl_take isl_map *map2);
2330 __isl_give isl_union_map *isl_union_map_apply_domain(
2331 __isl_take isl_union_map *umap1,
2332 __isl_take isl_union_map *umap2);
2333 __isl_give isl_map *isl_map_apply_range(
2334 __isl_take isl_map *map1,
2335 __isl_take isl_map *map2);
2336 __isl_give isl_union_map *isl_union_map_apply_range(
2337 __isl_take isl_union_map *umap1,
2338 __isl_take isl_union_map *umap2);
2340 =item * Cartesian Product
2342 __isl_give isl_set *isl_set_product(
2343 __isl_take isl_set *set1,
2344 __isl_take isl_set *set2);
2345 __isl_give isl_union_set *isl_union_set_product(
2346 __isl_take isl_union_set *uset1,
2347 __isl_take isl_union_set *uset2);
2348 __isl_give isl_basic_map *isl_basic_map_domain_product(
2349 __isl_take isl_basic_map *bmap1,
2350 __isl_take isl_basic_map *bmap2);
2351 __isl_give isl_basic_map *isl_basic_map_range_product(
2352 __isl_take isl_basic_map *bmap1,
2353 __isl_take isl_basic_map *bmap2);
2354 __isl_give isl_map *isl_map_domain_product(
2355 __isl_take isl_map *map1,
2356 __isl_take isl_map *map2);
2357 __isl_give isl_map *isl_map_range_product(
2358 __isl_take isl_map *map1,
2359 __isl_take isl_map *map2);
2360 __isl_give isl_union_map *isl_union_map_range_product(
2361 __isl_take isl_union_map *umap1,
2362 __isl_take isl_union_map *umap2);
2363 __isl_give isl_map *isl_map_product(
2364 __isl_take isl_map *map1,
2365 __isl_take isl_map *map2);
2366 __isl_give isl_union_map *isl_union_map_product(
2367 __isl_take isl_union_map *umap1,
2368 __isl_take isl_union_map *umap2);
2370 The above functions compute the cross product of the given
2371 sets or relations. The domains and ranges of the results
2372 are wrapped maps between domains and ranges of the inputs.
2373 To obtain a ``flat'' product, use the following functions
2376 __isl_give isl_basic_set *isl_basic_set_flat_product(
2377 __isl_take isl_basic_set *bset1,
2378 __isl_take isl_basic_set *bset2);
2379 __isl_give isl_set *isl_set_flat_product(
2380 __isl_take isl_set *set1,
2381 __isl_take isl_set *set2);
2382 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2383 __isl_take isl_basic_map *bmap1,
2384 __isl_take isl_basic_map *bmap2);
2385 __isl_give isl_map *isl_map_flat_domain_product(
2386 __isl_take isl_map *map1,
2387 __isl_take isl_map *map2);
2388 __isl_give isl_map *isl_map_flat_range_product(
2389 __isl_take isl_map *map1,
2390 __isl_take isl_map *map2);
2391 __isl_give isl_union_map *isl_union_map_flat_range_product(
2392 __isl_take isl_union_map *umap1,
2393 __isl_take isl_union_map *umap2);
2394 __isl_give isl_basic_map *isl_basic_map_flat_product(
2395 __isl_take isl_basic_map *bmap1,
2396 __isl_take isl_basic_map *bmap2);
2397 __isl_give isl_map *isl_map_flat_product(
2398 __isl_take isl_map *map1,
2399 __isl_take isl_map *map2);
2401 =item * Simplification
2403 __isl_give isl_basic_set *isl_basic_set_gist(
2404 __isl_take isl_basic_set *bset,
2405 __isl_take isl_basic_set *context);
2406 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2407 __isl_take isl_set *context);
2408 __isl_give isl_set *isl_set_gist_params(
2409 __isl_take isl_set *set,
2410 __isl_take isl_set *context);
2411 __isl_give isl_union_set *isl_union_set_gist(
2412 __isl_take isl_union_set *uset,
2413 __isl_take isl_union_set *context);
2414 __isl_give isl_union_set *isl_union_set_gist_params(
2415 __isl_take isl_union_set *uset,
2416 __isl_take isl_set *set);
2417 __isl_give isl_basic_map *isl_basic_map_gist(
2418 __isl_take isl_basic_map *bmap,
2419 __isl_take isl_basic_map *context);
2420 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2421 __isl_take isl_map *context);
2422 __isl_give isl_map *isl_map_gist_params(
2423 __isl_take isl_map *map,
2424 __isl_take isl_set *context);
2425 __isl_give isl_map *isl_map_gist_domain(
2426 __isl_take isl_map *map,
2427 __isl_take isl_set *context);
2428 __isl_give isl_map *isl_map_gist_range(
2429 __isl_take isl_map *map,
2430 __isl_take isl_set *context);
2431 __isl_give isl_union_map *isl_union_map_gist(
2432 __isl_take isl_union_map *umap,
2433 __isl_take isl_union_map *context);
2434 __isl_give isl_union_map *isl_union_map_gist_params(
2435 __isl_take isl_union_map *umap,
2436 __isl_take isl_set *set);
2437 __isl_give isl_union_map *isl_union_map_gist_domain(
2438 __isl_take isl_union_map *umap,
2439 __isl_take isl_union_set *uset);
2441 The gist operation returns a set or relation that has the
2442 same intersection with the context as the input set or relation.
2443 Any implicit equality in the intersection is made explicit in the result,
2444 while all inequalities that are redundant with respect to the intersection
2446 In case of union sets and relations, the gist operation is performed
2451 =head3 Lexicographic Optimization
2453 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2454 the following functions
2455 compute a set that contains the lexicographic minimum or maximum
2456 of the elements in C<set> (or C<bset>) for those values of the parameters
2457 that satisfy C<dom>.
2458 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2459 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2461 In other words, the union of the parameter values
2462 for which the result is non-empty and of C<*empty>
2465 __isl_give isl_set *isl_basic_set_partial_lexmin(
2466 __isl_take isl_basic_set *bset,
2467 __isl_take isl_basic_set *dom,
2468 __isl_give isl_set **empty);
2469 __isl_give isl_set *isl_basic_set_partial_lexmax(
2470 __isl_take isl_basic_set *bset,
2471 __isl_take isl_basic_set *dom,
2472 __isl_give isl_set **empty);
2473 __isl_give isl_set *isl_set_partial_lexmin(
2474 __isl_take isl_set *set, __isl_take isl_set *dom,
2475 __isl_give isl_set **empty);
2476 __isl_give isl_set *isl_set_partial_lexmax(
2477 __isl_take isl_set *set, __isl_take isl_set *dom,
2478 __isl_give isl_set **empty);
2480 Given a (basic) set C<set> (or C<bset>), the following functions simply
2481 return a set containing the lexicographic minimum or maximum
2482 of the elements in C<set> (or C<bset>).
2483 In case of union sets, the optimum is computed per space.
2485 __isl_give isl_set *isl_basic_set_lexmin(
2486 __isl_take isl_basic_set *bset);
2487 __isl_give isl_set *isl_basic_set_lexmax(
2488 __isl_take isl_basic_set *bset);
2489 __isl_give isl_set *isl_set_lexmin(
2490 __isl_take isl_set *set);
2491 __isl_give isl_set *isl_set_lexmax(
2492 __isl_take isl_set *set);
2493 __isl_give isl_union_set *isl_union_set_lexmin(
2494 __isl_take isl_union_set *uset);
2495 __isl_give isl_union_set *isl_union_set_lexmax(
2496 __isl_take isl_union_set *uset);
2498 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2499 the following functions
2500 compute a relation that maps each element of C<dom>
2501 to the single lexicographic minimum or maximum
2502 of the elements that are associated to that same
2503 element in C<map> (or C<bmap>).
2504 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2505 that contains the elements in C<dom> that do not map
2506 to any elements in C<map> (or C<bmap>).
2507 In other words, the union of the domain of the result and of C<*empty>
2510 __isl_give isl_map *isl_basic_map_partial_lexmax(
2511 __isl_take isl_basic_map *bmap,
2512 __isl_take isl_basic_set *dom,
2513 __isl_give isl_set **empty);
2514 __isl_give isl_map *isl_basic_map_partial_lexmin(
2515 __isl_take isl_basic_map *bmap,
2516 __isl_take isl_basic_set *dom,
2517 __isl_give isl_set **empty);
2518 __isl_give isl_map *isl_map_partial_lexmax(
2519 __isl_take isl_map *map, __isl_take isl_set *dom,
2520 __isl_give isl_set **empty);
2521 __isl_give isl_map *isl_map_partial_lexmin(
2522 __isl_take isl_map *map, __isl_take isl_set *dom,
2523 __isl_give isl_set **empty);
2525 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2526 return a map mapping each element in the domain of
2527 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2528 of all elements associated to that element.
