3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take a B<map> space as input. An old call
72 C<isl_map_identity(space)> can be rewritten to
73 C<isl_map_identity(isl_space_map_from_set(space))>.
75 =item * The function C<isl_map_power> no longer takes
76 a parameter position as input. Instead, the exponent
77 is now expressed as the domain of the resulting relation.
81 =head3 Changes since isl-0.06
85 =item * The format of C<isl_printer_print_qpolynomial>'s
86 C<ISL_FORMAT_ISL> output has changed.
87 Use C<ISL_FORMAT_C> to obtain the old output.
89 =item * The C<*_fast_*> functions have been renamed to C<*_plain_*>.
90 Some of the old names have been kept for backward compatibility,
91 but they will be removed in the future.
95 =head3 Changes since isl-0.07
99 =item * The function C<isl_pw_aff_max> has been renamed to
100 C<isl_pw_aff_union_max>.
101 Similarly, the function C<isl_pw_aff_add> has been renamed to
102 C<isl_pw_aff_union_add>.
104 =item * The C<isl_dim> type has been renamed to C<isl_space>
105 along with the associated functions.
106 Some of the old names have been kept for backward compatibility,
107 but they will be removed in the future.
109 =item * Spaces of maps, sets and parameter domains are now
110 treated differently. The distinction between map spaces and set spaces
111 has always been made on a conceptual level, but proper use of such spaces
112 was never checked. Furthermore, up until isl-0.07 there was no way
113 of explicitly creating a parameter space. These can now be created
114 directly using C<isl_space_params_alloc> or from other spaces using
117 =item * The space in which C<isl_aff>, C<isl_pw_aff>, C<isl_qpolynomial>,
118 C<isl_pw_qpolynomial>, C<isl_qpolynomial_fold> and C<isl_pw_qpolynomial_fold>
119 objects live is now a map space
120 instead of a set space. This means, for example, that the dimensions
121 of the domain of an C<isl_aff> are now considered to be of type
122 C<isl_dim_in> instead of C<isl_dim_set>. Extra functions have been
123 added to obtain the domain space. Some of the constructors still
124 take a domain space and have therefore been renamed.
126 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
127 now take an C<isl_local_space> instead of an C<isl_space>.
128 An C<isl_local_space> can be created from an C<isl_space>
129 using C<isl_local_space_from_space>.
131 =item * The C<isl_div> type has been removed. Functions that used
132 to return an C<isl_div> now return an C<isl_aff>.
133 Note that the space of an C<isl_aff> is that of relation.
134 When replacing a call to C<isl_div_get_coefficient> by a call to
135 C<isl_aff_get_coefficient> any C<isl_dim_set> argument needs
136 to be replaced by C<isl_dim_in>.
137 A call to C<isl_aff_from_div> can be replaced by a call
139 A call to C<isl_qpolynomial_div(div)> call be replaced by
142 isl_qpolynomial_from_aff(isl_aff_floor(div))
144 The function C<isl_constraint_div> has also been renamed
145 to C<isl_constraint_get_div>.
147 =item * The C<nparam> argument has been removed from
148 C<isl_map_read_from_str> and similar functions.
149 When reading input in the original PolyLib format,
150 the result will have no parameters.
151 If parameters are expected, the caller may want to perform
152 dimension manipulation on the result.
158 The source of C<isl> can be obtained either as a tarball
159 or from the git repository. Both are available from
160 L<http://freshmeat.net/projects/isl/>.
161 The installation process depends on how you obtained
164 =head2 Installation from the git repository
168 =item 1 Clone or update the repository
170 The first time the source is obtained, you need to clone
173 git clone git://repo.or.cz/isl.git
175 To obtain updates, you need to pull in the latest changes
179 =item 2 Generate C<configure>
185 After performing the above steps, continue
186 with the L<Common installation instructions>.
188 =head2 Common installation instructions
192 =item 1 Obtain C<GMP>
194 Building C<isl> requires C<GMP>, including its headers files.
195 Your distribution may not provide these header files by default
196 and you may need to install a package called C<gmp-devel> or something
197 similar. Alternatively, C<GMP> can be built from
198 source, available from L<http://gmplib.org/>.
202 C<isl> uses the standard C<autoconf> C<configure> script.
207 optionally followed by some configure options.
208 A complete list of options can be obtained by running
212 Below we discuss some of the more common options.
214 C<isl> can optionally use C<piplib>, but no
215 C<piplib> functionality is currently used by default.
216 The C<--with-piplib> option can
217 be used to specify which C<piplib>
218 library to use, either an installed version (C<system>),
219 an externally built version (C<build>)
220 or no version (C<no>). The option C<build> is mostly useful
221 in C<configure> scripts of larger projects that bundle both C<isl>
228 Installation prefix for C<isl>
230 =item C<--with-gmp-prefix>
232 Installation prefix for C<GMP> (architecture-independent files).
234 =item C<--with-gmp-exec-prefix>
236 Installation prefix for C<GMP> (architecture-dependent files).
238 =item C<--with-piplib>
240 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
242 =item C<--with-piplib-prefix>
244 Installation prefix for C<system> C<piplib> (architecture-independent files).
246 =item C<--with-piplib-exec-prefix>
248 Installation prefix for C<system> C<piplib> (architecture-dependent files).
250 =item C<--with-piplib-builddir>
252 Location where C<build> C<piplib> was built.
260 =item 4 Install (optional)
268 =head2 Initialization
270 All manipulations of integer sets and relations occur within
271 the context of an C<isl_ctx>.
272 A given C<isl_ctx> can only be used within a single thread.
273 All arguments of a function are required to have been allocated
274 within the same context.
275 There are currently no functions available for moving an object
276 from one C<isl_ctx> to another C<isl_ctx>. This means that
277 there is currently no way of safely moving an object from one
278 thread to another, unless the whole C<isl_ctx> is moved.
280 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
281 freed using C<isl_ctx_free>.
282 All objects allocated within an C<isl_ctx> should be freed
283 before the C<isl_ctx> itself is freed.
285 isl_ctx *isl_ctx_alloc();
286 void isl_ctx_free(isl_ctx *ctx);
290 All operations on integers, mainly the coefficients
291 of the constraints describing the sets and relations,
292 are performed in exact integer arithmetic using C<GMP>.
293 However, to allow future versions of C<isl> to optionally
294 support fixed integer arithmetic, all calls to C<GMP>
295 are wrapped inside C<isl> specific macros.
296 The basic type is C<isl_int> and the operations below
297 are available on this type.
298 The meanings of these operations are essentially the same
299 as their C<GMP> C<mpz_> counterparts.
300 As always with C<GMP> types, C<isl_int>s need to be
301 initialized with C<isl_int_init> before they can be used
302 and they need to be released with C<isl_int_clear>
304 The user should not assume that an C<isl_int> is represented
305 as a C<mpz_t>, but should instead explicitly convert between
306 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
307 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
311 =item isl_int_init(i)
313 =item isl_int_clear(i)
315 =item isl_int_set(r,i)
317 =item isl_int_set_si(r,i)
319 =item isl_int_set_gmp(r,g)
321 =item isl_int_get_gmp(i,g)
323 =item isl_int_abs(r,i)
325 =item isl_int_neg(r,i)
327 =item isl_int_swap(i,j)
329 =item isl_int_swap_or_set(i,j)
331 =item isl_int_add_ui(r,i,j)
333 =item isl_int_sub_ui(r,i,j)
335 =item isl_int_add(r,i,j)
337 =item isl_int_sub(r,i,j)
339 =item isl_int_mul(r,i,j)
341 =item isl_int_mul_ui(r,i,j)
343 =item isl_int_addmul(r,i,j)
345 =item isl_int_submul(r,i,j)
347 =item isl_int_gcd(r,i,j)
349 =item isl_int_lcm(r,i,j)
351 =item isl_int_divexact(r,i,j)
353 =item isl_int_cdiv_q(r,i,j)
355 =item isl_int_fdiv_q(r,i,j)
357 =item isl_int_fdiv_r(r,i,j)
359 =item isl_int_fdiv_q_ui(r,i,j)
361 =item isl_int_read(r,s)
363 =item isl_int_print(out,i,width)
367 =item isl_int_cmp(i,j)
369 =item isl_int_cmp_si(i,si)
371 =item isl_int_eq(i,j)
373 =item isl_int_ne(i,j)
375 =item isl_int_lt(i,j)
377 =item isl_int_le(i,j)
379 =item isl_int_gt(i,j)
381 =item isl_int_ge(i,j)
383 =item isl_int_abs_eq(i,j)
385 =item isl_int_abs_ne(i,j)
387 =item isl_int_abs_lt(i,j)
389 =item isl_int_abs_gt(i,j)
391 =item isl_int_abs_ge(i,j)
393 =item isl_int_is_zero(i)
395 =item isl_int_is_one(i)
397 =item isl_int_is_negone(i)
399 =item isl_int_is_pos(i)
401 =item isl_int_is_neg(i)
403 =item isl_int_is_nonpos(i)
405 =item isl_int_is_nonneg(i)
407 =item isl_int_is_divisible_by(i,j)
411 =head2 Sets and Relations
413 C<isl> uses six types of objects for representing sets and relations,
414 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
415 C<isl_union_set> and C<isl_union_map>.
416 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
417 can be described as a conjunction of affine constraints, while
418 C<isl_set> and C<isl_map> represent unions of
419 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
420 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
421 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
422 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
423 where spaces are considered different if they have a different number
424 of dimensions and/or different names (see L<"Spaces">).
425 The difference between sets and relations (maps) is that sets have
426 one set of variables, while relations have two sets of variables,
427 input variables and output variables.
429 =head2 Memory Management
431 Since a high-level operation on sets and/or relations usually involves
432 several substeps and since the user is usually not interested in
433 the intermediate results, most functions that return a new object
434 will also release all the objects passed as arguments.
435 If the user still wants to use one or more of these arguments
436 after the function call, she should pass along a copy of the
437 object rather than the object itself.
438 The user is then responsible for making sure that the original
439 object gets used somewhere else or is explicitly freed.
441 The arguments and return values of all documented functions are
442 annotated to make clear which arguments are released and which
443 arguments are preserved. In particular, the following annotations
450 C<__isl_give> means that a new object is returned.
451 The user should make sure that the returned pointer is
452 used exactly once as a value for an C<__isl_take> argument.
453 In between, it can be used as a value for as many
454 C<__isl_keep> arguments as the user likes.
455 There is one exception, and that is the case where the
456 pointer returned is C<NULL>. Is this case, the user
457 is free to use it as an C<__isl_take> argument or not.
461 C<__isl_take> means that the object the argument points to
462 is taken over by the function and may no longer be used
463 by the user as an argument to any other function.
464 The pointer value must be one returned by a function
465 returning an C<__isl_give> pointer.
466 If the user passes in a C<NULL> value, then this will
467 be treated as an error in the sense that the function will
468 not perform its usual operation. However, it will still
469 make sure that all the other C<__isl_take> arguments
474 C<__isl_keep> means that the function will only use the object
475 temporarily. After the function has finished, the user
476 can still use it as an argument to other functions.
477 A C<NULL> value will be treated in the same way as
478 a C<NULL> value for an C<__isl_take> argument.
484 Identifiers are used to identify both individual dimensions
485 and tuples of dimensions. They consist of a name and an optional
486 pointer. Identifiers with the same name but different pointer values
487 are considered to be distinct.
488 Identifiers can be constructed, copied, freed, inspected and printed
489 using the following functions.
492 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
493 __isl_keep const char *name, void *user);
494 __isl_give isl_id *isl_id_copy(isl_id *id);
495 void *isl_id_free(__isl_take isl_id *id);
497 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
498 void *isl_id_get_user(__isl_keep isl_id *id);
499 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
501 __isl_give isl_printer *isl_printer_print_id(
502 __isl_take isl_printer *p, __isl_keep isl_id *id);
504 Note that C<isl_id_get_name> returns a pointer to some internal
505 data structure, so the result can only be used while the
506 corresponding C<isl_id> is alive.
510 Whenever a new set or relation is created from scratch,
511 the space in which it lives needs to be specified using an C<isl_space>.
513 #include <isl/space.h>
514 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
515 unsigned nparam, unsigned n_in, unsigned n_out);
516 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
518 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
519 unsigned nparam, unsigned dim);
520 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
521 void isl_space_free(__isl_take isl_space *space);
522 unsigned isl_space_dim(__isl_keep isl_space *space,
523 enum isl_dim_type type);
525 The space used for creating a parameter domain
526 needs to be created using C<isl_space_params_alloc>.
527 For other sets, the space
528 needs to be created using C<isl_space_set_alloc>, while
529 for a relation, the space
530 needs to be created using C<isl_space_alloc>.
531 C<isl_space_dim> can be used
532 to find out the number of dimensions of each type in
533 a space, where type may be
534 C<isl_dim_param>, C<isl_dim_in> (only for relations),
535 C<isl_dim_out> (only for relations), C<isl_dim_set>
536 (only for sets) or C<isl_dim_all>.
538 To check whether a given space is that of a set or a map
539 or whether it is a parameter space, use these functions:
541 #include <isl/space.h>
542 int isl_space_is_params(__isl_keep isl_space *space);
543 int isl_space_is_set(__isl_keep isl_space *space);
545 It is often useful to create objects that live in the
546 same space as some other object. This can be accomplished
547 by creating the new objects
548 (see L<Creating New Sets and Relations> or
549 L<Creating New (Piecewise) Quasipolynomials>) based on the space
550 of the original object.
553 __isl_give isl_space *isl_basic_set_get_space(
554 __isl_keep isl_basic_set *bset);
555 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
557 #include <isl/union_set.h>
558 __isl_give isl_space *isl_union_set_get_space(
559 __isl_keep isl_union_set *uset);
562 __isl_give isl_space *isl_basic_map_get_space(
563 __isl_keep isl_basic_map *bmap);
564 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
566 #include <isl/union_map.h>
567 __isl_give isl_space *isl_union_map_get_space(
568 __isl_keep isl_union_map *umap);
570 #include <isl/constraint.h>
571 __isl_give isl_space *isl_constraint_get_space(
572 __isl_keep isl_constraint *constraint);
574 #include <isl/polynomial.h>
575 __isl_give isl_space *isl_qpolynomial_get_domain_space(
576 __isl_keep isl_qpolynomial *qp);
577 __isl_give isl_space *isl_qpolynomial_get_space(
578 __isl_keep isl_qpolynomial *qp);
579 __isl_give isl_space *isl_qpolynomial_fold_get_space(
580 __isl_keep isl_qpolynomial_fold *fold);
581 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
582 __isl_keep isl_pw_qpolynomial *pwqp);
583 __isl_give isl_space *isl_pw_qpolynomial_get_space(
584 __isl_keep isl_pw_qpolynomial *pwqp);
585 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
586 __isl_keep isl_pw_qpolynomial_fold *pwf);
587 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
588 __isl_keep isl_pw_qpolynomial_fold *pwf);
589 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
590 __isl_keep isl_union_pw_qpolynomial *upwqp);
591 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
592 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
595 __isl_give isl_space *isl_aff_get_domain_space(
596 __isl_keep isl_aff *aff);
597 __isl_give isl_space *isl_aff_get_space(
598 __isl_keep isl_aff *aff);
599 __isl_give isl_space *isl_pw_aff_get_domain_space(
600 __isl_keep isl_pw_aff *pwaff);
601 __isl_give isl_space *isl_pw_aff_get_space(
602 __isl_keep isl_pw_aff *pwaff);
603 __isl_give isl_space *isl_multi_aff_get_space(
604 __isl_keep isl_multi_aff *maff);
605 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
606 __isl_keep isl_pw_multi_aff *pma);
607 __isl_give isl_space *isl_pw_multi_aff_get_space(
608 __isl_keep isl_pw_multi_aff *pma);
610 #include <isl/point.h>
611 __isl_give isl_space *isl_point_get_space(
612 __isl_keep isl_point *pnt);
614 The identifiers or names of the individual dimensions may be set or read off
615 using the following functions.
617 #include <isl/space.h>
618 __isl_give isl_space *isl_space_set_dim_id(
619 __isl_take isl_space *space,
620 enum isl_dim_type type, unsigned pos,
621 __isl_take isl_id *id);
622 int isl_space_has_dim_id(__isl_keep isl_space *space,
623 enum isl_dim_type type, unsigned pos);
624 __isl_give isl_id *isl_space_get_dim_id(
625 __isl_keep isl_space *space,
626 enum isl_dim_type type, unsigned pos);
627 __isl_give isl_space *isl_space_set_dim_name(__isl_take isl_space *space,
628 enum isl_dim_type type, unsigned pos,
629 __isl_keep const char *name);
630 __isl_keep const char *isl_space_get_dim_name(__isl_keep isl_space *space,
631 enum isl_dim_type type, unsigned pos);
633 Note that C<isl_space_get_name> returns a pointer to some internal
634 data structure, so the result can only be used while the
635 corresponding C<isl_space> is alive.
636 Also note that every function that operates on two sets or relations
637 requires that both arguments have the same parameters. This also
638 means that if one of the arguments has named parameters, then the
639 other needs to have named parameters too and the names need to match.
640 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
641 arguments may have different parameters (as long as they are named),
642 in which case the result will have as parameters the union of the parameters of
645 Given the identifier or name of a dimension (typically a parameter),
646 its position can be obtained from the following function.
648 #include <isl/space.h>
649 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
650 enum isl_dim_type type, __isl_keep isl_id *id);
651 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
652 enum isl_dim_type type, const char *name);
654 The identifiers or names of entire spaces may be set or read off
655 using the following functions.
657 #include <isl/space.h>
658 __isl_give isl_space *isl_space_set_tuple_id(
659 __isl_take isl_space *space,
660 enum isl_dim_type type, __isl_take isl_id *id);
661 __isl_give isl_space *isl_space_reset_tuple_id(
662 __isl_take isl_space *space, enum isl_dim_type type);
663 int isl_space_has_tuple_id(__isl_keep isl_space *space,
664 enum isl_dim_type type);
665 __isl_give isl_id *isl_space_get_tuple_id(
666 __isl_keep isl_space *space, enum isl_dim_type type);
667 __isl_give isl_space *isl_space_set_tuple_name(
668 __isl_take isl_space *space,
669 enum isl_dim_type type, const char *s);
670 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
671 enum isl_dim_type type);
673 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
674 or C<isl_dim_set>. As with C<isl_space_get_name>,
675 the C<isl_space_get_tuple_name> function returns a pointer to some internal
677 Binary operations require the corresponding spaces of their arguments
678 to have the same name.
680 Spaces can be nested. In particular, the domain of a set or
681 the domain or range of a relation can be a nested relation.
