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_map_find_dim_by_name(__isl_keep isl_map *map,
1509 enum isl_dim_type type, const char *name);
1511 const char *isl_constraint_get_dim_name(
1512 __isl_keep isl_constraint *constraint,
1513 enum isl_dim_type type, unsigned pos);
1514 const char *isl_basic_set_get_dim_name(
1515 __isl_keep isl_basic_set *bset,
1516 enum isl_dim_type type, unsigned pos);
1517 const char *isl_set_get_dim_name(
1518 __isl_keep isl_set *set,
1519 enum isl_dim_type type, unsigned pos);
1520 const char *isl_basic_map_get_dim_name(
1521 __isl_keep isl_basic_map *bmap,
1522 enum isl_dim_type type, unsigned pos);
1523 const char *isl_map_get_dim_name(
1524 __isl_keep isl_map *map,
1525 enum isl_dim_type type, unsigned pos);
1527 These functions are mostly useful to obtain the identifiers, positions
1528 or names of the parameters. Identifiers of individual dimensions are
1529 essentially only useful for printing. They are ignored by all other
1530 operations and may not be preserved across those operations.
1534 =head3 Unary Properties
1540 The following functions test whether the given set or relation
1541 contains any integer points. The ``plain'' variants do not perform
1542 any computations, but simply check if the given set or relation
1543 is already known to be empty.
1545 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1546 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1547 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1548 int isl_set_is_empty(__isl_keep isl_set *set);
1549 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1550 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1551 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1552 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1553 int isl_map_is_empty(__isl_keep isl_map *map);
1554 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1556 =item * Universality
1558 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1559 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1560 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1562 =item * Single-valuedness
1564 int isl_map_is_single_valued(__isl_keep isl_map *map);
1565 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1569 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1570 int isl_map_is_injective(__isl_keep isl_map *map);
1571 int isl_union_map_plain_is_injective(
1572 __isl_keep isl_union_map *umap);
1573 int isl_union_map_is_injective(
1574 __isl_keep isl_union_map *umap);
1578 int isl_map_is_bijective(__isl_keep isl_map *map);
1579 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1583 int isl_basic_map_plain_is_fixed(
1584 __isl_keep isl_basic_map *bmap,
1585 enum isl_dim_type type, unsigned pos,
1587 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
1588 enum isl_dim_type type, unsigned pos,
1590 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1591 enum isl_dim_type type, unsigned pos,
1594 Check if the relation obviously lies on a hyperplane where the given dimension
1595 has a fixed value and if so, return that value in C<*val>.
1599 To check whether a set is a parameter domain, use this function:
1601 int isl_set_is_params(__isl_keep isl_set *set);
1602 int isl_union_set_is_params(
1603 __isl_keep isl_union_set *uset);
1607 The following functions check whether the domain of the given
1608 (basic) set is a wrapped relation.
1610 int isl_basic_set_is_wrapping(
1611 __isl_keep isl_basic_set *bset);
1612 int isl_set_is_wrapping(__isl_keep isl_set *set);
1614 =item * Internal Product
1616 int isl_basic_map_can_zip(
1617 __isl_keep isl_basic_map *bmap);
1618 int isl_map_can_zip(__isl_keep isl_map *map);
1620 Check whether the product of domain and range of the given relation
1622 i.e., whether both domain and range are nested relations.
1626 =head3 Binary Properties
1632 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1633 __isl_keep isl_set *set2);
1634 int isl_set_is_equal(__isl_keep isl_set *set1,
1635 __isl_keep isl_set *set2);
1636 int isl_union_set_is_equal(
1637 __isl_keep isl_union_set *uset1,
1638 __isl_keep isl_union_set *uset2);
1639 int isl_basic_map_is_equal(
1640 __isl_keep isl_basic_map *bmap1,
1641 __isl_keep isl_basic_map *bmap2);
1642 int isl_map_is_equal(__isl_keep isl_map *map1,
1643 __isl_keep isl_map *map2);
1644 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1645 __isl_keep isl_map *map2);
1646 int isl_union_map_is_equal(
1647 __isl_keep isl_union_map *umap1,
1648 __isl_keep isl_union_map *umap2);
1650 =item * Disjointness
1652 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1653 __isl_keep isl_set *set2);
1657 int isl_set_is_subset(__isl_keep isl_set *set1,
1658 __isl_keep isl_set *set2);
1659 int isl_set_is_strict_subset(
1660 __isl_keep isl_set *set1,
1661 __isl_keep isl_set *set2);
1662 int isl_union_set_is_subset(
1663 __isl_keep isl_union_set *uset1,
1664 __isl_keep isl_union_set *uset2);
1665 int isl_union_set_is_strict_subset(
1666 __isl_keep isl_union_set *uset1,
1667 __isl_keep isl_union_set *uset2);
1668 int isl_basic_map_is_subset(
1669 __isl_keep isl_basic_map *bmap1,
1670 __isl_keep isl_basic_map *bmap2);
1671 int isl_basic_map_is_strict_subset(
1672 __isl_keep isl_basic_map *bmap1,
1673 __isl_keep isl_basic_map *bmap2);
1674 int isl_map_is_subset(
1675 __isl_keep isl_map *map1,
1676 __isl_keep isl_map *map2);
1677 int isl_map_is_strict_subset(
1678 __isl_keep isl_map *map1,
1679 __isl_keep isl_map *map2);
1680 int isl_union_map_is_subset(
1681 __isl_keep isl_union_map *umap1,
1682 __isl_keep isl_union_map *umap2);
1683 int isl_union_map_is_strict_subset(
1684 __isl_keep isl_union_map *umap1,
1685 __isl_keep isl_union_map *umap2);
1689 =head2 Unary Operations
1695 __isl_give isl_set *isl_set_complement(
1696 __isl_take isl_set *set);
1700 __isl_give isl_basic_map *isl_basic_map_reverse(
1701 __isl_take isl_basic_map *bmap);
1702 __isl_give isl_map *isl_map_reverse(
1703 __isl_take isl_map *map);
1704 __isl_give isl_union_map *isl_union_map_reverse(
1705 __isl_take isl_union_map *umap);
1709 __isl_give isl_basic_set *isl_basic_set_project_out(
1710 __isl_take isl_basic_set *bset,
1711 enum isl_dim_type type, unsigned first, unsigned n);
1712 __isl_give isl_basic_map *isl_basic_map_project_out(
1713 __isl_take isl_basic_map *bmap,
1714 enum isl_dim_type type, unsigned first, unsigned n);
1715 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1716 enum isl_dim_type type, unsigned first, unsigned n);
1717 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1718 enum isl_dim_type type, unsigned first, unsigned n);
1719 __isl_give isl_basic_set *isl_basic_set_params(
1720 __isl_take isl_basic_set *bset);
1721 __isl_give isl_basic_set *isl_basic_map_domain(
1722 __isl_take isl_basic_map *bmap);
1723 __isl_give isl_basic_set *isl_basic_map_range(
1724 __isl_take isl_basic_map *bmap);
1725 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1726 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
1727 __isl_give isl_set *isl_map_domain(
1728 __isl_take isl_map *bmap);
1729 __isl_give isl_set *isl_map_range(
1730 __isl_take isl_map *map);
1731 __isl_give isl_set *isl_union_set_params(
1732 __isl_take isl_union_set *uset);
1733 __isl_give isl_set *isl_union_map_params(
1734 __isl_take isl_union_map *umap);
1735 __isl_give isl_union_set *isl_union_map_domain(
1736 __isl_take isl_union_map *umap);
1737 __isl_give isl_union_set *isl_union_map_range(
1738 __isl_take isl_union_map *umap);
1740 __isl_give isl_basic_map *isl_basic_map_domain_map(
1741 __isl_take isl_basic_map *bmap);
1742 __isl_give isl_basic_map *isl_basic_map_range_map(
1743 __isl_take isl_basic_map *bmap);
1744 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1745 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1746 __isl_give isl_union_map *isl_union_map_domain_map(
1747 __isl_take isl_union_map *umap);
1748 __isl_give isl_union_map *isl_union_map_range_map(
1749 __isl_take isl_union_map *umap);
1751 The functions above construct a (basic, regular or union) relation
1752 that maps (a wrapped version of) the input relation to its domain or range.
1756 __isl_give isl_set *isl_set_eliminate(
1757 __isl_take isl_set *set, enum isl_dim_type type,
1758 unsigned first, unsigned n);
1759 __isl_give isl_basic_map *isl_basic_map_eliminate(
1760 __isl_take isl_basic_map *bmap,
1761 enum isl_dim_type type,
1762 unsigned first, unsigned n);
1764 Eliminate the coefficients for the given dimensions from the constraints,
1765 without removing the dimensions.
1769 __isl_give isl_basic_set *isl_basic_set_fix(
1770 __isl_take isl_basic_set *bset,
1771 enum isl_dim_type type, unsigned pos,
1773 __isl_give isl_basic_set *isl_basic_set_fix_si(
1774 __isl_take isl_basic_set *bset,
1775 enum isl_dim_type type, unsigned pos, int value);
1776 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1777 enum isl_dim_type type, unsigned pos,
1779 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1780 enum isl_dim_type type, unsigned pos, int value);
1781 __isl_give isl_basic_map *isl_basic_map_fix_si(
1782 __isl_take isl_basic_map *bmap,
1783 enum isl_dim_type type, unsigned pos, int value);
1784 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1785 enum isl_dim_type type, unsigned pos, int value);
1787 Intersect the set or relation with the hyperplane where the given
1788 dimension has the fixed given value.
1790 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
1791 __isl_take isl_basic_map *bmap,
1792 enum isl_dim_type type, unsigned pos, int value);
1793 __isl_give isl_set *isl_set_lower_bound_si(
1794 __isl_take isl_set *set,
1795 enum isl_dim_type type, unsigned pos, int value);
1796 __isl_give isl_map *isl_map_lower_bound_si(
1797 __isl_take isl_map *map,
1798 enum isl_dim_type type, unsigned pos, int value);
1799 __isl_give isl_set *isl_set_upper_bound_si(
1800 __isl_take isl_set *set,
1801 enum isl_dim_type type, unsigned pos, int value);
1802 __isl_give isl_map *isl_map_upper_bound_si(
1803 __isl_take isl_map *map,
1804 enum isl_dim_type type, unsigned pos, int value);
1806 Intersect the set or relation with the half-space where the given
1807 dimension has a value bounded the fixed given value.
1809 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1810 enum isl_dim_type type1, int pos1,
1811 enum isl_dim_type type2, int pos2);
1812 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1813 enum isl_dim_type type1, int pos1,
1814 enum isl_dim_type type2, int pos2);
1816 Intersect the set or relation with the hyperplane where the given
1817 dimensions are equal to each other.
1819 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
1820 enum isl_dim_type type1, int pos1,
1821 enum isl_dim_type type2, int pos2);
1823 Intersect the relation with the hyperplane where the given
1824 dimensions have opposite values.
1828 __isl_give isl_map *isl_set_identity(
1829 __isl_take isl_set *set);
1830 __isl_give isl_union_map *isl_union_set_identity(
1831 __isl_take isl_union_set *uset);
1833 Construct an identity relation on the given (union) set.
1837 __isl_give isl_basic_set *isl_basic_map_deltas(
1838 __isl_take isl_basic_map *bmap);
1839 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1840 __isl_give isl_union_set *isl_union_map_deltas(
1841 __isl_take isl_union_map *umap);
1843 These functions return a (basic) set containing the differences
1844 between image elements and corresponding domain elements in the input.
1846 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1847 __isl_take isl_basic_map *bmap);
1848 __isl_give isl_map *isl_map_deltas_map(
1849 __isl_take isl_map *map);
1850 __isl_give isl_union_map *isl_union_map_deltas_map(
1851 __isl_take isl_union_map *umap);
1853 The functions above construct a (basic, regular or union) relation
1854 that maps (a wrapped version of) the input relation to its delta set.
1858 Simplify the representation of a set or relation by trying
1859 to combine pairs of basic sets or relations into a single
1860 basic set or relation.