2529 In case of union relations, the optimum is computed per space.
2531 __isl_give isl_map *isl_basic_map_lexmin(
2532 __isl_take isl_basic_map *bmap);
2533 __isl_give isl_map *isl_basic_map_lexmax(
2534 __isl_take isl_basic_map *bmap);
2535 __isl_give isl_map *isl_map_lexmin(
2536 __isl_take isl_map *map);
2537 __isl_give isl_map *isl_map_lexmax(
2538 __isl_take isl_map *map);
2539 __isl_give isl_union_map *isl_union_map_lexmin(
2540 __isl_take isl_union_map *umap);
2541 __isl_give isl_union_map *isl_union_map_lexmax(
2542 __isl_take isl_union_map *umap);
2544 The following functions return their result in the form of
2545 a piecewise multi-affine expression
2546 (See L<"Piecewise Multiple Quasi Affine Expressions">),
2547 but are otherwise equivalent to the corresponding functions
2548 returning a basic set or relation.
2550 __isl_give isl_pw_multi_aff *
2551 isl_basic_map_lexmin_pw_multi_aff(
2552 __isl_take isl_basic_map *bmap);
2553 __isl_give isl_pw_multi_aff *
2554 isl_basic_set_partial_lexmin_pw_multi_aff(
2555 __isl_take isl_basic_set *bset,
2556 __isl_take isl_basic_set *dom,
2557 __isl_give isl_set **empty);
2558 __isl_give isl_pw_multi_aff *
2559 isl_basic_set_partial_lexmax_pw_multi_aff(
2560 __isl_take isl_basic_set *bset,
2561 __isl_take isl_basic_set *dom,
2562 __isl_give isl_set **empty);
2563 __isl_give isl_pw_multi_aff *
2564 isl_basic_map_partial_lexmin_pw_multi_aff(
2565 __isl_take isl_basic_map *bmap,
2566 __isl_take isl_basic_set *dom,
2567 __isl_give isl_set **empty);
2568 __isl_give isl_pw_multi_aff *
2569 isl_basic_map_partial_lexmax_pw_multi_aff(
2570 __isl_take isl_basic_map *bmap,
2571 __isl_take isl_basic_set *dom,
2572 __isl_give isl_set **empty);
2576 Lists are defined over several element types, including
2577 C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2578 Here we take lists of C<isl_set>s as an example.
2579 Lists can be created, copied and freed using the following functions.
2581 #include <isl/list.h>
2582 __isl_give isl_set_list *isl_set_list_from_set(
2583 __isl_take isl_set *el);
2584 __isl_give isl_set_list *isl_set_list_alloc(
2585 isl_ctx *ctx, int n);
2586 __isl_give isl_set_list *isl_set_list_copy(
2587 __isl_keep isl_set_list *list);
2588 __isl_give isl_set_list *isl_set_list_add(
2589 __isl_take isl_set_list *list,
2590 __isl_take isl_set *el);
2591 __isl_give isl_set_list *isl_set_list_concat(
2592 __isl_take isl_set_list *list1,
2593 __isl_take isl_set_list *list2);
2594 void *isl_set_list_free(__isl_take isl_set_list *list);
2596 C<isl_set_list_alloc> creates an empty list with a capacity for
2597 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2600 Lists can be inspected using the following functions.
2602 #include <isl/list.h>
2603 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2604 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2605 __isl_give isl_set *isl_set_list_get_set(
2606 __isl_keep isl_set_list *list, int index);
2607 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2608 int (*fn)(__isl_take isl_set *el, void *user),
2611 Lists can be printed using
2613 #include <isl/list.h>
2614 __isl_give isl_printer *isl_printer_print_set_list(
2615 __isl_take isl_printer *p,
2616 __isl_keep isl_set_list *list);
2620 Matrices can be created, copied and freed using the following functions.
2622 #include <isl/mat.h>
2623 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2624 unsigned n_row, unsigned n_col);
2625 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2626 void isl_mat_free(__isl_take isl_mat *mat);
2628 Note that the elements of a newly created matrix may have arbitrary values.
2629 The elements can be changed and inspected using the following functions.
2631 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2632 int isl_mat_rows(__isl_keep isl_mat *mat);
2633 int isl_mat_cols(__isl_keep isl_mat *mat);
2634 int isl_mat_get_element(__isl_keep isl_mat *mat,
2635 int row, int col, isl_int *v);
2636 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2637 int row, int col, isl_int v);
2638 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2639 int row, int col, int v);
2641 C<isl_mat_get_element> will return a negative value if anything went wrong.
2642 In that case, the value of C<*v> is undefined.
2644 The following function can be used to compute the (right) inverse
2645 of a matrix, i.e., a matrix such that the product of the original
2646 and the inverse (in that order) is a multiple of the identity matrix.
2647 The input matrix is assumed to be of full row-rank.
2649 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2651 The following function can be used to compute the (right) kernel
2652 (or null space) of a matrix, i.e., a matrix such that the product of
2653 the original and the kernel (in that order) is the zero matrix.
2655 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2657 =head2 Piecewise Quasi Affine Expressions
2659 The zero quasi affine expression on a given domain can be created using
2661 __isl_give isl_aff *isl_aff_zero_on_domain(
2662 __isl_take isl_local_space *ls);
2664 Note that the space in which the resulting object lives is a map space
2665 with the given space as domain and a one-dimensional range.
2667 An empty piecewise quasi affine expression (one with no cells)
2668 or a piecewise quasi affine expression with a single cell can
2669 be created using the following functions.
2671 #include <isl/aff.h>
2672 __isl_give isl_pw_aff *isl_pw_aff_empty(
2673 __isl_take isl_space *space);
2674 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2675 __isl_take isl_set *set, __isl_take isl_aff *aff);
2676 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2677 __isl_take isl_aff *aff);
2679 Quasi affine expressions can be copied and freed using
2681 #include <isl/aff.h>
2682 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2683 void *isl_aff_free(__isl_take isl_aff *aff);
2685 __isl_give isl_pw_aff *isl_pw_aff_copy(
2686 __isl_keep isl_pw_aff *pwaff);
2687 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2689 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2690 using the following function. The constraint is required to have
2691 a non-zero coefficient for the specified dimension.
2693 #include <isl/constraint.h>
2694 __isl_give isl_aff *isl_constraint_get_bound(
2695 __isl_keep isl_constraint *constraint,
2696 enum isl_dim_type type, int pos);
2698 The entire affine expression of the constraint can also be extracted
2699 using the following function.
2701 #include <isl/constraint.h>
2702 __isl_give isl_aff *isl_constraint_get_aff(
2703 __isl_keep isl_constraint *constraint);
2705 Conversely, an equality constraint equating
2706 the affine expression to zero or an inequality constraint enforcing
2707 the affine expression to be non-negative, can be constructed using
2709 __isl_give isl_constraint *isl_equality_from_aff(
2710 __isl_take isl_aff *aff);
2711 __isl_give isl_constraint *isl_inequality_from_aff(
2712 __isl_take isl_aff *aff);
2714 The expression can be inspected using
2716 #include <isl/aff.h>
2717 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2718 int isl_aff_dim(__isl_keep isl_aff *aff,
2719 enum isl_dim_type type);
2720 __isl_give isl_local_space *isl_aff_get_domain_local_space(
2721 __isl_keep isl_aff *aff);
2722 __isl_give isl_local_space *isl_aff_get_local_space(
2723 __isl_keep isl_aff *aff);
2724 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2725 enum isl_dim_type type, unsigned pos);
2726 const char *isl_pw_aff_get_dim_name(
2727 __isl_keep isl_pw_aff *pa,
2728 enum isl_dim_type type, unsigned pos);
2729 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
2730 enum isl_dim_type type, unsigned pos);
2731 __isl_give isl_id *isl_pw_aff_get_dim_id(
2732 __isl_keep isl_pw_aff *pa,
2733 enum isl_dim_type type, unsigned pos);
2734 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2736 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2737 enum isl_dim_type type, int pos, isl_int *v);
2738 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2740 __isl_give isl_aff *isl_aff_get_div(
2741 __isl_keep isl_aff *aff, int pos);
2743 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2744 int (*fn)(__isl_take isl_set *set,
2745 __isl_take isl_aff *aff,
2746 void *user), void *user);
2748 int isl_aff_is_cst(__isl_keep isl_aff *aff);
2749 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
2751 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
2752 enum isl_dim_type type, unsigned first, unsigned n);
2753 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
2754 enum isl_dim_type type, unsigned first, unsigned n);
2756 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2757 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2758 enum isl_dim_type type);
2759 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2761 It can be modified using
2763 #include <isl/aff.h>
2764 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
2765 __isl_take isl_pw_aff *pwaff,
2766 enum isl_dim_type type, __isl_take isl_id *id);
2767 __isl_give isl_aff *isl_aff_set_dim_name(
2768 __isl_take isl_aff *aff, enum isl_dim_type type,
2769 unsigned pos, const char *s);
2770 __isl_give isl_aff *isl_aff_set_dim_id(
2771 __isl_take isl_aff *aff, enum isl_dim_type type,
2772 unsigned pos, __isl_take isl_id *id);
2773 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
2774 __isl_take isl_pw_aff *pma,
2775 enum isl_dim_type type, unsigned pos,
2776 __isl_take isl_id *id);
2777 __isl_give isl_aff *isl_aff_set_constant(
2778 __isl_take isl_aff *aff, isl_int v);
2779 __isl_give isl_aff *isl_aff_set_constant_si(
2780 __isl_take isl_aff *aff, int v);
2781 __isl_give isl_aff *isl_aff_set_coefficient(
2782 __isl_take isl_aff *aff,
2783 enum isl_dim_type type, int pos, isl_int v);
2784 __isl_give isl_aff *isl_aff_set_coefficient_si(
2785 __isl_take isl_aff *aff,
2786 enum isl_dim_type type, int pos, int v);
2787 __isl_give isl_aff *isl_aff_set_denominator(
2788 __isl_take isl_aff *aff, isl_int v);
2790 __isl_give isl_aff *isl_aff_add_constant(
2791 __isl_take isl_aff *aff, isl_int v);
2792 __isl_give isl_aff *isl_aff_add_constant_si(
2793 __isl_take isl_aff *aff, int v);
2794 __isl_give isl_aff *isl_aff_add_coefficient(
2795 __isl_take isl_aff *aff,
2796 enum isl_dim_type type, int pos, isl_int v);
2797 __isl_give isl_aff *isl_aff_add_coefficient_si(
2798 __isl_take isl_aff *aff,
2799 enum isl_dim_type type, int pos, int v);
2801 __isl_give isl_aff *isl_aff_insert_dims(
2802 __isl_take isl_aff *aff,
2803 enum isl_dim_type type, unsigned first, unsigned n);
2804 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
2805 __isl_take isl_pw_aff *pwaff,
2806 enum isl_dim_type type, unsigned first, unsigned n);
2807 __isl_give isl_aff *isl_aff_add_dims(
2808 __isl_take isl_aff *aff,
2809 enum isl_dim_type type, unsigned n);
2810 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
2811 __isl_take isl_pw_aff *pwaff,
2812 enum isl_dim_type type, unsigned n);
2813 __isl_give isl_aff *isl_aff_drop_dims(
2814 __isl_take isl_aff *aff,
2815 enum isl_dim_type type, unsigned first, unsigned n);
2816 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
2817 __isl_take isl_pw_aff *pwaff,
2818 enum isl_dim_type type, unsigned first, unsigned n);
2820 Note that the C<set_constant> and C<set_coefficient> functions
2821 set the I<numerator> of the constant or coefficient, while
2822 C<add_constant> and C<add_coefficient> add an integer value to
2823 the possibly rational constant or coefficient.