682 The following functions can be used to construct and deconstruct
685 #include <isl/space.h>
686 int isl_space_is_wrapping(__isl_keep isl_space *space);
687 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
688 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
690 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
691 be the space of a set, while that of
692 C<isl_space_wrap> should be the space of a relation.
693 Conversely, the output of C<isl_space_unwrap> is the space
694 of a relation, while that of C<isl_space_wrap> is the space of a set.
696 Spaces can be created from other spaces
697 using the following functions.
699 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
700 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
701 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
702 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
703 __isl_give isl_space *isl_space_params(
704 __isl_take isl_space *space);
705 __isl_give isl_space *isl_space_set_from_params(
706 __isl_take isl_space *space);
707 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
708 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
709 __isl_take isl_space *right);
710 __isl_give isl_space *isl_space_align_params(
711 __isl_take isl_space *space1, __isl_take isl_space *space2)
712 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
713 enum isl_dim_type type, unsigned pos, unsigned n);
714 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
715 enum isl_dim_type type, unsigned n);
716 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
717 enum isl_dim_type type, unsigned first, unsigned n);
718 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
719 enum isl_dim_type dst_type, unsigned dst_pos,
720 enum isl_dim_type src_type, unsigned src_pos,
722 __isl_give isl_space *isl_space_map_from_set(
723 __isl_take isl_space *space);
724 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
726 Note that if dimensions are added or removed from a space, then
727 the name and the internal structure are lost.
731 A local space is essentially a space with
732 zero or more existentially quantified variables.
733 The local space of a basic set or relation can be obtained
734 using the following functions.
737 __isl_give isl_local_space *isl_basic_set_get_local_space(
738 __isl_keep isl_basic_set *bset);
741 __isl_give isl_local_space *isl_basic_map_get_local_space(
742 __isl_keep isl_basic_map *bmap);
744 A new local space can be created from a space using
746 #include <isl/local_space.h>
747 __isl_give isl_local_space *isl_local_space_from_space(
748 __isl_take isl_space *space);
750 They can be inspected, modified, copied and freed using the following functions.
752 #include <isl/local_space.h>
753 isl_ctx *isl_local_space_get_ctx(
754 __isl_keep isl_local_space *ls);
755 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
756 int isl_local_space_dim(__isl_keep isl_local_space *ls,
757 enum isl_dim_type type);
758 const char *isl_local_space_get_dim_name(
759 __isl_keep isl_local_space *ls,
760 enum isl_dim_type type, unsigned pos);
761 __isl_give isl_local_space *isl_local_space_set_dim_name(
762 __isl_take isl_local_space *ls,
763 enum isl_dim_type type, unsigned pos, const char *s);
764 __isl_give isl_local_space *isl_local_space_set_dim_id(
765 __isl_take isl_local_space *ls,
766 enum isl_dim_type type, unsigned pos,
767 __isl_take isl_id *id);
768 __isl_give isl_space *isl_local_space_get_space(
769 __isl_keep isl_local_space *ls);
770 __isl_give isl_aff *isl_local_space_get_div(
771 __isl_keep isl_local_space *ls, int pos);
772 __isl_give isl_local_space *isl_local_space_copy(
773 __isl_keep isl_local_space *ls);
774 void *isl_local_space_free(__isl_take isl_local_space *ls);
776 Two local spaces can be compared using
778 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
779 __isl_keep isl_local_space *ls2);
781 Local spaces can be created from other local spaces
782 using the following functions.
784 __isl_give isl_local_space *isl_local_space_domain(
785 __isl_take isl_local_space *ls);
786 __isl_give isl_local_space *isl_local_space_from_domain(
787 __isl_take isl_local_space *ls);
788 __isl_give isl_local_space *isl_local_space_intersect(
789 __isl_take isl_local_space *ls1,
790 __isl_take isl_local_space *ls2);
791 __isl_give isl_local_space *isl_local_space_add_dims(
792 __isl_take isl_local_space *ls,
793 enum isl_dim_type type, unsigned n);
794 __isl_give isl_local_space *isl_local_space_insert_dims(
795 __isl_take isl_local_space *ls,
796 enum isl_dim_type type, unsigned first, unsigned n);
797 __isl_give isl_local_space *isl_local_space_drop_dims(
798 __isl_take isl_local_space *ls,
799 enum isl_dim_type type, unsigned first, unsigned n);
801 =head2 Input and Output
803 C<isl> supports its own input/output format, which is similar
804 to the C<Omega> format, but also supports the C<PolyLib> format
809 The C<isl> format is similar to that of C<Omega>, but has a different
810 syntax for describing the parameters and allows for the definition
811 of an existentially quantified variable as the integer division
812 of an affine expression.
813 For example, the set of integers C<i> between C<0> and C<n>
814 such that C<i % 10 <= 6> can be described as
816 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
819 A set or relation can have several disjuncts, separated
820 by the keyword C<or>. Each disjunct is either a conjunction
821 of constraints or a projection (C<exists>) of a conjunction
822 of constraints. The constraints are separated by the keyword
825 =head3 C<PolyLib> format
827 If the represented set is a union, then the first line
828 contains a single number representing the number of disjuncts.
829 Otherwise, a line containing the number C<1> is optional.
831 Each disjunct is represented by a matrix of constraints.
832 The first line contains two numbers representing
833 the number of rows and columns,
834 where the number of rows is equal to the number of constraints
835 and the number of columns is equal to two plus the number of variables.
836 The following lines contain the actual rows of the constraint matrix.
837 In each row, the first column indicates whether the constraint
838 is an equality (C<0>) or inequality (C<1>). The final column
839 corresponds to the constant term.
841 If the set is parametric, then the coefficients of the parameters
842 appear in the last columns before the constant column.
843 The coefficients of any existentially quantified variables appear
844 between those of the set variables and those of the parameters.
846 =head3 Extended C<PolyLib> format
848 The extended C<PolyLib> format is nearly identical to the
849 C<PolyLib> format. The only difference is that the line
850 containing the number of rows and columns of a constraint matrix
851 also contains four additional numbers:
852 the number of output dimensions, the number of input dimensions,
853 the number of local dimensions (i.e., the number of existentially
854 quantified variables) and the number of parameters.
855 For sets, the number of ``output'' dimensions is equal
856 to the number of set dimensions, while the number of ``input''
862 __isl_give isl_basic_set *isl_basic_set_read_from_file(
863 isl_ctx *ctx, FILE *input);
864 __isl_give isl_basic_set *isl_basic_set_read_from_str(
865 isl_ctx *ctx, const char *str);
866 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
868 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
872 __isl_give isl_basic_map *isl_basic_map_read_from_file(
873 isl_ctx *ctx, FILE *input);
874 __isl_give isl_basic_map *isl_basic_map_read_from_str(
875 isl_ctx *ctx, const char *str);
876 __isl_give isl_map *isl_map_read_from_file(
877 isl_ctx *ctx, FILE *input);
878 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
881 #include <isl/union_set.h>
882 __isl_give isl_union_set *isl_union_set_read_from_file(
883 isl_ctx *ctx, FILE *input);
884 __isl_give isl_union_set *isl_union_set_read_from_str(
885 isl_ctx *ctx, const char *str);
887 #include <isl/union_map.h>
888 __isl_give isl_union_map *isl_union_map_read_from_file(
889 isl_ctx *ctx, FILE *input);
890 __isl_give isl_union_map *isl_union_map_read_from_str(
891 isl_ctx *ctx, const char *str);
893 The input format is autodetected and may be either the C<PolyLib> format
894 or the C<isl> format.
898 Before anything can be printed, an C<isl_printer> needs to
901 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
903 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
904 void isl_printer_free(__isl_take isl_printer *printer);
905 __isl_give char *isl_printer_get_str(
906 __isl_keep isl_printer *printer);
908 The behavior of the printer can be modified in various ways
910 __isl_give isl_printer *isl_printer_set_output_format(
911 __isl_take isl_printer *p, int output_format);
912 __isl_give isl_printer *isl_printer_set_indent(
913 __isl_take isl_printer *p, int indent);
914 __isl_give isl_printer *isl_printer_indent(
915 __isl_take isl_printer *p, int indent);
916 __isl_give isl_printer *isl_printer_set_prefix(
917 __isl_take isl_printer *p, const char *prefix);
918 __isl_give isl_printer *isl_printer_set_suffix(
919 __isl_take isl_printer *p, const char *suffix);
921 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
922 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
923 and defaults to C<ISL_FORMAT_ISL>.
924 Each line in the output is indented by C<indent> (set by
925 C<isl_printer_set_indent>) spaces
926 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
927 In the C<PolyLib> format output,
928 the coefficients of the existentially quantified variables
929 appear between those of the set variables and those
931 The function C<isl_printer_indent> increases the indentation
932 by the specified amount (which may be negative).
934 To actually print something, use
937 __isl_give isl_printer *isl_printer_print_basic_set(
938 __isl_take isl_printer *printer,
939 __isl_keep isl_basic_set *bset);
940 __isl_give isl_printer *isl_printer_print_set(
941 __isl_take isl_printer *printer,
942 __isl_keep isl_set *set);
945 __isl_give isl_printer *isl_printer_print_basic_map(
946 __isl_take isl_printer *printer,
947 __isl_keep isl_basic_map *bmap);
948 __isl_give isl_printer *isl_printer_print_map(
949 __isl_take isl_printer *printer,
950 __isl_keep isl_map *map);
952 #include <isl/union_set.h>
953 __isl_give isl_printer *isl_printer_print_union_set(
954 __isl_take isl_printer *p,
955 __isl_keep isl_union_set *uset);
957 #include <isl/union_map.h>
958 __isl_give isl_printer *isl_printer_print_union_map(
959 __isl_take isl_printer *p,
960 __isl_keep isl_union_map *umap);
962 When called on a file printer, the following function flushes
963 the file. When called on a string printer, the buffer is cleared.
965 __isl_give isl_printer *isl_printer_flush(
966 __isl_take isl_printer *p);
968 =head2 Creating New Sets and Relations
970 C<isl> has functions for creating some standard sets and relations.
974 =item * Empty sets and relations
976 __isl_give isl_basic_set *isl_basic_set_empty(
977 __isl_take isl_space *space);
978 __isl_give isl_basic_map *isl_basic_map_empty(
979 __isl_take isl_space *space);
980 __isl_give isl_set *isl_set_empty(
981 __isl_take isl_space *space);
982 __isl_give isl_map *isl_map_empty(
983 __isl_take isl_space *space);
984 __isl_give isl_union_set *isl_union_set_empty(
985 __isl_take isl_space *space);
986 __isl_give isl_union_map *isl_union_map_empty(
987 __isl_take isl_space *space);
989 For C<isl_union_set>s and C<isl_union_map>s, the space
990 is only used to specify the parameters.
992 =item * Universe sets and relations
994 __isl_give isl_basic_set *isl_basic_set_universe(
995 __isl_take isl_space *space);
996 __isl_give isl_basic_map *isl_basic_map_universe(
997 __isl_take isl_space *space);
998 __isl_give isl_set *isl_set_universe(
999 __isl_take isl_space *space);
1000 __isl_give isl_map *isl_map_universe(
1001 __isl_take isl_space *space);
1002 __isl_give isl_union_set *isl_union_set_universe(
1003 __isl_take isl_union_set *uset);
1004 __isl_give isl_union_map *isl_union_map_universe(
1005 __isl_take isl_union_map *umap);
1007 The sets and relations constructed by the functions above
1008 contain all integer values, while those constructed by the
1009 functions below only contain non-negative values.
1011 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1012 __isl_take isl_space *space);
1013 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1014 __isl_take isl_space *space);
1015 __isl_give isl_set *isl_set_nat_universe(
1016 __isl_take isl_space *space);
1017 __isl_give isl_map *isl_map_nat_universe(
1018 __isl_take isl_space *space);
1020 =item * Identity relations
1022 __isl_give isl_basic_map *isl_basic_map_identity(
1023 __isl_take isl_space *space);
1024 __isl_give isl_map *isl_map_identity(
1025 __isl_take isl_space *space);
1027 The number of input and output dimensions in C<space> needs
1030 =item * Lexicographic order
1032 __isl_give isl_map *isl_map_lex_lt(
1033 __isl_take isl_space *set_space);
1034 __isl_give isl_map *isl_map_lex_le(
1035 __isl_take isl_space *set_space);
1036 __isl_give isl_map *isl_map_lex_gt(
1037 __isl_take isl_space *set_space);
1038 __isl_give isl_map *isl_map_lex_ge(
1039 __isl_take isl_space *set_space);
1040 __isl_give isl_map *isl_map_lex_lt_first(
1041 __isl_take isl_space *space, unsigned n);
1042 __isl_give isl_map *isl_map_lex_le_first(
1043 __isl_take isl_space *space, unsigned n);
1044 __isl_give isl_map *isl_map_lex_gt_first(
1045 __isl_take isl_space *space, unsigned n);
1046 __isl_give isl_map *isl_map_lex_ge_first(
1047 __isl_take isl_space *space, unsigned n);
1049 The first four functions take a space for a B<set>
1050 and return relations that express that the elements in the domain
1051 are lexicographically less
1052 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1053 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1054 than the elements in the range.
1055 The last four functions take a space for a map
1056 and return relations that express that the first C<n> dimensions
1057 in the domain are lexicographically less
1058 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1059 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1060 than the first C<n> dimensions in the range.
1064 A basic set or relation can be converted to a set or relation
1065 using the following functions.
1067 __isl_give isl_set *isl_set_from_basic_set(
1068 __isl_take isl_basic_set *bset);
1069 __isl_give isl_map *isl_map_from_basic_map(
1070 __isl_take isl_basic_map *bmap);
1072 Sets and relations can be converted to union sets and relations
1073 using the following functions.
1075 __isl_give isl_union_map *isl_union_map_from_map(
1076 __isl_take isl_map *map);
1077 __isl_give isl_union_set *isl_union_set_from_set(
1078 __isl_take isl_set *set);
1080 The inverse conversions below can only be used if the input
1081 union set or relation is known to contain elements in exactly one
1084 __isl_give isl_set *isl_set_from_union_set(
1085 __isl_take isl_union_set *uset);
1086 __isl_give isl_map *isl_map_from_union_map(
1087 __isl_take isl_union_map *umap);
1089 A zero-dimensional set can be constructed on a given parameter domain
1090 using the following function.
1092 __isl_give isl_set *isl_set_from_params(
1093 __isl_take isl_set *set);
1095 Sets and relations can be copied and freed again using the following
1098 __isl_give isl_basic_set *isl_basic_set_copy(
1099 __isl_keep isl_basic_set *bset);
1100 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1101 __isl_give isl_union_set *isl_union_set_copy(
1102 __isl_keep isl_union_set *uset);
1103 __isl_give isl_basic_map *isl_basic_map_copy(
1104 __isl_keep isl_basic_map *bmap);
1105 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1106 __isl_give isl_union_map *isl_union_map_copy(
1107 __isl_keep isl_union_map *umap);
1108 void isl_basic_set_free(__isl_take isl_basic_set *bset);
1109 void isl_set_free(__isl_take isl_set *set);
1110 void *isl_union_set_free(__isl_take isl_union_set *uset);
1111 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
1112 void isl_map_free(__isl_take isl_map *map);
1113 void *isl_union_map_free(__isl_take isl_union_map *umap);
1115 Other sets and relations can be constructed by starting
1116 from a universe set or relation, adding equality and/or
1117 inequality constraints and then projecting out the
1118 existentially quantified variables, if any.
1119 Constraints can be constructed, manipulated and
1120 added to (or removed from) (basic) sets and relations
1121 using the following functions.
1123 #include <isl/constraint.h>
1124 __isl_give isl_constraint *isl_equality_alloc(
1125 __isl_take isl_local_space *ls);
1126 __isl_give isl_constraint *isl_inequality_alloc(
1127 __isl_take isl_local_space *ls);
1128 __isl_give isl_constraint *isl_constraint_set_constant(
1129 __isl_take isl_constraint *constraint, isl_int v);
1130 __isl_give isl_constraint *isl_constraint_set_constant_si(
1131 __isl_take isl_constraint *constraint, int v);
1132 __isl_give isl_constraint *isl_constraint_set_coefficient(
1133 __isl_take isl_constraint *constraint,
1134 enum isl_dim_type type, int pos, isl_int v);
1135 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1136 __isl_take isl_constraint *constraint,
1137 enum isl_dim_type type, int pos, int v);
1138 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1139 __isl_take isl_basic_map *bmap,
1140 __isl_take isl_constraint *constraint);
1141 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1142 __isl_take isl_basic_set *bset,
1143 __isl_take isl_constraint *constraint);
1144 __isl_give isl_map *isl_map_add_constraint(
1145 __isl_take isl_map *map,
1146 __isl_take isl_constraint *constraint);
1147 __isl_give isl_set *isl_set_add_constraint(
1148 __isl_take isl_set *set,
1149 __isl_take isl_constraint *constraint);
1150 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1151 __isl_take isl_basic_set *bset,
1152 __isl_take isl_constraint *constraint);
1154 For example, to create a set containing the even integers
1155 between 10 and 42, you would use the following code.
1158 isl_local_space *ls;
1160 isl_basic_set *bset;
1162 space = isl_space_set_alloc(ctx, 0, 2);
1163 bset = isl_basic_set_universe(isl_space_copy(space));
1164 ls = isl_local_space_from_space(space);
1166 c = isl_equality_alloc(isl_local_space_copy(ls));
1167 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1168 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1169 bset = isl_basic_set_add_constraint(bset, c);
1171 c = isl_inequality_alloc(isl_local_space_copy(ls));
1172 c = isl_constraint_set_constant_si(c, -10);
1173 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1174 bset = isl_basic_set_add_constraint(bset, c);
1176 c = isl_inequality_alloc(ls);
1177 c = isl_constraint_set_constant_si(c, 42);
1178 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1179 bset = isl_basic_set_add_constraint(bset, c);
1181 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1185 isl_basic_set *bset;
1186 bset = isl_basic_set_read_from_str(ctx,
1187 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1189 A basic set or relation can also be constructed from two matrices
1190 describing the equalities and the inequalities.