1862 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1863 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1864 __isl_give isl_union_set *isl_union_set_coalesce(
1865 __isl_take isl_union_set *uset);
1866 __isl_give isl_union_map *isl_union_map_coalesce(
1867 __isl_take isl_union_map *umap);
1869 =item * Detecting equalities
1871 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1872 __isl_take isl_basic_set *bset);
1873 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1874 __isl_take isl_basic_map *bmap);
1875 __isl_give isl_set *isl_set_detect_equalities(
1876 __isl_take isl_set *set);
1877 __isl_give isl_map *isl_map_detect_equalities(
1878 __isl_take isl_map *map);
1879 __isl_give isl_union_set *isl_union_set_detect_equalities(
1880 __isl_take isl_union_set *uset);
1881 __isl_give isl_union_map *isl_union_map_detect_equalities(
1882 __isl_take isl_union_map *umap);
1884 Simplify the representation of a set or relation by detecting implicit
1887 =item * Removing redundant constraints
1889 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1890 __isl_take isl_basic_set *bset);
1891 __isl_give isl_set *isl_set_remove_redundancies(
1892 __isl_take isl_set *set);
1893 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1894 __isl_take isl_basic_map *bmap);
1895 __isl_give isl_map *isl_map_remove_redundancies(
1896 __isl_take isl_map *map);
1900 __isl_give isl_basic_set *isl_set_convex_hull(
1901 __isl_take isl_set *set);
1902 __isl_give isl_basic_map *isl_map_convex_hull(
1903 __isl_take isl_map *map);
1905 If the input set or relation has any existentially quantified
1906 variables, then the result of these operations is currently undefined.
1910 __isl_give isl_basic_set *isl_set_simple_hull(
1911 __isl_take isl_set *set);
1912 __isl_give isl_basic_map *isl_map_simple_hull(
1913 __isl_take isl_map *map);
1914 __isl_give isl_union_map *isl_union_map_simple_hull(
1915 __isl_take isl_union_map *umap);
1917 These functions compute a single basic set or relation
1918 that contains the whole input set or relation.
1919 In particular, the output is described by translates
1920 of the constraints describing the basic sets or relations in the input.
1924 (See \autoref{s:simple hull}.)
1930 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1931 __isl_take isl_basic_set *bset);
1932 __isl_give isl_basic_set *isl_set_affine_hull(
1933 __isl_take isl_set *set);
1934 __isl_give isl_union_set *isl_union_set_affine_hull(
1935 __isl_take isl_union_set *uset);
1936 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1937 __isl_take isl_basic_map *bmap);
1938 __isl_give isl_basic_map *isl_map_affine_hull(
1939 __isl_take isl_map *map);
1940 __isl_give isl_union_map *isl_union_map_affine_hull(
1941 __isl_take isl_union_map *umap);
1943 In case of union sets and relations, the affine hull is computed
1946 =item * Polyhedral hull
1948 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1949 __isl_take isl_set *set);
1950 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1951 __isl_take isl_map *map);
1952 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1953 __isl_take isl_union_set *uset);
1954 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1955 __isl_take isl_union_map *umap);
1957 These functions compute a single basic set or relation
1958 not involving any existentially quantified variables
1959 that contains the whole input set or relation.
1960 In case of union sets and relations, the polyhedral hull is computed
1963 =item * Optimization
1965 #include <isl/ilp.h>
1966 enum isl_lp_result isl_basic_set_max(
1967 __isl_keep isl_basic_set *bset,
1968 __isl_keep isl_aff *obj, isl_int *opt)
1969 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
1970 __isl_keep isl_aff *obj, isl_int *opt);
1971 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
1972 __isl_keep isl_aff *obj, isl_int *opt);
1974 Compute the minimum or maximum of the integer affine expression C<obj>
1975 over the points in C<set>, returning the result in C<opt>.
1976 The return value may be one of C<isl_lp_error>,
1977 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
1979 =item * Parametric optimization
1981 __isl_give isl_pw_aff *isl_set_dim_min(
1982 __isl_take isl_set *set, int pos);
1983 __isl_give isl_pw_aff *isl_set_dim_max(
1984 __isl_take isl_set *set, int pos);
1985 __isl_give isl_pw_aff *isl_map_dim_max(
1986 __isl_take isl_map *map, int pos);
1988 Compute the minimum or maximum of the given set or output dimension
1989 as a function of the parameters (and input dimensions), but independently
1990 of the other set or output dimensions.
1991 For lexicographic optimization, see L<"Lexicographic Optimization">.
1995 The following functions compute either the set of (rational) coefficient
1996 values of valid constraints for the given set or the set of (rational)
1997 values satisfying the constraints with coefficients from the given set.
1998 Internally, these two sets of functions perform essentially the
1999 same operations, except that the set of coefficients is assumed to
2000 be a cone, while the set of values may be any polyhedron.
2001 The current implementation is based on the Farkas lemma and
2002 Fourier-Motzkin elimination, but this may change or be made optional
2003 in future. In particular, future implementations may use different
2004 dualization algorithms or skip the elimination step.
2006 __isl_give isl_basic_set *isl_basic_set_coefficients(
2007 __isl_take isl_basic_set *bset);
2008 __isl_give isl_basic_set *isl_set_coefficients(
2009 __isl_take isl_set *set);
2010 __isl_give isl_union_set *isl_union_set_coefficients(
2011 __isl_take isl_union_set *bset);
2012 __isl_give isl_basic_set *isl_basic_set_solutions(
2013 __isl_take isl_basic_set *bset);
2014 __isl_give isl_basic_set *isl_set_solutions(
2015 __isl_take isl_set *set);
2016 __isl_give isl_union_set *isl_union_set_solutions(
2017 __isl_take isl_union_set *bset);
2021 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2023 __isl_give isl_union_map *isl_union_map_power(
2024 __isl_take isl_union_map *umap, int *exact);
2026 Compute a parametric representation for all positive powers I<k> of C<map>.
2027 The result maps I<k> to a nested relation corresponding to the
2028 I<k>th power of C<map>.
2029 The result may be an overapproximation. If the result is known to be exact,
2030 then C<*exact> is set to C<1>.
2032 =item * Transitive closure
2034 __isl_give isl_map *isl_map_transitive_closure(
2035 __isl_take isl_map *map, int *exact);
2036 __isl_give isl_union_map *isl_union_map_transitive_closure(
2037 __isl_take isl_union_map *umap, int *exact);
2039 Compute the transitive closure of C<map>.
2040 The result may be an overapproximation. If the result is known to be exact,
2041 then C<*exact> is set to C<1>.
2043 =item * Reaching path lengths
2045 __isl_give isl_map *isl_map_reaching_path_lengths(
2046 __isl_take isl_map *map, int *exact);
2048 Compute a relation that maps each element in the range of C<map>
2049 to the lengths of all paths composed of edges in C<map> that
2050 end up in the given element.
2051 The result may be an overapproximation. If the result is known to be exact,
2052 then C<*exact> is set to C<1>.
2053 To compute the I<maximal> path length, the resulting relation
2054 should be postprocessed by C<isl_map_lexmax>.
2055 In particular, if the input relation is a dependence relation
2056 (mapping sources to sinks), then the maximal path length corresponds
2057 to the free schedule.
2058 Note, however, that C<isl_map_lexmax> expects the maximum to be
2059 finite, so if the path lengths are unbounded (possibly due to
2060 the overapproximation), then you will get an error message.
2064 __isl_give isl_basic_set *isl_basic_map_wrap(
2065 __isl_take isl_basic_map *bmap);
2066 __isl_give isl_set *isl_map_wrap(
2067 __isl_take isl_map *map);
2068 __isl_give isl_union_set *isl_union_map_wrap(
2069 __isl_take isl_union_map *umap);
2070 __isl_give isl_basic_map *isl_basic_set_unwrap(
2071 __isl_take isl_basic_set *bset);
2072 __isl_give isl_map *isl_set_unwrap(
2073 __isl_take isl_set *set);
2074 __isl_give isl_union_map *isl_union_set_unwrap(
2075 __isl_take isl_union_set *uset);
2079 Remove any internal structure of domain (and range) of the given
2080 set or relation. If there is any such internal structure in the input,
2081 then the name of the space is also removed.
2083 __isl_give isl_basic_set *isl_basic_set_flatten(
2084 __isl_take isl_basic_set *bset);
2085 __isl_give isl_set *isl_set_flatten(
2086 __isl_take isl_set *set);
2087 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2088 __isl_take isl_basic_map *bmap);
2089 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2090 __isl_take isl_basic_map *bmap);
2091 __isl_give isl_map *isl_map_flatten_range(
2092 __isl_take isl_map *map);
2093 __isl_give isl_map *isl_map_flatten_domain(
2094 __isl_take isl_map *map);
2095 __isl_give isl_basic_map *isl_basic_map_flatten(
2096 __isl_take isl_basic_map *bmap);
2097 __isl_give isl_map *isl_map_flatten(
2098 __isl_take isl_map *map);
2100 __isl_give isl_map *isl_set_flatten_map(
2101 __isl_take isl_set *set);
2103 The function above constructs a relation
2104 that maps the input set to a flattened version of the set.
2108 Lift the input set to a space with extra dimensions corresponding
2109 to the existentially quantified variables in the input.
2110 In particular, the result lives in a wrapped map where the domain
2111 is the original space and the range corresponds to the original
2112 existentially quantified variables.
2114 __isl_give isl_basic_set *isl_basic_set_lift(
2115 __isl_take isl_basic_set *bset);
2116 __isl_give isl_set *isl_set_lift(
2117 __isl_take isl_set *set);
2118 __isl_give isl_union_set *isl_union_set_lift(
2119 __isl_take isl_union_set *uset);
2121 Given a local space that contains the existentially quantified
2122 variables of a set, a basic relation that, when applied to
2123 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2124 can be constructed using the following function.
2126 #include <isl/local_space.h>
2127 __isl_give isl_basic_map *isl_local_space_lifting(
2128 __isl_take isl_local_space *ls);
2130 =item * Internal Product
2132 __isl_give isl_basic_map *isl_basic_map_zip(
2133 __isl_take isl_basic_map *bmap);
2134 __isl_give isl_map *isl_map_zip(
2135 __isl_take isl_map *map);
2136 __isl_give isl_union_map *isl_union_map_zip(
2137 __isl_take isl_union_map *umap);
2139 Given a relation with nested relations for domain and range,
2140 interchange the range of the domain with the domain of the range.
2142 =item * Aligning parameters
2144 __isl_give isl_set *isl_set_align_params(
2145 __isl_take isl_set *set,
2146 __isl_take isl_space *model);
2147 __isl_give isl_map *isl_map_align_params(
2148 __isl_take isl_map *map,
2149 __isl_take isl_space *model);
2151 Change the order of the parameters of the given set or relation
2152 such that the first parameters match those of C<model>.
2153 This may involve the introduction of extra parameters.
2154 All parameters need to be named.
2156 =item * Dimension manipulation
2158 __isl_give isl_set *isl_set_add_dims(
2159 __isl_take isl_set *set,
2160 enum isl_dim_type type, unsigned n);
2161 __isl_give isl_map *isl_map_add_dims(
2162 __isl_take isl_map *map,
2163 enum isl_dim_type type, unsigned n);
2164 __isl_give isl_set *isl_set_insert_dims(
2165 __isl_take isl_set *set,
2166 enum isl_dim_type type, unsigned pos, unsigned n);
2167 __isl_give isl_map *isl_map_insert_dims(
2168 __isl_take isl_map *map,
2169 enum isl_dim_type type, unsigned pos, unsigned n);
2170 __isl_give isl_basic_set *isl_basic_set_move_dims(
2171 __isl_take isl_basic_set *bset,
2172 enum isl_dim_type dst_type, unsigned dst_pos,
2173 enum isl_dim_type src_type, unsigned src_pos,
2175 __isl_give isl_basic_map *isl_basic_map_move_dims(
2176 __isl_take isl_basic_map *bmap,
2177 enum isl_dim_type dst_type, unsigned dst_pos,
2178 enum isl_dim_type src_type, unsigned src_pos,
2180 __isl_give isl_set *isl_set_move_dims(
2181 __isl_take isl_set *set,
2182 enum isl_dim_type dst_type, unsigned dst_pos,
2183 enum isl_dim_type src_type, unsigned src_pos,
2185 __isl_give isl_map *isl_map_move_dims(
2186 __isl_take isl_map *map,
2187 enum isl_dim_type dst_type, unsigned dst_pos,
2188 enum isl_dim_type src_type, unsigned src_pos,
2191 It is usually not advisable to directly change the (input or output)
2192 space of a set or a relation as this removes the name and the internal
2193 structure of the space. However, the above functions can be useful
2194 to add new parameters, assuming
2195 C<isl_set_align_params> and C<isl_map_align_params>
2200 =head2 Binary Operations
2202 The two arguments of a binary operation not only need to live
2203 in the same C<isl_ctx>, they currently also need to have
2204 the same (number of) parameters.