2825 To check whether an affine expressions is obviously zero
2826 or obviously equal to some other affine expression, use
2828 #include <isl/aff.h>
2829 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
2830 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
2831 __isl_keep isl_aff *aff2);
2832 int isl_pw_aff_plain_is_equal(
2833 __isl_keep isl_pw_aff *pwaff1,
2834 __isl_keep isl_pw_aff *pwaff2);
2838 #include <isl/aff.h>
2839 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2840 __isl_take isl_aff *aff2);
2841 __isl_give isl_pw_aff *isl_pw_aff_add(
2842 __isl_take isl_pw_aff *pwaff1,
2843 __isl_take isl_pw_aff *pwaff2);
2844 __isl_give isl_pw_aff *isl_pw_aff_min(
2845 __isl_take isl_pw_aff *pwaff1,
2846 __isl_take isl_pw_aff *pwaff2);
2847 __isl_give isl_pw_aff *isl_pw_aff_max(
2848 __isl_take isl_pw_aff *pwaff1,
2849 __isl_take isl_pw_aff *pwaff2);
2850 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2851 __isl_take isl_aff *aff2);
2852 __isl_give isl_pw_aff *isl_pw_aff_sub(
2853 __isl_take isl_pw_aff *pwaff1,
2854 __isl_take isl_pw_aff *pwaff2);
2855 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2856 __isl_give isl_pw_aff *isl_pw_aff_neg(
2857 __isl_take isl_pw_aff *pwaff);
2858 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2859 __isl_give isl_pw_aff *isl_pw_aff_ceil(
2860 __isl_take isl_pw_aff *pwaff);
2861 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
2862 __isl_give isl_pw_aff *isl_pw_aff_floor(
2863 __isl_take isl_pw_aff *pwaff);
2864 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
2866 __isl_give isl_pw_aff *isl_pw_aff_mod(
2867 __isl_take isl_pw_aff *pwaff, isl_int mod);
2868 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2870 __isl_give isl_pw_aff *isl_pw_aff_scale(
2871 __isl_take isl_pw_aff *pwaff, isl_int f);
2872 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2874 __isl_give isl_aff *isl_aff_scale_down_ui(
2875 __isl_take isl_aff *aff, unsigned f);
2876 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
2877 __isl_take isl_pw_aff *pwaff, isl_int f);
2879 __isl_give isl_pw_aff *isl_pw_aff_list_min(
2880 __isl_take isl_pw_aff_list *list);
2881 __isl_give isl_pw_aff *isl_pw_aff_list_max(
2882 __isl_take isl_pw_aff_list *list);
2884 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
2885 __isl_take isl_pw_aff *pwqp);
2887 __isl_give isl_pw_aff *isl_pw_aff_align_params(
2888 __isl_take isl_pw_aff *pwaff,
2889 __isl_take isl_space *model);
2891 __isl_give isl_aff *isl_aff_gist_params(
2892 __isl_take isl_aff *aff,
2893 __isl_take isl_set *context);
2894 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
2895 __isl_take isl_set *context);
2896 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
2897 __isl_take isl_pw_aff *pwaff,
2898 __isl_take isl_set *context);
2899 __isl_give isl_pw_aff *isl_pw_aff_gist(
2900 __isl_take isl_pw_aff *pwaff,
2901 __isl_take isl_set *context);
2903 __isl_give isl_set *isl_pw_aff_domain(
2904 __isl_take isl_pw_aff *pwaff);
2905 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
2906 __isl_take isl_pw_aff *pa,
2907 __isl_take isl_set *set);
2908 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
2909 __isl_take isl_pw_aff *pa,
2910 __isl_take isl_set *set);
2912 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
2913 __isl_take isl_aff *aff2);
2914 __isl_give isl_pw_aff *isl_pw_aff_mul(
2915 __isl_take isl_pw_aff *pwaff1,
2916 __isl_take isl_pw_aff *pwaff2);
2918 When multiplying two affine expressions, at least one of the two needs
2921 #include <isl/aff.h>
2922 __isl_give isl_basic_set *isl_aff_le_basic_set(
2923 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2924 __isl_give isl_basic_set *isl_aff_ge_basic_set(
2925 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2926 __isl_give isl_set *isl_pw_aff_eq_set(
2927 __isl_take isl_pw_aff *pwaff1,
2928 __isl_take isl_pw_aff *pwaff2);
2929 __isl_give isl_set *isl_pw_aff_ne_set(
2930 __isl_take isl_pw_aff *pwaff1,
2931 __isl_take isl_pw_aff *pwaff2);
2932 __isl_give isl_set *isl_pw_aff_le_set(
2933 __isl_take isl_pw_aff *pwaff1,
2934 __isl_take isl_pw_aff *pwaff2);
2935 __isl_give isl_set *isl_pw_aff_lt_set(
2936 __isl_take isl_pw_aff *pwaff1,
2937 __isl_take isl_pw_aff *pwaff2);
2938 __isl_give isl_set *isl_pw_aff_ge_set(
2939 __isl_take isl_pw_aff *pwaff1,
2940 __isl_take isl_pw_aff *pwaff2);
2941 __isl_give isl_set *isl_pw_aff_gt_set(
2942 __isl_take isl_pw_aff *pwaff1,
2943 __isl_take isl_pw_aff *pwaff2);
2945 __isl_give isl_set *isl_pw_aff_list_eq_set(
2946 __isl_take isl_pw_aff_list *list1,
2947 __isl_take isl_pw_aff_list *list2);
2948 __isl_give isl_set *isl_pw_aff_list_ne_set(
2949 __isl_take isl_pw_aff_list *list1,
2950 __isl_take isl_pw_aff_list *list2);
2951 __isl_give isl_set *isl_pw_aff_list_le_set(
2952 __isl_take isl_pw_aff_list *list1,
2953 __isl_take isl_pw_aff_list *list2);
2954 __isl_give isl_set *isl_pw_aff_list_lt_set(
2955 __isl_take isl_pw_aff_list *list1,
2956 __isl_take isl_pw_aff_list *list2);
2957 __isl_give isl_set *isl_pw_aff_list_ge_set(
2958 __isl_take isl_pw_aff_list *list1,
2959 __isl_take isl_pw_aff_list *list2);
2960 __isl_give isl_set *isl_pw_aff_list_gt_set(
2961 __isl_take isl_pw_aff_list *list1,
2962 __isl_take isl_pw_aff_list *list2);
2964 The function C<isl_aff_ge_basic_set> returns a basic set
2965 containing those elements in the shared space
2966 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
2967 The function C<isl_aff_ge_set> returns a set
2968 containing those elements in the shared domain
2969 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
2970 The functions operating on C<isl_pw_aff_list> apply the corresponding
2971 C<isl_pw_aff> function to each pair of elements in the two lists.
2973 #include <isl/aff.h>
2974 __isl_give isl_set *isl_pw_aff_nonneg_set(
2975 __isl_take isl_pw_aff *pwaff);
2976 __isl_give isl_set *isl_pw_aff_zero_set(
2977 __isl_take isl_pw_aff *pwaff);
2978 __isl_give isl_set *isl_pw_aff_non_zero_set(
2979 __isl_take isl_pw_aff *pwaff);
2981 The function C<isl_pw_aff_nonneg_set> returns a set
2982 containing those elements in the domain
2983 of C<pwaff> where C<pwaff> is non-negative.