1192 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1193 __isl_take isl_space *space,
1194 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1195 enum isl_dim_type c1,
1196 enum isl_dim_type c2, enum isl_dim_type c3,
1197 enum isl_dim_type c4);
1198 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1199 __isl_take isl_space *space,
1200 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1201 enum isl_dim_type c1,
1202 enum isl_dim_type c2, enum isl_dim_type c3,
1203 enum isl_dim_type c4, enum isl_dim_type c5);
1205 The C<isl_dim_type> arguments indicate the order in which
1206 different kinds of variables appear in the input matrices
1207 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1208 C<isl_dim_set> and C<isl_dim_div> for sets and
1209 of C<isl_dim_cst>, C<isl_dim_param>,
1210 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1212 A (basic) set or relation can also be constructed from a (piecewise)
1213 (multiple) affine expression
1214 or a list of affine expressions
1215 (See L<"Piecewise Quasi Affine Expressions"> and
1216 L<"Piecewise Multiple Quasi Affine Expressions">).
1218 __isl_give isl_basic_map *isl_basic_map_from_aff(
1219 __isl_take isl_aff *aff);
1220 __isl_give isl_set *isl_set_from_pw_aff(
1221 __isl_take isl_pw_aff *pwaff);
1222 __isl_give isl_map *isl_map_from_pw_aff(
1223 __isl_take isl_pw_aff *pwaff);
1224 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1225 __isl_take isl_space *domain_space,
1226 __isl_take isl_aff_list *list);
1227 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1228 __isl_take isl_multi_aff *maff)
1229 __isl_give isl_set *isl_set_from_pw_multi_aff(
1230 __isl_take isl_pw_multi_aff *pma);
1231 __isl_give isl_map *isl_map_from_pw_multi_aff(
1232 __isl_take isl_pw_multi_aff *pma);
1234 The C<domain_dim> argument describes the domain of the resulting
1235 basic relation. It is required because the C<list> may consist
1236 of zero affine expressions.
1238 =head2 Inspecting Sets and Relations
1240 Usually, the user should not have to care about the actual constraints
1241 of the sets and maps, but should instead apply the abstract operations
1242 explained in the following sections.
1243 Occasionally, however, it may be required to inspect the individual
1244 coefficients of the constraints. This section explains how to do so.
1245 In these cases, it may also be useful to have C<isl> compute
1246 an explicit representation of the existentially quantified variables.
1248 __isl_give isl_set *isl_set_compute_divs(
1249 __isl_take isl_set *set);
1250 __isl_give isl_map *isl_map_compute_divs(
1251 __isl_take isl_map *map);
1252 __isl_give isl_union_set *isl_union_set_compute_divs(
1253 __isl_take isl_union_set *uset);
1254 __isl_give isl_union_map *isl_union_map_compute_divs(
1255 __isl_take isl_union_map *umap);
1257 This explicit representation defines the existentially quantified
1258 variables as integer divisions of the other variables, possibly
1259 including earlier existentially quantified variables.
1260 An explicitly represented existentially quantified variable therefore
1261 has a unique value when the values of the other variables are known.
1262 If, furthermore, the same existentials, i.e., existentials
1263 with the same explicit representations, should appear in the
1264 same order in each of the disjuncts of a set or map, then the user should call
1265 either of the following functions.
1267 __isl_give isl_set *isl_set_align_divs(
1268 __isl_take isl_set *set);
1269 __isl_give isl_map *isl_map_align_divs(
1270 __isl_take isl_map *map);
1272 Alternatively, the existentially quantified variables can be removed
1273 using the following functions, which compute an overapproximation.
1275 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1276 __isl_take isl_basic_set *bset);
1277 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1278 __isl_take isl_basic_map *bmap);
1279 __isl_give isl_set *isl_set_remove_divs(
1280 __isl_take isl_set *set);
1281 __isl_give isl_map *isl_map_remove_divs(
1282 __isl_take isl_map *map);
1284 To iterate over all the sets or maps in a union set or map, use
1286 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1287 int (*fn)(__isl_take isl_set *set, void *user),
1289 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1290 int (*fn)(__isl_take isl_map *map, void *user),
1293 The number of sets or maps in a union set or map can be obtained
1296 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1297 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1299 To extract the set or map in a given space from a union, use
1301 __isl_give isl_set *isl_union_set_extract_set(
1302 __isl_keep isl_union_set *uset,
1303 __isl_take isl_space *space);
1304 __isl_give isl_map *isl_union_map_extract_map(
1305 __isl_keep isl_union_map *umap,
1306 __isl_take isl_space *space);
1308 To iterate over all the basic sets or maps in a set or map, use
1310 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1311 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1313 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1314 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1317 The callback function C<fn> should return 0 if successful and
1318 -1 if an error occurs. In the latter case, or if any other error
1319 occurs, the above functions will return -1.
1321 It should be noted that C<isl> does not guarantee that
1322 the basic sets or maps passed to C<fn> are disjoint.
1323 If this is required, then the user should call one of
1324 the following functions first.
1326 __isl_give isl_set *isl_set_make_disjoint(
1327 __isl_take isl_set *set);
1328 __isl_give isl_map *isl_map_make_disjoint(
1329 __isl_take isl_map *map);
1331 The number of basic sets in a set can be obtained
1334 int isl_set_n_basic_set(__isl_keep isl_set *set);
1336 To iterate over the constraints of a basic set or map, use
1338 #include <isl/constraint.h>
1340 int isl_basic_map_foreach_constraint(
1341 __isl_keep isl_basic_map *bmap,
1342 int (*fn)(__isl_take isl_constraint *c, void *user),
1344 void *isl_constraint_free(__isl_take isl_constraint *c);
1346 Again, the callback function C<fn> should return 0 if successful and
1347 -1 if an error occurs. In the latter case, or if any other error
1348 occurs, the above functions will return -1.
1349 The constraint C<c> represents either an equality or an inequality.
1350 Use the following function to find out whether a constraint
1351 represents an equality. If not, it represents an inequality.
1353 int isl_constraint_is_equality(
1354 __isl_keep isl_constraint *constraint);
1356 The coefficients of the constraints can be inspected using
1357 the following functions.
1359 void isl_constraint_get_constant(
1360 __isl_keep isl_constraint *constraint, isl_int *v);
1361 void isl_constraint_get_coefficient(
1362 __isl_keep isl_constraint *constraint,
1363 enum isl_dim_type type, int pos, isl_int *v);
1364 int isl_constraint_involves_dims(
1365 __isl_keep isl_constraint *constraint,
1366 enum isl_dim_type type, unsigned first, unsigned n);
1368 The explicit representations of the existentially quantified
1369 variables can be inspected using the following function.
1370 Note that the user is only allowed to use this function
1371 if the inspected set or map is the result of a call
1372 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1373 The existentially quantified variable is equal to the floor
1374 of the returned affine expression. The affine expression
1375 itself can be inspected using the functions in
1376 L<"Piecewise Quasi Affine Expressions">.
1378 __isl_give isl_aff *isl_constraint_get_div(
1379 __isl_keep isl_constraint *constraint, int pos);
1381 To obtain the constraints of a basic set or map in matrix
1382 form, use the following functions.
1384 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1385 __isl_keep isl_basic_set *bset,
1386 enum isl_dim_type c1, enum isl_dim_type c2,
1387 enum isl_dim_type c3, enum isl_dim_type c4);
1388 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1389 __isl_keep isl_basic_set *bset,
1390 enum isl_dim_type c1, enum isl_dim_type c2,
1391 enum isl_dim_type c3, enum isl_dim_type c4);
1392 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1393 __isl_keep isl_basic_map *bmap,
1394 enum isl_dim_type c1,
1395 enum isl_dim_type c2, enum isl_dim_type c3,
1396 enum isl_dim_type c4, enum isl_dim_type c5);
1397 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1398 __isl_keep isl_basic_map *bmap,
1399 enum isl_dim_type c1,
1400 enum isl_dim_type c2, enum isl_dim_type c3,
1401 enum isl_dim_type c4, enum isl_dim_type c5);
1403 The C<isl_dim_type> arguments dictate the order in which
1404 different kinds of variables appear in the resulting matrix
1405 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1406 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1408 The number of parameters, input, output or set dimensions can
1409 be obtained using the following functions.
1411 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1412 enum isl_dim_type type);
1413 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1414 enum isl_dim_type type);
1415 unsigned isl_set_dim(__isl_keep isl_set *set,
1416 enum isl_dim_type type);
1417 unsigned isl_map_dim(__isl_keep isl_map *map,
1418 enum isl_dim_type type);
1420 To check whether the description of a set or relation depends
1421 on one or more given dimensions, it is not necessary to iterate over all
1422 constraints. Instead the following functions can be used.
1424 int isl_basic_set_involves_dims(
1425 __isl_keep isl_basic_set *bset,
1426 enum isl_dim_type type, unsigned first, unsigned n);
1427 int isl_set_involves_dims(__isl_keep isl_set *set,
1428 enum isl_dim_type type, unsigned first, unsigned n);
1429 int isl_basic_map_involves_dims(
1430 __isl_keep isl_basic_map *bmap,
1431 enum isl_dim_type type, unsigned first, unsigned n);
1432 int isl_map_involves_dims(__isl_keep isl_map *map,
1433 enum isl_dim_type type, unsigned first, unsigned n);
1435 Similarly, the following functions can be used to check whether
1436 a given dimension is involved in any lower or upper bound.
1438 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1439 enum isl_dim_type type, unsigned pos);
1440 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1441 enum isl_dim_type type, unsigned pos);
1443 The identifiers or names of the domain and range spaces of a set
1444 or relation can be read off or set using the following functions.
1446 __isl_give isl_set *isl_set_set_tuple_id(
1447 __isl_take isl_set *set, __isl_take isl_id *id);
1448 __isl_give isl_set *isl_set_reset_tuple_id(
1449 __isl_take isl_set *set);
1450 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1451 __isl_give isl_id *isl_set_get_tuple_id(
1452 __isl_keep isl_set *set);
1453 __isl_give isl_map *isl_map_set_tuple_id(
1454 __isl_take isl_map *map, enum isl_dim_type type,
1455 __isl_take isl_id *id);
1456 __isl_give isl_map *isl_map_reset_tuple_id(
1457 __isl_take isl_map *map, enum isl_dim_type type);
1458 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1459 enum isl_dim_type type);
1460 __isl_give isl_id *isl_map_get_tuple_id(
1461 __isl_keep isl_map *map, enum isl_dim_type type);
1463 const char *isl_basic_set_get_tuple_name(
1464 __isl_keep isl_basic_set *bset);
1465 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1466 __isl_take isl_basic_set *set, const char *s);
1467 const char *isl_set_get_tuple_name(
1468 __isl_keep isl_set *set);
1469 const char *isl_basic_map_get_tuple_name(
1470 __isl_keep isl_basic_map *bmap,
1471 enum isl_dim_type type);
1472 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1473 __isl_take isl_basic_map *bmap,
1474 enum isl_dim_type type, const char *s);
1475 const char *isl_map_get_tuple_name(
1476 __isl_keep isl_map *map,
1477 enum isl_dim_type type);
1479 As with C<isl_space_get_tuple_name>, the value returned points to
1480 an internal data structure.
1481 The identifiers, positions or names of individual dimensions can be
1482 read off using the following functions.
1484 __isl_give isl_set *isl_set_set_dim_id(
1485 __isl_take isl_set *set, enum isl_dim_type type,
1486 unsigned pos, __isl_take isl_id *id);
1487 int isl_set_has_dim_id(__isl_keep isl_set *set,
1488 enum isl_dim_type type, unsigned pos);
1489 __isl_give isl_id *isl_set_get_dim_id(
1490 __isl_keep isl_set *set, enum isl_dim_type type,
1492 int isl_basic_map_has_dim_id(
1493 __isl_keep isl_basic_map *bmap,
1494 enum isl_dim_type type, unsigned pos);
1495 __isl_give isl_map *isl_map_set_dim_id(
1496 __isl_take isl_map *map, enum isl_dim_type type,
1497 unsigned pos, __isl_take isl_id *id);
1498 int isl_map_has_dim_id(__isl_keep isl_map *map,
1499 enum isl_dim_type type, unsigned pos);
1500 __isl_give isl_id *isl_map_get_dim_id(
1501 __isl_keep isl_map *map, enum isl_dim_type type,
1504 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1505 enum isl_dim_type type, __isl_keep isl_id *id);
1506 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1507 enum isl_dim_type type, __isl_keep isl_id *id);
1508 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1509 enum isl_dim_type type, const char *name);
1510 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1511 enum isl_dim_type type, const char *name);
1513 const char *isl_constraint_get_dim_name(
1514 __isl_keep isl_constraint *constraint,
1515 enum isl_dim_type type, unsigned pos);
1516 const char *isl_basic_set_get_dim_name(
1517 __isl_keep isl_basic_set *bset,
1518 enum isl_dim_type type, unsigned pos);
1519 const char *isl_set_get_dim_name(
1520 __isl_keep isl_set *set,
1521 enum isl_dim_type type, unsigned pos);
1522 const char *isl_basic_map_get_dim_name(
1523 __isl_keep isl_basic_map *bmap,
1524 enum isl_dim_type type, unsigned pos);
1525 const char *isl_map_get_dim_name(
1526 __isl_keep isl_map *map,
1527 enum isl_dim_type type, unsigned pos);
1529 These functions are mostly useful to obtain the identifiers, positions
1530 or names of the parameters. Identifiers of individual dimensions are
1531 essentially only useful for printing. They are ignored by all other
1532 operations and may not be preserved across those operations.
1536 =head3 Unary Properties
1542 The following functions test whether the given set or relation
1543 contains any integer points. The ``plain'' variants do not perform
1544 any computations, but simply check if the given set or relation
1545 is already known to be empty.
1547 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1548 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1549 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1550 int isl_set_is_empty(__isl_keep isl_set *set);
1551 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1552 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1553 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1554 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1555 int isl_map_is_empty(__isl_keep isl_map *map);
1556 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1558 =item * Universality
1560 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1561 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1562 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1564 =item * Single-valuedness
1566 int isl_map_is_single_valued(__isl_keep isl_map *map);
1567 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1571 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1572 int isl_map_is_injective(__isl_keep isl_map *map);
1573 int isl_union_map_plain_is_injective(
1574 __isl_keep isl_union_map *umap);
1575 int isl_union_map_is_injective(
1576 __isl_keep isl_union_map *umap);
1580 int isl_map_is_bijective(__isl_keep isl_map *map);
1581 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1585 int isl_basic_map_plain_is_fixed(
1586 __isl_keep isl_basic_map *bmap,
1587 enum isl_dim_type type, unsigned pos,
1589 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
1590 enum isl_dim_type type, unsigned pos,
1592 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1593 enum isl_dim_type type, unsigned pos,
1596 Check if the relation obviously lies on a hyperplane where the given dimension
1597 has a fixed value and if so, return that value in C<*val>.
1601 To check whether a set is a parameter domain, use this function:
1603 int isl_set_is_params(__isl_keep isl_set *set);
1604 int isl_union_set_is_params(
1605 __isl_keep isl_union_set *uset);
1609 The following functions check whether the domain of the given
1610 (basic) set is a wrapped relation.
1612 int isl_basic_set_is_wrapping(
1613 __isl_keep isl_basic_set *bset);
1614 int isl_set_is_wrapping(__isl_keep isl_set *set);
1616 =item * Internal Product
1618 int isl_basic_map_can_zip(
1619 __isl_keep isl_basic_map *bmap);
1620 int isl_map_can_zip(__isl_keep isl_map *map);
1622 Check whether the product of domain and range of the given relation
1624 i.e., whether both domain and range are nested relations.
1628 =head3 Binary Properties
1634 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1635 __isl_keep isl_set *set2);
1636 int isl_set_is_equal(__isl_keep isl_set *set1,
1637 __isl_keep isl_set *set2);
1638 int isl_union_set_is_equal(
1639 __isl_keep isl_union_set *uset1,
1640 __isl_keep isl_union_set *uset2);
1641 int isl_basic_map_is_equal(
1642 __isl_keep isl_basic_map *bmap1,
1643 __isl_keep isl_basic_map *bmap2);
1644 int isl_map_is_equal(__isl_keep isl_map *map1,
1645 __isl_keep isl_map *map2);
1646 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1647 __isl_keep isl_map *map2);
1648 int isl_union_map_is_equal(
1649 __isl_keep isl_union_map *umap1,
1650 __isl_keep isl_union_map *umap2);
1652 =item * Disjointness
1654 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1655 __isl_keep isl_set *set2);
1659 int isl_set_is_subset(__isl_keep isl_set *set1,
1660 __isl_keep isl_set *set2);
1661 int isl_set_is_strict_subset(
1662 __isl_keep isl_set *set1,
1663 __isl_keep isl_set *set2);
1664 int isl_union_set_is_subset(
1665 __isl_keep isl_union_set *uset1,
1666 __isl_keep isl_union_set *uset2);
1667 int isl_union_set_is_strict_subset(
1668 __isl_keep isl_union_set *uset1,
1669 __isl_keep isl_union_set *uset2);
1670 int isl_basic_map_is_subset(
1671 __isl_keep isl_basic_map *bmap1,
1672 __isl_keep isl_basic_map *bmap2);
1673 int isl_basic_map_is_strict_subset(
1674 __isl_keep isl_basic_map *bmap1,
1675 __isl_keep isl_basic_map *bmap2);
1676 int isl_map_is_subset(
1677 __isl_keep isl_map *map1,
1678 __isl_keep isl_map *map2);
1679 int isl_map_is_strict_subset(
1680 __isl_keep isl_map *map1,
1681 __isl_keep isl_map *map2);
1682 int isl_union_map_is_subset(
1683 __isl_keep isl_union_map *umap1,
1684 __isl_keep isl_union_map *umap2);
1685 int isl_union_map_is_strict_subset(
1686 __isl_keep isl_union_map *umap1,
1687 __isl_keep isl_union_map *umap2);
1691 =head2 Unary Operations
1697 __isl_give isl_set *isl_set_complement(
1698 __isl_take isl_set *set);
1702 __isl_give isl_basic_map *isl_basic_map_reverse(
1703 __isl_take isl_basic_map *bmap);
1704 __isl_give isl_map *isl_map_reverse(
1705 __isl_take isl_map *map);
1706 __isl_give isl_union_map *isl_union_map_reverse(
1707 __isl_take isl_union_map *umap);
1711 __isl_give isl_basic_set *isl_basic_set_project_out(
1712 __isl_take isl_basic_set *bset,
1713 enum isl_dim_type type, unsigned first, unsigned n);
1714 __isl_give isl_basic_map *isl_basic_map_project_out(
1715 __isl_take isl_basic_map *bmap,
1716 enum isl_dim_type type, unsigned first, unsigned n);
1717 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1718 enum isl_dim_type type, unsigned first, unsigned n);
1719 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1720 enum isl_dim_type type, unsigned first, unsigned n);
1721 __isl_give isl_basic_set *isl_basic_set_params(
1722 __isl_take isl_basic_set *bset);
1723 __isl_give isl_basic_set *isl_basic_map_domain(
1724 __isl_take isl_basic_map *bmap);
1725 __isl_give isl_basic_set *isl_basic_map_range(
1726 __isl_take isl_basic_map *bmap);
1727 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1728 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
1729 __isl_give isl_set *isl_map_domain(
1730 __isl_take isl_map *bmap);
1731 __isl_give isl_set *isl_map_range(
1732 __isl_take isl_map *map);
1733 __isl_give isl_set *isl_union_set_params(
1734 __isl_take isl_union_set *uset);
1735 __isl_give isl_set *isl_union_map_params(
1736 __isl_take isl_union_map *umap);
1737 __isl_give isl_union_set *isl_union_map_domain(
1738 __isl_take isl_union_map *umap);
1739 __isl_give isl_union_set *isl_union_map_range(
1740 __isl_take isl_union_map *umap);
1742 __isl_give isl_basic_map *isl_basic_map_domain_map(
1743 __isl_take isl_basic_map *bmap);
1744 __isl_give isl_basic_map *isl_basic_map_range_map(
1745 __isl_take isl_basic_map *bmap);
1746 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1747 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1748 __isl_give isl_union_map *isl_union_map_domain_map(
1749 __isl_take isl_union_map *umap);
1750 __isl_give isl_union_map *isl_union_map_range_map(
1751 __isl_take isl_union_map *umap);
1753 The functions above construct a (basic, regular or union) relation
1754 that maps (a wrapped version of) the input relation to its domain or range.