2206 =head3 Basic Operations
2210 =item * Intersection
2212 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2213 __isl_take isl_basic_set *bset1,
2214 __isl_take isl_basic_set *bset2);
2215 __isl_give isl_basic_set *isl_basic_set_intersect(
2216 __isl_take isl_basic_set *bset1,
2217 __isl_take isl_basic_set *bset2);
2218 __isl_give isl_set *isl_set_intersect_params(
2219 __isl_take isl_set *set,
2220 __isl_take isl_set *params);
2221 __isl_give isl_set *isl_set_intersect(
2222 __isl_take isl_set *set1,
2223 __isl_take isl_set *set2);
2224 __isl_give isl_union_set *isl_union_set_intersect_params(
2225 __isl_take isl_union_set *uset,
2226 __isl_take isl_set *set);
2227 __isl_give isl_union_map *isl_union_map_intersect_params(
2228 __isl_take isl_union_map *umap,
2229 __isl_take isl_set *set);
2230 __isl_give isl_union_set *isl_union_set_intersect(
2231 __isl_take isl_union_set *uset1,
2232 __isl_take isl_union_set *uset2);
2233 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2234 __isl_take isl_basic_map *bmap,
2235 __isl_take isl_basic_set *bset);
2236 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2237 __isl_take isl_basic_map *bmap,
2238 __isl_take isl_basic_set *bset);
2239 __isl_give isl_basic_map *isl_basic_map_intersect(
2240 __isl_take isl_basic_map *bmap1,
2241 __isl_take isl_basic_map *bmap2);
2242 __isl_give isl_map *isl_map_intersect_params(
2243 __isl_take isl_map *map,
2244 __isl_take isl_set *params);
2245 __isl_give isl_map *isl_map_intersect_domain(
2246 __isl_take isl_map *map,
2247 __isl_take isl_set *set);
2248 __isl_give isl_map *isl_map_intersect_range(
2249 __isl_take isl_map *map,
2250 __isl_take isl_set *set);
2251 __isl_give isl_map *isl_map_intersect(
2252 __isl_take isl_map *map1,
2253 __isl_take isl_map *map2);
2254 __isl_give isl_union_map *isl_union_map_intersect_domain(
2255 __isl_take isl_union_map *umap,
2256 __isl_take isl_union_set *uset);
2257 __isl_give isl_union_map *isl_union_map_intersect_range(
2258 __isl_take isl_union_map *umap,
2259 __isl_take isl_union_set *uset);
2260 __isl_give isl_union_map *isl_union_map_intersect(
2261 __isl_take isl_union_map *umap1,
2262 __isl_take isl_union_map *umap2);
2266 __isl_give isl_set *isl_basic_set_union(
2267 __isl_take isl_basic_set *bset1,
2268 __isl_take isl_basic_set *bset2);
2269 __isl_give isl_map *isl_basic_map_union(
2270 __isl_take isl_basic_map *bmap1,
2271 __isl_take isl_basic_map *bmap2);
2272 __isl_give isl_set *isl_set_union(
2273 __isl_take isl_set *set1,
2274 __isl_take isl_set *set2);
2275 __isl_give isl_map *isl_map_union(
2276 __isl_take isl_map *map1,
2277 __isl_take isl_map *map2);
2278 __isl_give isl_union_set *isl_union_set_union(
2279 __isl_take isl_union_set *uset1,
2280 __isl_take isl_union_set *uset2);
2281 __isl_give isl_union_map *isl_union_map_union(
2282 __isl_take isl_union_map *umap1,
2283 __isl_take isl_union_map *umap2);
2285 =item * Set difference
2287 __isl_give isl_set *isl_set_subtract(
2288 __isl_take isl_set *set1,
2289 __isl_take isl_set *set2);
2290 __isl_give isl_map *isl_map_subtract(
2291 __isl_take isl_map *map1,
2292 __isl_take isl_map *map2);
2293 __isl_give isl_map *isl_map_subtract_domain(
2294 __isl_take isl_map *map,
2295 __isl_take isl_set *dom);
2296 __isl_give isl_map *isl_map_subtract_range(
2297 __isl_take isl_map *map,
2298 __isl_take isl_set *dom);
2299 __isl_give isl_union_set *isl_union_set_subtract(
2300 __isl_take isl_union_set *uset1,
2301 __isl_take isl_union_set *uset2);
2302 __isl_give isl_union_map *isl_union_map_subtract(
2303 __isl_take isl_union_map *umap1,
2304 __isl_take isl_union_map *umap2);
2308 __isl_give isl_basic_set *isl_basic_set_apply(
2309 __isl_take isl_basic_set *bset,
2310 __isl_take isl_basic_map *bmap);
2311 __isl_give isl_set *isl_set_apply(
2312 __isl_take isl_set *set,
2313 __isl_take isl_map *map);
2314 __isl_give isl_union_set *isl_union_set_apply(
2315 __isl_take isl_union_set *uset,
2316 __isl_take isl_union_map *umap);
2317 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2318 __isl_take isl_basic_map *bmap1,
2319 __isl_take isl_basic_map *bmap2);
2320 __isl_give isl_basic_map *isl_basic_map_apply_range(
2321 __isl_take isl_basic_map *bmap1,
2322 __isl_take isl_basic_map *bmap2);
2323 __isl_give isl_map *isl_map_apply_domain(
2324 __isl_take isl_map *map1,
2325 __isl_take isl_map *map2);
2326 __isl_give isl_union_map *isl_union_map_apply_domain(
2327 __isl_take isl_union_map *umap1,
2328 __isl_take isl_union_map *umap2);
2329 __isl_give isl_map *isl_map_apply_range(
2330 __isl_take isl_map *map1,
2331 __isl_take isl_map *map2);
2332 __isl_give isl_union_map *isl_union_map_apply_range(
2333 __isl_take isl_union_map *umap1,
2334 __isl_take isl_union_map *umap2);
2336 =item * Cartesian Product
2338 __isl_give isl_set *isl_set_product(
2339 __isl_take isl_set *set1,
2340 __isl_take isl_set *set2);
2341 __isl_give isl_union_set *isl_union_set_product(
2342 __isl_take isl_union_set *uset1,
2343 __isl_take isl_union_set *uset2);
2344 __isl_give isl_basic_map *isl_basic_map_domain_product(
2345 __isl_take isl_basic_map *bmap1,
2346 __isl_take isl_basic_map *bmap2);
2347 __isl_give isl_basic_map *isl_basic_map_range_product(
2348 __isl_take isl_basic_map *bmap1,
2349 __isl_take isl_basic_map *bmap2);
2350 __isl_give isl_map *isl_map_domain_product(
2351 __isl_take isl_map *map1,
2352 __isl_take isl_map *map2);
2353 __isl_give isl_map *isl_map_range_product(
2354 __isl_take isl_map *map1,
2355 __isl_take isl_map *map2);
2356 __isl_give isl_union_map *isl_union_map_range_product(
2357 __isl_take isl_union_map *umap1,
2358 __isl_take isl_union_map *umap2);
2359 __isl_give isl_map *isl_map_product(
2360 __isl_take isl_map *map1,
2361 __isl_take isl_map *map2);
2362 __isl_give isl_union_map *isl_union_map_product(
2363 __isl_take isl_union_map *umap1,
2364 __isl_take isl_union_map *umap2);
2366 The above functions compute the cross product of the given
2367 sets or relations. The domains and ranges of the results
2368 are wrapped maps between domains and ranges of the inputs.
2369 To obtain a ``flat'' product, use the following functions
2372 __isl_give isl_basic_set *isl_basic_set_flat_product(
2373 __isl_take isl_basic_set *bset1,
2374 __isl_take isl_basic_set *bset2);
2375 __isl_give isl_set *isl_set_flat_product(
2376 __isl_take isl_set *set1,
2377 __isl_take isl_set *set2);
2378 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2379 __isl_take isl_basic_map *bmap1,
2380 __isl_take isl_basic_map *bmap2);
2381 __isl_give isl_map *isl_map_flat_domain_product(
2382 __isl_take isl_map *map1,
2383 __isl_take isl_map *map2);
2384 __isl_give isl_map *isl_map_flat_range_product(
2385 __isl_take isl_map *map1,
2386 __isl_take isl_map *map2);
2387 __isl_give isl_union_map *isl_union_map_flat_range_product(
2388 __isl_take isl_union_map *umap1,
2389 __isl_take isl_union_map *umap2);
2390 __isl_give isl_basic_map *isl_basic_map_flat_product(
2391 __isl_take isl_basic_map *bmap1,
2392 __isl_take isl_basic_map *bmap2);
2393 __isl_give isl_map *isl_map_flat_product(
2394 __isl_take isl_map *map1,
2395 __isl_take isl_map *map2);
2397 =item * Simplification
2399 __isl_give isl_basic_set *isl_basic_set_gist(
2400 __isl_take isl_basic_set *bset,
2401 __isl_take isl_basic_set *context);
2402 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2403 __isl_take isl_set *context);
2404 __isl_give isl_set *isl_set_gist_params(
2405 __isl_take isl_set *set,
2406 __isl_take isl_set *context);
2407 __isl_give isl_union_set *isl_union_set_gist(
2408 __isl_take isl_union_set *uset,
2409 __isl_take isl_union_set *context);
2410 __isl_give isl_union_set *isl_union_set_gist_params(
2411 __isl_take isl_union_set *uset,
2412 __isl_take isl_set *set);
2413 __isl_give isl_basic_map *isl_basic_map_gist(
2414 __isl_take isl_basic_map *bmap,
2415 __isl_take isl_basic_map *context);
2416 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2417 __isl_take isl_map *context);
2418 __isl_give isl_map *isl_map_gist_params(
2419 __isl_take isl_map *map,
2420 __isl_take isl_set *context);
2421 __isl_give isl_map *isl_map_gist_domain(
2422 __isl_take isl_map *map,
2423 __isl_take isl_set *context);
2424 __isl_give isl_map *isl_map_gist_range(
2425 __isl_take isl_map *map,
2426 __isl_take isl_set *context);
2427 __isl_give isl_union_map *isl_union_map_gist(
2428 __isl_take isl_union_map *umap,
2429 __isl_take isl_union_map *context);
2430 __isl_give isl_union_map *isl_union_map_gist_params(
2431 __isl_take isl_union_map *umap,
2432 __isl_take isl_set *set);
2433 __isl_give isl_union_map *isl_union_map_gist_domain(
2434 __isl_take isl_union_map *umap,
2435 __isl_take isl_union_set *uset);
2437 The gist operation returns a set or relation that has the
2438 same intersection with the context as the input set or relation.
2439 Any implicit equality in the intersection is made explicit in the result,
2440 while all inequalities that are redundant with respect to the intersection
2442 In case of union sets and relations, the gist operation is performed
2447 =head3 Lexicographic Optimization
2449 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2450 the following functions
2451 compute a set that contains the lexicographic minimum or maximum
2452 of the elements in C<set> (or C<bset>) for those values of the parameters
2453 that satisfy C<dom>.
2454 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2455 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2457 In other words, the union of the parameter values
2458 for which the result is non-empty and of C<*empty>
2461 __isl_give isl_set *isl_basic_set_partial_lexmin(
2462 __isl_take isl_basic_set *bset,
2463 __isl_take isl_basic_set *dom,
2464 __isl_give isl_set **empty);
2465 __isl_give isl_set *isl_basic_set_partial_lexmax(
2466 __isl_take isl_basic_set *bset,
2467 __isl_take isl_basic_set *dom,
2468 __isl_give isl_set **empty);
2469 __isl_give isl_set *isl_set_partial_lexmin(
2470 __isl_take isl_set *set, __isl_take isl_set *dom,
2471 __isl_give isl_set **empty);
2472 __isl_give isl_set *isl_set_partial_lexmax(
2473 __isl_take isl_set *set, __isl_take isl_set *dom,
2474 __isl_give isl_set **empty);
2476 Given a (basic) set C<set> (or C<bset>), the following functions simply
2477 return a set containing the lexicographic minimum or maximum
2478 of the elements in C<set> (or C<bset>).
2479 In case of union sets, the optimum is computed per space.
2481 __isl_give isl_set *isl_basic_set_lexmin(
2482 __isl_take isl_basic_set *bset);
2483 __isl_give isl_set *isl_basic_set_lexmax(
2484 __isl_take isl_basic_set *bset);
2485 __isl_give isl_set *isl_set_lexmin(
2486 __isl_take isl_set *set);
2487 __isl_give isl_set *isl_set_lexmax(
2488 __isl_take isl_set *set);
2489 __isl_give isl_union_set *isl_union_set_lexmin(
2490 __isl_take isl_union_set *uset);
2491 __isl_give isl_union_set *isl_union_set_lexmax(
2492 __isl_take isl_union_set *uset);
2494 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2495 the following functions
2496 compute a relation that maps each element of C<dom>
2497 to the single lexicographic minimum or maximum
2498 of the elements that are associated to that same
2499 element in C<map> (or C<bmap>).
2500 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2501 that contains the elements in C<dom> that do not map
2502 to any elements in C<map> (or C<bmap>).