2985 #include <isl/aff.h>
2986 __isl_give isl_pw_aff *isl_pw_aff_cond(
2987 __isl_take isl_set *cond,
2988 __isl_take isl_pw_aff *pwaff_true,
2989 __isl_take isl_pw_aff *pwaff_false);
2991 The function C<isl_pw_aff_cond> performs a conditional operator
2992 and returns an expression that is equal to C<pwaff_true>
2993 for elements in C<cond> and equal to C<pwaff_false> for elements
2996 #include <isl/aff.h>
2997 __isl_give isl_pw_aff *isl_pw_aff_union_min(
2998 __isl_take isl_pw_aff *pwaff1,
2999 __isl_take isl_pw_aff *pwaff2);
3000 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3001 __isl_take isl_pw_aff *pwaff1,
3002 __isl_take isl_pw_aff *pwaff2);
3003 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3004 __isl_take isl_pw_aff *pwaff1,
3005 __isl_take isl_pw_aff *pwaff2);
3007 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3008 expression with a domain that is the union of those of C<pwaff1> and
3009 C<pwaff2> and such that on each cell, the quasi-affine expression is
3010 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3011 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3012 associated expression is the defined one.
3014 An expression can be read from input using
3016 #include <isl/aff.h>
3017 __isl_give isl_aff *isl_aff_read_from_str(
3018 isl_ctx *ctx, const char *str);
3019 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3020 isl_ctx *ctx, const char *str);
3022 An expression can be printed using
3024 #include <isl/aff.h>
3025 __isl_give isl_printer *isl_printer_print_aff(
3026 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3028 __isl_give isl_printer *isl_printer_print_pw_aff(
3029 __isl_take isl_printer *p,
3030 __isl_keep isl_pw_aff *pwaff);
3032 =head2 Piecewise Multiple Quasi Affine Expressions
3034 An C<isl_multi_aff> object represents a sequence of
3035 zero or more affine expressions, all defined on the same domain space.
3037 An C<isl_multi_aff> can be constructed from a C<isl_aff_list> using the
3040 #include <isl/aff.h>
3041 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3042 __isl_take isl_space *space,
3043 __isl_take isl_aff_list *list);
3045 An empty piecewise multiple quasi affine expression (one with no cells) or
3046 a piecewise multiple quasi affine expression with a single cell can
3047 be created using the following functions.
3049 #include <isl/aff.h>
3050 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3051 __isl_take isl_space *space);
3052 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3053 __isl_take isl_set *set,
3054 __isl_take isl_multi_aff *maff);
3056 A piecewise multiple quasi affine expression can also be initialized
3057 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3058 and the C<isl_map> is single-valued.
3060 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3061 __isl_take isl_set *set);
3062 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3063 __isl_take isl_map *map);
3065 Multiple quasi affine expressions can be copied and freed using
3067 #include <isl/aff.h>
3068 __isl_give isl_multi_aff *isl_multi_aff_copy(
3069 __isl_keep isl_multi_aff *maff);
3070 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
3072 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3073 __isl_keep isl_pw_multi_aff *pma);
3074 void *isl_pw_multi_aff_free(
3075 __isl_take isl_pw_multi_aff *pma);
3077 The expression can be inspected using
3079 #include <isl/aff.h>
3080 isl_ctx *isl_multi_aff_get_ctx(
3081 __isl_keep isl_multi_aff *maff);
3082 isl_ctx *isl_pw_multi_aff_get_ctx(
3083 __isl_keep isl_pw_multi_aff *pma);
3084 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
3085 enum isl_dim_type type);
3086 unsigned isl_pw_multi_aff_dim(
3087 __isl_keep isl_pw_multi_aff *pma,
3088 enum isl_dim_type type);
3089 __isl_give isl_aff *isl_multi_aff_get_aff(
3090 __isl_keep isl_multi_aff *multi, int pos);
3091 const char *isl_pw_multi_aff_get_dim_name(
3092 __isl_keep isl_pw_multi_aff *pma,
3093 enum isl_dim_type type, unsigned pos);
3094 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
3095 __isl_keep isl_pw_multi_aff *pma,
3096 enum isl_dim_type type, unsigned pos);
3097 const char *isl_multi_aff_get_tuple_name(
3098 __isl_keep isl_multi_aff *multi,
3099 enum isl_dim_type type);
3100 const char *isl_pw_multi_aff_get_tuple_name(
3101 __isl_keep isl_pw_multi_aff *pma,
3102 enum isl_dim_type type);
3103 int isl_pw_multi_aff_has_tuple_id(
3104 __isl_keep isl_pw_multi_aff *pma,
3105 enum isl_dim_type type);
3106 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
3107 __isl_keep isl_pw_multi_aff *pma,
3108 enum isl_dim_type type);
3110 int isl_pw_multi_aff_foreach_piece(
3111 __isl_keep isl_pw_multi_aff *pma,
3112 int (*fn)(__isl_take isl_set *set,
3113 __isl_take isl_multi_aff *maff,
3114 void *user), void *user);
3116 It can be modified using
3118 #include <isl/aff.h>
3119 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
3120 __isl_take isl_multi_aff *maff,
3121 enum isl_dim_type type, unsigned pos, const char *s);
3122 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
3123 __isl_take isl_pw_multi_aff *pma,
3124 enum isl_dim_type type, __isl_take isl_id *id);
3126 To check whether two multiple affine expressions are
3127 obviously equal to each other, use
3129 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
3130 __isl_keep isl_multi_aff *maff2);
3131 int isl_pw_multi_aff_plain_is_equal(
3132 __isl_keep isl_pw_multi_aff *pma1,
3133 __isl_keep isl_pw_multi_aff *pma2);
3137 #include <isl/aff.h>
3138 __isl_give isl_multi_aff *isl_multi_aff_add(
3139 __isl_take isl_multi_aff *maff1,
3140 __isl_take isl_multi_aff *maff2);
3141 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
3142 __isl_take isl_pw_multi_aff *pma1,
3143 __isl_take isl_pw_multi_aff *pma2);
3144 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
3145 __isl_take isl_pw_multi_aff *pma1,
3146 __isl_take isl_pw_multi_aff *pma2);
3147 __isl_give isl_multi_aff *isl_multi_aff_scale(
3148 __isl_take isl_multi_aff *maff,
3150 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
3151 __isl_take isl_pw_multi_aff *pma,
3152 __isl_take isl_set *set);
3153 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
3154 __isl_take isl_pw_multi_aff *pma,
3155 __isl_take isl_set *set);
3156 __isl_give isl_multi_aff *isl_multi_aff_lift(
3157 __isl_take isl_multi_aff *maff,
3158 __isl_give isl_local_space **ls);
3159 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
3160 __isl_take isl_multi_aff *maff,
3161 __isl_take isl_set *context);
3162 __isl_give isl_multi_aff *isl_multi_aff_gist(
3163 __isl_take isl_multi_aff *maff,
3164 __isl_take isl_set *context);
3165 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
3166 __isl_take isl_pw_multi_aff *pma,
3167 __isl_take isl_set *set);
3168 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
3169 __isl_take isl_pw_multi_aff *pma,
3170 __isl_take isl_set *set);
3172 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
3173 then it is assigned the local space that lies at the basis of
3174 the lifting applied.
3176 An expression can be read from input using
3178 #include <isl/aff.h>
3179 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3180 isl_ctx *ctx, const char *str);
3181 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3182 isl_ctx *ctx, const char *str);
3184 An expression can be printed using
3186 #include <isl/aff.h>
3187 __isl_give isl_printer *isl_printer_print_multi_aff(
3188 __isl_take isl_printer *p,
3189 __isl_keep isl_multi_aff *maff);
3190 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3191 __isl_take isl_printer *p,
3192 __isl_keep isl_pw_multi_aff *pma);
3196 Points are elements of a set. They can be used to construct
3197 simple sets (boxes) or they can be used to represent the
3198 individual elements of a set.