1758 __isl_give isl_set *isl_set_eliminate(
1759 __isl_take isl_set *set, enum isl_dim_type type,
1760 unsigned first, unsigned n);
1761 __isl_give isl_basic_map *isl_basic_map_eliminate(
1762 __isl_take isl_basic_map *bmap,
1763 enum isl_dim_type type,
1764 unsigned first, unsigned n);
1766 Eliminate the coefficients for the given dimensions from the constraints,
1767 without removing the dimensions.
1771 __isl_give isl_basic_set *isl_basic_set_fix(
1772 __isl_take isl_basic_set *bset,
1773 enum isl_dim_type type, unsigned pos,
1775 __isl_give isl_basic_set *isl_basic_set_fix_si(
1776 __isl_take isl_basic_set *bset,
1777 enum isl_dim_type type, unsigned pos, int value);
1778 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1779 enum isl_dim_type type, unsigned pos,
1781 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1782 enum isl_dim_type type, unsigned pos, int value);
1783 __isl_give isl_basic_map *isl_basic_map_fix_si(
1784 __isl_take isl_basic_map *bmap,
1785 enum isl_dim_type type, unsigned pos, int value);
1786 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1787 enum isl_dim_type type, unsigned pos, int value);
1789 Intersect the set or relation with the hyperplane where the given
1790 dimension has the fixed given value.
1792 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
1793 __isl_take isl_basic_map *bmap,
1794 enum isl_dim_type type, unsigned pos, int value);
1795 __isl_give isl_set *isl_set_lower_bound_si(
1796 __isl_take isl_set *set,
1797 enum isl_dim_type type, unsigned pos, int value);
1798 __isl_give isl_map *isl_map_lower_bound_si(
1799 __isl_take isl_map *map,
1800 enum isl_dim_type type, unsigned pos, int value);
1801 __isl_give isl_set *isl_set_upper_bound_si(
1802 __isl_take isl_set *set,
1803 enum isl_dim_type type, unsigned pos, int value);
1804 __isl_give isl_map *isl_map_upper_bound_si(
1805 __isl_take isl_map *map,
1806 enum isl_dim_type type, unsigned pos, int value);
1808 Intersect the set or relation with the half-space where the given
1809 dimension has a value bounded the fixed given value.
1811 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1812 enum isl_dim_type type1, int pos1,
1813 enum isl_dim_type type2, int pos2);
1814 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1815 enum isl_dim_type type1, int pos1,
1816 enum isl_dim_type type2, int pos2);
1818 Intersect the set or relation with the hyperplane where the given
1819 dimensions are equal to each other.
1821 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
1822 enum isl_dim_type type1, int pos1,
1823 enum isl_dim_type type2, int pos2);
1825 Intersect the relation with the hyperplane where the given
1826 dimensions have opposite values.
1830 __isl_give isl_map *isl_set_identity(
1831 __isl_take isl_set *set);
1832 __isl_give isl_union_map *isl_union_set_identity(
1833 __isl_take isl_union_set *uset);
1835 Construct an identity relation on the given (union) set.
1839 __isl_give isl_basic_set *isl_basic_map_deltas(
1840 __isl_take isl_basic_map *bmap);
1841 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1842 __isl_give isl_union_set *isl_union_map_deltas(
1843 __isl_take isl_union_map *umap);
1845 These functions return a (basic) set containing the differences
1846 between image elements and corresponding domain elements in the input.
1848 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1849 __isl_take isl_basic_map *bmap);
1850 __isl_give isl_map *isl_map_deltas_map(
1851 __isl_take isl_map *map);
1852 __isl_give isl_union_map *isl_union_map_deltas_map(
1853 __isl_take isl_union_map *umap);
1855 The functions above construct a (basic, regular or union) relation
1856 that maps (a wrapped version of) the input relation to its delta set.
1860 Simplify the representation of a set or relation by trying
1861 to combine pairs of basic sets or relations into a single
1862 basic set or relation.
1864 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1865 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1866 __isl_give isl_union_set *isl_union_set_coalesce(
1867 __isl_take isl_union_set *uset);
1868 __isl_give isl_union_map *isl_union_map_coalesce(
1869 __isl_take isl_union_map *umap);
1871 =item * Detecting equalities
1873 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1874 __isl_take isl_basic_set *bset);
1875 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1876 __isl_take isl_basic_map *bmap);
1877 __isl_give isl_set *isl_set_detect_equalities(
1878 __isl_take isl_set *set);
1879 __isl_give isl_map *isl_map_detect_equalities(
1880 __isl_take isl_map *map);
1881 __isl_give isl_union_set *isl_union_set_detect_equalities(
1882 __isl_take isl_union_set *uset);
1883 __isl_give isl_union_map *isl_union_map_detect_equalities(
1884 __isl_take isl_union_map *umap);
1886 Simplify the representation of a set or relation by detecting implicit
1889 =item * Removing redundant constraints
1891 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1892 __isl_take isl_basic_set *bset);
1893 __isl_give isl_set *isl_set_remove_redundancies(
1894 __isl_take isl_set *set);
1895 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1896 __isl_take isl_basic_map *bmap);
1897 __isl_give isl_map *isl_map_remove_redundancies(
1898 __isl_take isl_map *map);
1902 __isl_give isl_basic_set *isl_set_convex_hull(
1903 __isl_take isl_set *set);
1904 __isl_give isl_basic_map *isl_map_convex_hull(
1905 __isl_take isl_map *map);
1907 If the input set or relation has any existentially quantified
1908 variables, then the result of these operations is currently undefined.
1912 __isl_give isl_basic_set *isl_set_simple_hull(
1913 __isl_take isl_set *set);
1914 __isl_give isl_basic_map *isl_map_simple_hull(
1915 __isl_take isl_map *map);
1916 __isl_give isl_union_map *isl_union_map_simple_hull(
1917 __isl_take isl_union_map *umap);
1919 These functions compute a single basic set or relation
1920 that contains the whole input set or relation.
1921 In particular, the output is described by translates
1922 of the constraints describing the basic sets or relations in the input.
1926 (See \autoref{s:simple hull}.)
1932 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1933 __isl_take isl_basic_set *bset);
1934 __isl_give isl_basic_set *isl_set_affine_hull(
1935 __isl_take isl_set *set);
1936 __isl_give isl_union_set *isl_union_set_affine_hull(
1937 __isl_take isl_union_set *uset);
1938 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1939 __isl_take isl_basic_map *bmap);
1940 __isl_give isl_basic_map *isl_map_affine_hull(
1941 __isl_take isl_map *map);
1942 __isl_give isl_union_map *isl_union_map_affine_hull(
1943 __isl_take isl_union_map *umap);
1945 In case of union sets and relations, the affine hull is computed
1948 =item * Polyhedral hull
1950 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1951 __isl_take isl_set *set);
1952 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1953 __isl_take isl_map *map);
1954 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1955 __isl_take isl_union_set *uset);
1956 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1957 __isl_take isl_union_map *umap);
1959 These functions compute a single basic set or relation
1960 not involving any existentially quantified variables
1961 that contains the whole input set or relation.
1962 In case of union sets and relations, the polyhedral hull is computed
1965 =item * Optimization
1967 #include <isl/ilp.h>
1968 enum isl_lp_result isl_basic_set_max(
1969 __isl_keep isl_basic_set *bset,
1970 __isl_keep isl_aff *obj, isl_int *opt)
1971 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
1972 __isl_keep isl_aff *obj, isl_int *opt);
1973 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
1974 __isl_keep isl_aff *obj, isl_int *opt);
1976 Compute the minimum or maximum of the integer affine expression C<obj>
1977 over the points in C<set>, returning the result in C<opt>.
1978 The return value may be one of C<isl_lp_error>,
1979 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
1981 =item * Parametric optimization
1983 __isl_give isl_pw_aff *isl_set_dim_min(
1984 __isl_take isl_set *set, int pos);
1985 __isl_give isl_pw_aff *isl_set_dim_max(
1986 __isl_take isl_set *set, int pos);
1987 __isl_give isl_pw_aff *isl_map_dim_max(
1988 __isl_take isl_map *map, int pos);
1990 Compute the minimum or maximum of the given set or output dimension
1991 as a function of the parameters (and input dimensions), but independently
1992 of the other set or output dimensions.
1993 For lexicographic optimization, see L<"Lexicographic Optimization">.
1997 The following functions compute either the set of (rational) coefficient
1998 values of valid constraints for the given set or the set of (rational)
1999 values satisfying the constraints with coefficients from the given set.
2000 Internally, these two sets of functions perform essentially the
2001 same operations, except that the set of coefficients is assumed to
2002 be a cone, while the set of values may be any polyhedron.
2003 The current implementation is based on the Farkas lemma and
2004 Fourier-Motzkin elimination, but this may change or be made optional
2005 in future. In particular, future implementations may use different
2006 dualization algorithms or skip the elimination step.
2008 __isl_give isl_basic_set *isl_basic_set_coefficients(
2009 __isl_take isl_basic_set *bset);
2010 __isl_give isl_basic_set *isl_set_coefficients(
2011 __isl_take isl_set *set);
2012 __isl_give isl_union_set *isl_union_set_coefficients(
2013 __isl_take isl_union_set *bset);
2014 __isl_give isl_basic_set *isl_basic_set_solutions(
2015 __isl_take isl_basic_set *bset);
2016 __isl_give isl_basic_set *isl_set_solutions(
2017 __isl_take isl_set *set);
2018 __isl_give isl_union_set *isl_union_set_solutions(
2019 __isl_take isl_union_set *bset);
2023 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2025 __isl_give isl_union_map *isl_union_map_power(
2026 __isl_take isl_union_map *umap, int *exact);
2028 Compute a parametric representation for all positive powers I<k> of C<map>.
2029 The result maps I<k> to a nested relation corresponding to the
2030 I<k>th power of C<map>.
2031 The result may be an overapproximation. If the result is known to be exact,
2032 then C<*exact> is set to C<1>.
2034 =item * Transitive closure
2036 __isl_give isl_map *isl_map_transitive_closure(
2037 __isl_take isl_map *map, int *exact);
2038 __isl_give isl_union_map *isl_union_map_transitive_closure(
2039 __isl_take isl_union_map *umap, int *exact);
2041 Compute the transitive closure of C<map>.
2042 The result may be an overapproximation. If the result is known to be exact,
2043 then C<*exact> is set to C<1>.
2045 =item * Reaching path lengths
2047 __isl_give isl_map *isl_map_reaching_path_lengths(
2048 __isl_take isl_map *map, int *exact);
2050 Compute a relation that maps each element in the range of C<map>
2051 to the lengths of all paths composed of edges in C<map> that
2052 end up in the given element.
2053 The result may be an overapproximation. If the result is known to be exact,
2054 then C<*exact> is set to C<1>.
2055 To compute the I<maximal> path length, the resulting relation
2056 should be postprocessed by C<isl_map_lexmax>.
2057 In particular, if the input relation is a dependence relation
2058 (mapping sources to sinks), then the maximal path length corresponds
2059 to the free schedule.
2060 Note, however, that C<isl_map_lexmax> expects the maximum to be
2061 finite, so if the path lengths are unbounded (possibly due to
2062 the overapproximation), then you will get an error message.
2066 __isl_give isl_basic_set *isl_basic_map_wrap(
2067 __isl_take isl_basic_map *bmap);
2068 __isl_give isl_set *isl_map_wrap(
2069 __isl_take isl_map *map);
2070 __isl_give isl_union_set *isl_union_map_wrap(
2071 __isl_take isl_union_map *umap);
2072 __isl_give isl_basic_map *isl_basic_set_unwrap(
2073 __isl_take isl_basic_set *bset);
2074 __isl_give isl_map *isl_set_unwrap(
2075 __isl_take isl_set *set);
2076 __isl_give isl_union_map *isl_union_set_unwrap(
2077 __isl_take isl_union_set *uset);
2081 Remove any internal structure of domain (and range) of the given
2082 set or relation. If there is any such internal structure in the input,
2083 then the name of the space is also removed.
2085 __isl_give isl_basic_set *isl_basic_set_flatten(
2086 __isl_take isl_basic_set *bset);
2087 __isl_give isl_set *isl_set_flatten(
2088 __isl_take isl_set *set);
2089 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2090 __isl_take isl_basic_map *bmap);
2091 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2092 __isl_take isl_basic_map *bmap);
2093 __isl_give isl_map *isl_map_flatten_range(
2094 __isl_take isl_map *map);
2095 __isl_give isl_map *isl_map_flatten_domain(
2096 __isl_take isl_map *map);
2097 __isl_give isl_basic_map *isl_basic_map_flatten(
2098 __isl_take isl_basic_map *bmap);
2099 __isl_give isl_map *isl_map_flatten(
2100 __isl_take isl_map *map);
2102 __isl_give isl_map *isl_set_flatten_map(
2103 __isl_take isl_set *set);
2105 The function above constructs a relation
2106 that maps the input set to a flattened version of the set.
2110 Lift the input set to a space with extra dimensions corresponding
2111 to the existentially quantified variables in the input.
2112 In particular, the result lives in a wrapped map where the domain
2113 is the original space and the range corresponds to the original
2114 existentially quantified variables.
2116 __isl_give isl_basic_set *isl_basic_set_lift(
2117 __isl_take isl_basic_set *bset);
2118 __isl_give isl_set *isl_set_lift(
2119 __isl_take isl_set *set);
2120 __isl_give isl_union_set *isl_union_set_lift(
2121 __isl_take isl_union_set *uset);
2123 Given a local space that contains the existentially quantified
2124 variables of a set, a basic relation that, when applied to
2125 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2126 can be constructed using the following function.
2128 #include <isl/local_space.h>
2129 __isl_give isl_basic_map *isl_local_space_lifting(
2130 __isl_take isl_local_space *ls);
2132 =item * Internal Product
2134 __isl_give isl_basic_map *isl_basic_map_zip(
2135 __isl_take isl_basic_map *bmap);
2136 __isl_give isl_map *isl_map_zip(
2137 __isl_take isl_map *map);
2138 __isl_give isl_union_map *isl_union_map_zip(
2139 __isl_take isl_union_map *umap);
2141 Given a relation with nested relations for domain and range,
2142 interchange the range of the domain with the domain of the range.
2144 =item * Aligning parameters
2146 __isl_give isl_set *isl_set_align_params(
2147 __isl_take isl_set *set,
2148 __isl_take isl_space *model);
2149 __isl_give isl_map *isl_map_align_params(
2150 __isl_take isl_map *map,
2151 __isl_take isl_space *model);
2153 Change the order of the parameters of the given set or relation
2154 such that the first parameters match those of C<model>.
2155 This may involve the introduction of extra parameters.
2156 All parameters need to be named.
2158 =item * Dimension manipulation
2160 __isl_give isl_set *isl_set_add_dims(
2161 __isl_take isl_set *set,
2162 enum isl_dim_type type, unsigned n);
2163 __isl_give isl_map *isl_map_add_dims(
2164 __isl_take isl_map *map,
2165 enum isl_dim_type type, unsigned n);
2166 __isl_give isl_set *isl_set_insert_dims(
2167 __isl_take isl_set *set,
2168 enum isl_dim_type type, unsigned pos, unsigned n);
2169 __isl_give isl_map *isl_map_insert_dims(
2170 __isl_take isl_map *map,
2171 enum isl_dim_type type, unsigned pos, unsigned n);
2172 __isl_give isl_basic_set *isl_basic_set_move_dims(
2173 __isl_take isl_basic_set *bset,
2174 enum isl_dim_type dst_type, unsigned dst_pos,
2175 enum isl_dim_type src_type, unsigned src_pos,
2177 __isl_give isl_basic_map *isl_basic_map_move_dims(
2178 __isl_take isl_basic_map *bmap,
2179 enum isl_dim_type dst_type, unsigned dst_pos,
2180 enum isl_dim_type src_type, unsigned src_pos,
2182 __isl_give isl_set *isl_set_move_dims(
2183 __isl_take isl_set *set,
2184 enum isl_dim_type dst_type, unsigned dst_pos,
2185 enum isl_dim_type src_type, unsigned src_pos,
2187 __isl_give isl_map *isl_map_move_dims(
2188 __isl_take isl_map *map,
2189 enum isl_dim_type dst_type, unsigned dst_pos,
2190 enum isl_dim_type src_type, unsigned src_pos,
2193 It is usually not advisable to directly change the (input or output)
2194 space of a set or a relation as this removes the name and the internal
2195 structure of the space. However, the above functions can be useful
2196 to add new parameters, assuming
2197 C<isl_set_align_params> and C<isl_map_align_params>
2202 =head2 Binary Operations
2204 The two arguments of a binary operation not only need to live
2205 in the same C<isl_ctx>, they currently also need to have
2206 the same (number of) parameters.