2503 In other words, the union of the domain of the result and of C<*empty>
2506 __isl_give isl_map *isl_basic_map_partial_lexmax(
2507 __isl_take isl_basic_map *bmap,
2508 __isl_take isl_basic_set *dom,
2509 __isl_give isl_set **empty);
2510 __isl_give isl_map *isl_basic_map_partial_lexmin(
2511 __isl_take isl_basic_map *bmap,
2512 __isl_take isl_basic_set *dom,
2513 __isl_give isl_set **empty);
2514 __isl_give isl_map *isl_map_partial_lexmax(
2515 __isl_take isl_map *map, __isl_take isl_set *dom,
2516 __isl_give isl_set **empty);
2517 __isl_give isl_map *isl_map_partial_lexmin(
2518 __isl_take isl_map *map, __isl_take isl_set *dom,
2519 __isl_give isl_set **empty);
2521 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2522 return a map mapping each element in the domain of
2523 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2524 of all elements associated to that element.
2525 In case of union relations, the optimum is computed per space.
2527 __isl_give isl_map *isl_basic_map_lexmin(
2528 __isl_take isl_basic_map *bmap);
2529 __isl_give isl_map *isl_basic_map_lexmax(
2530 __isl_take isl_basic_map *bmap);
2531 __isl_give isl_map *isl_map_lexmin(
2532 __isl_take isl_map *map);
2533 __isl_give isl_map *isl_map_lexmax(
2534 __isl_take isl_map *map);
2535 __isl_give isl_union_map *isl_union_map_lexmin(
2536 __isl_take isl_union_map *umap);
2537 __isl_give isl_union_map *isl_union_map_lexmax(
2538 __isl_take isl_union_map *umap);
2540 The following functions return their result in the form of
2541 a piecewise multi-affine expression
2542 (See L<"Piecewise Multiple Quasi Affine Expressions">),
2543 but are otherwise equivalent to the corresponding functions
2544 returning a basic set or relation.
2546 __isl_give isl_pw_multi_aff *
2547 isl_basic_map_lexmin_pw_multi_aff(
2548 __isl_take isl_basic_map *bmap);
2549 __isl_give isl_pw_multi_aff *
2550 isl_basic_set_partial_lexmin_pw_multi_aff(
2551 __isl_take isl_basic_set *bset,
2552 __isl_take isl_basic_set *dom,
2553 __isl_give isl_set **empty);
2554 __isl_give isl_pw_multi_aff *
2555 isl_basic_set_partial_lexmax_pw_multi_aff(
2556 __isl_take isl_basic_set *bset,
2557 __isl_take isl_basic_set *dom,
2558 __isl_give isl_set **empty);
2559 __isl_give isl_pw_multi_aff *
2560 isl_basic_map_partial_lexmin_pw_multi_aff(
2561 __isl_take isl_basic_map *bmap,
2562 __isl_take isl_basic_set *dom,
2563 __isl_give isl_set **empty);
2564 __isl_give isl_pw_multi_aff *
2565 isl_basic_map_partial_lexmax_pw_multi_aff(
2566 __isl_take isl_basic_map *bmap,
2567 __isl_take isl_basic_set *dom,
2568 __isl_give isl_set **empty);
2572 Lists are defined over several element types, including
2573 C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2574 Here we take lists of C<isl_set>s as an example.
2575 Lists can be created, copied and freed using the following functions.
2577 #include <isl/list.h>
2578 __isl_give isl_set_list *isl_set_list_from_set(
2579 __isl_take isl_set *el);
2580 __isl_give isl_set_list *isl_set_list_alloc(
2581 isl_ctx *ctx, int n);
2582 __isl_give isl_set_list *isl_set_list_copy(
2583 __isl_keep isl_set_list *list);
2584 __isl_give isl_set_list *isl_set_list_add(
2585 __isl_take isl_set_list *list,
2586 __isl_take isl_set *el);
2587 __isl_give isl_set_list *isl_set_list_concat(
2588 __isl_take isl_set_list *list1,
2589 __isl_take isl_set_list *list2);
2590 void *isl_set_list_free(__isl_take isl_set_list *list);
2592 C<isl_set_list_alloc> creates an empty list with a capacity for
2593 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2596 Lists can be inspected using the following functions.
2598 #include <isl/list.h>
2599 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2600 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2601 __isl_give isl_set *isl_set_list_get_set(
2602 __isl_keep isl_set_list *list, int index);
2603 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2604 int (*fn)(__isl_take isl_set *el, void *user),
2607 Lists can be printed using
2609 #include <isl/list.h>
2610 __isl_give isl_printer *isl_printer_print_set_list(
2611 __isl_take isl_printer *p,
2612 __isl_keep isl_set_list *list);
2616 Matrices can be created, copied and freed using the following functions.
2618 #include <isl/mat.h>
2619 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2620 unsigned n_row, unsigned n_col);
2621 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2622 void isl_mat_free(__isl_take isl_mat *mat);
2624 Note that the elements of a newly created matrix may have arbitrary values.
2625 The elements can be changed and inspected using the following functions.
2627 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2628 int isl_mat_rows(__isl_keep isl_mat *mat);
2629 int isl_mat_cols(__isl_keep isl_mat *mat);
2630 int isl_mat_get_element(__isl_keep isl_mat *mat,
2631 int row, int col, isl_int *v);
2632 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2633 int row, int col, isl_int v);
2634 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2635 int row, int col, int v);
2637 C<isl_mat_get_element> will return a negative value if anything went wrong.
2638 In that case, the value of C<*v> is undefined.
2640 The following function can be used to compute the (right) inverse
2641 of a matrix, i.e., a matrix such that the product of the original
2642 and the inverse (in that order) is a multiple of the identity matrix.
2643 The input matrix is assumed to be of full row-rank.
2645 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2647 The following function can be used to compute the (right) kernel
2648 (or null space) of a matrix, i.e., a matrix such that the product of
2649 the original and the kernel (in that order) is the zero matrix.
2651 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2653 =head2 Piecewise Quasi Affine Expressions
2655 The zero quasi affine expression on a given domain can be created using
2657 __isl_give isl_aff *isl_aff_zero_on_domain(
2658 __isl_take isl_local_space *ls);
2660 Note that the space in which the resulting object lives is a map space
2661 with the given space as domain and a one-dimensional range.
2663 An empty piecewise quasi affine expression (one with no cells)
2664 or a piecewise quasi affine expression with a single cell can
2665 be created using the following functions.
2667 #include <isl/aff.h>
2668 __isl_give isl_pw_aff *isl_pw_aff_empty(
2669 __isl_take isl_space *space);
2670 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2671 __isl_take isl_set *set, __isl_take isl_aff *aff);
2672 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2673 __isl_take isl_aff *aff);
2675 Quasi affine expressions can be copied and freed using
2677 #include <isl/aff.h>
2678 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2679 void *isl_aff_free(__isl_take isl_aff *aff);
2681 __isl_give isl_pw_aff *isl_pw_aff_copy(
2682 __isl_keep isl_pw_aff *pwaff);
2683 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2685 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2686 using the following function. The constraint is required to have
2687 a non-zero coefficient for the specified dimension.
2689 #include <isl/constraint.h>
2690 __isl_give isl_aff *isl_constraint_get_bound(
2691 __isl_keep isl_constraint *constraint,
2692 enum isl_dim_type type, int pos);
2694 The entire affine expression of the constraint can also be extracted
2695 using the following function.
2697 #include <isl/constraint.h>
2698 __isl_give isl_aff *isl_constraint_get_aff(
2699 __isl_keep isl_constraint *constraint);
2701 Conversely, an equality constraint equating
2702 the affine expression to zero or an inequality constraint enforcing
2703 the affine expression to be non-negative, can be constructed using
2705 __isl_give isl_constraint *isl_equality_from_aff(
2706 __isl_take isl_aff *aff);
2707 __isl_give isl_constraint *isl_inequality_from_aff(
2708 __isl_take isl_aff *aff);
2710 The expression can be inspected using
2712 #include <isl/aff.h>
2713 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2714 int isl_aff_dim(__isl_keep isl_aff *aff,
2715 enum isl_dim_type type);
2716 __isl_give isl_local_space *isl_aff_get_domain_local_space(
2717 __isl_keep isl_aff *aff);
2718 __isl_give isl_local_space *isl_aff_get_local_space(
2719 __isl_keep isl_aff *aff);
2720 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2721 enum isl_dim_type type, unsigned pos);
2722 const char *isl_pw_aff_get_dim_name(
2723 __isl_keep isl_pw_aff *pa,
2724 enum isl_dim_type type, unsigned pos);
2725 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
2726 enum isl_dim_type type, unsigned pos);
2727 __isl_give isl_id *isl_pw_aff_get_dim_id(
2728 __isl_keep isl_pw_aff *pa,
2729 enum isl_dim_type type, unsigned pos);
2730 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2732 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2733 enum isl_dim_type type, int pos, isl_int *v);
2734 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2736 __isl_give isl_aff *isl_aff_get_div(
2737 __isl_keep isl_aff *aff, int pos);
2739 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2740 int (*fn)(__isl_take isl_set *set,
2741 __isl_take isl_aff *aff,
2742 void *user), void *user);
2744 int isl_aff_is_cst(__isl_keep isl_aff *aff);
2745 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
2747 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
2748 enum isl_dim_type type, unsigned first, unsigned n);
2749 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
2750 enum isl_dim_type type, unsigned first, unsigned n);
2752 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2753 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2754 enum isl_dim_type type);
2755 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2757 It can be modified using
2759 #include <isl/aff.h>
2760 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
2761 __isl_take isl_pw_aff *pwaff,
2762 enum isl_dim_type type, __isl_take isl_id *id);
2763 __isl_give isl_aff *isl_aff_set_dim_name(
2764 __isl_take isl_aff *aff, enum isl_dim_type type,
2765 unsigned pos, const char *s);
2766 __isl_give isl_aff *isl_aff_set_dim_id(
2767 __isl_take isl_aff *aff, enum isl_dim_type type,
2768 unsigned pos, __isl_take isl_id *id);
2769 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
2770 __isl_take isl_pw_aff *pma,
2771 enum isl_dim_type type, unsigned pos,
2772 __isl_take isl_id *id);
2773 __isl_give isl_aff *isl_aff_set_constant(
2774 __isl_take isl_aff *aff, isl_int v);
2775 __isl_give isl_aff *isl_aff_set_constant_si(
2776 __isl_take isl_aff *aff, int v);
2777 __isl_give isl_aff *isl_aff_set_coefficient(
2778 __isl_take isl_aff *aff,
2779 enum isl_dim_type type, int pos, isl_int v);
2780 __isl_give isl_aff *isl_aff_set_coefficient_si(
2781 __isl_take isl_aff *aff,
2782 enum isl_dim_type type, int pos, int v);
2783 __isl_give isl_aff *isl_aff_set_denominator(
2784 __isl_take isl_aff *aff, isl_int v);
2786 __isl_give isl_aff *isl_aff_add_constant(
2787 __isl_take isl_aff *aff, isl_int v);
2788 __isl_give isl_aff *isl_aff_add_constant_si(
2789 __isl_take isl_aff *aff, int v);
2790 __isl_give isl_aff *isl_aff_add_coefficient(
2791 __isl_take isl_aff *aff,
2792 enum isl_dim_type type, int pos, isl_int v);
2793 __isl_give isl_aff *isl_aff_add_coefficient_si(
2794 __isl_take isl_aff *aff,
2795 enum isl_dim_type type, int pos, int v);
2797 __isl_give isl_aff *isl_aff_insert_dims(
2798 __isl_take isl_aff *aff,
2799 enum isl_dim_type type, unsigned first, unsigned n);
2800 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
2801 __isl_take isl_pw_aff *pwaff,
2802 enum isl_dim_type type, unsigned first, unsigned n);
2803 __isl_give isl_aff *isl_aff_add_dims(
2804 __isl_take isl_aff *aff,
2805 enum isl_dim_type type, unsigned n);
2806 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
2807 __isl_take isl_pw_aff *pwaff,
2808 enum isl_dim_type type, unsigned n);
2809 __isl_give isl_aff *isl_aff_drop_dims(
2810 __isl_take isl_aff *aff,
2811 enum isl_dim_type type, unsigned first, unsigned n);
2812 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
2813 __isl_take isl_pw_aff *pwaff,
2814 enum isl_dim_type type, unsigned first, unsigned n);
2816 Note that the C<set_constant> and C<set_coefficient> functions
2817 set the I<numerator> of the constant or coefficient, while
2818 C<add_constant> and C<add_coefficient> add an integer value to
2819 the possibly rational constant or coefficient.