3199 The zero point (the origin) can be created using
3201 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
3203 The coordinates of a point can be inspected, set and changed
3206 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
3207 enum isl_dim_type type, int pos, isl_int *v);
3208 __isl_give isl_point *isl_point_set_coordinate(
3209 __isl_take isl_point *pnt,
3210 enum isl_dim_type type, int pos, isl_int v);
3212 __isl_give isl_point *isl_point_add_ui(
3213 __isl_take isl_point *pnt,
3214 enum isl_dim_type type, int pos, unsigned val);
3215 __isl_give isl_point *isl_point_sub_ui(
3216 __isl_take isl_point *pnt,
3217 enum isl_dim_type type, int pos, unsigned val);
3219 Other properties can be obtained using
3221 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
3223 Points can be copied or freed using
3225 __isl_give isl_point *isl_point_copy(
3226 __isl_keep isl_point *pnt);
3227 void isl_point_free(__isl_take isl_point *pnt);
3229 A singleton set can be created from a point using
3231 __isl_give isl_basic_set *isl_basic_set_from_point(
3232 __isl_take isl_point *pnt);
3233 __isl_give isl_set *isl_set_from_point(
3234 __isl_take isl_point *pnt);
3236 and a box can be created from two opposite extremal points using
3238 __isl_give isl_basic_set *isl_basic_set_box_from_points(
3239 __isl_take isl_point *pnt1,
3240 __isl_take isl_point *pnt2);
3241 __isl_give isl_set *isl_set_box_from_points(
3242 __isl_take isl_point *pnt1,
3243 __isl_take isl_point *pnt2);
3245 All elements of a B<bounded> (union) set can be enumerated using
3246 the following functions.
3248 int isl_set_foreach_point(__isl_keep isl_set *set,
3249 int (*fn)(__isl_take isl_point *pnt, void *user),
3251 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
3252 int (*fn)(__isl_take isl_point *pnt, void *user),
3255 The function C<fn> is called for each integer point in
3256 C<set> with as second argument the last argument of
3257 the C<isl_set_foreach_point> call. The function C<fn>
3258 should return C<0> on success and C<-1> on failure.
3259 In the latter case, C<isl_set_foreach_point> will stop
3260 enumerating and return C<-1> as well.
3261 If the enumeration is performed successfully and to completion,
3262 then C<isl_set_foreach_point> returns C<0>.
3264 To obtain a single point of a (basic) set, use
3266 __isl_give isl_point *isl_basic_set_sample_point(
3267 __isl_take isl_basic_set *bset);
3268 __isl_give isl_point *isl_set_sample_point(
3269 __isl_take isl_set *set);
3271 If C<set> does not contain any (integer) points, then the
3272 resulting point will be ``void'', a property that can be
3275 int isl_point_is_void(__isl_keep isl_point *pnt);
3277 =head2 Piecewise Quasipolynomials
3279 A piecewise quasipolynomial is a particular kind of function that maps
3280 a parametric point to a rational value.
3281 More specifically, a quasipolynomial is a polynomial expression in greatest
3282 integer parts of affine expressions of parameters and variables.
3283 A piecewise quasipolynomial is a subdivision of a given parametric
3284 domain into disjoint cells with a quasipolynomial associated to
3285 each cell. The value of the piecewise quasipolynomial at a given
3286 point is the value of the quasipolynomial associated to the cell
3287 that contains the point. Outside of the union of cells,
3288 the value is assumed to be zero.
3289 For example, the piecewise quasipolynomial
3291 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3293 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
3294 A given piecewise quasipolynomial has a fixed domain dimension.
3295 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
3296 defined over different domains.
3297 Piecewise quasipolynomials are mainly used by the C<barvinok>
3298 library for representing the number of elements in a parametric set or map.
3299 For example, the piecewise quasipolynomial above represents
3300 the number of points in the map
3302 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3304 =head3 Input and Output
3306 Piecewise quasipolynomials can be read from input using
3308 __isl_give isl_union_pw_qpolynomial *
3309 isl_union_pw_qpolynomial_read_from_str(
3310 isl_ctx *ctx, const char *str);
3312 Quasipolynomials and piecewise quasipolynomials can be printed
3313 using the following functions.
3315 __isl_give isl_printer *isl_printer_print_qpolynomial(
3316 __isl_take isl_printer *p,
3317 __isl_keep isl_qpolynomial *qp);
3319 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3320 __isl_take isl_printer *p,
3321 __isl_keep isl_pw_qpolynomial *pwqp);
3323 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3324 __isl_take isl_printer *p,
3325 __isl_keep isl_union_pw_qpolynomial *upwqp);
3327 The output format of the printer
3328 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3329 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
3331 In case of printing in C<ISL_FORMAT_C>, the user may want
3332 to set the names of all dimensions
3334 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
3335 __isl_take isl_qpolynomial *qp,
3336 enum isl_dim_type type, unsigned pos,
3338 __isl_give isl_pw_qpolynomial *
3339 isl_pw_qpolynomial_set_dim_name(
3340 __isl_take isl_pw_qpolynomial *pwqp,
3341 enum isl_dim_type type, unsigned pos,
3344 =head3 Creating New (Piecewise) Quasipolynomials
3346 Some simple quasipolynomials can be created using the following functions.
3347 More complicated quasipolynomials can be created by applying
3348 operations such as addition and multiplication
3349 on the resulting quasipolynomials
3351 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3352 __isl_take isl_space *domain);
3353 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3354 __isl_take isl_space *domain);
3355 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3356 __isl_take isl_space *domain);
3357 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3358 __isl_take isl_space *domain);
3359 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3360 __isl_take isl_space *domain);
3361 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
3362 __isl_take isl_space *domain,
3363 const isl_int n, const isl_int d);
3364 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3365 __isl_take isl_space *domain,
3366 enum isl_dim_type type, unsigned pos);
3367 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3368 __isl_take isl_aff *aff);
3370 Note that the space in which a quasipolynomial lives is a map space
3371 with a one-dimensional range. The C<domain> argument in some of
3372 the functions above corresponds to the domain of this map space.
3374 The zero piecewise quasipolynomial or a piecewise quasipolynomial
3375 with a single cell can be created using the following functions.
3376 Multiple of these single cell piecewise quasipolynomials can
3377 be combined to create more complicated piecewise quasipolynomials.
3379 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3380 __isl_take isl_space *space);
3381 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3382 __isl_take isl_set *set,
3383 __isl_take isl_qpolynomial *qp);
3384 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3385 __isl_take isl_qpolynomial *qp);
3386 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3387 __isl_take isl_pw_aff *pwaff);
3389 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3390 __isl_take isl_space *space);
3391 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3392 __isl_take isl_pw_qpolynomial *pwqp);
3393 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3394 __isl_take isl_union_pw_qpolynomial *upwqp,
3395 __isl_take isl_pw_qpolynomial *pwqp);
3397 Quasipolynomials can be copied and freed again using the following
3400 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3401 __isl_keep isl_qpolynomial *qp);
3402 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3404 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3405 __isl_keep isl_pw_qpolynomial *pwqp);
3406 void *isl_pw_qpolynomial_free(
3407 __isl_take isl_pw_qpolynomial *pwqp);
3409 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3410 __isl_keep isl_union_pw_qpolynomial *upwqp);
3411 void isl_union_pw_qpolynomial_free(
3412 __isl_take isl_union_pw_qpolynomial *upwqp);
3414 =head3 Inspecting (Piecewise) Quasipolynomials
3416 To iterate over all piecewise quasipolynomials in a union
3417 piecewise quasipolynomial, use the following function
3419 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3420 __isl_keep isl_union_pw_qpolynomial *upwqp,
3421 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3424 To extract the piecewise quasipolynomial in a given space from a union, use
3426 __isl_give isl_pw_qpolynomial *
3427 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3428 __isl_keep isl_union_pw_qpolynomial *upwqp,
3429 __isl_take isl_space *space);
3431 To iterate over the cells in a piecewise quasipolynomial,
3432 use either of the following two functions
3434 int isl_pw_qpolynomial_foreach_piece(
3435 __isl_keep isl_pw_qpolynomial *pwqp,
3436 int (*fn)(__isl_take isl_set *set,
3437 __isl_take isl_qpolynomial *qp,
3438 void *user), void *user);
3439 int isl_pw_qpolynomial_foreach_lifted_piece(
3440 __isl_keep isl_pw_qpolynomial *pwqp,
3441 int (*fn)(__isl_take isl_set *set,
3442 __isl_take isl_qpolynomial *qp,
3443 void *user), void *user);
3445 As usual, the function C<fn> should return C<0> on success
3446 and C<-1> on failure. The difference between
3447 C<isl_pw_qpolynomial_foreach_piece> and
3448 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3449 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3450 compute unique representations for all existentially quantified
3451 variables and then turn these existentially quantified variables
3452 into extra set variables, adapting the associated quasipolynomial
3453 accordingly. This means that the C<set> passed to C<fn>
3454 will not have any existentially quantified variables, but that
3455 the dimensions of the sets may be different for different
3456 invocations of C<fn>.