2208 =head3 Basic Operations
2212 =item * Intersection
2214 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2215 __isl_take isl_basic_set *bset1,
2216 __isl_take isl_basic_set *bset2);
2217 __isl_give isl_basic_set *isl_basic_set_intersect(
2218 __isl_take isl_basic_set *bset1,
2219 __isl_take isl_basic_set *bset2);
2220 __isl_give isl_set *isl_set_intersect_params(
2221 __isl_take isl_set *set,
2222 __isl_take isl_set *params);
2223 __isl_give isl_set *isl_set_intersect(
2224 __isl_take isl_set *set1,
2225 __isl_take isl_set *set2);
2226 __isl_give isl_union_set *isl_union_set_intersect_params(
2227 __isl_take isl_union_set *uset,
2228 __isl_take isl_set *set);
2229 __isl_give isl_union_map *isl_union_map_intersect_params(
2230 __isl_take isl_union_map *umap,
2231 __isl_take isl_set *set);
2232 __isl_give isl_union_set *isl_union_set_intersect(
2233 __isl_take isl_union_set *uset1,
2234 __isl_take isl_union_set *uset2);
2235 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2236 __isl_take isl_basic_map *bmap,
2237 __isl_take isl_basic_set *bset);
2238 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2239 __isl_take isl_basic_map *bmap,
2240 __isl_take isl_basic_set *bset);
2241 __isl_give isl_basic_map *isl_basic_map_intersect(
2242 __isl_take isl_basic_map *bmap1,
2243 __isl_take isl_basic_map *bmap2);
2244 __isl_give isl_map *isl_map_intersect_params(
2245 __isl_take isl_map *map,
2246 __isl_take isl_set *params);
2247 __isl_give isl_map *isl_map_intersect_domain(
2248 __isl_take isl_map *map,
2249 __isl_take isl_set *set);
2250 __isl_give isl_map *isl_map_intersect_range(
2251 __isl_take isl_map *map,
2252 __isl_take isl_set *set);
2253 __isl_give isl_map *isl_map_intersect(
2254 __isl_take isl_map *map1,
2255 __isl_take isl_map *map2);
2256 __isl_give isl_union_map *isl_union_map_intersect_domain(
2257 __isl_take isl_union_map *umap,
2258 __isl_take isl_union_set *uset);
2259 __isl_give isl_union_map *isl_union_map_intersect_range(
2260 __isl_take isl_union_map *umap,
2261 __isl_take isl_union_set *uset);
2262 __isl_give isl_union_map *isl_union_map_intersect(
2263 __isl_take isl_union_map *umap1,
2264 __isl_take isl_union_map *umap2);
2268 __isl_give isl_set *isl_basic_set_union(
2269 __isl_take isl_basic_set *bset1,
2270 __isl_take isl_basic_set *bset2);
2271 __isl_give isl_map *isl_basic_map_union(
2272 __isl_take isl_basic_map *bmap1,
2273 __isl_take isl_basic_map *bmap2);
2274 __isl_give isl_set *isl_set_union(
2275 __isl_take isl_set *set1,
2276 __isl_take isl_set *set2);
2277 __isl_give isl_map *isl_map_union(
2278 __isl_take isl_map *map1,
2279 __isl_take isl_map *map2);
2280 __isl_give isl_union_set *isl_union_set_union(
2281 __isl_take isl_union_set *uset1,
2282 __isl_take isl_union_set *uset2);
2283 __isl_give isl_union_map *isl_union_map_union(
2284 __isl_take isl_union_map *umap1,
2285 __isl_take isl_union_map *umap2);
2287 =item * Set difference
2289 __isl_give isl_set *isl_set_subtract(
2290 __isl_take isl_set *set1,
2291 __isl_take isl_set *set2);
2292 __isl_give isl_map *isl_map_subtract(
2293 __isl_take isl_map *map1,
2294 __isl_take isl_map *map2);
2295 __isl_give isl_map *isl_map_subtract_domain(
2296 __isl_take isl_map *map,
2297 __isl_take isl_set *dom);
2298 __isl_give isl_map *isl_map_subtract_range(
2299 __isl_take isl_map *map,
2300 __isl_take isl_set *dom);
2301 __isl_give isl_union_set *isl_union_set_subtract(
2302 __isl_take isl_union_set *uset1,
2303 __isl_take isl_union_set *uset2);
2304 __isl_give isl_union_map *isl_union_map_subtract(
2305 __isl_take isl_union_map *umap1,
2306 __isl_take isl_union_map *umap2);
2310 __isl_give isl_basic_set *isl_basic_set_apply(
2311 __isl_take isl_basic_set *bset,
2312 __isl_take isl_basic_map *bmap);
2313 __isl_give isl_set *isl_set_apply(
2314 __isl_take isl_set *set,
2315 __isl_take isl_map *map);
2316 __isl_give isl_union_set *isl_union_set_apply(
2317 __isl_take isl_union_set *uset,
2318 __isl_take isl_union_map *umap);
2319 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2320 __isl_take isl_basic_map *bmap1,
2321 __isl_take isl_basic_map *bmap2);
2322 __isl_give isl_basic_map *isl_basic_map_apply_range(
2323 __isl_take isl_basic_map *bmap1,
2324 __isl_take isl_basic_map *bmap2);
2325 __isl_give isl_map *isl_map_apply_domain(
2326 __isl_take isl_map *map1,
2327 __isl_take isl_map *map2);
2328 __isl_give isl_union_map *isl_union_map_apply_domain(
2329 __isl_take isl_union_map *umap1,
2330 __isl_take isl_union_map *umap2);
2331 __isl_give isl_map *isl_map_apply_range(
2332 __isl_take isl_map *map1,
2333 __isl_take isl_map *map2);
2334 __isl_give isl_union_map *isl_union_map_apply_range(
2335 __isl_take isl_union_map *umap1,
2336 __isl_take isl_union_map *umap2);
2338 =item * Cartesian Product
2340 __isl_give isl_set *isl_set_product(
2341 __isl_take isl_set *set1,
2342 __isl_take isl_set *set2);
2343 __isl_give isl_union_set *isl_union_set_product(
2344 __isl_take isl_union_set *uset1,
2345 __isl_take isl_union_set *uset2);
2346 __isl_give isl_basic_map *isl_basic_map_domain_product(
2347 __isl_take isl_basic_map *bmap1,
2348 __isl_take isl_basic_map *bmap2);
2349 __isl_give isl_basic_map *isl_basic_map_range_product(
2350 __isl_take isl_basic_map *bmap1,
2351 __isl_take isl_basic_map *bmap2);
2352 __isl_give isl_map *isl_map_domain_product(
2353 __isl_take isl_map *map1,
2354 __isl_take isl_map *map2);
2355 __isl_give isl_map *isl_map_range_product(
2356 __isl_take isl_map *map1,
2357 __isl_take isl_map *map2);
2358 __isl_give isl_union_map *isl_union_map_range_product(
2359 __isl_take isl_union_map *umap1,
2360 __isl_take isl_union_map *umap2);
2361 __isl_give isl_map *isl_map_product(
2362 __isl_take isl_map *map1,
2363 __isl_take isl_map *map2);
2364 __isl_give isl_union_map *isl_union_map_product(
2365 __isl_take isl_union_map *umap1,
2366 __isl_take isl_union_map *umap2);
2368 The above functions compute the cross product of the given
2369 sets or relations. The domains and ranges of the results
2370 are wrapped maps between domains and ranges of the inputs.
2371 To obtain a ``flat'' product, use the following functions
2374 __isl_give isl_basic_set *isl_basic_set_flat_product(
2375 __isl_take isl_basic_set *bset1,
2376 __isl_take isl_basic_set *bset2);
2377 __isl_give isl_set *isl_set_flat_product(
2378 __isl_take isl_set *set1,
2379 __isl_take isl_set *set2);
2380 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2381 __isl_take isl_basic_map *bmap1,
2382 __isl_take isl_basic_map *bmap2);
2383 __isl_give isl_map *isl_map_flat_domain_product(
2384 __isl_take isl_map *map1,
2385 __isl_take isl_map *map2);
2386 __isl_give isl_map *isl_map_flat_range_product(
2387 __isl_take isl_map *map1,
2388 __isl_take isl_map *map2);
2389 __isl_give isl_union_map *isl_union_map_flat_range_product(
2390 __isl_take isl_union_map *umap1,
2391 __isl_take isl_union_map *umap2);
2392 __isl_give isl_basic_map *isl_basic_map_flat_product(
2393 __isl_take isl_basic_map *bmap1,
2394 __isl_take isl_basic_map *bmap2);
2395 __isl_give isl_map *isl_map_flat_product(
2396 __isl_take isl_map *map1,
2397 __isl_take isl_map *map2);
2399 =item * Simplification
2401 __isl_give isl_basic_set *isl_basic_set_gist(
2402 __isl_take isl_basic_set *bset,
2403 __isl_take isl_basic_set *context);
2404 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2405 __isl_take isl_set *context);
2406 __isl_give isl_set *isl_set_gist_params(
2407 __isl_take isl_set *set,
2408 __isl_take isl_set *context);
2409 __isl_give isl_union_set *isl_union_set_gist(
2410 __isl_take isl_union_set *uset,
2411 __isl_take isl_union_set *context);
2412 __isl_give isl_union_set *isl_union_set_gist_params(
2413 __isl_take isl_union_set *uset,
2414 __isl_take isl_set *set);
2415 __isl_give isl_basic_map *isl_basic_map_gist(
2416 __isl_take isl_basic_map *bmap,
2417 __isl_take isl_basic_map *context);
2418 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2419 __isl_take isl_map *context);
2420 __isl_give isl_map *isl_map_gist_params(
2421 __isl_take isl_map *map,
2422 __isl_take isl_set *context);
2423 __isl_give isl_map *isl_map_gist_domain(
2424 __isl_take isl_map *map,
2425 __isl_take isl_set *context);
2426 __isl_give isl_map *isl_map_gist_range(
2427 __isl_take isl_map *map,
2428 __isl_take isl_set *context);
2429 __isl_give isl_union_map *isl_union_map_gist(
2430 __isl_take isl_union_map *umap,
2431 __isl_take isl_union_map *context);
2432 __isl_give isl_union_map *isl_union_map_gist_params(
2433 __isl_take isl_union_map *umap,
2434 __isl_take isl_set *set);
2435 __isl_give isl_union_map *isl_union_map_gist_domain(
2436 __isl_take isl_union_map *umap,
2437 __isl_take isl_union_set *uset);
2439 The gist operation returns a set or relation that has the
2440 same intersection with the context as the input set or relation.
2441 Any implicit equality in the intersection is made explicit in the result,
2442 while all inequalities that are redundant with respect to the intersection
2444 In case of union sets and relations, the gist operation is performed
2449 =head3 Lexicographic Optimization
2451 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2452 the following functions
2453 compute a set that contains the lexicographic minimum or maximum
2454 of the elements in C<set> (or C<bset>) for those values of the parameters
2455 that satisfy C<dom>.
2456 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2457 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2459 In other words, the union of the parameter values
2460 for which the result is non-empty and of C<*empty>
2463 __isl_give isl_set *isl_basic_set_partial_lexmin(
2464 __isl_take isl_basic_set *bset,
2465 __isl_take isl_basic_set *dom,
2466 __isl_give isl_set **empty);
2467 __isl_give isl_set *isl_basic_set_partial_lexmax(
2468 __isl_take isl_basic_set *bset,
2469 __isl_take isl_basic_set *dom,
2470 __isl_give isl_set **empty);
2471 __isl_give isl_set *isl_set_partial_lexmin(
2472 __isl_take isl_set *set, __isl_take isl_set *dom,
2473 __isl_give isl_set **empty);
2474 __isl_give isl_set *isl_set_partial_lexmax(
2475 __isl_take isl_set *set, __isl_take isl_set *dom,
2476 __isl_give isl_set **empty);
2478 Given a (basic) set C<set> (or C<bset>), the following functions simply
2479 return a set containing the lexicographic minimum or maximum
2480 of the elements in C<set> (or C<bset>).
2481 In case of union sets, the optimum is computed per space.
2483 __isl_give isl_set *isl_basic_set_lexmin(
2484 __isl_take isl_basic_set *bset);
2485 __isl_give isl_set *isl_basic_set_lexmax(
2486 __isl_take isl_basic_set *bset);
2487 __isl_give isl_set *isl_set_lexmin(
2488 __isl_take isl_set *set);
2489 __isl_give isl_set *isl_set_lexmax(
2490 __isl_take isl_set *set);
2491 __isl_give isl_union_set *isl_union_set_lexmin(
2492 __isl_take isl_union_set *uset);
2493 __isl_give isl_union_set *isl_union_set_lexmax(
2494 __isl_take isl_union_set *uset);
2496 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2497 the following functions
2498 compute a relation that maps each element of C<dom>
2499 to the single lexicographic minimum or maximum
2500 of the elements that are associated to that same
2501 element in C<map> (or C<bmap>).
2502 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2503 that contains the elements in C<dom> that do not map
2504 to any elements in C<map> (or C<bmap>).
2505 In other words, the union of the domain of the result and of C<*empty>
2508 __isl_give isl_map *isl_basic_map_partial_lexmax(
2509 __isl_take isl_basic_map *bmap,
2510 __isl_take isl_basic_set *dom,
2511 __isl_give isl_set **empty);
2512 __isl_give isl_map *isl_basic_map_partial_lexmin(
2513 __isl_take isl_basic_map *bmap,
2514 __isl_take isl_basic_set *dom,
2515 __isl_give isl_set **empty);
2516 __isl_give isl_map *isl_map_partial_lexmax(
2517 __isl_take isl_map *map, __isl_take isl_set *dom,
2518 __isl_give isl_set **empty);
2519 __isl_give isl_map *isl_map_partial_lexmin(
2520 __isl_take isl_map *map, __isl_take isl_set *dom,
2521 __isl_give isl_set **empty);
2523 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2524 return a map mapping each element in the domain of
2525 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2526 of all elements associated to that element.
2527 In case of union relations, the optimum is computed per space.
2529 __isl_give isl_map *isl_basic_map_lexmin(
2530 __isl_take isl_basic_map *bmap);
2531 __isl_give isl_map *isl_basic_map_lexmax(
2532 __isl_take isl_basic_map *bmap);
2533 __isl_give isl_map *isl_map_lexmin(
2534 __isl_take isl_map *map);
2535 __isl_give isl_map *isl_map_lexmax(
2536 __isl_take isl_map *map);
2537 __isl_give isl_union_map *isl_union_map_lexmin(
2538 __isl_take isl_union_map *umap);
2539 __isl_give isl_union_map *isl_union_map_lexmax(
2540 __isl_take isl_union_map *umap);
2542 The following functions return their result in the form of
2543 a piecewise multi-affine expression
2544 (See L<"Piecewise Multiple Quasi Affine Expressions">),
2545 but are otherwise equivalent to the corresponding functions
2546 returning a basic set or relation.
2548 __isl_give isl_pw_multi_aff *
2549 isl_basic_map_lexmin_pw_multi_aff(
2550 __isl_take isl_basic_map *bmap);
2551 __isl_give isl_pw_multi_aff *
2552 isl_basic_set_partial_lexmin_pw_multi_aff(
2553 __isl_take isl_basic_set *bset,
2554 __isl_take isl_basic_set *dom,
2555 __isl_give isl_set **empty);
2556 __isl_give isl_pw_multi_aff *
2557 isl_basic_set_partial_lexmax_pw_multi_aff(
2558 __isl_take isl_basic_set *bset,
2559 __isl_take isl_basic_set *dom,
2560 __isl_give isl_set **empty);
2561 __isl_give isl_pw_multi_aff *
2562 isl_basic_map_partial_lexmin_pw_multi_aff(
2563 __isl_take isl_basic_map *bmap,
2564 __isl_take isl_basic_set *dom,
2565 __isl_give isl_set **empty);
2566 __isl_give isl_pw_multi_aff *
2567 isl_basic_map_partial_lexmax_pw_multi_aff(
2568 __isl_take isl_basic_map *bmap,
2569 __isl_take isl_basic_set *dom,
2570 __isl_give isl_set **empty);
2574 Lists are defined over several element types, including
2575 C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2576 Here we take lists of C<isl_set>s as an example.
2577 Lists can be created, copied and freed using the following functions.
2579 #include <isl/list.h>
2580 __isl_give isl_set_list *isl_set_list_from_set(
2581 __isl_take isl_set *el);
2582 __isl_give isl_set_list *isl_set_list_alloc(
2583 isl_ctx *ctx, int n);
2584 __isl_give isl_set_list *isl_set_list_copy(
2585 __isl_keep isl_set_list *list);
2586 __isl_give isl_set_list *isl_set_list_add(
2587 __isl_take isl_set_list *list,
2588 __isl_take isl_set *el);
2589 __isl_give isl_set_list *isl_set_list_concat(
2590 __isl_take isl_set_list *list1,
2591 __isl_take isl_set_list *list2);
2592 void *isl_set_list_free(__isl_take isl_set_list *list);
2594 C<isl_set_list_alloc> creates an empty list with a capacity for
2595 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2598 Lists can be inspected using the following functions.
2600 #include <isl/list.h>
2601 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2602 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2603 __isl_give isl_set *isl_set_list_get_set(
2604 __isl_keep isl_set_list *list, int index);
2605 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2606 int (*fn)(__isl_take isl_set *el, void *user),
2609 Lists can be printed using
2611 #include <isl/list.h>
2612 __isl_give isl_printer *isl_printer_print_set_list(
2613 __isl_take isl_printer *p,
2614 __isl_keep isl_set_list *list);
2618 Matrices can be created, copied and freed using the following functions.
2620 #include <isl/mat.h>
2621 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2622 unsigned n_row, unsigned n_col);
2623 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2624 void isl_mat_free(__isl_take isl_mat *mat);
2626 Note that the elements of a newly created matrix may have arbitrary values.
2627 The elements can be changed and inspected using the following functions.
2629 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2630 int isl_mat_rows(__isl_keep isl_mat *mat);
2631 int isl_mat_cols(__isl_keep isl_mat *mat);
2632 int isl_mat_get_element(__isl_keep isl_mat *mat,
2633 int row, int col, isl_int *v);
2634 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2635 int row, int col, isl_int v);
2636 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2637 int row, int col, int v);
2639 C<isl_mat_get_element> will return a negative value if anything went wrong.
2640 In that case, the value of C<*v> is undefined.
2642 The following function can be used to compute the (right) inverse
2643 of a matrix, i.e., a matrix such that the product of the original
2644 and the inverse (in that order) is a multiple of the identity matrix.
2645 The input matrix is assumed to be of full row-rank.
2647 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2649 The following function can be used to compute the (right) kernel
2650 (or null space) of a matrix, i.e., a matrix such that the product of
2651 the original and the kernel (in that order) is the zero matrix.
2653 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2655 =head2 Piecewise Quasi Affine Expressions
2657 The zero quasi affine expression on a given domain can be created using
2659 __isl_give isl_aff *isl_aff_zero_on_domain(
2660 __isl_take isl_local_space *ls);
2662 Note that the space in which the resulting object lives is a map space
2663 with the given space as domain and a one-dimensional range.
2665 An empty piecewise quasi affine expression (one with no cells)
2666 or a piecewise quasi affine expression with a single cell can
2667 be created using the following functions.
2669 #include <isl/aff.h>
2670 __isl_give isl_pw_aff *isl_pw_aff_empty(
2671 __isl_take isl_space *space);
2672 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2673 __isl_take isl_set *set, __isl_take isl_aff *aff);
2674 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2675 __isl_take isl_aff *aff);
2677 Quasi affine expressions can be copied and freed using
2679 #include <isl/aff.h>
2680 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2681 void *isl_aff_free(__isl_take isl_aff *aff);
2683 __isl_give isl_pw_aff *isl_pw_aff_copy(
2684 __isl_keep isl_pw_aff *pwaff);
2685 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2687 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2688 using the following function. The constraint is required to have
2689 a non-zero coefficient for the specified dimension.
2691 #include <isl/constraint.h>
2692 __isl_give isl_aff *isl_constraint_get_bound(
2693 __isl_keep isl_constraint *constraint,
2694 enum isl_dim_type type, int pos);
2696 The entire affine expression of the constraint can also be extracted
2697 using the following function.