2821 To check whether an affine expressions is obviously zero
2822 or obviously equal to some other affine expression, use
2824 #include <isl/aff.h>
2825 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
2826 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
2827 __isl_keep isl_aff *aff2);
2828 int isl_pw_aff_plain_is_equal(
2829 __isl_keep isl_pw_aff *pwaff1,
2830 __isl_keep isl_pw_aff *pwaff2);
2834 #include <isl/aff.h>
2835 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2836 __isl_take isl_aff *aff2);
2837 __isl_give isl_pw_aff *isl_pw_aff_add(
2838 __isl_take isl_pw_aff *pwaff1,
2839 __isl_take isl_pw_aff *pwaff2);
2840 __isl_give isl_pw_aff *isl_pw_aff_min(
2841 __isl_take isl_pw_aff *pwaff1,
2842 __isl_take isl_pw_aff *pwaff2);
2843 __isl_give isl_pw_aff *isl_pw_aff_max(
2844 __isl_take isl_pw_aff *pwaff1,
2845 __isl_take isl_pw_aff *pwaff2);
2846 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2847 __isl_take isl_aff *aff2);
2848 __isl_give isl_pw_aff *isl_pw_aff_sub(
2849 __isl_take isl_pw_aff *pwaff1,
2850 __isl_take isl_pw_aff *pwaff2);
2851 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2852 __isl_give isl_pw_aff *isl_pw_aff_neg(
2853 __isl_take isl_pw_aff *pwaff);
2854 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2855 __isl_give isl_pw_aff *isl_pw_aff_ceil(
2856 __isl_take isl_pw_aff *pwaff);
2857 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
2858 __isl_give isl_pw_aff *isl_pw_aff_floor(
2859 __isl_take isl_pw_aff *pwaff);
2860 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
2862 __isl_give isl_pw_aff *isl_pw_aff_mod(
2863 __isl_take isl_pw_aff *pwaff, isl_int mod);
2864 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2866 __isl_give isl_pw_aff *isl_pw_aff_scale(
2867 __isl_take isl_pw_aff *pwaff, isl_int f);
2868 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2870 __isl_give isl_aff *isl_aff_scale_down_ui(
2871 __isl_take isl_aff *aff, unsigned f);
2872 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
2873 __isl_take isl_pw_aff *pwaff, isl_int f);
2875 __isl_give isl_pw_aff *isl_pw_aff_list_min(
2876 __isl_take isl_pw_aff_list *list);
2877 __isl_give isl_pw_aff *isl_pw_aff_list_max(
2878 __isl_take isl_pw_aff_list *list);
2880 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
2881 __isl_take isl_pw_aff *pwqp);
2883 __isl_give isl_pw_aff *isl_pw_aff_align_params(
2884 __isl_take isl_pw_aff *pwaff,
2885 __isl_take isl_space *model);
2887 __isl_give isl_aff *isl_aff_gist_params(
2888 __isl_take isl_aff *aff,
2889 __isl_take isl_set *context);
2890 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
2891 __isl_take isl_set *context);
2892 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
2893 __isl_take isl_pw_aff *pwaff,
2894 __isl_take isl_set *context);
2895 __isl_give isl_pw_aff *isl_pw_aff_gist(
2896 __isl_take isl_pw_aff *pwaff,
2897 __isl_take isl_set *context);
2899 __isl_give isl_set *isl_pw_aff_domain(
2900 __isl_take isl_pw_aff *pwaff);
2901 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
2902 __isl_take isl_pw_aff *pa,
2903 __isl_take isl_set *set);
2904 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
2905 __isl_take isl_pw_aff *pa,
2906 __isl_take isl_set *set);
2908 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
2909 __isl_take isl_aff *aff2);
2910 __isl_give isl_pw_aff *isl_pw_aff_mul(
2911 __isl_take isl_pw_aff *pwaff1,
2912 __isl_take isl_pw_aff *pwaff2);
2914 When multiplying two affine expressions, at least one of the two needs
2917 #include <isl/aff.h>
2918 __isl_give isl_basic_set *isl_aff_le_basic_set(
2919 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2920 __isl_give isl_basic_set *isl_aff_ge_basic_set(
2921 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2922 __isl_give isl_set *isl_pw_aff_eq_set(
2923 __isl_take isl_pw_aff *pwaff1,
2924 __isl_take isl_pw_aff *pwaff2);
2925 __isl_give isl_set *isl_pw_aff_ne_set(
2926 __isl_take isl_pw_aff *pwaff1,
2927 __isl_take isl_pw_aff *pwaff2);
2928 __isl_give isl_set *isl_pw_aff_le_set(
2929 __isl_take isl_pw_aff *pwaff1,
2930 __isl_take isl_pw_aff *pwaff2);
2931 __isl_give isl_set *isl_pw_aff_lt_set(
2932 __isl_take isl_pw_aff *pwaff1,
2933 __isl_take isl_pw_aff *pwaff2);
2934 __isl_give isl_set *isl_pw_aff_ge_set(
2935 __isl_take isl_pw_aff *pwaff1,
2936 __isl_take isl_pw_aff *pwaff2);
2937 __isl_give isl_set *isl_pw_aff_gt_set(
2938 __isl_take isl_pw_aff *pwaff1,
2939 __isl_take isl_pw_aff *pwaff2);
2941 __isl_give isl_set *isl_pw_aff_list_eq_set(
2942 __isl_take isl_pw_aff_list *list1,
2943 __isl_take isl_pw_aff_list *list2);
2944 __isl_give isl_set *isl_pw_aff_list_ne_set(
2945 __isl_take isl_pw_aff_list *list1,
2946 __isl_take isl_pw_aff_list *list2);
2947 __isl_give isl_set *isl_pw_aff_list_le_set(
2948 __isl_take isl_pw_aff_list *list1,
2949 __isl_take isl_pw_aff_list *list2);
2950 __isl_give isl_set *isl_pw_aff_list_lt_set(
2951 __isl_take isl_pw_aff_list *list1,
2952 __isl_take isl_pw_aff_list *list2);
2953 __isl_give isl_set *isl_pw_aff_list_ge_set(
2954 __isl_take isl_pw_aff_list *list1,
2955 __isl_take isl_pw_aff_list *list2);
2956 __isl_give isl_set *isl_pw_aff_list_gt_set(
2957 __isl_take isl_pw_aff_list *list1,
2958 __isl_take isl_pw_aff_list *list2);
2960 The function C<isl_aff_ge_basic_set> returns a basic set
2961 containing those elements in the shared space
2962 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
2963 The function C<isl_aff_ge_set> returns a set
2964 containing those elements in the shared domain
2965 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
2966 The functions operating on C<isl_pw_aff_list> apply the corresponding
2967 C<isl_pw_aff> function to each pair of elements in the two lists.
2969 #include <isl/aff.h>
2970 __isl_give isl_set *isl_pw_aff_nonneg_set(
2971 __isl_take isl_pw_aff *pwaff);
2972 __isl_give isl_set *isl_pw_aff_zero_set(
2973 __isl_take isl_pw_aff *pwaff);
2974 __isl_give isl_set *isl_pw_aff_non_zero_set(
2975 __isl_take isl_pw_aff *pwaff);
2977 The function C<isl_pw_aff_nonneg_set> returns a set
2978 containing those elements in the domain
2979 of C<pwaff> where C<pwaff> is non-negative.
2981 #include <isl/aff.h>
2982 __isl_give isl_pw_aff *isl_pw_aff_cond(
2983 __isl_take isl_set *cond,
2984 __isl_take isl_pw_aff *pwaff_true,
2985 __isl_take isl_pw_aff *pwaff_false);
2987 The function C<isl_pw_aff_cond> performs a conditional operator
2988 and returns an expression that is equal to C<pwaff_true>
2989 for elements in C<cond> and equal to C<pwaff_false> for elements
2992 #include <isl/aff.h>
2993 __isl_give isl_pw_aff *isl_pw_aff_union_min(
2994 __isl_take isl_pw_aff *pwaff1,
2995 __isl_take isl_pw_aff *pwaff2);
2996 __isl_give isl_pw_aff *isl_pw_aff_union_max(
2997 __isl_take isl_pw_aff *pwaff1,
2998 __isl_take isl_pw_aff *pwaff2);
2999 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3000 __isl_take isl_pw_aff *pwaff1,
3001 __isl_take isl_pw_aff *pwaff2);
3003 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3004 expression with a domain that is the union of those of C<pwaff1> and
3005 C<pwaff2> and such that on each cell, the quasi-affine expression is
3006 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3007 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3008 associated expression is the defined one.
3010 An expression can be read from input using
3012 #include <isl/aff.h>
3013 __isl_give isl_aff *isl_aff_read_from_str(
3014 isl_ctx *ctx, const char *str);
3015 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3016 isl_ctx *ctx, const char *str);
3018 An expression can be printed using
3020 #include <isl/aff.h>
3021 __isl_give isl_printer *isl_printer_print_aff(
3022 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3024 __isl_give isl_printer *isl_printer_print_pw_aff(
3025 __isl_take isl_printer *p,
3026 __isl_keep isl_pw_aff *pwaff);
3028 =head2 Piecewise Multiple Quasi Affine Expressions
3030 An C<isl_multi_aff> object represents a sequence of
3031 zero or more affine expressions, all defined on the same domain space.
3033 An C<isl_multi_aff> can be constructed from a C<isl_aff_list> using the
3036 #include <isl/aff.h>
3037 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3038 __isl_take isl_space *space,
3039 __isl_take isl_aff_list *list);
3041 An empty piecewise multiple quasi affine expression (one with no cells) or
3042 a piecewise multiple quasi affine expression with a single cell can
3043 be created using the following functions.
3045 #include <isl/aff.h>
3046 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3047 __isl_take isl_space *space);
3048 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3049 __isl_take isl_set *set,
3050 __isl_take isl_multi_aff *maff);
3052 A piecewise multiple quasi affine expression can also be initialized
3053 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3054 and the C<isl_map> is single-valued.
3056 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3057 __isl_take isl_set *set);
3058 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3059 __isl_take isl_map *map);
3061 Multiple quasi affine expressions can be copied and freed using
3063 #include <isl/aff.h>
3064 __isl_give isl_multi_aff *isl_multi_aff_copy(
3065 __isl_keep isl_multi_aff *maff);
3066 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
3068 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3069 __isl_keep isl_pw_multi_aff *pma);
3070 void *isl_pw_multi_aff_free(
3071 __isl_take isl_pw_multi_aff *pma);
3073 The expression can be inspected using
3075 #include <isl/aff.h>
3076 isl_ctx *isl_multi_aff_get_ctx(
3077 __isl_keep isl_multi_aff *maff);
3078 isl_ctx *isl_pw_multi_aff_get_ctx(
3079 __isl_keep isl_pw_multi_aff *pma);
3080 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
3081 enum isl_dim_type type);
3082 unsigned isl_pw_multi_aff_dim(
3083 __isl_keep isl_pw_multi_aff *pma,
3084 enum isl_dim_type type);
3085 __isl_give isl_aff *isl_multi_aff_get_aff(
3086 __isl_keep isl_multi_aff *multi, int pos);
3087 const char *isl_pw_multi_aff_get_dim_name(
3088 __isl_keep isl_pw_multi_aff *pma,
3089 enum isl_dim_type type, unsigned pos);
3090 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
3091 __isl_keep isl_pw_multi_aff *pma,
3092 enum isl_dim_type type, unsigned pos);
3093 const char *isl_multi_aff_get_tuple_name(
3094 __isl_keep isl_multi_aff *multi,
3095 enum isl_dim_type type);
3096 const char *isl_pw_multi_aff_get_tuple_name(
3097 __isl_keep isl_pw_multi_aff *pma,
3098 enum isl_dim_type type);
3099 int isl_pw_multi_aff_has_tuple_id(
3100 __isl_keep isl_pw_multi_aff *pma,
3101 enum isl_dim_type type);
3102 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
3103 __isl_keep isl_pw_multi_aff *pma,
3104 enum isl_dim_type type);
3106 int isl_pw_multi_aff_foreach_piece(
3107 __isl_keep isl_pw_multi_aff *pma,
3108 int (*fn)(__isl_take isl_set *set,
3109 __isl_take isl_multi_aff *maff,
3110 void *user), void *user);
3112 It can be modified using
3114 #include <isl/aff.h>
3115 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
3116 __isl_take isl_multi_aff *maff,
3117 enum isl_dim_type type, unsigned pos, const char *s);
3118 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
3119 __isl_take isl_pw_multi_aff *pma,
3120 enum isl_dim_type type, __isl_take isl_id *id);
3122 To check whether two multiple affine expressions are
3123 obviously equal to each other, use
3125 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
3126 __isl_keep isl_multi_aff *maff2);
3127 int isl_pw_multi_aff_plain_is_equal(
3128 __isl_keep isl_pw_multi_aff *pma1,
3129 __isl_keep isl_pw_multi_aff *pma2);
3133 #include <isl/aff.h>
3134 __isl_give isl_multi_aff *isl_multi_aff_add(
3135 __isl_take isl_multi_aff *maff1,
3136 __isl_take isl_multi_aff *maff2);
3137 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
3138 __isl_take isl_pw_multi_aff *pma1,
3139 __isl_take isl_pw_multi_aff *pma2);
3140 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
3141 __isl_take isl_pw_multi_aff *pma1,
3142 __isl_take isl_pw_multi_aff *pma2);
3143 __isl_give isl_multi_aff *isl_multi_aff_scale(
3144 __isl_take isl_multi_aff *maff,
3146 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
3147 __isl_take isl_pw_multi_aff *pma,
3148 __isl_take isl_set *set);
3149 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
3150 __isl_take isl_pw_multi_aff *pma,
3151 __isl_take isl_set *set);
3152 __isl_give isl_multi_aff *isl_multi_aff_lift(
3153 __isl_take isl_multi_aff *maff,
3154 __isl_give isl_local_space **ls);
3155 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
3156 __isl_take isl_multi_aff *maff,
3157 __isl_take isl_set *context);
3158 __isl_give isl_multi_aff *isl_multi_aff_gist(
3159 __isl_take isl_multi_aff *maff,
3160 __isl_take isl_set *context);
3161 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
3162 __isl_take isl_pw_multi_aff *pma,
3163 __isl_take isl_set *set);
3164 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
3165 __isl_take isl_pw_multi_aff *pma,
3166 __isl_take isl_set *set);
3168 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
3169 then it is assigned the local space that lies at the basis of
3170 the lifting applied.