3458 To iterate over all terms in a quasipolynomial,
3461 int isl_qpolynomial_foreach_term(
3462 __isl_keep isl_qpolynomial *qp,
3463 int (*fn)(__isl_take isl_term *term,
3464 void *user), void *user);
3466 The terms themselves can be inspected and freed using
3469 unsigned isl_term_dim(__isl_keep isl_term *term,
3470 enum isl_dim_type type);
3471 void isl_term_get_num(__isl_keep isl_term *term,
3473 void isl_term_get_den(__isl_keep isl_term *term,
3475 int isl_term_get_exp(__isl_keep isl_term *term,
3476 enum isl_dim_type type, unsigned pos);
3477 __isl_give isl_aff *isl_term_get_div(
3478 __isl_keep isl_term *term, unsigned pos);
3479 void isl_term_free(__isl_take isl_term *term);
3481 Each term is a product of parameters, set variables and
3482 integer divisions. The function C<isl_term_get_exp>
3483 returns the exponent of a given dimensions in the given term.
3484 The C<isl_int>s in the arguments of C<isl_term_get_num>
3485 and C<isl_term_get_den> need to have been initialized
3486 using C<isl_int_init> before calling these functions.
3488 =head3 Properties of (Piecewise) Quasipolynomials
3490 To check whether a quasipolynomial is actually a constant,
3491 use the following function.
3493 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3494 isl_int *n, isl_int *d);
3496 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3497 then the numerator and denominator of the constant
3498 are returned in C<*n> and C<*d>, respectively.
3500 To check whether two union piecewise quasipolynomials are
3501 obviously equal, use
3503 int isl_union_pw_qpolynomial_plain_is_equal(
3504 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3505 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3507 =head3 Operations on (Piecewise) Quasipolynomials
3509 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3510 __isl_take isl_qpolynomial *qp, isl_int v);
3511 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3512 __isl_take isl_qpolynomial *qp);
3513 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3514 __isl_take isl_qpolynomial *qp1,
3515 __isl_take isl_qpolynomial *qp2);
3516 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3517 __isl_take isl_qpolynomial *qp1,
3518 __isl_take isl_qpolynomial *qp2);
3519 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3520 __isl_take isl_qpolynomial *qp1,
3521 __isl_take isl_qpolynomial *qp2);
3522 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3523 __isl_take isl_qpolynomial *qp, unsigned exponent);
3525 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3526 __isl_take isl_pw_qpolynomial *pwqp1,
3527 __isl_take isl_pw_qpolynomial *pwqp2);
3528 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3529 __isl_take isl_pw_qpolynomial *pwqp1,
3530 __isl_take isl_pw_qpolynomial *pwqp2);
3531 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3532 __isl_take isl_pw_qpolynomial *pwqp1,
3533 __isl_take isl_pw_qpolynomial *pwqp2);
3534 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3535 __isl_take isl_pw_qpolynomial *pwqp);
3536 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3537 __isl_take isl_pw_qpolynomial *pwqp1,
3538 __isl_take isl_pw_qpolynomial *pwqp2);
3539 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3540 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3542 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3543 __isl_take isl_union_pw_qpolynomial *upwqp1,
3544 __isl_take isl_union_pw_qpolynomial *upwqp2);
3545 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3546 __isl_take isl_union_pw_qpolynomial *upwqp1,
3547 __isl_take isl_union_pw_qpolynomial *upwqp2);
3548 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3549 __isl_take isl_union_pw_qpolynomial *upwqp1,
3550 __isl_take isl_union_pw_qpolynomial *upwqp2);
3552 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
3553 __isl_take isl_pw_qpolynomial *pwqp,
3554 __isl_take isl_point *pnt);
3556 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
3557 __isl_take isl_union_pw_qpolynomial *upwqp,
3558 __isl_take isl_point *pnt);
3560 __isl_give isl_set *isl_pw_qpolynomial_domain(
3561 __isl_take isl_pw_qpolynomial *pwqp);
3562 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
3563 __isl_take isl_pw_qpolynomial *pwpq,
3564 __isl_take isl_set *set);
3565 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
3566 __isl_take isl_pw_qpolynomial *pwpq,
3567 __isl_take isl_set *set);
3569 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3570 __isl_take isl_union_pw_qpolynomial *upwqp);
3571 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
3572 __isl_take isl_union_pw_qpolynomial *upwpq,
3573 __isl_take isl_union_set *uset);
3574 __isl_give isl_union_pw_qpolynomial *
3575 isl_union_pw_qpolynomial_intersect_params(
3576 __isl_take isl_union_pw_qpolynomial *upwpq,
3577 __isl_take isl_set *set);
3579 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3580 __isl_take isl_qpolynomial *qp,
3581 __isl_take isl_space *model);
3583 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
3584 __isl_take isl_qpolynomial *qp);
3585 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
3586 __isl_take isl_pw_qpolynomial *pwqp);
3588 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
3589 __isl_take isl_union_pw_qpolynomial *upwqp);
3591 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
3592 __isl_take isl_qpolynomial *qp,
3593 __isl_take isl_set *context);
3594 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
3595 __isl_take isl_qpolynomial *qp,
3596 __isl_take isl_set *context);
3598 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
3599 __isl_take isl_pw_qpolynomial *pwqp,
3600 __isl_take isl_set *context);
3601 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
3602 __isl_take isl_pw_qpolynomial *pwqp,
3603 __isl_take isl_set *context);
3605 __isl_give isl_union_pw_qpolynomial *
3606 isl_union_pw_qpolynomial_gist_params(
3607 __isl_take isl_union_pw_qpolynomial *upwqp,
3608 __isl_take isl_set *context);
3609 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
3610 __isl_take isl_union_pw_qpolynomial *upwqp,
3611 __isl_take isl_union_set *context);
3613 The gist operation applies the gist operation to each of
3614 the cells in the domain of the input piecewise quasipolynomial.
3615 The context is also exploited
3616 to simplify the quasipolynomials associated to each cell.
3618 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
3619 __isl_take isl_pw_qpolynomial *pwqp, int sign);
3620 __isl_give isl_union_pw_qpolynomial *
3621 isl_union_pw_qpolynomial_to_polynomial(
3622 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
3624 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
3625 the polynomial will be an overapproximation. If C<sign> is negative,
3626 it will be an underapproximation. If C<sign> is zero, the approximation
3627 will lie somewhere in between.
3629 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
3631 A piecewise quasipolynomial reduction is a piecewise
3632 reduction (or fold) of quasipolynomials.
3633 In particular, the reduction can be maximum or a minimum.
3634 The objects are mainly used to represent the result of
3635 an upper or lower bound on a quasipolynomial over its domain,
3636 i.e., as the result of the following function.
3638 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
3639 __isl_take isl_pw_qpolynomial *pwqp,
3640 enum isl_fold type, int *tight);
3642 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
3643 __isl_take isl_union_pw_qpolynomial *upwqp,
3644 enum isl_fold type, int *tight);
3646 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
3647 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
3648 is the returned bound is known be tight, i.e., for each value
3649 of the parameters there is at least
3650 one element in the domain that reaches the bound.
3651 If the domain of C<pwqp> is not wrapping, then the bound is computed
3652 over all elements in that domain and the result has a purely parametric
3653 domain. If the domain of C<pwqp> is wrapping, then the bound is
3654 computed over the range of the wrapped relation. The domain of the
3655 wrapped relation becomes the domain of the result.
3657 A (piecewise) quasipolynomial reduction can be copied or freed using the
3658 following functions.
3660 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
3661 __isl_keep isl_qpolynomial_fold *fold);
3662 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
3663 __isl_keep isl_pw_qpolynomial_fold *pwf);
3664 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
3665 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3666 void isl_qpolynomial_fold_free(
3667 __isl_take isl_qpolynomial_fold *fold);
3668 void *isl_pw_qpolynomial_fold_free(
3669 __isl_take isl_pw_qpolynomial_fold *pwf);
3670 void isl_union_pw_qpolynomial_fold_free(
3671 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3673 =head3 Printing Piecewise Quasipolynomial Reductions
3675 Piecewise quasipolynomial reductions can be printed
3676 using the following function.
3678 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
3679 __isl_take isl_printer *p,
3680 __isl_keep isl_pw_qpolynomial_fold *pwf);
3681 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
3682 __isl_take isl_printer *p,
3683 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3685 For C<isl_printer_print_pw_qpolynomial_fold>,
3686 output format of the printer
3687 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3688 For C<isl_printer_print_union_pw_qpolynomial_fold>,
3689 output format of the printer
3690 needs to be set to C<ISL_FORMAT_ISL>.
3691 In case of printing in C<ISL_FORMAT_C>, the user may want
3692 to set the names of all dimensions
3694 __isl_give isl_pw_qpolynomial_fold *
3695 isl_pw_qpolynomial_fold_set_dim_name(
3696 __isl_take isl_pw_qpolynomial_fold *pwf,
3697 enum isl_dim_type type, unsigned pos,
3700 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
3702 To iterate over all piecewise quasipolynomial reductions in a union
3703 piecewise quasipolynomial reduction, use the following function
3705 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3706 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3707 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3708 void *user), void *user);
3710 To iterate over the cells in a piecewise quasipolynomial reduction,
3711 use either of the following two functions
3713 int isl_pw_qpolynomial_fold_foreach_piece(
3714 __isl_keep isl_pw_qpolynomial_fold *pwf,
3715 int (*fn)(__isl_take isl_set *set,
3716 __isl_take isl_qpolynomial_fold *fold,
3717 void *user), void *user);
3718 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
3719 __isl_keep isl_pw_qpolynomial_fold *pwf,
3720 int (*fn)(__isl_take isl_set *set,
3721 __isl_take isl_qpolynomial_fold *fold,
3722 void *user), void *user);
3724 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
3725 of the difference between these two functions.