2699 #include <isl/constraint.h>
2700 __isl_give isl_aff *isl_constraint_get_aff(
2701 __isl_keep isl_constraint *constraint);
2703 Conversely, an equality constraint equating
2704 the affine expression to zero or an inequality constraint enforcing
2705 the affine expression to be non-negative, can be constructed using
2707 __isl_give isl_constraint *isl_equality_from_aff(
2708 __isl_take isl_aff *aff);
2709 __isl_give isl_constraint *isl_inequality_from_aff(
2710 __isl_take isl_aff *aff);
2712 The expression can be inspected using
2714 #include <isl/aff.h>
2715 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2716 int isl_aff_dim(__isl_keep isl_aff *aff,
2717 enum isl_dim_type type);
2718 __isl_give isl_local_space *isl_aff_get_domain_local_space(
2719 __isl_keep isl_aff *aff);
2720 __isl_give isl_local_space *isl_aff_get_local_space(
2721 __isl_keep isl_aff *aff);
2722 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2723 enum isl_dim_type type, unsigned pos);
2724 const char *isl_pw_aff_get_dim_name(
2725 __isl_keep isl_pw_aff *pa,
2726 enum isl_dim_type type, unsigned pos);
2727 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
2728 enum isl_dim_type type, unsigned pos);
2729 __isl_give isl_id *isl_pw_aff_get_dim_id(
2730 __isl_keep isl_pw_aff *pa,
2731 enum isl_dim_type type, unsigned pos);
2732 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2734 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2735 enum isl_dim_type type, int pos, isl_int *v);
2736 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2738 __isl_give isl_aff *isl_aff_get_div(
2739 __isl_keep isl_aff *aff, int pos);
2741 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2742 int (*fn)(__isl_take isl_set *set,
2743 __isl_take isl_aff *aff,
2744 void *user), void *user);
2746 int isl_aff_is_cst(__isl_keep isl_aff *aff);
2747 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
2749 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
2750 enum isl_dim_type type, unsigned first, unsigned n);
2751 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
2752 enum isl_dim_type type, unsigned first, unsigned n);
2754 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2755 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2756 enum isl_dim_type type);
2757 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2759 It can be modified using
2761 #include <isl/aff.h>
2762 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
2763 __isl_take isl_pw_aff *pwaff,
2764 enum isl_dim_type type, __isl_take isl_id *id);
2765 __isl_give isl_aff *isl_aff_set_dim_name(
2766 __isl_take isl_aff *aff, enum isl_dim_type type,
2767 unsigned pos, const char *s);
2768 __isl_give isl_aff *isl_aff_set_dim_id(
2769 __isl_take isl_aff *aff, enum isl_dim_type type,
2770 unsigned pos, __isl_take isl_id *id);
2771 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
2772 __isl_take isl_pw_aff *pma,
2773 enum isl_dim_type type, unsigned pos,
2774 __isl_take isl_id *id);
2775 __isl_give isl_aff *isl_aff_set_constant(
2776 __isl_take isl_aff *aff, isl_int v);
2777 __isl_give isl_aff *isl_aff_set_constant_si(
2778 __isl_take isl_aff *aff, int v);
2779 __isl_give isl_aff *isl_aff_set_coefficient(
2780 __isl_take isl_aff *aff,
2781 enum isl_dim_type type, int pos, isl_int v);
2782 __isl_give isl_aff *isl_aff_set_coefficient_si(
2783 __isl_take isl_aff *aff,
2784 enum isl_dim_type type, int pos, int v);
2785 __isl_give isl_aff *isl_aff_set_denominator(
2786 __isl_take isl_aff *aff, isl_int v);
2788 __isl_give isl_aff *isl_aff_add_constant(
2789 __isl_take isl_aff *aff, isl_int v);
2790 __isl_give isl_aff *isl_aff_add_constant_si(
2791 __isl_take isl_aff *aff, int v);
2792 __isl_give isl_aff *isl_aff_add_coefficient(
2793 __isl_take isl_aff *aff,
2794 enum isl_dim_type type, int pos, isl_int v);
2795 __isl_give isl_aff *isl_aff_add_coefficient_si(
2796 __isl_take isl_aff *aff,
2797 enum isl_dim_type type, int pos, int v);
2799 __isl_give isl_aff *isl_aff_insert_dims(
2800 __isl_take isl_aff *aff,
2801 enum isl_dim_type type, unsigned first, unsigned n);
2802 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
2803 __isl_take isl_pw_aff *pwaff,
2804 enum isl_dim_type type, unsigned first, unsigned n);
2805 __isl_give isl_aff *isl_aff_add_dims(
2806 __isl_take isl_aff *aff,
2807 enum isl_dim_type type, unsigned n);
2808 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
2809 __isl_take isl_pw_aff *pwaff,
2810 enum isl_dim_type type, unsigned n);
2811 __isl_give isl_aff *isl_aff_drop_dims(
2812 __isl_take isl_aff *aff,
2813 enum isl_dim_type type, unsigned first, unsigned n);
2814 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
2815 __isl_take isl_pw_aff *pwaff,
2816 enum isl_dim_type type, unsigned first, unsigned n);
2818 Note that the C<set_constant> and C<set_coefficient> functions
2819 set the I<numerator> of the constant or coefficient, while
2820 C<add_constant> and C<add_coefficient> add an integer value to
2821 the possibly rational constant or coefficient.
2823 To check whether an affine expressions is obviously zero
2824 or obviously equal to some other affine expression, use
2826 #include <isl/aff.h>
2827 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
2828 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
2829 __isl_keep isl_aff *aff2);
2830 int isl_pw_aff_plain_is_equal(
2831 __isl_keep isl_pw_aff *pwaff1,
2832 __isl_keep isl_pw_aff *pwaff2);
2836 #include <isl/aff.h>
2837 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2838 __isl_take isl_aff *aff2);
2839 __isl_give isl_pw_aff *isl_pw_aff_add(
2840 __isl_take isl_pw_aff *pwaff1,
2841 __isl_take isl_pw_aff *pwaff2);
2842 __isl_give isl_pw_aff *isl_pw_aff_min(
2843 __isl_take isl_pw_aff *pwaff1,
2844 __isl_take isl_pw_aff *pwaff2);
2845 __isl_give isl_pw_aff *isl_pw_aff_max(
2846 __isl_take isl_pw_aff *pwaff1,
2847 __isl_take isl_pw_aff *pwaff2);
2848 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2849 __isl_take isl_aff *aff2);
2850 __isl_give isl_pw_aff *isl_pw_aff_sub(
2851 __isl_take isl_pw_aff *pwaff1,
2852 __isl_take isl_pw_aff *pwaff2);
2853 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2854 __isl_give isl_pw_aff *isl_pw_aff_neg(
2855 __isl_take isl_pw_aff *pwaff);
2856 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2857 __isl_give isl_pw_aff *isl_pw_aff_ceil(
2858 __isl_take isl_pw_aff *pwaff);
2859 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
2860 __isl_give isl_pw_aff *isl_pw_aff_floor(
2861 __isl_take isl_pw_aff *pwaff);
2862 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
2864 __isl_give isl_pw_aff *isl_pw_aff_mod(
2865 __isl_take isl_pw_aff *pwaff, isl_int mod);
2866 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2868 __isl_give isl_pw_aff *isl_pw_aff_scale(
2869 __isl_take isl_pw_aff *pwaff, isl_int f);
2870 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2872 __isl_give isl_aff *isl_aff_scale_down_ui(
2873 __isl_take isl_aff *aff, unsigned f);
2874 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
2875 __isl_take isl_pw_aff *pwaff, isl_int f);
2877 __isl_give isl_pw_aff *isl_pw_aff_list_min(
2878 __isl_take isl_pw_aff_list *list);
2879 __isl_give isl_pw_aff *isl_pw_aff_list_max(
2880 __isl_take isl_pw_aff_list *list);
2882 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
2883 __isl_take isl_pw_aff *pwqp);
2885 __isl_give isl_pw_aff *isl_pw_aff_align_params(
2886 __isl_take isl_pw_aff *pwaff,
2887 __isl_take isl_space *model);
2889 __isl_give isl_aff *isl_aff_gist_params(
2890 __isl_take isl_aff *aff,
2891 __isl_take isl_set *context);
2892 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
2893 __isl_take isl_set *context);
2894 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
2895 __isl_take isl_pw_aff *pwaff,
2896 __isl_take isl_set *context);
2897 __isl_give isl_pw_aff *isl_pw_aff_gist(
2898 __isl_take isl_pw_aff *pwaff,
2899 __isl_take isl_set *context);
2901 __isl_give isl_set *isl_pw_aff_domain(
2902 __isl_take isl_pw_aff *pwaff);
2903 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
2904 __isl_take isl_pw_aff *pa,
2905 __isl_take isl_set *set);
2906 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
2907 __isl_take isl_pw_aff *pa,
2908 __isl_take isl_set *set);
2910 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
2911 __isl_take isl_aff *aff2);
2912 __isl_give isl_pw_aff *isl_pw_aff_mul(
2913 __isl_take isl_pw_aff *pwaff1,
2914 __isl_take isl_pw_aff *pwaff2);
2916 When multiplying two affine expressions, at least one of the two needs
2919 #include <isl/aff.h>
2920 __isl_give isl_basic_set *isl_aff_le_basic_set(
2921 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2922 __isl_give isl_basic_set *isl_aff_ge_basic_set(
2923 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2924 __isl_give isl_set *isl_pw_aff_eq_set(
2925 __isl_take isl_pw_aff *pwaff1,
2926 __isl_take isl_pw_aff *pwaff2);
2927 __isl_give isl_set *isl_pw_aff_ne_set(
2928 __isl_take isl_pw_aff *pwaff1,
2929 __isl_take isl_pw_aff *pwaff2);
2930 __isl_give isl_set *isl_pw_aff_le_set(
2931 __isl_take isl_pw_aff *pwaff1,
2932 __isl_take isl_pw_aff *pwaff2);
2933 __isl_give isl_set *isl_pw_aff_lt_set(
2934 __isl_take isl_pw_aff *pwaff1,
2935 __isl_take isl_pw_aff *pwaff2);
2936 __isl_give isl_set *isl_pw_aff_ge_set(
2937 __isl_take isl_pw_aff *pwaff1,
2938 __isl_take isl_pw_aff *pwaff2);
2939 __isl_give isl_set *isl_pw_aff_gt_set(
2940 __isl_take isl_pw_aff *pwaff1,
2941 __isl_take isl_pw_aff *pwaff2);
2943 __isl_give isl_set *isl_pw_aff_list_eq_set(
2944 __isl_take isl_pw_aff_list *list1,
2945 __isl_take isl_pw_aff_list *list2);
2946 __isl_give isl_set *isl_pw_aff_list_ne_set(
2947 __isl_take isl_pw_aff_list *list1,
2948 __isl_take isl_pw_aff_list *list2);
2949 __isl_give isl_set *isl_pw_aff_list_le_set(
2950 __isl_take isl_pw_aff_list *list1,
2951 __isl_take isl_pw_aff_list *list2);
2952 __isl_give isl_set *isl_pw_aff_list_lt_set(
2953 __isl_take isl_pw_aff_list *list1,
2954 __isl_take isl_pw_aff_list *list2);
2955 __isl_give isl_set *isl_pw_aff_list_ge_set(
2956 __isl_take isl_pw_aff_list *list1,
2957 __isl_take isl_pw_aff_list *list2);
2958 __isl_give isl_set *isl_pw_aff_list_gt_set(
2959 __isl_take isl_pw_aff_list *list1,
2960 __isl_take isl_pw_aff_list *list2);
2962 The function C<isl_aff_ge_basic_set> returns a basic set
2963 containing those elements in the shared space
2964 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
2965 The function C<isl_aff_ge_set> returns a set
2966 containing those elements in the shared domain
2967 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
2968 The functions operating on C<isl_pw_aff_list> apply the corresponding
2969 C<isl_pw_aff> function to each pair of elements in the two lists.
2971 #include <isl/aff.h>
2972 __isl_give isl_set *isl_pw_aff_nonneg_set(
2973 __isl_take isl_pw_aff *pwaff);
2974 __isl_give isl_set *isl_pw_aff_zero_set(
2975 __isl_take isl_pw_aff *pwaff);
2976 __isl_give isl_set *isl_pw_aff_non_zero_set(
2977 __isl_take isl_pw_aff *pwaff);
2979 The function C<isl_pw_aff_nonneg_set> returns a set
2980 containing those elements in the domain
2981 of C<pwaff> where C<pwaff> is non-negative.
2983 #include <isl/aff.h>
2984 __isl_give isl_pw_aff *isl_pw_aff_cond(
2985 __isl_take isl_set *cond,
2986 __isl_take isl_pw_aff *pwaff_true,
2987 __isl_take isl_pw_aff *pwaff_false);
2989 The function C<isl_pw_aff_cond> performs a conditional operator
2990 and returns an expression that is equal to C<pwaff_true>
2991 for elements in C<cond> and equal to C<pwaff_false> for elements
2994 #include <isl/aff.h>
2995 __isl_give isl_pw_aff *isl_pw_aff_union_min(
2996 __isl_take isl_pw_aff *pwaff1,
2997 __isl_take isl_pw_aff *pwaff2);
2998 __isl_give isl_pw_aff *isl_pw_aff_union_max(
2999 __isl_take isl_pw_aff *pwaff1,
3000 __isl_take isl_pw_aff *pwaff2);
3001 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3002 __isl_take isl_pw_aff *pwaff1,
3003 __isl_take isl_pw_aff *pwaff2);
3005 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3006 expression with a domain that is the union of those of C<pwaff1> and
3007 C<pwaff2> and such that on each cell, the quasi-affine expression is
3008 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3009 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3010 associated expression is the defined one.
3012 An expression can be read from input using
3014 #include <isl/aff.h>
3015 __isl_give isl_aff *isl_aff_read_from_str(
3016 isl_ctx *ctx, const char *str);
3017 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3018 isl_ctx *ctx, const char *str);
3020 An expression can be printed using
3022 #include <isl/aff.h>
3023 __isl_give isl_printer *isl_printer_print_aff(
3024 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3026 __isl_give isl_printer *isl_printer_print_pw_aff(
3027 __isl_take isl_printer *p,
3028 __isl_keep isl_pw_aff *pwaff);
3030 =head2 Piecewise Multiple Quasi Affine Expressions
3032 An C<isl_multi_aff> object represents a sequence of
3033 zero or more affine expressions, all defined on the same domain space.
3035 An C<isl_multi_aff> can be constructed from a C<isl_aff_list> using the
3038 #include <isl/aff.h>
3039 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3040 __isl_take isl_space *space,
3041 __isl_take isl_aff_list *list);
3043 An empty piecewise multiple quasi affine expression (one with no cells) or
3044 a piecewise multiple quasi affine expression with a single cell can
3045 be created using the following functions.
3047 #include <isl/aff.h>
3048 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3049 __isl_take isl_space *space);
3050 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3051 __isl_take isl_set *set,
3052 __isl_take isl_multi_aff *maff);
3054 A piecewise multiple quasi affine expression can also be initialized
3055 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3056 and the C<isl_map> is single-valued.
3058 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3059 __isl_take isl_set *set);
3060 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3061 __isl_take isl_map *map);
3063 Multiple quasi affine expressions can be copied and freed using
3065 #include <isl/aff.h>
3066 __isl_give isl_multi_aff *isl_multi_aff_copy(
3067 __isl_keep isl_multi_aff *maff);
3068 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
3070 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3071 __isl_keep isl_pw_multi_aff *pma);
3072 void *isl_pw_multi_aff_free(
3073 __isl_take isl_pw_multi_aff *pma);
3075 The expression can be inspected using
3077 #include <isl/aff.h>
3078 isl_ctx *isl_multi_aff_get_ctx(
3079 __isl_keep isl_multi_aff *maff);
3080 isl_ctx *isl_pw_multi_aff_get_ctx(
3081 __isl_keep isl_pw_multi_aff *pma);
3082 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
3083 enum isl_dim_type type);
3084 unsigned isl_pw_multi_aff_dim(
3085 __isl_keep isl_pw_multi_aff *pma,
3086 enum isl_dim_type type);
3087 __isl_give isl_aff *isl_multi_aff_get_aff(
3088 __isl_keep isl_multi_aff *multi, int pos);
3089 const char *isl_pw_multi_aff_get_dim_name(
3090 __isl_keep isl_pw_multi_aff *pma,
3091 enum isl_dim_type type, unsigned pos);
3092 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
3093 __isl_keep isl_pw_multi_aff *pma,
3094 enum isl_dim_type type, unsigned pos);
3095 const char *isl_multi_aff_get_tuple_name(
3096 __isl_keep isl_multi_aff *multi,
3097 enum isl_dim_type type);
3098 const char *isl_pw_multi_aff_get_tuple_name(
3099 __isl_keep isl_pw_multi_aff *pma,
3100 enum isl_dim_type type);
3101 int isl_pw_multi_aff_has_tuple_id(
3102 __isl_keep isl_pw_multi_aff *pma,
3103 enum isl_dim_type type);
3104 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
3105 __isl_keep isl_pw_multi_aff *pma,
3106 enum isl_dim_type type);
3108 int isl_pw_multi_aff_foreach_piece(
3109 __isl_keep isl_pw_multi_aff *pma,
3110 int (*fn)(__isl_take isl_set *set,
3111 __isl_take isl_multi_aff *maff,
3112 void *user), void *user);
3114 It can be modified using
3116 #include <isl/aff.h>
3117 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
3118 __isl_take isl_multi_aff *maff,
3119 enum isl_dim_type type, unsigned pos, const char *s);
3120 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
3121 __isl_take isl_pw_multi_aff *pma,
3122 enum isl_dim_type type, __isl_take isl_id *id);
3124 To check whether two multiple affine expressions are
3125 obviously equal to each other, use
3127 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
3128 __isl_keep isl_multi_aff *maff2);
3129 int isl_pw_multi_aff_plain_is_equal(
3130 __isl_keep isl_pw_multi_aff *pma1,
3131 __isl_keep isl_pw_multi_aff *pma2);
3135 #include <isl/aff.h>
3136 __isl_give isl_multi_aff *isl_multi_aff_add(
3137 __isl_take isl_multi_aff *maff1,
3138 __isl_take isl_multi_aff *maff2);
3139 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
3140 __isl_take isl_pw_multi_aff *pma1,
3141 __isl_take isl_pw_multi_aff *pma2);
3142 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
3143 __isl_take isl_pw_multi_aff *pma1,
3144 __isl_take isl_pw_multi_aff *pma2);
3145 __isl_give isl_multi_aff *isl_multi_aff_scale(
3146 __isl_take isl_multi_aff *maff,
3148 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
3149 __isl_take isl_pw_multi_aff *pma,
3150 __isl_take isl_set *set);
3151 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
3152 __isl_take isl_pw_multi_aff *pma,
3153 __isl_take isl_set *set);
3154 __isl_give isl_multi_aff *isl_multi_aff_lift(
3155 __isl_take isl_multi_aff *maff,
3156 __isl_give isl_local_space **ls);
3157 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
3158 __isl_take isl_multi_aff *maff,
3159 __isl_take isl_set *context);
3160 __isl_give isl_multi_aff *isl_multi_aff_gist(
3161 __isl_take isl_multi_aff *maff,
3162 __isl_take isl_set *context);
3163 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
3164 __isl_take isl_pw_multi_aff *pma,
3165 __isl_take isl_set *set);
3166 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
3167 __isl_take isl_pw_multi_aff *pma,
3168 __isl_take isl_set *set);
3170 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
3171 then it is assigned the local space that lies at the basis of
3172 the lifting applied.