3172 An expression can be read from input using
3174 #include <isl/aff.h>
3175 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3176 isl_ctx *ctx, const char *str);
3177 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3178 isl_ctx *ctx, const char *str);
3180 An expression can be printed using
3182 #include <isl/aff.h>
3183 __isl_give isl_printer *isl_printer_print_multi_aff(
3184 __isl_take isl_printer *p,
3185 __isl_keep isl_multi_aff *maff);
3186 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3187 __isl_take isl_printer *p,
3188 __isl_keep isl_pw_multi_aff *pma);
3192 Points are elements of a set. They can be used to construct
3193 simple sets (boxes) or they can be used to represent the
3194 individual elements of a set.
3195 The zero point (the origin) can be created using
3197 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
3199 The coordinates of a point can be inspected, set and changed
3202 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
3203 enum isl_dim_type type, int pos, isl_int *v);
3204 __isl_give isl_point *isl_point_set_coordinate(
3205 __isl_take isl_point *pnt,
3206 enum isl_dim_type type, int pos, isl_int v);
3208 __isl_give isl_point *isl_point_add_ui(
3209 __isl_take isl_point *pnt,
3210 enum isl_dim_type type, int pos, unsigned val);
3211 __isl_give isl_point *isl_point_sub_ui(
3212 __isl_take isl_point *pnt,
3213 enum isl_dim_type type, int pos, unsigned val);
3215 Other properties can be obtained using
3217 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
3219 Points can be copied or freed using
3221 __isl_give isl_point *isl_point_copy(
3222 __isl_keep isl_point *pnt);
3223 void isl_point_free(__isl_take isl_point *pnt);
3225 A singleton set can be created from a point using
3227 __isl_give isl_basic_set *isl_basic_set_from_point(
3228 __isl_take isl_point *pnt);
3229 __isl_give isl_set *isl_set_from_point(
3230 __isl_take isl_point *pnt);
3232 and a box can be created from two opposite extremal points using
3234 __isl_give isl_basic_set *isl_basic_set_box_from_points(
3235 __isl_take isl_point *pnt1,
3236 __isl_take isl_point *pnt2);
3237 __isl_give isl_set *isl_set_box_from_points(
3238 __isl_take isl_point *pnt1,
3239 __isl_take isl_point *pnt2);
3241 All elements of a B<bounded> (union) set can be enumerated using
3242 the following functions.
3244 int isl_set_foreach_point(__isl_keep isl_set *set,
3245 int (*fn)(__isl_take isl_point *pnt, void *user),
3247 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
3248 int (*fn)(__isl_take isl_point *pnt, void *user),
3251 The function C<fn> is called for each integer point in
3252 C<set> with as second argument the last argument of
3253 the C<isl_set_foreach_point> call. The function C<fn>
3254 should return C<0> on success and C<-1> on failure.
3255 In the latter case, C<isl_set_foreach_point> will stop
3256 enumerating and return C<-1> as well.
3257 If the enumeration is performed successfully and to completion,
3258 then C<isl_set_foreach_point> returns C<0>.
3260 To obtain a single point of a (basic) set, use
3262 __isl_give isl_point *isl_basic_set_sample_point(
3263 __isl_take isl_basic_set *bset);
3264 __isl_give isl_point *isl_set_sample_point(
3265 __isl_take isl_set *set);
3267 If C<set> does not contain any (integer) points, then the
3268 resulting point will be ``void'', a property that can be
3271 int isl_point_is_void(__isl_keep isl_point *pnt);
3273 =head2 Piecewise Quasipolynomials
3275 A piecewise quasipolynomial is a particular kind of function that maps
3276 a parametric point to a rational value.
3277 More specifically, a quasipolynomial is a polynomial expression in greatest
3278 integer parts of affine expressions of parameters and variables.
3279 A piecewise quasipolynomial is a subdivision of a given parametric
3280 domain into disjoint cells with a quasipolynomial associated to
3281 each cell. The value of the piecewise quasipolynomial at a given
3282 point is the value of the quasipolynomial associated to the cell
3283 that contains the point. Outside of the union of cells,
3284 the value is assumed to be zero.
3285 For example, the piecewise quasipolynomial
3287 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3289 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
3290 A given piecewise quasipolynomial has a fixed domain dimension.
3291 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
3292 defined over different domains.
3293 Piecewise quasipolynomials are mainly used by the C<barvinok>
3294 library for representing the number of elements in a parametric set or map.
3295 For example, the piecewise quasipolynomial above represents
3296 the number of points in the map
3298 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3300 =head3 Input and Output
3302 Piecewise quasipolynomials can be read from input using
3304 __isl_give isl_union_pw_qpolynomial *
3305 isl_union_pw_qpolynomial_read_from_str(
3306 isl_ctx *ctx, const char *str);
3308 Quasipolynomials and piecewise quasipolynomials can be printed
3309 using the following functions.
3311 __isl_give isl_printer *isl_printer_print_qpolynomial(
3312 __isl_take isl_printer *p,
3313 __isl_keep isl_qpolynomial *qp);
3315 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3316 __isl_take isl_printer *p,
3317 __isl_keep isl_pw_qpolynomial *pwqp);
3319 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3320 __isl_take isl_printer *p,
3321 __isl_keep isl_union_pw_qpolynomial *upwqp);
3323 The output format of the printer
3324 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3325 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
3327 In case of printing in C<ISL_FORMAT_C>, the user may want
3328 to set the names of all dimensions
3330 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
3331 __isl_take isl_qpolynomial *qp,
3332 enum isl_dim_type type, unsigned pos,
3334 __isl_give isl_pw_qpolynomial *
3335 isl_pw_qpolynomial_set_dim_name(
3336 __isl_take isl_pw_qpolynomial *pwqp,
3337 enum isl_dim_type type, unsigned pos,
3340 =head3 Creating New (Piecewise) Quasipolynomials
3342 Some simple quasipolynomials can be created using the following functions.
3343 More complicated quasipolynomials can be created by applying
3344 operations such as addition and multiplication
3345 on the resulting quasipolynomials
3347 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3348 __isl_take isl_space *domain);
3349 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3350 __isl_take isl_space *domain);
3351 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3352 __isl_take isl_space *domain);
3353 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3354 __isl_take isl_space *domain);
3355 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3356 __isl_take isl_space *domain);
3357 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
3358 __isl_take isl_space *domain,
3359 const isl_int n, const isl_int d);
3360 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3361 __isl_take isl_space *domain,
3362 enum isl_dim_type type, unsigned pos);
3363 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3364 __isl_take isl_aff *aff);
3366 Note that the space in which a quasipolynomial lives is a map space
3367 with a one-dimensional range. The C<domain> argument in some of
3368 the functions above corresponds to the domain of this map space.
3370 The zero piecewise quasipolynomial or a piecewise quasipolynomial
3371 with a single cell can be created using the following functions.
3372 Multiple of these single cell piecewise quasipolynomials can
3373 be combined to create more complicated piecewise quasipolynomials.
3375 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3376 __isl_take isl_space *space);
3377 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3378 __isl_take isl_set *set,
3379 __isl_take isl_qpolynomial *qp);
3380 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3381 __isl_take isl_qpolynomial *qp);
3382 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3383 __isl_take isl_pw_aff *pwaff);
3385 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3386 __isl_take isl_space *space);
3387 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3388 __isl_take isl_pw_qpolynomial *pwqp);
3389 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3390 __isl_take isl_union_pw_qpolynomial *upwqp,
3391 __isl_take isl_pw_qpolynomial *pwqp);
3393 Quasipolynomials can be copied and freed again using the following
3396 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3397 __isl_keep isl_qpolynomial *qp);
3398 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3400 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3401 __isl_keep isl_pw_qpolynomial *pwqp);
3402 void *isl_pw_qpolynomial_free(
3403 __isl_take isl_pw_qpolynomial *pwqp);
3405 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3406 __isl_keep isl_union_pw_qpolynomial *upwqp);
3407 void isl_union_pw_qpolynomial_free(
3408 __isl_take isl_union_pw_qpolynomial *upwqp);
3410 =head3 Inspecting (Piecewise) Quasipolynomials
3412 To iterate over all piecewise quasipolynomials in a union
3413 piecewise quasipolynomial, use the following function
3415 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3416 __isl_keep isl_union_pw_qpolynomial *upwqp,
3417 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3420 To extract the piecewise quasipolynomial in a given space from a union, use
3422 __isl_give isl_pw_qpolynomial *
3423 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3424 __isl_keep isl_union_pw_qpolynomial *upwqp,
3425 __isl_take isl_space *space);
3427 To iterate over the cells in a piecewise quasipolynomial,
3428 use either of the following two functions
3430 int isl_pw_qpolynomial_foreach_piece(
3431 __isl_keep isl_pw_qpolynomial *pwqp,
3432 int (*fn)(__isl_take isl_set *set,
3433 __isl_take isl_qpolynomial *qp,
3434 void *user), void *user);
3435 int isl_pw_qpolynomial_foreach_lifted_piece(
3436 __isl_keep isl_pw_qpolynomial *pwqp,
3437 int (*fn)(__isl_take isl_set *set,
3438 __isl_take isl_qpolynomial *qp,
3439 void *user), void *user);
3441 As usual, the function C<fn> should return C<0> on success
3442 and C<-1> on failure. The difference between
3443 C<isl_pw_qpolynomial_foreach_piece> and
3444 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3445 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3446 compute unique representations for all existentially quantified
3447 variables and then turn these existentially quantified variables
3448 into extra set variables, adapting the associated quasipolynomial
3449 accordingly. This means that the C<set> passed to C<fn>
3450 will not have any existentially quantified variables, but that
3451 the dimensions of the sets may be different for different
3452 invocations of C<fn>.
3454 To iterate over all terms in a quasipolynomial,
3457 int isl_qpolynomial_foreach_term(
3458 __isl_keep isl_qpolynomial *qp,
3459 int (*fn)(__isl_take isl_term *term,
3460 void *user), void *user);
3462 The terms themselves can be inspected and freed using
3465 unsigned isl_term_dim(__isl_keep isl_term *term,
3466 enum isl_dim_type type);
3467 void isl_term_get_num(__isl_keep isl_term *term,
3469 void isl_term_get_den(__isl_keep isl_term *term,
3471 int isl_term_get_exp(__isl_keep isl_term *term,
3472 enum isl_dim_type type, unsigned pos);
3473 __isl_give isl_aff *isl_term_get_div(
3474 __isl_keep isl_term *term, unsigned pos);
3475 void isl_term_free(__isl_take isl_term *term);
3477 Each term is a product of parameters, set variables and
3478 integer divisions. The function C<isl_term_get_exp>
3479 returns the exponent of a given dimensions in the given term.
3480 The C<isl_int>s in the arguments of C<isl_term_get_num>
3481 and C<isl_term_get_den> need to have been initialized
3482 using C<isl_int_init> before calling these functions.
3484 =head3 Properties of (Piecewise) Quasipolynomials
3486 To check whether a quasipolynomial is actually a constant,
3487 use the following function.
3489 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3490 isl_int *n, isl_int *d);
3492 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3493 then the numerator and denominator of the constant
3494 are returned in C<*n> and C<*d>, respectively.