3727 To iterate over all quasipolynomials in a reduction, use
3729 int isl_qpolynomial_fold_foreach_qpolynomial(
3730 __isl_keep isl_qpolynomial_fold *fold,
3731 int (*fn)(__isl_take isl_qpolynomial *qp,
3732 void *user), void *user);
3734 =head3 Properties of Piecewise Quasipolynomial Reductions
3736 To check whether two union piecewise quasipolynomial reductions are
3737 obviously equal, use
3739 int isl_union_pw_qpolynomial_fold_plain_is_equal(
3740 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
3741 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
3743 =head3 Operations on Piecewise Quasipolynomial Reductions
3745 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
3746 __isl_take isl_qpolynomial_fold *fold, isl_int v);
3748 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
3749 __isl_take isl_pw_qpolynomial_fold *pwf1,
3750 __isl_take isl_pw_qpolynomial_fold *pwf2);
3752 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
3753 __isl_take isl_pw_qpolynomial_fold *pwf1,
3754 __isl_take isl_pw_qpolynomial_fold *pwf2);
3756 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
3757 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
3758 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
3760 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
3761 __isl_take isl_pw_qpolynomial_fold *pwf,
3762 __isl_take isl_point *pnt);
3764 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
3765 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3766 __isl_take isl_point *pnt);
3768 __isl_give isl_pw_qpolynomial_fold *
3769 sl_pw_qpolynomial_fold_intersect_params(
3770 __isl_take isl_pw_qpolynomial_fold *pwf,
3771 __isl_take isl_set *set);
3773 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
3774 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3775 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
3776 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3777 __isl_take isl_union_set *uset);
3778 __isl_give isl_union_pw_qpolynomial_fold *
3779 isl_union_pw_qpolynomial_fold_intersect_params(
3780 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3781 __isl_take isl_set *set);
3783 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
3784 __isl_take isl_pw_qpolynomial_fold *pwf);
3786 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
3787 __isl_take isl_pw_qpolynomial_fold *pwf);
3789 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
3790 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3792 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
3793 __isl_take isl_qpolynomial_fold *fold,
3794 __isl_take isl_set *context);
3795 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
3796 __isl_take isl_qpolynomial_fold *fold,
3797 __isl_take isl_set *context);
3799 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
3800 __isl_take isl_pw_qpolynomial_fold *pwf,
3801 __isl_take isl_set *context);
3802 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
3803 __isl_take isl_pw_qpolynomial_fold *pwf,
3804 __isl_take isl_set *context);
3806 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
3807 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3808 __isl_take isl_union_set *context);
3809 __isl_give isl_union_pw_qpolynomial_fold *
3810 isl_union_pw_qpolynomial_fold_gist_params(
3811 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3812 __isl_take isl_set *context);
3814 The gist operation applies the gist operation to each of
3815 the cells in the domain of the input piecewise quasipolynomial reduction.
3816 In future, the operation will also exploit the context
3817 to simplify the quasipolynomial reductions associated to each cell.
3819 __isl_give isl_pw_qpolynomial_fold *
3820 isl_set_apply_pw_qpolynomial_fold(
3821 __isl_take isl_set *set,
3822 __isl_take isl_pw_qpolynomial_fold *pwf,
3824 __isl_give isl_pw_qpolynomial_fold *
3825 isl_map_apply_pw_qpolynomial_fold(
3826 __isl_take isl_map *map,
3827 __isl_take isl_pw_qpolynomial_fold *pwf,
3829 __isl_give isl_union_pw_qpolynomial_fold *
3830 isl_union_set_apply_union_pw_qpolynomial_fold(
3831 __isl_take isl_union_set *uset,
3832 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3834 __isl_give isl_union_pw_qpolynomial_fold *
3835 isl_union_map_apply_union_pw_qpolynomial_fold(
3836 __isl_take isl_union_map *umap,
3837 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3840 The functions taking a map
3841 compose the given map with the given piecewise quasipolynomial reduction.
3842 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
3843 over all elements in the intersection of the range of the map
3844 and the domain of the piecewise quasipolynomial reduction
3845 as a function of an element in the domain of the map.
3846 The functions taking a set compute a bound over all elements in the
3847 intersection of the set and the domain of the
3848 piecewise quasipolynomial reduction.
3850 =head2 Dependence Analysis
3852 C<isl> contains specialized functionality for performing
3853 array dataflow analysis. That is, given a I<sink> access relation
3854 and a collection of possible I<source> access relations,
3855 C<isl> can compute relations that describe
3856 for each iteration of the sink access, which iteration
3857 of which of the source access relations was the last
3858 to access the same data element before the given iteration
3860 The resulting dependence relations map source iterations
3861 to the corresponding sink iterations.
3862 To compute standard flow dependences, the sink should be
3863 a read, while the sources should be writes.
3864 If any of the source accesses are marked as being I<may>
3865 accesses, then there will be a dependence from the last
3866 I<must> access B<and> from any I<may> access that follows
3867 this last I<must> access.
3868 In particular, if I<all> sources are I<may> accesses,
3869 then memory based dependence analysis is performed.
3870 If, on the other hand, all sources are I<must> accesses,
3871 then value based dependence analysis is performed.
3873 #include <isl/flow.h>
3875 typedef int (*isl_access_level_before)(void *first, void *second);
3877 __isl_give isl_access_info *isl_access_info_alloc(
3878 __isl_take isl_map *sink,
3879 void *sink_user, isl_access_level_before fn,
3881 __isl_give isl_access_info *isl_access_info_add_source(
3882 __isl_take isl_access_info *acc,
3883 __isl_take isl_map *source, int must,
3885 void isl_access_info_free(__isl_take isl_access_info *acc);
3887 __isl_give isl_flow *isl_access_info_compute_flow(
3888 __isl_take isl_access_info *acc);
3890 int isl_flow_foreach(__isl_keep isl_flow *deps,
3891 int (*fn)(__isl_take isl_map *dep, int must,
3892 void *dep_user, void *user),
3894 __isl_give isl_map *isl_flow_get_no_source(
3895 __isl_keep isl_flow *deps, int must);
3896 void isl_flow_free(__isl_take isl_flow *deps);
3898 The function C<isl_access_info_compute_flow> performs the actual
3899 dependence analysis. The other functions are used to construct
3900 the input for this function or to read off the output.
3902 The input is collected in an C<isl_access_info>, which can
3903 be created through a call to C<isl_access_info_alloc>.
3904 The arguments to this functions are the sink access relation
3905 C<sink>, a token C<sink_user> used to identify the sink
3906 access to the user, a callback function for specifying the
3907 relative order of source and sink accesses, and the number
3908 of source access relations that will be added.
3909 The callback function has type C<int (*)(void *first, void *second)>.
3910 The function is called with two user supplied tokens identifying
3911 either a source or the sink and it should return the shared nesting
3912 level and the relative order of the two accesses.
3913 In particular, let I<n> be the number of loops shared by
3914 the two accesses. If C<first> precedes C<second> textually,
3915 then the function should return I<2 * n + 1>; otherwise,
3916 it should return I<2 * n>.
3917 The sources can be added to the C<isl_access_info> by performing
3918 (at most) C<max_source> calls to C<isl_access_info_add_source>.
3919 C<must> indicates whether the source is a I<must> access
3920 or a I<may> access. Note that a multi-valued access relation
3921 should only be marked I<must> if every iteration in the domain
3922 of the relation accesses I<all> elements in its image.
3923 The C<source_user> token is again used to identify
3924 the source access. The range of the source access relation
3925 C<source> should have the same dimension as the range
3926 of the sink access relation.
3927 The C<isl_access_info_free> function should usually not be
3928 called explicitly, because it is called implicitly by
3929 C<isl_access_info_compute_flow>.
3931 The result of the dependence analysis is collected in an
3932 C<isl_flow>. There may be elements of
3933 the sink access for which no preceding source access could be
3934 found or for which all preceding sources are I<may> accesses.
3935 The relations containing these elements can be obtained through
3936 calls to C<isl_flow_get_no_source>, the first with C<must> set
3937 and the second with C<must> unset.
3938 In the case of standard flow dependence analysis,
3939 with the sink a read and the sources I<must> writes,
3940 the first relation corresponds to the reads from uninitialized
3941 array elements and the second relation is empty.
3942 The actual flow dependences can be extracted using
3943 C<isl_flow_foreach>. This function will call the user-specified
3944 callback function C<fn> for each B<non-empty> dependence between
3945 a source and the sink. The callback function is called
3946 with four arguments, the actual flow dependence relation
3947 mapping source iterations to sink iterations, a boolean that
3948 indicates whether it is a I<must> or I<may> dependence, a token
3949 identifying the source and an additional C<void *> with value
3950 equal to the third argument of the C<isl_flow_foreach> call.