3174 An expression can be read from input using
3176 #include <isl/aff.h>
3177 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3178 isl_ctx *ctx, const char *str);
3179 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3180 isl_ctx *ctx, const char *str);
3182 An expression can be printed using
3184 #include <isl/aff.h>
3185 __isl_give isl_printer *isl_printer_print_multi_aff(
3186 __isl_take isl_printer *p,
3187 __isl_keep isl_multi_aff *maff);
3188 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3189 __isl_take isl_printer *p,
3190 __isl_keep isl_pw_multi_aff *pma);
3194 Points are elements of a set. They can be used to construct
3195 simple sets (boxes) or they can be used to represent the
3196 individual elements of a set.
3197 The zero point (the origin) can be created using
3199 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
3201 The coordinates of a point can be inspected, set and changed
3204 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
3205 enum isl_dim_type type, int pos, isl_int *v);
3206 __isl_give isl_point *isl_point_set_coordinate(
3207 __isl_take isl_point *pnt,
3208 enum isl_dim_type type, int pos, isl_int v);
3210 __isl_give isl_point *isl_point_add_ui(
3211 __isl_take isl_point *pnt,
3212 enum isl_dim_type type, int pos, unsigned val);
3213 __isl_give isl_point *isl_point_sub_ui(
3214 __isl_take isl_point *pnt,
3215 enum isl_dim_type type, int pos, unsigned val);
3217 Other properties can be obtained using
3219 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
3221 Points can be copied or freed using
3223 __isl_give isl_point *isl_point_copy(
3224 __isl_keep isl_point *pnt);
3225 void isl_point_free(__isl_take isl_point *pnt);
3227 A singleton set can be created from a point using
3229 __isl_give isl_basic_set *isl_basic_set_from_point(
3230 __isl_take isl_point *pnt);
3231 __isl_give isl_set *isl_set_from_point(
3232 __isl_take isl_point *pnt);
3234 and a box can be created from two opposite extremal points using
3236 __isl_give isl_basic_set *isl_basic_set_box_from_points(
3237 __isl_take isl_point *pnt1,
3238 __isl_take isl_point *pnt2);
3239 __isl_give isl_set *isl_set_box_from_points(
3240 __isl_take isl_point *pnt1,
3241 __isl_take isl_point *pnt2);
3243 All elements of a B<bounded> (union) set can be enumerated using
3244 the following functions.
3246 int isl_set_foreach_point(__isl_keep isl_set *set,
3247 int (*fn)(__isl_take isl_point *pnt, void *user),
3249 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
3250 int (*fn)(__isl_take isl_point *pnt, void *user),
3253 The function C<fn> is called for each integer point in
3254 C<set> with as second argument the last argument of
3255 the C<isl_set_foreach_point> call. The function C<fn>
3256 should return C<0> on success and C<-1> on failure.
3257 In the latter case, C<isl_set_foreach_point> will stop
3258 enumerating and return C<-1> as well.
3259 If the enumeration is performed successfully and to completion,
3260 then C<isl_set_foreach_point> returns C<0>.
3262 To obtain a single point of a (basic) set, use
3264 __isl_give isl_point *isl_basic_set_sample_point(
3265 __isl_take isl_basic_set *bset);
3266 __isl_give isl_point *isl_set_sample_point(
3267 __isl_take isl_set *set);
3269 If C<set> does not contain any (integer) points, then the
3270 resulting point will be ``void'', a property that can be
3273 int isl_point_is_void(__isl_keep isl_point *pnt);
3275 =head2 Piecewise Quasipolynomials
3277 A piecewise quasipolynomial is a particular kind of function that maps
3278 a parametric point to a rational value.
3279 More specifically, a quasipolynomial is a polynomial expression in greatest
3280 integer parts of affine expressions of parameters and variables.
3281 A piecewise quasipolynomial is a subdivision of a given parametric
3282 domain into disjoint cells with a quasipolynomial associated to
3283 each cell. The value of the piecewise quasipolynomial at a given
3284 point is the value of the quasipolynomial associated to the cell
3285 that contains the point. Outside of the union of cells,
3286 the value is assumed to be zero.
3287 For example, the piecewise quasipolynomial
3289 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3291 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
3292 A given piecewise quasipolynomial has a fixed domain dimension.
3293 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
3294 defined over different domains.
3295 Piecewise quasipolynomials are mainly used by the C<barvinok>
3296 library for representing the number of elements in a parametric set or map.
3297 For example, the piecewise quasipolynomial above represents
3298 the number of points in the map
3300 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3302 =head3 Input and Output
3304 Piecewise quasipolynomials can be read from input using
3306 __isl_give isl_union_pw_qpolynomial *
3307 isl_union_pw_qpolynomial_read_from_str(
3308 isl_ctx *ctx, const char *str);
3310 Quasipolynomials and piecewise quasipolynomials can be printed
3311 using the following functions.
3313 __isl_give isl_printer *isl_printer_print_qpolynomial(
3314 __isl_take isl_printer *p,
3315 __isl_keep isl_qpolynomial *qp);
3317 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3318 __isl_take isl_printer *p,
3319 __isl_keep isl_pw_qpolynomial *pwqp);
3321 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3322 __isl_take isl_printer *p,
3323 __isl_keep isl_union_pw_qpolynomial *upwqp);
3325 The output format of the printer
3326 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3327 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
3329 In case of printing in C<ISL_FORMAT_C>, the user may want
3330 to set the names of all dimensions
3332 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
3333 __isl_take isl_qpolynomial *qp,
3334 enum isl_dim_type type, unsigned pos,
3336 __isl_give isl_pw_qpolynomial *
3337 isl_pw_qpolynomial_set_dim_name(
3338 __isl_take isl_pw_qpolynomial *pwqp,
3339 enum isl_dim_type type, unsigned pos,
3342 =head3 Creating New (Piecewise) Quasipolynomials
3344 Some simple quasipolynomials can be created using the following functions.
3345 More complicated quasipolynomials can be created by applying
3346 operations such as addition and multiplication
3347 on the resulting quasipolynomials
3349 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3350 __isl_take isl_space *domain);
3351 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3352 __isl_take isl_space *domain);
3353 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3354 __isl_take isl_space *domain);
3355 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3356 __isl_take isl_space *domain);
3357 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3358 __isl_take isl_space *domain);
3359 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
3360 __isl_take isl_space *domain,
3361 const isl_int n, const isl_int d);
3362 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3363 __isl_take isl_space *domain,
3364 enum isl_dim_type type, unsigned pos);
3365 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3366 __isl_take isl_aff *aff);
3368 Note that the space in which a quasipolynomial lives is a map space
3369 with a one-dimensional range. The C<domain> argument in some of
3370 the functions above corresponds to the domain of this map space.
3372 The zero piecewise quasipolynomial or a piecewise quasipolynomial
3373 with a single cell can be created using the following functions.
3374 Multiple of these single cell piecewise quasipolynomials can
3375 be combined to create more complicated piecewise quasipolynomials.
3377 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3378 __isl_take isl_space *space);
3379 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3380 __isl_take isl_set *set,
3381 __isl_take isl_qpolynomial *qp);
3382 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3383 __isl_take isl_qpolynomial *qp);
3384 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3385 __isl_take isl_pw_aff *pwaff);
3387 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3388 __isl_take isl_space *space);
3389 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3390 __isl_take isl_pw_qpolynomial *pwqp);
3391 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3392 __isl_take isl_union_pw_qpolynomial *upwqp,
3393 __isl_take isl_pw_qpolynomial *pwqp);
3395 Quasipolynomials can be copied and freed again using the following
3398 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3399 __isl_keep isl_qpolynomial *qp);
3400 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3402 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3403 __isl_keep isl_pw_qpolynomial *pwqp);
3404 void *isl_pw_qpolynomial_free(
3405 __isl_take isl_pw_qpolynomial *pwqp);
3407 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3408 __isl_keep isl_union_pw_qpolynomial *upwqp);
3409 void isl_union_pw_qpolynomial_free(
3410 __isl_take isl_union_pw_qpolynomial *upwqp);
3412 =head3 Inspecting (Piecewise) Quasipolynomials
3414 To iterate over all piecewise quasipolynomials in a union
3415 piecewise quasipolynomial, use the following function
3417 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3418 __isl_keep isl_union_pw_qpolynomial *upwqp,
3419 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3422 To extract the piecewise quasipolynomial in a given space from a union, use
3424 __isl_give isl_pw_qpolynomial *
3425 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3426 __isl_keep isl_union_pw_qpolynomial *upwqp,
3427 __isl_take isl_space *space);
3429 To iterate over the cells in a piecewise quasipolynomial,
3430 use either of the following two functions
3432 int isl_pw_qpolynomial_foreach_piece(
3433 __isl_keep isl_pw_qpolynomial *pwqp,
3434 int (*fn)(__isl_take isl_set *set,
3435 __isl_take isl_qpolynomial *qp,
3436 void *user), void *user);
3437 int isl_pw_qpolynomial_foreach_lifted_piece(
3438 __isl_keep isl_pw_qpolynomial *pwqp,
3439 int (*fn)(__isl_take isl_set *set,
3440 __isl_take isl_qpolynomial *qp,
3441 void *user), void *user);
3443 As usual, the function C<fn> should return C<0> on success
3444 and C<-1> on failure. The difference between
3445 C<isl_pw_qpolynomial_foreach_piece> and
3446 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3447 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3448 compute unique representations for all existentially quantified
3449 variables and then turn these existentially quantified variables
3450 into extra set variables, adapting the associated quasipolynomial
3451 accordingly. This means that the C<set> passed to C<fn>
3452 will not have any existentially quantified variables, but that
3453 the dimensions of the sets may be different for different
3454 invocations of C<fn>.
3456 To iterate over all terms in a quasipolynomial,
3459 int isl_qpolynomial_foreach_term(
3460 __isl_keep isl_qpolynomial *qp,
3461 int (*fn)(__isl_take isl_term *term,
3462 void *user), void *user);
3464 The terms themselves can be inspected and freed using
3467 unsigned isl_term_dim(__isl_keep isl_term *term,
3468 enum isl_dim_type type);
3469 void isl_term_get_num(__isl_keep isl_term *term,
3471 void isl_term_get_den(__isl_keep isl_term *term,
3473 int isl_term_get_exp(__isl_keep isl_term *term,
3474 enum isl_dim_type type, unsigned pos);
3475 __isl_give isl_aff *isl_term_get_div(
3476 __isl_keep isl_term *term, unsigned pos);
3477 void isl_term_free(__isl_take isl_term *term);
3479 Each term is a product of parameters, set variables and
3480 integer divisions. The function C<isl_term_get_exp>
3481 returns the exponent of a given dimensions in the given term.
3482 The C<isl_int>s in the arguments of C<isl_term_get_num>
3483 and C<isl_term_get_den> need to have been initialized
3484 using C<isl_int_init> before calling these functions.
3486 =head3 Properties of (Piecewise) Quasipolynomials
3488 To check whether a quasipolynomial is actually a constant,
3489 use the following function.
3491 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3492 isl_int *n, isl_int *d);
3494 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3495 then the numerator and denominator of the constant
3496 are returned in C<*n> and C<*d>, respectively.
3498 To check whether two union piecewise quasipolynomials are
3499 obviously equal, use
3501 int isl_union_pw_qpolynomial_plain_is_equal(
3502 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3503 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3505 =head3 Operations on (Piecewise) Quasipolynomials
3507 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3508 __isl_take isl_qpolynomial *qp, isl_int v);
3509 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3510 __isl_take isl_qpolynomial *qp);
3511 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3512 __isl_take isl_qpolynomial *qp1,
3513 __isl_take isl_qpolynomial *qp2);
3514 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3515 __isl_take isl_qpolynomial *qp1,
3516 __isl_take isl_qpolynomial *qp2);
3517 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3518 __isl_take isl_qpolynomial *qp1,
3519 __isl_take isl_qpolynomial *qp2);
3520 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3521 __isl_take isl_qpolynomial *qp, unsigned exponent);
3523 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3524 __isl_take isl_pw_qpolynomial *pwqp1,
3525 __isl_take isl_pw_qpolynomial *pwqp2);
3526 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3527 __isl_take isl_pw_qpolynomial *pwqp1,
3528 __isl_take isl_pw_qpolynomial *pwqp2);
3529 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3530 __isl_take isl_pw_qpolynomial *pwqp1,
3531 __isl_take isl_pw_qpolynomial *pwqp2);
3532 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3533 __isl_take isl_pw_qpolynomial *pwqp);
3534 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3535 __isl_take isl_pw_qpolynomial *pwqp1,
3536 __isl_take isl_pw_qpolynomial *pwqp2);
3537 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3538 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3540 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3541 __isl_take isl_union_pw_qpolynomial *upwqp1,
3542 __isl_take isl_union_pw_qpolynomial *upwqp2);
3543 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3544 __isl_take isl_union_pw_qpolynomial *upwqp1,
3545 __isl_take isl_union_pw_qpolynomial *upwqp2);
3546 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3547 __isl_take isl_union_pw_qpolynomial *upwqp1,
3548 __isl_take isl_union_pw_qpolynomial *upwqp2);
3550 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
3551 __isl_take isl_pw_qpolynomial *pwqp,
3552 __isl_take isl_point *pnt);
3554 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
3555 __isl_take isl_union_pw_qpolynomial *upwqp,
3556 __isl_take isl_point *pnt);
3558 __isl_give isl_set *isl_pw_qpolynomial_domain(
3559 __isl_take isl_pw_qpolynomial *pwqp);
3560 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
3561 __isl_take isl_pw_qpolynomial *pwpq,
3562 __isl_take isl_set *set);
3563 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
3564 __isl_take isl_pw_qpolynomial *pwpq,
3565 __isl_take isl_set *set);
3567 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3568 __isl_take isl_union_pw_qpolynomial *upwqp);
3569 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
3570 __isl_take isl_union_pw_qpolynomial *upwpq,
3571 __isl_take isl_union_set *uset);
3572 __isl_give isl_union_pw_qpolynomial *
3573 isl_union_pw_qpolynomial_intersect_params(
3574 __isl_take isl_union_pw_qpolynomial *upwpq,
3575 __isl_take isl_set *set);
3577 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3578 __isl_take isl_qpolynomial *qp,
3579 __isl_take isl_space *model);
3581 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
3582 __isl_take isl_qpolynomial *qp);
3583 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
3584 __isl_take isl_pw_qpolynomial *pwqp);
3586 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
3587 __isl_take isl_union_pw_qpolynomial *upwqp);
3589 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
3590 __isl_take isl_qpolynomial *qp,
3591 __isl_take isl_set *context);
3592 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
3593 __isl_take isl_qpolynomial *qp,
3594 __isl_take isl_set *context);
3596 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
3597 __isl_take isl_pw_qpolynomial *pwqp,
3598 __isl_take isl_set *context);
3599 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
3600 __isl_take isl_pw_qpolynomial *pwqp,
3601 __isl_take isl_set *context);
3603 __isl_give isl_union_pw_qpolynomial *
3604 isl_union_pw_qpolynomial_gist_params(
3605 __isl_take isl_union_pw_qpolynomial *upwqp,
3606 __isl_take isl_set *context);
3607 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
3608 __isl_take isl_union_pw_qpolynomial *upwqp,
3609 __isl_take isl_union_set *context);
3611 The gist operation applies the gist operation to each of
3612 the cells in the domain of the input piecewise quasipolynomial.
3613 The context is also exploited
3614 to simplify the quasipolynomials associated to each cell.
3616 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
3617 __isl_take isl_pw_qpolynomial *pwqp, int sign);
3618 __isl_give isl_union_pw_qpolynomial *
3619 isl_union_pw_qpolynomial_to_polynomial(
3620 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
3622 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
3623 the polynomial will be an overapproximation. If C<sign> is negative,
3624 it will be an underapproximation. If C<sign> is zero, the approximation
3625 will lie somewhere in between.
3627 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
3629 A piecewise quasipolynomial reduction is a piecewise
3630 reduction (or fold) of quasipolynomials.
3631 In particular, the reduction can be maximum or a minimum.
3632 The objects are mainly used to represent the result of
3633 an upper or lower bound on a quasipolynomial over its domain,
3634 i.e., as the result of the following function.
3636 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
3637 __isl_take isl_pw_qpolynomial *pwqp,
3638 enum isl_fold type, int *tight);
3640 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
3641 __isl_take isl_union_pw_qpolynomial *upwqp,
3642 enum isl_fold type, int *tight);
3644 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
3645 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
3646 is the returned bound is known be tight, i.e., for each value
3647 of the parameters there is at least
3648 one element in the domain that reaches the bound.
3649 If the domain of C<pwqp> is not wrapping, then the bound is computed
3650 over all elements in that domain and the result has a purely parametric
3651 domain. If the domain of C<pwqp> is wrapping, then the bound is
3652 computed over the range of the wrapped relation. The domain of the
3653 wrapped relation becomes the domain of the result.
3655 A (piecewise) quasipolynomial reduction can be copied or freed using the
3656 following functions.
3658 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
3659 __isl_keep isl_qpolynomial_fold *fold);
3660 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
3661 __isl_keep isl_pw_qpolynomial_fold *pwf);
3662 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
3663 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3664 void isl_qpolynomial_fold_free(
3665 __isl_take isl_qpolynomial_fold *fold);
3666 void *isl_pw_qpolynomial_fold_free(
3667 __isl_take isl_pw_qpolynomial_fold *pwf);
3668 void isl_union_pw_qpolynomial_fold_free(
3669 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3671 =head3 Printing Piecewise Quasipolynomial Reductions
3673 Piecewise quasipolynomial reductions can be printed
3674 using the following function.
3676 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
3677 __isl_take isl_printer *p,
3678 __isl_keep isl_pw_qpolynomial_fold *pwf);
3679 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
3680 __isl_take isl_printer *p,
3681 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3683 For C<isl_printer_print_pw_qpolynomial_fold>,
3684 output format of the printer
3685 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3686 For C<isl_printer_print_union_pw_qpolynomial_fold>,
3687 output format of the printer
3688 needs to be set to C<ISL_FORMAT_ISL>.