3496 To check whether two union piecewise quasipolynomials are
3497 obviously equal, use
3499 int isl_union_pw_qpolynomial_plain_is_equal(
3500 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3501 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3503 =head3 Operations on (Piecewise) Quasipolynomials
3505 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3506 __isl_take isl_qpolynomial *qp, isl_int v);
3507 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3508 __isl_take isl_qpolynomial *qp);
3509 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3510 __isl_take isl_qpolynomial *qp1,
3511 __isl_take isl_qpolynomial *qp2);
3512 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3513 __isl_take isl_qpolynomial *qp1,
3514 __isl_take isl_qpolynomial *qp2);
3515 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3516 __isl_take isl_qpolynomial *qp1,
3517 __isl_take isl_qpolynomial *qp2);
3518 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3519 __isl_take isl_qpolynomial *qp, unsigned exponent);
3521 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3522 __isl_take isl_pw_qpolynomial *pwqp1,
3523 __isl_take isl_pw_qpolynomial *pwqp2);
3524 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3525 __isl_take isl_pw_qpolynomial *pwqp1,
3526 __isl_take isl_pw_qpolynomial *pwqp2);
3527 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3528 __isl_take isl_pw_qpolynomial *pwqp1,
3529 __isl_take isl_pw_qpolynomial *pwqp2);
3530 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3531 __isl_take isl_pw_qpolynomial *pwqp);
3532 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3533 __isl_take isl_pw_qpolynomial *pwqp1,
3534 __isl_take isl_pw_qpolynomial *pwqp2);
3535 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3536 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3538 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3539 __isl_take isl_union_pw_qpolynomial *upwqp1,
3540 __isl_take isl_union_pw_qpolynomial *upwqp2);
3541 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3542 __isl_take isl_union_pw_qpolynomial *upwqp1,
3543 __isl_take isl_union_pw_qpolynomial *upwqp2);
3544 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3545 __isl_take isl_union_pw_qpolynomial *upwqp1,
3546 __isl_take isl_union_pw_qpolynomial *upwqp2);
3548 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
3549 __isl_take isl_pw_qpolynomial *pwqp,
3550 __isl_take isl_point *pnt);
3552 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
3553 __isl_take isl_union_pw_qpolynomial *upwqp,
3554 __isl_take isl_point *pnt);
3556 __isl_give isl_set *isl_pw_qpolynomial_domain(
3557 __isl_take isl_pw_qpolynomial *pwqp);
3558 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
3559 __isl_take isl_pw_qpolynomial *pwpq,
3560 __isl_take isl_set *set);
3561 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
3562 __isl_take isl_pw_qpolynomial *pwpq,
3563 __isl_take isl_set *set);
3565 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3566 __isl_take isl_union_pw_qpolynomial *upwqp);
3567 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
3568 __isl_take isl_union_pw_qpolynomial *upwpq,
3569 __isl_take isl_union_set *uset);
3570 __isl_give isl_union_pw_qpolynomial *
3571 isl_union_pw_qpolynomial_intersect_params(
3572 __isl_take isl_union_pw_qpolynomial *upwpq,
3573 __isl_take isl_set *set);
3575 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3576 __isl_take isl_qpolynomial *qp,
3577 __isl_take isl_space *model);
3579 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
3580 __isl_take isl_qpolynomial *qp);
3581 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
3582 __isl_take isl_pw_qpolynomial *pwqp);
3584 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
3585 __isl_take isl_union_pw_qpolynomial *upwqp);
3587 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
3588 __isl_take isl_qpolynomial *qp,
3589 __isl_take isl_set *context);
3590 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
3591 __isl_take isl_qpolynomial *qp,
3592 __isl_take isl_set *context);
3594 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
3595 __isl_take isl_pw_qpolynomial *pwqp,
3596 __isl_take isl_set *context);
3597 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
3598 __isl_take isl_pw_qpolynomial *pwqp,
3599 __isl_take isl_set *context);
3601 __isl_give isl_union_pw_qpolynomial *
3602 isl_union_pw_qpolynomial_gist_params(
3603 __isl_take isl_union_pw_qpolynomial *upwqp,
3604 __isl_take isl_set *context);
3605 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
3606 __isl_take isl_union_pw_qpolynomial *upwqp,
3607 __isl_take isl_union_set *context);
3609 The gist operation applies the gist operation to each of
3610 the cells in the domain of the input piecewise quasipolynomial.
3611 The context is also exploited
3612 to simplify the quasipolynomials associated to each cell.
3614 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
3615 __isl_take isl_pw_qpolynomial *pwqp, int sign);
3616 __isl_give isl_union_pw_qpolynomial *
3617 isl_union_pw_qpolynomial_to_polynomial(
3618 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
3620 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
3621 the polynomial will be an overapproximation. If C<sign> is negative,
3622 it will be an underapproximation. If C<sign> is zero, the approximation
3623 will lie somewhere in between.
3625 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
3627 A piecewise quasipolynomial reduction is a piecewise
3628 reduction (or fold) of quasipolynomials.
3629 In particular, the reduction can be maximum or a minimum.
3630 The objects are mainly used to represent the result of
3631 an upper or lower bound on a quasipolynomial over its domain,
3632 i.e., as the result of the following function.
3634 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
3635 __isl_take isl_pw_qpolynomial *pwqp,
3636 enum isl_fold type, int *tight);
3638 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
3639 __isl_take isl_union_pw_qpolynomial *upwqp,
3640 enum isl_fold type, int *tight);
3642 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
3643 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
3644 is the returned bound is known be tight, i.e., for each value
3645 of the parameters there is at least
3646 one element in the domain that reaches the bound.
3647 If the domain of C<pwqp> is not wrapping, then the bound is computed
3648 over all elements in that domain and the result has a purely parametric
3649 domain. If the domain of C<pwqp> is wrapping, then the bound is
3650 computed over the range of the wrapped relation. The domain of the
3651 wrapped relation becomes the domain of the result.
3653 A (piecewise) quasipolynomial reduction can be copied or freed using the
3654 following functions.
3656 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
3657 __isl_keep isl_qpolynomial_fold *fold);
3658 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
3659 __isl_keep isl_pw_qpolynomial_fold *pwf);
3660 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
3661 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3662 void isl_qpolynomial_fold_free(
3663 __isl_take isl_qpolynomial_fold *fold);
3664 void *isl_pw_qpolynomial_fold_free(
3665 __isl_take isl_pw_qpolynomial_fold *pwf);
3666 void isl_union_pw_qpolynomial_fold_free(
3667 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3669 =head3 Printing Piecewise Quasipolynomial Reductions
3671 Piecewise quasipolynomial reductions can be printed
3672 using the following function.
3674 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
3675 __isl_take isl_printer *p,
3676 __isl_keep isl_pw_qpolynomial_fold *pwf);
3677 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
3678 __isl_take isl_printer *p,
3679 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3681 For C<isl_printer_print_pw_qpolynomial_fold>,
3682 output format of the printer
3683 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3684 For C<isl_printer_print_union_pw_qpolynomial_fold>,
3685 output format of the printer
3686 needs to be set to C<ISL_FORMAT_ISL>.
3687 In case of printing in C<ISL_FORMAT_C>, the user may want
3688 to set the names of all dimensions
3690 __isl_give isl_pw_qpolynomial_fold *
3691 isl_pw_qpolynomial_fold_set_dim_name(
3692 __isl_take isl_pw_qpolynomial_fold *pwf,
3693 enum isl_dim_type type, unsigned pos,
3696 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
3698 To iterate over all piecewise quasipolynomial reductions in a union
3699 piecewise quasipolynomial reduction, use the following function
3701 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3702 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3703 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3704 void *user), void *user);
3706 To iterate over the cells in a piecewise quasipolynomial reduction,
3707 use either of the following two functions
3709 int isl_pw_qpolynomial_fold_foreach_piece(
3710 __isl_keep isl_pw_qpolynomial_fold *pwf,
3711 int (*fn)(__isl_take isl_set *set,
3712 __isl_take isl_qpolynomial_fold *fold,
3713 void *user), void *user);
3714 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
3715 __isl_keep isl_pw_qpolynomial_fold *pwf,
3716 int (*fn)(__isl_take isl_set *set,
3717 __isl_take isl_qpolynomial_fold *fold,
3718 void *user), void *user);
3720 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
3721 of the difference between these two functions.
3723 To iterate over all quasipolynomials in a reduction, use
3725 int isl_qpolynomial_fold_foreach_qpolynomial(
3726 __isl_keep isl_qpolynomial_fold *fold,
3727 int (*fn)(__isl_take isl_qpolynomial *qp,
3728 void *user), void *user);
3730 =head3 Properties of Piecewise Quasipolynomial Reductions
3732 To check whether two union piecewise quasipolynomial reductions are
3733 obviously equal, use
3735 int isl_union_pw_qpolynomial_fold_plain_is_equal(
3736 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
3737 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
3739 =head3 Operations on Piecewise Quasipolynomial Reductions
3741 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
3742 __isl_take isl_qpolynomial_fold *fold, isl_int v);
3744 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
3745 __isl_take isl_pw_qpolynomial_fold *pwf1,
3746 __isl_take isl_pw_qpolynomial_fold *pwf2);
3748 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
3749 __isl_take isl_pw_qpolynomial_fold *pwf1,
3750 __isl_take isl_pw_qpolynomial_fold *pwf2);
3752 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
3753 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
3754 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
3756 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
3757 __isl_take isl_pw_qpolynomial_fold *pwf,
3758 __isl_take isl_point *pnt);
3760 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
3761 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3762 __isl_take isl_point *pnt);
3764 __isl_give isl_pw_qpolynomial_fold *
3765 sl_pw_qpolynomial_fold_intersect_params(
3766 __isl_take isl_pw_qpolynomial_fold *pwf,
3767 __isl_take isl_set *set);
3769 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
3770 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3771 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
3772 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3773 __isl_take isl_union_set *uset);
3774 __isl_give isl_union_pw_qpolynomial_fold *
3775 isl_union_pw_qpolynomial_fold_intersect_params(
3776 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3777 __isl_take isl_set *set);
3779 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
3780 __isl_take isl_pw_qpolynomial_fold *pwf);
3782 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
3783 __isl_take isl_pw_qpolynomial_fold *pwf);
3785 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
3786 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3788 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
3789 __isl_take isl_qpolynomial_fold *fold,
3790 __isl_take isl_set *context);
3791 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
3792 __isl_take isl_qpolynomial_fold *fold,
3793 __isl_take isl_set *context);
3795 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
3796 __isl_take isl_pw_qpolynomial_fold *pwf,
3797 __isl_take isl_set *context);
3798 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
3799 __isl_take isl_pw_qpolynomial_fold *pwf,
3800 __isl_take isl_set *context);
3802 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
3803 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3804 __isl_take isl_union_set *context);
3805 __isl_give isl_union_pw_qpolynomial_fold *
3806 isl_union_pw_qpolynomial_fold_gist_params(
3807 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3808 __isl_take isl_set *context);
3810 The gist operation applies the gist operation to each of
3811 the cells in the domain of the input piecewise quasipolynomial reduction.
3812 In future, the operation will also exploit the context
3813 to simplify the quasipolynomial reductions associated to each cell.
3815 __isl_give isl_pw_qpolynomial_fold *
3816 isl_set_apply_pw_qpolynomial_fold(
3817 __isl_take isl_set *set,
3818 __isl_take isl_pw_qpolynomial_fold *pwf,
3820 __isl_give isl_pw_qpolynomial_fold *
3821 isl_map_apply_pw_qpolynomial_fold(
3822 __isl_take isl_map *map,
3823 __isl_take isl_pw_qpolynomial_fold *pwf,
3825 __isl_give isl_union_pw_qpolynomial_fold *
3826 isl_union_set_apply_union_pw_qpolynomial_fold(
3827 __isl_take isl_union_set *uset,
3828 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3830 __isl_give isl_union_pw_qpolynomial_fold *
3831 isl_union_map_apply_union_pw_qpolynomial_fold(
3832 __isl_take isl_union_map *umap,
3833 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3836 The functions taking a map
3837 compose the given map with the given piecewise quasipolynomial reduction.
3838 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
3839 over all elements in the intersection of the range of the map
3840 and the domain of the piecewise quasipolynomial reduction
3841 as a function of an element in the domain of the map.
3842 The functions taking a set compute a bound over all elements in the
3843 intersection of the set and the domain of the
3844 piecewise quasipolynomial reduction.
3846 =head2 Dependence Analysis
3848 C<isl> contains specialized functionality for performing
3849 array dataflow analysis. That is, given a I<sink> access relation
3850 and a collection of possible I<source> access relations,
3851 C<isl> can compute relations that describe
3852 for each iteration of the sink access, which iteration
3853 of which of the source access relations was the last
3854 to access the same data element before the given iteration
3856 The resulting dependence relations map source iterations
3857 to the corresponding sink iterations.
3858 To compute standard flow dependences, the sink should be
3859 a read, while the sources should be writes.
3860 If any of the source accesses are marked as being I<may>
3861 accesses, then there will be a dependence from the last
3862 I<must> access B<and> from any I<may> access that follows
3863 this last I<must> access.