3951 A dependence is marked I<must> if it originates from a I<must>
3952 source and if it is not followed by any I<may> sources.
3954 After finishing with an C<isl_flow>, the user should call
3955 C<isl_flow_free> to free all associated memory.
3957 A higher-level interface to dependence analysis is provided
3958 by the following function.
3960 #include <isl/flow.h>
3962 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
3963 __isl_take isl_union_map *must_source,
3964 __isl_take isl_union_map *may_source,
3965 __isl_take isl_union_map *schedule,
3966 __isl_give isl_union_map **must_dep,
3967 __isl_give isl_union_map **may_dep,
3968 __isl_give isl_union_map **must_no_source,
3969 __isl_give isl_union_map **may_no_source);
3971 The arrays are identified by the tuple names of the ranges
3972 of the accesses. The iteration domains by the tuple names
3973 of the domains of the accesses and of the schedule.
3974 The relative order of the iteration domains is given by the
3975 schedule. The relations returned through C<must_no_source>
3976 and C<may_no_source> are subsets of C<sink>.
3977 Any of C<must_dep>, C<may_dep>, C<must_no_source>
3978 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
3979 any of the other arguments is treated as an error.
3983 B<The functionality described in this section is fairly new
3984 and may be subject to change.>
3986 The following function can be used to compute a schedule
3987 for a union of domains. The generated schedule respects
3988 all C<validity> dependences. That is, all dependence distances
3989 over these dependences in the scheduled space are lexicographically
3990 positive. The generated schedule schedule also tries to minimize
3991 the dependence distances over C<proximity> dependences.
3992 Moreover, it tries to obtain sequences (bands) of schedule dimensions
3993 for groups of domains where the dependence distances have only
3994 non-negative values.
3995 The algorithm used to construct the schedule is similar to that
3998 #include <isl/schedule.h>
3999 __isl_give isl_schedule *isl_union_set_compute_schedule(
4000 __isl_take isl_union_set *domain,
4001 __isl_take isl_union_map *validity,
4002 __isl_take isl_union_map *proximity);
4003 void *isl_schedule_free(__isl_take isl_schedule *sched);
4005 A mapping from the domains to the scheduled space can be obtained
4006 from an C<isl_schedule> using the following function.
4008 __isl_give isl_union_map *isl_schedule_get_map(
4009 __isl_keep isl_schedule *sched);
4011 A representation of the schedule can be printed using
4013 __isl_give isl_printer *isl_printer_print_schedule(
4014 __isl_take isl_printer *p,
4015 __isl_keep isl_schedule *schedule);
4017 A representation of the schedule as a forest of bands can be obtained
4018 using the following function.
4020 __isl_give isl_band_list *isl_schedule_get_band_forest(
4021 __isl_keep isl_schedule *schedule);
4023 The list can be manipulated as explained in L<"Lists">.
4024 The bands inside the list can be copied and freed using the following
4027 #include <isl/band.h>
4028 __isl_give isl_band *isl_band_copy(
4029 __isl_keep isl_band *band);
4030 void *isl_band_free(__isl_take isl_band *band);
4032 Each band contains zero or more scheduling dimensions.
4033 These are referred to as the members of the band.
4034 The section of the schedule that corresponds to the band is
4035 referred to as the partial schedule of the band.
4036 For those nodes that participate in a band, the outer scheduling
4037 dimensions form the prefix schedule, while the inner scheduling
4038 dimensions form the suffix schedule.
4039 That is, if we take a cut of the band forest, then the union of
4040 the concatenations of the prefix, partial and suffix schedules of
4041 each band in the cut is equal to the entire schedule (modulo
4042 some possible padding at the end with zero scheduling dimensions).
4043 The properties of a band can be inspected using the following functions.
4045 #include <isl/band.h>
4046 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
4048 int isl_band_has_children(__isl_keep isl_band *band);
4049 __isl_give isl_band_list *isl_band_get_children(
4050 __isl_keep isl_band *band);
4052 __isl_give isl_union_map *isl_band_get_prefix_schedule(
4053 __isl_keep isl_band *band);
4054 __isl_give isl_union_map *isl_band_get_partial_schedule(
4055 __isl_keep isl_band *band);
4056 __isl_give isl_union_map *isl_band_get_suffix_schedule(
4057 __isl_keep isl_band *band);
4059 int isl_band_n_member(__isl_keep isl_band *band);
4060 int isl_band_member_is_zero_distance(
4061 __isl_keep isl_band *band, int pos);
4063 Note that a scheduling dimension is considered to be ``zero
4064 distance'' if it does not carry any proximity dependences
4066 That is, if the dependence distances of the proximity
4067 dependences are all zero in that direction (for fixed
4068 iterations of outer bands).
4070 A representation of the band can be printed using
4072 #include <isl/band.h>
4073 __isl_give isl_printer *isl_printer_print_band(
4074 __isl_take isl_printer *p,
4075 __isl_keep isl_band *band);
4079 #include <isl/schedule.h>
4080 int isl_options_set_schedule_outer_zero_distance(
4081 isl_ctx *ctx, int val);
4082 int isl_options_get_schedule_outer_zero_distance(
4087 =item * schedule_outer_zero_distance
4089 It this option is set, then we try to construct schedules
4090 where the outermost scheduling dimension in each band
4091 results in a zero dependence distance over the proximity
4096 =head2 Parametric Vertex Enumeration
4098 The parametric vertex enumeration described in this section
4099 is mainly intended to be used internally and by the C<barvinok>
4102 #include <isl/vertices.h>
4103 __isl_give isl_vertices *isl_basic_set_compute_vertices(
4104 __isl_keep isl_basic_set *bset);
4106 The function C<isl_basic_set_compute_vertices> performs the
4107 actual computation of the parametric vertices and the chamber
4108 decomposition and store the result in an C<isl_vertices> object.
4109 This information can be queried by either iterating over all
4110 the vertices or iterating over all the chambers or cells
4111 and then iterating over all vertices that are active on the chamber.
4113 int isl_vertices_foreach_vertex(
4114 __isl_keep isl_vertices *vertices,
4115 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4118 int isl_vertices_foreach_cell(
4119 __isl_keep isl_vertices *vertices,
4120 int (*fn)(__isl_take isl_cell *cell, void *user),
4122 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
4123 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4126 Other operations that can be performed on an C<isl_vertices> object are
4129 isl_ctx *isl_vertices_get_ctx(
4130 __isl_keep isl_vertices *vertices);
4131 int isl_vertices_get_n_vertices(
4132 __isl_keep isl_vertices *vertices);
4133 void isl_vertices_free(__isl_take isl_vertices *vertices);
4135 Vertices can be inspected and destroyed using the following functions.
4137 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
4138 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
4139 __isl_give isl_basic_set *isl_vertex_get_domain(
4140 __isl_keep isl_vertex *vertex);
4141 __isl_give isl_basic_set *isl_vertex_get_expr(
4142 __isl_keep isl_vertex *vertex);
4143 void isl_vertex_free(__isl_take isl_vertex *vertex);
4145 C<isl_vertex_get_expr> returns a singleton parametric set describing
4146 the vertex, while C<isl_vertex_get_domain> returns the activity domain
4148 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
4149 B<rational> basic sets, so they should mainly be used for inspection
4150 and should not be mixed with integer sets.
4152 Chambers can be inspected and destroyed using the following functions.
4154 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
4155 __isl_give isl_basic_set *isl_cell_get_domain(
4156 __isl_keep isl_cell *cell);
4157 void isl_cell_free(__isl_take isl_cell *cell);
4161 Although C<isl> is mainly meant to be used as a library,
4162 it also contains some basic applications that use some
4163 of the functionality of C<isl>.
4164 The input may be specified in either the L<isl format>
4165 or the L<PolyLib format>.
4167 =head2 C<isl_polyhedron_sample>
4169 C<isl_polyhedron_sample> takes a polyhedron as input and prints
4170 an integer element of the polyhedron, if there is any.
4171 The first column in the output is the denominator and is always
4172 equal to 1. If the polyhedron contains no integer points,
4173 then a vector of length zero is printed.
4177 C<isl_pip> takes the same input as the C<example> program
4178 from the C<piplib> distribution, i.e., a set of constraints
4179 on the parameters, a line containing only -1 and finally a set
4180 of constraints on a parametric polyhedron.
4181 The coefficients of the parameters appear in the last columns
4182 (but before the final constant column).
4183 The output is the lexicographic minimum of the parametric polyhedron.
4184 As C<isl> currently does not have its own output format, the output
4185 is just a dump of the internal state.
4187 =head2 C<isl_polyhedron_minimize>
4189 C<isl_polyhedron_minimize> computes the minimum of some linear
4190 or affine objective function over the integer points in a polyhedron.
4191 If an affine objective function
4192 is given, then the constant should appear in the last column.
4194 =head2 C<isl_polytope_scan>
4196 Given a polytope, C<isl_polytope_scan> prints
4197 all integer points in the polytope.