3689 In case of printing in C<ISL_FORMAT_C>, the user may want
3690 to set the names of all dimensions
3692 __isl_give isl_pw_qpolynomial_fold *
3693 isl_pw_qpolynomial_fold_set_dim_name(
3694 __isl_take isl_pw_qpolynomial_fold *pwf,
3695 enum isl_dim_type type, unsigned pos,
3698 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
3700 To iterate over all piecewise quasipolynomial reductions in a union
3701 piecewise quasipolynomial reduction, use the following function
3703 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3704 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3705 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3706 void *user), void *user);
3708 To iterate over the cells in a piecewise quasipolynomial reduction,
3709 use either of the following two functions
3711 int isl_pw_qpolynomial_fold_foreach_piece(
3712 __isl_keep isl_pw_qpolynomial_fold *pwf,
3713 int (*fn)(__isl_take isl_set *set,
3714 __isl_take isl_qpolynomial_fold *fold,
3715 void *user), void *user);
3716 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
3717 __isl_keep isl_pw_qpolynomial_fold *pwf,
3718 int (*fn)(__isl_take isl_set *set,
3719 __isl_take isl_qpolynomial_fold *fold,
3720 void *user), void *user);
3722 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
3723 of the difference between these two functions.
3725 To iterate over all quasipolynomials in a reduction, use
3727 int isl_qpolynomial_fold_foreach_qpolynomial(
3728 __isl_keep isl_qpolynomial_fold *fold,
3729 int (*fn)(__isl_take isl_qpolynomial *qp,
3730 void *user), void *user);
3732 =head3 Properties of Piecewise Quasipolynomial Reductions
3734 To check whether two union piecewise quasipolynomial reductions are
3735 obviously equal, use
3737 int isl_union_pw_qpolynomial_fold_plain_is_equal(
3738 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
3739 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
3741 =head3 Operations on Piecewise Quasipolynomial Reductions
3743 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
3744 __isl_take isl_qpolynomial_fold *fold, isl_int v);
3746 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
3747 __isl_take isl_pw_qpolynomial_fold *pwf1,
3748 __isl_take isl_pw_qpolynomial_fold *pwf2);
3750 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
3751 __isl_take isl_pw_qpolynomial_fold *pwf1,
3752 __isl_take isl_pw_qpolynomial_fold *pwf2);
3754 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
3755 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
3756 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
3758 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
3759 __isl_take isl_pw_qpolynomial_fold *pwf,
3760 __isl_take isl_point *pnt);
3762 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
3763 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3764 __isl_take isl_point *pnt);
3766 __isl_give isl_pw_qpolynomial_fold *
3767 sl_pw_qpolynomial_fold_intersect_params(
3768 __isl_take isl_pw_qpolynomial_fold *pwf,
3769 __isl_take isl_set *set);
3771 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
3772 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3773 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
3774 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3775 __isl_take isl_union_set *uset);
3776 __isl_give isl_union_pw_qpolynomial_fold *
3777 isl_union_pw_qpolynomial_fold_intersect_params(
3778 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3779 __isl_take isl_set *set);
3781 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
3782 __isl_take isl_pw_qpolynomial_fold *pwf);
3784 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
3785 __isl_take isl_pw_qpolynomial_fold *pwf);
3787 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
3788 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3790 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
3791 __isl_take isl_qpolynomial_fold *fold,
3792 __isl_take isl_set *context);
3793 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
3794 __isl_take isl_qpolynomial_fold *fold,
3795 __isl_take isl_set *context);
3797 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
3798 __isl_take isl_pw_qpolynomial_fold *pwf,
3799 __isl_take isl_set *context);
3800 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
3801 __isl_take isl_pw_qpolynomial_fold *pwf,
3802 __isl_take isl_set *context);
3804 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
3805 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3806 __isl_take isl_union_set *context);
3807 __isl_give isl_union_pw_qpolynomial_fold *
3808 isl_union_pw_qpolynomial_fold_gist_params(
3809 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3810 __isl_take isl_set *context);
3812 The gist operation applies the gist operation to each of
3813 the cells in the domain of the input piecewise quasipolynomial reduction.
3814 In future, the operation will also exploit the context
3815 to simplify the quasipolynomial reductions associated to each cell.
3817 __isl_give isl_pw_qpolynomial_fold *
3818 isl_set_apply_pw_qpolynomial_fold(
3819 __isl_take isl_set *set,
3820 __isl_take isl_pw_qpolynomial_fold *pwf,
3822 __isl_give isl_pw_qpolynomial_fold *
3823 isl_map_apply_pw_qpolynomial_fold(
3824 __isl_take isl_map *map,
3825 __isl_take isl_pw_qpolynomial_fold *pwf,
3827 __isl_give isl_union_pw_qpolynomial_fold *
3828 isl_union_set_apply_union_pw_qpolynomial_fold(
3829 __isl_take isl_union_set *uset,
3830 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3832 __isl_give isl_union_pw_qpolynomial_fold *
3833 isl_union_map_apply_union_pw_qpolynomial_fold(
3834 __isl_take isl_union_map *umap,
3835 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3838 The functions taking a map
3839 compose the given map with the given piecewise quasipolynomial reduction.
3840 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
3841 over all elements in the intersection of the range of the map
3842 and the domain of the piecewise quasipolynomial reduction
3843 as a function of an element in the domain of the map.
3844 The functions taking a set compute a bound over all elements in the
3845 intersection of the set and the domain of the
3846 piecewise quasipolynomial reduction.
3848 =head2 Dependence Analysis
3850 C<isl> contains specialized functionality for performing
3851 array dataflow analysis. That is, given a I<sink> access relation
3852 and a collection of possible I<source> access relations,
3853 C<isl> can compute relations that describe
3854 for each iteration of the sink access, which iteration
3855 of which of the source access relations was the last
3856 to access the same data element before the given iteration
3858 The resulting dependence relations map source iterations
3859 to the corresponding sink iterations.
3860 To compute standard flow dependences, the sink should be
3861 a read, while the sources should be writes.
3862 If any of the source accesses are marked as being I<may>
3863 accesses, then there will be a dependence from the last
3864 I<must> access B<and> from any I<may> access that follows
3865 this last I<must> access.
3866 In particular, if I<all> sources are I<may> accesses,
3867 then memory based dependence analysis is performed.
3868 If, on the other hand, all sources are I<must> accesses,
3869 then value based dependence analysis is performed.
3871 #include <isl/flow.h>
3873 typedef int (*isl_access_level_before)(void *first, void *second);
3875 __isl_give isl_access_info *isl_access_info_alloc(
3876 __isl_take isl_map *sink,
3877 void *sink_user, isl_access_level_before fn,
3879 __isl_give isl_access_info *isl_access_info_add_source(
3880 __isl_take isl_access_info *acc,
3881 __isl_take isl_map *source, int must,
3883 void isl_access_info_free(__isl_take isl_access_info *acc);
3885 __isl_give isl_flow *isl_access_info_compute_flow(
3886 __isl_take isl_access_info *acc);
3888 int isl_flow_foreach(__isl_keep isl_flow *deps,
3889 int (*fn)(__isl_take isl_map *dep, int must,
3890 void *dep_user, void *user),
3892 __isl_give isl_map *isl_flow_get_no_source(
3893 __isl_keep isl_flow *deps, int must);
3894 void isl_flow_free(__isl_take isl_flow *deps);
3896 The function C<isl_access_info_compute_flow> performs the actual
3897 dependence analysis. The other functions are used to construct
3898 the input for this function or to read off the output.
3900 The input is collected in an C<isl_access_info>, which can
3901 be created through a call to C<isl_access_info_alloc>.
3902 The arguments to this functions are the sink access relation
3903 C<sink>, a token C<sink_user> used to identify the sink
3904 access to the user, a callback function for specifying the
3905 relative order of source and sink accesses, and the number
3906 of source access relations that will be added.
3907 The callback function has type C<int (*)(void *first, void *second)>.
3908 The function is called with two user supplied tokens identifying
3909 either a source or the sink and it should return the shared nesting
3910 level and the relative order of the two accesses.
3911 In particular, let I<n> be the number of loops shared by
3912 the two accesses. If C<first> precedes C<second> textually,
3913 then the function should return I<2 * n + 1>; otherwise,
3914 it should return I<2 * n>.
3915 The sources can be added to the C<isl_access_info> by performing
3916 (at most) C<max_source> calls to C<isl_access_info_add_source>.
3917 C<must> indicates whether the source is a I<must> access
3918 or a I<may> access. Note that a multi-valued access relation
3919 should only be marked I<must> if every iteration in the domain
3920 of the relation accesses I<all> elements in its image.
3921 The C<source_user> token is again used to identify
3922 the source access. The range of the source access relation
3923 C<source> should have the same dimension as the range
3924 of the sink access relation.
3925 The C<isl_access_info_free> function should usually not be
3926 called explicitly, because it is called implicitly by
3927 C<isl_access_info_compute_flow>.
3929 The result of the dependence analysis is collected in an
3930 C<isl_flow>. There may be elements of
3931 the sink access for which no preceding source access could be
3932 found or for which all preceding sources are I<may> accesses.
3933 The relations containing these elements can be obtained through
3934 calls to C<isl_flow_get_no_source>, the first with C<must> set
3935 and the second with C<must> unset.
3936 In the case of standard flow dependence analysis,
3937 with the sink a read and the sources I<must> writes,
3938 the first relation corresponds to the reads from uninitialized
3939 array elements and the second relation is empty.
3940 The actual flow dependences can be extracted using
3941 C<isl_flow_foreach>. This function will call the user-specified
3942 callback function C<fn> for each B<non-empty> dependence between
3943 a source and the sink. The callback function is called
3944 with four arguments, the actual flow dependence relation
3945 mapping source iterations to sink iterations, a boolean that
3946 indicates whether it is a I<must> or I<may> dependence, a token
3947 identifying the source and an additional C<void *> with value
3948 equal to the third argument of the C<isl_flow_foreach> call.
3949 A dependence is marked I<must> if it originates from a I<must>
3950 source and if it is not followed by any I<may> sources.
3952 After finishing with an C<isl_flow>, the user should call
3953 C<isl_flow_free> to free all associated memory.
3955 A higher-level interface to dependence analysis is provided
3956 by the following function.
3958 #include <isl/flow.h>
3960 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
3961 __isl_take isl_union_map *must_source,
3962 __isl_take isl_union_map *may_source,
3963 __isl_take isl_union_map *schedule,
3964 __isl_give isl_union_map **must_dep,
3965 __isl_give isl_union_map **may_dep,
3966 __isl_give isl_union_map **must_no_source,
3967 __isl_give isl_union_map **may_no_source);
3969 The arrays are identified by the tuple names of the ranges
3970 of the accesses. The iteration domains by the tuple names
3971 of the domains of the accesses and of the schedule.
3972 The relative order of the iteration domains is given by the
3973 schedule. The relations returned through C<must_no_source>
3974 and C<may_no_source> are subsets of C<sink>.
3975 Any of C<must_dep>, C<may_dep>, C<must_no_source>
3976 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
3977 any of the other arguments is treated as an error.
3981 B<The functionality described in this section is fairly new
3982 and may be subject to change.>
3984 The following function can be used to compute a schedule
3985 for a union of domains. The generated schedule respects
3986 all C<validity> dependences. That is, all dependence distances
3987 over these dependences in the scheduled space are lexicographically
3988 positive. The generated schedule schedule also tries to minimize
3989 the dependence distances over C<proximity> dependences.
3990 Moreover, it tries to obtain sequences (bands) of schedule dimensions
3991 for groups of domains where the dependence distances have only
3992 non-negative values.
3993 The algorithm used to construct the schedule is similar to that
3996 #include <isl/schedule.h>
3997 __isl_give isl_schedule *isl_union_set_compute_schedule(
3998 __isl_take isl_union_set *domain,
3999 __isl_take isl_union_map *validity,
4000 __isl_take isl_union_map *proximity);
4001 void *isl_schedule_free(__isl_take isl_schedule *sched);
4003 A mapping from the domains to the scheduled space can be obtained
4004 from an C<isl_schedule> using the following function.
4006 __isl_give isl_union_map *isl_schedule_get_map(
4007 __isl_keep isl_schedule *sched);
4009 A representation of the schedule can be printed using
4011 __isl_give isl_printer *isl_printer_print_schedule(
4012 __isl_take isl_printer *p,
4013 __isl_keep isl_schedule *schedule);
4015 A representation of the schedule as a forest of bands can be obtained
4016 using the following function.
4018 __isl_give isl_band_list *isl_schedule_get_band_forest(
4019 __isl_keep isl_schedule *schedule);
4021 The list can be manipulated as explained in L<"Lists">.
4022 The bands inside the list can be copied and freed using the following
4025 #include <isl/band.h>
4026 __isl_give isl_band *isl_band_copy(
4027 __isl_keep isl_band *band);
4028 void *isl_band_free(__isl_take isl_band *band);
4030 Each band contains zero or more scheduling dimensions.
4031 These are referred to as the members of the band.
4032 The section of the schedule that corresponds to the band is
4033 referred to as the partial schedule of the band.
4034 For those nodes that participate in a band, the outer scheduling
4035 dimensions form the prefix schedule, while the inner scheduling
4036 dimensions form the suffix schedule.
4037 That is, if we take a cut of the band forest, then the union of
4038 the concatenations of the prefix, partial and suffix schedules of
4039 each band in the cut is equal to the entire schedule (modulo
4040 some possible padding at the end with zero scheduling dimensions).
4041 The properties of a band can be inspected using the following functions.
4043 #include <isl/band.h>
4044 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
4046 int isl_band_has_children(__isl_keep isl_band *band);
4047 __isl_give isl_band_list *isl_band_get_children(
4048 __isl_keep isl_band *band);
4050 __isl_give isl_union_map *isl_band_get_prefix_schedule(
4051 __isl_keep isl_band *band);
4052 __isl_give isl_union_map *isl_band_get_partial_schedule(
4053 __isl_keep isl_band *band);
4054 __isl_give isl_union_map *isl_band_get_suffix_schedule(
4055 __isl_keep isl_band *band);
4057 int isl_band_n_member(__isl_keep isl_band *band);
4058 int isl_band_member_is_zero_distance(
4059 __isl_keep isl_band *band, int pos);
4061 Note that a scheduling dimension is considered to be ``zero
4062 distance'' if it does not carry any proximity dependences
4064 That is, if the dependence distances of the proximity
4065 dependences are all zero in that direction (for fixed
4066 iterations of outer bands).
4068 A representation of the band can be printed using
4070 #include <isl/band.h>
4071 __isl_give isl_printer *isl_printer_print_band(
4072 __isl_take isl_printer *p,
4073 __isl_keep isl_band *band);
4077 #include <isl/schedule.h>
4078 int isl_options_set_schedule_outer_zero_distance(
4079 isl_ctx *ctx, int val);
4080 int isl_options_get_schedule_outer_zero_distance(
4085 =item * schedule_outer_zero_distance
4087 It this option is set, then we try to construct schedules
4088 where the outermost scheduling dimension in each band
4089 results in a zero dependence distance over the proximity
4094 =head2 Parametric Vertex Enumeration
4096 The parametric vertex enumeration described in this section
4097 is mainly intended to be used internally and by the C<barvinok>
4100 #include <isl/vertices.h>
4101 __isl_give isl_vertices *isl_basic_set_compute_vertices(
4102 __isl_keep isl_basic_set *bset);
4104 The function C<isl_basic_set_compute_vertices> performs the
4105 actual computation of the parametric vertices and the chamber
4106 decomposition and store the result in an C<isl_vertices> object.
4107 This information can be queried by either iterating over all
4108 the vertices or iterating over all the chambers or cells
4109 and then iterating over all vertices that are active on the chamber.
4111 int isl_vertices_foreach_vertex(
4112 __isl_keep isl_vertices *vertices,
4113 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4116 int isl_vertices_foreach_cell(
4117 __isl_keep isl_vertices *vertices,
4118 int (*fn)(__isl_take isl_cell *cell, void *user),
4120 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
4121 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4124 Other operations that can be performed on an C<isl_vertices> object are
4127 isl_ctx *isl_vertices_get_ctx(
4128 __isl_keep isl_vertices *vertices);
4129 int isl_vertices_get_n_vertices(
4130 __isl_keep isl_vertices *vertices);
4131 void isl_vertices_free(__isl_take isl_vertices *vertices);
4133 Vertices can be inspected and destroyed using the following functions.
4135 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
4136 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
4137 __isl_give isl_basic_set *isl_vertex_get_domain(
4138 __isl_keep isl_vertex *vertex);
4139 __isl_give isl_basic_set *isl_vertex_get_expr(
4140 __isl_keep isl_vertex *vertex);
4141 void isl_vertex_free(__isl_take isl_vertex *vertex);
4143 C<isl_vertex_get_expr> returns a singleton parametric set describing
4144 the vertex, while C<isl_vertex_get_domain> returns the activity domain
4146 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
4147 B<rational> basic sets, so they should mainly be used for inspection
4148 and should not be mixed with integer sets.
4150 Chambers can be inspected and destroyed using the following functions.
4152 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
4153 __isl_give isl_basic_set *isl_cell_get_domain(
4154 __isl_keep isl_cell *cell);
4155 void isl_cell_free(__isl_take isl_cell *cell);
4159 Although C<isl> is mainly meant to be used as a library,
4160 it also contains some basic applications that use some
4161 of the functionality of C<isl>.
4162 The input may be specified in either the L<isl format>
4163 or the L<PolyLib format>.
4165 =head2 C<isl_polyhedron_sample>
4167 C<isl_polyhedron_sample> takes a polyhedron as input and prints
4168 an integer element of the polyhedron, if there is any.
4169 The first column in the output is the denominator and is always
4170 equal to 1. If the polyhedron contains no integer points,
4171 then a vector of length zero is printed.
4175 C<isl_pip> takes the same input as the C<example> program
4176 from the C<piplib> distribution, i.e., a set of constraints
4177 on the parameters, a line containing only -1 and finally a set
4178 of constraints on a parametric polyhedron.
4179 The coefficients of the parameters appear in the last columns
4180 (but before the final constant column).
4181 The output is the lexicographic minimum of the parametric polyhedron.
4182 As C<isl> currently does not have its own output format, the output
4183 is just a dump of the internal state.
4185 =head2 C<isl_polyhedron_minimize>
4187 C<isl_polyhedron_minimize> computes the minimum of some linear
4188 or affine objective function over the integer points in a polyhedron.
4189 If an affine objective function
4190 is given, then the constant should appear in the last column.
4192 =head2 C<isl_polytope_scan>
4194 Given a polytope, C<isl_polytope_scan> prints
4195 all integer points in the polytope.