3864 In particular, if I<all> sources are I<may> accesses,
3865 then memory based dependence analysis is performed.
3866 If, on the other hand, all sources are I<must> accesses,
3867 then value based dependence analysis is performed.
3869 #include <isl/flow.h>
3871 typedef int (*isl_access_level_before)(void *first, void *second);
3873 __isl_give isl_access_info *isl_access_info_alloc(
3874 __isl_take isl_map *sink,
3875 void *sink_user, isl_access_level_before fn,
3877 __isl_give isl_access_info *isl_access_info_add_source(
3878 __isl_take isl_access_info *acc,
3879 __isl_take isl_map *source, int must,
3881 void isl_access_info_free(__isl_take isl_access_info *acc);
3883 __isl_give isl_flow *isl_access_info_compute_flow(
3884 __isl_take isl_access_info *acc);
3886 int isl_flow_foreach(__isl_keep isl_flow *deps,
3887 int (*fn)(__isl_take isl_map *dep, int must,
3888 void *dep_user, void *user),
3890 __isl_give isl_map *isl_flow_get_no_source(
3891 __isl_keep isl_flow *deps, int must);
3892 void isl_flow_free(__isl_take isl_flow *deps);
3894 The function C<isl_access_info_compute_flow> performs the actual
3895 dependence analysis. The other functions are used to construct
3896 the input for this function or to read off the output.
3898 The input is collected in an C<isl_access_info>, which can
3899 be created through a call to C<isl_access_info_alloc>.
3900 The arguments to this functions are the sink access relation
3901 C<sink>, a token C<sink_user> used to identify the sink
3902 access to the user, a callback function for specifying the
3903 relative order of source and sink accesses, and the number
3904 of source access relations that will be added.
3905 The callback function has type C<int (*)(void *first, void *second)>.
3906 The function is called with two user supplied tokens identifying
3907 either a source or the sink and it should return the shared nesting
3908 level and the relative order of the two accesses.
3909 In particular, let I<n> be the number of loops shared by
3910 the two accesses. If C<first> precedes C<second> textually,
3911 then the function should return I<2 * n + 1>; otherwise,
3912 it should return I<2 * n>.
3913 The sources can be added to the C<isl_access_info> by performing
3914 (at most) C<max_source> calls to C<isl_access_info_add_source>.
3915 C<must> indicates whether the source is a I<must> access
3916 or a I<may> access. Note that a multi-valued access relation
3917 should only be marked I<must> if every iteration in the domain
3918 of the relation accesses I<all> elements in its image.
3919 The C<source_user> token is again used to identify
3920 the source access. The range of the source access relation
3921 C<source> should have the same dimension as the range
3922 of the sink access relation.
3923 The C<isl_access_info_free> function should usually not be
3924 called explicitly, because it is called implicitly by
3925 C<isl_access_info_compute_flow>.
3927 The result of the dependence analysis is collected in an
3928 C<isl_flow>. There may be elements of
3929 the sink access for which no preceding source access could be
3930 found or for which all preceding sources are I<may> accesses.
3931 The relations containing these elements can be obtained through
3932 calls to C<isl_flow_get_no_source>, the first with C<must> set
3933 and the second with C<must> unset.
3934 In the case of standard flow dependence analysis,
3935 with the sink a read and the sources I<must> writes,
3936 the first relation corresponds to the reads from uninitialized
3937 array elements and the second relation is empty.
3938 The actual flow dependences can be extracted using
3939 C<isl_flow_foreach>. This function will call the user-specified
3940 callback function C<fn> for each B<non-empty> dependence between
3941 a source and the sink. The callback function is called
3942 with four arguments, the actual flow dependence relation
3943 mapping source iterations to sink iterations, a boolean that
3944 indicates whether it is a I<must> or I<may> dependence, a token
3945 identifying the source and an additional C<void *> with value
3946 equal to the third argument of the C<isl_flow_foreach> call.
3947 A dependence is marked I<must> if it originates from a I<must>
3948 source and if it is not followed by any I<may> sources.
3950 After finishing with an C<isl_flow>, the user should call
3951 C<isl_flow_free> to free all associated memory.
3953 A higher-level interface to dependence analysis is provided
3954 by the following function.
3956 #include <isl/flow.h>
3958 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
3959 __isl_take isl_union_map *must_source,
3960 __isl_take isl_union_map *may_source,
3961 __isl_take isl_union_map *schedule,
3962 __isl_give isl_union_map **must_dep,
3963 __isl_give isl_union_map **may_dep,
3964 __isl_give isl_union_map **must_no_source,
3965 __isl_give isl_union_map **may_no_source);
3967 The arrays are identified by the tuple names of the ranges
3968 of the accesses. The iteration domains by the tuple names
3969 of the domains of the accesses and of the schedule.
3970 The relative order of the iteration domains is given by the
3971 schedule. The relations returned through C<must_no_source>
3972 and C<may_no_source> are subsets of C<sink>.
3973 Any of C<must_dep>, C<may_dep>, C<must_no_source>
3974 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
3975 any of the other arguments is treated as an error.
3979 B<The functionality described in this section is fairly new
3980 and may be subject to change.>
3982 The following function can be used to compute a schedule
3983 for a union of domains. The generated schedule respects
3984 all C<validity> dependences. That is, all dependence distances
3985 over these dependences in the scheduled space are lexicographically
3986 positive. The generated schedule schedule also tries to minimize
3987 the dependence distances over C<proximity> dependences.
3988 Moreover, it tries to obtain sequences (bands) of schedule dimensions
3989 for groups of domains where the dependence distances have only
3990 non-negative values.
3991 The algorithm used to construct the schedule is similar to that
3994 #include <isl/schedule.h>
3995 __isl_give isl_schedule *isl_union_set_compute_schedule(
3996 __isl_take isl_union_set *domain,
3997 __isl_take isl_union_map *validity,
3998 __isl_take isl_union_map *proximity);
3999 void *isl_schedule_free(__isl_take isl_schedule *sched);
4001 A mapping from the domains to the scheduled space can be obtained
4002 from an C<isl_schedule> using the following function.
4004 __isl_give isl_union_map *isl_schedule_get_map(
4005 __isl_keep isl_schedule *sched);
4007 A representation of the schedule can be printed using
4009 __isl_give isl_printer *isl_printer_print_schedule(
4010 __isl_take isl_printer *p,
4011 __isl_keep isl_schedule *schedule);
4013 A representation of the schedule as a forest of bands can be obtained
4014 using the following function.
4016 __isl_give isl_band_list *isl_schedule_get_band_forest(
4017 __isl_keep isl_schedule *schedule);
4019 The list can be manipulated as explained in L<"Lists">.
4020 The bands inside the list can be copied and freed using the following
4023 #include <isl/band.h>
4024 __isl_give isl_band *isl_band_copy(
4025 __isl_keep isl_band *band);
4026 void *isl_band_free(__isl_take isl_band *band);
4028 Each band contains zero or more scheduling dimensions.
4029 These are referred to as the members of the band.
4030 The section of the schedule that corresponds to the band is
4031 referred to as the partial schedule of the band.
4032 For those nodes that participate in a band, the outer scheduling
4033 dimensions form the prefix schedule, while the inner scheduling
4034 dimensions form the suffix schedule.
4035 That is, if we take a cut of the band forest, then the union of
4036 the concatenations of the prefix, partial and suffix schedules of
4037 each band in the cut is equal to the entire schedule (modulo
4038 some possible padding at the end with zero scheduling dimensions).
4039 The properties of a band can be inspected using the following functions.
4041 #include <isl/band.h>
4042 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
4044 int isl_band_has_children(__isl_keep isl_band *band);
4045 __isl_give isl_band_list *isl_band_get_children(
4046 __isl_keep isl_band *band);
4048 __isl_give isl_union_map *isl_band_get_prefix_schedule(
4049 __isl_keep isl_band *band);
4050 __isl_give isl_union_map *isl_band_get_partial_schedule(
4051 __isl_keep isl_band *band);
4052 __isl_give isl_union_map *isl_band_get_suffix_schedule(
4053 __isl_keep isl_band *band);
4055 int isl_band_n_member(__isl_keep isl_band *band);
4056 int isl_band_member_is_zero_distance(
4057 __isl_keep isl_band *band, int pos);
4059 Note that a scheduling dimension is considered to be ``zero
4060 distance'' if it does not carry any proximity dependences
4062 That is, if the dependence distances of the proximity
4063 dependences are all zero in that direction (for fixed
4064 iterations of outer bands).
4066 A representation of the band can be printed using
4068 #include <isl/band.h>
4069 __isl_give isl_printer *isl_printer_print_band(
4070 __isl_take isl_printer *p,
4071 __isl_keep isl_band *band);
4075 #include <isl/schedule.h>
4076 int isl_options_set_schedule_outer_zero_distance(
4077 isl_ctx *ctx, int val);
4078 int isl_options_get_schedule_outer_zero_distance(
4083 =item * schedule_outer_zero_distance
4085 It this option is set, then we try to construct schedules
4086 where the outermost scheduling dimension in each band
4087 results in a zero dependence distance over the proximity
4092 =head2 Parametric Vertex Enumeration
4094 The parametric vertex enumeration described in this section
4095 is mainly intended to be used internally and by the C<barvinok>
4098 #include <isl/vertices.h>
4099 __isl_give isl_vertices *isl_basic_set_compute_vertices(
4100 __isl_keep isl_basic_set *bset);
4102 The function C<isl_basic_set_compute_vertices> performs the
4103 actual computation of the parametric vertices and the chamber
4104 decomposition and store the result in an C<isl_vertices> object.
4105 This information can be queried by either iterating over all
4106 the vertices or iterating over all the chambers or cells
4107 and then iterating over all vertices that are active on the chamber.
4109 int isl_vertices_foreach_vertex(
4110 __isl_keep isl_vertices *vertices,
4111 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4114 int isl_vertices_foreach_cell(
4115 __isl_keep isl_vertices *vertices,
4116 int (*fn)(__isl_take isl_cell *cell, void *user),
4118 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
4119 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4122 Other operations that can be performed on an C<isl_vertices> object are
4125 isl_ctx *isl_vertices_get_ctx(
4126 __isl_keep isl_vertices *vertices);
4127 int isl_vertices_get_n_vertices(
4128 __isl_keep isl_vertices *vertices);
4129 void isl_vertices_free(__isl_take isl_vertices *vertices);
4131 Vertices can be inspected and destroyed using the following functions.
4133 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
4134 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
4135 __isl_give isl_basic_set *isl_vertex_get_domain(
4136 __isl_keep isl_vertex *vertex);
4137 __isl_give isl_basic_set *isl_vertex_get_expr(
4138 __isl_keep isl_vertex *vertex);
4139 void isl_vertex_free(__isl_take isl_vertex *vertex);
4141 C<isl_vertex_get_expr> returns a singleton parametric set describing
4142 the vertex, while C<isl_vertex_get_domain> returns the activity domain
4144 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
4145 B<rational> basic sets, so they should mainly be used for inspection
4146 and should not be mixed with integer sets.
4148 Chambers can be inspected and destroyed using the following functions.
4150 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
4151 __isl_give isl_basic_set *isl_cell_get_domain(
4152 __isl_keep isl_cell *cell);
4153 void isl_cell_free(__isl_take isl_cell *cell);
4157 Although C<isl> is mainly meant to be used as a library,
4158 it also contains some basic applications that use some
4159 of the functionality of C<isl>.
4160 The input may be specified in either the L<isl format>
4161 or the L<PolyLib format>.
4163 =head2 C<isl_polyhedron_sample>
4165 C<isl_polyhedron_sample> takes a polyhedron as input and prints
4166 an integer element of the polyhedron, if there is any.
4167 The first column in the output is the denominator and is always
4168 equal to 1. If the polyhedron contains no integer points,
4169 then a vector of length zero is printed.
4173 C<isl_pip> takes the same input as the C<example> program
4174 from the C<piplib> distribution, i.e., a set of constraints
4175 on the parameters, a line containing only -1 and finally a set
4176 of constraints on a parametric polyhedron.
4177 The coefficients of the parameters appear in the last columns
4178 (but before the final constant column).
4179 The output is the lexicographic minimum of the parametric polyhedron.
4180 As C<isl> currently does not have its own output format, the output
4181 is just a dump of the internal state.
4183 =head2 C<isl_polyhedron_minimize>
4185 C<isl_polyhedron_minimize> computes the minimum of some linear
4186 or affine objective function over the integer points in a polyhedron.
4187 If an affine objective function
4188 is given, then the constant should appear in the last column.
4190 =head2 C<isl_polytope_scan>
4192 Given a polytope, C<isl_polytope_scan> prints
4193 all integer points in the polytope.